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Chemical master equation

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https://www.readbyqxmd.com/read/29353313/general-solution-of-the-chemical-master-equation-and-modality-of-marginal-distributions-for-hierarchic-first-order-reaction-networks
#1
Matthias Reis, Justus A Kromer, Edda Klipp
Multimodality is a phenomenon which complicates the analysis of statistical data based exclusively on mean and variance. Here, we present criteria for multimodality in hierarchic first-order reaction networks, consisting of catalytic and splitting reactions. Those networks are characterized by independent and dependent subnetworks. First, we prove the general solvability of the Chemical Master Equation (CME) for this type of reaction network and thereby extend the class of solvable CME's. Our general solution is analytical in the sense that it allows for a detailed analysis of its statistical properties...
January 20, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29347590/emergent-l%C3%A3-vy-behavior-in-single-cell-stochastic-gene-expression
#2
Chen Jia, Michael Q Zhang, Hong Qian
Single-cell gene expression is inherently stochastic; its emergent behavior can be defined in terms of the chemical master equation describing the evolution of the mRNA and protein copy numbers as the latter tends to infinity. We establish two types of "macroscopic limits": the Kurtz limit is consistent with the classical chemical kinetics, while the Lévy limit provides a theoretical foundation for an empirical equation proposed in N. Friedman et al., Phys. Rev. Lett. 97, 168302 (2006)PRLTAO0031-900710.1103/PhysRevLett...
October 2017: Physical Review. E
https://www.readbyqxmd.com/read/29327936/a-simple-boxed-molecular-kinetics-approach-to-accelerate-rare-events-in-the-stochastic-kinetic-master-equation
#3
Robin Shannon, David R Glowacki
The chemical master equation is a powerful theoretical tool for analysing the kinetics of complex multi-well potential energy surfaces in a wide range of different domains of chemical kinetics spanning combustion, atmospheric chemistry, gas-surface chemistry, solution phase chemistry, and biochemistry. There are two well-established methodologies for solving the chemical master equation: a stochastic "kinetic Monte Carlo" approach and a matrix-based approach. In principle, the results yielded by both approaches are identical; the decision of which approach is better suited to a particular study depends on the details of the specific system under investigation...
January 12, 2018: Journal of Physical Chemistry. A
https://www.readbyqxmd.com/read/29306304/a-variational-approach-to-moment-closure-approximations-for-the-kinetics-of-biomolecular-reaction-networks
#4
Leo Bronstein, Heinz Koeppl
Approximate solutions of the chemical master equation and the chemical Fokker-Planck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the moment-closure approach used to obtain such approximations, calling it an ad hoc method. In this article, we give a new variational derivation of moment-closure equations which provides us with an intuitive understanding of their properties and failure modes and allows us to correct some of these problems...
January 7, 2018: Journal of Chemical Physics
https://www.readbyqxmd.com/read/29286686/chemical-continuous-time-random-walks
#5
Tomás Aquino, Marco Dentz
Kinetic Monte Carlo methods such as the Gillespie algorithm model chemical reactions as random walks in particle number space. The interreaction times are exponentially distributed under the assumption that the system is well mixed. We introduce an arbitrary interreaction time distribution, which may account for the impact of incomplete mixing on chemical reactions, and in general stochastic reaction delay, which may represent the impact of extrinsic noise. This process defines an inhomogeneous continuous time random walk in particle number space, from which we derive a generalized chemical master equation...
December 8, 2017: Physical Review Letters
https://www.readbyqxmd.com/read/29272940/applicability-of-transfer-tensor-method-for-open-quantum-system-dynamics
#6
Andrius Gelzinis, Edvardas Rybakovas, Leonas Valkunas
Accurate simulations of open quantum system dynamics is a long standing issue in the field of chemical physics. Exact methods exist, but are costly, while perturbative methods are limited in their applicability. Recently a new black-box type method, called transfer tensor method (TTM), was proposed [J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014)]. It allows one to accurately simulate long time dynamics with a numerical cost of solving a time-convolution master equation, provided many initial system evolution trajectories are obtained from some exact method beforehand...
December 21, 2017: Journal of Chemical Physics
https://www.readbyqxmd.com/read/29272930/mesoscopic-microscopic-spatial-stochastic-simulation-with-automatic-system-partitioning
#7
Stefan Hellander, Andreas Hellander, Linda Petzold
The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian dynamics or Green's function reaction dynamics, the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution...
