Langevin Trajectories between Fixed Concentrations

We consider the trajectories of particles diffusing between two infinite baths of fixed concentrations connected by a channel, e.g. a protein channel of a biological membrane. The steady state influx and efflux of Langevin trajectories at the boundaries of a finite volume containing the channel and parts of the two baths is replicated by termination of outgoing trajectories and injection according to a residual phase space density. We present a simulation scheme that maintains averaged fixed concentrations without creating spurious boundary layers, consistent with the assumed physics

Roving vehicle motion control Quarterly report, 1 Mar. - 31 May 1967

System and subsystem requirements for remote control of roving space vehicle motio

Roving vehicle motion control Final report

Roving vehicle motion control for unmanned planetary and lunar exploratio

Scaling in Complex Systems: Analytical Theory of Charged Pores

In this paper we find an analytical solution of the equilibrium ion distribution for a toroidal model of a ionic channel, using the Perfect Screening Theorem (PST). The ions are charged hard spheres, and are treated using a variational Mean Spherical Approximation (VMSA) . Understanding ion channels is still a very open problem, because of the many exquisite tuning details of real life channels. It is clear that the electric field plays a major role in the channel behaviour, and for that reason there has been a lot of work on simple models that are able to provide workable theories. Recently a number of interesting papers have appeared that discuss models in which the effect of the geometry, excluded volume and non-linear behaviour is considered. We present here a 3D model of ionic channels which consists of a charged, deformable torus with a circular or elliptical cross section, which can be flat or vertical (close to a cylinder). Extensive comparisons to MC simulations were performed. The new solution opens new possibilities, such as studying flexible pores, and water phase transformations inside the pores using an approach similar to that used on flat crystal surfaces

Extracellular electrical signals in a neuron-surface junction: model of heterogeneous membrane conductivity

Signals recorded from neurons with extracellular planar sensors have a wide range of waveforms and amplitudes. This variety is a result of different physical conditions affecting the ion currents through a cellular membrane. The transmembrane currents are often considered by macroscopic membrane models as essentially a homogeneous process. However, this assumption is doubtful, since ions move through ion channels, which are scattered within the membrane. Accounting for this fact, the present work proposes a theoretical model of heterogeneous membrane conductivity. The model is based on the hypothesis that both potential and charge are distributed inhomogeneously on the membrane surface, concentrated near channel pores, as the direct consequence of the inhomogeneous transmembrane current. A system of continuity equations having non-stationary and quasi-stationary forms expresses this fact mathematically. The present work performs mathematical analysis of the proposed equations, following by the synthesis of the equivalent electric element of a heterogeneous membrane current. This element is further used to construct a model of the cell-surface electric junction in a form of the equivalent electrical circuit. After that a study of how the heterogeneous membrane conductivity affects parameters of the extracellular electrical signal is performed. As the result it was found that variation of the passive characteristics of the cell-surface junction, conductivity of the cleft and the cleft height, could lead to different shapes of the extracellular signals