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Accelerated regression-based summary statistics for discrete stochastic systems via approximate simulators

BMC BIOINFORMATICS 2021年第1期22卷 339-339页

作者： Jiang, Richard M. Wrede, Fredrik Singh, Prashant Hellander, Andreas Petzold, Linda R. Univ Calif Santa Barbara Dept Comp Sci Santa Barbara CA 93106 USA Uppsala Univ Dept Informat Technol Uppsala Sweden

Background Approximate Bayesian Computation (ABC) has become a key tool for calibrating the parameters of discrete stochastic biochemical models. For higher dimensional models and data, its performance is strongly dependent on having a representative set of summary statistics. While regression-based methods have been demonstrated to allow for the automatic construction of effective summary statistics, their reliance on first simulating a large training set creates a significant overhead when applying these methods to discrete stochastic models for which simulation is relatively expensive. In this tau work, we present a method to reduce this computational burden by leveraging approximate simulators of these systems, such as ordinary differential equations and tau-Leaping approximations. Results We have developed an algorithm to accelerate the construction of regression-based summary statistics for Approximate Bayesian Computation by selectively using the faster approximate algorithms for simulations. By posing the problem as one of ratio estimation, we use state-of-the-art methods in machine learning to show that, in many cases, our algorithm can significantly reduce the number of simulations from the full resolution model at a minimal cost to accuracy and little additional tuning from the user. We demonstrate the usefulness and robustness of our method with four different experiments. Conclusions We provide a novel algorithm for accelerating the construction of summary statistics for stochastic biochemical systems. Compared to the standard practice of exclusively training from exact simulator samples, our method is able to dramatically reduce the number of required calls to the stochastic simulator at a minimal loss in accuracy. This can immediately be implemented to increase the overall speed of the ABC workflow for estimating parameters in complex systems.

关键词： Approximate Bayesian Computation Summary statistics Discrete stochastic reaction systems Biochemical reaction systems gillespie algorithm

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A NEW STOCHASTIC SIQR (SUSCEPTIBLE-INFECTED- QUARANTINE-REMOVED) MODEL WITH TWO DELAYS: FORECASTING COVID-19 DIFFUSION

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INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING-THEORY APPLICATIONS AND PRACTICE 2023年第3期30卷 607-622页

作者： Lee, Han Sol Chang, Byeong-Yun Ajou Univ Dept E Business Suwon South Korea Ajou Univ Sch Business Suwon South Korea

There have been many efforts to prevent the spread of COVID-19 disease, such as developing medicine and vaccine or studying forecasting epidemic diffusion. In this study, we propose a new stochastic Susceptible-Infected-Quarantine Removed (SIQR) model with two delays. Unlike the traditional model, the SIQR model considers asymptomatic or pre symptomatic patients who can transmit the disease. We developed the observation delay to adjust the time differences between the true occurrence, the observation in the real world, and the reaction delay to reflect gradual changes in diffusion trends. Finally, we built a simulation of the complex model using the gillespie algorithm. We find that in terms of MAPE, RMSE, and MAD, the proposed SIQR model explains COVID-19 epidemic diffusion better than the traditional Susceptible-Exposed-Infected-Released (SEIR). In addition, over a relatively long-term period of time, the SIQR model shows better performance compared to the SEIR model with two delays.

关键词： Epidemic Diffusion Model gillespie algorithm Delay Chemical Reaction Model Simulation

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Protein pattern formation induced by the joint effect of noise and delay in a multi-cellular system*

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MATHEMATICAL MODELLING OF NATURAL PHENOMENA 2022年第0期17卷 16-16页

作者： Bratsun, Dmitry Perm Natl Res Polytech Univ Dept Appl Phys Perm 614990 Russia

We explore the combined effect of the intrinsic noise and time delay on the spatial pattern formation within the framework of a multi-scale mobile lattice model mimicking two-dimensional epithelium tissues. Every cell is represented by an elastic polygon changing its form and size under pressure from the surrounding cells. The model includes the procedure of minimization of the potential energy of tissue. The protein fluctuations in the tissue are driven by transcription/translation processes in epithelial cells exchanging chemical and mechanical signals. Network architecture includes a simple autorepressor model with time-delayed negative feedback, in which the only gene defines the oscillatory activity. Simultaneously, the expressed protein of the autorepressor acts as a positive regulator of the signaling protein by activating its transcription. The signaling species is assumed to spread from one cell to the other by the diffusion mechanism. We provide both deterministic and stochastic descriptions. The numerical simulation of spatially-extended stochastic oscillations is performed using a generalized gillespie algorithm. We developed this method earlier to account for the non-Markovian properties of random biochemical events with delay. Finally, we demonstrate that time delay, intrinsic noise, and spatial signaling can cause a system to develop the protein pattern even when its deterministic counterpart exhibits no pattern formation.

