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Data-Driven Method for Efficient Characterization of Rare Event Probabilities in Biochemical Systems

BULLETIN OF MATHEMATICAL BIOLOGY 2019年第8期81卷 3097-3120页

作者： Roh, Min K. Inst Dis Modeling 3150 139th Ave SE Bellevue WA 98005 USA

As mathematical models and computational tools become more sophisticated and powerful to accurately depict system dynamics, numerical methods that were previously considered computationally impractical started being utilized for large-scale simulations. Methods that characterize a rare event in biochemical systems are part of such phenomenon, as many of them are computationally expensive and require highperformance computing. In this paper, we introduce an enhanced version of the doubly weighted stochastic simulation algorithm (dwSSA) (Daigle et al. in J Chem Phys 134: 044110, 2011), called dwSSA ++, that significantly improves the speed of convergence to the rare event of interest when the conventional multilevel cross-entropy method in dwSSA is either unable to converge or converges very slowly. This achievement is enabled by a novel polynomial leaping method that uses past data to detect slow convergence and attempts to push the system toward the rare event. We demonstrate the performance of dwSSA ++ on two systems-a susceptible-infectious-recoveredsusceptible disease dynamics model and a yeast polarization model-and compare its computational efficiency to that of dwSSA.

关键词： Stochastic simulation Rare event probability estimation SSA dwSSA gillespie algorithm Importance sampling

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A simple method for simulating biochemical reaction networks

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ARTIFICIAL LIFE AND ROBOTICS 2009年第2期13卷 566-569页

作者： Umeki, Mai Suzuki, Yasuhiro Nagoya Univ Grad Sch Informat Sci Dept Complex Syst Sci Chikusa Ku Nagoya Aichi 4648603 Japan

We propose a simple method of simulating chemical reaction networks by using a multiset rewriting system: abstract rewriting system on multisets (ARMS). We simulate the oregonator model, a mathematical model of the Belousov-Zhabotinskii reaction, and we obtain the same behavior when the differential equations or the gillespie method are used. We also compose a 1- and 2-dimensional cellular automata by using ARMS, and confirm that it shows the pattern forming that is observed in the BZ reaction.

关键词： Artificial chemistries Cellular automata gillespie algorithm Pattern formation Belousov-Zhabotinskiin reaction Abstract rewriting system on multisets (ARMS)

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Modelling of translation of human protein disulfide isomerase in Escherichia coli -: A case study of gene optimisation

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JOURNAL OF BIOTECHNOLOGY 2005年第1期120卷 11-24页

作者： Niemitalo, O Neubauer, A Liebal, U Myllyharju, J Juffer, AH Neubauer, P Univ Oulu Dept Proc & Environm Engn Bioproc Engn Lab Oulu Finland Univ Oulu Collagen Res Unit Dept Med Biochem & Mol Biol Oulu Finland Triacle Biocomp Oulu Finland Bioctr Oulu Oulu Finland

Recombinant human protein disulfide isomerase (PDI) was expressed in vivo in Escherichia coli using a non-optimised gene sequence and an optimised sequence with four 5' codons substituted by synonymous codons that take less time to translate. The optimisation resulted in a 2-fold increase of total PDI concentration and by successive optimisation with expression at low temperature in a 10-fold increase of the amount of soluble PDI in comparison with the original wild-type construct. The improvement can be due to a faster clearing of the ribosome binding site on the mRNA, elevating the translation initiation rate and resulting in higher ribosome loading and better ribosome protection of the PDI mRNA against endonucleolytic cleavage by RNase. This hypothesis was supported by a novel computer simulation model of E. coli translational ribosome traffic based upon the stochastic gillespie algorithm. The study indicates the applicability of such models in optimisation of recombinant protein sequences. (c) 2005 Elsevier B.V All rights reserved.

关键词： codon usage gillespie algorithm translation PDI recombinant protein Escherichia coli computer simulation

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A review of the nondeterministic waiting time algorithm

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NATURAL COMPUTING 2011年第1期10卷 139-149页

作者： Jack, John Paun, Andrei Rodriguez-Paton, Alfonso IfM Louisiana Tech Univ Dept Comp Sci Ruston LA 71272 USA Univ Politecn Madrid Dept Inteligencia Artificial Fac Informat E-28660 Madrid Spain Natl Inst Res & Dev Biol Sci Bioinformat Dept Bucharest Romania

We provide the description for the nondeterministic waiting time (NWT) algorithm, a biochemical modeling approach based on the membrane systems paradigm of computation. The technique provides a unique (different to gillespie's algorithm or ODE modeling) perspective on the biochemical evolution of the cell. That is, depending on the reactions and molecular multiplicities of a given model, our simulator is capable of producing results comparable to the alternative techniques-continuous and deterministic or discrete and stochastic. Some results for sample models are given, illustrating the differences between the NWT algorithm, the gillespie algorithm, and the solutions to systems of ordinary differential equations. We have previously used this simulation technique to address issues surrounding Fas-induced apoptosis in cancerous cells and so-called latent HIV-infected cells.

