**2. Motivation of Single-molecule Imaging Measurements of Molecular Interactions**

### **2.1. Single-molecule versus ensemble-molecule measurements**

Before considering about technological issues, it might be important to discuss why we need SMI measurements of molecular interactions. The operation of biological molecular ma‐ chines is basically stochastic. Therefore, in ensemble average measurements, in which only the averages over a huge number of reaction events are observed, details of the reaction process are obscured. In SMI measurements, it is possible to virtually synchronize a particu‐ lar point in the reaction process for kinetic analysis. For example, imagine the observation of an enzyme reaction. The substrate solution is added to the enzyme solution to start the reac‐ tion. In ensemble measurements, the time of the two solutions mixing is set to time 0, and the concentration of the product is monitored with time. In the mixture, first, a substrate molecule needs to diffuse and collide with an enzyme molecule to form an enzyme-sub‐ strate (ES) complex; then, a chemical reaction starts on the enzyme molecule. The time 0 in ensemble measurements is not the time of ES complex formation. The time of ES complex formation is different for each molecule due to the stochasticity of molecular reactions, and this difference obscures the measurements of chemical reactions. In SMI measurements, the time point of each ES complex formation is detected, and after the observation, all the time points for individual molecules are aligned to time 0. Hence, in SMI measurements, we se‐ lectively extract the process of chemical reactions, removing the diffusion and collision for kinetic analysis.

This principle of SMI measurements also allows separation of forward and backward reac‐ tions. Here, imagine an association-dissociation reaction between two species of molecules. In the reaction mixture, both association and dissociation occur in parallel (on the different molecules). Even if we monitor the initial process of complex formation soon after the mix‐ ing of the two solutions, it is impossible to separate forward and backward reactions com‐ pletely, and in the equilibrium, it is absolutely impossible to measure reaction kinetics, at least when the numbers of molecules are large. In SMI measurements, each association or dissociation event is detected individually; therefore, after the observations, association (or dissociation) events can be selected for pure kinetic analysis of association (dissociation) re‐ actions. Because of this, kinetic analysis based on SMI, is possible, even in the equilibrium (or steady state) conditions.

Structures of biological macromolecules, especially proteins, often show multiple metasta‐ ble points (this phenomenon is called polymorphism). Each single molecule is drifting among these metastable points in various timescales. post-translational modifications, such as phos‐ phorylation, may stabilize one or some of the metastable structures, according to each sin‐ gle molecule. SMI measurements are good to detect distributions and fluctuations of reactions and structures caused by static and dynamic polymorphisms of biological macromole‐ cules [3,9-11]. In some cases, non-random reactions of proteins have been detected using SMI [3,9,11].

### **2.2. Single molecule measurements in living cells**

the main subject of this chapter is the technical issue, these two examples of applications are chosen to explain how to analyze single-molecule data to understand kinetics of molecular interactions quantitatively in living cells. At the present time, we have several textbooks spe‐ cialized for the technologies and applications of SMI in a wide field [6-8]. Please refer to

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

**2. Motivation of Single-molecule Imaging Measurements of Molecular**

Before considering about technological issues, it might be important to discuss why we need SMI measurements of molecular interactions. The operation of biological molecular ma‐ chines is basically stochastic. Therefore, in ensemble average measurements, in which only the averages over a huge number of reaction events are observed, details of the reaction process are obscured. In SMI measurements, it is possible to virtually synchronize a particu‐ lar point in the reaction process for kinetic analysis. For example, imagine the observation of an enzyme reaction. The substrate solution is added to the enzyme solution to start the reac‐ tion. In ensemble measurements, the time of the two solutions mixing is set to time 0, and the concentration of the product is monitored with time. In the mixture, first, a substrate molecule needs to diffuse and collide with an enzyme molecule to form an enzyme-sub‐ strate (ES) complex; then, a chemical reaction starts on the enzyme molecule. The time 0 in ensemble measurements is not the time of ES complex formation. The time of ES complex formation is different for each molecule due to the stochasticity of molecular reactions, and this difference obscures the measurements of chemical reactions. In SMI measurements, the time point of each ES complex formation is detected, and after the observation, all the time points for individual molecules are aligned to time 0. Hence, in SMI measurements, we se‐ lectively extract the process of chemical reactions, removing the diffusion and collision for

