相关论文: On the Hill relation and the mean reaction time fo…
In molecular dynamics, statistics of transitions, such as the mean transition time, are macroscopic observables which provide important dynamical information on the underlying microscopic stochastic process. A direct estimation using…
This study address the computational determination of catalytic reaction rates by moving beyond traditional Transition State Theory (TST), addressing its limitations in complex systems. The Hill relation framework, integrated with Adaptive…
A perturbation framework is developed to analyze metastable behavior in stochastic processes with random internal and external states. The process is assumed to be under weak noise conditions, and the case where the deterministic limit is…
The probability that a configuration of a physical system reacts, or transitions from one metastable state to another, is quantified by the committor function. This function contains richly detailed mechanistic information about transition…
In this paper, we consider semi-Markov processes whose transition times and transition probabilities depend on a small parameter $\varepsilon$. Understanding the asymptotic behavior of such processes is needed in order to study the…
The Hill function is relevant for describing enzyme binding and other processes in gene regulatory networks. Despite its theoretical foundation, it is often empirically used as a useful fitting function. Theoretical predictions suggest that…
Biochemical systems are inherently stochastic, particularly those with small-molecule populations. The spatial distribution of molecules plays a critical role and requires the inclusion of spatial coordinates in their analysis. Stochastic…
We are interested in the connection between a metastable continuous state space Markov process (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process in a discrete state space. More precisely, we use the…
We develop a quasilinear theory of the Vlasov equation in order to describe the approach of systems with long-range interactions to quasi-stationary states. We derive a diffusion equation governing the evolution of the velocity distribution…
The reversible A <-> B reaction-diffusion process, when species A and B are initially mixed and diffuse with different diffusion coefficients, is investigated using the boundary layer function method. It is assumed that the ratio of the…
Describing reaction rates in stochastic bio-circuits is commonly done by directly introducing the deterministically deduced Hill function into the master equation. However, when fluctuations in enzymatic reaction rates are not neglectable,…
We consider reversible ergodic Markov chains with finite state space, and we introduce a new notion of quasi-stationary distribution that does not require the presence of any absorbing state. In our setting, the hitting time of the…
Non-Maxwellian distributions are commonly observed across a wide range of systems and scales. While direct observations provide the strongest evidence for these distributions, they also manifest indirectly through their influence on…
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…
Dissipation and fluctuations of one-body observables in heavy-ion reactions around the Coulomb barrier are investigated with a microscopic stochastic mean-field approach. By projecting the stochastic mean-field dynamics on a suitable…
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…
Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant…
In this paper we reconsider the Mass Action Law (MAL) for the anomalous reversible reaction $A\rightleftarrows B$ with diffusion. We provide a mesoscopic description of this reaction when the transitions between two states $A$ and $B$ are…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
We consider a system of reaction-diffusion equations in a bounded interval of the real line, with emphasis on the metastable dynamics, whereby the time-dependent solution approaches the steady state in an asymptotically exponentially long…