**A Proposal for a Machine Learning Classifier for Viral Infection in Living Cells Based on Mitochondrial Distribution**

## Juan Carlos Cardona-Gomez, Leandro Fabio Ariza-Jimenez and Juan Carlos Gallego-Gomez

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/61293

#### **Abstract**

The study of viral infections using live cell imaging (LCI) is an important area with multiple opportunities for new developments in computational cell biology. Here, this point is illustrated by the analysis of the sub-cellular distribution of mitochon‐ drium in cell cultures infected by Dengue virus (DENV) and in uninfected cell cul‐ tures (Mock-infections). Several videos were recorded from the overnight experiments performed in a confocal microscopy of spinning disk. The density dis‐ tribution of mitochondrium around the nuclei as a function of time and space *ρ*(*r*, *θ*, *t*) was numerically modeled as a smooth interpolation function from the image data and used in further analysis. A graphical study shows that the behavior of the mitochondrial density is substantially different when the infection is present. The DENV-infected cells show a more diffuse distribution and a stronger angular variation on it. This behavior can be quantified by using some usual image process‐ ing descriptors called *entropy* and *uniformity*. Interestingly, the marked difference found in the mitochondria density distribution for mock and for infected cell is present in every frame and not an evidence of time dependence was found, which indicate that from the start of the infections the cells are showing an altered subcel‐ lular pattern in mitochondrium distribution. Ulteriorly, it would be important to study by analysis of time series for clearing if there is some tendency or approxi‐ mate cycles. Those findings are suggesting that using the image descriptors *entropy* and *uniformity* it is possible to create a machine learning classifier that could recog‐ nize if a single selected cell in a culture has been infected or not.

**Keywords:** Computational Cell Biology, Dengue Virus, Mitochondria, Machine Learning

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### **1. Introduction**

At the latter years of the past century, cell biology experienced a fast growth, thanks to the convergence of several techniques, which have substantially improved the confocal micro‐ scopy field. Now, the observation in real time of the structural and functional unit of life is possible. The ultrarefrigerated CCD-cameras with electromultipliers; the implementation of confocality based on disk spinning without the necessity of high-energy lasers (which could damage the living cells in a few seconds); the increasing capacity of computational processors; and the ability of the genetic engineering for coding fluorescent proteins mutants [1, 2], offering the possibility of a color palette that was previously unthinkable for the cell molecular biologists [3, 4]. All together with the ability to generate cells with fluorescent compartments, opened the doors to maybe the most remarkable and important scientific and technological development for a new era in cell biology named Live Cell Imaging. Before the 1990'-s this kind of research was known by the unpopular name "time-lapse video microscopy", as it is detailed in a protocol book widely known at that time written by A.J. Lacey [5].

At the beginning of the new millennium, the necessity of introducing new and improved mathematical and computational tools was made evident. This was because the amount of data produced in a single experiment could overload the capacity of personal computers and the conventional software was not loaded with the required algorithms to process such data. Then a strategic alliance with researchers on the areas of artificial intelligence, applied mathematics, and physics was apparent. These new cooperations make perfect sense due that even from the beginning of life science studies, it was clear that the dynamical rules involved were complex, non-linear, and possibly not even deterministic but probabilistic. The virolo‐ gists, for example, have discovered that the infection rate is governed by a non-linear pattern and the cellular physiology of several processes turn out to be more complicated than it was expected. In consequence, the mathematical modeling became the main strategy in the journey for knowing and understanding the cell biology. The amount of the data available nowadays could not be analyzed by conventional human heuristics. Fortunately, the computational biology field and its tools offer the required resolution and robustness in diverse problems. It goes even further, because the computational algorithms work evenly in any case. When dealing with complex biological problems, to have a working computational model will get us closer to the reality and help us avoiding the human bias present in heuristic approaches. It is in complex problems where the convenience of using powerful statistical tools to build models became apparent. The main strategy here is to try to "learn" the model directly from the experimental or observational data.

The term "machine learning" (ML) refers to a branch of the artificial intelligence field, that concerns to the study and construction of algorithms with the ability to learn from the existing data. In such algorithms, a set of parameters is fitted to provide the best input-output rela‐ tionship between the information available. When talking about a computational code that implements the techniques, algorithms, or principles found in machine learning theory, it is usually called a machine learning program. The literature on this topic is quite large; however, some very popular books are those by Duda et al. [6], Webb [7], and Bishop [8].

A commonly accepted definition of the process of "learning" is due to Tom M. Mitchell [9]: *a machine learns to perform a task T if its performance as measured by* P *increases with the experience E*. The experience *E* is the feedback the machine received to validate its output. The ML set of techniques have a broad range of applications in several fields of knowledge, including the building of autonomous robots [10], the astrophysical data mining [11], the study of dynamical systems and complex networks without the explicit knowledge of the dynamical equations [12], the patterns and shape recognition [6, 8] in images as used by the face recognition programs in social networks web pages, the hand writing OCR (optical character recognition), and of course, in medicine (automatic diagnosis based on symptoms) and biology (gene sequencer, classification of cellular morphology, etc.).

**1. Introduction**

4 Cell Biology - New Insights

the experimental or observational data.

At the latter years of the past century, cell biology experienced a fast growth, thanks to the convergence of several techniques, which have substantially improved the confocal micro‐ scopy field. Now, the observation in real time of the structural and functional unit of life is possible. The ultrarefrigerated CCD-cameras with electromultipliers; the implementation of confocality based on disk spinning without the necessity of high-energy lasers (which could damage the living cells in a few seconds); the increasing capacity of computational processors; and the ability of the genetic engineering for coding fluorescent proteins mutants [1, 2], offering the possibility of a color palette that was previously unthinkable for the cell molecular biologists [3, 4]. All together with the ability to generate cells with fluorescent compartments, opened the doors to maybe the most remarkable and important scientific and technological development for a new era in cell biology named Live Cell Imaging. Before the 1990'-s this kind of research was known by the unpopular name "time-lapse video microscopy", as it is

detailed in a protocol book widely known at that time written by A.J. Lacey [5].

At the beginning of the new millennium, the necessity of introducing new and improved mathematical and computational tools was made evident. This was because the amount of data produced in a single experiment could overload the capacity of personal computers and the conventional software was not loaded with the required algorithms to process such data. Then a strategic alliance with researchers on the areas of artificial intelligence, applied mathematics, and physics was apparent. These new cooperations make perfect sense due that even from the beginning of life science studies, it was clear that the dynamical rules involved were complex, non-linear, and possibly not even deterministic but probabilistic. The virolo‐ gists, for example, have discovered that the infection rate is governed by a non-linear pattern and the cellular physiology of several processes turn out to be more complicated than it was expected. In consequence, the mathematical modeling became the main strategy in the journey for knowing and understanding the cell biology. The amount of the data available nowadays could not be analyzed by conventional human heuristics. Fortunately, the computational biology field and its tools offer the required resolution and robustness in diverse problems. It goes even further, because the computational algorithms work evenly in any case. When dealing with complex biological problems, to have a working computational model will get us closer to the reality and help us avoiding the human bias present in heuristic approaches. It is in complex problems where the convenience of using powerful statistical tools to build models became apparent. The main strategy here is to try to "learn" the model directly from

The term "machine learning" (ML) refers to a branch of the artificial intelligence field, that concerns to the study and construction of algorithms with the ability to learn from the existing data. In such algorithms, a set of parameters is fitted to provide the best input-output rela‐ tionship between the information available. When talking about a computational code that implements the techniques, algorithms, or principles found in machine learning theory, it is usually called a machine learning program. The literature on this topic is quite large; however,

some very popular books are those by Duda et al. [6], Webb [7], and Bishop [8].

Particularly, the shape recognition capabilities have important applications to live cell image processing. For example, in 2006, Neumann and collaborators use live cell imaging to study the RNAi screening [13]. They developed a ML that recognize the morphologies present in the cells images and associate them (classify) with the corresponding phenomenology: interphase, mitosis, apoptosis and binucleated cells morphologies were studied through a multi-class classifier using support vector machine (SVM). They reported to obtain up to 97% accuracy from the SVM in comparison with "manual" classification through the observation by some very well-trained biologists.

Due to the huge amount of data provided by a live cell image (LCI) measure, it becomes unpractical to relay only on the lecture and interpretation by a well-trained researcher. It is also possible to have different interpretations coming from different scientists when analyzing the same image. Then, the ML ability to recognize and characterize particular morphologies present in an image is very useful to avoid the slow and tedious process of visual discrimina‐ tion. Also, it can avoid some human bias by following well-defined rules. However, to fully train the machine, it can be necessary to have a large number of image samples from the phenotype under study. It means, to have enough sample cells expressing the phenotype and some other cells to use as a control group. Sometimes, that condition is not fulfilled. In order to asset this kind of problem, Thouis R. Jones and collaborators implement a ML with inter‐ active feedback to characterize diverse and complex morphological phenotypes [14]. They use the criteria of well-trained researchers as a feedback in the learning stage of the machine, and provide the code [15] for the world to use under a free license.

Several generic implementations of ML techniques have been developed and presented as toolbox in scientific software. However, it is pretty common to find the particular phenomenon under study to be better fitted by some unique implementation developed explicitly to deal with it. This can be a consequence of the particularities of the problem or sometimes this is just due to the lack of proper documentation on the available tools.

This chapter is organized as follows: first, a brief description of some common methods used to build a ML are provided, followed by a description of the performed experiment and computational analysis to obtain the information from the graphical data. Finally, the results and a proposal to create a ML to characterize viral infection are presented.

#### **2. Machine learning concepts overview**

From the mathematical point of view, a ML can have one of two primary objectives: regression and classification. When the machine is used to compute the best response to a given situation among a continuous range of possible answers, it is called a regression problem. And when the machine is due to choose among a discrete set of possibilities, it is called a classification problem.

The shape recognition and feature extraction from images is a classification problem, where the duty of the machine is to find the class which has the highest probability to contain the current input value. In this context, a class is defined based on a set of measurable attributes found in an image; it can be geometrical attributes (length, shape, eccentricity, size), pixel intensity, etc. In general, the input for a ML program is a set of measurable variables or attributes, which are set in vectors. It is common in ML literature to call these attributes *features* and the vectors *feature vectors*, so these names will be used in such framework in the rest of this chapter. Each input in a feature vector represents an attribute and each vector represents a state of the system.

Before the machine is ready to be used as a classifier or predictor, it needs to be trained among some data. Here, "training" refers to the process of parameters optimization, where the machine is optimized to get the best result against the training set. This process is not perfect, and some human criteria need to be implemented. If the model has not enough freedom to fit to the training set, it gets under fitted and do not reproduce the characteristics of the system under study. On the other hand, having too much freedom in the ML leads to a model that fits pretty well in the training set, but is unable to predict accurately the outcome for a feature vector outside of the training set. This is called bias. To avoid bias, it is customary to split the available data in two sets, the training set and the testing set. A trained machine is challenged with the testing set, and the accepted ML model is the one that has the best results against it.

There are two main paradigms for the training of a classifier, the supervised and the unsu‐ pervised learning. In supervised learning, each sample in the training set is consisting on a features vector and a class flag, i.e., the classes to which each sample in training set belongs are known a priori. After the learning process, a computational model that can predict the right class flag for most of the training set is obtained, and hopefully, it would predict the correct class for a new sample with high accuracy. Also, the classifier must return information about how confident its prediction is, i.e., a value of dude must be reported.

When no predefined classification is available, a ML algorithm can be used to search for common patterns or similarities into the training set, which do not contain class information yet. The machine would cluster samples with similar feature vectors to define a class, and then, it will use the found class to characterize new input data. To do that, it is necessary to define some measure of similarity (Euclidean distance in features space, for example) that can be used to group the input vectors into clusters. The objectives of this kind of ML are first to cluster the data from the training set into classes, and then, set a classifier to characterize new inputs. ML are suitable to treat complex problems in which the explicit mathematical form describing the interactions occurring in the process are not known, i.e., the dynamical equation ruling the systems are unknown. Being so, the computations involved in a model built with ML are not deterministic but probabilistic, based on the information gathered by direct measures. The more data are available to train the machine, the more accurate the prediction will become.

#### **2.1. Supervised learning**

**2. Machine learning concepts overview**

problem.

6 Cell Biology - New Insights

state of the system.

From the mathematical point of view, a ML can have one of two primary objectives: regression and classification. When the machine is used to compute the best response to a given situation among a continuous range of possible answers, it is called a regression problem. And when the machine is due to choose among a discrete set of possibilities, it is called a classification

The shape recognition and feature extraction from images is a classification problem, where the duty of the machine is to find the class which has the highest probability to contain the current input value. In this context, a class is defined based on a set of measurable attributes found in an image; it can be geometrical attributes (length, shape, eccentricity, size), pixel intensity, etc. In general, the input for a ML program is a set of measurable variables or attributes, which are set in vectors. It is common in ML literature to call these attributes *features* and the vectors *feature vectors*, so these names will be used in such framework in the rest of this chapter. Each input in a feature vector represents an attribute and each vector represents a

Before the machine is ready to be used as a classifier or predictor, it needs to be trained among some data. Here, "training" refers to the process of parameters optimization, where the machine is optimized to get the best result against the training set. This process is not perfect, and some human criteria need to be implemented. If the model has not enough freedom to fit to the training set, it gets under fitted and do not reproduce the characteristics of the system under study. On the other hand, having too much freedom in the ML leads to a model that fits pretty well in the training set, but is unable to predict accurately the outcome for a feature vector outside of the training set. This is called bias. To avoid bias, it is customary to split the available data in two sets, the training set and the testing set. A trained machine is challenged with the testing set, and the accepted ML model is the one that has the best results against it.

There are two main paradigms for the training of a classifier, the supervised and the unsu‐ pervised learning. In supervised learning, each sample in the training set is consisting on a features vector and a class flag, i.e., the classes to which each sample in training set belongs are known a priori. After the learning process, a computational model that can predict the right class flag for most of the training set is obtained, and hopefully, it would predict the correct class for a new sample with high accuracy. Also, the classifier must return information about

When no predefined classification is available, a ML algorithm can be used to search for common patterns or similarities into the training set, which do not contain class information yet. The machine would cluster samples with similar feature vectors to define a class, and then, it will use the found class to characterize new input data. To do that, it is necessary to define some measure of similarity (Euclidean distance in features space, for example) that can be used to group the input vectors into clusters. The objectives of this kind of ML are first to cluster the data from the training set into classes, and then, set a classifier to characterize new inputs.

how confident its prediction is, i.e., a value of dude must be reported.

The objective of the classifier is to draw a frontier that splits the feature space into *k* disjoint subsets [16] called the border line or border hyperplane. Hopefully, each subset will contain the feature subspace associated with one single class.

#### *2.1.1. Hypothesis function*

Let the features space be called X , where a feature vector is *x*, and let the whole set of classes be Y , with an individual class denoted *y*. Develop a ML model consists in building a function *h* : X →Y that is a good predictor of the corresponding *y* to a given input *x*. In supervised learning, a computational model function with adaptable parameters *θ*, *h <sup>θ</sup>*(*x*)must be build; this function is usually called "hypothesis". Also, a cost function *J*(*θ*) must be defined to provide an idea of how accurate the hypothesis is when predicting the output values or classes for the whole training set. A common choice is the least square cost function:

$$J(\mathcal{O}) = \frac{1}{2} \sum\_{i=1}^{m} \left( h\_{\theta} \left( \mathbf{x}^{(i)} \right) - \mathbf{y}^{(i)} \right)^{2},\tag{1}$$

where *m* is the number of samples or elements in the training set, and the notation *x* (*i*) and *y* (*i*) denotes the feature vector of the i-th sample and the class value for it. The optimization of the model (learning process) is then achieved by minimizing the cost function. Once the ML model is set up, the predictions are made with the optimized hypothesis as *y* = *h* (*x*). Depending on if *h* (*x*) is a continuous function or a discrete one, the machine will be doing regression or classification respectively.

Another approach comes from a probabilistic interpretation of the hypothesis function. Suppose that *y* (*i*) =*h* (*x* (*i*) ) + ∈(*i*) , where ∈(*i*) is a random error which takes care of unmodeled effects and possibly random noise. And assume that ∈(*i*) are IID (independent and identically distributed), and follows a Normal distribution (Gaussian distribution), of mean zero and some variance *σ* <sup>2</sup> , *P*(∈(*i*) )= <sup>1</sup> <sup>2</sup>*πσ* exp( <sup>−</sup> ( (*i*) )2 <sup>2</sup>*<sup>σ</sup>* <sup>2</sup> ), then the probability of *<sup>y</sup>* (*i*) conditioned to *<sup>x</sup>* (*i*) and parametrized by *θ* is:

$$P\left(y^{(i)} \mid \mathbf{x}^{(i)}; \boldsymbol{\theta}\right) = \frac{1}{\sqrt{2\pi\sigma}} \exp\left(\frac{-\left(h\_{\boldsymbol{\theta}}\left(\mathbf{x}^{(i)}\right) - y^{(i)}\right)^{2}}{2\sigma^{2}}\right). \tag{2}$$

As any set (*x* (*i*) , *y* (*i*) ) is independent from the others, the probability of the whole set *P*(Y | X ;*θ*) is the product of all the individual probabilities. When *P*(Y | X ;*θ*) is taken as a function of the parameters *θ*, it is called the likelihood function:

$$\mathcal{L}\left(\boldsymbol{\theta}\right) = \prod\_{i=1}^{m} P\left(\boldsymbol{y}^{(i)} \mid \boldsymbol{x}^{(i)}; \boldsymbol{\theta}\right). \tag{3}$$

The principle of maximum likelihood establishes that the best model representation of the data is given by the set of parameters *θ* that provides the maximum probability. Then, maximizing the likelihood function for the whole training set (or any monotonically increasing function of it) is equivalent to minimize the cost function Eq. (1).

