Coarse-grained kinetic Monte Carlo models: Complex lattices, multicomponent systems, and homogenization at the stochastic level

BackgroundAn adaptive coarse-grained (kinetic) Monte Carlo (ACGMC) simulation framework is applied to reaction and diffusion dynamics in inhomogeneous domains. The presented model is relevant to the diffusion and dimerization dynamics of epidermal growth factor receptor (EGFR) in the presence of plasma membrane heterogeneity and specifically receptor clustering. We perform simulations representing EGFR cluster dissipation in heterogeneous plasma membranes consisting of higher density clusters of receptors surrounded by low population areas using the ACGMC method. We further investigate the effect of key parameters on the cluster lifetime.ResultsCoarse-graining of dimerization, rather than of diffusion, may lead to computational error. It is shown that the ACGMC method is an effective technique to minimize error in diffusion-reaction processes and is superior to the microscopic kinetic Monte Carlo simulation in terms of computational cost while retaining accuracy. The low computational cost enables sensitivity analysis calculations. Sensitivity analysis indicates that it may be possible to retain clusters of receptors over the time scale of minutes under suitable conditions and the cluster lifetime may depend on both receptor density and cluster size.ConclusionsThe ACGMC method is an ideal platform to resolve large length and time scales in heterogeneous biological systems well beyond the plasma membrane and the EGFR system studied here. Our results demonstrate that cluster size must be considered in conjunction with receptor density, as they synergistically affect EGFR cluster lifetime. Further, the cluster lifetime being of the order of several seconds suggests that any mechanisms responsible for EGFR aggregation must operate on shorter timescales (at most a fraction of a second), to overcome dissipation and produce stable clusters observed experimentally.

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“…for the case where k = k ' and ϕ 1 ≠ ϕ 2 (see Table three in [31,38] for more details on how to evaluate coarse propensities).…”

Section: Monte Carlo Methodsmentioning

confidence: 99%

Adaptive coarse-grained Monte Carlo simulation of reaction and diffusion dynamics in heterogeneous plasma membranes

2010

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“…the homogenised CGMC method for complex lattices and multicomponent systems (Collins et al, 2008), the local quasi-chemical approximation for CGMC (Chatterjee and Vlachos, 2006) and the temporal coarse-graining method for microscopic lattice KMC simulations introduced by Vlachos (2008). Despite the recent progress on mesoscopic algorithms, this strategy remains as the least developed in multiscale modelling.…”

Section: Physical Processmentioning

confidence: 99%

Current challenges in the design and control of multiscale systems

Ricardez‐Sandoval

2011

Can J Chem Eng

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Multiscale modelling is a new emerging field in process systems engineering. Although the idea of linking events occurring across time and length scales is not new, the numerical solution of these models is challenging because of computational limitations and the difficulty in coupling modelling methods with different characteristics. Although an extensive set of tools are currently available to improve the performance of processes described using continuum models, most of these tools are not suitable to design and control a multiscale process. This work presents the approaches that are currently available to perform multiscale modelling and identifies the key challenges that need to be addressed to improve the performance of macroscopic processes by controlling events occurring at the atomistic, molecular and nanoscopic levels.

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“…Since we are dealing with a lattice model we can only develop a dynamics by considering stochastic dynamic processes that allow the system to evolve from an out of equilibrium state to an equilibrium one. Such approaches are commonly used in modeling the dynamics of chemical reaction systems [44] and for diffusion in zeolites [45]. In recent years they have also been used to understand the relaxation dynamics for fluids in mesopores [21].…”

Section: Dynamic Mean Field Theorymentioning

confidence: 99%

Fluids Confined in Porous Materials: Towards a Unified Understanding of Thermodynamics and Dynamics

Monson

2011

Chemie Ingenieur Technik

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A recently developed theoretical approach to understand the relaxation processes for fluids confined in mesoporous materials, especially in adsorption/desorption from bulk gases, is discussed. The theory is based on a lattice gas formulation of the molecular interactions in the system and is referred to as dynamic mean field theory. The theory has the important property that the limiting behavior at long times is consistent with the results from mean field theory (or density functional theory) for the model. In this sense it provides a unified picture of thermodynamics and relaxation dynamics for the system. Two illustrative applications are presented. The first is to the dynamics of capillary condensation in a finite length slit pore in contact with a bulk gas. The second application is to the dynamics of cavitation during desorption from an inkbottle pore in contact with the bulk gas. The outlook for future developments and applications of the approach is also discussed.

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Coarse-grained kinetic Monte Carlo models: Complex lattices, multicomponent systems, and homogenization at the stochastic level

Cited by 27 publications

References 34 publications

Adaptive coarse-grained Monte Carlo simulation of reaction and diffusion dynamics in heterogeneous plasma membranes

Adaptive coarse-grained Monte Carlo simulation of reaction and diffusion dynamics in heterogeneous plasma membranes

Current challenges in the design and control of multiscale systems

Fluids Confined in Porous Materials: Towards a Unified Understanding of Thermodynamics and Dynamics

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