Monte Carlo simulation for statistical mechanics model of ion channel cooperativity in cell membranes

Voltage-gated ion channels are key molecules for the generation and propagation of electrical signals in excitable cell membranes. The voltage-dependent switching of these channels between conducting and nonconducting states is a major factor in controlling the transmembrane voltage. In this study, a statistical mechanics model of these molecules has been discussed on the basis of a two-dimensional spin model. A new Hamiltonian and a new Monte Carlo simulation algorithm are introduced to simulate such a model. It was shown that the results well match the experimental data obtained from batrachotoxin-modified sodium channels in the squid giant axon using the cut-open axon technique.Comment: Paper has been revise

Steady state existence of passive vector fields under the Kraichnan model

The steady state existence problem for Kraichnan advected passive vector models is considered for isotropic and anisotropic initial values in arbitrary dimension. The model includes the magnetohydrodynamic (MHD) equations, linear pressure model (LPM) and linearized Navier-Stokes (LNS) equations. In addition to reproducing the previously known results for the MHD and linear pressure model, we obtain the values of the Kraichnan model roughness parameter $\xi$ for which the LNS steady state exists.Comment: Improved text & figures, added references & other correction

Kinetic models of ion transport through a nanopore

Kinetic equations for the stationary state distribution function of ions moving through narrow pores are solved for a number of one-dimensional models of single ion transport. Ions move through pores of length $L$, under the action of a constant external field and of a concentration gradient. The interaction of single ions with the confining pore surface and with water molecules inside the pore are modelled by a Fokker-Planck term in the kinetic equation, or by uncorrelated collisions with thermalizing centres distributed along the pore. The temporary binding of ions to polar residues lining the pore is modelled by stopping traps or energy barriers. Analytic expressions for the stationary ion current through the pore are derived for several versions of the model, as functions of key physical parameters. In all cases, saturation of the current at high fields is predicted. Such simple models, for which results are analytic, may prove useful in the study of the current/voltage relations of ion channels through membranes

Non-Markovian Stochastic Resonance: three state model of ion channel gating

Stochastic Resonance in single voltage-dependent ion channels is investigated within a three state non-Markovian modeling of the ion channel conformational dynamics. In contrast to a two-state description one assumes the presence of an additional closed state for the ion channel which mimics the manifold of voltage-independent closed subconformations (inactivated ``state''). The conformational transition into the open state occurs through a domain of voltage-dependent closed subconformations (closed ``state''). At distinct variance with a standard two-state or also three-state Markovian approach, the inactivated state is characterized by a broad, non-exponential probability distribution of corresponding residence times. The linear response to a periodic voltage signal is determined for arbitrary distributions of the channel's recovery times. Analytical results are obtained for the spectral amplification of the applied signal and the corresponding signal-to-noise ratio. Alternatively, these results are also derived by use of a corresponding two-state non-Markovian theory which is based on driven integral renewal equations [I. Goychuk and P. Hanggi, Phys. Rev. E 69, 021104 (2004)]. The non-Markovian features of stochastic resonance are studied for a power law distribution of the residence time-intervals in the inactivated state which exhibits a large variance. A comparison with the case of bi-exponentially distributed residence times possessing the same mean value, i.e. a simplest non-Markovian two-state description, is also presented

Collective shuttling of attracting particles in asymmetric narrow channels

The rectification of a single file of attracting particles subjected to a low frequency ac drive is proposed as a working mechanism for particle shuttling in an asymmetric narrow channel. Increasing the particle attraction results in the file condensing, as signalled by the dramatic enhancement of the net particle current. Magnitude and direction of the current become extremely sensitive to the actual size of the condensate, which can then be made to shuttle between two docking stations, transporting particles in one direction, with an efficiency much larger than conventional diffusive models predict

Soft disks in a narrow channel

The pressure components of "soft" disks in a two dimensional narrow channel are analyzed in the dilute gas regime using the Mayer cluster expansion and molecular dynamics. Channels with either periodic or reflecting boundaries are considered. It is found that when the two-body potential, u(r), is singular at some distance r_0, the dependence of the pressure components on the channel width exhibits a singularity at one or more channel widths which are simply related to r_0. In channels with periodic boundary conditions and for potentials which are discontinuous at r_0, the transverse and longitudinal pressure components exhibit a 1/2 and 3/2 singularity, respectively. Continuous potentials with a power law singularity result in weaker singularities of the pressure components. In channels with reflecting boundary conditions the singularities are found to be weaker than those corresponding to periodic boundaries

How the asymmetry of internal potential influences the shape of I-V characteristic of nanochannels

Ion transport in biological and synthetic nanochannels is characterized by such phenomena as ion current fluctuations, rectification, and pumping. Recently, it has been shown that the nanofabricated synthetic pores could be considered as analogous to biological channels with respect to their transport characteristics \cite{Apel, Siwy}. The ion current rectification is analyzed. Ion transport through cylindrical nanopores is described by the Smoluchowski equation. The model is considering the symmetric nanopore with asymmetric charge distribution. In this model, the current rectification in asymmetrically charged nanochannels shows a diode-like shape of $I-V$ characteristic. It is shown that this feature may be induced by the coupling between the degree of asymmetry and the depth of internal electric potential well. The role of concentration gradient is discussed

Effective zero-thickness model for a conductive membrane driven by an electric field

The behavior of a conductive membrane in a static (DC) electric field is investigated theoretically. An effective zero-thickness model is constructed based on a Robin-type boundary condition for the electric potential at the membrane, originally developed for electrochemical systems. Within such a framework, corrections to the elastic moduli of the membrane are obtained, which arise from charge accumulation in the Debye layers due to capacitive effects and electric currents through the membrane and can lead to an undulation instability of the membrane. The fluid flow surrounding the membrane is also calculated, which clarifies issues regarding these flows sharing many similarities with flows produced by induced charge electro-osmosis (ICEO). Non-equilibrium steady states of the membrane and of the fluid can be effectively described by this method. It is both simpler, due to the zero thickness approximation which is widely used in the literature on fluid membranes, and more general than previous approaches. The predictions of this model are compared to recent experiments on supported membranes in an electric field.Comment: 14 pages, 5 figure

Cosmology and the Korteweg-de Vries Equation

The Korteweg-de Vries (KdV) equation is a non-linear wave equation that has played a fundamental role in diverse branches of mathematical and theoretical physics. In the present paper, we consider its significance to cosmology. It is found that the KdV equation arises in a number of important scenarios, including inflationary cosmology, the cyclic universe, loop quantum cosmology and braneworld models. Analogies can be drawn between cosmic dynamics and the propagation of the solitonic wave solution to the equation, whereby quantities such as the speed and amplitude profile of the wave can be identified with cosmological parameters such as the spectral index of the density perturbation spectrum and the energy density of the universe. The unique mathematical properties of the Schwarzian derivative operator are important to the analysis. A connection with dark solitons in Bose-Einstein condensates is briefly discussed.Comment: 7 pages; References adde