#### *2.1.2. Logistic regression*

Suppose the problem at hand is to determine if the measure of some experiment belong to one out of two possible outputs (like, for example, to determine if a tumor is benign or malign). A class flag 0 or 1 must be associated for each output. In this case, a common approach is to propose a logistic function (also known as sigmoid function) as a classifier, it is called a *logistic regression*:

$$\log\left(\boldsymbol{\theta}^{\top}\mathbf{x}\right) = \text{sig}\left(\boldsymbol{\theta}^{\top}\mathbf{x}\right) = \frac{1}{1 + \exp\left(-\boldsymbol{\theta}^{\top}\mathbf{x}\right)}\tag{4}$$

$$\mathcal{H}\_{\boldsymbol{\theta}}\left(\mathbf{x}\right) = \mathcal{g}\left(\boldsymbol{\theta}^{\mathrm{T}}\mathbf{x}\right) \tag{5}$$

The sigmoid function sig(*z*) has asymptotic values of 1 when *z* →*∞* and 0 when *z* → −*∞*. So the conditional probability for the feature vector *x* to belong to each one of the two available classes is written as:

$$\begin{aligned} P\left(y = 1 \mid \mathbf{x}; \boldsymbol{\theta}\right) &= h\_{\boldsymbol{\theta}}\left(\mathbf{x}\right), \\ P\left(y = 0 \mid \mathbf{x}; \boldsymbol{\theta}\right) &= 1 - h\_{\boldsymbol{\theta}}\left(\mathbf{x}\right). \end{aligned} \tag{6}$$

Which can be summarized in a single probability density function (PDF)

$$P\left(y \mid \mathbf{x}; \theta\right) = \left(h\_{\theta}\left(\mathbf{x}\right)\right)^{y} \left(1 - h\_{\theta}\left(\mathbf{x}\right)\right)^{1-y}.\tag{7}$$

Once the PDF is set, the process of learning consist in maximizing the likelihood of such PDF to the training data set. By computational simplicity, it is convenient to maximize instead some monotonically increasing function of the likelihood. It is common to work with the logarithm of the likelihood (log-likelihood function). When using the logistic regression, this hypothesis function would not return the prediction of an output class, but the probability for the sample feature vector belongs to a given class.

If it is needed to get a class value as an output, it can be done by setting *z* =sig(*θ <sup>T</sup> x*) instead of Eq. (4) and defining

$$\mathbf{g}\left(\boldsymbol{\theta}^{T}\mathbf{x}\right) = \begin{cases} \mathbf{1} & \text{if } z > 0.5, \\ \mathbf{0} & \text{otherwise}, \end{cases} \tag{8}$$

then minimizing the cost function Eq. (1). This last strategy is known as the *perceptron learning algorithm*. The classifier in this example can be extended to *k* classes by a simple one vs all algorithm. It is, defining a logistic regression to compute the probability for any of the *k* classes, *h <sup>θ</sup>*1,1 (*x*), *<sup>h</sup> <sup>θ</sup>*2,2 (*x*), *<sup>h</sup> <sup>θ</sup><sup>k</sup>* <sup>−</sup>1,*<sup>k</sup>* <sup>−</sup><sup>1</sup> (*x*),..., *<sup>h</sup> <sup>θ</sup><sup>k</sup>* ,*<sup>k</sup>* (*x*), and returning the class which has the highest probability. Note that for each class, a parameters vector *θ<sup>i</sup>* must be optimized.

#### *2.1.3. Non-linear classifiers*

As any set (*x* (*i*)

8 Cell Biology - New Insights

*2.1.2. Logistic regression*

*regression*:

is written as:

, *y* (*i*)

is the product of all the individual probabilities. When *P*(

parameters *θ*, it is called the likelihood function:

it) is equivalent to minimize the cost function Eq. (1).

) is independent from the others, the probability of the whole set *P*(


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( ) ( ) ( ) ( ) 1

*i*

=

q

*<sup>m</sup> i i*

*Py x*

The principle of maximum likelihood establishes that the best model representation of the data is given by the set of parameters *θ* that provides the maximum probability. Then, maximizing the likelihood function for the whole training set (or any monotonically increasing function of

Suppose the problem at hand is to determine if the measure of some experiment belong to one out of two possible outputs (like, for example, to determine if a tumor is benign or malign). A class flag 0 or 1 must be associated for each output. In this case, a common approach is to propose a logistic function (also known as sigmoid function) as a classifier, it is called a *logistic*

> ( ) ( ) ( ) <sup>1</sup> sig , 1 exp

> > ( ) ( ) *<sup>T</sup> hx g x*

( ) ( ) ( ) ( ) 1| ; , 0| ; 1 .

q

*Py x h x Py x h x*

= =

q

( ) ( ( )) ( ( ))

; <sup>1</sup> .| *y y Pyx h x h x* q


Once the PDF is set, the process of learning consist in maximizing the likelihood of such PDF to the training data set. By computational simplicity, it is convenient to maximize instead some

Which can be summarized in a single probability density function (PDF)

q

q

The sigmoid function sig(*z*) has asymptotic values of 1 when *z* →*∞* and 0 when *z* → −*∞*. So the conditional probability for the feature vector *x* to belong to each one of the two available classes

q

q

 q 1

*<sup>T</sup> gx x*

 q

q=

*T T*

q

Y | X

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= = + - (4)

= = - (6)

= - (7)

(5)

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<sup>l</sup> <sup>=</sup> Õ (3)

Y | X;*θ*)

;*θ*) is taken as a function of the

One limitation of the techniques summarized so far is that they provide a linear model for the classifier, i.e., the decision border is represented by a straight line or hyperplane. This can work perfectly fine if the data are linear separable, or if a linear border line provides enough accuracy in the final prediction. What happens if the feature space requires a more complex non-linear decision border? i.e., if the decision border is given considerably better by an hyper surface? One possible way to create non-linear models is to use *neural networks* (NN). A neuron is a computational unit, i.e., a piece of code that performs a single task or function, usually called the activation function. This method was developed as a gross mimic of a biological neuron, where each computational neuron has a set of wires connecting it with its input and a set of wires that are used to communicate its output to the next set of neurons. Each wire between two neurons has associated a parameter, sometimes called "weight", which is adjusted in the leaning process. So the computational model is created as an array of neurons, configured in layers that can be fully or partially connected. This kind of computational structure allows the creation of pretty complex nonlinear functions just by the selection of the network wires. After optimization, the NN computes a continuous function ready to be used for regression. For classification, a helper selection function can be implemented. A simple and yet powerful arrangement is the feedforward structure (see Figure 1), in which the neurons are arranged in a network where each layer receives its inputs directly from the layer before, and provides its outputs only to the layer after it, i.e., where the i-th layer receives the information from the (i - 1)-th layer, and sends its output to be the inputs to the (i + 1)-th layer. A common neural network used for classifiers is a three layer fully connected network, i.e., each neuron receives information for any neuron in the layer before. The first layer, called input layer, has a computational unit for each attribute in the feature vector. This unit sends its associated value to any neuron in the second or hidden layer, where each neuron computes a sigmoid function *h θi* (*x*)= *g*(*θ<sup>i</sup> <sup>T</sup> <sup>x</sup>*) as in Eq. (4). *θ<sup>i</sup>* is the parameters vector, containing the weights for each input wire to neuron *i*. Each neuron in the hidden layer sends its output to any neuron in the third or output layer. And finally, the neurons in the output layer computes another logistic function *h* (*θ<sup>j</sup>* '*<sup>T</sup> <sup>z</sup>*), where *<sup>z</sup>* is the vector of outputs from the second layer and *θ<sup>j</sup>* ' is the vector of weights for each input wire to the output neuron *j*. *h* (*θ<sup>j</sup>* '*<sup>T</sup> z*) corresponds to the probability for the input feature vector to belong to the class *j*. Then, a selector function chooses the class with the highest probability to be assigned as the final output of the classifier.

**Figure 1.** A schematic figure of a feed-forward three layers neural network. Here, an input vector of three features is classified in one out of two known classes. The hidden and output layers compute logistic functions in each neuron, represented by the s-like curve. *θi*, *<sup>j</sup>* is the weight of the i-th wire to the neuron j.

Any neuron in the second and third layer has an associated vector of parameters that need to be trained. The training of a NN is a difficult task, where the weights connecting each pair of neuron must be learned for all neuron in any layer. For the output layer, the cost function can be computed taking into account the expected values in the training set. But for the inner layers, no expected value is known. As a consequence of this, the cost function associated to a NN is in general a non-convex function. This has strong repercussions in the optimization problem. Due to the existence of several local minimum, the convergence to a global minimum is not guaranteed.

The variational parameters have several ways to be changed that will provide approximately the same level of correction from one iteration to the next. One strategy to find the "right direction" to move the network is to take minimal changes, i.e., from all the possible variation of parameters providing the same level of correction, the network is changed in the way that the set of parameters defers the less from its previous state. This is done by applying a generalization of the gradient descent method to deal with multilayer networks, called the back propagation algorithm, the complete description of which will be found elsewhere [17].

#### *2.1.4. Support vector machine*

Another method to create a nonlinear classifier is the *support vector machine* SVM. To illustrate the idea behind SVM, consider a two class problem. The main objective is to draw the decision border between two classes that provides the best separation of sub sets among all the possible border lines (see Figure 2).

*h θi*

*h* (*θ<sup>j</sup>*

(*x*)= *g*(*θ<sup>i</sup>*

10 Cell Biology - New Insights

*<sup>T</sup> <sup>x</sup>*) as in Eq. (4). *θ<sup>i</sup>* is the parameters vector, containing the weights for each input

'

'*<sup>T</sup> z*) corresponds to the probability for the input

is the vector of weights

wire to neuron *i*. Each neuron in the hidden layer sends its output to any neuron in the third or output layer. And finally, the neurons in the output layer computes another logistic function

feature vector to belong to the class *j*. Then, a selector function chooses the class with the

**Figure 1.** A schematic figure of a feed-forward three layers neural network. Here, an input vector of three features is classified in one out of two known classes. The hidden and output layers compute logistic functions in each neuron,

Any neuron in the second and third layer has an associated vector of parameters that need to be trained. The training of a NN is a difficult task, where the weights connecting each pair of neuron must be learned for all neuron in any layer. For the output layer, the cost function can be computed taking into account the expected values in the training set. But for the inner layers, no expected value is known. As a consequence of this, the cost function associated to a NN is in general a non-convex function. This has strong repercussions in the optimization problem. Due to the existence of several local minimum, the convergence to a global minimum is not

The variational parameters have several ways to be changed that will provide approximately the same level of correction from one iteration to the next. One strategy to find the "right direction" to move the network is to take minimal changes, i.e., from all the possible variation of parameters providing the same level of correction, the network is changed in the way that the set of parameters defers the less from its previous state. This is done by applying a generalization of the gradient descent method to deal with multilayer networks, called the back propagation algorithm, the complete description of which will be found elsewhere [17].

Another method to create a nonlinear classifier is the *support vector machine* SVM. To illustrate the idea behind SVM, consider a two class problem. The main objective is to draw the decision

is the weight of the i-th wire to the neuron j.

'*<sup>T</sup> <sup>z</sup>*), where *<sup>z</sup>* is the vector of outputs from the second layer and *θ<sup>j</sup>*

highest probability to be assigned as the final output of the classifier.

for each input wire to the output neuron *j*. *h* (*θ<sup>j</sup>*

represented by the s-like curve. *θi*, *<sup>j</sup>*

*2.1.4. Support vector machine*

guaranteed.

**Figure 2.** Among all the possible border lines, SVM chooses the one that provides the maximum margin between the classes. Here, two classes, marked with a circle and an x in a two-dimensional feature space are shown. a) Some possi‐ ble non-optimal border lines. b) The right, the maximum margin border. Margins are shown in dots.

SVM finds the border line that has the largest margin or distance from the closest sample of each class. The equation of the decision border is then the equation of the hyperplane:

$$\mathcal{W}^{\mathrm{T}}\mathfrak{x} + \mathfrak{b} = \mathbf{0} \tag{9}$$

*W* is a vector perpendicular to the hyperplane. *x* is a vector in feature space and *b* is a bias term. In this part, it is convenient to split the optimization parameters *θ* in *W* and *b*, to explicitly take the interception term apart from others. Now propose the hypothesis function:

$$h(\mathbf{x}) = \mathbf{g}\left(\mathbf{W}^T\mathbf{x} + \mathbf{b}\right);\tag{10}$$

$$\log\left(z\right) = \begin{cases} 1 \text{if } z \ge 1, \\ -1 \text{if } z \le 1, \end{cases} \tag{11}$$

and the optimization problem is to find the optimal values for *W* and *b* that maximize the margin size. Starting from the Lagrangian

$$\mathcal{L}\left(\boldsymbol{W},\boldsymbol{b},\boldsymbol{\alpha}\right) = \frac{1}{2}\boldsymbol{W}^{T}\boldsymbol{W} - \sum\_{i=1}^{n} \alpha\_{i} \left[\boldsymbol{y}^{(i)}\left(\boldsymbol{W}^{T}\boldsymbol{x}^{(i)} + \boldsymbol{b}\right) - 1\right],\tag{12}$$

which includes the Lagrange multipliers *αi* to hold the restrictions imposed by *g*(*z*) in Eq. (11). The optimality conditions for the objective function are found by differentiating Eq. (12) against *W* and *b* and setting it equal to zero. It can be found that *<sup>W</sup>* <sup>=</sup>∑*<sup>α</sup><sup>i</sup> <sup>y</sup>* (*i*) *x* (*i*) and ∑ *i m <sup>α</sup><sup>i</sup> <sup>y</sup>* (*i*) =0. Also, the multipliers vanish for all the feature vectors outside the margin lines, the remaining vectors are called support vectors and give rise to the method's name. After some algebra, the minimization problems turn out to be the maximization of the objec‐ tive function [17]

$$\mathcal{J}\left(\boldsymbol{\alpha}\right) = \sum\_{i}^{m} \alpha\_{i} - \frac{1}{2} \sum\_{i}^{m} \sum\_{j}^{m} \alpha\_{i} \alpha\_{j} y^{(i)} y^{(j)} \mathcal{K}\left(\mathbf{x}^{(i)}, \mathbf{x}^{(j)}\right),\tag{13}$$

under the constrains *α<sup>i</sup>* <sup>≥</sup>0 and ∑ *i m <sup>α</sup><sup>i</sup> <sup>y</sup>* (*i*) =0. Here, the kernel function is just the inner product

*K*(*x* (*i*) , *x* (*i*) ) =(*x* (*i*) )*<sup>T</sup> x* (*i*) that corresponds to a linear classifier, i.e., when the two classes can be separated by a straight line. In the case that the data are not linear separable, SVM can become non-linear by simply replacing the kernel by a non-linear one. If the kernel represents the inner product of two vectors in the feature space, what does it mean a non-linear kernel function? When changing the kernel, a representation of the feature space in a higher dimensional space is obtained, related to the original feature space by some nonlinear transformation than is not necessary to know. The only thing required is the form of the inner product in the new coordinates expressed in terms of the original ones. This "kernel trick" allows the computation of pretty complex decision borders. However, not any function of two features constitutes a valid kernel. To solve this situation, a special case of Mercer's theorem [18] guarantees the validity of a kernel function, as far as the kernel matrix *ki*, *<sup>j</sup>* <sup>=</sup> *<sup>K</sup>*(*<sup>x</sup>* (*i*) , *x* ( *<sup>j</sup>*) ) is a symmetric positive semi-definitive matrix.

In real application, it is common to find that the training set at hand is not separable, i.e., it is not possible to find a border hyper surface that splits the feature space without misclassifica‐ tion of some training samples. And forcing the model to fit any training vector will produce high bias. Then it is a good practice to implement *regularization*. This is done by introducing

the regularization term *C*∑ *i n ξ*( *θ <sup>i</sup>* ) in the cost to minimize. Here *θ <sup>i</sup>* is the i-th component of the parameter vector, *ξ* is a penalty function which accomplish *ξ*(*θ*)≥0 and *C* is the regulari‐ zation parameter set by the user. *C* allows to control how much bias is acceptable for the final model.

#### *2.1.5. Confusion matrix*

To assess the accuracy of the ML model a *confusion matrix* for our classifier can be build. The confusion matrix is an evaluation of how many feature vectors in the training and/or testing set are misclassified. The matrix is built by contrasting the predicted class flag with the real one for each feature vector. For example, consider a two class problem (like the benign or malign tumor problem) that when trained against a set of 100 feature vectors report the classification presented in table 1:

A Proposal for a Machine Learning Classifier for Viral Infection in Living Cells Based on Mitochondrial Distribution http://dx.doi.org/10.5772/61293 13


**Table 1.** Example of a confusion matrix for a two classes clasiffier based on imaginary benign or malign tumor data.

In the example, 45 benign tumors have been classified as benign by the ML, and 15 have been misclassified as malign tumors. The error estimate for a ML code is computed as the average of miscalculated classes over the total of samples. It is the sum over all the off diagonal elements over the total number of cases. In the example, the error range of 30%. And the accuracy, defined as 1 − *err* is 70%.

#### **2.2. Unsupervised learning**

In this case, the first objective of the ML is to find some similarities among the data, which can be used to divide it into clusters. Each cluster will then define a class, and new inputs to the machine (outside the training set) will be classified following the clustering of the training space.

