Related papers: Rigorous derivation of Michaelis-Menten kinetics i…
Enzyme-catalysed reactions involve two distinct timescales. There is a short timescale on which enzymes bind to substrate molecules to produce bound complexes, and a comparatively long timescale on which the complex is transformed into a…
Catalytically active enzymes have recently been observed to exhibit enhanced diffusion. In a recent work [C. Riedel et al., Nature 517, 227 (2015)], it has been suggested that this phenomenon is correlated with the degree of exothermicity…
A central challenge in materials science is characterizing chemical processes that are elusive to direct measurement, particularly in functional materials operating under realistic conditions. Here, we demonstrate that mechanical strain…
The century-long Michaelis-Menten rate law and its modifications in the modeling of biochemical rate processes stand on the assumption that the concentration of the complex of interacting molecules, at each moment, rapidly approaches an…
We present a model of an ATP-fueled molecular machine which push a polymer through a pore channel. The machine acts between two levels (working-waiting), and the working one remains active for a fixed time giving a constant force. The…
We study a class of Stochastic Differential Equations (SDEs) with jumps modeling multistage Michaelis--Menten enzyme kinetics, in which a substrate is sequentially transformed into a product via a cascade of intermediate complexes. These…
Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with…
The chemical master equation (CME) is the exact mathematical formulation of chemical reactions occurring in a dilute and well-mixed volume. The reaction-diffusion master equation (RDME) is a stochastic description of reaction-diffusion…
There is a vast amount of literature concerning the appropriateness of various perturbation parameters for the standard quasi-steady state approximation in the Michaelis-Menten reaction mechanism, and also concerning the relevance of these…
A hybrid mesoscopic multi-particle collision model is used to study diffusion-influenced reaction kinetics. The mesoscopic particle dynamics conserves mass, momentum and energy so that hydrodynamic effects are fully taken into account.…
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…
In this paper, a new method to efficiently simulate diffusion controlled second order chemical reactions is derived and applied to site-specific DNA-binding proteins. The protein enters a spherical cell and propagates via two competing…
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…
Quantum mechanics/molecular mechanics (QM/MM) is a standard computational tool for describing chemical reactivity in systems with many degrees of freedom, including polymers, enzymes, and reacting molecules in complex solvents. However,…
Recent fluorescence spectroscopy measurements of single-enzyme kinetics have shown that enzymatic turnovers form a renewal stochastic process in which the inverse of the mean waiting time between turnovers follows the Michaelis-Menten…
Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special…
We study kinetics of single species reactions ("A+A -> 0") for general local reactivity Q and dynamical exponent z (rms displacement x_t ~ t^{1/z}.) For small molecules z=2, whilst z=4,8 for certain polymer systems. For dimensions d above…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
The kinetics of geminate subdiffusion-assisted reactions (SDARs) of interacting particles is analyzed in detail with the use of the non-Markovian fractional Smoluchowki equation (FSE). It is suggested that the interparticle interaction…
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…