Cell Signaling Reactions: Single-Molecular Kinetic Analysis

Showing of 4 extracted citations. Todd Washington , Maria Spies Methods in enzymology Exploration of the spontaneous fluctuating activity of single enzyme molecules. Anne Schwabe , Timo R. Maarleveld , Frank J. Bruggeman FEBS letters References Publications referenced by this paper.

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MATSUOKA Satomi

Noisy signal amplification in ultrasensitive signal transduction. Devreotes Annual review of biophysics Methods Mol Biol Single-molecule imaging of stochastic events in living cells. Single molecule imaging of green fluorescent proteins in living cells: Interestingly, the estimation of the rate constant was far more stable than that of the RSS, which allowed the accurate determination of rate constants for first-order reactions which were even faster than 0.

This result indicates that the overall trend of the reaction progress was preserved despite the presence of inaccuracies in the subpopulation ratio measured at each time point, which were caused by the number of trajectories acquired over a brief period being insufficient to rapidly extract subpopulation ratios of the complex states from the diffusion coefficient distribution.

Next, the effects of the diffusion coefficients of two complex states on determining rate constants were examined Fig. The rate constant estimates were accurate when the diffusion coefficient distribution of each state was well discerned. The RSS for the fitting of the reaction progress data started to increase as the diffusion coefficient distributions of the two states became inseparable Fig.

However, the estimation error for the rate constant was less stable compared to RSS because the uncertainty in the determination of the diffusion coefficient of each state from the diffusion coefficient distribution produced systematic bias for the extraction of the subpopulation ratio over the entire course of the reaction.

Because the uncertainty of the diffusion coefficient depends on the trajectory length, the estimation error for sptRPKA caused by an indistinguishable mixture of two diffusion coefficient distributions could be improved by using trajectories with longer lengths. However, to obtain longer trajectories, the particle density must be lowered to circumvent the high probability that more than one particle would be observed in a diffraction limit during tracking because of the complication of the correct linking of two particles in consecutive frames.

Research Areas

Thus, it was expected that the temporal resolution the fastest rate constant that could be accurately estimated of sptRPKA would be compromised if longer trajectories were used because the number of trajectories in a given time interval would be decreased. This inversely proportional relationship between the separability of the diffusion coefficient distribution and the temporal resolution of sptRPKA was observed with respect to trajectory length [see Fig. This result indicates that interconversion between the temporal resolution and the amount of diffusional information for sptRPKA can be accomplished by simply controlling the trajectory length, which can be adjusted according to the dynamic or static nature of the cellular processes of interest.

Lastly, the effect of the number of complex states on determining rate constants was explored. The first-order sequential reactions were analyzed simultaneously and this involved up to seven complex states under a condition of maximal separation among the mean diffusion coefficients of multiple states Fig. One of the benefits of using sptRPKA, in which a reaction is examined over an entire time course, is that the diffusion coefficient of each complex state can be determined at a different time point, such point when the complexity of the diffusion coefficient distribution for that state is the lowest e.

With this advantage, the reaction progress data Fig. However, it was not feasible to precisely estimate the rate constants for reactions involving more than five complex states because of the generation of inseparable diffusion coefficient distributions when significant amounts of all the complex states appeared simultaneously in the middle of the reaction.

It was confirmed that utilizing trajectories longer than 15 frames made it possible to estimate rate constants for the reactions with five complex states see Fig. Unlike simulated conditions, the membranes of living cells are structurally and dynamically heterogeneous.

It is uncertain whether diffusion coefficient distributions produced by multiple independent measurements of diffusion coefficients from individual trajectories acquired at different points in space and time on the membrane of a living cell can be sufficiently consistent for accurate comparisons over a long period of time.

Cell Signaling Reactions: Single-Molecular Kinetic Analysis - Google Книги

The cell morphology was not altered after the measurement, confirming that negligible photodamage to the cell occurred during the imaging see Fig. The diffusion coefficient was calculated from the EGFR trajectories using the following equation: EGFR is highly relevant to various types of cancers, 21 and cetuximab, a monoclonal antibody targeting EGFR, is an anti-cancer drug in clinical use. Because it had been confirmed statistically that the diffusion coefficient distribution of EGFR could be reliably obtained using trajectories longer than eight frames with a frame rate of The first such map was generated by treating COS-7 cells with immunoglobulin G IgG for 2 h following a mock treatment for 30 min to ensure that the basal steady state of the EGFR diffusional dynamics was not altered by nonspecific treatments Fig.

Next, the cells were treated with cetuximab 30 min after the mock treatment Fig. To objectively identify the number of EGFR complex states involved in this process, the EGFR diffusion coefficient distributions probability densities obtained after cetuximab treatment were subtracted from the distribution obtained before cetuximab treatment, and this representing the change in the distribution caused by cetuximab treatment.

Then, based on the Bayesian information criterion BIC analysis, the number of Gaussian mixtures were determined from the subtracted distributions that were transformed to a logarithmic scale because diffusion coefficients from a single state follow empirically a log normal distribution when the short trajectories are used. With increasing time after cetuximab treatment, the number of EGFR complex states increased from two to four Fig. This result indicates that at least four different EGFR complex states are involved in the cetuximab induced EGFR cellular process for up to 2 h after treatment.

Singular value decomposition analysis of the subtracted distribution, which provides a non-parametric criterion to determine the effective rank to properly represent the characteristics in both the diffusion coefficient and time dimension simultaneously, supported the number of states determined see Fig. Thus, it was predicted that this slow diffusive primarily immobilized subpopulation might represent a transient state of EGFR inside a CCP before its internalization into the cytosol. To examine whether this slow subpopulation induced by cetuximab was related to CCPs, the cells were pretreated with Pitstop 2, an inhibitor of clathrin-mediated endocytosis, 31 for 30 min prior to cetuximab treatment Fig.