#### *2.2.1. Clustering*

∑ *i*

*K*(*x* (*i*)

, *x* (*i*)

*<sup>α</sup><sup>i</sup> <sup>y</sup>* (*i*)

12 Cell Biology - New Insights

tive function [17]

J a

under the constrains *α<sup>i</sup>* <sup>≥</sup>0 and ∑

) =(*x* (*i*)

semi-definitive matrix.

the regularization term *C*∑

*2.1.5. Confusion matrix*

classification presented in table 1:

model.

=0. Also, the multipliers vanish for all the feature vectors outside the margin lines,

= - å åå *y y Kx x* (13)

)*<sup>T</sup> x* (*i*) that corresponds to a linear classifier, i.e., when the two classes can be

=0. Here, the kernel function is just the inner product

, *x* ( *<sup>j</sup>*)

) is a symmetric positive

is the i-th component of

the remaining vectors are called support vectors and give rise to the method's name. After some algebra, the minimization problems turn out to be the maximization of the objec‐

> ( ) () ( ) () ( ) ( ) <sup>1</sup> , , <sup>2</sup> *m mm ij i j*

separated by a straight line. In the case that the data are not linear separable, SVM can become non-linear by simply replacing the kernel by a non-linear one. If the kernel represents the inner product of two vectors in the feature space, what does it mean a non-linear kernel function? When changing the kernel, a representation of the feature space in a higher dimensional space is obtained, related to the original feature space by some nonlinear transformation than is not necessary to know. The only thing required is the form of the inner product in the new coordinates expressed in terms of the original ones. This "kernel trick" allows the computation of pretty complex decision borders. However, not any function of two features constitutes a valid kernel. To solve this situation, a special case of Mercer's theorem [18] guarantees the

In real application, it is common to find that the training set at hand is not separable, i.e., it is not possible to find a border hyper surface that splits the feature space without misclassifica‐ tion of some training samples. And forcing the model to fit any training vector will produce high bias. Then it is a good practice to implement *regularization*. This is done by introducing

the parameter vector, *ξ* is a penalty function which accomplish *ξ*(*θ*)≥0 and *C* is the regulari‐ zation parameter set by the user. *C* allows to control how much bias is acceptable for the final

To assess the accuracy of the ML model a *confusion matrix* for our classifier can be build. The confusion matrix is an evaluation of how many feature vectors in the training and/or testing set are misclassified. The matrix is built by contrasting the predicted class flag with the real one for each feature vector. For example, consider a two class problem (like the benign or malign tumor problem) that when trained against a set of 100 feature vectors report the

) in the cost to minimize. Here *θ <sup>i</sup>*

 aa

*i i j i ij*

 a

*i*

validity of a kernel function, as far as the kernel matrix *ki*, *<sup>j</sup>* <sup>=</sup> *<sup>K</sup>*(*<sup>x</sup>* (*i*)

*i*

*ξ*( *θ <sup>i</sup>*

*n*

*<sup>α</sup><sup>i</sup> <sup>y</sup>* (*i*)

*m*

*m*

So far, the feature vector is represented as a set of numerical values in real space. From the mathematical point of view, each input "box" inside a vector is called a dimension and the value in the box is a coordinate. The length of the vector is the number of dimensions of the containing space. A space is a collection of vectors that follow a set of rules (an algebra). If a distance measure for any two points in the space (features vectors) can be build, then the data can be clustered [19]. A common choice is the Euclidean distance, defined as the square root of the sums of the squares of the differences between the coordinates of the two vectors in each dimension, i.e., if **A**, **B** are vectors in ℝ*<sup>n</sup>*, the Euclidean distance between them is given by:

$$\left\|A - B\right\| = \sqrt{\sum\_{i=1}^{n} \left(\mathbf{x}\_{A,i} - \mathbf{x}\_{B,i}\right)^2} \tag{14}$$

#### *2.2.2. K-means*

A common clustering algorithm known as K-means is as follows: chooses a number of clusters k to be found, and initialize the clusters centroids µ1 , µ2 ,...,µ*k* randomly. Then assign each one of the training feature vectors to a cluster by relating it to the closest centroid (the one which has the minimum distance to the sample). When all vectors in the training set are labeled, recompute the position of the centroids as the average of the feature vectors inside the cluster, for each cluster. If there are centroids without any feature vector assigned, it can be dismissed or repositioned randomly. Now iterate again relabeling the training set and recomputing the centroids positions until convergence is achieved.

#### *2.2.3. Hierarchical clustering*

It is a quite expensive algorithm to obtain clusters which is based on finding a partition hierarchy among the data. It can be started by making each feature vector a cluster with one single member. Then, the distance between any pair of vectors is computed. If the distance is lesser than some selection parameter, the clusters are mixed to form one. In the new distribu‐ tion of clusters, each cluster is represented by its centroid, and iterates the process until some convergence criteria is achieved. For example, a predefined number of clusters is reached. Due to the computational cost involved in hierarchical clustering, it is not recommended for problems with large training set.

#### *2.2.4. The CURE algorithm*

This is a large-scale-clustering algorithm. When centroids are used to define clusters, it is expected that any cluster would have a regular shape in features space, and the space is expected to be Euclidean. The clustering using representatives (CURE) algorithm is a little more general, due that it can handle irregular shaped clusters. This method defines a cluster in terms of a set of representative members of the cluster. These representatives must be chosen in a way that they are as far as possible from each other. Then, the representatives are points on the "surface" of the cluster. This kind of construction allows any shape for the cluster, including rings. To apply the CURE algorithm, first an initial clustering must be done, then the representatives are chosen for each cluster, and finally, two clusters are united if they have a pair of representatives that are close enough following some user-definedcriteria.

#### **3. LCI experiments and data extraction**

#### **3.1. Experiment description**

#### *3.1.1. Materials and methods*

#### *3.1.1.1. Cell lines expressing fluorescent mithondria (Vero-Mito)*

The Vero epithelial cells (ATCC) were maintained under standard culture conditions as described in other works from this lab [20-21], and in another chapter of this book [22]. The temperature was set at 37°C in a humidified atmosphere of 95% air and 5% carbon dioxide. The monoclonal cell line over-expressing the plasmid pmKate2-Mito (Evrogen®) were obtained with a cell sorter (Moflo XDP, Beckman Coulter®), with ulterior antibiotic selection (Kanamycin) of transfectants during 21 days in accordance to the experimental procedures described in detail in [23].

#### *3.1.1.2. Virus preparation, titration and infection protocols*

The strain New Guinea of Dengue Virus Serotype 2 (DENV-2) was grown and maintained in insect cells C6/36 HT under the standard practices as described in [20, 21], and this book [22]. Briefly the DENV were amplified at a very low MOI (multiplicity of infection) to avoid genetic drift and apparition of DIs (defective interfering particles), which could be altering the whole data concerning the real synchronized infections [24]. Viral titers were detected by plaque assay, using a Vero cell monolayer culture under 1% methylcellulose overlay medium as it was reported by [20, 21]. The viral infections were done by the same way of our previously reported works [20, 21], with the difference that for live cell imaging the cells were seed and registered in 35-mm glass bottom dishes (MatTek Corporation) with 0.7 mm in thickness of the glass coverslides, which is adequate in refraction index for this kind of inverted confocal microscope for registering living cells. The negative controls of infections were named mock infections, as it had been standardized traditionally for the virology community [24].

#### *3.1.1.3. Live cell imaging*

*2.2.3. Hierarchical clustering*

14 Cell Biology - New Insights

problems with large training set.

**3. LCI experiments and data extraction**

*3.1.1.1. Cell lines expressing fluorescent mithondria (Vero-Mito)*

*3.1.1.2. Virus preparation, titration and infection protocols*

*2.2.4. The CURE algorithm*

**3.1. Experiment description**

*3.1.1. Materials and methods*

described in detail in [23].

It is a quite expensive algorithm to obtain clusters which is based on finding a partition hierarchy among the data. It can be started by making each feature vector a cluster with one single member. Then, the distance between any pair of vectors is computed. If the distance is lesser than some selection parameter, the clusters are mixed to form one. In the new distribu‐ tion of clusters, each cluster is represented by its centroid, and iterates the process until some convergence criteria is achieved. For example, a predefined number of clusters is reached. Due to the computational cost involved in hierarchical clustering, it is not recommended for

This is a large-scale-clustering algorithm. When centroids are used to define clusters, it is expected that any cluster would have a regular shape in features space, and the space is expected to be Euclidean. The clustering using representatives (CURE) algorithm is a little more general, due that it can handle irregular shaped clusters. This method defines a cluster in terms of a set of representative members of the cluster. These representatives must be chosen in a way that they are as far as possible from each other. Then, the representatives are points on the "surface" of the cluster. This kind of construction allows any shape for the cluster, including rings. To apply the CURE algorithm, first an initial clustering must be done, then the representatives are chosen for each cluster, and finally, two clusters are united if they have

a pair of representatives that are close enough following some user-definedcriteria.

The Vero epithelial cells (ATCC) were maintained under standard culture conditions as described in other works from this lab [20-21], and in another chapter of this book [22]. The temperature was set at 37°C in a humidified atmosphere of 95% air and 5% carbon dioxide. The monoclonal cell line over-expressing the plasmid pmKate2-Mito (Evrogen®) were obtained with a cell sorter (Moflo XDP, Beckman Coulter®), with ulterior antibiotic selection (Kanamycin) of transfectants during 21 days in accordance to the experimental procedures

The strain New Guinea of Dengue Virus Serotype 2 (DENV-2) was grown and maintained in insect cells C6/36 HT under the standard practices as described in [20, 21], and this book [22].

The Vero-Mito (3x105 cells) cell line was seed in Petri dishes adequate for living cells with bottom with coverslide of 0.17 mm, and previous to the register the normal culture medium used was changed by a DMEM without red phenol for avoiding the autofluorescence of this pH-indicator chemical. The videos of living cells over expressing fluorescent mitochondria (+/ infections) were obtained with a confocal microscopy based on disk spinning Unit (Olym‐ pus®IX-81 DSU), coupled to incubator and mixing gases Tokai-Hit Co® systems, which regulate the micro environment of cell culture with temperature and carbon dioxide in all system. The mock infections and infections of the overnight micrographs were captured in an OrcaR2CCD (Hamamatsu®) ultra-refrigerated camera with electro multiplier, coupled to the illumination systems with Arc burners of 150 W constituted by mercury-xenon or xenon lamps (Olympus®-MT10 Illumination System). The photonic signals emitted by the biological specimen were transduced to electromagnetic waves for the CCD (charge coupled device), transmitted by a light fiber 2 m of single quartz to the Workstation Xcellence-Pro (Olympus®) for image processing, which also include the application of deconvolution tools for improving the signal/noise ratio of images.

#### **3.2. Image segmentation and extraction of information**

A total of nine videos generated by LCI where studied. Four of them correspond to mock cells (uninfected) and five to infected cells. Each video has 36 frames taken each 20 min for a period of 12 h. The videos are recorded in color at 1024x1344ppi resolution. As the color has no relevant information, they have been converted into gray scale. The last 34 vertical lines of each frame were dismissed in order to get rid of the microscope watermark. Then the resolution has been decreased to 495 x 672. The cells in this study have been selected under the following criteria:


Under this procedure, 11 cells were selected, 4 mock and 7 infected. Any selected cells were modeled as having an elliptical nuclei, by manually choosing four points on the nuclei borderline and applying the Hough transform [25] (see Figure 3 and 4). The nucleus and the cell are proven to be approximately aligned [26] so the nuclear envelope is approximated by another ellipsis centered in the nuclei, with the same inclination and the axis twice as long. This rudimentary model provides us with the necessary segmentation to perform the cell tracking by simply creating a mask over the region where the ellipsis is located for any frame in the video. The images are stored as intensity matrices where each entry is a pixel. Masks are stored as matrices of the same dimension, whose entries take values of zero or one. If the pixel belongs to the segmented region the associated mask value is one. Those matrices are stored in binary format to be processed in a Python script that takes advantage of numpy and Scipy libraries for further analysis.

**Figure 3.** An infected cell appearing in the original image present on video.

**Figure 4.** The segmented region used to track and study the cell. Nucleus is modeled as having an elliptic shape. The exterior membrane is modeled as a concentric ellipsis with the major semi axis twice as long as the nucleus.

#### **3.3. Information processing**

borderline and applying the Hough transform [25] (see Figure 3 and 4). The nucleus and the cell are proven to be approximately aligned [26] so the nuclear envelope is approximated by another ellipsis centered in the nuclei, with the same inclination and the axis twice as long. This rudimentary model provides us with the necessary segmentation to perform the cell tracking by simply creating a mask over the region where the ellipsis is located for any frame in the video. The images are stored as intensity matrices where each entry is a pixel. Masks are stored as matrices of the same dimension, whose entries take values of zero or one. If the pixel belongs to the segmented region the associated mask value is one. Those matrices are stored in binary format to be processed in a Python script that takes advantage of numpy and Scipy

**Figure 4.** The segmented region used to track and study the cell. Nucleus is modeled as having an elliptic shape. The

exterior membrane is modeled as a concentric ellipsis with the major semi axis twice as long as the nucleus.

libraries for further analysis.

16 Cell Biology - New Insights

**Figure 3.** An infected cell appearing in the original image present on video.

In the gray-scale video, the mitochondrial distribution is shown as bright points, been more brilliant those places where the density of mitochondrium is higher. Then, the density distribution of mitochondrium can be estimated as proportional to the intensity distribution *ρ*(*x*, *y*, *t*) = *αI*(*x*, *y*, *t*). In each frame of each video, a discrete set of pixel intensity values is recorded. This means that the intensity distribution in a discrete grid of point (*X* , *Y* ) has been measured, where *x* ∈ *X* and *y* ∈ *Y* are the sets of pixels coordinates.

The shape of the density distribution of mitochondrium is the same shape of the intensity distribution. Those functions differ only by a constant of proportionality that became irrelevant when the density function is normalized. So further in this reading both functions would be referred indistinguishable as *ρ*(*x*, *y*, *t*).

The continuous density function can be approximated from the set of pixel intensity meas‐ urements by some interpolation method. In this work, a two-dimensional interpolation in terms of bivariate splines has been used on each segmented frame. This procedure allows us to extract important information about the mitochondrial behavior. Each frame is taken after a fixed period of time of 20 mins, so they form a time series of the density distribution function *ρ*(*x*, *y*, *t*) through the whole experiment.

#### **4. Results and discussion**

In cell biology studies live cell imaging is a newcomer; however, the innovation in computa‐ tional biology tools is been forced by the convergence of distinct research programs. Being so, LCI is no longer only a "technique" but a new exploratory science [27], that brings the possibility of encompassing cross-disciplines. In this sense, the subcellular patterns of distinct cellular organelles and macromolecular structures within the cell are important for dynamical studies, which will be useful in predictive medicine [28].

The mitochondrial morphology is a remarkable area for biomedical research since more than a decade [29], because these cellular organelles change under physiological and pathological conditions, like metabolism, thermogenesis, homeostasis of calcium and several kinds of cell death [30, 31]. But there is lacking information about the subcellular distribution of mitochon‐ drium after a cell injury like the viral infections, and this quantitative information is key for tracking some cellular events of virus cycle that have been covered to the computational cell biology exploration.

New developments have been focused in the high-resolution microscopy images of the fine morphology of mitochondria [32]. Having in mind the improved time resolution, this infor‐ mation is decisive for understanding of the dynamics and functioning of these cellular organelles at high-throughput screenings [33].

But here, the work was mainly directed to study and characterize the subcellular distribution of mitochondria with and without Dengue virus infections on epithelial cells that are consti‐ tutively expressing these organelles in red fluorescence.

Recently, it had demonstrated that not only shape, number and size of the organelles are important for the cellular function, but also their subcellular distribution, which is the consequence of the intracellular transport [34]. Since Dengue virus like many other members of the most diverse viral families are using the cytoskeleton [22], here we have tried to follow indirectly the infection process using the alterations of subcellular distributions of mitochondria.

Both mock and DENGV infected cells have been prepared by a standardized procedure that provides approximately the same initial state among all cells of each type even when different experiments are considered. So at frame 0 each of the studied cells provides a possible initial state. Each of these states must adjust to the density distribution of mitochondrium. Assuming that any possible initial state is equally probable, then our approximation to the density function at time zero *ρ*(*r*, *θ*, *t* = 0) must come from the average over all the known (meas‐ ured) possible states. Each frame has the same time spacing for all the videos (20 minutes), so the same analysis is valid for the i−th frame and the mitochondria density distribution at time *t* would be the average over all the known states for all cells of the same kind.

The distribution as a function of two variables given by the pixel position related to the center of the cell is *ρ*(*x*, *y*). However, before taking the average, it has to be taken into account that a single cell can have any random orientation. The elliptical shape of the nucleus makes the distribution not symmetrical. This means that all function must be rotated to have the same orientation before been able to average over them.

A Python script was written to automatically determine the major semi axis of each cell in each frame by measuring the maximum distance between two points into the segmented region. The center of the ellipsis is found as the average of all the coordinates in the image. To get *ρ*(*r, θ, t*) for any cell referred to the same polar axis, and so be able to compute the density average, the polar axis is set equal to the major semi axis in each of the cells analyzed. In polar coordi‐ nates *ρ*(*r*, *θ*) will give us the density of mitochondrium at a distance *r* from the nuclei center and at an angle *θ* from the major semi axis.

The average density of mitochondrium distribution *ρ*(*r, θ, t*) is shown for three frames (t = 0, 320, 720 minutes) in Figures 5, 6, and 7. Those are the initial state, one intermediate state and the final state of the study. The vertical axis is the level of intensity (proportional to the mitochondrium density) and the horizontal axis is the distance to the nuclei center in pixels. In each subplot the projection of *ρ*(*r, θ, t*) for a given angle in radians is presented.

