**4. Applications and DetaAnalysis**

#### **4.1. Single-molecule kinetic analysis**

#### *4.1.1. Principle*

Durations and intervals of molecular interactions contain information about reaction kinet‐ ics. Hereafter, we call the durations of the colocalization of two molecules as 'on-times', and the intervals from the dissociation of two molecules to the association of the next molecule with one of the dissociated two molecules as 'off-times'. On-times and off-times can be measured for single events using SMI. Dual-color SMI (Figure 3) is possible to detect ontimes, but in practice, due to photobleach, it is difficult to detect successive multiple ontimes for a single molecule and not easy to detect even a single off-time.

density of the non-labeled molecules. However, even in living cells, measurements of the waiting times of the first association after some perturbation and measurements of off-times

Single-Molecule Imaging Measurements of Protein-Protein Interactions in Living Cells

A→ *k*

(Disappearance of A state is the appearance of ϕ state in the reaction equation (1).)

dϕ(*t*)

Hence, the on-time distribution is the reaction rate equation,

d*ϕ*(*t*)

allel; therefore, in ensemble molecules, the reaction equation should be

Here, A and ϕ represent association and dissociation states, respectively, for example, and then *k* is the dissociation rate constant. The on-time distribution, which is the normalized histogram to show the fraction of on-times observed in each time interval from *t* to *t*+Δt, means changes of the nomarlized frequency to observe disappearance of the association state as a function of time. In other words, the on-time distribution represents the reaction rate to produce the dissociation state with time after the formation of the association state.

Here, the reaction is assumed to proceed according to a simple mass action model. Differ‐ ent from the kinetic analyses in conventional biochemical techniques that deal with the concentration changes, the reaction rate equations in SMI describe state changes of a sin‐ gle molecule with time; i.e., in equation (2), *A*(*t*) and *ϕ*(*t*) do not mean the concentrations but the probabilities with which each of the states is observed. Because every single mole‐ cule takes one of the two states in this reaction model, and because at the starting point of each on-time the molecule takes A state, equation (2) has a conservation condition; *A*(*t*) + *ϕ*(t) = 1, and the initial condition; *A*(0) = 1. Under these conditions, equation (2) is solved

By fitting the on-time distribution with equation (3), the best-fit value for *k* is obtained.

This procedure is similar to that used in a conventional biochemical analysis based on en‐ semble-molecule measurements. However, there are two major different points between SMI and ensemble-molecule analyses. First, the initial condition *A*(0) = 1 is not always appli‐ cable in ensemble-molecule analysis. Second, and more importantly, in SMI analysis, the for‐ ward and backward reactions can be analyzed completely separately. In the presence of many molecules in the reactant, the association and dissociation reactions take place in par‐

<sup>ϕ</sup> (1)

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441

dt =*kA*(*t*). (2)

dt <sup>=</sup>*kA*(*t*)=*<sup>k</sup>* exp(−*kt*). (3)

are usually possible for kinetic analyses.

*4.1.2. Estimation of the reaction parameters*

Consider a reaction of state change,

as *A*(*t*)=exp (-*kt*). Then,

**Figure 3.** Dual-color single-molecule imaging of TMR-labeled epidermal growth factor (EGF; magenta) and GFP-Sos (green) in a living HeLa cell. Basal cell surface was observed using a dual-colour total internal reflection fluores‐ cence microscope. EGF receptors (EGFR) on the cell surface are activated by EGF binding. Then, Sos molecule,complexed with Grb2, associates to the activated EGFR. White spots represent the EGF-EGFR-Grb2-Sos complexes in the plas‐ ma membrane.

More practical single-molecule measurements of on- and off-times are achieved for the in‐ teractions between a soluble molecule and a molecule stably attached on stationary struc‐ tures. Because of the rapid Brownian movements in solution, soluble molecules cannot be observed as clear fluorescent spots and can only be imaged when they associate with fixed or slowly moving molecules. Therefore, *in vitro* SMI measurements, interactions between fluorescently labelled soluble molecules and a (non-labeled) molecule fixed on the substrate are often observed [1, 11]. In such cases, because different soluble molecules interact with a fixed molecule in turn, photobleach has minimal effect. Similar measurements can be ach‐ ieved in living cells when interactions are observed between a fluorescently labelled soluble molecule (either in the extracellular solution or in the cytoplasm) and molecules in the mem‐ brane or cytoskeleton structures. Inside living cells, detection of the successive on-times as well as the single off-time is difficult by this way because of the movements and/or high density of the non-labeled molecules. However, even in living cells, measurements of the waiting times of the first association after some perturbation and measurements of off-times are usually possible for kinetic analyses.

#### *4.1.2. Estimation of the reaction parameters*

Consider a reaction of state change,

**4. Applications and DetaAnalysis**

Durations and intervals of molecular interactions contain information about reaction kinet‐ ics. Hereafter, we call the durations of the colocalization of two molecules as 'on-times', and the intervals from the dissociation of two molecules to the association of the next molecule with one of the dissociated two molecules as 'off-times'. On-times and off-times can be measured for single events using SMI. Dual-color SMI (Figure 3) is possible to detect ontimes, but in practice, due to photobleach, it is difficult to detect successive multiple on-

An Integrated View of the Molecular Recognition and Toxinology - From Analytical Procedures to Biomedical

**Figure 3.** Dual-color single-molecule imaging of TMR-labeled epidermal growth factor (EGF; magenta) and GFP-Sos (green) in a living HeLa cell. Basal cell surface was observed using a dual-colour total internal reflection fluores‐ cence microscope. EGF receptors (EGFR) on the cell surface are activated by EGF binding. Then, Sos molecule,complexed with Grb2, associates to the activated EGFR. White spots represent the EGF-EGFR-Grb2-Sos complexes in the plas‐

More practical single-molecule measurements of on- and off-times are achieved for the in‐ teractions between a soluble molecule and a molecule stably attached on stationary struc‐ tures. Because of the rapid Brownian movements in solution, soluble molecules cannot be observed as clear fluorescent spots and can only be imaged when they associate with fixed or slowly moving molecules. Therefore, *in vitro* SMI measurements, interactions between fluorescently labelled soluble molecules and a (non-labeled) molecule fixed on the substrate are often observed [1, 11]. In such cases, because different soluble molecules interact with a fixed molecule in turn, photobleach has minimal effect. Similar measurements can be ach‐ ieved in living cells when interactions are observed between a fluorescently labelled soluble molecule (either in the extracellular solution or in the cytoplasm) and molecules in the mem‐ brane or cytoskeleton structures. Inside living cells, detection of the successive on-times as well as the single off-time is difficult by this way because of the movements and/or high

times for a single molecule and not easy to detect even a single off-time.

