Related papers: Reduction for stochastic biochemical reaction netw…
Biochemical networks play a crucial role in biological systems, implementing a broad range of vital functions. They normally operate at low copy numbers and in spatial settings, but this is often ignored and well-stirred conditions are…
We present a method for estimating parameters in stochastic models of biochemical reaction networks by fitting steady-state distributions using Wasserstein distances. We simulate a reaction network at different parameter settings and train…
Models of reaction chemistry based on the stochastic simulation algorithm (SSA) have become a crucial tool for simulating complicated biological reaction networks due to their ability to handle extremely complicated reaction networks and to…
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some…
We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these…
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…
We present a novel multiscale simulation approach for modeling stochasticity in chemical reaction networks. The approach seamlessly integrates exact-stochastic and "leaping" methodologies into a single "partitioned leaping" algorithmic…
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…
The computer revolution has been driven by a sustained increase of computational speed of approximately one order of magnitude (a factor of ten) every five years since about 1950. In natural sciences this has led to a continuous increase of…
The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit…
In the past few decades, the development of fluorescent technologies and microscopic techniques has greatly improved scientists' ability to observe real-time single-cell activities. In this paper, we consider the filtering problem associate…
We present an efficient finite difference method for the approximation of second derivatives, with respect to system parameters, of expectations for a class of discrete stochastic chemical reaction networks. The method uses a coupling of…
Surfaces serve as highly efficient catalysts for a vast variety of chemical reactions. Typically, such surface reactions involve billions of molecules which diffuse and react over macroscopic areas. Therefore, stochastic fluctuations are…
A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be…
Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms to estimate system…
We consider the important problem of estimating parameter sensitivities for stochastic models of reaction networks that describe the dynamics as a continuous-time Markov process over a discrete lattice. These sensitivity values are useful…
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…
Motivation: Stochastic reaction networks are a widespread model to describe biological systems where the presence of noise is relevant, such as in cell regulatory processes. Unfortu-nately, in all but simplest models the resulting discrete…
Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…