It can be seen that mock cells present prominent peaks for some radial positions, i.e., the distance between the peak and the closest local minimum is large compared with the back‐ ground density. Also, the background density is low. This suggests that mock cells have the mitochondrium distributed in clusters around the nuclei. At variance, the infected cells average mitochondrium density distribution presents a higher background intensity com‐ pared with the maximum of the distribution. The peaks are less defined than those for mock cells, which means that the mitochondrium clusters are less defined or inexistent. And the mitochondrium tends to fill all the space available. Is also noticeable that the infected cells

A Proposal for a Machine Learning Classifier for Viral Infection in Living Cells Based on Mitochondrial Distribution http://dx.doi.org/10.5772/61293 19

Recently, it had demonstrated that not only shape, number and size of the organelles are important for the cellular function, but also their subcellular distribution, which is the consequence of the intracellular transport [34]. Since Dengue virus like many other members of the most diverse viral families are using the cytoskeleton [22], here we have tried to follow indirectly the infection process using the alterations of subcellular distributions of

Both mock and DENGV infected cells have been prepared by a standardized procedure that provides approximately the same initial state among all cells of each type even when different experiments are considered. So at frame 0 each of the studied cells provides a possible initial state. Each of these states must adjust to the density distribution of mitochondrium. Assuming that any possible initial state is equally probable, then our approximation to the density function at time zero *ρ*(*r*, *θ*, *t* = 0) must come from the average over all the known (meas‐ ured) possible states. Each frame has the same time spacing for all the videos (20 minutes), so the same analysis is valid for the i−th frame and the mitochondria density distribution at time

The distribution as a function of two variables given by the pixel position related to the center of the cell is *ρ*(*x*, *y*). However, before taking the average, it has to be taken into account that a single cell can have any random orientation. The elliptical shape of the nucleus makes the distribution not symmetrical. This means that all function must be rotated to have the same

A Python script was written to automatically determine the major semi axis of each cell in each frame by measuring the maximum distance between two points into the segmented region. The center of the ellipsis is found as the average of all the coordinates in the image. To get *ρ*(*r, θ, t*) for any cell referred to the same polar axis, and so be able to compute the density average, the polar axis is set equal to the major semi axis in each of the cells analyzed. In polar coordi‐ nates *ρ*(*r*, *θ*) will give us the density of mitochondrium at a distance *r* from the nuclei center

The average density of mitochondrium distribution *ρ*(*r, θ, t*) is shown for three frames (t = 0, 320, 720 minutes) in Figures 5, 6, and 7. Those are the initial state, one intermediate state and the final state of the study. The vertical axis is the level of intensity (proportional to the mitochondrium density) and the horizontal axis is the distance to the nuclei center in pixels.

It can be seen that mock cells present prominent peaks for some radial positions, i.e., the distance between the peak and the closest local minimum is large compared with the back‐ ground density. Also, the background density is low. This suggests that mock cells have the mitochondrium distributed in clusters around the nuclei. At variance, the infected cells average mitochondrium density distribution presents a higher background intensity com‐ pared with the maximum of the distribution. The peaks are less defined than those for mock cells, which means that the mitochondrium clusters are less defined or inexistent. And the mitochondrium tends to fill all the space available. Is also noticeable that the infected cells

In each subplot the projection of *ρ*(*r, θ, t*) for a given angle in radians is presented.

*t* would be the average over all the known states for all cells of the same kind.

orientation before been able to average over them.

and at an angle *θ* from the major semi axis.

mitochondria.

18 Cell Biology - New Insights

**Figure 5.** Average density of mitochondria *ρ*(*r, θ, t*), for *t* = 0 min. Mock cell mitochondrial density average is in blue (color online) dashed line and infected mitochondrial density is in red continuous line.

show more local maximum, which suggest that the distribution is somehow disorganized (more random).

These findings imply that a general structural change in mitochondrium distribution is caused by viral infection and it can be evidenced directly by examination of a cell's picture. The clustered behavior presented by mitochondrium on mock cells implies that they are grouped when normal function of the cell is in process. This is an organized distribution. On the other hand, the lack of clusters in infected cells shows that when infected the mitochondrium distribution became erratic, maybe random, which will be associated with a lack of organization.

A possible way to detect the presence of a viral infection will be to measure the level of randomness present in mitochondrium distribution. Remembering that *ρ*(*r, θ, t*) is experi‐ mentally measured through the pixel intensity in each video frame, it is found that the randomness in mitochondrium distribution will be the same than the randomness in pixel intensity distribution of the segmented image.

An image on gray scale is described digitally in terms of intensity values ranging from 0 (black) to 255 (white), a total of 256 possible shades of gray, each one of those possibilities is known as a level of intensity. A common descriptor used to classify a picture is the *entropy*

**Figure 6.** Average density of mitochondria *ρ*(*r, θ, t*), for *t* = 320 min. Mock cell mitochondrial density average is in blue (color online) dashed line and infected mitochondrial density is in red continuous line.

$$E = -\sum\_{i=0}^{295} P(i) \log\_2 \left( P(i) \right). \tag{15}$$

This is a measure of how "random" the levels of intensity are distributed on a gray scale picture. *P*(*i*)is the probability of finding the i−th level of intensity inside the image. As mock cells shows more order than infected cells in *ρ*(*r, θ, t*), it can be expected that for the entropy in mock cell's image to be lesser than the entropy in the image of an infected one.

Another commonly used descriptor for images is *uniformity*, defined as:

$$\mu = \sum\_{i=0}^{293} P\left(i\right)^2,\tag{16}$$

which is a measure of how much the levels of intensity change through the image. This descriptor is maximum if all the image presents one single level, and decreases with the level changes. By carefully looking at Figures 5, 6, and 7 the reader will note that infected cells shows more oscillations in the density of mitochondrium (local peaks). In terms of pixel intensity, it

A Proposal for a Machine Learning Classifier for Viral Infection in Living Cells Based on Mitochondrial Distribution http://dx.doi.org/10.5772/61293 21

**Figure 7.** Average density of mitochondria *ρ*(*r, θ, t*), for *t* = 720 min. Mock cell mitochondrial density average is in blue (color online) dashed line and infected mitochondrial density is in red continuous line.

means that the intensity is changing more frequently, so the tone in the pictures is less uniform. Then it can be expected from the uniformity descriptor on the picture of an infected cell to be low.

In Figure 8, a plot on the uniformity vs entropy parameters space shows the computed values for those image descriptors for all studied cell in all frames. It can be seen that the mock and infected cells occupy mainly different regions on parameter space. So, these descriptors constitute a promising candidate to be a feature vector (or a part of it) in a machine learning code designed to classify infected cells.

#### **5. Conclusion**

( ) ( ( )) <sup>255</sup> 2

<sup>9</sup> <sup>θ</sup> = 1 · <sup>2</sup><sup>π</sup>

<sup>9</sup> <sup>θ</sup> = 4 · <sup>2</sup><sup>π</sup>

This is a measure of how "random" the levels of intensity are distributed on a gray scale picture. *P*(*i*)is the probability of finding the i−th level of intensity inside the image. As mock cells shows more order than infected cells in *ρ*(*r, θ, t*), it can be expected that for the entropy in mock cell's

> ( ) <sup>255</sup> <sup>2</sup> 0

*i u Pi* =

,

which is a measure of how much the levels of intensity change through the image. This descriptor is maximum if all the image presents one single level, and decreases with the level changes. By carefully looking at Figures 5, 6, and 7 the reader will note that infected cells shows more oscillations in the density of mitochondrium (local peaks). In terms of pixel intensity, it

*E Pi Pi* =

log .

40 50 60 70 80 90 100 110 120

Distance from nuclei center in pixels

**Figure 6.** Average density of mitochondria *ρ*(*r, θ, t*), for *t* = 320 min. Mock cell mitochondrial density average is in blue

<sup>θ</sup> = 7 · <sup>2</sup><sup>π</sup> 9

= -å (15)

<sup>9</sup> <sup>θ</sup> = 2 · <sup>2</sup><sup>π</sup>

<sup>9</sup> <sup>θ</sup> = 5 · <sup>2</sup><sup>π</sup>

40 50 60 70 80 90 100 110 120

9

9

<sup>θ</sup> = 8 · <sup>2</sup><sup>π</sup> 9

<sup>=</sup> å (16)

0

*i*

(color online) dashed line and infected mitochondrial density is in red continuous line.

image to be lesser than the entropy in the image of an infected one.

20 Cell Biology - New Insights

Average

Instensity

 level

<sup>θ</sup> = 0 · <sup>2</sup><sup>π</sup>

<sup>θ</sup> = 3 · <sup>2</sup><sup>π</sup>

<sup>θ</sup> = 6 · <sup>2</sup><sup>π</sup> 9

40 50 60 70 80 90 100 110 120

Another commonly used descriptor for images is *uniformity*, defined as:

A detailed analysis of the mitochondrium distribution around the nuclei for seven infected cells and four mock cells in nine videos has been performed. The study shows that mock cells clusters its mitochondrium and present an organized distribution in space. The organized character of the mitochondrium density distribution is maintained through time. At variance, infected cells loose these organized characteristics and the distribution of mitochondrium become erratic. This suggests that the mitochondrium are clustered when the healthy cell is

**Figure 8.** (Color online) Parameter space graph for Mock cell (blue x) and infected cells (red dots). Each marker repre‐ sents the value for a single cell in a single time instant.

performing its natural process. But when a DENV infection is affecting the cell, those natural process are interrupted and it is reflected in the way how mitochondrium behaves. From this analysis, two image attributes are found to be suitable to be used as *features* in a ML classifier between infected and mock cells. These features are simple common image processing descriptors: *entropy* and *uniformity*, whose computation is easy and fast. Entropy is related with the randomness presented in the gray tones of the image and uniformity is related with the prevalence of a single gray tone. Both image attributes in a LCI photograph taken over a cell culture prepared with coloured cells are directly related with the mitochondrium density distribution behavior *ρ*(*r, θ, t*). The presence of clusters in mock cells and the softer *ρ*(*r, θ, t*) behavior are translated to higher values of uniformity and lower values of entropy image descriptors than those present in infected cells images.

#### **Acknowledgements**

This research was supported by COLCIENCIAS grant 111554531592 from the Colombian government. JCGG was the recipient of a Full-Time Professor Program (Exclusive Dedication) for the Medicine Faculty at University of Antioquia for 2014–2015.

#### **Author details**

Juan Carlos Cardona-Gomez1\*, Leandro Fabio Ariza-Jimenez2 and Juan Carlos Gallego-Gomez2\*

\*Address all correspondence to: juanc.gallegomez@gmail.com; jccg77@gmail.com

1 Optical Spectrometry Group, Faculty of Basic Sciences, Universidad del Atlántico, Barran‐ quilla, Colombia

2 Translational and Molecular Medicine Group, Medellín Medical Research Institute, Facul‐ ty of Medicine, Universidad de Antioquia, Medellín, Colombia

#### **References**

performing its natural process. But when a DENV infection is affecting the cell, those natural process are interrupted and it is reflected in the way how mitochondrium behaves. From this analysis, two image attributes are found to be suitable to be used as *features* in a ML classifier between infected and mock cells. These features are simple common image processing descriptors: *entropy* and *uniformity*, whose computation is easy and fast. Entropy is related with the randomness presented in the gray tones of the image and uniformity is related with the prevalence of a single gray tone. Both image attributes in a LCI photograph taken over a cell culture prepared with coloured cells are directly related with the mitochondrium density distribution behavior *ρ*(*r, θ, t*). The presence of clusters in mock cells and the softer *ρ*(*r, θ, t*) behavior are translated to higher values of uniformity and lower values of entropy image

**Figure 8.** (Color online) Parameter space graph for Mock cell (blue x) and infected cells (red dots). Each marker repre‐

0.00 0.05 0.10 0.15 0.20 0.25 Uniformity

This research was supported by COLCIENCIAS grant 111554531592 from the Colombian government. JCGG was the recipient of a Full-Time Professor Program (Exclusive Dedication)

and

descriptors than those present in infected cells images.

4.5

sents the value for a single cell in a single time instant.

5.0

5.5

6.0

Entropy

6.5

7.0

7.5

8.0

22 Cell Biology - New Insights

for the Medicine Faculty at University of Antioquia for 2014–2015.

Juan Carlos Cardona-Gomez1\*, Leandro Fabio Ariza-Jimenez2

\*Address all correspondence to: juanc.gallegomez@gmail.com; jccg77@gmail.com

**Acknowledgements**

**Author details**

Juan Carlos Gallego-Gomez2\*


[27] Wang Y.-l. Hahn K.M., Murphy R.F., Horwitz A.F. From imaging to understanding: frontiers in live cell imaging, Bethesda, MD, April 19–21, 2006. J Cell Biol. 2006;174 (4):481-484. DOI: 10.1083/jcb.200607097

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[22] Orozco-García E., Trujillo-Correa A., Gallego-Gómez J. Cell biology of virus infec‐ tion: The role of cytoskeletal dynamics integrity in the effectiveness of dengue virus

[23] Acevedo-Ospina H. Biología celular de la infección por virus dengue: Relación entre las mitocondrias y los virus [thesis]. Medellín, Colombia: Institute of Biology, Uni‐

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[24] Mahy B.W.J. The Dictionary of Virology. 4th ed. Academic Press; 2008. 520 p.

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**Molecular and Cellular Regulatory Mechanisms**

## **Epithelial Na+,K+-ATPase — A Sticky Pump**

Jorge Alberto Lobato Álvarez, Teresa del Carmen López Murillo, Claudia Andrea Vilchis Nestor, María Luisa Roldán Gutierrez, Omar Páez Gómez and Liora Shoshani

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/61244

#### **Abstract**

Na+ ,K+ -ATPase is an ATP-powered ion pump that establishes concentration gradients for Na+ and K+ ions across the plasma membrane in all animal cells by pumping Na+ from the cytoplasm and K+ from the extracellular medium. This heterodimeric enzyme, a member of P-type ATPases, is composed of a catalytic α-subunit with ten transmembrane do‐ mains and a heavily glycosylated auxiliary β-subunit. The Na+ ,K+ -ATPase is specifically inhibited by cardiotonic steroids like ouabain, which bind to the enzyme's α-subunit from the extracellular side and thereby block the ion pumping cycle. Na+ ,K+ -ATPAse gen‐ erates ion gradients that establishes the driving force for the transepithelial transport of several solutes and nutrients. The effectiveness of this vectorial transport motivated by Na+ ,K+ -ATPase depends on the integrity of epithelial junctions that are essential for the maintenance of the polarized localization of membrane transporters, including the lateral sodium pump. This chapter reviews the facts showing that, in addition to pumping ions, the Na+ ,K+ -ATPase located at the cell borders functions as a cell adhesion molecule and discusses the role of the Na+ ,K+ -ATPase β-subunit in establishing and maintaining cell– cell interactions. Furthermore, Na+ ,K+ -ATPase is a multifunctional protein that, in addi‐ tion to pumping ions asymmetrically and participating in cell–cell contacts, acts as specif‐ ic receptor for the hormone ouabain and transduces extracellular signals. Thus, when bearing in mind with transporting epithelia phenotype, the importance of modulation of cell contacts by Na+ ,K+ -ATPase can hardly be underestimated.

**Keywords:** Epithelial cells, Na+ , K+ -ATPase, Polarity, cell adhesion

#### **1. Introduction**

Epithelium is the name given to the cells that line a surface. Epithelia separate biological compartments with different composition, a fundamental role that depends on the establish‐

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ment of occluding junctions. Thus, epithelial cells are always contiguous with one another and are usually joined by special junctions—the tight junctions. The functions of epithelia differ markedly. Although all form a barrier, some are much more impermeable than others. The trans-epithelial movement of ions and molecules is reached by the action of a multitude of specialized transporting proteins that are asymmetrically distributed on the apical or basolat‐ eral plasma membrane domains of epithelial cells. This remarkable polarity of epithelial cells depends on the selective insertion and the recycling of newly synthesized proteins and lipids into distinct plasma membrane domains and on the maintenance and modulation of these specialized domains once they are established during epithelial development. The two basic characters of epithelial transporting phenotype are polarity and tight junctions (TJs). Polarity offers the necessary direction for substances transported across epithelia to be absorbed or secreted. TJs guarantee that the transported substances do not leak back through the intercel‐ lular space [1, 2]. The Na+ ,K+ -ATPase, known as the sodium pump, has been shown to play a central role in the transporting phenotype of epithelia. Today, we already know its crystal structure, the chemical composition as well as the spatial arrangement of its three subunits (α, β, and γ) (Fig. 1A), the relationship between ATP hydrolysis and ion movement, and several diseases related to its malfunction. Surprisingly, despite such detailed information, we keep finding new remarkable properties and new physiological functions of the Na+ ,K+ -ATPase. The present chapter is focused on three recently found properties: its expression at the lateral membrane of epithelial cells due to the self-adhesive property of the β-subunit, its role as hormone receptor, and its ability to modulate several types of cell contacts.

