Related papers: Approximation scheme based on effective interactio…
A widely used approach to describe the dynamics of gene regulatory networks is based on the chemical master equation, which considers probability distributions over all possible combinations of molecular counts. The analysis of such models…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
We present an approach for constructing dynamic models for the simulation of gene regulatory networks from simple computational elements. Each element is called a ``gene gate'' and defines an input/output-relationship corresponding to the…
Engineering biology requires precise control of biomolecular circuits, and Cybergenetics is the field dedicated to achieving this goal. A significant challenge in developing controllers for cellular functions is designing systems that can…
Many cellular behaviors are regulated by gene regulation networks, kinetics of which is one of the main subjects in the study of systems biology. Because of the low number molecules in these reacting systems, stochastic effects are…
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…
A detailed stochastic model of single-gene auto-regulation is established and its solutions are explored when mRNA dynamics is fast compared with protein dynamics and in the opposite regime. The model includes all the sources of randomness…
We study an approximation scheme based on a second quantization method for a chemical master equation. Small systems, such as cells, could not be studied by the traditional rate equation approach because fluctuation effects are very large…
The chemical master equation (CME), which describes the discrete and stochastic molecule number dynamics associated with biological processes like transcription, is difficult to solve analytically. It is particularly hard to solve for…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible…
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
There has been an increasing demand for formal methods in the design process of safety-critical synthetic genetic circuits. Probabilistic model checking techniques have demonstrated significant potential in analyzing the intrinsic…
Biochemical reactions involving three or more reactants, called higher-molecular reactions, play an important role in theoretical systems and synthetic biology. In particular, such reactions underpin a variety of important bio-dynamical…
We show how to construct a reduced description of interacting genes in noisy, small regulatory networks using coupled binary "spin" variables. Treating both the protein number and gene expression state variables stochastically and on equal…
This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the…
The recent development of single-cell transcriptomics has enabled gene expression to be measured in individual cells instead of being population-averaged. Despite this considerable precision improvement, inferring regulatory networks…
Models invoking the chemical master equation are used in many areas of science, and, hence, their simulation is of interest to many researchers. The complexity of the problems at hand often requires considerable computational power, so a…