**4.1. Single-molecule kinetic analysis**

*4.1.1. Principle*

Applications

440

ma membrane.

$$\mathbf{A} \xrightarrow{k} \boldsymbol{\Phi} \tag{1}$$

Here, A and ϕ represent association and dissociation states, respectively, for example, and then *k* is the dissociation rate constant. The on-time distribution, which is the normalized histogram to show the fraction of on-times observed in each time interval from *t* to *t*+Δt, means changes of the nomarlized frequency to observe disappearance of the association state as a function of time. In other words, the on-time distribution represents the reaction rate to produce the dissociation state with time after the formation of the association state. (Disappearance of A state is the appearance of ϕ state in the reaction equation (1).)

Hence, the on-time distribution is the reaction rate equation,

$$\frac{d\phi(t)}{dt} = kA(t). \tag{2}$$

Here, the reaction is assumed to proceed according to a simple mass action model. Differ‐ ent from the kinetic analyses in conventional biochemical techniques that deal with the concentration changes, the reaction rate equations in SMI describe state changes of a sin‐ gle molecule with time; i.e., in equation (2), *A*(*t*) and *ϕ*(*t*) do not mean the concentrations but the probabilities with which each of the states is observed. Because every single mole‐ cule takes one of the two states in this reaction model, and because at the starting point of each on-time the molecule takes A state, equation (2) has a conservation condition; *A*(*t*) + *ϕ*(t) = 1, and the initial condition; *A*(0) = 1. Under these conditions, equation (2) is solved as *A*(*t*)=exp (-*kt*). Then,

$$\frac{d\phi(t)}{dt} = kA(t) = k \cdot \exp(-kt). \tag{3}$$

By fitting the on-time distribution with equation (3), the best-fit value for *k* is obtained.

This procedure is similar to that used in a conventional biochemical analysis based on en‐ semble-molecule measurements. However, there are two major different points between SMI and ensemble-molecule analyses. First, the initial condition *A*(0) = 1 is not always appli‐ cable in ensemble-molecule analysis. Second, and more importantly, in SMI analysis, the for‐ ward and backward reactions can be analyzed completely separately. In the presence of many molecules in the reactant, the association and dissociation reactions take place in par‐ allel; therefore, in ensemble molecules, the reaction equation should be

$$\begin{array}{c} \stackrel{k\_+}{\underset{k\_-}{\rightleftharpoons}} \phi. \tag{4} \\ \stackrel{k\_-}{\underset{k\_-}{\rightleftharpoons}} \phi. \end{array} \tag{4}$$

d*B*(*t*)

dt <sup>=</sup>*k*2*B*(*t*)= - *<sup>k</sup>*1*k*<sup>2</sup>

Additional experiments or information is required for the assignment.

*4.1.3. spFRET measurements for detection of molecular interactions*

*k*<sup>1</sup> - *k*<sup>2</sup>

*A*(0) = 1, and *B*(0) = *ϕ*(0) = 0,

obtain high FRET efficiency.

*4.2.1. EGF and its receptor*

**dimerization**

the cell surface.

dϕ(*t*)

Solving the coupled differential equations (8-10) under the conditions *A*(*t*) + *B*(*t*) + *ϕ*(*t*) = 1,

This distribution is peaked; conversely, from the peaked distribution of on-times, presence of a reaction intermediate (or multiple intermediates) can be noticed. By fitting the on-time distribution by equation (11), two reaction rate constants can be determined. However, in this case, even two values of the rate constants are obtained, it is impossible to assign which one is the value of each rate constant, because *k*1 and *k*<sup>2</sup> are interchangeable in equation (11).

In some case, more direct evidence for interactions between two species of single mole‐ cules should be required. Although the spatial resolution of optical microscopy is worse than 200 nm, the position (centroid) of each single-molecule image can be determined at nm-level resolution, if sufficient signal is obtained [22]. Dual-color SMI (Figure 3) allows detection of colocalization within several tens of nm in typical conditions. More accurate detection of direct molecular interactions is allowed by detecting single-pair FRET (spFRET) signal [4,23]. spFRET has a power to detect molecular interactions in crowding conditions, because FRET from sparsely distributed donors to dense acceptors yields sparse signal from the acceptors, which can be detected in single molecules [24]. However, usage of spFRET is limited due to its weakness to photobleach and difficulty to tuning labeling conditions to

**4.2. Interactions between epidermal growth factor (EGF) and EGF receptor, and receptor**

Ligand-receptor interactions are one of the basic reactions in cell signaling systems. Here, we used SMI for detection of interactions between an extracellular ligand and receptor on

Epidermal growth factor, EGF, is a soluble cell signaling protein in the extracellular medi‐ um. EGF associates with its receptor, EGF receptor (EGFR), in the plasma membrane to stimulate cell proliferation [25]. EGFR is a single membrane spanning protein expressed in various types of animal cells. At the extracellular domain, an EGFR molecule associates with a single molecule of EGF; then, the conformational change of EGFR is thought to induce di‐ merization of two EGF-associated EGFR molecules. In addition to monomers of vacant

dt <sup>=</sup>*k*1*A*(*t*) - *<sup>k</sup>* <sup>2</sup>*B*(*t*). (10)

Single-Molecule Imaging Measurements of Protein-Protein Interactions in Living Cells

{exp (-*k*1*t*) - exp (-*k*2*t*)}. (11)

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443

Then, the rate equation is

$$\frac{d\phi(t)}{dt} = \mathbf{k}\_{+}A(t) \text{ - } k\_{-}L \text{ } \phi(t). \tag{5}$$

Here, *L* means the concentration of the ligand molecule, which can be thought of as a con‐ stant in the presence of excess amount of the ligand. The solution for *A*(*t*) under the same conditions, *A*(*t*) + *ϕ*(t) = 1 and *A*(0) = 1, is

$$A(t) = \frac{k\_{\text{+}}}{k\_{\text{+}} + k\_{\text{-}}L} \exp\{- \{k\_{\text{+}} + k\_{\text{-}}L\_{\text{-}}\} t\} + \frac{k\_{\text{-}}L}{k\_{\text{+}} + k\_{\text{-}}L},\tag{6}$$

indicating that the association (*k*+) and dissociation (k- ) rate constants are never able to deter‐ mined independently by fitting to a timecourse describing the concentration change of A state. (In ensemble-molecule measurements, obtaining multiple timecourses by changing the ligand concentration, *L*, the association and dissociation rate constants can be determined separately. However, in this case, there is an additional assumption that the rate constants are independent of the concentration.)

