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Stochastic Modeling and Simulation of Filament Aggregation in Alzheimer's Disease

PROCESSES 2024年第1期12卷 157页

作者： Ojha, Vaghawan Prasad Yarahmadian, Shantia Om, Madhav Mississippi State Univ Dept Math & Stat Starkville MS 39762 USA IKebana Solut LLC Tokyo 1100015 Japan 10 Andes St Truganina Vic 3029 Australia

Alzheimer's disease has been a serious problem for humankind, one without a promising cure for a long time now, and researchers around the world have been working to better understand this disease mathematically, biologically and computationally so that a better cure can be developed and finally humanity can get some relief from this disease. In this study, we try to understand the progression of Alzheimer's disease by modeling the progression of amyloid-beta aggregation, leading to the formation of filaments using the stochastic method. In a noble approach, we treat the progression of filaments as a random chemical reaction process and apply the Monte Carlo simulation of the kinetics to simulate the progression of filaments of lengths up to 8. By modeling the progression of disease as a progression of filaments and treating this process as a stochastic process, we aim to understand the inherent randomness and complex spatial-temporal features and the convergence of filament propagation process. We also analyze different reaction events and observe the events such as primary as well as secondary elongation, aggregations and fragmentation using different propensities for different possible reactions. We also introduce the random switching of the propensity at random time, which further changes the convergence of the overall dynamics. Our findings show that the stochastic modeling can be utilized to understand the progression of amyloid-beta aggregation, which eventually leads to larger plaques and the development of Alzheimer disease in the patients. This method can be generalized for protein aggregation in any disease, which includes both the primary and secondary aggregation and fragmentation of proteins.

关键词： Alzheimer's AD stochastic modeling chemical reaction gillespie algorithm

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Multinomial tau-leaping method for stochastic kinetic simulations

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JOURNAL OF CHEMICAL PHYSICS 2007年第8期126卷 84101-1-84101-页

作者： Pettigrew, Michel F. Resat, Haluk Pacific NW Natl Lab Computat Biol & Bioinformat Grp Richland WA 99352 USA Pettigrew Consulting Edgewood WA 98371 USA

We introduce the multinomial tau-leaping (M tau L) method for general reaction networks with multichannel reactant dependencies. The M tau L method is an extension of the binomial tau-leaping method where efficiency is improved in several ways. First, tau-leaping steps are determined simply and efficiently using a priori information and Poisson distribution-based estimates of expectation values for reaction numbers over a tentative tau-leaping step. Second, networks are partitioned into closed groups of reactions and corresponding reactants in which no group reactant set is found in any other group. Third, product formation is factored into upper-bound estimation of the number of times a particular reaction occurs. Together, these features allow larger time steps where the numbers of reactions occurring simultaneously in a multichannel manner are estimated accurately using a multinomial distribution. Furthermore, we develop a simple procedure that places a specific upper bound on the total reaction number to ensure non-negativity of species populations over a single multiple-reaction step. Using two disparate test case problems involving cellular processes-epidermal growth factor receptor signaling and a lactose operon model-we show that the tau-leaping based methods such as the M tau L algorithm can significantly reduce the number of simulation steps thus increasing the numerical efficiency over the exact stochastic simulation algorithm by orders of magnitude. (c) 2007 American Institute of Physics.

关键词： CHEMICALLY REACTING SYSTEMS GROWTH-FACTOR RECEPTOR gillespie algorithm SIGNAL-TRANSDUCTION TIME-EVOLUTION NETWORKS

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Stochastic modeling of the chemostat

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ECOLOGICAL MODELLING 2011年第15期222卷 2676-2689页

作者： Campillo, F. Joannides, M. Larramendy-Valverde, I. UMR MISTEA INRIA INRA MERE Project Team F-34060 Montpellier 01 France Univ Montpellier 2 13M F-34095 Montpellier 5 France

The chemostat is classically represented, at large population scale, as a system of ordinary differential equations. Our goal is to establish a set of stochastic models that are valid at different scales: from the small population scale to the scale immediately preceding the one corresponding to the deterministic model. At a microscopic scale we present a pure jump stochastic model that gives rise, at the macroscopic scale, to the ordinary differential equation model. At an intermediate scale, an approximation diffusion allows us to propose a model in the form of a system of stochastic differential equations. We expound the mechanism to switch from one model to another, together with the associated simulation procedures. We also describe the domain of validity of the different models. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Stochastic differential equations Chemostat Pure jump process Diffusion approximation Tau-leap method Monte Carlo method gillespie algorithm

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***: Stochastic simulation in Julia

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COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2018年 167卷 23-35页

作者： Landeros, Alfonso Stutz, Timothy Keys, Kevin L. Alekseyenko, Alexander Sinsheimer, Janet S. Lange, Kenneth Sehl, Mary E. Univ Calif Los Angeles David Geffen Sch Med Dept Biomath Los Angeles CA 90095 USA Univ Calif San Francisco Dept Med San Francisco CA 94143 USA Med Univ South Carolina Dept Publ Hlth Sci Charleston SC 29425 USA Univ Calif Los Angeles David Geffen Sch Med Dept Human Genet Los Angeles CA 90095 USA

