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Chemical master equation

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 15, 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
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
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
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
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
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
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
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
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
Gamze Gursoy, Anna Terebus, Youfang Cao, Jie Liang
Stochasticity plays important roles in regulation of biochemical reaction networks when the copy numbers of molecular species are small. Studies based on Stochastic Simulation Algorithm (SSA) has shown that a basic reaction system can display stochastic focusing (SF) by increasing the sensitivity of the network as a result of the signal noise. Although SSA has been widely used to study stochastic networks, it is ineffective in examining rare events and this becomes a significant issue when the tails of probability distributions are relevant as is the case of SF...
August 2016: Conference Proceedings: Annual International Conference of the IEEE Engineering in Medicine and Biology Society
Gamze Giirsoy, Anna Terebus, Youfang Cao, Jie Liang, Gamze Gursoy, Anna Terebus, Youfang Cao, Jie Liang, Gamze Gursoy, Youfang Cao, Anna Terebus, Jie Liang
Stochasticity plays important roles in regulation of biochemical reaction networks when the copy numbers of molecular species are small. Studies based on Stochastic Simulation Algorithm (SSA) has shown that a basic reaction system can display stochastic focusing (SF) by increasing the sensitivity of the network as a result of the signal noise. Although SSA has been widely used to study stochastic networks, it is ineffective in examining rare events and this becomes a significant issue when the tails of probability distributions are relevant as is the case of SF...
August 2016: Conference Proceedings: Annual International Conference of the IEEE Engineering in Medicine and Biology Society
Chao E, Baogen Duan, Jin Yu
Nucleotide selection is crucial for transcription fidelity control, in particular, for viral T7 RNA polymerase (RNAP) lack of proofreading activity. It has been recognized that multiple kinetic checkpoints exist prior to full nucleotide incorporation. In this work, we implemented intensive atomistic molecular dynamics (MD) simulations to quantify how strong the nucleotide selection is at the initial checkpoint of an elongation cycle of T7 RNAP. The incoming nucleotides bind into a preinsertion site where a critical tyrosine residue locates nearby to assist the nucleotide selection...
April 20, 2017: Journal of Physical Chemistry. B
Brian K Chu, Margaret J Tse, Royce R Sato, Elizabeth L Read
BACKGROUND: Gene regulatory networks with dynamics characterized by multiple stable states underlie cell fate-decisions. Quantitative models that can link molecular-level knowledge of gene regulation to a global understanding of network dynamics have the potential to guide cell-reprogramming strategies. Networks are often modeled by the stochastic Chemical Master Equation, but methods for systematic identification of key properties of the global dynamics are currently lacking. RESULTS: The method identifies the number, phenotypes, and lifetimes of long-lived states for a set of common gene regulatory network models...
February 6, 2017: BMC Systems Biology
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