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Dissecting cooperative calmodulin binding to CaM kinase II: a detailed stochastic model

JOURNAL OF COMPUTATIONAL NEUROSCIENCE 2009年第3期27卷 621-638页

作者： Byrne, Michael J. Putkey, John A. Waxham, M. Neal Kubota, Yoshihisa Univ Texas Houston Dept Neurobiol & Anat Sch Med Houston TX 77030 USA Univ Texas Houston Dept Biochem & Mol Biol Sch Med Houston TX 77030 USA

Calmodulin (CaM) is a major Ca2+ binding protein involved in two opposing processes of synaptic plasticity of CA1 pyramidal neurons: long-term potentiation (LTP) and depression (LTD). The N- and C-terminal lobes of CaM bind to its target separately but cooperatively and introduce complex dynamics that cannot be well understood by experimental measurement. Using a detailed stochastic model constructed upon experimental data, we have studied the interaction between CaM and Ca2+-CaM-dependent protein kinase II (CaMKII), a key enzyme underlying LTP. The model suggests that the accelerated binding of one lobe of CaM to CaMKII, when the opposing lobe is already bound to CaMKII, is a critical determinant of the cooperative interaction between Ca2+, CaM, and CaMKII. The model indicates that the target-bound Ca2+ free N-lobe has an extended lifetime and may regulate the Ca2+ response of CaMKII during LTP induction. The model also reveals multiple kinetic pathways which have not been previously predicted for CaM-dissociation from CaMKII.

关键词： Calmodulin CaMKII Synaptic plasticity gillespie algorithm Particle swarm theory

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TEMPERATURE EFFECTS ON THE STOCHASTIC GATING OF THE IP3R CALCIUM RELEASE CHANNEL: A NUMERICAL SIMULATION STUDY

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JOURNAL OF BIOLOGICAL SYSTEMS 2009年第4期17卷 817-852页

作者： Haeri, H. H. Hashemianzadeh, S. M. Monajjemi, M. Islamic Azad Univ Dept Phys Chem Tehran Sharq Branch Tehran Iran Islamic Azad Univ Dept Phys Chem Sci & Res Campus Tehran Iran Iran Univ Sci & Technol Coll Chem Tehran Iran

The importance of the kinetic study of endoplasmatic calcium ion channels in different intracellular processes is known today. Although there are few experimental reports on the temperature dependency of IP3R channel functions, we did not find any detailed theoretical study on this subject. For this purpose, we used a modified gillespie algorithm to investigate the effect of temperature on the conditions affecting the open state of a single subunit of the De Young-Keizer (DYK) model. Population of the states was considered as the subject of fluctuation. Key features of the channel, such as bell-shaped dependency of open probability to the Calcium concentrations were modeled at different temperatures, too. The range of temperature variation was selected by regarding the experimental data on IP3R channel. By increasing the temperature, we had the very slow time domains (t: 10(-1) s) and the much slower time domains (t: 10(0) s) in addition to other time domains, which could be seen as new time categories in InsP3R studies, and so the results were reported in these time domains, as well. We found out that increase in temperature declined the open probability in some concentrations of Ca2+ and/or IP3. Also, by introducing the intensity graphs, broadening of the range of fluctuations and lowering of the order of frequency of fluctuations for the population of each state were observed due to the temperature increments. The temperature effects on the activation and inactivation states of the channel were studied in the framework of the reaction paths. We did not find similar paths at different time domains;several paths observed which were totally different all together. These time-dependent reaction paths are also depending on the Ca2+ and/or the IP3 concentrations. So, one can predict the most probable reaction paths at different concentrations and temperatures and also determine which kind of the path it is;a path for closing the channel or a path to open it. Finally, t

关键词： Kinetic Monte Carlo Temperature Effect Stochasticity gillespie algorithm Channel Gating Reaction Paths

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Slow update stochastic simulation algorithms for modeling complex biochemical networks

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BIOSYSTEMS 2017年 162卷 135-146页

作者： Ghosh, Debraj De, Rajat K. Indian Stat Inst Machine Intelligence Unit Kolkata 700108 India