Reactions are not always as simple as described in equation (1). Multi-component reactions, described by a sum of exponential functions, are usual for proteins [11,15]. Also, reaction in‐ termediates are sometimes involved. Such reaction structures could be noticed from the shape of the on(off)-time distributions. For example, sequential dissociations of two binding sites in a single molecule are described by the tandem reaction model [14],

$$\begin{array}{ccccc}k\_1 & k\_2 & \\ \cline{1-3} \mathbf{A} \rightharpoonup \mathbf{B} \rightharpoonup \boldsymbol{\phi} & & \end{array} \tag{7}$$

Here, ϕ state is the off state again,and the on-time distribution is

$$\frac{d\phi(t)}{dt} = k\_2 B(t). \tag{8}$$

At the same time,

$$\frac{d A(t)}{dt} = -k\_1 A(t) \,\text{s} \tag{9}$$

and

Single-Molecule Imaging Measurements of Protein-Protein Interactions in Living Cells http://dx.doi.org/10.5772/52386 443

$$k\frac{d\,B(t)}{dt} = k\_1 A(t) \text{ - } k\_2 B(t). \tag{10}$$

Solving the coupled differential equations (8-10) under the conditions *A*(*t*) + *B*(*t*) + *ϕ*(*t*) = 1, *A*(0) = 1, and *B*(0) = *ϕ*(0) = 0,

$$\frac{d\phi(t)}{dt} = k\_2 B(t) = -\frac{k\_1 k\_2}{k\_1 \cdot k\_2} [\exp\left(-k\_1 t\right) - \exp\left(-k\_2 t\right)].\tag{11}$$

This distribution is peaked; conversely, from the peaked distribution of on-times, presence of a reaction intermediate (or multiple intermediates) can be noticed. By fitting the on-time distribution by equation (11), two reaction rate constants can be determined. However, in this case, even two values of the rate constants are obtained, it is impossible to assign which one is the value of each rate constant, because *k*1 and *k*<sup>2</sup> are interchangeable in equation (11). Additional experiments or information is required for the assignment.

#### *4.1.3. spFRET measurements for detection of molecular interactions*

In some case, more direct evidence for interactions between two species of single mole‐ cules should be required. Although the spatial resolution of optical microscopy is worse than 200 nm, the position (centroid) of each single-molecule image can be determined at nm-level resolution, if sufficient signal is obtained [22]. Dual-color SMI (Figure 3) allows detection of colocalization within several tens of nm in typical conditions. More accurate detection of direct molecular interactions is allowed by detecting single-pair FRET (spFRET) signal [4,23]. spFRET has a power to detect molecular interactions in crowding conditions, because FRET from sparsely distributed donors to dense acceptors yields sparse signal from the acceptors, which can be detected in single molecules [24]. However, usage of spFRET is limited due to its weakness to photobleach and difficulty to tuning labeling conditions to obtain high FRET efficiency.

#### **4.2. Interactions between epidermal growth factor (EGF) and EGF receptor, and receptor dimerization**

#### *4.2.1. EGF and its receptor*

<sup>A</sup><sup>→</sup> *k*+

dt =k+*A*(*t*) - *k*-

*<sup>k</sup>*<sup>+</sup> <sup>+</sup> *<sup>k</sup>*-*<sup>L</sup>* exp{-(*k*<sup>+</sup> + *k*-

sites in a single molecule are described by the tandem reaction model [14],

Here, ϕ state is the off state again,and the on-time distribution is

A→ *k*1 B→ *k*2

dϕ(*t*)

d*A*(*t*)

Here, *L* means the concentration of the ligand molecule, which can be thought of as a con‐ stant in the presence of excess amount of the ligand. The solution for *A*(*t*) under the same

mined independently by fitting to a timecourse describing the concentration change of A state. (In ensemble-molecule measurements, obtaining multiple timecourses by changing the ligand concentration, *L*, the association and dissociation rate constants can be determined separately. However, in this case, there is an additional assumption that the rate constants

Reactions are not always as simple as described in equation (1). Multi-component reactions, described by a sum of exponential functions, are usual for proteins [11,15]. Also, reaction in‐ termediates are sometimes involved. Such reaction structures could be noticed from the shape of the on(off)-time distributions. For example, sequential dissociations of two binding

*L* )*t*} +

*k*-*L*

dϕ(*t*)

Then, the rate equation is

Applications

442

conditions, *A*(*t*) + *ϕ*(t) = 1 and *A*(0) = 1, is

are independent of the concentration.)

At the same time,

and

*<sup>A</sup>*(*t*)= *<sup>k</sup>*<sup>+</sup>

indicating that the association (*k*+) and dissociation (k-

← *k*-*L*

An Integrated View of the Molecular Recognition and Toxinology - From Analytical Procedures to Biomedical

ϕ. (4)

*L* ϕ(*t*). (5)

*<sup>k</sup>*<sup>+</sup> <sup>+</sup> *<sup>k</sup>*-*<sup>L</sup>* , (6)

) rate constants are never able to deter‐

<sup>ϕ</sup> (7)

dt =*k*2*B*(*t*). (8)

dt =-*k* <sup>1</sup>*A*(*t*), (9)

Ligand-receptor interactions are one of the basic reactions in cell signaling systems. Here, we used SMI for detection of interactions between an extracellular ligand and receptor on the cell surface.

