The stochastic simulation algorithm （SSA） accurately depicts spatially homogeneous wellstirred chemically reacting systems with small populations of chemical species and properly represents noise, but it is often ab...The stochastic simulation algorithm （SSA） accurately depicts spatially homogeneous wellstirred chemically reacting systems with small populations of chemical species and properly represents noise, but it is often abandoned when modeling larger systems because of its computational complexity. In this work, a twin support vector regression based stochastic simulations algorithm （TS^3A） is proposed by combining the twin support vector regression and SSA, the former is a well-known robust regression method in machine learning. Numerical results indicate that this proposed algorithm can be applied to a wide range of chemically reacting systems and obtain significant improvements on efficiency and accuracy with fewer simulating runs over the existing methods.展开更多
The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifyi...The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifying the propensity of the diffusive jump over the reactive boundary. As compared to the literature, the present approach does not require any correction factors for the propensity. Also, the current expression relaxes the constraint on the compartment size allowing the problem to be solved with a coarser grid and therefore saves considerable computational cost. The modified algorithm is then applied to simulate three reaction-diffusion systems with reactive boundaries.展开更多
In this paper,we revisit the Nested Stochastic Simulation Algorithm(NSSA)for stochastic chemical reacting networks by first proving its strong convergence.We then study a speed up of the algorithm by using the explici...In this paper,we revisit the Nested Stochastic Simulation Algorithm(NSSA)for stochastic chemical reacting networks by first proving its strong convergence.We then study a speed up of the algorithm by using the explicit Tau-Leaping method as the Inner solver to approximate invariant measures of fast processes,for which strong error estimates can also be obtained.Numerical experiments are presented to demonstrate the validity of our analysis.展开更多
Presented here is an L-leap method for accelerating stochastic simulation of well-stirred chemically reacting systems, in which the number of reactions occurring in a reaction channel with the largest propensity funct...Presented here is an L-leap method for accelerating stochastic simulation of well-stirred chemically reacting systems, in which the number of reactions occurring in a reaction channel with the largest propensity function is calculated from the leap condition and the number of reactions occurring in the other reaction channels are generated by using binomial random variables during a leap. The L-leap method can better satisfy the leap condition. Numerical simulation results indicate that the L-leap method can obtain better performance than established methods.展开更多
In this paper, we develop a modified accelerated stochastic simulation method for chemically reacting systems, called the ＂final all possible steps＂ （FAPS） method, which obtains the reliable statistics of all spec...In this paper, we develop a modified accelerated stochastic simulation method for chemically reacting systems, called the ＂final all possible steps＂ （FAPS） method, which obtains the reliable statistics of all species in any time during the time course with fewer simulation times. Moreover, the FAPS method can be incorporated into the leap methods, which makes the simulation of larger systems more efficient. Numerical results indicate that the proposed methods can be applied to a wide range of chemically reacting systems with a high-precision level and obtain a significant improvement on efficiency over the existing methods.展开更多
Biochemical systems have numerous practical applications, in particular to the study of critical intracellular processes. Frequently, biochemical kinetic models depict cellular processes as systems of chemical reactio...Biochemical systems have numerous practical applications, in particular to the study of critical intracellular processes. Frequently, biochemical kinetic models depict cellular processes as systems of chemical reactions. Many biological processes in a cell are inherently stochastic, due to the existence of some low molecular amounts. These stochastic fluctuations may have a great effect on the biochemical system’s behaviour. In such cases, stochastic models are necessary to accurately describe the system’s dynamics. Biochemical systems at the cellular level may entail many species or reactions and their mathematical models may be non-linear and with multiple scales in time. In this work, we provide a numerical technique for simplifying stochastic discrete models of well-stirred biochemical systems, which ensures that the main properties of the original system are preserved. The proposed technique employs sensitivity analysis and requires solving an optimization problem. The numerical tests on several models of practical interest show that our model reduction strategy performs very well.展开更多
Cellular environments are in essence stochastic, owing to the random character of the biochemical reaction events in a single cell. Stochastic fluctuations may substantially contribute to the dynamics of systems with ...Cellular environments are in essence stochastic, owing to the random character of the biochemical reaction events in a single cell. Stochastic fluctuations may substantially contribute to the dynamics of systems with small copy numbers of some biochemical species. Then, stochastic models are indispensable for properly portraying the behaviour of the system. Sensitivity analysis is one of the central tools for studying stochastic models of cellular dynamics. Here, we propose some finite-difference strategies for estimating parametric sensitivities of higher-order moments of the system state for stochastic discrete biochemical kinetic models. To reduce the variance of the sensitivity estimator, we employ various coupling techniques. The advantages of the proposed methods are illustrated in several models of biochemical systems of practical relevance.展开更多