Background and Objectives: Biological systems with intertwined feedback loops pose a challenge to mathematical modeling efforts. Moreover, rare events, such as mutation and extinction, complicate system dynamics. Stochastic simulation algorithms are useful in generating time-evolution trajectories for these systems because they can adequately capture the influence of random fluctuations and quantify rare events. We present a simple and flexible package, ***, for implementing the gillespie algorithm, tau-leaping, and related stochastic simulation algorithms. The objective of this work is to provide scientists across domains with fast, user-friendly simulation tools. Methods: We used the high-performance programming language Julia because of its emphasis on scientific computing. Our software package implements a suite of stochastic simulation algorithms based on Markov chain theory. We provide the ability to (a) diagram Petri Nets describing interactions, (b) plot average trajectories and attached standard deviations of each participating species over time, and (c) generate frequency distributions of each species at a specified time. Results: ***'s interface allows users to build models programmatically within Julia. A model is then passed to the simulate routine to generate simulation data. The built-in tools allow one to visualize results and compute summary statistics. Our examples highlight the broad applicability of our software to systems of varying complexity from ecology, systems biology, chemistry, and genetics. Conclusion: The user-friendly nature of *** encourages the use of stochastic simulation, minimizes tedious programming efforts, and reduces errors during model specification. (C) 2018 Published by Elsevier B.V.

关键词： Stochastic simulation gillespie algorithm tau-leaping Systems biology Julia language

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Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales

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JOURNAL OF COMPUTATIONAL PHYSICS 2007年第1期221卷 158-180页

作者： Weinan, E. Liu, Di Vanden-Eijnden, Eric Michigan State Univ Dept Math E Lansing MI 48824 USA Princeton Univ Dept Math & PACM Princeton NJ 08544 USA NYU Courant Inst Math Sci New York NY 10012 USA

We present an efficient numerical algorithm for simulating chemical kinetic systems with multiple time scales. This algorithm is an improvement of the traditional stochastic simulation algorithm (SSA), also known as gillespie's algorithm. It is in the form of a nested SSA and uses an outer SSA to simulate the slow reactions with rates computed from realizations of inner SSAs that simulate the fast reactions. The algorithm itself is quite general and seamless, and it amounts to a small modification of the original SSA. Our analysis of such multi-scale chemical kinetic systems allows us to identify the slow variables in the system, derive effective dynamics on the slow time scale, and provide error estimates for the nested SSA. Efficiency of the nested SSA is discussed using these error estimates, and illustrated through several numerical examples. (c) 2006 Elsevier Inc. All rights reserved.

关键词： kinetic Monte-Carlo continuous-time Markov chains chemical master equations stochastic Petri nets gillespie algorithm averaging theorems multiscale numerical methods homogenization stochastic modeling multi-scale computation chemical kinetic systems

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Stochastic Models and Numerical algorithms for a Class of Regulatory Gene Networks

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BULLETIN OF MATHEMATICAL BIOLOGY 2009年第6期71卷 1394-1431页

作者： Fournier, Thomas Gabriel, Jean-Pierre Pasquier, Jerome Mazza, Christian Galbete, Jose Mermod, Nicolas Univ Fribourg Dept Math CH-1700 Fribourg Switzerland Univ Lausanne Inst Biotechnol CH-1015 Lausanne Switzerland

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

关键词： gillespie algorithm Gene network Self-promoter Quasi-equilibrium Dimerization Mean field Time delay

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Simulated maximum likelihood method for estimating kinetic rates in gene expression

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BIOINFORMATICS 2007年第1期23卷 84-91页

作者： Tian, Tianhai Xu, Songlin Gao, Junbin Burrage, Kevin Univ Queensland Adv Computat Modelling Ctr Brisbane Qld 4072 Australia Hubei Univ Technol Dept Math Wuhan 430068 Hubei Peoples R China Charles Sturt Univ Sch Informat Technol Bathurst NSW 2795 Australia

Motivation: Kinetic rate in gene expression is a key measurement of the stability of gene products and gives important information for the reconstruction of genetic regulatory networks. Recent developments in experimental technologies have made it possible to measure the numbers of transcripts and protein molecules in single cells. Although estimation methods based on deterministic models have been proposed aimed at evaluating kinetic rates from experimental observations, these methods cannot tackle noise in gene expression that may arise from discrete processes of gene expression, small numbers of mRNA transcript, fluctuations in the activity of transcriptional factors and variability in the experimental environment. Results: In this paper, we develop effective methods for estimating kinetic rates in genetic regulatory networks. The simulated maximum likelihood method is used to evaluate parameters in stochastic models described by either stochastic differential equations or discrete biochemical reactions. Different types of non-parametric density functions are used to measure the transitional probability of experimental observations. For stochastic models described by biochemical reactions, we propose to use the simulated frequency distribution to evaluate the transitional density based on the discrete nature of stochastic simulations. The genetic optimization algorithm is used as an efficient tool to search for optimal reaction rates. Numerical results indicate that the proposed methods can give robust estimations of kinetic rates with good accuracy. >

