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Chemical master equation

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
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
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
Jason Hudzik, Joseph William 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 understand 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 1, 2017: Journal of Physical Chemistry. A
Stefanie Winkelmann, Christof Schütte
Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest. We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments, and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method...
December 7, 2016: Journal of Chemical Physics
A Sahai, B Lopez, C O Johnston, M Panesi
A novel reduced-order method is presented for modeling reacting flows characterized by strong non-equilibrium of the internal energy level distribution of chemical species in the gas. The approach seeks for a reduced-order representation of the distribution function by grouping individual energy states into macroscopic bins, and then reconstructing state population using the maximum entropy principle. This work introduces an adaptive grouping methodology to identify and lump together groups of states that are likely to equilibrate faster with respect to each other...
August 7, 2017: Journal of Chemical Physics
Pierre M Winter, Michael Rheaume, Andrew L Cooksy
We have calculated the temperature-dependent rate coefficients of the addition reactions of butadien-2-yl (C4H5) and acroylyl (C3H3O) radicals with ethene (C2H4), carbon monoxide (CO), formaldehyde (H2CO), hydrogen cyanide (HCN), and ketene (H2CCO), in order to explore the balance between kinetic and thermodynamic control in these combustion-related reactions. For the C4H5 radical, the 1,3-diene form of the addition products is more stable than the 1,2-diene, but the 1,2-diene form of the radical intermediate is stabilized by an allylic delocalization, which may influence the relative activation energies...
August 7, 2017: Journal of Chemical Physics
Huy D Vo, Roger B Sidje
Solving the chemical master equation directly is difficult due to the curse of dimensionality. We tackle that challenge by a numerical scheme based on the quantized tensor train (QTT) format, which enables us to represent the solution in a compressed form that scales linearly with the dimension. We recast the finite state projection in this QTT framework and allow it to expand adaptively based on proven error criteria. The end result is a QTT-formatted matrix exponential that we evaluate through a combination of the inexact uniformization technique and the alternating minimal energy algorithm...
July 28, 2017: Journal of Chemical Physics
Greg T Drozd, Theo Kurtén, Neil M Donahue, Marsha I Lester
We used the steady-state master equation to model unimolecular decay of the Criegee intermediate formed from ozonolysis of 2,3-dimethyl-2-butene (tetramethylethylene, TME). Our results show the relative importance and time scales for both the prompt and thermal unimolecular decay of the dimethyl-substituted Criegee intermediate, (CH3)2COO. Calculated reactive fluxes show the importance of quantum mechanical tunneling for both prompt and thermal decay to OH radical products. We constrained the initial energy distribution of chemically activated (CH3)2COO formed in TME ozonolysis by combining microcanonical rates k(E) measured experimentally under collision-free conditions and modeled using semiclassical transition-state theory (SCTST) with pressure-dependent yields of stabilized Criegee intermediates measured with scavengers in flow-tube experiments...
August 2, 2017: Journal of Physical Chemistry. A
J David Van Dyken
Microscopic randomness and the small volumes of living cells combine to generate random fluctuations in molecule concentrations called "noise". Here I investigate the effect of noise on biochemical reactions obeying Michaelis-Menten kinetics, concluding that substrate noise causes these reactions to slow. I derive a general expression for the time evolution of the joint probability density of chemical species in arbitrarily connected networks of non-linear chemical reactions in small volumes. This equation is a generalization of the chemical master equation (CME), a common tool for investigating stochastic chemical kinetics, extended to reaction networks occurring in small volumes, such as living cells...
July 1, 2017: Journal of Theoretical Biology
Basil S Bayati
We describe a novel approach to quantifying the uncertainty inherent in the chemical kinetic master equation with stochastic coefficients. A stochastic collocation method is coupled to an analytical expansion of the master equation to analyze the effects of both extrinsic and intrinsic noise. The method consists of an analytical moment-closure method resulting in a large set of differential equations with stochastic coefficients that are in turn solved via a Smolyak sparse grid collocation method. We discuss the error of the method relative to the dimension of the model and clarify which methods are most suitable for the problem...
June 28, 2017: Journal of Chemical Physics
Wun-Sin Jhang, Shih-Chiang Lo, Chen-Chao Yeh, Che-Chi Shu
The cellular behaviors under the control of genetic circuits are subject to stochastic fluctuations, or noise. The stochasticity in gene regulation, far from a nuisance, has been gradually appreciated for its unusual function in cellular activities. In this work, with Chemical Master Equation (CME), we discovered that the addition of inhibitors altered the stochasticity of regulatory proteins. For a bistable system of a mutually inhibitory network, such a change of noise led to the migration of cells in the bimodal distribution...