We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics.The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a cons...We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics.The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo method to simulate time-dependent statistical characteristics of growing cell populations.To benchmark performance,we compare simulation results with steadystate and time-dependent analytical solutions for several scenarios,including steadystate and time-dependent gene expression,and the effects on population heterogeneity of cell growth,division,and DNA replication.This comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene expression.We also use the algorithm to model gene expression dynamics within"bet-hedging"cell populations during their adaption to environmental stress.These simulations indicate that the algorithm provides a framework suitable for simulating and analyzing realistic models of heterogeneous population dynamics combining molecular-level stochastic reaction kinetics,relevant physiological details and phenotypic variability.展开更多
We use the recently proposed Nested Stochastic Simulation Algorithm(Nested SSA)to simulate the cell cycle model for budding yeast.The results show that Nested SSA is able to significantly reduce the computational cost...We use the recently proposed Nested Stochastic Simulation Algorithm(Nested SSA)to simulate the cell cycle model for budding yeast.The results show that Nested SSA is able to significantly reduce the computational cost while capturing the essential dynamical features of the system.展开更多
A methodology for kinetic modeling of conversion processes is presented.The proposed approach allows to overcome the lack of molecular detail of the petroleum fractions and to simulate the reactions of the process by ...A methodology for kinetic modeling of conversion processes is presented.The proposed approach allows to overcome the lack of molecular detail of the petroleum fractions and to simulate the reactions of the process by means of a two-step procedure.In the first step,a synthetic mixture of molecules representing the feedstock is generated via a molecular reconstruction method,termed SR-REM molecular reconstruction.In the second step,a kinetic Monte Carlo method,termed stochastic simulation algorithm(SSA),is used to simulate the effect of the conversion reactions on the mixture of molecules.The resulting methodology is applied to the Athabasca vacuum residue hydrocracking.An adequate molecular representation of the vacuum residue is obtained using the SR-REM algorithm.The reaction simulations present a good agreement with the laboratory data for Athabasca vacuum residue conversion.In addition,the proposed methodology provides the molecular detail of the vacuum residue conversion throughout the reactions simulations.展开更多
We present an accelerated method for stochastically simulating the dynamics of heterogeneous cell populations.The algorithm combines a Monte Carlo approach for simulating the biochemical kinetics in single cells with ...We present an accelerated method for stochastically simulating the dynamics of heterogeneous cell populations.The algorithm combines a Monte Carlo approach for simulating the biochemical kinetics in single cells with a constant-number Monte Carlo method for simulating the reproductive fitness and the statistical characteristics of growing cell populations.To benchmark accuracy and performance,we compare simulation results with those generated from a previously validated population dynamics algorithm.The comparison demonstrates that the accelerated method accurately simulates population dynamics with significant reductions in runtime under commonly invoked steady-state and symmetric cell division assumptions.Considering the increasing complexity of cell population models,the method is an important addition to the arsenal of existing algorithms for simulating cellular and population dynamics that enables efficient,coarse-grained exploration of parameter space.展开更多
基金This work was supported by the National Natural Science Foundation of China （No.30871341）, the National High-Tech Research and Development Program of China （No.2006AA02-Z190）, the Shanghai Leading Academic Discipline Project （No.S30405）, and the Natural Science Foundation of Shanghai Normal University （No.SK200937）.
文摘The stochastic simulation algorithm （SSA） accurately depicts spatially homogeneous wellstirred chemically reacting systems with small populations of chemical species and properly represents noise, but it is often abandoned when modeling larger systems because of its computational complexity. In this work, a twin support vector regression based stochastic simulations algorithm （TS^3A） is proposed by combining the twin support vector regression and SSA, the former is a well-known robust regression method in machine learning. Numerical results indicate that this proposed algorithm can be applied to a wide range of chemically reacting systems and obtain significant improvements on efficiency and accuracy with fewer simulating runs over the existing methods.
文摘The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifying the propensity of the diffusive jump over the reactive boundary. As compared to the literature, the present approach does not require any correction factors for the propensity. Also, the current expression relaxes the constraint on the compartment size allowing the problem to be solved with a coarser grid and therefore saves considerable computational cost. The modified algorithm is then applied to simulate three reaction-diffusion systems with reactive boundaries.
基金The research of D.Liu and C.Huang is supported by National Science Foundation DMS0845061.
文摘In this paper,we revisit the Nested Stochastic Simulation Algorithm(NSSA)for stochastic chemical reacting networks by first proving its strong convergence.We then study a speed up of the algorithm by using the explicit Tau-Leaping method as the Inner solver to approximate invariant measures of fast processes,for which strong error estimates can also be obtained.Numerical experiments are presented to demonstrate the validity of our analysis.
基金Project supported by the National Natural Science Foundation of China (No.30571059)the National High-Tech Research and Development Program of China(No.2006AA02Z190).
文摘Presented here is an L-leap method for accelerating stochastic simulation of well-stirred chemically reacting systems, in which the number of reactions occurring in a reaction channel with the largest propensity function is calculated from the leap condition and the number of reactions occurring in the other reaction channels are generated by using binomial random variables during a leap. The L-leap method can better satisfy the leap condition. Numerical simulation results indicate that the L-leap method can obtain better performance than established methods.
