![]() ![]() Mavrovouniotis, "Simplification of Mathematical Models of Chemical Reaction Systems," Chemical Rev., vol. Kaznessis, "An Adaptive Time Step Scheme for a System of Stochastic Differential Equations with Multiple Multiplicative Noise: Chemical Langevin Equation, a Proof of Concept," J. Gillespie, "The Chemical Langevin Equation," J. Khammash, "The Finite State Projection Algorithm for the Solution of the Chemical Master Equation," J. Eijnden, "Nested Stochastic Simulation Algorithm for Chemical Kinetic Systems with Disparate Rates," J. Burrage, "Binomial Leap Methods for Simulating Stochastic Chemical Kinetics," J. Petzold, "The Slow-Scale Stochastic Simulation Algorithm," J. Petzold, "Efficient Formulation of the Stochastic Simulation Algorithm for Chemically Reacting Systems," J. Vlachos, "Overcoming Stiffness in Stochastic Simulation Stemming from Partial Equilibrium: A Multiscale Monte Carlo Algorithm," J. Kaznessis, "Accurate Hybrid Stochastic Simulation of a System of Coupled Chemical or Biochemical Reactions," J. Kaznessis, "An Equation-Free Probabilistic Steady-State Approximation: Dynamic Application to the Stochastic Simulation of Biochemical Reaction Networks," J. Arkin, "Stochastic Chemical Kinetics and the Quasi-Steady-State Assumption: Application to the Gillespie Algorithm," J. Gillespie, "Approximate Accelerated Stochastic Simulation of Chemically Reacting Systems," J. Bruck, "Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels," J. Gillespie, "Exact Stochastic Simulation of Coupled Chemical Reactions," J. Gillespie, "A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions," J. Swain, "Stochastic Gene Expression in a Single Cell," Science, vol. Kaznessis, "Computer-Aided Design of Modular Protein Devices: Boolean AND Gene Activation," Physical Biology, vol. Kaznessis, "Synthetic Tetracycline Inducible Regulatory Networks: Computer-Aided Design of Dynamic Phenotypes," BMC Systems Biology, vol. Kaznessis, "Model-Driven Designs of an Oscillating Gene Network," Biophysical J., vol. Kaznessis, "Numerical Simulation of Stochastic Gene Circuits," Computers and Chemical Eng., vol. Arkin, "Fifteen Minutes of Fim: Control of Type 1 Pili Expression in E. Kaznessis, "Multi-Scale Models for Gene Network Engineering," Chemical Eng. Collins, "Stochasticity in Gene Expression: From Theories to Phenotypes," Nature Rev. Kaznessis, "Models for Synthetic Biology," BMC Systems Biology, vol. We describe and illustrate the application of a semianalytical reduction framework for chemical Langevin equations that results in significant gains in computational cost. These are particularly challenging systems to model, requiring prohibitively small integration step sizes. In this paper, the focus is on the dynamics of reaction sets governed by stiff chemical Langevin equations, i.e., stiff stochastic differential equations. In the last decade, significant efforts have been expended on the development of stochastic chemical kinetics models to capture the dynamics of biomolecular systems, and on the development of robust multiscale algorithms, able to handle stiffness. Second, models must take into consideration the disparate spectrum of time scales observed in biological phenomena, such as slow transcription events and fast dimerization reactions. Often, biological systems cannot be modeled with traditional continuous-deterministic models. First, models must account for the inherent probabilistic nature of systems far from the thermodynamic limit. Two very important characteristics of biological reaction networks need to be considered carefully when modeling these systems. ![]()
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