Related papers: Adaptive Hybrid Simulations for Multiscale Stochas…
The application of the quasi-steady-state approximation to the Michaelis-Menten reaction embedded in large open chemical reaction networks is a popular model reduction technique in deterministic and stochastic simulations of biochemical…
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…
At the cellular scale, biochemical processes are governed by random interactions between reactant molecules with small copy counts, leading to behavior that is inherently stochastic. Such systems are often modeled as continuous-time Markov…
In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate…
We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process, computational cost can be prohibitive for networks of…
The stochastic dynamics of biochemical reaction networks can be accurately described by discrete-state Markov processes where each chemical reaction corresponds to a state transition of the process. Due to the largeness problem of the state…
Numerical solution of the chemical master equation for stochastic reaction networks typically suffers from the state space explosion problem due to the curse of dimensionality and from stiffness due to multiple time scales. The dimension of…
We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…
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…
Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on $\mathbb Z^d_{\ge 0}$, and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes,…
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…
The behavior of some stochastic chemical reaction networks is largely unaffected by slight inaccuracies in reaction rates. We formalize the robustness of state probabilities to reaction rate deviations, and describe a formal connection…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
The discrete chemical master equation (dCME) provides a fundamental framework for studying stochasticity in mesoscopic networks. Because of the multi-scale nature of many networks where reaction rates have large disparity, directly solving…
While ordinary differential equations (ODEs) form the conceptual framework for modelling many cellular processes, specific situations demand stochastic models to capture the influence of noise. The most common formulation of stochastic…
We consider the problem of estimating parameter sensitivities for stochastic models of multiscale reaction networks. These sensitivity values are important for model analysis, and, the methods that currently exist for sensitivity estimation…
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…
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…
The stochastic kinetics of BRN are described by a chemical master equation (CME) and the underlying laws of mass action. The CME must be usually solved numerically by generating enough traces of random reaction events. The resulting…
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via…