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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 19 (5 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
Efficient attenuation of stochasticity in gene expression through posttranscriptional control
 J MOL BIOL
, 2004
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Problems of high dimension in molecular biology
 In Proc. 19th GAMM Seminar Leipzig
, 2003
"... The deterministic reaction rate equations are not an accurate description of many systems in molecular biology where the number of molecules of each species often is small. The master equation of chemical reactions is a more accurate stochastic description suitable for small molecular numbers. A com ..."
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Cited by 14 (3 self)
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The deterministic reaction rate equations are not an accurate description of many systems in molecular biology where the number of molecules of each species often is small. The master equation of chemical reactions is a more accurate stochastic description suitable for small molecular numbers. A computational difficulty is the high dimensionality of the equation. We describe how it can be solved by first approximating it by the FokkerPlanck equation. Then this equation is discretized in space and time by a finite difference method. The method is compared to a Monte Carlo method by Gillespie. The method is applied to a fourdimensional problem of interest in the regulation of cell processes. This paper was presented at the 19th GAMMSeminar in Leipzig, January 23–25, 2003.
Programmability of Chemical Reaction Networks
"... Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a wellstirred solution according to standard c ..."
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Cited by 8 (2 self)
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Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a wellstirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and
Robust Stochastic Chemical Reaction Networks and Bounded TauLeaping
, 803
"... 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 between robustness and efficiency of simulation. Without robustn ..."
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Cited by 3 (2 self)
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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 between robustness and efficiency of simulation. Without robustness guarantees, stochastic simulation seems to require computational time proportional to the total number of reaction events. Even if the concentration (molecular count per volume) stays bounded, the number of reaction events can be linear in the duration of simulated time and total molecular count. We show that the behavior of robust systems can be predicted such that the computational work scales linearly with the duration of simulated time and concentration, and only polylogarithmically in the total molecular count. Thus our asymptotic analysis captures the dramatic speedup when molecular counts are large, and shows that for bounded concentrations the computation time is essentially invariant with molecular count. Finally, by noticing that even robust stochastic chemical reaction networks are capable of embedding complex computational problems, we argue that the linear dependence on simulated time and concentration is likely optimal. 1
Manchester Grand Hyatt Hotel
"... On the modelling of a bistable genetic switch Abstract — A bistable switch is a common motif in a genetic regulatory network. There have been relatively few in vivo measurements made of such a network. Its natural closed loop nature makes the living switch difficult to measure experimentally. Hence ..."
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On the modelling of a bistable genetic switch Abstract — A bistable switch is a common motif in a genetic regulatory network. There have been relatively few in vivo measurements made of such a network. Its natural closed loop nature makes the living switch difficult to measure experimentally. Hence not much have been reported on derivation of a model from in vivo data, which is expected to be different from the macroscopic scale in vitro measurements. We present a heuristic for modelling a naturally occurring switch from relatively few in vivo experimental data points, yielding a model suited to dynamical simulation, and give predictions of the unmeasured protein in the system. I.
Simulation of Genetic Regulatory Networks
"... Abstract: Dizzy is a chemical kinetics simulation software framework. On up gradating this package to simulate the dynamics of complex gene regulatory networks. Using Tauleap simplex and Tauleap complex algorithms, implemented in Java. Procedure have been improved for determining the maximum leap si ..."
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Abstract: Dizzy is a chemical kinetics simulation software framework. On up gradating this package to simulate the dynamics of complex gene regulatory networks. Using Tauleap simplex and Tauleap complex algorithms, implemented in Java. Procedure have been improved for determining the maximum leap size which accelerates the speed of simulation. This paper focuses mainly on simulating Genetic Regulatory Networks using stochastic methods of simulation and introducing τ to accelerate the speed of simulation.