关键词： Systems biology Biochemical modeling Stochastic Discrete gillespie algorithm Lotka-Volterra Circadian rhythm

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Serial transfer can aid the evolution of autocatalytic sets

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Journal of Systems Chemistry 2014年第1期5卷 1-8页

作者： Hordijk, Wim Vaidya, Nilesh Lehman, Niles *** Lausanne Switzerland Department of Chemistry Portland State University PO Box 751 Portland 97207 OR United States Department of Chemical and Biological Engineering Princeton University Princeton 08544 NJ United States

Background: The concept of an autocatalytic set of molecules has been posited theoretically and demonstrated empirically with catalytic RNA molecules. For this concept to have significance in a realistic origins-of-life scenario, it will be important to demonstrate the evolvability of such sets. Here, we employ a gillespie algorithm to improve and expand on previous simulations of an empirical system of self-assembling RNA fragments that has the ability to spontaneously form autocatalytic networks. We specifically examine the role of serial transfer as a plausible means to allow time-dependent changes in set composition, and compare the results to equilibrium, or "batch" scenarios. Results: We show that the simulation model produces results that are in close agreement with the original experimental observations in terms of generating varying autocatalytic (sub)sets over time. Furthermore, the model results indicate that in a "batch" scenario the equilibrium distribution is largely determined by competition for resources and stochastic fluctuations. However, with serial transfer the system is prevented from reaching such an equilibrium state, and the dynamics are mostly determined by differences in reaction rates. This is a consistent pattern that can be repeated, or made stronger or weaker by varying the reaction rates or the duration of the transfer steps. Increasing the number of molecules in the simulation actually strengthens the potential for selection. Conclusions: These simulations provide a more realistic emulation of wet lab conditions using self-assembling catalytic RNAs that form interaction networks. In doing so, they highlight the potential evolutionary advantage to a prebiotic scenario that involves cyclic dehydration/rehydration events. We posit that such cyclicity is a plausible means to promote evolution in primordial autocatalytic sets, which could later lead to the establishment of individual-based biology. © 2014 Hordijk et al.

关键词： Autocatalytic set gillespie algorithm Origins of life RNA Serial transfer

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Stochastic Gene Expression Modeling with Hill Function for Switch-like Gene Responses

Stochastic Gene Expression Modeling with Hill Function for S...

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IEEE International Conference on Bioinformatics and Biomedicine (BIBM)

作者： Kim, Haseong Gelenbe, Erol Imperial Coll London Dept Elect & Elect Engn Intelligent Syst & Networks Grp London England

ISBN: (纸本)9781424483075

Gene expression models play a key role to understand the mechanisms of gene regulation whose aspects are grade and switch-like responses. Though many stochastic approaches attempt to explain the gene expression mechanisms, the gillespie algorithm which is commonly used to simulate the stochastic models hardly explain the switch-like behaviors of gene responses. In this study, we propose a stochastic gene expression model which can describe the switch-like behaviors of gene responses by employing Hill functions to the conventional gillespie algorithm. We assume eight processes of gene expression and their biologically appropriate reaction rates are estimated based on published literatures. Our negative regulatory model shows that the modified gillespie algorithm successfully describes the switch-like behaviors of gene responses, which is consistent with a published experimental study. We observe that the state of the system of the toggled switch model is rarely changed since the Hill function prevents the activation of involved proteins when their concentrations stay at low level. In ScbA/ScbR system which can control the antibiotic metabolite production of microorganisms, our proposed stochastic approach successfully models its switch-like gene response and oscillatory expressions.

