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427
COPASI  a COmplex PAthway SImulator
 BIOINFORMATICS
, 2006
"... Motivation: Simulation and modeling is becoming a standard approach to understand complex biochemical processes. Therefore, there is a big need for software tools that allow access to diverse simulation and modeling methods as well as support for the usage of these methods. Results: Here, we present ..."
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Cited by 270 (6 self)
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Motivation: Simulation and modeling is becoming a standard approach to understand complex biochemical processes. Therefore, there is a big need for software tools that allow access to diverse simulation and modeling methods as well as support for the usage of these methods. Results: Here, we present COPASI, a platformindependent and userfriendly biochemical simulator that offers several unique features. We discuss numerical issues with these features, in particular the criteria to switch between stochastic and deterministic simulation methods, hybrid deterministicstochastic methods, and the importance of random number generator numerical resolution in stochastic simulation. Availability: The complete software is available in binary (executable) for MS Windows, OS X, Linux (Intel), and Sun Solaris (SPARC), as well as the full source code under an open source license from
Stochastic simulation of chemical kinetics
 Annu. Rev. Phys. Chem
"... Abstract Stochastic chemical kinetics describes the time evolution of a wellstirred chemically reacting system in a way that takes into account the fact that molecules come in whole numbers and exhibit some degree of randomness in their dynamical behavior. Researchers are increasingly using this ap ..."
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Cited by 200 (0 self)
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Abstract Stochastic chemical kinetics describes the time evolution of a wellstirred chemically reacting system in a way that takes into account the fact that molecules come in whole numbers and exhibit some degree of randomness in their dynamical behavior. Researchers are increasingly using this approach to chemical kinetics in the analysis of cellular systems in biology, where the small molecular populations of only a few reactant species can lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. After reviewing the supporting theory of stochastic chemical kinetics, I discuss some recent advances in methods for using that theory to make numerical simulations. These include improvements to the exact stochastic simulation algorithm (SSA) and the approximate explicit tauleaping procedure, as well as the development of two approximate strategies for simulating systems that are dynamically stiff: implicit tauleaping and the slowscale SSA.
Modelling and analysis of gene regulatory networks,
 Nat Rev Mol Cell Biol
, 2008
"... The genome encodes thousands of genes whose pro ducts enable cell survival and numerous cellular func tions. The amounts and the temporal pattern in which these products appear in the cell are crucial to the pro cesses of life. Gene regulatory networks govern the levels of these gene products. A ge ..."
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Cited by 118 (2 self)
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The genome encodes thousands of genes whose pro ducts enable cell survival and numerous cellular func tions. The amounts and the temporal pattern in which these products appear in the cell are crucial to the pro cesses of life. Gene regulatory networks govern the levels of these gene products. A gene regulatory net work is the collection of molecular species and their inter actions, which together control geneproduct abundance. Numerous cellular processes are affected by regulatory networks. Innovations in experimental methods have ena bled largescale studies of gene regulatory networks and can reveal the mechanisms that underlie them. Consequently, biologists must come to grips with extremely complex networks and must analyse and integrate great quantities of experimental data. Essential to this challenge are computational tools, which can answer various questions: what is the full range of behaviours that this system exhibits under different conditions? What changes are expected in the dynamics of the system if certain parts stop functioning? How robust is the system under extreme conditions? Various computational models have been developed for regulatory network analysis. These models can be roughly divided into three classes. The first class, logi cal models, describes regulatory networks qualitatively. They allow users to obtain a basic understanding of the different functionalities of a given network under dif ferent conditions. Their qualitative nature makes them flexible and easy to fit to biological phenomena, although they can only answer qualitative questions. To under stand and manipulate behaviours that depend on finer timing and exact molecular concentrations, a second class of models was developed continuous models. For example, to simulate the effects of dietary restriction on yeast cells under different nutrient concentrations 1 , users must resort to the finer resolution of continuous models. A third class of models was introduced follow ing the observation that the functionality of regulatory networks is often affected by noise. As the majority of these models account for interactions between individual molecules, they are referred to here as singlemolecule level models. Singlemolecule level models explain the relationship between stochasticity and gene regulation. Predictive computational models of regulatory net works are expected to benefit several fields. In medi cine, mechanisms of diseases that are characterized by dysfunction of regulatory processes can be elucidated. Biotechnological projects can benefit from predictive models that will replace some tedious and costly lab experiments. And, computational analysis may con tribute to basic biological research, for example, by explaining developmental mechanisms or new aspects of the evolutionary process. Here we review the available methodologies for mod elling and analysing regulatory networks. These meth odologies have already proved to be a valuable research tool, both for the development of network models and for the analysis of their functionality. We discuss their relative advantages and limitations, and outline some open questions regarding regulatory networks, includ ing how structure, dynamics and functionality relate to each other, how organisms use regulatory networks to adapt to their environments, and the interplay between regulatory networks and other cellular processes, such as metabolism. Stochasticity The property of a system whose behaviour depends on probabilities. In a model with stochasticity, a single initial state can evolve into several different trajectories, each with an associated probability. Modelling and analysis of gene regulatory networks Guy Karlebach and Ron Shamir Abstract  Gene regulatory networks have an important role in every process of life, including cell differentiation, metabolism, the cell cycle and signal transduction. By understanding the dynamics of these networks we can shed light on the mechanisms of diseases that occur when these cellular processes are dysregulated. Accurate prediction of the behaviour of regulatory networks will also speed up biotechnological projects, as such predictions are quicker and cheaper than lab experiments. Computational methods, both for supporting the development of network models and for the analysis of their functionality, have already proved to be a valuable research tool.