The stochastic simulation algorithm (SSA) based modeling is a well recognized approach to predict the stochastic behavior of biological networks. The stochastic simulation of large complex biochemical networks is a challenge as it takes a large amount of time for simulation due to high update cost. In order to reduce the propensity update cost, we proposed two algorithms: slow update exact stochastic simulation algorithm (SUESSA) and slow update exact sorting stochastic simulation algorithm (SUESSSA). We applied cache-based linear search (CBLS) in these two algorithms for improving the search operation for finding reactions to be executed. Data structure used for incorporating CBLS is very simple and the cost of maintaining this during propensity update operation is very low. Hence, time taken during propensity updates, for simulating strongly coupled networks, is very fast;which leads to reduction of total simulation time. SUESSA and SUESSSA are not only restricted to elementary reactions, they support higher order reactions too. We used linear chain model and colloidal aggregation model to perform a comparative analysis of the performances of our methods with the existing algorithms. We also compared the performances of our methods with the existing ones, for large biochemical networks including B cell receptor and FcERI signaling networks. (C) 2017 Elsevier B.V. All rights reserved.

关键词： gillespie algorithm B cell receptor signaling network Fc epsilon RI signaling network Stochastic modeling

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Mesoscopic behavior from microscopic Markov dynamics and its application to calcium release channels

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JOURNAL OF THEORETICAL BIOLOGY 2014年 343卷 102-112页

作者： Christian, Nils Skupin, Alexander Morante, Silvia Jansen, Karl Rossi, Giancarlo Ebenhoeh, Oliver Univ Aberdeen Dept Phys Aberdeen AB24 3UE Scotland Univ Luxembourg Luxembourg Ctr Syst Biomed L-4362 Esch Sur Alzette Luxembourg Inst Syst Biol Seattle WA 98109 USA Univ Roma Tor Vergata I-00133 Rome Italy Ist Nazl Fis Nucl Sez Roma I-00133 Rome Italy NIC DESY Zeuthen D-15738 Zeuthen Germany Helmholtz Ctr Potsdam GFZ German Res Ctr Geosci D-14473 Potsdam Germany Univ Dusseldorf Cluster Excellence Plant Sci CEPLAS D-40225 Dusseldorf Germany

A major challenge in biology is to understand how molecular processes determine phenotypic features. We address this fundamental problem in a class of model systems by developing a general mathematical framework that allows the calculation of mesoscopic properties from the knowledge of microscopic Markovian transition probabilities. We show how exact analytic formulae for the first and second moments of resident time distributions in mesostates can be derived from microscopic resident times and transition probabilities even for systems with a large number of microstates. We apply our formalism to models of the inositol trisphosphate receptor, which plays a key role in generating calcium signals triggering a wide variety of cellular responses. We demonstrate how experimentally accessible quantities, such as opening and closing times and the coefficient of variation of inter-spike intervals, and other, more elaborated, quantities can be analytically calculated from the underlying microscopic Markovian dynamics. A virtue of our approach is that we do not need to follow the detailed time evolution of the whole system, as we derive the relevant properties of its steady state without having to take into account the often extremely complicated transient features. We emphasize that our formulae fully agree with results obtained by stochastic simulations and approaches based on a full determination of the microscopic system's time evolution. We also illustrate how experiments can be devised to discriminate between alternative molecular models of the inositol trisphosphate receptor. The developed approach is applicable to any system described by a Markov process and, owing to the analytic nature of the resulting formulae, provides an easy way to characterize also rare events that are of particular importance to understand the intermittency properties of complex dynamic systems. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Calcium signaling IP3 receptor Emergent properties of mesostates gillespie algorithm

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A Multi-stage Representation of Cell Proliferation as a Markov Process

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BULLETIN OF MATHEMATICAL BIOLOGY 2017年第12期79卷 2905-2928页

作者： Yates, Christian A. Ford, Matthew J. Mort, Richard L. Univ Bath Dept Math Sci Ctr Math Biol Bath BA2 7AY Avon England Univ Lancaster Div Biomed & Life Sci Fac Hlth & Med Furness Bldg Lancaster LA1 4YG England Univ Edinburgh Western Gen Hosp MRC Human Genet Unit MRC IGMM Edinburgh EH4 2XU Midlothian Scotland McGill Univ Dept Human Genet Rosalind & Morris Goodman Canc Res Ctr 1160 Pine Ave West Montreal PQ H3A 1A3 Canada