Epidermal growth factor, EGF, is a soluble cell signaling protein in the extracellular medi‐ um. EGF associates with its receptor, EGF receptor (EGFR), in the plasma membrane to stimulate cell proliferation [25]. EGFR is a single membrane spanning protein expressed in various types of animal cells. At the extracellular domain, an EGFR molecule associates with a single molecule of EGF; then, the conformational change of EGFR is thought to induce di‐ merization of two EGF-associated EGFR molecules. In addition to monomers of vacant

EGFR molecules, predimers of EGFR molecules (dimers without association of EGF mole‐ cules) are known to present on the cell surface. However, it is widely believed that only after formation of doubly liganded dimers (signaling dimers), EGFR molecules are activated through phosphorylation at the cytoplasmic domain. These phosphorylations are carried out through the mutual phosphorylations in the signaling dimers using the kinase activity in the cytoplasmic side of EGFR molecules (Figure 4). We tried to determine the kinetic process of EGF-EGFR associations and formation of signaling dimers of EGFR using SMI measurements [26,27].

nM-1s-1. The difference between two types of EGF association sites in the association rate constant of EGF has not been fully known, but it is possible that the latter (*k*2) is the associa‐ tion rate constant of the first EGF molecule to the predimers of EGFR, because the associa‐

Single-Molecule Imaging Measurements of Protein-Protein Interactions in Living Cells

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445

The waiting time distributions for the second associations to the double association sites were peaked (Figure 5C). The distributions were analyzed using the tandem reaction model (equation 7). By changing the concentration of EGF, the rate constants for the intermediate formation (*k*3) and for the association of the second EGF molecule (*k*4) were assigned: *k*<sup>3</sup> was independent of the EGF concentration, suggesting that it was the rate constant for a confor‐ mational change induced by the first EGF association, while *k*<sup>4</sup> was proportional to EGF con‐ centration, suggesting they were the association rate constants for the second association of soluble EGF molecules with the singly-liganded EGFR dimers. The values were *k*<sup>3</sup> = 4.0 s-1 and *k*4/*L* = 2.4 nM-1s-1. The intermediate between the first and the second associations of EGF molecules was first detected using SMI. These results suggest that the association rate con‐ stant with EGF is increased by the formation of predimer of EGFR and, after the association of the first EGF molecule to the EGFR dimer, increased further. These properties of EGF-EGFR interactions facilitate the formation of signaling dimers of EGFR. Similar results were

tion rate constant for the single association sites was the same as *k*1 (Figure 5B).

observed on HeLa cells [26] and other EGFR family members on MCF-7 cells [27].

**Figure 5.** Single-molecule measurement of the associations between EGF and EGFR. (A) Single-molecule detections of the associations of EGF with EGFR are illustrated schematically. Waiting times of the association (appearance) of fluo‐ rescent spots on the cell surface (τ1) were measured individually after the application of TMR-EGF to the cell culture medium. Second associations of TMR-EGF, which could be detected by a step-like increase of the fluorescence intensi‐ ty, were observed in some association sites. The waiting times of the second association after the first association (τ2) were also measured. (B) The distributions of τ1 were measured for all association sites (red bars) and for the single association sites (green bars) in the presence of 4 nM TMR-EGF. The numbers of events were 57 (red) and 31 (green). Lines show the results of fitting with the reaction models. The red histogram was fitted with a two-component expo‐ nential function, suggesting the presence of two different association sites. The green histogram was fitted with a sin‐ gle-component exponential function. See text for the values of rate constants. (C) The distributions of τ<sup>2</sup> were measured in the presence of 2 nM (red bars) or 4 nM (green bars) of TMR-EGF. The numbers of events were 30 (red) and 81 (green). The distributions were analyzed by the tandem reaction model. In this model, the first and second steps are the state change and association of the second EGF molecule, respectively. Therefore, the reaction rate of the first step is independent to the EGF concentration, but the second step should be proportional to the EGF concen‐ tration. The best-fit values of the first-order reaction rate constants for the second step were 4.7 and 4.7 s-1 (2 nM), and 3.4 and 10 s-1 (4 nM), suggesting that the rate constant of the first step were 4.7 (2 nM) and 3.4 (4 nM) s-1, and the

**Figure 4.** A schematic model of associations between EGF and EGFR and formation of signaling dimers of EGFR.

### *4.2.2. Single-molecule imaging of EGF association*

EGF can be conjugated with chemical fluorophores like TMR at the N-terminus without dis‐ ruption of its biological activity. After applications of nM orders of TMR-labeled EGF to the culture medium of cells under an oblique illumination fluorescence microscope, associations of single EGF molecules on the apical surface of living cells were observed in real time (Fig‐ ure 1C). Movies of EGF associations were acquired in 20 frames/s. In this experiment, a hu‐ man breast cancer cell line, MCF-7, was used. From the single-molecule movies, associations of single EGF molecules were detected individually as the sudden appearance of fluorescent spots on the cell surface (Figure 5A). When the association sites contained more than one EGFR molecule, the second associations were observed at the same positions of the first as‐ sociation sites. Some of the double association sites could be predimers of EGFR, and others could be two EGFR molecules presented in close proximity by accident. In our experimental conditions, no association site showed more than double association.

The association kinetics between EGF and EGFR were analyzed from the distributions of the waiting times for associations of single EGF molecules (Figure 5B,C). The waiting time dis‐ tribution for the EGF association for the first EGF molecules could be described by a 2-com‐ ponent exponential function with rate constants of *k*1 = 1.4 x 10-3nM-1s-1 and *k*<sup>2</sup> = 3.8 x 10-2 nM-1s-1. The difference between two types of EGF association sites in the association rate constant of EGF has not been fully known, but it is possible that the latter (*k*2) is the associa‐ tion rate constant of the first EGF molecule to the predimers of EGFR, because the associa‐ tion rate constant for the single association sites was the same as *k*1 (Figure 5B).

EGFR molecules, predimers of EGFR molecules (dimers without association of EGF mole‐ cules) are known to present on the cell surface. However, it is widely believed that only after formation of doubly liganded dimers (signaling dimers), EGFR molecules are activated through phosphorylation at the cytoplasmic domain. These phosphorylations are carried out through the mutual phosphorylations in the signaling dimers using the kinase activity in the cytoplasmic side of EGFR molecules (Figure 4). We tried to determine the kinetic process of EGF-EGFR associations and formation of signaling dimers of EGFR using SMI

An Integrated View of the Molecular Recognition and Toxinology - From Analytical Procedures to Biomedical

**Figure 4.** A schematic model of associations between EGF and EGFR and formation of signaling dimers of EGFR.

conditions, no association site showed more than double association.

