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Chemical master equation

Long Zhao, Tao Yang, Ralf I Kaiser, Tyler Patrick Troy, Musahid Ahmed, Joao Marcelo Ribeiro, Daniel Belisario-Lara, Alexander Moiseevich Mebel
We investigated temperature-dependent products in the pyrolysis of helium-seeded n-dodecane, which represents a surrogate of the n-alkane fraction of Jet Propellant-8 (JP-8) aviation fuel. The experiments were performed in a high temperature chemical reactor over a temperature range of 1,200 K to 1,600 K at a pressure of 600 Torr, with in situ identification of the nascent products in a supersonic molecular beam using single photon vacuum ultraviolet (VUV) photoionization coupled with the analysis of the ions in a reflectron time-of-flight mass spectrometer (ReTOF)...
January 16, 2017: Journal of Physical Chemistry. A
Tao Hong, Zhengming Tang, Huacheng Zhu
The anomalous dielectric relaxation of disordered reaction with linear reaction dynamics is studied via the continuous time random walk model in the presence of space-dependent electric field. Two kinds of modified reaction-subdiffusion equations are derived for different linear reaction processes by the master equation, including the instantaneous annihilation reaction and the noninstantaneous annihilation reaction. If a constant proportion of walkers is added or removed instantaneously at the end of each step, there will be a modified reaction-subdiffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term...
December 28, 2016: Journal of Chemical Physics
C Groves
Charge transport simulation can be a valuable tool to better understand, optimise and design organic transistors (OTFTs), photovoltaics (OPVs), and light-emitting diodes (OLEDs). This review presents an overview of common charge transport and device models; namely drift-diffusion, master equation, mesoscale kinetic Monte Carlo and quantum chemical Monte Carlo, and a discussion of the relative merits of each. This is followed by a review of the application of these models as applied to charge transport in organic semiconductors and devices, highlighting in particular the insights made possible by modelling...
December 19, 2016: Reports on Progress in Physics
Luca Cardelli, Marta Kwiatkowska, Luca Laurenti
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species...
October 28, 2016: Bio Systems
Ramon Grima, André Leier
The rate of product formation is an important measure of the speed of enzyme reactions. Classical studies of enzyme reactions have been conducted in dilute solutions and under conditions that justified the substrate abundance assumption. However, such assumption is well-known to break down in the context of cellular biochemistry. Instead, the concentration of available substrate can become rate limiting. Here we use the chemical master equation to obtain expressions for the instantaneous and time averaged rate of product formation without invoking the conventional substrate abundance assumption...
December 27, 2016: Journal of Physical Chemistry. B
Anna Klimovskaia, Stefan Ganscha, Manfred Claassen
Stochastic chemical reaction networks constitute a model class to quantitatively describe dynamics and cell-to-cell variability in biological systems. The topology of these networks typically is only partially characterized due to experimental limitations. Current approaches for refining network topology are based on the explicit enumeration of alternative topologies and are therefore restricted to small problem instances with almost complete knowledge. We propose the reactionet lasso, a computational procedure that derives a stepwise sparse regression approach on the basis of the Chemical Master Equation, enabling large-scale structure learning for reaction networks by implicitly accounting for billions of topology variants...
December 2016: PLoS Computational Biology
Che-Chi Shu, Chen-Chao Yeh, Wun-Sin Jhang, Shih-Chiang Lo
The stochastic nature of gene regulatory networks described by Chemical Master Equation (CME) leads to the distribution of proteins. A deterministic bistability is usually reflected as a bimodal distribution in stochastic simulations. Within a certain range of the parameter space, a bistable system exhibits two stable steady states, one at the low end and the other at the high end. Consequently, it appears to have a bimodal distribution with one sub-population (mode) around the low end and the other around the high end...
2016: PloS One
Luca Cardelli, Marta Kwiatkowska, Luca Laurenti
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analyzed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species...
November 2016: Bio Systems
Youfang Cao, Anna Terebus, Jie Liang
The discrete chemical master equation (dCME) provides a fundamental framework for studying stochasticity in mesoscopic networks. Because of the multi-scale nature of many networks where reaction rates have large disparity, directly solving dCMEs is intractable due to the exploding size of the state space. It is important to truncate the state space effectively with quantified errors, so accurate solutions can be computed. It is also important to know if all major probabilistic peaks have been computed. Here we introduce the Accurate CME (ACME) algorithm for obtaining direct solutions to dCMEs...
2016: Multiscale Modeling & Simulation: a SIAM Interdisciplinary Journal
Neil U M Howes, James P A Lockhart, Mark A Blitz, Scott A Carr, Maria Teresa Baeza-Romero, Dwayne E Heard, Robin J Shannon, Paul W Seakins, T Varga
Using laser flash photolysis coupled to photo-ionization time-of-flight mass spectrometry (PIMS), methyl radicals (CH3) have been detected as primary products from the reaction of OH radicals with acetaldehyde (ethanal, CH3CHO) with a yield of ∼15% at 1-2 Torr of helium bath gas. Supporting measurements based on laser induced fluorescence studies of OH recycling in the OH/CH3CHO/O2 system are consistent with the PIMS study. Master equation calculations suggest that the origin of the methyl radicals is from prompt dissociation of chemically activated acetyl products and hence is consistent with previous studies which have shown that abstraction, rather than addition/elimination, is the sole route for the OH + acetaldehyde reaction...
