Network theory of microscopic and macroscopic behavior of master equation systems

Schnakenberg, J.

doi:10.1103/revmodphys.48.571

Cited by 1,012 publications

(1,401 citation statements)

References 21 publications

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“…In a constant external magnetic field, Eq. (4) represents a system of linear first-order differential equations subject to an initial condition p(0), and the general solution can be expressed by diagonalisation of the transition matrix [5,9], yielding the time evolution of the probability of each state as:…”

Section: Methodsmentioning

confidence: 99%

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Consistent energy barrier distributions in magnetic particle chains

Laslett

Ruta

Chantrell

et al. 2016

Physica B: Condensed Matter

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We investigate long-time thermal activation behaviour in magnetic particle chains of variable length. Chains are modelled as Stoner-Wohlfarth particles coupled by dipolar interactions. Thermal activation is described as a hopping process over a multidimensional energy landscape using the discrete orientation model limit of the Landau-Lifshitz-Gilbert dynamics. The underlying master equation is solved by diagonalising the associated transition matrix, which allows the evaluation of distributions of time scales of intrinsic thermal activation modes and their energy representation. It is shown that as a result of the interaction dependence of these distributions, increasing the particle chain length can lead to acceleration or deceleration of the overall relaxation process depending on the initialisation procedure.

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Section: Methodsmentioning

confidence: 99%

“…The probability that the system resides in a microstate α at a time t is denoted p α (t). The time evolution of all microstate probabilities p(t) is studied by solving the master equation [9,10] motivated by the discrete orientation model limit of the Landau-Lifshitz-Gilbert dynamics [6]:…”

Section: Methodsmentioning

confidence: 99%

Consistent energy barrier distributions in magnetic particle chains

Laslett

Ruta

Chantrell

et al. 2016

Physica B: Condensed Matter

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“…where the last equality follows from (48). Therefore, the postulated relation (45) is indeed valid for a two-state system coupled to a heat reservoir.…”

Section: Appendix: Local and Nonlocal Balance Relationsmentioning

confidence: 73%

“…Energy conservation during a transition |ab from state a to state b is now described by U b − U a = −Q ab (48) which represents a special case of local energy conservation as described by (7). …”

Section: Appendix: Local and Nonlocal Balance Relationsmentioning

confidence: 99%

Energy Conversion by Molecular Motors Coupled to Nucleotide Hydrolysis

2009

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Recent theoretical work on the energy conversion by molecular motors coupled to nucleotide hydrolysis is reviewed. The most abundant nucleotide is provided by adenosine triphosphate (ATP) which is cleaved into adenosine diphosphate (ADP) and inorganic phosphate. The motors have several catalytic domains (or active sites), each of which can be empty or occupied by ATP or ADP. The chemical composition of all catalytic domains defines distinct nucleotide states of the motor which form a discrete state space. Each of these motor states is connected to several other states via chemical transitions. For stepping motors such as kinesin, which walk along cytoskeletal filaments, some motor states are also connected by mechanical transitions, during which the motor is displaced along the filament and able to perform mechanical work. The different motor states together with the possible chemical and mechanical transitions provide a network representation for the chemomechanical coupling of the motor molecule. The stochastic motor dynamics on these networks exhibits several distinct motor cycles, which represent the dominant pathways for different regimes of nucleotide concentrations and load force. For the kinesin motor, the competition of two such cycles determines the stall force, at which the motor velocity vanishes and the motor reverses its direction of motion. In general, kinesin is found to be governed by the competition of three distinct chemomechanical cycles. The corresponding network representation provides a unified description for all motor properties that have been determined by single molecule experiments.

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“…The above results for the 3-state driven system can be generalized to any single macromolecules in aqueous solution with stochastic dynamics, either in terms of discrete master equations [23] or continuous Brownian dynamics [24,19]. The discrete approach is a tradition of chemical kinetics.…”

Section: Nepf Based On Stochastic Macromolecule Mechanics Of Driven Smentioning

confidence: 96%

Nonequilibrium Potential Function of Chemically Driven Single Macromolecules via Jarzynski-Type Log-Mean-Exponential Heat

Qian

2005

J. Phys. Chem. B

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Applying the method from recently developed fluctuation theorems to the stochastic dynamics of single macromolecules in ambient fluid at constant temperature, we establish two Jarzynski-type equalities: (1) between the log-mean-exponential (LME) of the irreversible heat dissiption of a driven molecule in nonequilibrium steady-state (NESS) and ln P ness (x), and (2) between the LME of the work done by the internal force of the molecule and nonequilibrium chemical potential function µ ness (x) ≡ U(x) + k B T ln P ness (x), where P ness (x) is the NESS probability density in the phase space of the macromolecule and U(x) is its internal potential function. Ψ = µ ness (x)P ness (x)dx is shown to be a nonequilibrium generalization of the Helmholtz free energy and ∆Ψ = ∆U−T ∆S for nonequilibrium processes, where S = −k B P (x) ln P (x)dx is the Gibbs entropy associated with P (x). LME of heat dissipation generalizes the concept of entropy, and the equalities define thermodynamic potential functions for open systems far from equilibrium.

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Network theory of microscopic and macroscopic behavior of master equation systems

Cited by 1,012 publications

References 21 publications

Consistent energy barrier distributions in magnetic particle chains

Consistent energy barrier distributions in magnetic particle chains

Energy Conversion by Molecular Motors Coupled to Nucleotide Hydrolysis

Nonequilibrium Potential Function of Chemically Driven Single Macromolecules via Jarzynski-Type Log-Mean-Exponential Heat

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