关键词： Stochastic gene expression modeling Gene regulatory networks Switch-like gene responses gillespie algorithm

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Silent circulation of poliovirus in small populations

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Infectious Disease Modelling 2017年第4期2卷 431-440页

作者： Celeste Vallejo James Keesling James Koopman Burton Singer Department of Mathematics 1400 Stadium RdUniversity of FloridaGainesvilleFL 32611United States School of Public Health 1415 Washington HeightsAnn ArborMI 48109-2029United States Emerging Pathogens Institute University of FloridaP.O.Box 1000092055 Mowry RoadGainesvilleFL 32610United States University of Florida Department of MathematicsUnited States University of Michigan Department of EpidemiologyUnited States Emerging Pathogens Institute at the University of Florida United States

Background:Small populations that have been isolated by conflict make vaccination and surveillance difficult,threatening polio *** circulation is caused by asymptomatic *** is currently not clear whether the dynamics of waning immunity also influence the risk of silent circulation in the absence of *** circulation can,nevertheless,be present following a declaration of elimination as a result of inadequate acute flaccid paralysis surveillance(AFPS)or environmental surveillance(ES).Methods:We have constructed a stochastic model to understand how stochastic effects alter the ability of small populations to sustain virus circulation in the absence of *** analyzed how the stochastic process determinants of the duration of silent circulation that could have been detected by ES were affected by R0,waning dynamics,population size,and AFPS sensitivity in a discrete individual stochastic model with homogeneous contagiousness and random *** measured the duration of silent circulation both by the interval between detected acute flaccid paralysis(AFP)cases and the duration of circulation until ***:As R0 increased and population size increased,the interval between detected AFP cases and the duration of circulation until elimination *** AFPS detection rates decreased,the interval between detected AFP cases *** was up to a 22%chance of silent circulation lasting for more than 3 years with 100%AFP *** duration of silent circulation was not affected by the waning immunity ***:We demonstrated that small populations have the potential to sustain prolonged silent *** in these areas should be intensified before declaring *** further validate these conclusions,it is necessary to realistically relax the simplifying assumptions about mixing and waning.

关键词： Poliovirus Silent circulation Acute flaccid paralysis surveillance Microsimulation model gillespie algorithm

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Modeling stochastic noise in gene regulatory systems

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Frontiers of Electrical and Electronic Engineering in China 2014年第1期9卷 1-29页

作者： Arwen Meister Chao Du Ye Henry Li Wing Hung Wong Computational Biology Lab Bio-X Program Stanford University Stanford CA 94305 USA

The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady- states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems.

关键词： gene regulation stochastic modeling simulation Master equation gillespie algorithm Langevin equation

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Non-Markovian processes in gene regulation

Non-Markovian processes in gene regulation

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Conference on Noise in Complex Systems and Stochastic Dynamics III

作者： Bratsun, DA Volfson, DN Hasty, J Tsimring, LS Univ Calif San Diego Dept Bioengn La Jolla CA 92093 USA

ISBN: (纸本)0819458406

We study the stochastic properties of gene regulation taking into account the non-Markovian character of gene transcription and translation. We show that time delay in protein production or degradation may change the behavior of the system from stationary to oscillatory even when a deterministic counterpart of the stochastic system exhibits no oscillations. Assuming significant decorrelation on the time scale of gene transcription, we deduce a truncated master equation of the reactive system and derive an analytical expression for the autocorrelation function of the protein concentration. For weak feedback the theory agrees well with with numerical simulations based on the modified direct gillespie method.

关键词： gene regulatory networks intrinsic noise non-Markovian processes time delay gillespie algorithm

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Biophysical Modeling of a Drosophila Photoreceptor

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16th International Conference on Neural Information Processing (ICONIP 2009)

作者： Song, Zhuoyi Coca, Daniel Billings, Stephen Postma, Marten Hardie, Roger C. Juusola, Mikko Univ Sheffield Dept Automat Control & Syst Engn Mappin St Sheffield S1 3JD S Yorkshire England Univ Sheffield Western Bank Dept Biomed Sci Sheffield S10 2TN S Yorkshire England Univ Cambridge Dept Physiol Dev & Neurosci Cambridge CB2 3DY England

ISBN: (纸本)9783642106767

It remains unclear how visual information is co-processed by different layers of neurons in the retina. In particular, relatively little is known how retina translates vast environmental light changes into neural responses of limited range. We began examining this question in a bottom-up way in a relatively simple fly eye. To gain understanding of how complex bio-molecular interactions govern the conversion of light input into voltage output (phototransduction), we are building a biophysical model of the Drosophila R1-R6 photoreceptor. Our model, which relates molecular dynamics of the underlying biochemical reactions to external light input, attempts to capture the molecular dynamics of phototransduction gain control in a quantitative way.

关键词： Biophysical model Drosophila photoreceptor phototransduction cascade gillespie algorithm Hodgkin-Huxley model

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