September 29, 2016: Physical Chemistry Chemical Physics: PCCP
Cyrille Costentin, Jean-Michel Savéant
Among the many virtues ascribed to catalytic nanoparticles, the prospect that the passage from the macro- to the nanoscale may change product selectivity attracts increasing attention. To date, why such effects may exist lacks explanation. Guided by recent experimental reports, we propose that the effects may result from the coupling between the chemical steps in which the reactant, intermediates, and products are involved and transport of these species toward the catalytic surface. Considering as a thought experiment the competitive formation of hydrogen and formate upon reduction of hydrogenocarbonate ions on metals like palladium or platinum, a model is developed that allows one to identify the governing parameters and predict the effect of nanoscaling on selectivity...
October 18, 2016: Proceedings of the National Academy of Sciences of the United States of America
Colin S Gillespie, Andrew Golightly
Solving the chemical master equation exactly is typically not possible, so instead we must rely on simulation based methods. Unfortunately, drawing exact realisations, results in simulating every reaction that occurs. This will preclude the use of exact simulators for models of any realistic size and so approximate algorithms become important. In this paper we describe a general framework for assessing the accuracy of the linear noise and two moment approximations. By constructing an efficient space filling design over the parameter region of interest, we present a number of useful diagnostic tools that aids modellers in assessing whether the approximation is suitable...
October 1, 2016: Statistical Applications in Genetics and Molecular Biology
Sayuri K Hahl, Andreas Kremling
In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant...
2016: Frontiers in Genetics
Zachary Fox, Gregor Neuert, Brian Munsky
Emerging techniques now allow for precise quantification of distributions of biological molecules in single cells. These rapidly advancing experimental methods have created a need for more rigorous and efficient modeling tools. Here, we derive new bounds on the likelihood that observations of single-cell, single-molecule responses come from a discrete stochastic model, posed in the form of the chemical master equation. These strict upper and lower bounds are based on a finite state projection approach, and they converge monotonically to the exact likelihood value...
August 21, 2016: Journal of Chemical Physics
Mohamad Akbar Ali, Jason A Sonk, John R Barker
The reaction of methanimine (CH2NH) with the hydroperoxy (HO2) radical has been investigated by using a combination of ab initio and density functional theory (CCSD(T)/CBSB7//B3LYP+Dispersion/CBSB7) and master equation calculations based on transition state theory (TST). Variational TST was used to compute both canonical (CVTST) and microcanonical (μVTST) rate constants for barrierless reactions. The title reaction starts with the reversible formation of a cyclic prereactive complex (PRC) that is bound by ∼11 kcal/mol and contains hydrogen bonds to both nitrogen and oxygen...
September 15, 2016: Journal of Physical Chemistry. A
Neil L Wesch, Laura J Burlock, Robert J Gooding
The lengths of the telomere regions of chromosomes in a population of cells are modelled using a chemical master equation formalism, from which the evolution of the average number of cells of each telomere length is extracted. In particular, the role of the telomere-elongating enzyme telomerase on these dynamics is investigated. We show that for biologically relevant rates of cell birth and death, one finds a critical rate, R crit, of telomerase activity such that the total number of cells diverges. Further, R crit is similar in magnitude to the rates of mitosis and cell death...
2016: Physical Biology
Bryan Lau, Ofer Kedem, Mark A Ratner, Emily A Weiss
Ratchets rectify the motion of randomly moving particles, which are driven by isotropic sources of energy such as thermal and chemical energy, without applying a net, time-averaged force between source and drain. This paper describes the behavior of a damped electron, modeled by a quantum Lindblad master equation, within a flashing ratchet (a one-dimensional potential that oscillates between a flat surface and a periodic asymmetric surface). By examining the complete space of all biharmonic potential shapes and a large range of oscillation frequencies, two modes of ratchet operation, differentiated by their oscillation frequencies (relative to the rate of electron relaxation), are identified...
June 2016: Physical Review. E
Daniil A Andrienko, Iain D Boyd
Investigation of O2-N collisions is performed by means of the quasi-classical trajectory method on the two lowest ab initio potential energy surfaces at temperatures relevant to hypersonic flows. A complete set of bound-bound and bound-free transition rates is obtained for each precollisional rovibrational state. Special attention is paid to the vibrational and rotational relaxations of oxygen as a result of chemically non-reactive interaction with nitrogen atoms. The vibrational relaxation of oxygen partially occurs via the formation of an intermediate NO2 complex...
July 7, 2016: Journal of Chemical Physics
Stephen Smith, Ramon Grima
The chemical master equation (CME) is the exact mathematical formulation of chemical reactions occurring in a dilute and well-mixed volume. The reaction-diffusion master equation (RDME) is a stochastic description of reaction-diffusion processes on a spatial lattice, assuming well mixing only on the length scale of the lattice. It is clear that, for the sake of consistency, the solution of the RDME of a chemical system should converge to the solution of the CME of the same system in the limit of fast diffusion: Indeed, this has been tacitly assumed in most literature concerning the RDME...
May 2016: Physical Review. E
Tyler M Earnest, John A Cole, Joseph R Peterson, Michael J Hallock, Thomas E Kuhlman, Zaida Luthey-Schulten
Ribosomes-the primary macromolecular machines responsible for translating the genetic code into proteins-are complexes of precisely folded RNA and proteins. The ways in which their production and assembly are managed by the living cell is of deep biological importance. Here we extend a recent spatially resolved whole-cell model of ribosome biogenesis in a fixed volume [Earnest et al., Biophys J 2015, 109, 1117-1135] to include the effects of growth, DNA replication, and cell division. All biological processes are described in terms of reaction-diffusion master equations and solved stochastically using the Lattice Microbes simulation software...
October 2016: Biopolymers
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