#### **2. Na+ ,K+ -ATPase in epithelia**

The history of Na+ ,K+ -ATPase can be compared to a double-sided step ladder, one climbed by biologists that investigated its intrinsic mechanisms and subunits the other by accomplished physicists who first criticized but finally solved immense theoretical obstacles in the road toward active transport. Thus, for a long while, the peculiar composition of the cytoplasm was attributed to presumed membrane impermeability to Na+ . This alternative was invalidated right after the Second World War, when radioisotopes became available for biological research, and it was discovered that tracer Na+ added to the bathing solution readily penetrates and distributes into the cell. This revived the question why Na+ in the cytoplasm remains at a concentration much lower (∼15 mM) than in the extracellular water (∼140 mM). The simplest assumption was that there should be an enzyme in the plasma membrane that dissipates metabolic free energy to pick up Na+ from the cell water and pump it out. This response was not readily accepted because it appeared in violation of the Curie principle: "Processes of different tensorial order cannot be coupled." In simple worlds, metabolism and ATP hydrol‐ ysis are chemical reactions, which at that time were taken to be *scalar* processes; hence, they could not drive a *vectorial* process like the extrusion of Na+ from the cytoplasm. Later on, it was argued that, in fact, chemical reactions are vectorial at microscopic level. However, this vectoriality is masked at macroscopic scale, in particular, when working with homogenized tissues where pumps point in all directions. However, if they were ordered in a membrane, the asymmetry would be recovered, and a macroscopic flux would take place. A model put forward by Koefoed-Johnson and Ussing [3] proposed a pump located asymmetrically on the basal side of the epithelial cell that together with the specific Na-permeability of the outer cell membrane and the specific K-permeability of the inner facing membrane is responsible for the net movement of Na+ . This made theoreticians happy, yet where was "the pump," i.e., the membrane molecule, that would align and be responsible for the sided, asymmetrical move‐ ment of Na+ ? On 1957, Jens Christian Skou prepared an extract of crab tissue that contained an enzyme that splits molecules of ATP (hence deserving the name "ATPase") into ADP + Pi, provided the medium contains K+ and Na+ ions at concentrations that compare with those in the cell and in the surrounding extracellular space. Therefore, the enzyme was aptly named Na+ ,K+ -ATPase. Interestingly, Skou [6] was able to inhibit the ATP splitting activity of his extract by adding *ouabain*, a substance of vegetal origin that was found a few years earlier to inhibit active potassium and sodium transport in erythrocyte membrane [5]. By performing the Na+ /K+ translocations cyclically, Na+ ,K+ -ATPase transfers those ions in a net amount toward the extracellular medium and toward the cytoplasm, respectively, so it was justified to call it "pump" [6]. Another experimental/theoretical conflict occurred with sugars and amino acids transported in a net amount across epithelia. Since this transport occurs in a net amount and can be inhibited with ouabain, for a while, it was taken as a proof that there exists a glucose pump as well as other pumps for diverse amino acid species. Yet eventually, it was demon‐ strated that carriers for sugars and for amino acids are not pumps as they are not *directly* coupled to metabolism. Therefore, the Na+ ,K+ -ATPase is the *primum movens*, responsible for the exchange of substances between the metazoan and the environment, across transporting epithelia, as well as for net exchange between the internal milieu and the cytoplasm.

#### **2.1. Structure–function relationship of Na+ ,K+ -ATPase**

Na+ ,K+ -ATPase is expressed in all animal cells and is one of the most important members of the P-type ATPases. The Na+ ,K+ -ATPase creates the Na+ and K+ concentration gradients across the plasma membranes of most higher eukaryotic cells. Per cycle, it pumps three Na+ ions out and two K+ ions into the cell, coupling the energy derived from the hydrolysis of one ATP molecule. The Na+ and K+ gradients originated and maintained by Na+ ,K+ -ATPase are the energy source for secondary active transport, which are used for the maintenance of cell osmolarity and volume, for the generation of action potentials along nerve cells, and for many other cellular purposes. The functional Na+ ,K+ -ATPase is a heterodimer of α- and β-subunits. In addition to the αβ heterodimer, there are tissue-specific regulatory γ-subunits, also known as FXYD proteins [7]. In this section, we will review the general structural and functional characteristic of each subunit and how the pumping of Na+ and K+ is achieved. Important findings about the function are briefly discussed in the light of several X-ray crystallography studies of Na+ ,K+ -ATPase published in recent years [8–10] (Fig. 1A).

#### *2.1.1. The α-subunit*

ment of occluding junctions. Thus, epithelial cells are always contiguous with one another and are usually joined by special junctions—the tight junctions. The functions of epithelia differ markedly. Although all form a barrier, some are much more impermeable than others. The trans-epithelial movement of ions and molecules is reached by the action of a multitude of specialized transporting proteins that are asymmetrically distributed on the apical or basolat‐ eral plasma membrane domains of epithelial cells. This remarkable polarity of epithelial cells depends on the selective insertion and the recycling of newly synthesized proteins and lipids into distinct plasma membrane domains and on the maintenance and modulation of these specialized domains once they are established during epithelial development. The two basic characters of epithelial transporting phenotype are polarity and tight junctions (TJs). Polarity offers the necessary direction for substances transported across epithelia to be absorbed or secreted. TJs guarantee that the transported substances do not leak back through the intercel‐

central role in the transporting phenotype of epithelia. Today, we already know its crystal structure, the chemical composition as well as the spatial arrangement of its three subunits (α, β, and γ) (Fig. 1A), the relationship between ATP hydrolysis and ion movement, and several diseases related to its malfunction. Surprisingly, despite such detailed information, we keep

The present chapter is focused on three recently found properties: its expression at the lateral membrane of epithelial cells due to the self-adhesive property of the β-subunit, its role as

biologists that investigated its intrinsic mechanisms and subunits the other by accomplished physicists who first criticized but finally solved immense theoretical obstacles in the road toward active transport. Thus, for a long while, the peculiar composition of the cytoplasm was

right after the Second World War, when radioisotopes became available for biological research,

concentration much lower (∼15 mM) than in the extracellular water (∼140 mM). The simplest assumption was that there should be an enzyme in the plasma membrane that dissipates metabolic free energy to pick up Na+ from the cell water and pump it out. This response was not readily accepted because it appeared in violation of the Curie principle: "Processes of different tensorial order cannot be coupled." In simple worlds, metabolism and ATP hydrol‐ ysis are chemical reactions, which at that time were taken to be *scalar* processes; hence, they

argued that, in fact, chemical reactions are vectorial at microscopic level. However, this vectoriality is masked at macroscopic scale, in particular, when working with homogenized tissues where pumps point in all directions. However, if they were ordered in a membrane,

finding new remarkable properties and new physiological functions of the Na+

hormone receptor, and its ability to modulate several types of cell contacts.



,K+

. This alternative was invalidated

in the cytoplasm remains at a

from the cytoplasm. Later on, it was

added to the bathing solution readily penetrates and


lular space [1, 2]. The Na+

30 Cell Biology - New Insights

**2. Na+**

**,K+**

The history of Na+

,K+

**-ATPase in epithelia**

attributed to presumed membrane impermeability to Na+

distributes into the cell. This revived the question why Na+

could not drive a *vectorial* process like the extrusion of Na+

,K+

and it was discovered that tracer Na+

The catalytic α-subunit is composed of approximately 1000 amino acid residues with a molecular mass of about 110 kDa. Since the first sequencing and cloning of the α-subunit of the Na+ ,K+ -ATPase [11], many biochemical studies pointed out to a model of ten transmem‐ brane domains (M1–M10) and three cytoplasmic domains: A (actuator), N (nucleotide binding), and P (phosphorylation domain) (Fig. 1A). Another myriad of studies identified motifs crucial for cation binding and conformational transitions [12]. Four distinct isoforms of the α-subunit have been identified (α1–α4) in which sequence differences are minor. Each isoform has different kinetic properties which may be essential in adapting cell Na+ ,K+ -ATPase activity to specific physiological requirements [3]. The major form α1 is found in most tissues and is the main or only form in kidney and most other epithelia.

The Na+ ,K+ -ATPase *A domain* consists of the N-terminal segment plus the loop between M2 and M3 (Lys212-Glu319), which form a distorted jelly roll structure plus two short helices in the 40 residues of the N-terminal segment. The movements of this domain, especially of the loop M2–M3, are determinants for the TM conformational rearrangements, needed for the occlusion and release of cations (see Fig. 1B) [14]. *N domain* contains the ATP-binding site and extends from the phosphorylation site Asp376, with the 377-KTGTL sequence, to the Cterminal 593-DPPR hinge motif. Finally the *P domain* can be described as a six-stranded parallel β-sheet and contains three important motifs: 376-DKTGTL, which contains the aspartic acid residue that phosphorylates during catalysis; 617-TGD on strand 3, which associates with the phosphorylation motif during the conformational transition E1 to E2; and 715-TGDGVND, which terminates the sixth β-strand of the P-domain where Asp717 is required for binding of Mg2+ and phosphorylation (Fig. 1B).

The first crystal structure of Na+ ,K+ -ATPase α-subunit published was that of Rb+ -bound pig renal Na+ ,K+ -ATPase. Each of the three cytoplasmic domains and transmembrane helices of α-subunit are superimposable with Ca2+-ATPase (SERCA). The two sites for K+ binding are found between helices M4, M5, and M6, and many of the residues involved had already been identified in various studies as cation-binding residues [8]. The first complete high-resolution crystal structure of Na+ ,K+ -ATPase was obtained in a potassium-bound state and provided further detail into the molecular basis for K+ specificity [9] (Fig. 1A). The carboxy terminal part of the L7/8 loop is the primary interaction site with the β-subunit, in which a consensus sequence 901 SFGQ, proposed as a key interaction site is located [15].

#### *2.1.2. The β-subunit*

The β-subunit of the Na<sup>+</sup> ,K+ -ATPase was initially identified as a glycoprotein associated with the α-subunit in purified functional enzyme preparations [16]. The association between α- and β-subunits is relatively strong and remains stable in most non-ionic detergents. All of the known β-subunit species and isoforms share a common domain structure: a short N-terminal cytoplasmic tail, a single transmembrane segment, and a large extracellular C-terminal domain containing six extracellular cysteine residues forming three disulfide bridges, whose locations are completely conserved among the isoforms. Na+ ,K+ -ATPase β-subunit is composed of approximately 310 residues with an apparent molecular mass of 55 kDa due to N-glycosyla‐ tion. The β-subunit of the Na+ ,K+ -ATPase has three isoforms designated β1, β2, and β3. Among these isoforms, there are various degrees of difference, and although all β-subunits are glycosylated, the number of N-glycosylation sites varies with the isoform. The β1 isoform of

the Na+

The Na+

renal Na+

,K+

Mg2+ and phosphorylation (Fig. 1B).

,K+

,K+

are completely conserved among the isoforms. Na+

,K+

further detail into the molecular basis for K+

The first crystal structure of Na+

,K+

crystal structure of Na+

*2.1.2. The β-subunit*

The β-subunit of the Na<sup>+</sup>

tion. The β-subunit of the Na+

,K+

32 Cell Biology - New Insights







,K+

specificity [9] (Fig. 1A). The carboxy terminal part



,K+



binding are

brane domains (M1–M10) and three cytoplasmic domains: A (actuator), N (nucleotide binding), and P (phosphorylation domain) (Fig. 1A). Another myriad of studies identified motifs crucial for cation binding and conformational transitions [12]. Four distinct isoforms of the α-subunit have been identified (α1–α4) in which sequence differences are minor. Each

activity to specific physiological requirements [3]. The major form α1 is found in most tissues

and M3 (Lys212-Glu319), which form a distorted jelly roll structure plus two short helices in the 40 residues of the N-terminal segment. The movements of this domain, especially of the loop M2–M3, are determinants for the TM conformational rearrangements, needed for the occlusion and release of cations (see Fig. 1B) [14]. *N domain* contains the ATP-binding site and extends from the phosphorylation site Asp376, with the 377-KTGTL sequence, to the Cterminal 593-DPPR hinge motif. Finally the *P domain* can be described as a six-stranded parallel β-sheet and contains three important motifs: 376-DKTGTL, which contains the aspartic acid residue that phosphorylates during catalysis; 617-TGD on strand 3, which associates with the phosphorylation motif during the conformational transition E1 to E2; and 715-TGDGVND, which terminates the sixth β-strand of the P-domain where Asp717 is required for binding of

isoform has different kinetic properties which may be essential in adapting cell Na+

and is the main or only form in kidney and most other epithelia.

,K+

sequence 901 SFGQ, proposed as a key interaction site is located [15].

α-subunit are superimposable with Ca2+-ATPase (SERCA). The two sites for K+

found between helices M4, M5, and M6, and many of the residues involved had already been identified in various studies as cation-binding residues [8]. The first complete high-resolution

of the L7/8 loop is the primary interaction site with the β-subunit, in which a consensus

the α-subunit in purified functional enzyme preparations [16]. The association between α- and β-subunits is relatively strong and remains stable in most non-ionic detergents. All of the known β-subunit species and isoforms share a common domain structure: a short N-terminal cytoplasmic tail, a single transmembrane segment, and a large extracellular C-terminal domain containing six extracellular cysteine residues forming three disulfide bridges, whose locations

approximately 310 residues with an apparent molecular mass of 55 kDa due to N-glycosyla‐

these isoforms, there are various degrees of difference, and although all β-subunits are glycosylated, the number of N-glycosylation sites varies with the isoform. The β1 isoform of

**Figure 1.** Structure of the Na+ ,K+ -ATPase. (A) Ribbon model of the crystal structure of shark Na+ ,K+ -ATPase [9; PDB code: 2ZXE], indicating α-subunit transmembrane domains in gray and cytoplasmic domains A, N, and P in red, green, and blue, respectively. The β-subunit is colored in orange and lacks most of its N-terminal cytoplasmic domain as in the crystal. The γ-subunit is colored in magenta. Alpha subunit transmembrane helices are numbered with the exception of TM 1 and 9, which are not visible from this projection. The two potassium ions occluded in the crystal structure are depicted in yellow. In the N domain, the ATP binding site is also indicated in yellow. (B) Schematic de‐ piction of the catalytic cycle of Na+ ,K+ -ATPase. A structural rearrangement, especially in domain A (pink-colored), is suggested by the cartoons at both conformational states E1 and E2. For simplicity, the rest of the cycle stages are repre‐ sented only with the TM region in gray. (A) The outward transport of three Na+ ions is coupled to the E1 to E2 transi‐ tion. (B) Two K+ ions bind at binding sites positioned to the extra cellular space. (C) Extracellularly bound K+ ions activate dephosphorylation that in turn results in ion occlusion. Ouabain (cardiotonic steroid silhouette in brown) binds at this conformational state halting the cycle. (D) ATP with a low affinity triggers the acceleration of inward transport of K+ ions through the pore as the pump enters the E1 conformational transition with low affinity for K+ . (E) Three Na+ ions bind the intracellularly oriented sites. (F) Phosphorylation from ATP occurs, and Na+ ions are occluded. Several transitional substates exist during the cycle; nevertheless, they are not depicted for simplification.

Na+ ,K+ -ATPase, which is consistently predicted to have three N-linked glycosylation sites, has been most extensively studied. All three consensus sites of β1 are glycosylated [17, 18], and the oligosaccharides are terminally sialylated. Treuheit et al. [19] showed by mass spectrometry that the oligosaccharides of the β1-subunit from dog and lamb kidney are of tetra-antennary structure with extensions of 2–4 *N*-acetyllactosamine units, and the units of extension seemed to differ between the dog and the lamb β1-subunits. Nevertheless, detailed information is not available for the oligosaccharide composition of the two other isoforms, but it seems clear that there is a high degree of species variability for the β2 isoform too. This isoform contains 7–9 Nglycosylation sites. It holds the high mannose-type carbohydrate epitopes L3 and L4 [20] also present on the neural recognition molecules L1, MAG, and P0 that mediate adhesion among neural cells [21]. Indeed, the β2 subunit was originally identified as an adhesion molecule, AMOG, in glial cells [22].

The essential function of the β-subunit is acting as the molecular chaperone of the α-subunit. Na+ ,K+ -ATPase α-subunit is inactive without its β-subunit. It has been demonstrated that the association of the β-subunit facilitates the correct packing and membrane integration of the newly synthesized α-subunit. Also, as the intimate partner of α-subunit, it modulates cationbinding affinity [23, 24]. The complete crystal structure of Na+ ,K+ -ATPase explains, at least partially, previous implications of the β-subunit in modulation of cation transport. The transmembrane helix of the β-subunit runs slightly separated from those of the α-subunit and is rather inclined than perpendicular to the membrane. It forms several interactions with M7 and M10 helices of the α-subunit. The extracellular domain of the β-subunit contains the wellconserved YYPYY motif that mediates several salt bridges with α-subunit L7/8 loop and also contains at least three additional clusters of residues interacting with α-subunit [9]. In epithelia, in addition to the classical chaperone function of the β-subunit, a cell-to-cell adhesion function has been ascribed to the β1 subunit. This novel role of the β1-subunit will be described in a separate part of this chapter.

#### *2.1.3. The γ-subunit*

In addition to the αβ heterodimer, there are tissue-specific regulatory γ-subunits, which are small membrane proteins characterized by an FXYD sequence, and therefore known also as FXYD proteins, of approximately 80–160 residues [24]. FXYD proteins mainly consist of a single transmembrane helix and an N-terminal extracellular domain where the FXYD motif is located. This domain anchors to the β-subunit extracellular and transmembrane domains. These proteins modulate the function of Na+ ,K+ -ATPase adapting kinetic properties of cation active transport to the specific needs of different tissues [7]. The most studied FXYD proteins are FXYD1 or phospholemman mainly expressed in heart and skeletal muscle and is involved in heart contractility. In epithelia, kidney-specific FXYD2 decreases affinity of Na+ ,K+ -ATPase for sodium and FXYD4 or CHIF, expressed in colon and kidney epithelia acts as a modulating several ion transport mechanisms that have Na+ ,K+ -ATPase as a common denominator [26, 27].