The stochastic simulation algorithm commonly known as gillespie's algorithm (originally derived for modelling well-mixed systems of chemical reactions) is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well-mixed scenarios at the sub-cellular level it is often reasonable to assume that times between successive reaction/interaction events are exponentially distributed and can be appropriately modelled as a Markov process and hence simulated by the gillespie algorithm. However, gillespie's algorithm is routinely applied to model biological systems for which it was never intended. In particular, processes in which cell proliferation is important (e.g. embryonic development, cancer formation) should not be simulated naively using the gillespie algorithm since the history-dependent nature of the cell cycle breaks the Markov process. The variance in experimentally measured cell cycle times is far less than in an exponential cell cycle time distribution with the same mean. Here we suggest a method of modelling the cell cycle that restores the memoryless property to the system and is therefore consistent with simulation via the gillespie algorithm. By breaking the cell cycle into a number of independent exponentially distributed stages, we can restore the Markov property at the same time as more accurately approximating the appropriate cell cycle time distributions. The consequences of our revised mathematical model are explored analytically as far as possible. We demonstrate the importance of employing the correct cell cycle time distribution by recapitulating the results from two models incorporating cellular proliferation (one spatial and one non-spatial) and demonstrating that changing the cell cycle time distribution makes quantitative and qualitative differences to the outcome of the models. Our adaptation will allow modellers and experimentalists alike to appropriately represent cellular prolifera

关键词： Cell cycle Markovian representation Stochastic simulation gillespie algorithm Exponentially modified Erlang

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Multiscale Stochastic Reaction-Diffusion algorithms Combining Markov Chain Models with Stochastic Partial Differential Equations

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BULLETIN OF MATHEMATICAL BIOLOGY 2019年第8期81卷 3185-3213页

作者： Kang, Hye-Won Erban, Radek Univ Maryland Baltimore Cty Dept Math & Stat 1000 Hilltop Circle Baltimore MD 21250 USA Univ Oxford Math Inst Radcliffe Observ Quarter Woodstock Rd Oxford OX2 6GG England

Two multiscale algorithms for stochastic simulations of reaction-diffusion processes are analysed. They are applicable to systems which include regions with significantly different concentrations of molecules. In both methods, a domain of interest is divided into two subsets where continuous-time Markov chain models and stochastic partial differential equations (SPDEs) are used, respectively. In the first algorithm, Markov chain (compartment-based) models are coupled with reaction-diffusion SPDEs by considering a pseudo-compartment (also called an overlap or handshaking region) in the SPDE part of the computational domain right next to the interface. In the second algorithm, no overlap region is used. Further extensions of both schemes are presented, including the case of an adaptively chosen boundary between different modelling approaches.

关键词： Stochastic reaction-diffusion systems Chemical reaction networks Markov chain gillespie algorithm Multiscale modelling Stochastic partial differential equations

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Who is afraid of modelling time as a continuous variable?

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METHODS IN ECOLOGY AND EVOLUTION 2024年第10期15卷 1736-1756页

作者： Kokko, Hanna Johannes Gutenberg Univ Mainz Inst Organismal & Mol Evolut Mainz Germany Johannes Gutenberg Univ Mainz Inst Quant & Computat Biosci Mainz Germany

Most models of ecological and eco-evolutionary processes involve creating trajectories of something, be it population densities, average trait values, or environmental states, over time. This requires decision-making regarding how to represent the flow of time in models. Most ecologists are exposed to continuous-time models (typically in the form of ordinary differential equations) as part of their training, especially since the famous Lotka-Volterra predator-prey dynamics are formulated this way. However, few appear sufficiently well trained to produce their own work with continuous-time models and may lack exposure to the true versatility of available methods. Specifically, knowledge that discrete individuals can be modelled in continuous time using the gillespie algorithm is not as widespread as it should be. I will illustrate the flexibility of continous-time modelling methods such that researchers can make informed choices, and not resort to discretizing time as a 'default' without a clear biological motivation to do so. I provide three example-based tutorials: (1) a comparison of deterministic and stochastic dynamics of the Lotka-Volterra predator-prey model, (2) an evaluation of matelessness in a hypothetical insect population (and of selection to mate more often by either searching more efficiently or by shortening the 'time out' after each mating) and (3) within-season density dependence followed by a birth pulse leading to Beverton-Holt or Ricker dynamics depending on whether the deaths of conspecifics help reduce the mortality of others or not (compensatory mortality). I highlight properties of the exponential distribution that, while counter-intuitive, are good to know when deriving expected lifetime reproductive success or other similar quantities. I also give guidance on how to proceed if the so-called memorylessness assumption does not hold in a given situation, and show how continuous and discrete times can be freely mixed if the biological situation

