Related papers: Spatial-Stochastic Simulation of Reaction-Diffusio…
We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in…
We used various analytical and numerical techniques to elucidate signal propagation in a small enzymatic cascade which is subjected to external and internal noise. The nonlinear character of catalytic reactions, which underlie protein…
Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology,…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…
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…
Advances in nanotechnology have allowed scientists to study biological processes on an unprecedented nanoscale molecule-by-molecule basis, opening the door to addressing many important biological problems. A phenomenon observed in recent…
In this paper we survey recent work on the use of statistical model checking techniques for biological applications. We begin with an overview of the basic modelling techniques for biochemical reactions and their corresponding stochastic…
Understanding the dynamic nature of biological systems is fundamental to deciphering cellular behavior, developmental processes, and disease progression. Single-cell RNA sequencing (scRNA-seq) has provided static snapshots of gene…
Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at…
Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…
Capturing the structure of a data-generating process by means of appropriate inductive biases can help in learning models that generalize well and are robust to changes in the input distribution. While methods that harness spatial and…
There exist several methods for simulating biological and physical systems as represented by chemical reaction networks. Systems with low numbers of particles are frequently modelled as discrete-state Markov jump processes and are typically…
Biological cells rely on precise spatiotemporal coordination of biochemical reactions to control their many functions. Such cell signaling networks have been a common focus for mathematical models, but they remain challenging to simulate,…
Reaction networks in the bulk and on surfaces are widespread in physical, chemical and biological systems. In macroscopic systems, which include large populations of reactive species, stochastic fluctuations are negligible and the reaction…
Many biological activities are induced by cellular chemical reactions of diffusing reactants. The dynamics of such systems can be captured by stochastic reaction networks. A recent numerical study has shown that diffusion can significantly…
Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
Molecular dynamics simulations have the potential to provide atomic-level detail and insight to important questions in chemical physics that cannot be observed in typical experiments. However, simply generating a long trajectory is…
Within systems biology there is an increasing interest in the stochastic behavior of genetic and biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous…