The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
Richard F. W. Bader - One of the best experts on this subject based on the ideXlab platform.
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professor Gillespie a symbiotic relationship
Coordination Chemistry Reviews, 2000Co-Authors: Richard F. W. BaderAbstract:Abstract This is an account of how the scientific interests of Professor Gillespie and myself eventually came to a common focus, resulting in a physical understanding of the VSEPR (Valence Shell Electron Pair Repulsion) model of molecular geometry and of how, from that point on, we have enjoyed a continuing exchange of ideas.
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Professor Gillespie—a symbiotic relationship
Coordination Chemistry Reviews, 2000Co-Authors: Richard F. W. BaderAbstract:Abstract This is an account of how the scientific interests of Professor Gillespie and myself eventually came to a common focus, resulting in a physical understanding of the VSEPR (Valence Shell Electron Pair Repulsion) model of molecular geometry and of how, from that point on, we have enjoyed a continuing exchange of ideas.
Adam P. Arkin - One of the best experts on this subject based on the ideXlab platform.
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Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm
The Journal of Chemical Physics, 2003Co-Authors: Christopher V. Rao, Adam P. ArkinAbstract:Biochemical dynamics are often determined by series of single molecule events such as gene expression and reactions involving protein concentrations at nanomolar concentrations. Molecular fluctuations, consequently, may be of biological significance. For example, heterogeneity in clonal populations is believed to arise from molecular fluctuations in gene expression. A realistic description, therefore, requires a probabilistic description of the biochemical dynamics as deterministic descriptions cannot capture the inherent molecular fluctuations. The Gillespie algorithm [D. T. Gillespie, J. Phys. Chem. 81, 2350 (1977)] is a stochastic procedure for simulating chemical systems at low concentrations. A limitation of stochastic kinetic models is that they require detailed information about the chemical kinetics often unavailable in biological systems. Furthermore, the Gillespie algorithm is computationally intensive when there are many molecules and reaction events. In this article, we explore one approximation technique, well known in deterministic kinetics, for simplifying the stochastic model: the quasi-steady-state assumption (QSSA). We illustrate how the QSSA can be applied to the Gillespie algorithm. Using the QSSA, we derive stochastic Michaelis–Menten rate expressions for simple enzymatic reactions and illustrate how the QSSA is applied when modeling and simulating a simple genetic circuit.
Luis E C Rocha - One of the best experts on this subject based on the ideXlab platform.
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a Gillespie algorithm for non markovian stochastic processes
Siam Review, 2018Co-Authors: Naoki Masuda, Luis E C RochaAbstract:The Gillespie algorithm provides statistically exact methods for simulating stochastic dynamics modeled as interacting sequences of discrete events including systems of biochemical reactions or earthquake occurrences, networks of queuing processes or spiking neurons, and epidemic and opinion formation processes on social networks. Empirically, the inter-event times of various phenomena obey long-tailed distributions. The Gillespie algorithm and its variants either assume Poisson processes (i.e., exponentially distributed inter-event times), use particular functions for time courses of the event rate, or work for non-Poissonian renewal processes, including the case of long-tailed distributions of inter-event times, but at a high computational cost. In the present study, we propose an innovative Gillespie algorithm for renewal processes on the basis of the Laplace transform. The algorithm makes use of the fact that a class of point processes is represented as a mixture of Poisson processes with different ev...
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A Gillespie algorithm for non-Markovian stochastic processes
SIAM Review, 2018Co-Authors: Naoki Masuda, Luis E C RochaAbstract:The Gillespie algorithm provides statistically exact methods for simulating stochastic dynamics modelled as interacting sequences of discrete events including systems of biochemical reactions or earthquake occurrences, networks of queuing processes or spiking neurons, and epidemic and opinion formation processes on social networks. Empirically, the inter-event times of various phenomena obey long-tailed distributions. The Gillespie algorithm and its variants either assume Poisson processes (i.e., exponentially distributed inter-event times), use particular functions for time courses of the event rate, or work for non-Poissonian renewal processes, including the case of long-tailed distributions of inter-event times, but at a high computational cost. In the present study, we propose an innovative Gillespie algorithm for renewal processes on the basis of the Laplace transform. The algorithm makes use of the fact that a class of point processes is represented as a mixture of Poisson processes with different event rates. The method is applicable to multivariate renewal processes whose survival function of inter-event times is completely monotone. It is an exact algorithm and works faster than a recently proposed Gillespie algorithm for general renewal processes, which is exact only in the limit of infinitely many processes. We also propose a method to generate sequences of event times with a tunable amount of positive correlation between inter-event times. We demonstrate our algorithm with exact simulations of epidemic processes on networks, finding that a realistic amount of positive correlation in inter-event times only slightly affects the epidemic dynamics.
