To investigate the behavior of biochemical systems, many runs of Gillespie's stochastic simulation algorithm (SSA) are generally needed, causing excessive computational costs on Central Processing Units (CPUs). Si...
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To investigate the behavior of biochemical systems, many runs of Gillespie's stochastic simulation algorithm (SSA) are generally needed, causing excessive computational costs on Central Processing Units (CPUs). Since all SSA runs are independent, the Intel Xeon Phi coprocessors based on the Many Integrated Core (MIC) architecture can be exploited to distribute the workload. We considered two execution modalities on MIC: one consisted in running exactly the same CPU code of SSA, while the other exploited MIC's vector instructions to reuse the CPU code with only few modifications. MIC performance was compared with Graphics Processing Units (GPUs), specifically implemented in CUDA to optimize the use of memory hierarchy. Our results show that GPU largely outperforms MIC and CPU, but required a complete redesign of SSA. MIC allows a relevant speedup, especially when vector instructions are used, with the additional advantage of requiring minimal modifications to CPU code.
The mathematical framework of the chemical master equation (CME) uses a Markov chain to model the biochemical reactions that are taking place within a biological cell. Computing the transient probability distribution ...
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The mathematical framework of the chemical master equation (CME) uses a Markov chain to model the biochemical reactions that are taking place within a biological cell. Computing the transient probability distribution of this Markov chain allows us to track the composition of molecules inside the cell over time, with important practical applications in a number of areas such as molecular biology or medicine. However the CME is typically difficult to solve, since the state space involved can be very large or even countably infinite. We present a novel way of using the stochastic simulation algorithm (SSA) to reduce the size of the finite state projection (FSP) method. Numerical experiments that demonstrate the effectiveness of the reduction are included. (C) 2015 Elsevier Inc. All rights reserved.
In this paper,we revisit the Nested stochastic simulation algorithm(NSSA)for stochastic chemical reacting networks by first proving its strong *** then study a speed up of the algorithm by using the explicit Tau-Leapi...
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In this paper,we revisit the Nested stochastic simulation algorithm(NSSA)for stochastic chemical reacting networks by first proving its strong *** 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 *** experiments are presented to demonstrate the validity of our analysis.
There are two main approaches in the mathematical modeling of coupled systems of (bio)chemical reactions: continuous, represented by differential equations whose variables are concentrations or discrete, represented b...
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ISBN:
(纸本)9780769549804
There are two main approaches in the mathematical modeling of coupled systems of (bio)chemical reactions: continuous, represented by differential equations whose variables are concentrations or discrete, represented by stochastic processes whose variables are numbers of molecules. The latter approach is used mostly for biochemical systems with a low to moderate number of molecules of certain species and this kind of systems are typically modeled as continuous time - discrete state Markov Process. There are exact stochasticalgorithms to simulate state trajectories of discrete, stochastic systems and these algorithms are based on methods that are rigorously equivalent to the Master Equation approach. Two of the most widely used methods for simulating the stochastic dynamics of a chemical system are the exact stochastic simulation algorithm (SSA, known also as Gillespie algorithm) and its approximate variant, the tau-leaping algorithm. This paper describes a modified version of SSA - First reaction method - by letting the intensity rates of the reactions to be functions of time. The importance of this adaptation is obvious when considering some classes of biological models (for example, the one involving circadian rhythm). The underlying assumptions are that the system is well stirred such that at any moment, each reactions occur with equal probability at any position, that each reaction, once occurred, completes instantaneously (there are no reactions with delay involved) and that the system is non stiff (there are no different time scales of the reactions involved).
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...
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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 stochasticsimulations 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.
The present study proposes a stochasticsimulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous stochastic simulation algorithm by modifyi...
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The present study proposes a stochasticsimulation 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.
We present an algorithm for the stochasticsimulation of gene expression and heterogeneous population *** algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-numb...
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We present an algorithm for the stochasticsimulation of gene expression and heterogeneous population *** 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 *** 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 *** comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene *** also use the algorithm to model gene expression dynamics within"bet-hedging"cell populations during their adaption to environmental *** 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.
Kinetic Monte Carlo (kMC) models are a well-established modelling framework for the simulation of complex free-radical kinetic systems. kMC models offer the advantage of discretely monitoring every chain sequence in t...
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Kinetic Monte Carlo (kMC) models are a well-established modelling framework for the simulation of complex free-radical kinetic systems. kMC models offer the advantage of discretely monitoring every chain sequence in the system, providing full accounting of the chain molecular weight distribution. These models are marred by the necessity to simulate a minimum number of molecules, which confers significant computational burden. This paper adapts and creates a highly generalizable methodology for scaling dilute radical populations in discrete stochastic models, such as Gillespie's stochastic simulation algorithm (SSA). The methodology is then applied to a kMC simulation of polystyrene (PS) pyrolysis, using a modelling framework adapted from literature. The results show that the required number of simulated molecules can be successfully reduced by up to three orders of magnitude with minimal loss of convergent behaviour, corresponding to a wall-clock simulation speed reduction of between 95.2 to 99.6 % at common pyrolysis temperatures.
Jumps can be seen in many natural processes. Classical deterministic modeling approach explains the dynamical behavior of such systems by using impulsive differential equations. This modeling strategy assumes that the...
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Jumps can be seen in many natural processes. Classical deterministic modeling approach explains the dynamical behavior of such systems by using impulsive differential equations. This modeling strategy assumes that the dynamical behavior of the whole system is deterministic, continuous, and it adds jumps to the state vector at certain times. Although deterministic approach is satisfactory in many cases, it is a well-known fact that stochasticity or uncertainty has crucial importance for dynamical behavior of many others. In this study, we propose to include this abrupt change in the stochastic modeling approach, beside the deterministic one. In our model, we introduce jumps to chemical master equation and use the Gillespie direct method to simulate the evolutionary system. To illustrate the idea and distinguish the differences, we present some numerically solved examples.
Background: Although oligonucleotide microarray technology is ubiquitous in genomic research, reproducibility and standardization of expression measurements still concern many researchers. Cross-hybridization between ...
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Background: Although oligonucleotide microarray technology is ubiquitous in genomic research, reproducibility and standardization of expression measurements still concern many researchers. Cross-hybridization between microarray probes and non-target ssDNA has been implicated as a primary factor in sensitivity and selectivity loss. Since hybridization is a chemical process, it may be modeled at a population-level using a combination of material balance equations and thermodynamics. However, the hybridization reaction network may be exceptionally large for commercial arrays, which often possess at least one reporter per transcript. Quantification of the kinetics and equilibrium of exceptionally large chemical systems of this type is numerically infeasible with customary approaches. Results: In this paper, we present a robust and computationally efficient algorithm for the simulation of hybridization processes underlying microarray assays. Our method may be utilized to identify the extent to which nucleic acid targets (e. g. cDNA) will cross-hybridize with probes, and by extension, characterize probe robustnessusing the information specified by MAGE-TAB. Using this algorithm, we characterize cross-hybridization in a modified commercial microarray assay. Conclusions: By integrating stochasticsimulation with thermodynamic prediction tools for DNA hybridization, one may robustly and rapidly characterize of the selectivity of a proposed microarray design at the probe and "system" levels. Our code is available at http://***.
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