Related papers: Individual molecules dynamics in reaction network …
Stochastic simulation is a widely used method for estimating quantities in models of chemical reaction networks where uncertainty plays a crucial role. However, reducing the statistical uncertainty of the corresponding estimators requires…
Since gene regulatory systems contain sometimes only a small number of molecules, these systems are not described well by macroscopic rate equations; a master equation approach is needed for such cases. We develop an approximation scheme…
Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach…
Computational chemistry allows researchers to experiment in sillico: by running a computer simulations of a biological or chemical processes of interest. Molecular dynamics with molecular mechanics model of interactions simulates N-body…
Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often…
The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the…
We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte…
Traditional mathematical approaches to studying analytically the dynamics of neural networks rely on the mean-field approximation, which is rigorously applicable only to networks of infinite size. However, all existing real biological…
Finding reduced models of spatially-distributed chemical reaction networks requires an estimation of which effective dynamics are relevant. We propose a machine learning approach to this coarse graining problem, where a maximum entropy…
We present a numerical algorithm that allows the approximation of optimal controls for stochastic reaction-diffusion equations with additive noise by first reducing the problem to controls of feedback form and then approximating the…
The propagation of signalling molecules within cellular networks is affected by network topology, but also by the spatial arrangement of cells in the networks. Understanding the collective reaction--diffusion behaviour in space of signals…
We describe collective-move Monte Carlo algorithms designed to approximate the overdamped dynamics of self-assembling nanoscale components equipped with strong, short-ranged and anisotropic interactions. Conventional Monte Carlo simulations…
We show how one can trace in a systematic way the coarse-grained solutions of individual-based stochastic epidemic models evolving on heterogeneous complex networks with respect to their topological characteristics. In particular, we have…
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…
Tracking of objects in cellular environments has become a vital tool in molecular cell biology. A particularly important example is single molecule tracking which enables the study of the motion of a molecule in cellular environments and…
Mathematical models of gene regulatory networks are widely used to study cell fate changes and transcriptional regulation. When designing such models, it is important to accurately account for sources of stochasticity. However, doing so can…
Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical…
In this paper a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect…
The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or…
Reaction networks are often used to model interacting species in fields such as biochemistry and ecology. When the counts of the species are sufficiently large, the dynamics of their concentrations are typically modeled via a system of…