#### **2.2. The pumping catalytic cycle**

Ion movements through the Na+ ,K+ -ATPase have been studied by biophysical experiments for many years [28–30]. Those studies were incorporated into the conceptual framework called post-Albers cycle that depicts the sequence of reaction steps that couple ion transport and ATP hydrolysis (Fig. 1B). Na+ and K+ transport follow a "ping-pong" mechanism, wherein the two ion species are transported sequentially. Pumping of ions is achieved by alternation between two major conformational states, E1 and E2 [31, 32]. In E1, the cation-binding sites have high affinity for Na+ and face the cytoplasm; in E2, the cation-binding sites have low affinity for Na + but high affinity for K+ and face the extracellular. As it is the case for all P-type ATPases, Na + ,K+ -ATPase autophosphorylates and dephosphorylates during each reaction cycle. In E1, after three Na+ ions are bound at the cytoplasmic face, the phosphoryl group is transferred to a conserved aspartic residue in the P-domain. At this point, the pump enters the E1P state with occluded Na+ ions, and when ADP leaves, another conformational change occurs, and the Na+ ions are released atthe extracellularface.Atthis stage,the enzyme is no longer sensitive toADP addition but to aqueous hydrolysis (E2P state) so that Pi is released at the catalytic site and so are two K+ ions occluded at the extracellular face. To complete the cycle, ATP binds the phosphorylation site leading to the departure of the two K+ ions in the cytoplasm. At this point, the pump returns to the E1 state with high affinity for Na+ ready to launch a new catalytic cycle (Fig. 1B).

The first crystal structures of Na+ ,K+ -ATPase have been obtained in the E2 state, which is more stable [8, 9]. Nevertheless, they lack information about the Na+ -bound state and in particular the location of the third Na+ site. Two recently published crystals both of Na+ ,K+ -ATPase from pig kidney are of E1 states. These crystals are stable analogues of the transition state (E1P-ADP + ▪3Na<sup>+</sup> ) preceding E1P▪3Na<sup>+</sup> . The molecular comparison ofthe two states, E1 and E2, show that the α-subunit suffers important conformational changes in its cytoplasmic domains, especial‐ ly in the A domain, which is rotated around an axis nearly perpendicularto the membrane. The transmembrane helices involved in cation binding also undergo important conformation changes, most of all TM 4, 5, and 6 (Fig. 1B). Based on these structural evidences, the third Na + -binding site has been clearly localized, and a cooperative process for the sequential binding of Na+ has now been formulated in detail [33, 34].

#### **2.3. Mechanism of Na+ ,K+ -ATPase polarity in epithelia**

binding affinity [23, 24]. The complete crystal structure of Na+

separate part of this chapter.

proteins modulate the function of Na+

**2.2. The pumping catalytic cycle**

Ion movements through the Na+

hydrolysis (Fig. 1B). Na+

but high affinity for K+

affinity for Na+

occluded Na+

(Fig. 1B).

+

+ ,K+

several ion transport mechanisms that have Na+

*2.1.3. The γ-subunit*

34 Cell Biology - New Insights

partially, previous implications of the β-subunit in modulation of cation transport. The transmembrane helix of the β-subunit runs slightly separated from those of the α-subunit and is rather inclined than perpendicular to the membrane. It forms several interactions with M7 and M10 helices of the α-subunit. The extracellular domain of the β-subunit contains the wellconserved YYPYY motif that mediates several salt bridges with α-subunit L7/8 loop and also contains at least three additional clusters of residues interacting with α-subunit [9]. In epithelia, in addition to the classical chaperone function of the β-subunit, a cell-to-cell adhesion function has been ascribed to the β1 subunit. This novel role of the β1-subunit will be described in a

In addition to the αβ heterodimer, there are tissue-specific regulatory γ-subunits, which are small membrane proteins characterized by an FXYD sequence, and therefore known also as FXYD proteins, of approximately 80–160 residues [24]. FXYD proteins mainly consist of a single transmembrane helix and an N-terminal extracellular domain where the FXYD motif is located. This domain anchors to the β-subunit extracellular and transmembrane domains. These

transport to the specific needs of different tissues [7]. The most studied FXYD proteins are FXYD1 or phospholemman mainly expressed in heart and skeletal muscle and is involved in

sodium and FXYD4 or CHIF, expressed in colon and kidney epithelia acts as a modulating

many years [28–30]. Those studies were incorporated into the conceptual framework called post-Albers cycle that depicts the sequence of reaction steps that couple ion transport and ATP

ion species are transported sequentially. Pumping of ions is achieved by alternation between two major conformational states, E1 and E2 [31, 32]. In E1, the cation-binding sites have high


ions are released atthe extracellularface.Atthis stage,the enzyme is no longer sensitive toADP addition but to aqueous hydrolysis (E2P state) so that Pi is released at the catalytic site and so are two K+ ions occluded at the extracellular face. To complete the cycle, ATP binds the

and face the cytoplasm; in E2, the cation-binding sites have low affinity for Na

ions, and when ADP leaves, another conformational change occurs, and the Na+

and face the extracellular. As it is the case for all P-type ATPases, Na

,K+

,K+

heart contractility. In epithelia, kidney-specific FXYD2 decreases affinity of Na+

,K+

and K+

phosphorylation site leading to the departure of the two K+

the pump returns to the E1 state with high affinity for Na+

,K+



transport follow a "ping-pong" mechanism, wherein the two


ions in the cytoplasm. At this point,

ready to launch a new catalytic cycle


,K+


The apical and basolateral plasma membrane proteins of epithelial cells are synthesized in the endoplasmic reticulum (ER) and then sorted in the tans-Golgi network (TGN) to be sent into different carrier vesicles to apical or basolateral domain [35, 36]. The polarity of those routes depends significantly on specific signals encoded inside the membrane proteins. The basolat‐ eral proteins have short peptides sequences in the cytoplasmic domain. Some signals resemble endocytic signals (dileucine, YXXϕ, and NPXY), while others are unrelated to endocytic signals (the tyrosine motifs in LDL receptor [37] and the G-protein of the VSV [38]). Early studies demonstrated that the Na+ ,K+ -ATPase, comprised of α- and β-subunits, is sorted in the TGN and delivered directly to the basolateral membrane without significant appearance at the apical surface in certain strains of the Madin–Darby canine kidney cells (MDCK) [39, 40]. Therefore, a basolateral signal was assumed to exist in the α-subunit of the Na+ ,K+ -ATPase. The Na+ ,K+ -ATPase and the H+ ,K+ -ATPase are highly homologous ion pumps, yet in LLC-PK1 cells they are polarized to the basolateral and the apical domains, respectively. The polarized expression of chimeric constructs of the α-subunit of the H+ ,K+ -ATPase and the Na+ ,K+ -ATPase in LLC-PK1 cells has been studied [41–43]. Uncommonly, an apical sorting information in the α-subunit of the H+ ,K+ -ATPase was recognized within the fourth transmembrane domain. Swapping this domain into the Na+ ,K+ -ATPase resulted in the redirection of that basolateral pump to the apical surface of LLC-PK1 cells [44]. Nevertheless, these studies do not clarify whether the α-subunit of the Na<sup>+</sup> ,K+ -ATPase contains a basolateral sorting signal in its fourth transmembrane domain. Therefore, it seems that a non-canonical polarity signal is involved in the basolateral targeting of Na+ ,K+ -ATPase.

Clathrin plays a fundamental role in basolateral sorting. It interacts with endocytic or baso‐ lateral proteins through a variety of clathrin adaptors [45]. It has been shown that the adaptor involved in basolateral protein sorting is the epithelial cell-specific AP-1B (adaptor protein 1B). Nevertheless, the basolateral localization of the Na+ ,K+ -ATPase is independent of AP-1B expression because its localization was not significantly affected by knocking down clathrin expression and it remained localized to the basolateral surface in both the µ1B-deficient cell line LLC-PK1 [46] and in MDCK cells in which µ1B expression had been suppressed via RNAi [47]. By taking advantage of the SNAP tag system to reveal the trafficking itinerary of the newly synthesized Na+ ,K+ -ATPase, it was shown that the basolateral delivery of the Na+ ,K+ -ATPase is very fast (at 5 minutes after Golgi release, 50% of newly synthesized Na pump is colocalizing with the PM) and does not involve passage through recycling endosomes en route to the plasma membrane. Moreover, Na+ ,K+ -ATPase trafficking is not regulated by the same small GTPases as other basolateral proteins [48]. Some membrane proteins may achieve polarity by selective retention at the apical or basolateral surface. Although less well understood, this polarity may reflect interactions with extracellular ligands or with intracellular scaffolds, such as cytoskeletal elements or arrays of PDZ domain-containing proteins [35, 49–51]. As described and discussed below, this is also the case of the epithelial Na+ ,K+ -ATPase, which is retained at the lateral membrane domain due to *trans* adhesion of its β1 subunits on neighboring cells.

#### **3. Na+ ,K+ -ATPase β subunit as an adhesion molecule**

#### **3.1. The β1-isoform is a self-adhesion molecule in epithelia**

The β-subunit is a glycoprotein of 40–60 kDa that was shown to be involved in the structural and functional maturation of the holoenzyme [52, 53] and subsequent transport of the αsubunit to the plasma membrane [54–56]. Ion transport requires the participation of both αand β-subunits [54, 57]. The β-subunit has a short cytoplasmic tail, a single transmembrane segment, and a long extracellular domain heavily glycosylated, a typical structure of a cellattachment protein [25]. Fig. 1A depicts the position and arrangement of the three subunits of Na+ ,K+ -ATPase: α-subunit, β-subunit, and γ-subunit obtained by crystallography. Note that the β-subunit is mostly exposed toward the intercellular space, while most of the α-subunit is contained in the cytoplasm [9]. Observations made in MDCK cells suggested that the β-subunit is a cell–cell attachment protein: (1) As most transporting epithelia, the monolayer of MDCK expresses Na+ ,K+ -ATPase polarized toward the basolateral side [58]. Nevertheless, confocal immunofluorescence analysis of Na+ ,K+ -ATPase localization shows that the pump is not located on the *basal* domain of the plasma membrane, but only in the *lateral*, at cell–cell contacts (Fig. 2A). (2) Upon previous treatment with EGTA, the confocal images show the apparent single green line splits into two indicating that in order to express Na+ ,K+ -ATPase at a cell–cell contact both neighboring cells have to contribute part of the enzyme. (3) The expression of the Na+ ,K+ -ATPase at a given lateral borders is observed when both contributing neighboring cells are homotypic and from the same species, for instance, MDCK/MDCK (dog/dog, Fig. 2A) but not MDCK/NRK (dog/rat) [59] (Fig. 2B). (4) When CHO cells (fibroblasts from Chinese Hamster Ovary) were transfected with a gene coding for the β1-subunit of the dog (CHO-dog β1), these cells become more adhesive, as estimated by aggregation assays [60]. (5) On the other hand, mixed monolayers of MDCK and NRK-dog β<sup>1</sup> show that MDCK cells expose the Na+ ,K + -ATPase at the heterotypic border (Fig. 2C).

All together, these observations indicated that the lateral localization of the Na+ ,K+ -ATPase in MDCK cells depends on the recognition and adhesion between the β1-subunits of neighboring cells [60] (Fig. 2D). Of course, the first question that arises is whether two corresponding βsubunits from different cells would get close enough to be able to span the intercellular space and interact directly as proposed. To answer this question, several protein–protein interaction

is very fast (at 5 minutes after Golgi release, 50% of newly synthesized Na pump is colocalizing with the PM) and does not involve passage through recycling endosomes en route to the

GTPases as other basolateral proteins [48]. Some membrane proteins may achieve polarity by selective retention at the apical or basolateral surface. Although less well understood, this polarity may reflect interactions with extracellular ligands or with intracellular scaffolds, such as cytoskeletal elements or arrays of PDZ domain-containing proteins [35, 49–51]. As described

the lateral membrane domain due to *trans* adhesion of its β1 subunits on neighboring cells.

The β-subunit is a glycoprotein of 40–60 kDa that was shown to be involved in the structural and functional maturation of the holoenzyme [52, 53] and subsequent transport of the αsubunit to the plasma membrane [54–56]. Ion transport requires the participation of both αand β-subunits [54, 57]. The β-subunit has a short cytoplasmic tail, a single transmembrane segment, and a long extracellular domain heavily glycosylated, a typical structure of a cellattachment protein [25]. Fig. 1A depicts the position and arrangement of the three subunits of


located on the *basal* domain of the plasma membrane, but only in the *lateral*, at cell–cell contacts (Fig. 2A). (2) Upon previous treatment with EGTA, the confocal images show the apparent

contact both neighboring cells have to contribute part of the enzyme. (3) The expression of the

MDCK cells depends on the recognition and adhesion between the β1-subunits of neighboring cells [60] (Fig. 2D). Of course, the first question that arises is whether two corresponding βsubunits from different cells would get close enough to be able to span the intercellular space and interact directly as proposed. To answer this question, several protein–protein interaction




,K+


,K+

,K



,K+


,K+

**-ATPase β subunit as an adhesion molecule**

,K+

All together, these observations indicated that the lateral localization of the Na+

single green line splits into two indicating that in order to express Na+

and discussed below, this is also the case of the epithelial Na+

**3.1. The β1-isoform is a self-adhesion molecule in epithelia**

plasma membrane. Moreover, Na+

**3. Na+**

Na+ ,K+

Na+ ,K+

+

expresses Na+

,K+

immunofluorescence analysis of Na+


**,K+**

36 Cell Biology - New Insights

**Figure 2.** Hints to propose a model for the polarized distribution of Na+ ,K+ -ATPase in transporting epithelia. (A) Mon‐ olayer of MDCK cells in a horizontal and a transversal section. Na+ ,K+ -ATPase is stained in green, and nuclei in red, showing that the pump is expressed on the lateral membrane of the cells. (B) A confocal image of a monolayer pre‐ pared with a mixture of MDCK cells and NRK (normal rat kidney) cells; notice that the MDCK cells surrounding the NRK cell (previously stained in red with CMTMR) in the center only express their Na+ ,K+ -ATPase on the membrane contacting MDCK cells, but not on the side contacting the NRK epithelial cell (indicated by arrows). (C) A confocal image showing a mixture of MDCK and NRK cells transfected with dog β1-subunit. Arrows indicate the presence of Na+ ,K+ -ATPase at heterotypic borders. (D) Proposed model for the polarized distribution of Na+ ,K+ -ATPase in trans‐ porting epithelia. Scheme showing Na+ ,K+ -ATPase α- and β-subunits expressed at the lateral border, where they are anchored by the β-subunits interaction at the intercellular space. Scale bar: 10 µm.

assays have been performed: (1) By pull-down assay, it was shown that dog β1-subunit immobilized on Ni-beads could specifically bind to the soluble extracellular domain of β1 subunits of the same animal species (dog). (2) Co-IP experiments have shown that rat β1 subunits on NRK cells co-precipitate with rat YFP-β1 subunit transfected in MDCK cells. (3) FRET (fluorescence resonance energy transfer) analysis of monolayers with a mixed popula‐ tion of MDCK cells transfected with a β1-subunit fused to a cyan fluorescent protein (*CFP*), or with a β1-subunit fused to yellow fluorescent protein (YFP), has shown that energy can be transferred from the first to the second cell type; in other words, two β1-subunits can interact directly at <10 nm, thereby anchoring the whole enzyme at the cell membrane facing the intercellular space. Taken together, these evidences [61] supported by works from other groups [62-65] indicated that the β1 subunit is indeed an adhesion molecule in epithelia.

In Moloney sarcoma virus-transformed MDCK cells (MSV-MDCK) that have an invasive phenotype, the level of Na+ ,K+ -ATPase β1-subunit is reduced as well as the expression level of E-cadherin. As expected, these transformed cells are also deficient in tight and desmosome junctions. Interestingly, transfection of both E-cadherin and Na+ ,K+ -ATPase β1-subunit induces the formation of junction complexes, reestablishes epithelial polarity, and suppresses inva‐ siveness and motility, suggesting that β-subunit and E-cadherin are required to maintain the polarized epithelial phenotype [66]. Furthermore, stable adherens junctions are a requisite for proper tight junction function. In this regard, improving the Na+ ,K+ -ATPase β1–β1 interaction by reducing the complexity of the N-glycans of the β-subunit increases the resistance to detergent extraction of junction proteins and decreases the paracellular permeability. In other words, the fewer the branches are in β-subunit's N-glycans, the tighter are the intercellular junctions. Conversely, the impairment of the β1–β1 binding by removing the N-glycans or altering the amino acid sequence of one of the interacting proteins decreases detergent resistance and increases the paracellular permeability, indicating that stability of adherens, and in turn tight junctions, does depend on β1–β1 interaction [65, 67].

Studies in Drosophila have also shown that the β-subunits (in drosophila are named Nrv1, Nrv2, and Nrv3) are determinant of the Na+ ,K+ -ATPase subcellular localization as well as function. Of the three Drosophila isoforms, Nrv1 and Nrv2 are localized in epithelia, while Nrv3 is expressed in the nervous system. Remarkably, while Nrv1 is expressed in the baso‐ lateral membrane of almost all epithelial cells, Nrv2 is localized at the septate junctions (tight junctions in insect) and co-localizes with coracle [68]. Furthermore, it has been shown that the extracellular domain of Nrv2 regulates the function of septate junctions and the size of the tracheal tube in a free manner independent of the pumping task [69].