关键词： Time delay intrinsic noise gene regulation gillespie algorithm pattern formation

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The ISI distribution of the stochastic Hodgkin-Huxley neuron

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FRONTIERS IN COMPUTATIONAL NEUROSCIENCE 2014年第OCT期8卷 111页

作者： Rowat, Peter F. Greenwood, Priscilla E. Univ Calif San Diego Inst Neural Computat La Jolla CA 92093 USA Univ British Columbia Dept Math Vancouver BC Canada

The simulation of ion-channel noise has an important role in computational neuroscience. In recent years several approximate methods of carrying out this simulation have been published, based on stochastic differential equations, and all giving slightly different results. The obvious, and essential, question is: which method is the most accurate and which is most computationally efficient? Here we make a contribution to the answer. We compare interspike interval histograms from simulated data using four different approximate stochastic differential equation (SDE) models of the stochastic Hodgkin-Huxley neuron, as well as the exact Markov chain model simulated by the gillespie algorithm. One of the recent SDE models is the same as the Kurtz approximation first published in 1978. All the models considered give similar ISI histograms over a wide range of deterministic and stochastic input. Three features of these histograms are an initial peak, followed by one or more bumps, and then an exponential tail. We explore how these features depend on deterministic input and on level of channel noise, and explain the results using the stochastic dynamics of the model. We conclude with a rough ranking of the four SDE models with respect to the similarity of their ISI histograms to the histogram of the exact Markov chain model.

关键词： ISI distribution Hodgkin-Huxley stochastic dynamics stochastic differential equation ISI histogram gillespie algorithm Kurtz approximation

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Implementing sequence-based antigenic distance calculation into immunological shape space model

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BMC BIOINFORMATICS 2020年第1期21卷 256-256页

作者： Anderson, Christopher S. Sangster, Mark Y. Yang, Hongmei Mariani, Thomas J. Chaudhury, Sidhartha Topham, David J. Univ Rochester Sch Med & Dent Dept Pediat Med Ctr Rochester NY 14642 USA Univ Rochester Sch Med & Dent Dept Microbiol & Immunol David Smith Ctr Vaccine Biol & ImmunolNew York I Rochester NY 14642 USA Univ Rochester Sch Med & Dent Dept Biostat & Computat Biol Rochester NY USA Walter Reed Army Inst Res Ctr Enabling Capabil Silver Spring MD USA

Background In 2009, a novel influenza vaccine was distributed worldwide to combat the H1N1 influenza "swine flu" pandemic. However, antibodies induced by the vaccine display differences in their specificity and cross-reactivity dependent on pre-existing immunity. Here, we present a computational model that can capture the effect of pre-existing immunity on influenza vaccine responses. The model predicts the region of the virus hemagglutinin (HA) protein targeted by antibodies after vaccination as well as the level of cross-reactivity induced by the vaccine. We tested our model by simulating a scenario similar to the 2009 pandemic vaccine and compared the results to antibody binding data obtained from human subjects vaccinated with the monovalent 2009 H1N1 influenza vaccine. Results We found that both specificity and cross-reactivity of the antibodies induced by the 2009 H1N1 influenza HA protein were affected by the viral strain the individual was originally exposed. Specifically, the level of antigenic relatedness between the original exposure HA antigen and the 2009 HA protein affected antigenic-site immunodominance. Moreover, antibody cross-reactivity was increased when the individual's pre-existing immunity was specific to an HA protein antigenically distinct from the 2009 pandemic strain. Comparison of simulation data with antibody binding data from human serum samples demonstrated qualitative and quantitative similarities between the model and real-life immune responses to the 2009 vaccine. Conclusion We provide a novel method to evaluate expected outcomes in antibody specificity and cross-reactivity after influenza vaccination in individuals with different influenza HA antigen exposure histories. The model produced similar outcomes as what has been previously reported in humans after receiving the 2009 influenza pandemic vaccine. Our results suggest that differences in cross-reactivity after influenza vaccination should be expected in individuals with differe

关键词： gillespie algorithm Shape space Antigenic distance Epitopes Antigenic sites Hemagglutinin Influenza Vaccines Computational immunology HA Stalk Stem 2009 pandemic Artificial immune systems Humoral immune system Simulations

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

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2012年第4期9卷 973-979页

作者： Kim, Haseong Gelenbe, Erol Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2BT England

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 requires additional gene cascade to explain the switch-like behaviors of gene responses. In this study, we propose a stochastic gene expression model describing the switch-like behaviors of a gene 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. We observed 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 below a criterion. In ScbA-ScbR system, which can control the antibiotic metabolite production of microorganisms, our modified gillespie algorithm successfully describes the switch-like behaviors of gene responses and oscillatory expressions which are consistent with the published experimental study.