EGF can be conjugated with chemical fluorophores like TMR at the N-terminus without dis‐ ruption of its biological activity. After applications of nM orders of TMR-labeled EGF to the culture medium of cells under an oblique illumination fluorescence microscope, associations of single EGF molecules on the apical surface of living cells were observed in real time (Fig‐ ure 1C). Movies of EGF associations were acquired in 20 frames/s. In this experiment, a hu‐ man breast cancer cell line, MCF-7, was used. From the single-molecule movies, associations of single EGF molecules were detected individually as the sudden appearance of fluorescent spots on the cell surface (Figure 5A). When the association sites contained more than one EGFR molecule, the second associations were observed at the same positions of the first as‐ sociation sites. Some of the double association sites could be predimers of EGFR, and others could be two EGFR molecules presented in close proximity by accident. In our experimental

The association kinetics between EGF and EGFR were analyzed from the distributions of the waiting times for associations of single EGF molecules (Figure 5B,C). The waiting time dis‐ tribution for the EGF association for the first EGF molecules could be described by a 2-com‐ ponent exponential function with rate constants of *k*1 = 1.4 x 10-3nM-1s-1 and *k*<sup>2</sup> = 3.8 x 10-2

*4.2.2. Single-molecule imaging of EGF association*

measurements [26,27].

Applications

444

The waiting time distributions for the second associations to the double association sites were peaked (Figure 5C). The distributions were analyzed using the tandem reaction model (equation 7). By changing the concentration of EGF, the rate constants for the intermediate formation (*k*3) and for the association of the second EGF molecule (*k*4) were assigned: *k*<sup>3</sup> was independent of the EGF concentration, suggesting that it was the rate constant for a confor‐ mational change induced by the first EGF association, while *k*<sup>4</sup> was proportional to EGF con‐ centration, suggesting they were the association rate constants for the second association of soluble EGF molecules with the singly-liganded EGFR dimers. The values were *k*<sup>3</sup> = 4.0 s-1 and *k*4/*L* = 2.4 nM-1s-1. The intermediate between the first and the second associations of EGF molecules was first detected using SMI. These results suggest that the association rate con‐ stant with EGF is increased by the formation of predimer of EGFR and, after the association of the first EGF molecule to the EGFR dimer, increased further. These properties of EGF-EGFR interactions facilitate the formation of signaling dimers of EGFR. Similar results were observed on HeLa cells [26] and other EGFR family members on MCF-7 cells [27].

**Figure 5.** Single-molecule measurement of the associations between EGF and EGFR. (A) Single-molecule detections of the associations of EGF with EGFR are illustrated schematically. Waiting times of the association (appearance) of fluo‐ rescent spots on the cell surface (τ1) were measured individually after the application of TMR-EGF to the cell culture medium. Second associations of TMR-EGF, which could be detected by a step-like increase of the fluorescence intensi‐ ty, were observed in some association sites. The waiting times of the second association after the first association (τ2) were also measured. (B) The distributions of τ1 were measured for all association sites (red bars) and for the single association sites (green bars) in the presence of 4 nM TMR-EGF. The numbers of events were 57 (red) and 31 (green). Lines show the results of fitting with the reaction models. The red histogram was fitted with a two-component expo‐ nential function, suggesting the presence of two different association sites. The green histogram was fitted with a sin‐ gle-component exponential function. See text for the values of rate constants. (C) The distributions of τ<sup>2</sup> were measured in the presence of 2 nM (red bars) or 4 nM (green bars) of TMR-EGF. The numbers of events were 30 (red) and 81 (green). The distributions were analyzed by the tandem reaction model. In this model, the first and second steps are the state change and association of the second EGF molecule, respectively. Therefore, the reaction rate of the first step is independent to the EGF concentration, but the second step should be proportional to the EGF concen‐ tration. The best-fit values of the first-order reaction rate constants for the second step were 4.7 and 4.7 s-1 (2 nM), and 3.4 and 10 s-1 (4 nM), suggesting that the rate constant of the first step were 4.7 (2 nM) and 3.4 (4 nM) s-1, and the

second-order rate constants were 4.7/2 (2 nM) and 10/4 (4 nM) nM-1s-1. The averages of the rate constants weighted with the event number are 4.0 s-1 and 2.4 nM-1s-1.

for RBD, CRD, and CRD-CAD fragments. RBD-CRD fragments accumulated on the membrane independent of EGF stim‐ ulation. (B) RAF contains two Ras-association domains (RBD and CRD) and has two conformations (open and closed).

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C-RAF, which is a ubiquitous isoform of RAF, was tagged with GFP (GFP-RAF) and ex‐ pressed in HeLa cells. GFP-RAF presented in the cytoplasm of quiescent cells and translo‐ cated to the plasma membrane upon activation of cells with EGF. The translocation of whole molecules of RAF was observed in ensemble-molecule imaging. Only a small amount of the RBD fragment of RAF showed translocation, and the RBD-CRD fragment bound to the plas‐ ma membrane independently of cell stimulation (Figure 6A). The RBD-CRD fragment with a mutation to inactive RBD (CRD) and a mutant of RAF in the open form with inactive RBD (CRD-CAD) did not show remarkable translocation to the plasma membrane in ensemble

Reducing the expression levels of GFP-tagged molecules, single molecules of RAF and its fragments were observed on the plasma membrane (Figure 7). For all molecules, transient associations with the plasma membrane were observed in single molecules after EGF stimu‐ lation, and for the molecules containing RBD (RAF, RBD, and RBD-CRD), associations of a small amount of molecules were observed, even in quiescent cells. The densities of mem‐ brane-associated molecules increased with overexpressions of Ras, suggesting Ras-specific

**Figure 7.** Single-molecule images of RAF and RAF fragments in HeLa cells. These images were observed in a HeLa cells

On-time distributions of RAF molecules were obtained in cells after EGF stimulation (Figure 8A). RBD and CRD showed single exponential on-time distributions with the decay rate constants of 3.8 and 2.4 s-1, respectively. Because the decay of on-time distributions is deter‐ mined by both dissociation and photobleach as the reasons of disappearance of the fluores‐ cent spots, the decay rate constants are the sum of the rate constants for dissociation and photobleach. After the corrections for the photobleaching rate constant, which was deter‐ mined by SMI in fixed cells, the dissociation rate constants for RBD (*k*1) and CRD (*k*2) were determined as *k*1 = 3.7 and *k*2 =2.3 s-1, respectively. Corrections of photobleach were also car‐ ried out in the following analyses (see supplement information of [28] for details). The ontime distribution of RBD-CRD was peaked, suggesting sequential dissociation of RBD and

*4.3.2. Single-molecule imaging of RAF translocation*

molecules, even after EGF stimulation.

membrane interactions of RAF molecules.

