Kinetics of nonstationary, single species, bimolecular, diffusion‐influenced irreversible reactions

Simulation of Biochemical Reactions with ANN-Dependent Kinetic Parameter Extraction Method

The measurement of thermodynamic properties of chemical or biological reactions were often confined to experimental means, which produced overall measurements of properties being investigated, but were usually susceptible to pitfalls of being too general. Among the thermodynamic properties that are of interest, reaction rates hold the greatest significance, as they play a critical role in reaction processes where speed is of essence, especially when fast association may enhance binding affinity of reaction molecules. Association reactions with high affinities often involve the formation of a intermediate state, which can be demonstrated by a hyperbolic reaction curve, but whose low abundance in reaction mixture often preclude the possibility of experimental measurement. Therefore, we resorted to computational methods using predefined reaction models that model the intermediate state as the reaction progresses. Here, we present a novel method called AKPE (ANN-Dependent Kinetic Parameter Extraction), our goal is to investigate the association/dissociation rate constants and the concentration dynamics of lowly-populated states (intermediate states) in the reaction landscape. To reach our goal, we simulated the chemical or biological reactions as system of differential equations, employed artificial neural networks (ANN) to model experimentally measured data, and utilized Particle Swarm Optimization (PSO) algorithm to obtain the globally optimum parameters in both the simulation and data fitting. In the Results section, we have successfully modeled a protein association reaction using AKPE, obtained the kinetic rate constants of the reaction, and constructed a full concentration versus reaction time curve of the intermediate state during the reaction. Furthermore, judging from the various validation methods that the method proposed in this paper has strong robustness and accuracy.

Combined effect of periodic gates and external fields on the diffusion coefficient of a single particle

A general analytical expression to describe the diffusion of a single particle in a one-dimensional lattice with periodically distributed gates of lifetime (tau) and while under the influence of a constant external field is calculated. A formulation based on a microscopic model and a diffusion relaxation condition is used to derive an equation for the diffusion coefficient as a function of the concentration of gates (c), the lifetime (tau) of such gates, and the strength of the external field (p). The theory is compared against Monte Carlo simulations, and limiting cases are used to reproduce previously published results on a variety of phenomena.

Single species diffusion-influenced reaction A+A-->alphaA: validity of the smoluchowski approach

We investigate the single species diffusion-influenced reaction, A+A-->alphaA with a finite reactivity in all dimensions. The reaction model includes a pure coagulation (alpha=1) or a pure annihilation (alpha=0) model. We apply the hierarchical Smoluchowski approach to study the dimensional aspects of the fluctuation, reactivity, particle size, and alpha(0</=alpha</=1). The theoretical results are compared with those of the Monte Carlo simulations in one, two, and three regular dimensions. The simulation results reveal that the classical Smoluchowski approach is exact in the short time limit in all dimensions and in the long time limit in three dimensions. The hierarchical Smoluchowski approach is found to be numerically exact at all times in two and three dimensions. A numerical method to obtain the exact result of the annihilation for a finite reactivity in one dimension is presented. We also propose a quite accurate analytic solution for an arbitrary alpha for the infinite reactivity in one dimension.