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Chemical master equation

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https://www.readbyqxmd.com/read/28692269/unimolecular-decay-of-the-dimethyl-substituted-criegee-intermediate-in-alkene-ozonolysis-decay-timescales-and-the-importance-of-tunneling
#1
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 (tetramethyl ethylene, TME). Our results show the relative importance and timescales 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 determined 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 semi-classical transition-state theory (SCTST) with pressure-dependent yields of stabilized Criegee intermediates measured with scavengers in flow-tube experiments...
July 10, 2017: Journal of Physical Chemistry. A
https://www.readbyqxmd.com/read/28676416/noise-slows-the-rate-of-michaelis-menten-reactions
#2
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
https://www.readbyqxmd.com/read/28668036/quantifying-uncertainty-in-the-chemical-master-equation
#3
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
https://www.readbyqxmd.com/read/28667253/inhibitors-alter-the-stochasticity-of-regulatory-proteins-to-force-cells-to-switch-to-the-other-state-in-the-bistable-system
#4
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
https://www.readbyqxmd.com/read/28618775/thermal-decomposition-of-2-3-3-3-and-trans-1-3-3-3-tetrafluoropropenes
#5
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
https://www.readbyqxmd.com/read/28618626/stochastic-lattice-model-of-synaptic-membrane-protein-domains
#6
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
https://www.readbyqxmd.com/read/28591615/transient-thresholding-a-mechanism-enabling-noncooperative-transcriptional-circuitry-to-form-a-switch
#7
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
https://www.readbyqxmd.com/read/28566513/recursively-constructing-analytic-expressions-for-equilibrium-distributions-of-stochastic-biochemical-reaction-networks
#8
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
https://www.readbyqxmd.com/read/28537287/reaction-mechanism-and-product-branching-ratios-of-the-ch-c3h4-reactions-a-theoretical-study
#9
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
https://www.readbyqxmd.com/read/28534618/microsecond-time-scale-proton-rotating-frame-relaxation-under-magic-angle-spinning
#10
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
https://www.readbyqxmd.com/read/28483564/the-influence-of-nuclear-compartmentalisation-on-stochastic-dynamics-of-self-repressing-gene-expression
#11
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
https://www.readbyqxmd.com/read/28463205/aggregation-for-computing-multi-modal-stationary-distributions-in-1-d-gene-regulatory-networks
#12
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
https://www.readbyqxmd.com/read/28451881/theoretical-study-of-the-h-hcn-%C3%A2-h-hcn-process
#13
Eberth Correa, Washington Barbosa da Silva, Patricia R P Barreto, Alessandra F Albernaz
We present a theoretical study on the detailed mechanism and kinetics of the H + HCN → H + HNC process. The potential energy surface was calculated at the complete basis set quantum chemical method, CBS-QB3. The vibrational frequencies and geometries for four isomers (H 2CN, cis-HCNH, trans-HCNH, CNH 2), and seven saddle points (TSn where n = 1 - 7) are very important and must be considered during the process of formation of the HNC in the reaction were calculated at the B3LYP/6-311G(2d,d,p) level, within CBS-QB3 method...
May 2017: Journal of Molecular Modeling
https://www.readbyqxmd.com/read/28435938/obtaining-effective-rate-coefficients-to-describe-the-decomposition-kinetics-of-the-corannulene-oxyradical-at-high-temperatures
#14
Hongmiao Wang, Xiaoqing You, Mark A Blitz, Michael J Pilling, Struan H Robertson
Unimolecular reactions play an important role in combustion kinetics. An important task of reaction kinetic analysis is to obtain the phenomenological rate coefficients for unimolecular reactions based on the master equation approach. In most cases, the eigenvalues of the transition matrix describing collisional internal energy relaxation are of much larger magnitude than and well separated from the chemically significant eigenvalues, so that phenomenological rate coefficients may be unequivocally derived for incorporation in combustion mechanisms...