June 30, 2017: Scientific Reports
Akira Matsugi, Kazuo Takahashi
The thermal decomposition reactions of 2,3,3,3- and trans-1,3,3,3-tetrafluoropropenes (TFPs) have been studied both experimentally and computationally to elucidate their kinetics and mechanism. The experiments were performed by observing the temporal profiles of HF produced in the decomposition of the tetrafluoropropenes behind shock waves at temperatures of 1540-1952 K (for 2,3,3,3-TFP) or 1525-1823 K (for trans-1,3,3,3-TFP) and pressure of 100-200 kPa in Ar bath. The reaction pathways responsible for the profiles were explored based on quantum chemical calculations...
June 27, 2017: Journal of Physical Chemistry. A
Yiwei Li, Osman Kahraman, Christoph A Haselwandter
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments...
May 2017: Physical Review. E
Katherine H Aull, Elizabeth J Tanner, Matthew Thomson, Leor S Weinberger
Threshold generation in fate-selection circuits is often achieved through deterministic bistability, which requires cooperativity (i.e., nonlinear activation) and associated hysteresis. However, the Tat positive-feedback loop that controls HIV's fate decision between replication and proviral latency lacks self-cooperativity and deterministic bistability. Absent cooperativity, it is unclear how HIV can temporarily remain in an off-state long enough for the kinetically slower epigenetic silencing mechanisms to act-expression fluctuations should rapidly trigger active positive feedback and replication, precluding establishment of latency...
June 6, 2017: Biophysical Journal
X Flora Meng, Ania-Ariadna Baetica, Vipul Singhal, Richard M Murray
Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses...
May 2017: Journal of the Royal Society, Interface
Joao Marcelo Ribeiro, Alexander M Mebel
Two ground-state CH radical reactions with the C3H4 isomers allene and methylacetylene occurring along the C4H5 potential energy surface (PES) were studied to probe the reaction mechanisms and final product distributions. The calculations were performed using a CCSD(T)-F12//B2PLYPD3 PES in combination with the 1-D chemical master equation. The reaction between the CH radical and allene was found to lead to exclusive "funneling" of the energized C4H5 intermediates into linear C4H5 configurations before reaching the exit channels, regardless of the specific nature of the initial bimolecular reactive encounter...
June 7, 2017: Physical Chemistry Chemical Physics: PCCP
Petra Rovó, Rasmus Linser
This paper deals with the theoretical foundation of proton magic angle spinning rotating-frame relaxation (R1ρ) and establishes the range of validity and accuracy of the presented approach to describe low-amplitude microsecond time scale motion in the solid state. Beside heteronuclear dipolar and chemical shift anisotropy interactions, a major source of relaxation for protons is the homonuclear dipolar interaction. For this latter relaxation process, no general analytical equation has been published until now, which would describe the R1ρ relaxation at any spinning speed, spin-lock field, or tilt angle...
June 14, 2017: Journal of Physical Chemistry. B
Marc Sturrock, Shiyu Li, Vahid Shahrezaei
Gene expression is an inherently noisy process. This noise is generally thought to be deleterious as precise internal regulation of biochemical reactions is essential for cell growth and survival. Self-repression of gene expression, which is the simplest form of a negative feedback loop, is commonly believed to be employed by cellular systems to decrease the stochastic fluctuations in gene expression. When there is some delay in autoregulation, it is also believed that this system can generate oscillations...
May 5, 2017: Journal of Theoretical Biology
Neslihan Avcu, Nihal Pekergin, Ferhan Pekergin, Cuneyt Guzelis
This paper proposes aggregation-based, three-stage algorithms to overcome the numerical problems encountered in computing stationary distributions and mean first passage times for multi-modal birth-death processes of large state space sizes. The considered birth-death processes which are defined by Chemical Master Equations are used in modeling stochastic behavior of gene regulatory networks. Computing stationary probabilities for a multi-modal distribution from Chemical Master Equations is subject to have numerical problems due to the probability values running out of the representation range of the standard programming languages with the increasing size of the state space...
April 27, 2017: IEEE/ACM Transactions on Computational Biology and Bioinformatics
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