2-5 min periods after stimulation with EGF.

*4.3.3. Kinetic analysis of RAF activation*

#### **4.3. Interaction between a small GTPaseRaf and a cytoplasmic kinase RAF**

#### *4.3.1. Ras and RAF*

As the second example of SMI kinetic analysis, intracellular molecular reactions of RAF were analyzed [14,28,29]. As a downstream signaling of EGFR, EGF stimulation induces ac‐ tivation of a small GTPase, Ras, on the cytoplasmic side of the plasma membrane. The active form of Ras is recognized by a cytoplasmic serine/threonine kinase, RAF, which is the MAPKKK of the RAF-MEK-ERK MAPK cascade; thus, RAF translocates from the cytoplasm to the plasma membrane upon activation of Ras (Figure 6A). The active form of Ras induces translocation of RAF but does not activate RAF directory. RAF activation was induced though phosphorylations by still undetermined kinase(s) on the plasma membrane. RAF contains two association sites for Ras (the Ras-binding domain RBD and the cysteine-rich domain CRD). In addition, RAF has at least two conformations, open and closed. In the closed form, due to intramolecular interactions, CRD and the catalytic domain (CAD) of RAF are covered from Ras and the kinase(s), respectively (Figure 6B). Thus, the kinetics of RAF activation in the ternary complex among Ras, RAF, and the kinase(s) should be compli‐ cated. Actually, the kinetics of RAF activation has not been known at all. It cannot be stud‐ ied *in vitro,* since the kinase(s) is(are) not determined. However, in living cells, SMI measurement is applicable.

**Figure 6.** Translocation of RAF.(A) C-RAF1 and its fragments tagged with GFP at the N-terminus was expressed in He‐ La cells and observed in ensemble-molecules before (upper panel) and after (lower panel) stimulation of cells with EGF. RAF (whole molecule) translocated from the cytoplasm to the plasma membrane. Translocation was not evident

for RBD, CRD, and CRD-CAD fragments. RBD-CRD fragments accumulated on the membrane independent of EGF stim‐ ulation. (B) RAF contains two Ras-association domains (RBD and CRD) and has two conformations (open and closed).

#### *4.3.2. Single-molecule imaging of RAF translocation*

second-order rate constants were 4.7/2 (2 nM) and 10/4 (4 nM) nM-1s-1. The averages of the rate constants weighted

An Integrated View of the Molecular Recognition and Toxinology - From Analytical Procedures to Biomedical

As the second example of SMI kinetic analysis, intracellular molecular reactions of RAF were analyzed [14,28,29]. As a downstream signaling of EGFR, EGF stimulation induces ac‐ tivation of a small GTPase, Ras, on the cytoplasmic side of the plasma membrane. The active form of Ras is recognized by a cytoplasmic serine/threonine kinase, RAF, which is the MAPKKK of the RAF-MEK-ERK MAPK cascade; thus, RAF translocates from the cytoplasm to the plasma membrane upon activation of Ras (Figure 6A). The active form of Ras induces translocation of RAF but does not activate RAF directory. RAF activation was induced though phosphorylations by still undetermined kinase(s) on the plasma membrane. RAF contains two association sites for Ras (the Ras-binding domain RBD and the cysteine-rich domain CRD). In addition, RAF has at least two conformations, open and closed. In the closed form, due to intramolecular interactions, CRD and the catalytic domain (CAD) of RAF are covered from Ras and the kinase(s), respectively (Figure 6B). Thus, the kinetics of RAF activation in the ternary complex among Ras, RAF, and the kinase(s) should be compli‐ cated. Actually, the kinetics of RAF activation has not been known at all. It cannot be stud‐ ied *in vitro,* since the kinase(s) is(are) not determined. However, in living cells, SMI

**Figure 6.** Translocation of RAF.(A) C-RAF1 and its fragments tagged with GFP at the N-terminus was expressed in He‐ La cells and observed in ensemble-molecules before (upper panel) and after (lower panel) stimulation of cells with EGF. RAF (whole molecule) translocated from the cytoplasm to the plasma membrane. Translocation was not evident

**4.3. Interaction between a small GTPaseRaf and a cytoplasmic kinase RAF**

with the event number are 4.0 s-1 and 2.4 nM-1s-1.

*4.3.1. Ras and RAF*

Applications

446

measurement is applicable.

C-RAF, which is a ubiquitous isoform of RAF, was tagged with GFP (GFP-RAF) and ex‐ pressed in HeLa cells. GFP-RAF presented in the cytoplasm of quiescent cells and translo‐ cated to the plasma membrane upon activation of cells with EGF. The translocation of whole molecules of RAF was observed in ensemble-molecule imaging. Only a small amount of the RBD fragment of RAF showed translocation, and the RBD-CRD fragment bound to the plas‐ ma membrane independently of cell stimulation (Figure 6A). The RBD-CRD fragment with a mutation to inactive RBD (CRD) and a mutant of RAF in the open form with inactive RBD (CRD-CAD) did not show remarkable translocation to the plasma membrane in ensemble molecules, even after EGF stimulation.

Reducing the expression levels of GFP-tagged molecules, single molecules of RAF and its fragments were observed on the plasma membrane (Figure 7). For all molecules, transient associations with the plasma membrane were observed in single molecules after EGF stimu‐ lation, and for the molecules containing RBD (RAF, RBD, and RBD-CRD), associations of a small amount of molecules were observed, even in quiescent cells. The densities of mem‐ brane-associated molecules increased with overexpressions of Ras, suggesting Ras-specific membrane interactions of RAF molecules.

**Figure 7.** Single-molecule images of RAF and RAF fragments in HeLa cells. These images were observed in a HeLa cells 2-5 min periods after stimulation with EGF.

