BioMOCA: A Transport Monte Carlo Model for Ion Channels

Straaten, Trudy van der; Kathawala, G.

doi:10.1023/b:jcel.0000011430.99984.cd

Cited by 9 publications

(7 citation statements)

References 10 publications

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“…(27) and (37) are identical. This is no mere coincidence: both controls are special cases of renewal controls.…”

Section: ͑38͒mentioning

confidence: 92%

“…The formulation of boundary conditions for the particle concentration is obvious in macroscopic models, but formulation of boundary conditions for the underlying trajectories is not so clear cut, particularly because many different physical or computational control mechanisms can maintain a constant average density at prescribed locations, usually near the boundaries [11][12][13][14][15]19,[22][23][24][25][26][27][28]. Many boundary conditions used in Brownian and Langevin simulations produce spuri-ous boundary layers that do not exist at those locations in the physical systems being simulated.…”

Section: Introductionmentioning

confidence: 99%

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Memoryless control of boundary concentrations of diffusing particles

et al. 2004

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Flux between regions of different concentration occurs in nearly every device involving diffusion, whether an electrochemical cell, a bipolar transistor, or a protein channel in a biological membrane. Diffusion theory has calculated that flux since the time of Fick (1855), and the flux has been known to arise from the stochastic behavior of Brownian trajectories since the time of Einstein (1905), yet the mathematical description of the behavior of trajectories corresponding to different types of boundaries is not complete. We consider the trajectories of noninteracting particles diffusing in a finite region connecting two baths of fixed concentrations. Inside the region, the trajectories of diffusing particles are governed by the Langevin equation. To maintain average concentrations at the boundaries of the region at their values in the baths, a control mechanism is needed to set the boundary dynamics of the trajectories. Different control mechanisms are used in Langevin and Brownian simulations of such systems. We analyze models of controllers and derive equations for the time evolution and spatial distribution of particles inside the domain. Our analysis shows a distinct difference between the time evolution and the steady state concentrations. While the time evolution of the density is governed by an integral operator, the spatial distribution is governed by the familiar Fokker-Planck operator. The boundary conditions for the time dependent density depend on the model of the controller; however, this dependence disappears in the steady state, if the controller is of a renewal type. Renewal-type controllers, however, produce spurious boundary layers that can be catastrophic in simulations of charged particles, because even a tiny net charge can have global effects. The design of a nonrenewal controller that maintains concentrations of noninteracting particles without creating spurious boundary layers at the interface requires the solution of the time-dependent Fokker-Planck equation with absorption of outgoing trajectories and a source of ingoing trajectories on the boundary (the so called albedo problem).

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“…(27) and (37) are identical. This is no mere coincidence: both controls are special cases of renewal controls.…”

Section: ͑38͒mentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Memoryless control of boundary concentrations of diffusing particles

et al. 2004

View full text Add to dashboard Cite

show abstract

“…(27) and (37) are identical. This is no mere coincidence: both controls are special cases of renewal controls.…”

Section: The Renewal Control Theoremmentioning

confidence: 99%

Models of boundary behavior of particles diffusing between two concentrations

et al. 2004

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Flux between regions of different concentration occurs in nearly every device involving diffusion, whether an electrochemical cell, a bipolar transistor, or a protein channel in a biological membrane. Diffusion theory has calculated that flux since the time of Fick (1855), and the flux has been known to arise from the stochastic behavior of Brownian trajectories since the time of Einstein (1905), yet the mathematical description of the behavior of trajectories corresponding to different types of boundaries is not complete. We consider the trajectories of non-interacting particles diffusing in a finite region connecting two baths of fixed concentrations. Inside the region, the trajectories of diffusing particles are governed by the Langevin equation. At the interface between the region and the baths, trajectories are set by a control mechanism that modifies dynamics so the concentration of particles remains (nearly) constant. We analyze different models of controllers and derive equations for the time evolution and spatial distribution of particles inside the domain. Our analysis shows a distinct difference between the time evolution and the steady state concentrations. While the time evolution of the density is governed by an integral operator, the spatial distribution is governed by the familiar Fokker-Planck operator. The boundary conditions for the time dependent density depend on the model of the controller; however, this dependence disappears in the steady state, if the controller is of a renewal type. Renewal-type controllers, however, produce spurious boundary layers that can be catastrophic in simulations of charged particles, because even a tiny net charge can have global effects. The design of a non-renewal controller that maintains concentrations of non-interacting particles without creating spurious boundary layers at the interface requires the solution of the time-dependent Fokker-Planck equation with absorption of outgoing trajectories and a source of ingoing trajectories on the boundary (the so called albedo problem).

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“…1,2 Because of this importance, many theoretical and computational approaches as well as experimental studies have been devoted to the understanding of ion transport. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] Among the theoretical and computational approaches is Poisson-Nernst-Planck ͑PNP͒ mean field theory, which is based on a dielectric continuum model. 7,11,17 In PNP theory, proteins, membranes, ions, and water are considered as continuum dielectric materials, and the atomistic details of the proteins and membranes are ignored.…”

Section: Introductionmentioning

confidence: 99%

Kinetic lattice grand canonical Monte Carlo simulation for ion current calculations in a model ion channel system

Hwang

Schatz

Ratner

2007

The Journal of Chemical Physics

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An algorithm in which kinetic lattice grand canonical Monte Carlo simulations are combined with mean field theory (KLGCMC/MF) is presented to calculate ion currents in a model ion channel system. In this simulation, the relevant region of the system is treated by KLGCMC simulations, while the rest of the system is described by modified Poisson-Boltzmann mean field theory. Calculation of reaction field due to induced charges on the channel/water and membrane/water boundaries is carried out using a basis-set expansion method [Im and Roux, J. Chem. Phys. 115, 4850 (2001)]. Calculation of ion currents, electrostatic potentials, and ion concentrations, as obtained from the KLGCMC/MF simulations, shows good agreement with Poisson-Nernst-Planck (PNP) theory predictions when the channel and membrane have the same dielectric constant as water. If the channel and membrane have a lower dielectric constant than water, however, there is a considerable difference between the KLGCMC/MF and PNP predictions. This difference is attributed to the reaction field, which is missing in PNP theory. It is demonstrated that the reaction field as well as fixed charges in the channel play key roles in selective ion transport. Limitations and further development of the current KLGCMC/MF approach are also discussed.

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BioMOCA: A Transport Monte Carlo Model for Ion Channels

Cited by 9 publications

References 10 publications

Memoryless control of boundary concentrations of diffusing particles

Memoryless control of boundary concentrations of diffusing particles

Models of boundary behavior of particles diffusing between two concentrations

Kinetic lattice grand canonical Monte Carlo simulation for ion current calculations in a model ion channel system

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