Related papers: Stochastic analysis of a miRNA-protein toggle swit…
Stochastic kinetic models describe systems across biology, chemistry, and physics where discrete events and small populations render deterministic approximations inadequate. Parameter inference and inverse design in these systems require…
Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems…
Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations…
Bistable biochemical switches are ubiquitous in gene regulatory networks and signal transduction pathways. Their switching dynamics, however, are difficult to study directly in experiments or conventional computer simulations, because…
Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or 'noise', is predominantly generated by interactions of the system…
The chemical birth-death process, whose chemical master equation (CME) is exactly solvable, is a paradigmatic toy problem often used to get intuition for how stochasticity affects chemical kinetics. In a certain limit, it can be…
The optimal control of epidemic-like stochastic processes is important both historically and for emerging applications today, where it can be especially important to include time-varying parameters that impact viral epidemic-like…
We discuss the symbolic dynamics of biochemical networks with separate timescales. We show that symbolic dynamics of monomolecular reaction networks with separated rate constants can be described by deterministic, acyclic automata with a…
The importance of stochasticity within biological systems has been shown repeatedly during the last years and has raised the need for efficient stochastic tools. We present SABRE, a tool for stochastic analysis of biochemical reaction…
Stochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential-equation approach by generating typical system histories instead of just statistical measures such as the mean and…
Bistability is considered wide-spread among bacteria and eukaryotic cells, useful e.g. for enzyme induction, bet hedging, and epigenetic switching. However, this phenomenon has mostly been described with deterministic dynamic or well-mixed…
Cell-to-cell variability is inherent to numerous biological processes, including cell migration. Quantifying and characterizing the variability of migrating cells is challenging, as it requires monitoring many cells for long time windows…
We study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion equation governing the nutrient proportion. We prove strong…
Chemical reaction networks offer a natural nonlinear generalisation of linear Markov jump processes on a finite state-space. In this paper, we analyse the dynamical large deviations of such models, starting from their microscopic version,…
The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially…
Planning of biorefinery operations is complicated by the stochastic nature of physical and chemical characteristics of biomass feedstock, such as, moisture level and carbohydrate content. Biomass characteristics affect the performance of…
The diversity of cell populations is regulated by extracellular and intracellular variability. The latter includes genetic, epigenetic and stochastic variability, all contributing to the experimentally observed heterogeneity in response to…
Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to…
During tissue development, patterns of gene expression determine the spatial arrangement of cell types. In many cases, gradients of secreted signaling molecules - morphogens - guide this process. The continuous positional information…
Biochemical reactions with oscillatory behavior play an essential role in synthetic biology at the microscopic scale. Although a robust stability theory for deterministic chemical oscillators in the macroscopic limit exists, the dynamical…