This principle of SMI measurements also allows separation of forward and backward reac‐ tions. Here, imagine an association-dissociation reaction between two species of molecules. In the reaction mixture, both association and dissociation occur in parallel (on the different molecules). Even if we monitor the initial process of complex formation soon after the mix‐ ing of the two solutions, it is impossible to separate forward and backward reactions com‐ pletely, and in the equilibrium, it is absolutely impossible to measure reaction kinetics, at least when the numbers of molecules are large. In SMI measurements, each association or dissociation event is detected individually; therefore, after the observations, association (or dissociation) events can be selected for pure kinetic analysis of association (dissociation) re‐ actions. Because of this, kinetic analysis based on SMI, is possible, even in the equilibrium

Structures of biological macromolecules, especially proteins, often show multiple metasta‐ ble points (this phenomenon is called polymorphism). Each single molecule is drifting among

these books for information lacking in this chapter.

**2.1. Single-molecule versus ensemble-molecule measurements**

**Interactions**

Applications

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kinetic analysis.

(or steady state) conditions.

In a cellular context, it is difficult to perform long time-series analyses of the reaction on the same single molecules due to high density and lateral movements of the molecules. Howev‐ er, SMI measurements still have advantages over conventional ensemble average measure‐ ments. SMI allows *in situ,* non-destructive quantitative measurements. SMI measurements provide absolute values of the kinetic and dynamic parameters of the molecular reactions and dynamics, including number, density, reaction rate constants, lateral diffusion coeffi‐ cient, and transport velocity, with the smallest disruption of the living cell systems [8,12,13].

As mentioned above, for the time-series analyses, SMI measurements do not require physi‐ cal synchronization, which is indispensable in ensemble molecule measurements. Synchro‐ nization, like concentration or temperature jumps, generally alters the condition of cell cultures, possibly affecting many cellular reactions in addition to the subject of the experi‐ ment. Therefore, it sometimes becomes ambiguous if the changes of the measured value re‐ flect the reaction kinetics itself or the cellular dynamics triggered by the changed culture conditions. SMI measurements allow kinetic analysis in steady state, avoiding changes of culture conditions. For example, Hibino et al. [14] measured dissociation kinetics between two protein species, Ras and RAF, using SMI in quiescent cells in a steady state.

SMI measurements can detect small numbers of reactions in a limited volume inside living cells, because they are based on imaging with spatial resolution and possess the extreme sensitivity to detect single molecules. Using SMI measurement, Ueda et al. [15] measured the numbers and rate constants of the reactions between cAMP and its receptor, comparing the front and rear halves of a single *Dictyostelium* amoeba during chemotaxis. Tani et al. [16] analyzed reaction kinetics at the growth cone of nerve cells. These works have revealed that kinetic parameters of the same reactions diverged according to the positions in single cells. In addition, SMI measurements have directly revealed that cellular responses, such as neu‐ rite elongation [16] and calcium response [17], are caused by signaling of tens or hundreds of protein molecules.

The range of application of SMI measurements is broad, covering various fields of biological sciences of cells, including not only basic biochemistry and biophysics but systems biology, pathology of genetic diseases, action points analyses in pharmacology, and toxinology. SMI measurements provide absolute values of reaction parameters, which can be substituted in‐ to the reaction models described using mathematical equations. Since these values are deter‐ mined in live cell conditions, SMI measurements are good to use in combination with mathematical modeling constructed to explain and predict dynamics of complex intracellu‐ lar reaction networks.