April 24, 2017: Physical Chemistry Chemical Physics: PCCP
https://www.readbyqxmd.com/read/28388111/stochastic-simulation-of-reaction-diffusion-systems-a-fluctuating-hydrodynamics-approach
#15
Changho Kim, Andy Nonaka, John B Bell, Alejandro L Garcia, Aleksandar Donev
We develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuatinghydrodynamics (FHD). For hydrodynamicsystems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poissonfluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i...
March 28, 2017: Journal of Chemical Physics
https://www.readbyqxmd.com/read/28383887/kinetics-of-thermal-unimolecular-decomposition-of-acetic-anhydride-an-integrated-deterministic-and-stochastic-model
#16
Tam V-T Mai, Minh V Duong, Hieu T Nguyen, Kuang C Lin, Lam K Huynh
An integrated deterministic and stochastic model within the master equation/Rice-Ramsperger-Kassel-Marcus (ME/RRKM) framework was first used to characterize temperature- and pressure-dependent behaviors of thermal decomposition of acetic anhydride in a wide range of conditions (i.e., 300-1500 K and 0.001-100 atm). Particularly, using potential energy surface and molecular properties obtained from high-level electronic structure calculations at CCSD(T)/CBS, macroscopic thermodynamic properties and rate coefficients of the title reaction were derived with corrections for hindered internal rotation and tunneling treatments...
April 14, 2017: Journal of Physical Chemistry. A
https://www.readbyqxmd.com/read/28341132/stochastic-modeling-and-numerical-simulation-of-gene-regulatory-networks-with-protein-bursting
#17
Manuel Pájaro, Antonio A Alonso, Irene Otero-Muras, Carlos Vázquez
Gene expression is inherently stochastic. Advanced single-cell microscopy techniques together with mathematical models for single gene expression led to important insights in elucidating the sources of intrinsic noise in prokaryotic and eukaryotic cells. In addition to the finite size effects due to low copy numbers, translational bursting is a dominant source of stochasticity in cell scenarios involving few short lived mRNA transcripts with high translational efficiency (as is typically the case for prokaryotes), causing protein synthesis to occur in random bursts...
March 21, 2017: Journal of Theoretical Biology
https://www.readbyqxmd.com/read/28320908/reaction-and-relaxation-at-surface-hotspots-using-molecular-dynamics-and-the-energy-grained-master-equation-to-describe-diamond-etching
#18
David R Glowacki, W J Rodgers, Robin Shannon, Struan H Robertson, Jeremy N Harvey
The extent to which vibrational energy transfer dynamics can impact reaction outcomes beyond the gas phase remains an active research question. Molecular dynamics (MD) simulations are the method of choice for investigating such questions; however, they can be extremely expensive, and therefore it is worth developing cheaper models that are capable of furnishing reasonable results. This paper has two primary aims. First, we investigate the competition between energy relaxation and reaction at 'hotspots' that form on the surface of diamond during the chemical vapour deposition process...
April 28, 2017: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28306551/master-equations-and-the-theory-of-stochastic-path-integrals
#19
Markus F Weber, Erwin Frey
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations...
April 2017: Reports on Progress in Physics
https://www.readbyqxmd.com/read/28301761/reaction-mechanisms-on-multiwell-potential-energy-surfaces-in-combustion-and-atmospheric-chemistry
#20
David L Osborn
Chemical reactions occurring on a potential energy surface with multiple wells are ubiquitous in low-temperature combustion and in the oxidation of volatile organic compounds in Earth's atmosphere. The rich variety of structural isomerizations that compete with collisional stabilization makes characterizing such complex-forming reactions challenging. This review describes recent experimental and theoretical advances that deliver increasingly complete views of their reaction mechanisms. New methods for creating reactive intermediates coupled with multiplexed measurements provide many experimental observables simultaneously...
May 5, 2017: Annual Review of Physical Chemistry
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