Daniel T. Gillespie

Bio: Daniel T. Gillespie is an academic researcher from Naval Air Warfare Center Weapons Division. The author has contributed to research in topics: Stochastic simulation & Stochastic process. The author has an hindex of 39, co-authored 77 publications receiving 27786 citations.

Exact Stochastic Simulation of Coupled Chemical Reactions

Abstract: There are two formalisms for mathematically describing the time behavior of a spatially homogeneous chemical system: The deterministic approach regards the time evolution as a continuous, wholly predictable process which is governed by a set of coupled, ordinary differential equations (the “reaction-rate equations”); the stochastic approach regards the time evolution as a kind of random-walk process which is governed by a single differential-difference equation (the “master equation”). Fairly simple kinetic theory arguments show that the stochastic formulation of chemical kinetics has a firmer physical basis than the deterministic formulation, but unfortunately the stochastic master equation is often mathematically intractable. There is, however, a way to make exact numerical calculations within the framework of the stochastic formulation without having to deal with the master equation directly. It is a relatively simple digital computer algorithm which uses a rigorously derived Monte Carlo procedure to numerically simulate the time evolution of the given chemical system. Like the master equation, this “stochastic simulation algorithm” correctly accounts for the inherent fluctuations and correlations that are necessarily ignored in the deterministic formulation. In addition, unlike most procedures for numerically solving the deterministic reaction-rate equations, this algorithm never approximates infinitesimal time increments df by finite time steps At. The feasibility and utility of the simulation algorithm are demonstrated by applying it to several well-known model chemical systems, including the Lotka model, the Brusselator, and the Oregonator.

Stochastic Simulation of Chemical Kinetics

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 tau-leaping procedure, as well as the development of two approximate strategies for simulating systems that are dynamically stiff: implicit tau-leaping and the slow-scale SSA.

Approximate accelerated stochastic simulation of chemically reacting systems

Abstract: The stochastic simulation algorithm (SSA) is an essentially exact procedure for numerically simulating the time evolution of a well-stirred chemically reacting system. Despite recent major improvements in the efficiency of the SSA, its drawback remains the great amount of computer time that is often required to simulate a desired amount of system time. Presented here is the “τ-leap” method, an approximate procedure that in some circumstances can produce significant gains in simulation speed with acceptable losses in accuracy. Some primitive strategies for control parameter selection and error mitigation for the τ-leap method are described, and simulation results for two simple model systems are exhibited. With further refinement, the τ-leap method should provide a viable way of segueing from the exact SSA to the approximate chemical Langevin equation, and thence to the conventional deterministic reaction rate equation, as the system size becomes larger.

The chemical Langevin equation

Abstract: The stochastic dynamical behavior of a well-stirred mixture of N molecular species that chemically interact through M reaction channels is accurately described by the chemical master equation. It is shown here that, whenever two explicit dynamical conditions are satisfied, the microphysical premise from which the chemical master equation is derived leads directly to an approximate time-evolution equation of the Langevin type. This chemical Langevin equation is the same as one studied earlier by Kurtz, in contradistinction to some other earlier proposed forms that assume a deterministic macroscopic evolution law. The novel aspect of the present analysis is that it shows that the accuracy of the equation depends on the satisfaction of certain specific conditions that can change from moment to moment, rather than on a static system size parameter. The derivation affords a new perspective on the origin and magnitude of noise in a chemically reacting system. It also clarifies the connection between the stochas...

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Abstract: 抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

Reaction-rate theory: fifty years after Kramers

Abstract: The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

“Bioinformatics” 특집을 내면서

Abstract: BIOE 402. Medical Technology Assessment. 2 or 3 hours. Bioentrepreneur course. Assessment of medical technology in the context of commercialization. Objectives, competition, market share, funding, pricing, manufacturing, growth, and intellectual property; many issues unique to biomedical products. Course Information: 2 undergraduate hours. 3 graduate hours. Prerequisite(s): Junior standing or above and consent of the instructor.

A synthetic oscillatory network of transcriptional regulators

Abstract: Networks of interacting biomolecules carry out many essential functions in living cells, but the 'design principles' underlying the functioning of such intracellular networks remain poorly understood, despite intensive efforts including quantitative analysis of relatively simple systems Here we present a complementary approach to this problem: the design and construction of a synthetic network to implement a particular function We used three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network, termed the repressilator, in Escherichia coli The network periodically induces the synthesis of green fluorescent protein as a readout of its state in individual cells The resulting oscillations, with typical periods of hours, are slower than the cell-division cycle, so the state of the oscillator has to be transmitted from generation to generation This artificial clock displays noisy behaviour, possibly because of stochastic fluctuations of its components Such 'rational network design may lead both to the engineering of new cellular behaviours and to an improved understanding of naturally occurring networks

Cavity Optomechanics

Abstract: We review the field of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity quantum optomechanics experiments In addition, we describe the perspectives for fundamental quantum physics and for possible applications of optomechanical devices