Efficient, correct simulation of biological processes in the stochastic picalculus
 GILMORE (EDS.), PROC. INT. CONF. COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY (CMSB’07
, 2007
"... This paper presents a simulation algorithm for the stochastic πcalculus, designed for the efficient simulation of biological systems with large numbers of molecules. The cost of a simulation depends on the number of species, rather than the number of molecules, resulting in a significant gain in e ..."
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Cited by 65 (12 self)
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This paper presents a simulation algorithm for the stochastic πcalculus, designed for the efficient simulation of biological systems with large numbers of molecules. The cost of a simulation depends on the number of species, rather than the number of molecules, resulting in a significant gain in efficiency. The algorithm is proved correct with respect to the calculus, and then used as a basis for implementing the latest version of the SPiM stochastic simulator. The algorithm is also suitable for generating graphical animations of simulations, in order to visualise system dynamics.
Fast evaluation of fluctuations in biochemical networks with the linear noise approximation
 Genome Research
"... Biochemical networks in single cells can display large fluctuations in molecule numbers, making mesoscopic approaches necessary for correct system descriptions. We present a general method that allows rapid characterization of the stochastic properties of intracellular networks. The starting point i ..."
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Cited by 60 (3 self)
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Biochemical networks in single cells can display large fluctuations in molecule numbers, making mesoscopic approaches necessary for correct system descriptions. We present a general method that allows rapid characterization of the stochastic properties of intracellular networks. The starting point is a macroscopic description that identifies the system’s elementary reactions in terms of rate laws and stoichiometries. From this formulation follows directly the stationary solution of the linear noise approximation (LNA) of the Master equation for all the components in the network. The method complements bifurcation studies of the system’s parameter dependence by providing estimates of sizes, correlations, and time scales of stochastic fluctuations. We describe how the LNA can give precise system descriptions also near macroscopic instabilities by suitable variable changes and elimination of fast variables. [Supplemental material is available online at www.genome.org.] A key element in systems biology is the design of mathematical models that faithfully describe the dynamics of intracellular chemical networks. In general, chemical reactions in single cells occur far from thermodynamic equilibrium (Keizer 1987), and the molecule copy numbers can sometimes be very small (Guptasarama 1995). Both these properties make it mandatory to ana
Fast computation by population protocols with a leader
 IN DISTRIBUTED COMPUTING: 20TH INTERNATIONAL SYMPOSIUM, DISC 2006
, 2006
"... Fast algorithms are presented for performing computations in a probabilistic population model. This is a variant of the standard population protocol model—in which finitestate agents interact in pairs under the control of an adversary scheduler—where all pairs are equally likely to be chosen for ea ..."
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Cited by 58 (5 self)
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Fast algorithms are presented for performing computations in a probabilistic population model. This is a variant of the standard population protocol model—in which finitestate agents interact in pairs under the control of an adversary scheduler—where all pairs are equally likely to be chosen for each interaction. It is shown that when a unique leader agent is provided in the initial population, the population can simulate a virtual register machine in which standard arithmetic operations like comparison, addition, subtraction, multiplication, and division can be simulated in O(n log 4 n) interactions with high probability. Applications include a reduction of the cost of computing a semilinear predicate to O(n log 4 n) interactions from the previously bestknown bound of O(n 2 log n) interactions and simulation of a LOGSPACE Turing machine using the same O(n log 4 n) interactions per step. These bounds on interactions translate into O(log 4 n) time per step in a natural model in which each agent participates in an expected Θ(1) interactions per time unit. The central method is the extensive use of epidemics to propagate information from and to the leader, combined with an epidemicbased phase clock used to detect when these epidemics are likely to be complete.
