Nonclassical Kinetics of Clonal yet Heterogeneous Enzymes

Comparing the interactions of nitrendipine with lysozyme or human serum albumin and the effects of vitamin C and naringin on these interactions by spectroscopy and molecular docking methods

The interactions between drugs and proteins play a pivotal role in determining the pharmacological effects and disposition of drugs within the human body. This study focuses on exploring the interaction between nitrendipine and lysozyme/human serum albumin. Spectroscopic analysis indicated a compound static quenching, indicative of the formation of stable complexes between the drug and proteins. The addition of vitamin C or naringin resulted in a decrease of the binding constant between nitrendipine and lysozyme/human serum albumin. The presence of these compounds may disrupt the interactions between the drug and proteins, potentially leading to an increased concentration of free nitrendipine in the bloodstream. Nitrendipine binds more easily to human serum albumin at 310 K, and human serum albumin has an average binding site ratio with nitrendipine approximately 0.1 higher than that with lysozyme. Vitamin C has a greater impact on the binding constant of nitrendipine to human serum albumin and lysozyme. Compared to the binary system of proteins with the drug, the ternary system with the addition of vitamin C at 310 K reduces the binding constants of lysozyme and human serum albumin by 85%. In conclusion, this study explores the significance of considering drug-protein interactions in understanding drug behavior and potential drug-food interactions.

Reaction-path statistical mechanics of enzymatic kinetics

We introduce a reaction-path statistical mechanics formalism based on the principle of large deviations to quantify the kinetics of single-molecule enzymatic reaction processes under the Michaelis-Menten mechanism, which exemplifies an out-of-equilibrium process in the living system. Our theoretical approach begins with the principle of equal a priori probabilities and defines the reaction path entropy to construct a new nonequilibrium ensemble as a collection of possible chemical reaction paths. As a result, we evaluate a variety of path-based partition functions and free energies by using the formalism of statistical mechanics. They allow us to calculate the timescales of a given enzymatic reaction, even in the absence of an explicit boundary condition that is necessary for the equilibrium ensemble. We also consider the large deviation theory under a closed-boundary condition of the fixed observation time to quantify the enzyme-substrate unbinding rates. The result demonstrates the presence of a phase-separation-like, bimodal behavior in unbinding events at a finite timescale, and the behavior vanishes as its rate function converges to a single phase in the long-time limit.

Stochastic Kinetics of Nanocatalytic Systems

Catalytic reaction events occurring on the surface of a nanoparticle constitute a complex stochastic process. Although advances in modern single-molecule experiments enable direct measurements of individual catalytic turnover events occurring on a segment of a single nanoparticle, we do not yet know how to measure the number of catalytic sites in each segment or how the catalytic turnover counting statistics and the catalytic turnover time distribution are related to the microscopic dynamics of catalytic reactions. Here, we address these issues by presenting a stochastic kinetics for nanoparticle catalytic systems. We propose a new experimental measure of the number of catalytic sites in terms of the mean and variance of the catalytic event count. By considering three types of nanocatalytic systems, we investigate how the mean, the variance, and the distribution of the catalytic turnover time depend on the catalytic reaction dynamics, the heterogeneity of catalytic activity, and communication among catalytic sites. This work enables accurate quantitative analyses of single-molecule experiments for nanocatalytic systems and enzymes with multiple catalytic sites.

Frequency spectrum of chemical fluctuation: A probe of reaction mechanism and dynamics

Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically, and the frequency spectrum of this chemical fluctuation carries valuable information about the dynamics of the reactions creating these biomolecules. Recent advances in single-cell techniques enable direct monitoring of the time-traces of the protein number in each cell; however, it is not yet clear how the stochastic dynamics of these time-traces is related to the reaction mechanism and dynamics. Here, we derive a rigorous relation between the frequency-spectrum of the product number fluctuation and the reaction mechanism and dynamics, starting from a generalized master equation. This relation enables us to analyze the time-traces of the protein number and extract information about dynamics of mRNA number and transcriptional regulation, which cannot be directly observed by current experimental techniques. We demonstrate our frequency spectrum analysis of protein number fluctuation, using the gene network model of luciferase expression under the control of the Bmal 1a promoter in mouse fibroblast cells. We also discuss how the dynamic heterogeneity of transcription and translation rates affects the frequency-spectra of the mRNA and protein number.

Anomalous Dynamics of in Vivo Cargo Delivery by Motor Protein Multiplexes

Vesicle transport conducted by motor protein multiplexes (MPMs), which is ubiquitous among eukaryotes, shows anomalous and stochastic dynamics qualitatively different from the dynamics of thermal motion and artificial active matter; the relationship between in vivo vesicle-delivery dynamics and the underlying physicochemical processes is not yet quantitatively understood. Addressing this issue, we perform accurate tracking of individual vesicles, containing upconverting nanoparticles, transported by kinesin-dynein-multiplexes along axonal microtubules. The mean-square-displacement of vesicles along the microtubule exhibits unusual dynamic phase transitions that are seemingly inconsistent with the scaling behavior of the mean-first-passage time over the travel length. These paradoxical results and the vesicle displacement distribution are quantitatively explained and predicted by a multimode MPM model, developed in the current work, where ATP-hydrolysis-coupled motion of MPM has both unidirectional and bidirectional modes.

Bridging the Micro-Macro Gap between Single-Molecular Behavior and Bulk Hydrolysis Properties of Cellulase

The microscopic kinetics of enzymes at the single-molecule level often deviate considerably from those expected from bulk biochemical experiments. Here, we propose a coarse-grained-model approach to bridge this gap, focusing on the unexpectedly slow bulk hydrolysis of crystalline cellulose by cellulase, which constitutes a major obstacle to mass production of biofuels and biochemicals. Building on our previous success in tracking the movements of single molecules of cellulase on crystalline cellulose, we develop a mathematical description of the collective motion and function of enzyme molecules hydrolyzing the surface of cellulose. Model simulations robustly explained the experimental findings at both the microscopic and macroscopic levels and revealed a hitherto-unknown mechanism causing a considerable slowdown of the reaction, which we call the crowding-out effect. The size of the cellulase molecule impacted significantly on the collective dynamics, whereas the rate of molecular motion on the surface did not.

The Chemical Fluctuation Theorem governing gene expression

Gene expression is a complex stochastic process composed of numerous enzymatic reactions with rates coupled to hidden cell-state variables. Despite advances in single-cell technologies, the lack of a theory accurately describing the gene expression process has restricted a robust, quantitative understanding of gene expression variability among cells. Here we present the Chemical Fluctuation Theorem (CFT), providing an accurate relationship between the environment-coupled chemical dynamics of gene expression and gene expression variability. Combined with a general, accurate model of environment-coupled transcription processes, the CFT provides a unified explanation of mRNA variability for various experimental systems. From this analysis, we construct a quantitative model of transcription dynamics enabling analytic predictions for the dependence of mRNA noise on the mRNA lifetime distribution, confirmed against stochastic simulation. This work suggests promising new directions for quantitative investigation into cellular control over biological functions by making complex dynamics of intracellular reactions accessible to rigorous mathematical deductions.

A unified framework to understand gene expression noise is still lacking. Here the authors derive a universal theorem relating the biological noise with dynamics of birth and death processes and present a model of transcription dynamics, allowing analytical prediction of the dependence of mRNA noise on mRNA lifetime variability.