#### **3.2. β2/AMOG is a heterophilic adhesion molecule in nervous system**

The Na+ ,K+ -ATPase β2-subunit was first described in the nervous system. Schachner's group identified a cell surface glycoprotein and named it as Ca2+-independent adhesion molecule on glia (AMOG). AMOG was shown to mediate the neuron-to-astrocyte adhesion in the process of granule cell migration [70–72]. Further analysis revealed that AMOG is an isoform of the Na+ ,K+ -ATPase β-subunit, named as the β2-subunit [22]. A remarkable characteristic of the β2 subunit is the multiple N-glycosylation sites in the extracellular domain [13]. Treatment with endoglycosidase H produces the shift of the apparent molecular weight from 50 to 35 kDa [70,20]. In a mass spectrometry analysis of the endoglycosidase H, released oligosaccharides from the β2-subunit three molecular ions were found corresponding to oligosaccharides composed of one N-acetylglucosamine and 5, 6, or 7 mannoses [20]. The β2-subunit promotes the neurite outgrowth by AMOG-to-neuron binding [73]. Schachner's group has assayed different partners for AMOG association in *trans*. They found that AMOG-containing lipo‐ somes only bind to small cerebellar neurons. When L1 and N-CAM antibodies were added to a monolayer of cerebellar neurons, none of these antibodies inhibited binding of AMOGcontaining liposomes to neurons. Also, cells preincubation with an AMOG-antibody prior to addition of AMOG-containing liposomes did not reduce AMOG-containing liposomes-toneurons adhesion [71]. These experiments suggest that neither L1 nor N-CAM is the β2-subunit ligand; thus, AMOG/β2-subunit is a heterophilic CAM. As mentioned above, β1–β<sup>1</sup> adhesion in epithelial cells is homophilic. Accordingly, when assaying β1 to β2 adhesion, we found a null binding between these two isoforms, as well as between two β2-subunits (our unpublished results). These findings are in agreement with previous studies [71]. As heterophilic CAM, the β2-subunit was shown to *cis*-interact with an oligomannose binding lectin, basigin. Basigin or CD147 is an ancillary protein of the monocarboxylate transporters 1, 3, and 4-isoforms [74–77] and, as a receptor molecule for high mannose carbohydrates, basigin binds specifically with oligomannoside carrying glycoproteins and neoglycolipids [78]. Kleene and coworkers showed that PrP, the AMPA receptor subunit GluR2, the astroglial α2/β<sup>2</sup> ATPase, basigin, and the MCT1 form a functional complex at the plasma membrane of astrocytes. In this regard, the β2-subunit and basigin interact by means of the carbohydrate structure of the β2-subunit. The functional interplay of PrP, GluR2, the α2/β2 ATPase and basigin regulates the lactate transport via MCT1. Moreover, they observed that disturbing the oligomannose-mediated interaction of the β2-subunit and basigin leads to a deregulated and thus elevated glutamate-independent lactate transport [79].

#### **3.3. β2 isoform and apical polarity**

junctions. Interestingly, transfection of both E-cadherin and Na+

proper tight junction function. In this regard, improving the Na+

and in turn tight junctions, does depend on β1–β1 interaction [65, 67].

tracheal tube in a free manner independent of the pumping task [69].

**3.2. β2/AMOG is a heterophilic adhesion molecule in nervous system**

Nrv2, and Nrv3) are determinant of the Na+

The Na+

Na+ ,K+ ,K+

38 Cell Biology - New Insights

the formation of junction complexes, reestablishes epithelial polarity, and suppresses inva‐ siveness and motility, suggesting that β-subunit and E-cadherin are required to maintain the polarized epithelial phenotype [66]. Furthermore, stable adherens junctions are a requisite for

by reducing the complexity of the N-glycans of the β-subunit increases the resistance to detergent extraction of junction proteins and decreases the paracellular permeability. In other words, the fewer the branches are in β-subunit's N-glycans, the tighter are the intercellular junctions. Conversely, the impairment of the β1–β1 binding by removing the N-glycans or altering the amino acid sequence of one of the interacting proteins decreases detergent resistance and increases the paracellular permeability, indicating that stability of adherens,

Studies in Drosophila have also shown that the β-subunits (in drosophila are named Nrv1,

function. Of the three Drosophila isoforms, Nrv1 and Nrv2 are localized in epithelia, while Nrv3 is expressed in the nervous system. Remarkably, while Nrv1 is expressed in the baso‐ lateral membrane of almost all epithelial cells, Nrv2 is localized at the septate junctions (tight junctions in insect) and co-localizes with coracle [68]. Furthermore, it has been shown that the extracellular domain of Nrv2 regulates the function of septate junctions and the size of the

,K+



identified a cell surface glycoprotein and named it as Ca2+-independent adhesion molecule on glia (AMOG). AMOG was shown to mediate the neuron-to-astrocyte adhesion in the process of granule cell migration [70–72]. Further analysis revealed that AMOG is an isoform of the

,K+

,K+




The α1-subunit holds a basolateral sorting signal that commands the traffic of the epithelial sodium pump to this membrane domain [43]. However, the role of other α-subunit isoforms in the sorting of the Na+ ,K+ -ATPase has not been studied yet. On the other hand, little is known about sorting signals in any of the β-subunit isoforms, yet the β<sup>1</sup> and β<sup>3</sup> isoforms have exclusive basolateral localization in epithelial cells [80], and instead, the apical distribution of the sodium pump correlates with the expression of the β<sup>2</sup> isoform [81–84]. In this regard, studies from our laboratory provide evidence showing that the apical polarity of the Na+ ,K+ -ATPase in the retinal pigment epithelium (RPE) is related to the expression of the α2- and β2-subunits (Fig. 3A and B). Moreover, the time-dependent β2-subunit expression in the RPE model cells ARPE-19 correlates with the epithelialization of these cells (our unpublished results).

As we mentioned before, the β2-subunit possess up to 9 N-glycosylation sites (upon the species). Numerous studies have indicated the role of N-glycans in the polarity mechanism of apical proteins. For instance, the mutagenic removal of N-glycosylation sites in the gastric H + ,K+ -ATPase β-subunit [85], bile salt export pump [86], and glycine transporter 2 [87, 88], significantly decreased their apical content and increased their intracellular accumulation. Also, it has been shown that addition of N-glycans to various proteins changed their cellular localization toward the apical membrane domain. For example, a truncated occludin and a chimeric ERGIC-53 residing inside the Golgi in their nonglycosylated forms were apical redistributed after addition of N-glycans [89]. Indeed, engineering the β1-subunit by adding the N-glycosylation sites of the β<sup>2</sup> isoform leads to apical localization of the pump in HGT-1 cells [90]. All these evidences are consistent with the important role of N-glycosylation in apical polarization of Na+ ,K+ -ATPase.

#### **3.4. Structural insights into the self adhesion mechanism of Na+ ,K+ -ATPase β1 subunits**

The shark Na+ /K+ -ATPase crystal structure in the E2 state published by Shinoda and coworkers was the first resolving the atomic structure of the extracellular domain of the β-subunit (PDB: 2ZXE) [9]. The extracellular C-terminal domain of the protein folds into an Ig-like β-sheet sandwich as predicted in silico [91]; actually, deletion of this C-terminal domain abolishes the

**Figure 3.** Na+ ,K+ -ATPase expression at the apical domain of ARPE-19 cells (human retinal pigment epithelium). ARPE-19 cells were cultured on laminin-coated inserts for 4 weeks and treated for IF analysis. Confocal image of a monolayer stained with specific antibody against the α2 subunit (A) and against β<sup>2</sup> subunit (B). Notice the preferential distribution on apical domain of both subunits. Scale bar: 10 µm

β<sup>1</sup> adhesion capacity (unpublished observations). However, a large number of adhesion and nonadhesion proteins contain domains with an immunoglobulin-like topology (CATH database). Structural alignments of the β1 subunit extracellular domain against other wellstudied cell adhesion molecules reveal no structural homologue of β-subunits of any kind. Detailed inspection of the ectodomain structure uncovers several features distinctive to βsubunit family members. Namely, its Ig-like fold has a unique topology given that its β-sheet sandwich is interrupted by a long α-helix secondary structure and has an atypical β-sheet disposition in relation to classical Ig folds. Also, the β-subunit fold contains extensive loops and therefore its length is twice as that of a typical Ig domain. Furthermore, the β1 subunit is structurally compromised with the catalytic α-subunit in such a way that the C-terminal fold must be more rigid than the typical flexibility of whole adhesion domains such as in cadherins. Altogether, these observations suggest that the β-subunit of the Na<sup>+</sup> ,K+ -ATPase must possess an adhesion mechanism that is particular to this family, as shown in Figure 4.

The first attempt to clarify this adhesion mechanism on a molecular base is related to the regions of the ectodomain involved in β1–β1 recognition. Given that the interaction between two β<sup>1</sup> subunits of the same species (dog–dog or rat–rat) is more effective than the interaction between rat and dog β1 subunits [61], Tokhtaeva and colleagues [92] looked for surfaceexposed species-specific amino acids in the sequence of β1 subunit and identified four residues, which are different between both species and are contained in the 198–207 segment. Rat-like amino acid substitutions introduced in the dog β1 subunit weakens its interaction with the endogenous dog β1 subunit, whereas the insertion of the rat-specific Thr202 into the exogenous dog β1 subunit impairs its interaction with the endogenous dog β1 subunit to the level observed between dog and rat native subunits. The opposite effect is observed in the rat β1 subunit upon the introduction of dog-like residues and the deletion of Thr202. These results suggest that the amino acid residues important for β1–β1 binding are located upstream and downstream of the Thr insertion position. The insertion or removal of the Thr residues in one of the two interacting subunits probably misaligns these binding residues, and thus causes the characteristic difference in affinity between the two species [92].

**Figure 4.** The intercellular adhesion between Na+ ,K+ -ATPase β<sup>1</sup> subunit. A surface model based on the crystal structure illustrating the association of Na+ ,K+ -ATPase dimer (α in green and β in blue) at the intercellular space. The magnified square shows one of the representative models resulting from the docking algorithm performed for the coupling of two Na+ ,K+ -ATPase β<sup>1</sup> subunits structures obtained from the crystals. In this specific model, two loops form the core of the interaction, namely, the one containing the species-specific residues identified by [92] and the other comprised of an unusual sequence of eight consecutive charged residues (214KRDEDKDR221). This charged loop and other regions adjacent to the species-specific loop are suggested as the potential interface for β1–β1 interaction.

β<sup>1</sup> adhesion capacity (unpublished observations). However, a large number of adhesion and nonadhesion proteins contain domains with an immunoglobulin-like topology (CATH database). Structural alignments of the β1 subunit extracellular domain against other wellstudied cell adhesion molecules reveal no structural homologue of β-subunits of any kind. Detailed inspection of the ectodomain structure uncovers several features distinctive to βsubunit family members. Namely, its Ig-like fold has a unique topology given that its β-sheet sandwich is interrupted by a long α-helix secondary structure and has an atypical β-sheet disposition in relation to classical Ig folds. Also, the β-subunit fold contains extensive loops and therefore its length is twice as that of a typical Ig domain. Furthermore, the β1 subunit is structurally compromised with the catalytic α-subunit in such a way that the C-terminal fold must be more rigid than the typical flexibility of whole adhesion domains such as in cadherins.

ARPE-19 cells were cultured on laminin-coated inserts for 4 weeks and treated for IF analysis. Confocal image of a monolayer stained with specific antibody against the α2 subunit (A) and against β<sup>2</sup> subunit (B). Notice the preferential


The first attempt to clarify this adhesion mechanism on a molecular base is related to the regions of the ectodomain involved in β1–β1 recognition. Given that the interaction between two β<sup>1</sup> subunits of the same species (dog–dog or rat–rat) is more effective than the interaction between rat and dog β1 subunits [61], Tokhtaeva and colleagues [92] looked for surfaceexposed species-specific amino acids in the sequence of β1 subunit and identified four residues, which are different between both species and are contained in the 198–207 segment. Rat-like amino acid substitutions introduced in the dog β1 subunit weakens its interaction with the

,K+


Altogether, these observations suggest that the β-subunit of the Na<sup>+</sup>

**Figure 3.** Na+

40 Cell Biology - New Insights

,K+

distribution on apical domain of both subunits. Scale bar: 10 µm

an adhesion mechanism that is particular to this family, as shown in Figure 4.

How specie-specific residues adjacent to Thr202 coordinate with residues residing at sur‐ rounding regions on the same β1-subunit and with its interacting partner have yet to be elucidated. The segment 198–207 constitutes one of the characteristic protruding loops in the connecting β-strands B and C of the β1-subunit extracellular fold. The majority of the ectodo‐ main surface-exposed residues located most distal from the membrane reside within loops interconnecting β-strands, some of which must be involved in the dimer interface in conjunc‐ tion with segment 198–207. Since the crystal structure of the Na+ ,K+ -ATPase β1 subunits now available [33;93], we modeled and predicted interacting surfaces on β-subunit and thus identified putative amino acids that participate in β1–β<sup>1</sup> interaction. This approach will soon lead us to uncover a detailed adhesion mechanism, which is of great importance for epithelial physiology.

#### **4. The Na+ ,K+ -ATPase is the receptor of hormone ouabain**

#### **4.1. Cardiotonic steroids (CTSs)**

The CSTs have been used for at least 200 years to treat heart failure and tachycardia due to their inotropic effect on the heart [94]. They are specific steroids and are extracted from plants of genus *Digitalis* and *Strophanthus* and from vertebrates such as several species of toads [95]. The CSTs have a steroid nucleus and can sort as cardenolides (with a five-membered lactone ring) or bufadienolides (six-membered lactone ring) and contain various combinations of hydroxyl, sulfate, or carbohydrates groups (Fig. 5) [96]. All types of CST bind with its receptor, the α-subunit of Na+ ,K+ -ATPase, in a pocket formed by transmembrane segments M1–M6. The best affinity for the CST is of the E2P conformation [97]. The sensitivity of the sodium pump to CSTs is controlled by multiple elements mainly by the tissue specific distribution of α and β isoforms and by the glycosylation of CSTs. Thus, in the case of digoxin and digitoxin (Fig. 5), the affinity toward the Na+ ,K+ -ATPase improves with up to fourfold preference for α2/α<sup>3</sup> over α1 isoforms [98].

Many studies have demonstrated the endogenous productions of CSTs in mammals. Thus, ouabain was detected in plasma [99], digoxin in urine [100], and marinobufagenin in plasma [101]. An interesting feature of Na+ ,K+ -ATPase is the highly conserved nature of the CSTbinding site, suggesting that this site plays a significant physiological role [94]. The normal ranges for circulating ouabain vary between 2500 ±500 pmol/l and 176 000 ± 68 000 pmol/l, depending on the measuring condition and the test used [102]. Interestingly, the binding of cardenolides and bufadienolides to the α-subunit of the Na<sup>+</sup> ,K+ -ATPase results not just in the inhibition of Na+ ,K+ -ATPase ion transport activity but also in the activation of signaling cascades [103]. Moreover, endogenous ouabain is synthesized and secreted by the hypothal‐ amus [104, 105] and the adrenocortical gland [106–107]. A status of hormone was recommend‐ ed for the endogenous CSTs as it was demonstrated that it increases during exercise [108], salty meals [109–111], and pathological conditions such as arterial hypertension and myocardial infarction [112]. To confirm the hormone-like function, Arnaud-Batista and colleagues [113] showed that ouabain and bufalin induce diuresis, natriuresis, and kaliuresis, mediated by signal transduction in the isolated intact rat kidney. Furthermore, at the systemic level, cardenolides and bufadienolides have been implicated in many physiological and pathophy‐ siological mechanisms, including cell growth and cancer, body or organ weight gain, mood disorders, vascular tone homeostasis, blood pressure, hypertension, and natriuresis[114].

#### **4.2. The physiological role of hormone ouabain in epithelia**

Fifteen years ago, the evidence that ouabain is a hormone was convincing enough as to start wondering what may its physiological role be. Our search was oriented by the observation that (MDCK) epithelial cells exposed to high concentrations of ouabain (≥1 µM) do not show sign of damage, but retrieve from the plasma membrane molecules involved in cell–cell and cell-substrate attachment, and detach from each other and from the substrate. These observa‐ tions suggested that there is a mechanism that relates the occupancy of the pump (P) by ouabain to adhesion mechanisms (A). Accordingly, this mechanism was called P → A. We

**4. The Na+**

42 Cell Biology - New Insights

the α-subunit of Na+

over α1 isoforms [98].

inhibition of Na+

5), the affinity toward the Na+

[101]. An interesting feature of Na+

,K+

**,K+**

**4.1. Cardiotonic steroids (CTSs)**

,K+

,K+

cardenolides and bufadienolides to the α-subunit of the Na<sup>+</sup>

**4.2. The physiological role of hormone ouabain in epithelia**

,K+

**-ATPase is the receptor of hormone ouabain**

The CSTs have been used for at least 200 years to treat heart failure and tachycardia due to their inotropic effect on the heart [94]. They are specific steroids and are extracted from plants of genus *Digitalis* and *Strophanthus* and from vertebrates such as several species of toads [95]. The CSTs have a steroid nucleus and can sort as cardenolides (with a five-membered lactone ring) or bufadienolides (six-membered lactone ring) and contain various combinations of hydroxyl, sulfate, or carbohydrates groups (Fig. 5) [96]. All types of CST bind with its receptor,

best affinity for the CST is of the E2P conformation [97]. The sensitivity of the sodium pump to CSTs is controlled by multiple elements mainly by the tissue specific distribution of α and β isoforms and by the glycosylation of CSTs. Thus, in the case of digoxin and digitoxin (Fig.