基金the National Natural Science Foundation of China(No.30571059)the National High-Tech Research and Development Program of China(No.2006AA02Z190)
文摘In this paper, we develop a modified accelerated stochastic simulation method for chemically reacting systems, called the ＂final all possible steps＂ （FAPS） method, which obtains the reliable statistics of all species in any time during the time course with fewer simulation times. Moreover, the FAPS method can be incorporated into the leap methods, which makes the simulation of larger systems more efficient. Numerical results indicate that the proposed methods can be applied to a wide range of chemically reacting systems with a high-precision level and obtain a significant improvement on efficiency over the existing methods.
文摘Biochemical systems have numerous practical applications, in particular to the study of critical intracellular processes. Frequently, biochemical kinetic models depict cellular processes as systems of chemical reactions. Many biological processes in a cell are inherently stochastic, due to the existence of some low molecular amounts. These stochastic fluctuations may have a great effect on the biochemical system’s behaviour. In such cases, stochastic models are necessary to accurately describe the system’s dynamics. Biochemical systems at the cellular level may entail many species or reactions and their mathematical models may be non-linear and with multiple scales in time. In this work, we provide a numerical technique for simplifying stochastic discrete models of well-stirred biochemical systems, which ensures that the main properties of the original system are preserved. The proposed technique employs sensitivity analysis and requires solving an optimization problem. The numerical tests on several models of practical interest show that our model reduction strategy performs very well.
文摘Cellular environments are in essence stochastic, owing to the random character of the biochemical reaction events in a single cell. Stochastic fluctuations may substantially contribute to the dynamics of systems with small copy numbers of some biochemical species. Then, stochastic models are indispensable for properly portraying the behaviour of the system. Sensitivity analysis is one of the central tools for studying stochastic models of cellular dynamics. Here, we propose some finite-difference strategies for estimating parametric sensitivities of higher-order moments of the system state for stochastic discrete biochemical kinetic models. To reduce the variance of the sensitivity estimator, we employ various coupling techniques. The advantages of the proposed methods are illustrated in several models of biochemical systems of practical relevance.
基金the National Science and Engineering Research Council of Canada(NSERC)the Canadian Institutes of Health Research(CIHR)+1 种基金the Academy of Finland(Application Number 129657,Finnish Programme for Centres of Excellence in Research 2006-2011,and 124615)the Tampere Graduate School in Information Science and Engineering(TISE).
文摘We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics.The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo method to simulate time-dependent statistical characteristics of growing cell populations.To benchmark performance,we compare simulation results with steadystate and time-dependent analytical solutions for several scenarios,including steadystate and time-dependent gene expression,and the effects on population heterogeneity of cell growth,division,and DNA replication.This comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene expression.We also use the algorithm to model gene expression dynamics within"bet-hedging"cell populations during their adaption to environmental stress.These simulations indicate that the algorithm provides a framework suitable for simulating and analyzing realistic models of heterogeneous population dynamics combining molecular-level stochastic reaction kinetics,relevant physiological details and phenotypic variability.
基金supported by grants NSF-DMS 0845061 and NSF-DMS 0829515.
文摘We use the recently proposed Nested Stochastic Simulation Algorithm(Nested SSA)to simulate the cell cycle model for budding yeast.The results show that Nested SSA is able to significantly reduce the computational cost while capturing the essential dynamical features of the system.
文摘A methodology for kinetic modeling of conversion processes is presented.The proposed approach allows to overcome the lack of molecular detail of the petroleum fractions and to simulate the reactions of the process by means of a two-step procedure.In the first step,a synthetic mixture of molecules representing the feedstock is generated via a molecular reconstruction method,termed SR-REM molecular reconstruction.In the second step,a kinetic Monte Carlo method,termed stochastic simulation algorithm(SSA),is used to simulate the effect of the conversion reactions on the mixture of molecules.The resulting methodology is applied to the Athabasca vacuum residue hydrocracking.An adequate molecular representation of the vacuum residue is obtained using the SR-REM algorithm.The reaction simulations present a good agreement with the laboratory data for Athabasca vacuum residue conversion.In addition,the proposed methodology provides the molecular detail of the vacuum residue conversion throughout the reactions simulations.
基金supported financially by the National Science and Engineering Research Council of Canada(NSERC).
文摘We present an accelerated method for stochastically simulating the dynamics of heterogeneous cell populations.The algorithm combines a Monte Carlo approach for simulating the biochemical kinetics in single cells with a constant-number Monte Carlo method for simulating the reproductive fitness and the statistical characteristics of growing cell populations.To benchmark accuracy and performance,we compare simulation results with those generated from a previously validated population dynamics algorithm.The comparison demonstrates that the accelerated method accurately simulates population dynamics with significant reductions in runtime under commonly invoked steady-state and symmetric cell division assumptions.Considering the increasing complexity of cell population models,the method is an important addition to the arsenal of existing algorithms for simulating cellular and population dynamics that enables efficient,coarse-grained exploration of parameter space.
