Growth and Dissolution of Macromolecular Markov Chains

Gaspard, Pierre

doi:10.1007/s10955-016-1532-x

Cited by 30 publications

(62 citation statements)

References 44 publications

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“…We have demonstrated our results for coupled overdamped Langevin equations but expect our results to hold more generally for continuous processes, as is the case for the infimum of entropy production [11]. Using the Doob-Meyer decomposition of entropy production, our definition of entropic time can also be generalized to underdamped systems [43,44] and jump processes [45].…”

Section: A) B) C)mentioning

confidence: 63%

Generic Properties of Stochastic Entropy Production

et al. 2017

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We derive an Itô stochastic differential equation for entropy production in nonequilibrium Langevin processes. Introducing a random-time transformation, entropy production obeys a onedimensional drift-diffusion equation, independent of the underlying physical model. This transformation allows us to identify generic properties of entropy production. It also leads to an exact uncertainty equality relating the Fano factor of entropy production and the Fano factor of the random time, which we also generalize to non steady-state conditions. The laws of thermodynamics can be extended to mesoscopic systems [1][2][3][4][5]. For such systems, energy changes on the order of the thermal energy k B T are relevant. Here, k B is the Boltzmann constant and T the temperature. Therefore, thermodynamic observables associated with mesoscopic degrees of freedom are stochastic. A key example of such thermodynamics observables is the stochastic entropy production in nonequilibrium processes. Recent experimental advances in micromanipulation techniques permit the measurement of stochastic entropy production in the laboratory [6][7][8][9][10].Certain statistical properties of stochastic entropy production are generic, i.e., they are independent of the physical details of a system. Examples of such generic properties are the celebrated fluctuation theorems, for reviews see [2,4,5]. Recently, it was shown that infima and passage probabilities of entropy production are also generic [11]. Other statistical properties of entropy production are system-dependent, such as the mean value [12][13][14][15], the variance [16,17], the first-passage times of entropy production [18][19][20] and the large deviation function [21,22]. Nevertheless, these properties are sometimes constrained by universal bounds [11,14,16,17,[23][24][25][26][27]. It remains unclear which statistical properties of stochastic entropy production are generic, and why.In this Letter, we introduce a theoretical framework which addresses this question for nonequilibrium Langevin processes. We identify generic properties of entropy production by their independence of a stochastic variable τ which we call entropic time. We find that the evolution of steady-state entropy production as a function of τ is governed by a simple one-dimensional driftdiffusion process, independent of the underlying model. This allows us to identify a set of generic properties of entropy production and obtain exact results characterizing entropy production fluctuations.We consider a mesoscopic system described by n slow degrees of freedom X = (X 1 (t), X 2 (t), . . . , X n (t)) T . The system is in contact with a thermostat at temperature T . The stochastic dynamics of the system can be described by the probability distribution P ( X, t) to find the system in a configuration X at time t . This probability distribution satisfies the Smoluchowski equationwhere the probability current is given byHere we have introduced the force at time t, F = − ∇U ( X(t), t) + f ( X(t), t), where U is a potential and f is a...

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Section: A) B) C)mentioning

confidence: 63%

Generic Properties of Stochastic Entropy Production

et al. 2017

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“…With these definitions, Eqs. (14), (15),... of the hierarchy can be rewritten in the following matricial form:…”

Section: Introducing the Notationmentioning

confidence: 99%

Multistate reversible copolymerization of non-Markovian chains under low conversion conditions

Gaspard

2019

The Journal of Chemical Physics

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The reversible kinetics of copolymerization is solved analytically for the multistate mechanism proposed by B. D. T. G. Fox [J. Chem. Phys. 38, 1065 (1963)] under low conversion conditions where the concentrations of monomeric species are chemostatted and stay constant in time. Although the rates of this mechanism only depends on the currently attached or detached monomer, the growing macromolecular chain forms a nonMarkovian sequence that is characterized by matrices associated with every monomeric unit composing the sequence. These matrices are obtained by solving the kinetic equations and they determine the growth velocity of the copolymers, the statistical properties of its possible sequences, as well as the thermodynamics of the copolymerization process.

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“…For h-order processes, we set the initial seed as a given distribution q X1...X h α1...α h . One can follow the logic of Sec.II to obtain 13) or equivalently,…”

Section: Generalization To Higher Order Processesmentioning

confidence: 99%

Template-specific fidelity of DNA replication with high-order neighbor effects: A first-passage approach

Zheng

Shu

et al. 2019

Phys. Rev. E

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DNA replication fidelity is a critical issue in molecular biology. Biochemical experiments have provided key insights on the mechanism of fidelity control by DNAP in the past decades, whereas systematic theoretical studies on this issue began only recently. Because of the underlying difficulties of mathematical treatment, comprehensive surveys on the template-specific replication kinetics are still rare. Here we proposed a first-passage approach to address this problem, in particular the positional fidelity, for complicated processes with high-order neighbor effects. Under biologicallyrelevant conditions, we derived approximate analytical expressions of the positional fidelity which shows intuitively how some key kinetic pathways are coordinated to guarantee the high fidelity, as well as the high velocity, of the replication processes. It was also shown that the fidelity at any template position is dominantly determined by the nearest-neighbor template sequences, which is consistent with the idea that replication mutations are randomly distributed in the genome.

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Growth and Dissolution of Macromolecular Markov Chains

Cited by 30 publications

References 44 publications

Generic Properties of Stochastic Entropy Production

Generic Properties of Stochastic Entropy Production

Multistate reversible copolymerization of non-Markovian chains under low conversion conditions

Template-specific fidelity of DNA replication with high-order neighbor effects: A first-passage approach

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