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A Gillespie algorithm for non-Markovian stochastic processes: Laplace transform approach
arXiv: Physics and Society, 2016Co-Authors: Naoki Masuda, Luis E C RochaAbstract:The Gillespie algorithm provides statistically exact methods to simulate stochastic dynamics modelled as interacting sequences of discrete events including systems of biochemical reactions or earthquakes, networks of queuing processes or spiking neurons, and epidemic and opinion formation processes on social networks. Empirically, inter-event times of various human activities, in particular human communication, and some natural phenomena are often distributed according to long-tailed distributions. The Gillespie algorithm and its extant variants either assume the Poisson process, which produces exponentially distributed inter-event times, not long-tailed distributions, assume particular functional forms for time courses of the event rate, or works for non-Poissonian renewal processes including the case of long-tailed distributions of inter-event times but at a high computational cost. In the present study, we propose an innovative Gillespie algorithm for renewal processes on the basis of the Laplace transform. It uses the fact that a class of point processes is represented as a mixture of Poisson processes with different event rates. The method allows renewal processes whose survival function of inter-event times is completely monotone functions and works faster than a recently proposed Gillespie algorithm for general renewal processes. We also propose a method to generate sequences of event times with a given distribution of inter-event times and a tunable amount of positive correlation between inter-event times. We demonstrate our algorithm with exact simulations of epidemic processes on networks. We find that positive correlation in inter-event times modulates dynamics but in a quantitatively minor way with the amount of positive correlation comparable with empirical data.
Eric C Dykeman - One of the best experts on this subject based on the ideXlab platform.
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an implementation of the Gillespie algorithm for rna kinetics with logarithmic time update
Nucleic Acids Research, 2015Co-Authors: Eric C DykemanAbstract:In this paper I outline a fast method called KFOLD for implementing the Gillepie algorithm to stochastically sample the folding kinetics of an RNA molecule at single base-pair resolution. In the same fashion as the KINFOLD algorithm, which also uses the Gillespie algorithm to predict folding kinetics, KFOLD stochastically chooses a new RNA secondary structure state that is accessible from the current state by a single base-pair addition/deletion following the Gillespie procedure. However, unlike KINFOLD, the KFOLD algorithm utilizes the fact that many of the base-pair addition/deletion reactions and their corresponding rates do not change between each step in the algorithm. This allows KFOLD to achieve a substantial speed-up in the time required to compute a prediction of the folding pathway and, for a fixed number of base-pair moves, performs logarithmically with sequence size. This increase in speed opens up the possibility of studying the kinetics of much longer RNA sequences at single base-pair resolution while also allowing for the RNA folding statistics of smaller RNA sequences to be computed much more quickly.
Donghui Quan - One of the best experts on this subject based on the ideXlab platform.
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Accelerated Gillespie Algorithm for Gas-Grain Reaction Network Simulations Using Quasi-steady-state Assumption
The Astrophysical Journal, 2017Co-Authors: Qiang Chang, Donghui QuanAbstract:Although the Gillespie algorithm is accurate in simulating gas-grain reaction networks, so far its computational cost is so expensive that it cannot be used to simulate chemical reaction networks that include molecular hydrogen accretion or the chemical evolution of protoplanetary disks. We present an accelerated Gillespie algorithm that is based on a quasi-steady-state assumption with the further approximation that the population distribution of transient species depends only on the accretion and desorption processes. The new algorithm is tested against a few reaction networks that are simulated by the regular Gillespie algorithm. We found that the less likely it is that transient species are formed and destroyed on grain surfaces, the more accurate the new method is. We also apply the new method to simulate reaction networks that include molecular hydrogen accretion. The results show that surface chemical reactions involving molecular hydrogen are not important for the production of surface species under standard physical conditions of dense molecular clouds.
