An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

Bezzola, Andri; Bales, Benjamin B.; Alkire, Richard C.; Petzold, Linda R.

doi:10.1016/j.jcp.2013.08.053

Cited by 15 publications

(21 citation statements)

References 37 publications

(50 reference statements)

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“…To incorporate diffusion into the stochastic simulations, we use a First Passage Time Kinetic Monte Carlo algorithm, based on ref. [50]. We assume the enzyme travels with 1D diffusion coefficient D and unbinds with rate k off .…”

Section: Plos Computational Biologymentioning

confidence: 99%

Stochastic modeling reveals kinetic heterogeneity in post-replication DNA methylation

et al. 2020

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DNA methylation is a heritable epigenetic modification that plays an essential role in mammalian development. Genomic methylation patterns are dynamically maintained, with DNA methyltransferases mediating inheritance of methyl marks onto nascent DNA over cycles of replication. A recently developed experimental technique employing immunoprecipitation of bromodeoxyuridine labeled nascent DNA followed by bisulfite sequencing (Repli-BS) measures post-replication temporal evolution of cytosine methylation, thus enabling genomewide monitoring of methylation maintenance. In this work, we combine statistical analysis and stochastic mathematical modeling to analyze Repli-BS data from human embryonic stem cells. We estimate site-specific kinetic rate constants for the restoration of methyl marks on >10 million uniquely mapped cytosines within the CpG (cytosine-phosphate-guanine) dinucleotide context across the genome using Maximum Likelihood Estimation. We find that post-replication remethylation rate constants span approximately two orders of magnitude, with half-lives of per-site recovery of steady-state methylation levels ranging from shorter than ten minutes to five hours and longer. Furthermore, we find that kinetic constants of maintenance methylation are correlated among neighboring CpG sites. Stochastic mathematical modeling provides insight to the biological mechanisms underlying the inference results, suggesting that enzyme processivity and/or collaboration can produce the observed kinetic correlations. Our combined statistical/mathematical modeling approach expands the utility of genomic datasets and disentangles heterogeneity in methylation patterns arising from replication-associated temporal dynamics versus stable cell-to-cell differences.

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Section: Plos Computational Biologymentioning

confidence: 99%

Stochastic modeling reveals kinetic heterogeneity in post-replication DNA methylation

et al. 2020

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Section: Processive Mechanismmentioning

confidence: 99%

Stochastic Modeling Reveals Kinetic Heterogeneity in Post-replication DNA Methylation

Busto-Moner¹,

Morival²,

Fahim³

et al. 2019

Preprint

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AbstractDNA methylation is a heritable epigenetic modification that plays an essential role in mammalian development. Genomic methylation patterns are dynamically maintained, with DNA methyltransferases mediating inheritance of methyl marks onto nascent DNA over cycles of replication. A recently developed experimental technique employing immunoprecipitation of bromodeoxyuridine labeled nascent DNA followed by bisulfite sequencing (Repli-BS) measures post-replication temporal evolution of cytosine methylation, thus enabling genome-wide monitoring of methylation maintenance. In this work, we combine statistical analysis and stochastic mathematical modeling to analyze Repli-BS data from human embryonic stem cells. We estimate site-specific kinetic rate constants for the restoration of methyl marks on >10 million uniquely mapped cytosines within the CpG (cytosine-phosphate-guanine) dinucleotide context across the genome using Maximum Likelihood Estimation. We find that post-replication remethylation rate constants span approximately two orders of magnitude, with half-lives of per-site recovery of steady-state methylation levels ranging from shorter than ten minutes to five hours and longer. Furthermore, we find that kinetic constants of maintenance methylation are correlated among neighboring CpG sites. Stochastic mathematical modeling provides insight to the biological mechanisms underlying the inference results, suggesting that enzyme processivity and/or collaboration can produce the observed kinetic correlations. Our combined statistical/mathematical modeling approach expands the utility of genomic datasets and disentangles heterogeneity in methylation patterns arising from replication-associated temporal dynamics versus stable cell-to-cell differences.

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“…While the calculation of first passage times in continua requires the numerical calculation of the Green's function, the first passage time on discrete lattices can be calculated efficiently in closed form. 17 The ELFPT method is accurate over large distances with atomic scale resolution, and is considerably faster for conditions where the (D/F) ratio is high. The performance of ELFPT relies on the ability to quickly compute exact exit-time distributions and to determine distances to the nearest walker and deposited islands.…”

Section: Computational Methodologymentioning

confidence: 99%

“…The performance of ELFPT relies on the ability to quickly compute exact exit-time distributions and to determine distances to the nearest walker and deposited islands. For ideal situations where adatoms diffuse over large distances before nucleating or attaching to islands, it was found 17 that the method achieved a speedup up to 100× over comparable KMC simulations.…”

Section: Computational Methodologymentioning

confidence: 99%

Numerical Scaling Studies of Kinetically-Limited Electrochemical Nucleation and Growth with Accelerated Stochastic Simulations

Bezzola

Bales

Petzold

et al. 2014

J. Electrochem. Soc.

Self Cite

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A stochastic atomic-scale lattice-based numerical method based on the Exact Lattice First Passage Time method was developed for the simulation of the early stages of kinetically controlled electrochemical nucleation and growth. Electrochemical reaction and surface diffusion on a hexagonal lattice was accounted for in a pristine physical model system that included edge diffusion along steps, and movement over step edges with Ehrlich-Schwöbel barrier. Five cases were investigated: homoexpitaxy, heteroepitaxy, multi-layer growth, terraces, and confined regions. For each, the influence of the physical parameters, deposition conditions, and system geometry on growth morphology was investigated. Simulation based studies of multilayer surface morphology were able to distinguish between layer-by-layer and island growth modes. On stepped terraces, parameter regions associated with he surface diffusion to deposition flux ratio (D/F) and the Ehrlich-Schwöbel barrier were identified under which deposition occurred either at the step edge or by nucleation and growth of islands on the terraces. The probability of growing single crystals in a small confined region was found to scale with D/F and the radius squared.

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An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

Cited by 15 publications

References 37 publications

Stochastic modeling reveals kinetic heterogeneity in post-replication DNA methylation

Stochastic modeling reveals kinetic heterogeneity in post-replication DNA methylation

Stochastic Modeling Reveals Kinetic Heterogeneity in Post-replication DNA Methylation

Numerical Scaling Studies of Kinetically-Limited Electrochemical Nucleation and Growth with Accelerated Stochastic Simulations

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