A MultiAlgorithm, MultiTimescale Method for Cell Simulation
, 2004
"... Motivation: Many important problems in cell biology require the dense nonlinear interactions between functional modules to be considered. The importance of computer simulation in understanding cellular processes is now widely accepted, and a variety of simulation algorithms useful for studying certa ..."
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Cited by 55 (5 self)
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Motivation: Many important problems in cell biology require the dense nonlinear interactions between functional modules to be considered. The importance of computer simulation in understanding cellular processes is now widely accepted, and a variety of simulation algorithms useful for studying certain subsystems have been designed. Many of these are already widely used, and a large number of models constructed on these existing formalisms are available. A significant computational challenge is how we can integrate such subcellular models running on different types of algorithms to construct higher order models. Results: A modular, objectoriented simulation metaalgorithm based on a discreteevent scheduler and Hermite polynomial interpolation has been developed and implemented. It is shown that this new method can efficiently handle many components driven by different algorithms and different timescales. The utility of this simulation framework is demonstrated further with a ‘composite ’ heatshock response model that combines the Gillespie–Gibson stochastic algorithm and deterministic differential equations. Dramatic improvements in performance were obtained without significant accuracy drawbacks. A multitimescale demonstration of coupled harmonic oscillators is also shown. Availability: An implementation of the method is available as part of ECell Simulation Environment Version 3 downloadable from
Computation with finite stochastic chemical reaction networks
 Natural Computing
, 2008
"... Abstract. A highly desired part of the synthetic biology toolbox is an embedded chemical microcontroller, capable of autonomously following a logic program specified by a set of instructions, and interacting with its cellular environment. Strategies for incorporating logic in aqueous chemistry have ..."
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Cited by 53 (17 self)
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Abstract. A highly desired part of the synthetic biology toolbox is an embedded chemical microcontroller, capable of autonomously following a logic program specified by a set of instructions, and interacting with its cellular environment. Strategies for incorporating logic in aqueous chemistry have focused primarily on implementing components, such as logic gates, that are composed into larger circuits, with each logic gate in the circuit corresponding to one or more molecular species. With this paradigm, designing and producing new molecular species is necessary to perform larger computations. An alternative approach begins by noticing that chemical systems on the small scale are fundamentally discrete and stochastic. In particular, the exact molecular counts of each molecular species present, is an intrinsically available form of information. This might appear to be a very weak form of information, perhaps quite difficult for computations to utilize. Indeed, it has been shown that errorfree Turing universal computation is impossible in this setting. Nevertheless, we show a design of a chemical computer that achieves fast and reliable Turinguniversal computation using molecular counts. Our scheme uses only a small number of different molecular species to do computation of arbitrary complexity. The total probability of error of the computation can be made arbitrarily small (but not zero) by adjusting the initial molecular counts of certain species. While physical implementations would be difficult, these results demonstrate that molecular counts can be a useful form of information for small molecular systems such as those operating within cellular environments. Key words. stochastic chemical kinetics; molecular counts; Turinguniversal computation; probabilistic computation 1. Introduction. Many
Stochastic models for chemically reacting systems using polynomial stochastic hybrid systems
 Int. J. Robust Nonlinear Control
, 2005
"... Abstract. A stochastic model for chemical reactions is presented, which represents the population of various species involved in a chemical reaction as the continuous state of a polynomial Stochastic Hybrid System (pSHS). pSHSs correspond to stochastic hybrid systems with polynomial continuous vecto ..."
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Cited by 47 (18 self)
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Abstract. A stochastic model for chemical reactions is presented, which represents the population of various species involved in a chemical reaction as the continuous state of a polynomial Stochastic Hybrid System (pSHS). pSHSs correspond to stochastic hybrid systems with polynomial continuous vector fields, reset maps, and transition intensities. We show that for pSHSs, the dynamics of the statistical moments of its continuous states, evolves according to infinitedimensional linear ordinary differential equations (ODEs), which can be approximated by finitedimensional nonlinear ODEs with arbitrary precision. Based on this result, a procedure to build this types of approximation is provided. This procedure is used to construct approximate stochastic models for a variety of chemical reactions that have appeared in literature. These reactions include a simple bimolecular reaction, for which one can solve the master equation; a decayingdimerizing reaction set which exhibits two distinct time scales; a reaction for which the chemical rate equations have a continuum of equilibrium points; and the bistable Schögl reaction. The accuracy of the approximate models is investigated by comparing with Monte Carlo simulations or the solution to the Master equation, when available. 1