However, the generation of the slow EGFR subpopulation induced by cetuximab treatment was substantially inhibited by the Pitstop 2 pretreatment. This result confirmed that multiple processes exhibiting at least two different reaction kinetics exist in the alterations of this fast diffusive subpopulation induced by cetuximab.

Interestingly, the kinetics were similar to the association rate constant k on of cetuximab binding to EGFR, 32 suggesting that this immediate decrease in the diffusion coefficient after cetuximab treatment represents the direct binding reaction of cetuximab to EGFR. Although the existence of EGFR predimers has been suggested in many cancer cells, 35 , 36 no discernible changes were detected in the other states indicating the predimers except for the monomeric EGFR and the cetuximab bound EGFR immediately after cetuximab treatment likely because the amount of EGFR predimers in COS-7 cells at its basal status is not significantly high.

The predimers might have been detected, if a significant amount exists, because cetuximab plays a role in the dissociation of a dimer to a monomer. A global fit was applied with independent weights of Gaussian mixtures and shared parameters mean and variance of Gaussian mixtures to the log-scaled time series diffusion-coefficient distributions with the distribution at 0 min subtracted. It was assumed that the subpopulation ratio of the state for basal free diffusive EGFR was equal to 1 at the initial time point because the subtracted distribution immediately after cetuximab treatment clearly showed that only the state for basal free-diffusive EGFR was reduced the upper second panel in Fig.

Then, a temporal profile of the relative subpopulation ratio of each state was generated by calculating the area under the curve of the time series distributions of each state normalized by subtracting the cetuximab insensitive states at the basal condition see Fig. Because the change in the total expression level of EGFR in a cell surface was negligible up to 2 h of cetuximab treatment, the sum of subpopulation ratios was kept as one up to 2 h see Fig.

Next, a reaction model was determined that explained the dynamic variations in the relative subpopulation ratios involving the four different complex states of EGFR induced by cetuximab for up to 2 h. However, a simple sequential reaction model with first-order kinetics could not explain the measurements Fig. The reversible reaction models could also not explain the data see Fig. While searching for a reaction model to best account for this data from the selection of plausible reaction models, it was found that the unknown state required a high order rate law to fit the data.

1. Introduction

To examine whether the CCP-trapped state was derived from the unknown state, both sequential and parallel reaction models were analyzed for the CCP-trapped state Fig. Because the number of parameters in these two models was the same, the RSS for each state was utilized as a criterion to determine the best model. As expected, these two models exhibited no significant differences in RSS for the basal EGFR and cetuximab bound EGFR states because the two models were distinguished from the unknown intermediate state.

However, the parallel reaction model did not fit the CCP-trapped state well, whereas the sequential reaction model fit it almost perfectly Fig. Furthermore, the residuals from the parallel model exhibited a predictive pattern, whereas a random pattern was observed in the sequential model and this implies that the parallel model cannot capture the entire explanatory information of the CCP-trapped state see Fig. Taken together, a cooperative sequential reaction model is the most probable model for the cetuximab induced EGFR endocytosis in the membrane of living cells Fig.

This result was confirmed by analyzing the cooperativity of the intermediate state in EGFR expression dependent manner see Fig. This cetuximab-induced EGFR clustering observed by using super-resolution microscopy was also recently reported by Gao et al.

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

It was observed that cetuximab induced EGFR internalization exhibited strong sigmoidal dependence on the surface expression level of EGFR across normal and cancer cell lines, which was predicted well using this model Fig. Furthermore, this model indicates that the first-order binding process of cetuximab to EGFR could not be a selective mechanism for both normal and cancer cells, which implies that the binding process represents a side effect, consistent with the phenomena that the affinity of anti-EGFR antibody drugs is directly proportional to the side effects of the drugs.

Use of sptRPKA enables the simultaneous analysis of the sub-minute kinetics of multiple complex states of a membrane protein in a living cell. Utilizing the protein's intrinsic diffusivity allows the detection of different complex states without a requirement for specific labeling, which is remarkably advantageous when these states are unknown. A hidden state detected with sptRPKA can be identified further by analyzing the states before and after the hidden state using traditional biochemical or imaging tools, such as chemical inhibitors or co-localization techniques.

Various kinetic parameters, including reaction models, rate constants, and stoichiometry for a series of molecular reactions in a living cell, can be obtained by performing a minimal number of experiments using sptRPKA. Furthermore, use of sptRPKA guarantees statistical reliability by obtaining one data point for RPKA using tens of thousands of single molecule trajectory data, which is critical because the quality of kinetic analyses largely depends on accurate measurements. Combined with computational simulations generated by the numerical integration of a set of differential equations, 45 , 46 sptRPKA can be used to determine reaction models for cellular processes occurring in the membrane of living cells with significantly less uncertainty than traditional graphical methods.

The acquisition of longer trajectories by adopting brighter and more stable organic dyes can provide additional diffusional information, such as confined and directed motions. This unique diffusional information can be used to classify the more complex states of membrane proteins that are difficult to classify using only a diffusion coefficient. Single molecule diffusivity was introduced to RPKA for analysing in vivo kinetics of cellular processes in an intact membrane of living cells. A previously unknown intermediate state was identified, which was a clustering of EGFR, essential for the antibody—drug selectivity to EGFR-overexpressing cancer cells.

The diffusivity of membrane proteins can be used to monitor different types of cellular processes, including protein oligomerization, 48 cytoskeletal protein confinement, 49 focal adhesion organization, 25 membrane microdomain formation, 50 and directed protein transport. National Center for Biotechnology Information , U. Journal List Chem Sci v. Published online Apr Author information Article notes Copyright and License information Disclaimer.