A novel conceptual model is introduced in which ion permeation is coupled to the protein wall vibration and the
later in turn modulates exponentially strongly the permeation via radial oscillations of the potential of mean
force. In the framework of this model of ion-wall-water interaction we discuss problems of selectivity between
alike ions and coupling of ion permeation to gating.
Ionic motion in the bulk solution away from the mouth of a biological ion channel, and inside the channel, is
analyzed using Poisson-Nernst-Planck (PNP) equation. The one-dimensional method allows us to connect in
a self-consistent way ion dynamics in the bulk solution and inside the channel by taking into account access
resistance to the channel. In order to glue the PNP solution in the bulk to that inside the channel, a continuity
condition is used for the concentration and the current near the channel mouth at the surface of the hemisphere.
The resulting one dimensional (1D) current-voltage characteristics are compared with the Kurnikova16 results
which are in good agreement with experimental measurement on the channel, by using a filling factor as the
only fitting parameter. The filling factor compensates the fact that the radial charge distribution is non-uniform
in a real channel as compared to the cylindrically symmetrical channel used in the 1D approximation.
Ionic motion through an open ion channel is analyzed within the framework of self-consistent Brownian dynamics formalism. A novel conceptual model of coupling of the ion's motion to the vibrations of the pore walls is introduced. The model allows one to include into simulations an important additional mechanism of energy dissipation and the effects of self-induced strong modulation of the channel conductivity.
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).
The patch clamp technique opened a new field in biological research and shed light on membrane permittivity for ionic currents. The key element in patch clamp measurements is the detection of the ionic currents in a single biological channel. It is known that the channels open and close at random times, thus modulating the ionic currents. The measured current switches between two levels corresponding to the open and close states of the channel. Determining the statistics of the open and closed periods is of crucial importance to the experimenter, because it reflects the response of channel protein to drugs and other factors. The detected signal is strongly corrupted by instrumentation and other noises, rendering the detection of the opening and closing moments extremely difficult. We describe the use of the wavelet transform and its associated multiresolution (multiscale) analysis to detect the currents through single ionic channels corrupted with noise.
Conference Committee Involvement (1)
Fluctuations and Noise in Biological, Biophysical, and Biomedical Systems II
26 May 2004 | Maspalomas, Gran Canaria Island, Spain
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