#### *4.3.3. Kinetic analysis of RAF activation*

On-time distributions of RAF molecules were obtained in cells after EGF stimulation (Figure 8A). RBD and CRD showed single exponential on-time distributions with the decay rate constants of 3.8 and 2.4 s-1, respectively. Because the decay of on-time distributions is deter‐ mined by both dissociation and photobleach as the reasons of disappearance of the fluores‐ cent spots, the decay rate constants are the sum of the rate constants for dissociation and photobleach. After the corrections for the photobleaching rate constant, which was deter‐ mined by SMI in fixed cells, the dissociation rate constants for RBD (*k*1) and CRD (*k*2) were determined as *k*1 = 3.7 and *k*2 =2.3 s-1, respectively. Corrections of photobleach were also car‐ ried out in the following analyses (see supplement information of [28] for details). The ontime distribution of RBD-CRD was peaked, suggesting sequential dissociation of RBD and

CRD from Ras. Association with Ras using both RBD and CRD could induce firm mem‐ brane anchoring of RBD-CRD, even in the quiescent cells. Applying the dissociation rate constants of RBD and CRD, the on-time distributions of RBD-CRD could be described by the following reaction model [29]:

RC<sup>→</sup> *k*1 ← *k*1- C→ *k*2 ϕ. (12)

In this scheme, RC or C represents the state in which the molecule associates with Ras using both RBD and CRD, or only CRD, respectively. Since it is known that CRD of Ras molecules associates with Ras very rapidly after the association of RBD to Ras [14], R state (in which the molecule associates with Ras only with RBD) was neglected in this reaction scheme. Us‐ ing this scheme, *k*1- (the association rate constant between RBD and Ras from the C state) was determined to be 1.0 s-1.

RAF and CRD-CAD interact with the kinase(s) on the plasma membrane as the substrate. In addition, RAF contains open-close dynamics. Our previous study using spFRET [14] indicat‐ ed that the initial association form of RAF with the activated Ras (in our time resolution of ~0.1 s) is an open conformation. The reaction model (equation 12) was extended to include the phosphorylation by the kinase.

$$\begin{array}{c|c} \text{RC} & \xrightarrow[k\_{1.}]{k\_{1} = 3.6} & \text{C} & \xrightarrow{k\_{2} = 2.1} & \text{\$\phi\$} \\ \text{\$k\_{RC}\$} & \xrightarrow[k\_{3}]{k\_{3}} & \text{\$k\_{C}\$} & \left[ \text{\$k\_{3}\$} & \text{\$\phi\$} \\ \text{\$k\_{RC}\$} & \xrightarrow[k\_{1.}]{k\_{1}} & \text{\$\mathbf{C} \times \xrightarrow[k\_{2}]{k\_{2}}} & \text{\$\mathbf{X} \times \text{\$\phi\$}\$} \\ \text{\$k\_{4}\$} & & \text{\$k\_{4}\$} & \text{\$\phi\$} & \text{\$k\_{4}\$} \\ \text{\$\mathbf{R}\!C\!\rightarrow} & \text{\$k\_{1}\$} & \text{\$\mathbf{C}\!\rightarrow} & \text{\$k\_{2}\$} \\ \end{array}$$

(13)

Numerically solving the coupled differential equations for the time-dependent probability changes of the molecular states, functions to describe the on-time distributions of RAF and CRD-CAD were calculated and fitted simultaneously to the results of experiments to find the best-fit values of the rate constants. The results are shown in Figure 8B. The deformation of the RAF-kinese complex without enzymatic reaction was slow (*k*3< 10-4 s-1) and negligible, and the complex formation mostly took place from the RCX state, not from the C state. The large difference between the rates of complex formation with the kinase from the RC (47 s-1) and C (0.6 s-1) states suggests that interactions with Ras at the RBD and CRD coordinately work for effective presentation of RAF to the kinase. The very rapid association between RAF in the RC state and the kinase to form the RCX complex suggests a preexisting complex between Ras and the kinase. Simulation using the parameters determined by this analysis predicted that once associated with Ras, 95% of RAF molecules are released to the cytoplasm in the phos‐ phorylated (active) form. Thus, efficiency of phosphorylation on the plasma membrane is high, and the overall activation level of RAF in cells should be regulated by the translocation from

Single-Molecule Imaging Measurements of Protein-Protein Interactions in Living Cells

http://dx.doi.org/10.5772/52386

449

the cytoplasm to the membrane and/or dephosphorylation in the cytoplasm.

**Figure 8.** Single-molecule analysis of RAF activation. On-time distributions of RAF and fragments of RAF were ana‐ lyzed. Results of fittings with the kinetic models are shown (A). The best-fit values of the reaction rate constants (s-1)

Kinetic analysis of the protein-protein interactions using SMI is a general technology, and there have already been several examples in toxinology. *Staphylococcus aureus* leukocidin fast fraction (LukF) and γ-hemolysin second component (HS) assemble into hetro-oligomeric pores of γ-hemolysin on the cell surface to induce cell lysis. Detecting spFRET between LukF and HS, Nugyen et al. [24] have succeeded in determining equilibrium dissociation constants between the molecules in the intermediate complexes during the pore formation.

were determined (B).

**4.4. Applications in toxinology**

Here, for simplification, phosphorylation of RAF was assumed to be a single Michaelis-Menten type reaction. Suffixes X and p mean that each state forms complexes with the kin‐ ase(s) and is phospholylated, respectively. For the CRD-CAD fragment, RC, RCX, and RCp are not applicable.

Numerically solving the coupled differential equations for the time-dependent probability changes of the molecular states, functions to describe the on-time distributions of RAF and CRD-CAD were calculated and fitted simultaneously to the results of experiments to find the best-fit values of the rate constants. The results are shown in Figure 8B. The deformation of the RAF-kinese complex without enzymatic reaction was slow (*k*3< 10-4 s-1) and negligible, and the complex formation mostly took place from the RCX state, not from the C state. The large difference between the rates of complex formation with the kinase from the RC (47 s-1) and C (0.6 s-1) states suggests that interactions with Ras at the RBD and CRD coordinately work for effective presentation of RAF to the kinase. The very rapid association between RAF in the RC state and the kinase to form the RCX complex suggests a preexisting complex between Ras and the kinase. Simulation using the parameters determined by this analysis predicted that once associated with Ras, 95% of RAF molecules are released to the cytoplasm in the phos‐ phorylated (active) form. Thus, efficiency of phosphorylation on the plasma membrane is high, and the overall activation level of RAF in cells should be regulated by the translocation from the cytoplasm to the membrane and/or dephosphorylation in the cytoplasm.