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

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Entropy and stochastic properties in catalysis at nanoscale

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PHYSICA SCRIPTA 2021年第8期96卷 085006-085006页

作者： Castellanos-Jaramillo, Juan Miguel Castellanos-Moreno, Arnulfo Univ Sonora Dept Fis Hermosillo Sonora Mexico

This work approaches the Michaelis-Menten model for enzymatic reactions at a nanoscale, where we focus on the quasi-stationary state of the process. The entropy and the kinetics of the stochastic fluctuations are studied to obtain new understanding about the catalytic reaction. The treatment of this problem begins with a state space describing an initial amount of substrate and enzyme-substrate complex molecules. Using the van Kampen expansion, this state space is split into a deterministic one for the mean concentrations involved, and a stochastic one for the fluctuations of these concentrations. The probability density in the fluctuation space displays a behavior that can be described as a rotation, which can be better understood using the formalism of stochastic velocities. The key idea is to consider an ensemble of physical systems that can be handled as if they were a purely conceptual gas in the fluctuation space. The entropy of the system increases when the reaction starts and slightly diminishes once it is over, suggesting: 1. The existence of a rearrangement process during the reaction. 2. According to the second law of thermodynamics, the presence of an external energy source that causes the vibrations of the structure of the enzyme to vibrate, helping the catalytic process. For the sake of completeness and for a uniform notation throughout this work and the ones referenced, the initial sections are dedicated to a short examination of the master equation and the van Kampen method for the separation of the problem into a deterministic and stochastic parts. A Fokker-Planck equation (FPE) is obtained in the latter part, which is then used as grounds to discuss the formalism of stochastic velocities and the entropy of the system. The results are discussed based on the references cited in this work.

关键词： michaelis-menten stochastic velocities entropy rearrangement process simulation gillespie algorithm nanoscale

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Mathematical modeling shows the frequency of Ca 2+ sparks in cells depends on the ryanodine receptor’s arrangement

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Procedia Computer Science 2017年 119卷 190-196页

作者： B.I. Iaparov S.Yu. Khamzin A.S. Moskvin O.E. Solovyova Ural Federal University 19 Mira str. 620002 Ekaterinburg Russia Institute of Immunology and Physiology UB RAS 106 Pervomayskaya str. 620219 Ekaterinburg Russia

Calcium dynamics plays key role in many intracellular processes. Studying of calcium sparks, that is events of calcium release via groups of ryanodine receptors, or RyR channels, is of a great importance for live sciences. Recent experimental studies show, that RyRs have a non-uniform arrangement in calcium release units (CRU), however, to our knowledge, there is yet no published Ca 2+ spark model which takes into account this fact. In the paper we made use of a genetic simulated annealing (GSA) algorithm for the RyR cluster generation and gillespie algorithm for modeling calcium spark. Computer simulation of the model CRU taking into account a specific homotetrameric structure of the RyR channel shows that experimental nearest neighbor distances (NND) distributions of RyRs in CRU do not provide exact information about calcium spark probability. Having the same NND distribution, the CRUs can have different inverse distance matrices and hence different calcium spark properties. Our model approach opens novel perspectives for studying the calcium release process.

关键词： Ryanodine receptor Calcium sparks gillespie algorithm Global optimization genetic algorithm simulated annealing

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STOCHASTIC SIMULATION OF A DIMER SODIUM PUMP

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JOURNAL OF BIOLOGICAL SYSTEMS 2011年第4期19卷 551-560页

作者： Tewari, Shivendra G. Indian Stat Inst Syst Sci & Informat Unit Bangalore 560059 Karnataka India

Sodium pump is known to play an important role in almost all organs of our human body like heart, kidney, liver, brain, etc. A number of mechanisms for sodium pumping have been proposed till date, with Albers Post Model being most widely used. Recently, Clarke proposed a two-gear dimer sodium pump model to replace the classical Albers-Post Model. This dimer model has two gears of sodium pumping depending upon the available adenosine triphosphate (ATP) concentrations. The mathematical model governing the two gears of sodium pumping overestimated the total fluorescence change of sodium pump labeled with voltage-sensitve probe RH421, which responds to electrogenic reactions of the pump, for ATP concentrations lesser than 25 mu M. In this article, a modification has been proposed to the existing dimer mathematical model. Also, it is well known that stochastic chemical kinetics of enzymes has a stronger physical basis than classical reaction rate equations. Hence, the modified mathematical model is simulated using STochastic Engine for Pathway Simulation (STEPS). The stochastic results are used to perform comparative analysis with experimental and deterministic results to validate the modified model and consequently the dimeric nature of sodium pump. The modified model gave a better prediction of total fluorescence change for over all possible range of ATP concentrations. Similar approach can be used to stochastically simulate other ion pumping processes.

关键词： Sodium Pump Mathematical Model gillespie algorithm STEPS

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A Stochastic version of corticosteriod pharmacogenomic model

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AAPS JOURNAL 2005年第1期7卷 E134-E140页

作者： Qi, XH NPERC Shanghai 200437 Peoples R China

The purpose of this study was to develop a stochastic version of corticosteriod fifth generation pharmacogenomic model. The gillespie algorithm was used to generate the independent time courses of the receptor messenger RNA ( mRNA). Initial parameters for the stochastic simulation were adapted from the study by Jin et al. The result obtained from the proposed stochastic model showed an overall agreement with the deterministic fifth generation model. This study suggested that because the stochastic model takes into account the "noise" nature of gene regulation, it would have potential application in pharmacogenomic modeling.

关键词： pharmacogenomic modeling corticosteroid stochastic gene gillespie algorithm Monte Carlo simulation

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