December 21, 2017: Journal of Chemical Physics
https://www.readbyqxmd.com/read/29247320/time-dependent-propagators-for-stochastic-models-of-gene-expression-an-analytical-method
#8
Frits Veerman, Carsten Marr, Nikola Popović
The inherent stochasticity of gene expression in the context of regulatory networks profoundly influences the dynamics of the involved species. Mathematically speaking, the propagators which describe the evolution of such networks in time are typically defined as solutions of the corresponding chemical master equation (CME). However, it is not possible in general to obtain exact solutions to the CME in closed form, which is due largely to its high dimensionality. In the present article, we propose an analytical method for the efficient approximation of these propagators...
December 15, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29243748/global-minimum-profile-error-gmpe-a-least-squares-based-approach-for-extracting-macroscopic-rate-coefficients-for-complex-gas-phase-chemical-reactions
#9
Minh V Duong, Hieu T Nguyen, Tam V-T Mai, Lam K Huynh
Master equation/Rice-Ramsperger-Kassel-Marcus (ME/RRKM) has shown to be a powerful framework for modeling kinetic and dynamic behaviors of a complex gas-phase chemical system on a complicated multiple-species and multiple-channel potential energy surface (PES) for a wide range of temperatures and pressures. Derived from the ME time-resolved species profiles, the macroscopic or phenomenological rate coefficients are essential for many reaction engineering applications including those in combustion and atmospheric chemistry...
December 15, 2017: Physical Chemistry Chemical Physics: PCCP
https://www.readbyqxmd.com/read/29133841/nanopore-electric-snapshots-of-an-rna-tertiary-folding-pathway
#10
Xinyue Zhang, Dong Zhang, Chenhan Zhao, Kai Tian, Ruicheng Shi, Xiao Du, Andrew J Burcke, Jing Wang, Shi-Jie Chen, Li-Qun Gu
The chemical properties and biological mechanisms of RNAs are determined by their tertiary structures. Exploring the tertiary structure folding processes of RNA enables us to understand and control its biological functions. Here, we report a nanopore snapshot approach combined with coarse-grained molecular dynamics simulation and master equation analysis to elucidate the folding of an RNA pseudoknot structure. In this approach, single RNA molecules captured by the nanopore can freely fold from the unstructured state without constraint and can be programmed to terminate their folding process at different intermediates...
November 13, 2017: Nature Communications
https://www.readbyqxmd.com/read/29098989/an-application-of-the-krylov-fsp-ssa-method-to-parameter-fitting-with-maximum-likelihood
#11
Khanh N Dinh, Roger B Sidje
Monte Carlo methods such as the stochastic simulation algorithm (SSA) have traditionally been employed in gene regulation problems. However, there has been increasing interest to directly obtain the probability distribution of the molecules involved by solving the chemical master equation (CME). This requires addressing the curse of dimensionality that is inherent in most gene regulation problems. The finite state projection (FSP) seeks to address the challenge and there have been variants that further reduce the size of the projection or that accelerate the resulting matrix exponential...
November 3, 2017: Physical Biology
https://www.readbyqxmd.com/read/29064498/ephemeral-collision-complexes-mediate-chemically-termolecular-transformations-that-affect-system-chemistry
#12
Michael P Burke, Stephen J Klippenstein
Termolecular association reactions involve ephemeral collision complexes-formed from the collision of two molecules-that collide with a third and chemically inert 'bath gas' molecule that simply transfers energy to/from the complex. These collision complexes are generally not thought to react chemically on collision with a third molecule in the gas-phase systems of combustion and planetary atmospheres. Such 'chemically termolecular' reactions, in which all three molecules are involved in bond making and/or breaking, were hypothesized long ago in studies establishing radical chain branching mechanisms, but were later concluded to be unimportant...
November 2017: Nature Chemistry
https://www.readbyqxmd.com/read/29057418/the-reaction-of-criegee-intermediates-with-acids-and-enols
#13
L Vereecken
The reaction of CH2OO, the smallest carbonyl oxide (Criegee intermediate, CI), with several acids was investigated using the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ quantum chemical method, as well as microvariational transition state theory and RRKM master equation theoretical kinetic methodologies. For oxoacids HNO3 and HCOOH, a 1,4-insertion mechanism allows for barrierless reactions with high rate coefficients, in agreement with literature experimental data. This mechanism relies on the presence of a double bond in the α-position to the acidic OH group...