Many studies have demonstrated the endogenous productions of CSTs in mammals. Thus, ouabain was detected in plasma [99], digoxin in urine [100], and marinobufagenin in plasma

binding site, suggesting that this site plays a significant physiological role [94]. The normal ranges for circulating ouabain vary between 2500 ±500 pmol/l and 176 000 ± 68 000 pmol/l, depending on the measuring condition and the test used [102]. Interestingly, the binding of

cascades [103]. Moreover, endogenous ouabain is synthesized and secreted by the hypothal‐ amus [104, 105] and the adrenocortical gland [106–107]. A status of hormone was recommend‐ ed for the endogenous CSTs as it was demonstrated that it increases during exercise [108], salty meals [109–111], and pathological conditions such as arterial hypertension and myocardial infarction [112]. To confirm the hormone-like function, Arnaud-Batista and colleagues [113] showed that ouabain and bufalin induce diuresis, natriuresis, and kaliuresis, mediated by signal transduction in the isolated intact rat kidney. Furthermore, at the systemic level, cardenolides and bufadienolides have been implicated in many physiological and pathophy‐ siological mechanisms, including cell growth and cancer, body or organ weight gain, mood disorders, vascular tone homeostasis, blood pressure, hypertension, and natriuresis[114].

Fifteen years ago, the evidence that ouabain is a hormone was convincing enough as to start wondering what may its physiological role be. Our search was oriented by the observation that (MDCK) epithelial cells exposed to high concentrations of ouabain (≥1 µM) do not show sign of damage, but retrieve from the plasma membrane molecules involved in cell–cell and cell-substrate attachment, and detach from each other and from the substrate. These observa‐ tions suggested that there is a mechanism that relates the occupancy of the pump (P) by ouabain to adhesion mechanisms (A). Accordingly, this mechanism was called P → A. We



,K+




**Figure 5.** Structural features common for cardiotonic steroids (CTSs). All CTSs include a *cis–trans–cis* ring fused steroid core, which adopts a U-shaped conformation with a convex β-surface, a hydroxyl group at C14 (OH14β; purple). CTSs are classified as Cardenolides and Bufadienolides based on a five- or six-membered lactone ring in a β-conformation at position C17. Some CTSs have a carbohydrate moiety of one to four residues attached to C3. Ouabain, the most hydro‐ philic CTSs, is constituted of a steroid core with four hydroxyl groups at the β-surface (in blue), a hydroxyl group at the α-surface (purple), an unsaturated lactone ring of five members (green), and a rhamnose sugar moiety (pink). The structures of two members of the bufadienolides (marinobufagenin and bufalin) and three members of the cardeno‐ lides (ouabain, digitoxin, and digoxin) are illustrated.

discovered that P → A mechanism is associated with several signaling proteins such as cSrc and ERK1/2 (Fig. 6), and it consists of a loss of cytosolic K+ , an increase of cytosolic levels of Na+ and Ca+2 and the activation of protein tyrosine kinases and ERK1/2. Ouabain binding also increases p190Rho-GAP, which enhances the GTPase activity of RhoA [115]. Detachment may not be ascribed to the ensuing decrease of K+ content because lowering the K-content by incubating the cells in media with only 0.1 mM K+ (instead of the regular 4.0 mM) does not cause cell detachment [116].Therefore, we put forward the working hypothesis that ouabain at nanomolar concentrations, i.e., within the hormonal range in mammalian plasma, may act on the same junctional structures without provoking irreversible damages. To explore the plausibility of this idea, we experimentally tested the effect of ouabain on different cell–cell adhesion complexes starting with TJs. While toxic concentration of ouabain open the TJ, physiological concentrations of ouabain increase its hermeticity. Interestingly, the first effect depends on the pumping activity of Na+ ,K+ -ATPase, whose inhibition perturbs the ionic balance of the cell. On the contrary, physiological concentrations of ouabain (i.e., in the nanomolar range) neither inhibit K+ pumping nor disturb the K+ balance of the cell [117]. At these concentrations, the effects of ouabain depends mainly on the activation of the receptor complex of Na+ ,K+ -ATPase. While toxic levels of ouabain regulate the opening of TJs through endocytic and degradation processes, physiological concentrations of ouabain modulate TJs through changes in the molecular composition of the TJ through processes that provoke changes in transcription rate and expression of its proteins [118] (Fig. 6A). Another prominent cell–cell contact is the adherens junction (AJ) and one of the scaffolding proteins of this junction is β-catenin, a key member of the Wnt signaling pathway (Fig. 6B). During the activation of this pathway, β-catenin is translocated to the nucleus, where it modifies gene expression [119]. Interestingly, 10 nM and 1 µM ouabain provoke the translocation of β-catenin to the nucleus of MDCK cells [116]. Liu and co-workers [120] have recently found evidence that Na+ ,K+ - ATPase, and E-cadherin are closely associated, indicating that E-Cadherin could be part of the signalosome of the Na+ ,K+ -ATPase. To further explore the hypothesis that nanomolar concen‐ trations of ouabain modulate cell–cell contacts, the effect of 10 nM ouabain have been studied on another type of cell–cell contact, the gap junction. In MDCK cells treated with this concen‐ tration of ouabain cell–cell communication have been increases by up to 510% in one hour. Moreover, inhibitors of transcription and of translation do not affect the induction of Gap junction communication (GJC) by ouabain, indicating that cells express a sufficient level of connexins to account for the rapid enhancement of GJC [121].

Ouabain effects through signaling were observed also in cardiac myocytes when nontoxic concentrations of ouabain, that partially inhibit the Na+ ,K+ -ATPase, activate signaling path‐ ways that regulate growth [122, 123]. Ouabain can activate signal cascades that vary between cell types, depending on the dose and the α-subunit isoform expressed in the cell [124, 103]. The existence of two pools of Na+ ,K+ -ATPase within the plasma membrane with two distinct functions have been proposed: the classical ion pump whose partial inhibition by ouabain provokes an increase in [Ca2+]i, and the second, the signal transducing pool which through protein–protein interactions regulates cell growth, proliferation, differentiation, and apopto‐ sis. Part of the nontransporting Na+ ,K+ -ATPase is located in the caveolae. cSrc is usually bound to the Na+ ,K+ -ATPase in caveolae. Ouabain binding to the pump located in caveolae, stimulates cSrc activation, which consequently activates other downstream signaling pathways [125]. Signaling through Src is supported by the discovery that in a cell-free system, the addition of ouabain modifies the Na+ ,K+ -ATPase cSrc complex and activates cSrc [128]. Alongside, the epidermal growth factor receptor (EGFR) is transactivated upon ouabain binding to Na+ ,K+ - ATPase and additional signaling occurs that activate downstream targets including She, Grb, Ras, Raf, MEK, and ERK [125, 127] (Fig. 6). These signaling pathways regulate early response genes associated with cell growth and also regulate cell motility and a number of metabolic pathways [123,126]. Another signaling role was found by Aizman and coworkers [126]. In epithelial cells, the Na+ ,K+ -ATPase interacts with the inositol 1,4,5-triphosphate receptor (IP3R) within the signaling microdomain. They show that interaction of ouabain with the signaling Na+ ,K+ -ATPase provokes synchronized Ca2+ oscillations rising from the modification of such interaction. Those slow oscillations activate NF-kB.

nanomolar range) neither inhibit K+

,K+

complex of Na+

44 Cell Biology - New Insights

signalosome of the Na+

The existence of two pools of Na+

sis. Part of the nontransporting Na+

to the Na+

Na+ ,K+ ,K+

ouabain modifies the Na+

epithelial cells, the Na+

,K+

connexins to account for the rapid enhancement of GJC [121].

,K+

,K+

concentrations of ouabain, that partially inhibit the Na+

,K+

,K+

interaction. Those slow oscillations activate NF-kB.

pumping nor disturb the K+



,K+





these concentrations, the effects of ouabain depends mainly on the activation of the receptor

endocytic and degradation processes, physiological concentrations of ouabain modulate TJs through changes in the molecular composition of the TJ through processes that provoke changes in transcription rate and expression of its proteins [118] (Fig. 6A). Another prominent cell–cell contact is the adherens junction (AJ) and one of the scaffolding proteins of this junction is β-catenin, a key member of the Wnt signaling pathway (Fig. 6B). During the activation of this pathway, β-catenin is translocated to the nucleus, where it modifies gene expression [119]. Interestingly, 10 nM and 1 µM ouabain provoke the translocation of β-catenin to the nucleus of MDCK cells [116]. Liu and co-workers [120] have recently found evidence that Na+

ATPase, and E-cadherin are closely associated, indicating that E-Cadherin could be part of the

trations of ouabain modulate cell–cell contacts, the effect of 10 nM ouabain have been studied on another type of cell–cell contact, the gap junction. In MDCK cells treated with this concen‐ tration of ouabain cell–cell communication have been increases by up to 510% in one hour. Moreover, inhibitors of transcription and of translation do not affect the induction of Gap junction communication (GJC) by ouabain, indicating that cells express a sufficient level of

Ouabain effects through signaling were observed also in cardiac myocytes when nontoxic

ways that regulate growth [122, 123]. Ouabain can activate signal cascades that vary between cell types, depending on the dose and the α-subunit isoform expressed in the cell [124, 103].

functions have been proposed: the classical ion pump whose partial inhibition by ouabain provokes an increase in [Ca2+]i, and the second, the signal transducing pool which through protein–protein interactions regulates cell growth, proliferation, differentiation, and apopto‐

cSrc activation, which consequently activates other downstream signaling pathways [125]. Signaling through Src is supported by the discovery that in a cell-free system, the addition of

epidermal growth factor receptor (EGFR) is transactivated upon ouabain binding to Na+

ATPase and additional signaling occurs that activate downstream targets including She, Grb, Ras, Raf, MEK, and ERK [125, 127] (Fig. 6). These signaling pathways regulate early response genes associated with cell growth and also regulate cell motility and a number of metabolic pathways [123,126]. Another signaling role was found by Aizman and coworkers [126]. In

within the signaling microdomain. They show that interaction of ouabain with the signaling



balance of the cell [117]. At


,K+ -

,K+ -

**Figure 6.** Signaling in the ouabain-induced modulation of cell contacts. Ouabain (red silhouette) induces the formation of a signalosome, a caveolar complex (discontinued grey line) including the Na+ ,K+ -ATPase, its associated cSrc (cSRC) and the EGF receptor (EGFR). (A) Ouabain (300 nM) activates cSrc, which in turn transactivates the EGFR pathway, causing a phosphorylation of ERK1/2. The inhibition of the pump alters the ionic gradient that also contributes to the activation of ERK1/2. The activation of ERK1/2 is crucial for the clathrin- and dynamin-dependent endocytosis of TJ components. Two possible types of endocytic vesicles are formed: one containing a core complex with essential TJ pro‐ teins, such as ZO-1 (encircled Z); occludin (encircled O) and Claudin-4 (encircled 4) and a second one entailing compo‐ nents such as Claudin-2 (encircled 2) that makes TJs permeable to water and Na+ . ERK1/2 activation is required to reduce the levels of Occludin, Claudin-4 and ZO-1 proteins, but not that of Claudin-2. ERK1/2 is also necessary to re‐ duce Claudin-2 and ZO-1 mRNA levels. Notably, the cellular content of Claudin-4 and occludin mRNAs increases, during the opening of the TJs induced by Ouabain. (B) Epithelial cells treated with 10 nM of Ouabain (hormonal con‐ centration) show increased tight junction sealing [117]. Activation of ERK 1/2 modulates the expression of Claudins (1,2 and 4) at the tight junction and promotes the expression of Claudin-2 in the cilium. Moreover, under this condi‐ tion, cell-communication by gap junctions (red cylinder) is also increased by a mechanism still not well understood and β-catenin (khaki circles), a component of the Adherens junctions travels to the nucleus and modulates the expres‐ sion of genes involved in cell-junction regulation.

Signal cascades vary between different cells types. For example, in cardiac myocytes and renal cell lines derived from the porcine kidneys (LLC-PK1) and the opossum kidneys (OK), ouabain-mediated activation of a signaling cascade has been demonstrated to be dependent upon the activation of Src, MAPK, and PI-3K pathways [129,122], whereas in human breast (BT20), prostate (DU145) cancer cells, and PY-17 cells, ouabain activate Src and MAPK pathway, but not PI-3K pathway [130]. Downstream in the ouabain-activated signaling cascade, the level of complexity increases due to the activation of several cell-specific secondary messengers and the cross talk between distinct pathways [131]. For each cell type, different pathways and branches are activated and only part of their complexity is known. In the MAPK pathway, several secondary messengers, downstream targets of ERK1/2, have been identified. Upon activation, ERK1/2 is able to migrate to the nucleus and activate several transcription factors (STAT1/3, c-fos, CREB, Elk-1) or in the cytoplasm modulate ion channels, receptors, or cytoskeleton proteins by direct phosphorylation.

#### **5. Concluding remarks**

Although without its β-subunit the Na+ ,K+ -ATPase could not be expressed in the plasma membrane, nor have an enzymatic activity, no convincing role was detected for this subunit beyond of helping the α one to cage K+ . We have shown that, due to its adhesiveness, the β1 subunit may establish a linkage with an identical subunit located in a neighboring cell across the intercellular space, and be thereby responsible for the polarized expression of Na+ ,K+ - ATPase in epithelial cells. Furthermore, it has been demonstrated that β–β interaction stabilizes and maintains cell-junctions integrity in transporting epithelia. The molecular mechanism by which this interaction occurs is still far from being elucidated. Nevertheless, it is clear that both N-glycans and specific sequences exposed on the polypeptide surface are implicated. The observation that P → A mechanism is involved in the shuttling of β-catenin to the nucleus and thus in the Wnt/Wingless cascade, in the growth factor signaling pathways, as well as the ability of ouabain to enhance intercellular communication through gap junctions speaks of the important physiological role played by the hormone ouabain. The importance of this mecha‐ nism is compounded by the fact that in the meanwhile ouabain was shown to be a hormone that varies in response of several physiological and pathological conditions. Therefore, we may postulate that ouabain may determine the retrieval of the β-subunit from the plasma mem‐ brane and down regulates the expression of Na+ ,K+ -ATPase in the cell membrane and thus, indirectly regulates the absorption and secretion of ions and nutrients. Therefore, ouabain should be added to the list of hormones that affect transepithelial transport, along with aldosterone, antidiuretic hormone, and the like.

#### **Acknowledgements**

Our experimental work was supported by the National Research Council of México (CONA‐ CYT). J. Lobato, T. López, O. Páez, and C. Vilchis were recipients of a Doctoral Fellowship from CONACYT-MEXICO.

#### **Author details**

Signal cascades vary between different cells types. For example, in cardiac myocytes and renal cell lines derived from the porcine kidneys (LLC-PK1) and the opossum kidneys (OK), ouabain-mediated activation of a signaling cascade has been demonstrated to be dependent upon the activation of Src, MAPK, and PI-3K pathways [129,122], whereas in human breast (BT20), prostate (DU145) cancer cells, and PY-17 cells, ouabain activate Src and MAPK pathway, but not PI-3K pathway [130]. Downstream in the ouabain-activated signaling cascade, the level of complexity increases due to the activation of several cell-specific secondary messengers and the cross talk between distinct pathways [131]. For each cell type, different pathways and branches are activated and only part of their complexity is known. In the MAPK pathway, several secondary messengers, downstream targets of ERK1/2, have been identified. Upon activation, ERK1/2 is able to migrate to the nucleus and activate several transcription factors (STAT1/3, c-fos, CREB, Elk-1) or in the cytoplasm modulate ion channels, receptors, or

,K+

membrane, nor have an enzymatic activity, no convincing role was detected for this subunit

subunit may establish a linkage with an identical subunit located in a neighboring cell across the intercellular space, and be thereby responsible for the polarized expression of Na+

ATPase in epithelial cells. Furthermore, it has been demonstrated that β–β interaction stabilizes and maintains cell-junctions integrity in transporting epithelia. The molecular mechanism by which this interaction occurs is still far from being elucidated. Nevertheless, it is clear that both N-glycans and specific sequences exposed on the polypeptide surface are implicated. The observation that P → A mechanism is involved in the shuttling of β-catenin to the nucleus and thus in the Wnt/Wingless cascade, in the growth factor signaling pathways, as well as the ability of ouabain to enhance intercellular communication through gap junctions speaks of the important physiological role played by the hormone ouabain. The importance of this mecha‐ nism is compounded by the fact that in the meanwhile ouabain was shown to be a hormone that varies in response of several physiological and pathological conditions. Therefore, we may postulate that ouabain may determine the retrieval of the β-subunit from the plasma mem‐

,K+

indirectly regulates the absorption and secretion of ions and nutrients. Therefore, ouabain should be added to the list of hormones that affect transepithelial transport, along with

Our experimental work was supported by the National Research Council of México (CONA‐ CYT). J. Lobato, T. López, O. Páez, and C. Vilchis were recipients of a Doctoral Fellowship



,K+ -

. We have shown that, due to its adhesiveness, the β1-

cytoskeleton proteins by direct phosphorylation.

brane and down regulates the expression of Na+

aldosterone, antidiuretic hormone, and the like.

**Acknowledgements**

from CONACYT-MEXICO.

Although without its β-subunit the Na+

beyond of helping the α one to cage K+

**5. Concluding remarks**

46 Cell Biology - New Insights

Jorge Alberto Lobato Álvarez, Teresa del Carmen López Murillo, Claudia Andrea Vilchis Nestor, María Luisa Roldán Gutierrez, Omar Páez Gómez and Liora Shoshani\*

\*Address all correspondence to: shoshani@fisio.cinvestav.mx

Centro de Investigación y de EstudiosAvanzados del InstitutoPolitécnicoNacional (CINVES‐ TAV-IPN), Mexico city, Mexico

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