**Figure 8.** Single-molecule analysis of RAF activation. On-time distributions of RAF and fragments of RAF were ana‐ lyzed. Results of fittings with the kinetic models are shown (A). The best-fit values of the reaction rate constants (s-1) were determined (B).

#### **4.4. Applications in toxinology**

CRD from Ras. Association with Ras using both RBD and CRD could induce firm mem‐ brane anchoring of RBD-CRD, even in the quiescent cells. Applying the dissociation rate constants of RBD and CRD, the on-time distributions of RBD-CRD could be described by the

An Integrated View of the Molecular Recognition and Toxinology - From Analytical Procedures to Biomedical

RC<sup>→</sup> *k*1

← *k*1C→ *k*2

In this scheme, RC or C represents the state in which the molecule associates with Ras using both RBD and CRD, or only CRD, respectively. Since it is known that CRD of Ras molecules associates with Ras very rapidly after the association of RBD to Ras [14], R state (in which the molecule associates with Ras only with RBD) was neglected in this reaction scheme. Us‐ ing this scheme, *k*1- (the association rate constant between RBD and Ras from the C state)

RAF and CRD-CAD interact with the kinase(s) on the plasma membrane as the substrate. In addition, RAF contains open-close dynamics. Our previous study using spFRET [14] indicat‐ ed that the initial association form of RAF with the activated Ras (in our time resolution of ~0.1 s) is an open conformation. The reaction model (equation 12) was extended to include

(13)

Here, for simplification, phosphorylation of RAF was assumed to be a single Michaelis-Menten type reaction. Suffixes X and p mean that each state forms complexes with the kin‐ ase(s) and is phospholylated, respectively. For the CRD-CAD fragment, RC, RCX, and RCp

ϕ. (12)

following reaction model [29]:

Applications

448

was determined to be 1.0 s-1.

the phosphorylation by the kinase.

are not applicable.

Kinetic analysis of the protein-protein interactions using SMI is a general technology, and there have already been several examples in toxinology. *Staphylococcus aureus* leukocidin fast fraction (LukF) and γ-hemolysin second component (HS) assemble into hetro-oligomeric pores of γ-hemolysin on the cell surface to induce cell lysis. Detecting spFRET between LukF and HS, Nugyen et al. [24] have succeeded in determining equilibrium dissociation constants between the molecules in the intermediate complexes during the pore formation. A hydrophobic environmental sensitive fluorophore, badan, labeling LukF, has also been used to detect complex formation with HS in single molecules [30].

pathological mutant molecules, and in toxinology for the analyses of molecular mechanisms

[1] Funatsu, T., Harada, Y., Tokunaga, M., Saito, K., & Yanagida, T. (1995). Imaging of single fluorescent molecules and individual ATP turnovers by single myosin mole‐

[2] Sase, I., Miyata, H., Corrie, J. E. T., Craik, J. S., & Kinosita, K. Jr. (1995). Real time imaging of single fluorophores on moving actin with an epifluorescence microscope.

[3] Lu, H. P., Xun, L, & Xie, X. S. (1998). Single-molecule enzymatic dynamics. *Science*,

[4] Sako, Y., Minoguchi, S., & Yanagida, T. (2000). Single molecule imaging of EGFR sig‐

[5] Shütz, G. J., Kada, G., Pastuchenko, V. Ph, & Schindler, H. (2000). Properties of lipid microdomains in a muscle cell membrane visualized by single molecule microscopy.

[6] Selvin, P. R., & Ha, T. (2008). Single-molecule techniques. *A laboratory manual. Cold*

[7] Yanagida, T., & Ishii, Y. (2009). Single molecule dynamics in life science. *WILEY-*

[8] Sako, Y., & Ueda, M. (2010). Cell Signaling Reactions: Single-molecule Kinetic Analy‐

[9] Edman, L., & Rigler, R. (2000). Memory landscapes of single-enzyme molecules. *Proc*

nal transduction on the living cell surface. *Nat Cell Biol*, 2, 168-172.

and Yasushi Sako2\*

Single-Molecule Imaging Measurements of Protein-Protein Interactions in Living Cells

http://dx.doi.org/10.5772/52386

451

, Michio Hiroshima1,2, Yuki Nakamura2

1 Laboratory for Cell Signaling Dynamics, RIKEN QBiC, Japan

2 Cellular Informatics Laboratory, RIKEN. 2-1 Hirosawa, Japan

cules in aqueous solution. *Nature*, 374, 555-559.

\*Address all correspondence to: sako@riken.jp

*Biophys J*, 69, 323-328.

*EMBO J*, 19, 829-901.

*VCHWeinhim*.

ses. *Springer London*.

*Natl Acad Sci USA*, 97, 8266-8271.

*Spring Harbor Laboratory Press New York*.

282, 1877-1882.

of toxic functions.

**Author details**

Kayo Hibino1

**References**

Groulx et al. [31] measured the stoichiometry of oligomerization of another pore-forming toxin using SMI. Monomers of *Bacillus thuringiensis* toxin Cry1Aa were labeled with a fluo‐ rophore at a cysteine residue. After the complex formation, molecules were attached on a coverslip to observe the photobleaching process. Counting the step number during the pho‐ tobleach, it was concluded that the toxin forms a tetramer.

Nabika et al. [32] used SMI for observation of lateral diffusion of cholera toxin B subunit (CTX) on the artificial lipid bilayer containing GM1, which is the receptor of CTX. The diffu‐ sion coefficient was one order smaller than that of lipid molecules in the membrane, and there were higher (0.4 μm2 /s) and lower (< 0.1 μm2 /s) diffusive fractions. This observation was explained by assuming multivalent binding between CTX and GM1 molecules.

On the contrary, toxin has been used for single-molecule measurement. Since direct fixation of molecules to a substrate possibly induces artifacts in the measurements, single molecules are sometimes entrapped into fixed tiny liposomes in which the molecules can move more freely. In this case, however, the solution around the molecules cannot be changed during the experiment, limiting experimental conditions. Okumus et al. [33] used liposomes, recon‐ stituting pore-forming toxin, to allow exchange of inside solutions.