November 1, 2017: Physical Chemistry Chemical Physics: PCCP
https://www.readbyqxmd.com/read/29055349/a-finite-state-projection-algorithm-for-the-stationary-solution-of-the-chemical-master-equation
#14
Ankit Gupta, Jan Mikelson, Mustafa Khammash
The chemical master equation (CME) is frequently used in systems biology to quantify the effects of stochastic fluctuations that arise due to biomolecular species with low copy numbers. The CME is a system of ordinary differential equations that describes the evolution of probability density for each population vector in the state-space of the stochastic reaction dynamics. For many examples of interest, this state-space is infinite, making it difficult to obtain exact solutions of the CME. To deal with this problem, the Finite State Projection (FSP) algorithm was developed by Munsky and Khammash [J...
October 21, 2017: Journal of Chemical Physics
https://www.readbyqxmd.com/read/29040384/selansi-a-toolbox-for-simulation-of-stochastic-gene-regulatory-networks
#15
Manuel Pájaro, Irene Otero-Muras, Carlos Vázquez, Antonio A Alonso
Motivation: Gene regulation is inherently stochastic. In many applications concerning Systems and Synthetic Biology such as the reverse engineering and the de novo design of genetic circuits, stochastic effects (yet potentially crucial) are often neglected due to the high computational cost of stochastic simulations. With advances in these fields there is an increasing need of tools providing accurate approximations of the stochastic dynamics of gene regulatory networks (GRNs) with reduced computational effort...
October 11, 2017: Bioinformatics
https://www.readbyqxmd.com/read/28976756/barrierless-reactions-with-loose-transition-states-govern-the-yields-and-lifetimes-of-organic-nitrates-derived-from-isoprene
#16
Ivan R Piletic, Edward O Edney, Libero J Bartolotti
The chemical reaction mechanism of NO addition to two β and δ isoprene hydroxy-peroxy radical isomers is examined in detail using density functional theory, coupled cluster methods, and the energy resolved master equation formalism to provide estimates of rate constants and organic nitrate yields. At the M06-2x/aug-cc-pVTZ level, the potential energy surfaces of NO reacting with β-(1,2)-HO-IsopOO(•) and δ-Z-(1,4)-HO-IsopOO(•) possess barrierless reactions that produce alkoxy radicals/NO2 and organic nitrates...
October 20, 2017: Journal of Physical Chemistry. A
https://www.readbyqxmd.com/read/28938803/hybrid-models-for-chemical-reaction-networks-multiscale-theory-and-application-to-gene-regulatory-systems
#17
Stefanie Winkelmann, Christof Schütte
Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations...
September 21, 2017: Journal of Chemical Physics
https://www.readbyqxmd.com/read/28886641/length-and-sequence-relaxation-of-copolymers-under-recombination-reactions
#18
Alex Blokhuis, David Lacoste
We describe the kinetics and thermodynamics of copolymers undergoing recombination reactions, which are important for prebiotic chemistry. We use two approaches: the first one, based on chemical rate equations and the mass-action law describes the infinite size limit, while the second one, based on the chemical master equation, describes systems of finite size. We compare the predictions of both approaches for the relaxation of thermodynamic quantities towards equilibrium. We find that for some choice of initial conditions, the entropy of the sequence distribution can be lowered at the expense of increasing the entropy of the length distribution...
September 7, 2017: Journal of Chemical Physics
https://www.readbyqxmd.com/read/28881987/efficient-simulation-of-intrinsic-extrinsic-and-external-noise-in-biochemical-systems
#19
Dennis Pischel, Kai Sundmacher, Robert J Flassig
Motivation: Biological cells operate in a noisy regime influenced by intrinsic, extrinsic and external noise, which leads to large differences of individual cell states. Stochastic effects must be taken into account to characterize biochemical kinetics accurately. Since the exact solution of the chemical master equation, which governs the underlying stochastic process, cannot be derived for most biochemical systems, approximate methods are used to obtain a solution. Results: In this study, a method to efficiently simulate the various sources of noise simultaneously is proposed and benchmarked on several examples...
July 15, 2017: Bioinformatics
https://www.readbyqxmd.com/read/28862457/reaction-paths-and-chemical-activation-reactions-of-2-methyl-5-furanyl-radical-with-3-o2
#20
Jason M Hudzik, Joseph W Bozzelli
Interest in high-energy substituted furans has been increasing due to their occurrence in biofuel production and their versatility in conversion to other useful products. Methylfurans are the simplest substituted furans and understanding their reaction pathways, thermochemical properties, including intermediate species stability, and chemical kinetics would aid in the study of larger furans. Furan ring C-H bonds have been shown to be extremely strong, approximately 120 kcal mol(-1), due in part to the placement of the oxygen atom and aromatic-like resonance, both within the ring...
September 26, 2017: Journal of Physical Chemistry. A
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