关键词： Beverton-Holt model evolutionary dynamics gillespie algorithm mate searching population dynamics predator-prey dynamics Ricker model

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Extending the Multi-level Method for the Simulation of Stochastic Biological Systems

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BULLETIN OF MATHEMATICAL BIOLOGY 2016年第8期78卷 1640-1677页

作者： Lester, Christopher Baker, Ruth E. Giles, Michael B. Yates, Christian A. Univ Oxford Math Inst Woodstock Rd Oxford OX2 6GG England Univ Bath Dept Math Sci Bath BA2 7AY Avon England

The multi-level method for discrete-state systems, first introduced by Anderson and Higham (SIAM Multiscale Model Simul 10(1):146-179, 2012), is a highly efficient simulation technique that can be used to elucidate statistical characteristics of biochemical reaction networks. A single point estimator is produced in a cost-effective manner by combining a number of estimators of differing accuracy in a telescoping sum, and, as such, the method has the potential to revolutionise the field of stochastic simulation. In this paper, we present several refinements of the multi-level method which render it easier to understand and implement, and also more efficient. Given the substantial and complex nature of the multi-level method, the first part of this work reviews existing literature, with the aim of providing a practical guide to the use of the multi-level method. The second part provides the means for a deft implementation of the technique and concludes with a discussion of a number of open problems.

关键词： Stochastic simulation Gene regulatory networks Multi-level gillespie algorithm Tau-leaping

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Exploring the Molecular Origin of the High Selectivity of Multisubunit RNA Polymerases by Stochastic Kinetic Models

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INTERDISCIPLINARY SCIENCES-COMPUTATIONAL LIFE SCIENCES 2009年第2期1卷 91-98页

作者： Zhu, Rui de la Lande, Aurelien Zhang, Rui Salahub, Dennis R. Univ Calgary Dept Chem Calgary AB T2N 1N4 Canada Univ Calgary Inst Biocomplex & Informat Calgary AB T2N 1N4 Canada Univ Calgary Inst Sustainable Energy Environm & Econ Calgary AB T2N 1N4 Canada

RNA polymerases are molecular machines of great fidelity, which can recognize matched NTPs from unmatched NTPs and 2'-dNTPs. We investigated by a stochastic simulation algorithm the whole nucleotide addition cycle based on an event-driven model. This model allows us to examine possible molecular origins of the high fidelity of RNA polymerases. For unmatched NTP selectivity, the conclusions drawn from simulated elongation rates corroborate those derived from structural analysis. The presence of two conformations (Esite and pre-insertion site) for the incoming nucleotide before the polymerization reaction is sufficient to allow selectivity. Concerning sugar selectivity, our results indicate that selectivity is only achievable if slow chemical reactions occur for 2'-dNTP. These results can be used to understand recent experimental observations.

关键词： gene transcription multisubunit RNA polymerase nucleotide addition stochastic kinetics gillespie algorithm

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In silico simulation of biological network dynamics

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NATURE BIOTECHNOLOGY 2004年第8期22卷 1017-1019页

作者： Salwinski, L Eisenberg, D Univ Calif Los Angeles DOE Inst Gen & Prote Howard Hughes Med InstMol Biol Inst Los Angeles CA 90095 USA

Realistic simulation of biological networks requires stochastic simulation approaches because of the small numbers of molecules per cell. The high computational cost of stochastic simulation on conventional microprocessor-based computers arises from the intrinsic disparity between the sequential steps executed by a microprocessor program and the highly parallel nature of information flow within biochemical networks. This disparity is reduced with the Field Programmable Gate Array (FPGA)-based approach presented here. The parallel architecture of FPGAs, which can simulate the basic reaction steps of biological networks, attains simulation rates at least an order of magnitude greater than currently available microprocessors.

关键词： Stochastic chemical-kinetics gillespie algorithm Systems Cells

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