关键词： STOCHASTIC CHEMICAL-KINETICS REGULATORY NETWORKS DIFFERENTIAL-EQUATIONS BIOCHEMICAL REACTIONS PARAMETER-ESTIMATION BIOLOGICAL NETWORKS gillespie algorithm ESCHERICHIA-COLI TOGGLE SWITCH SYSTEMS

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Simulation of anaerobic digestion processes using stochastic algorithm

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JOURNAL OF ENVIRONMENTAL HEALTH SCIENCE AND ENGINEERING 2014年第1期12卷 1-8页

作者： Palanichamy, Jegathambal Palani, Sundarambal Karunya Univ Water Inst Coimbatore 641114 Tamil Nadu India Natl Univ Singapore Trop Marine Sci Inst Singapore 119227 Singapore

Background: The Anaerobic Digestion (AD) processes involve numerous complex biological and chemical reactions occurring simultaneously. Appropriate and efficient models are to be developed for simulation of anaerobic digestion systems. Although several models have been developed, mostly they suffer from lack of knowledge on constants, complexity and weak generalization. The basis of the deterministic approach for modelling the physico and bio-chemical reactions occurring in the AD system is the law of mass action, which gives the simple relationship between the reaction rates and the species concentrations. The assumptions made in the deterministic models are not hold true for the reactions involving chemical species of low concentration. The stochastic behaviour of the physicochemical processes can be modeled at mesoscopic level by application of the stochastic algorithms. Method: In this paper a stochastic algorithm (gillespie Tau Leap Method) developed in MATLAB was applied to predict the concentration of glucose, acids and methane formation at different time intervals. By this the performance of the digester system can be controlled. The processes given by ADM1 (Anaerobic Digestion Model 1) were taken for verification of the model. Results: The proposed model was verified by comparing the results of gillespie's algorithms with the deterministic solution for conversion of glucose into methane through degraders. At higher value of 'tau' (timestep), the computational time required for reaching the steady state is more since the number of chosen reactions is less. When the simulation time step is reduced, the results are similar to ODE solver. Conclusion: It was concluded that the stochastic algorithm is a suitable approach for the simulation of complex anaerobic digestion processes. The accuracy of the results depends on the optimum selection of tau value.

关键词： Anaerobic digestion Stochastic algorithm gillespie algorithm Modeling

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Modeling and simulation of transmembrane ionic transport of cells exposed to magnetic field using the Monte Carlo method

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JOURNAL OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2021年第1期21卷 243-254页

作者： Barrero-Moreno, M. C. Restrepo-Parra, E. Torres-Osorio, J. Univ Nacl Colombia Dept Fis & Quim Grp PCM Computat Applicat Manizales Colombia Univ Caldas Dept Fis Grp Invest Campos Electromagnet Medioambiente & S Manizales Colombia

This work presents a model for the simulation of plasmatic transmembrane ionic transport that may be exposed to a static gradient magnetic field. The simulation was carried out using the Monte Carlo method to simulate the transmembrane cell transport of five types of ions and obtain observables such as membrane potential, ionic current, and osmotic pressure. To implement the Monte Carlo method, a Hamiltonian was used that includes the contributions of the energy due to the cellular electric field, the electrostatic interaction between the ions, the friction force generated by moving the ion in the center and the contribution given by subduing a cell to a magnetic field gradient. The input parameters to carry out a simulation are the intra and extracellular concentrations of each ionic species, the length of the extracellular medium, the number of Monte Carlo steps (MCS) and the value of the magnetic gradient. The model was validated contrasting it with gillespie's algorithm to obtain variations less than 3 % in terms of membrane potential. The Monte Carlo Method combined with the Metropolis algorithm were considered for recreating the stochastic behavior of ion movement.

关键词： Ion channels membrane potential ionic current magnetic gradient gillespie algorithm

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Low Variance Couplings for Stochastic Models of Intracellular Processes with Time-Dependent Rate Functions

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BULLETIN OF MATHEMATICAL BIOLOGY 2019年第8期81卷 2902-2930页

作者： Anderson, David F. Yuan, Chaojie Univ Wisconsin Dept Math Madison WI 53706 USA

A number of coupling strategies are presented for stochastically modeled biochemical processes with time-dependent parameters. In particular, the stacked coupling is introduced and is shown via a number of examples to provide an exceptionally low variance between the generated paths. This coupling will be useful in the numerical computation of parametric sensitivities and the fast estimation of expectations via multilevel Monte Carlo methods. We provide the requisite estimators in both cases.

关键词： Stochastic chemical kinetics Variance reduction gillespie algorithm Stochastic simulation Non-homogeneous Markov chains

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