Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session X21: Focus Session: MultiScale Analysis of Ions in Solutions, Proteins, and Channels: Analysis |
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Sponsoring Units: DBP Chair: Robert Eisenberg, Rush Medical Center Room: LACC 409A |
Friday, March 25, 2005 8:00AM - 8:36AM |
X21.00001: Theoretical and Computational Models of Ion Channels Invited Speaker: |
Friday, March 25, 2005 8:36AM - 8:48AM |
X21.00002: Narrow Escape Amit Singer, Zeev Schuss, David Holcman, Bob Eisenberg A Brownian particle is confined in a finite domain (2D or 3D) where it can exit only through a small opening of the boundary. The calculation of the mean exit time is formulated as a mixed Neumann-Dirichlet boundary value problem in potential theory. We find an asymptotic expansion for the mean exit time in terms of the geometry. The singular flux profile through the opening is obtained. When the small opening is located at non-smooth parts of the boundary, such as corners and cusps, the asymptotic expansion takes a different form. The problem arises in several biological applications, such as ion permeation in protein channels (3D) and receptor diffusion on the surface of nerve cells (2D Riemann surface). The rate at which ions arrive to the mouth of a protein channel (or to a microscopic simulation volume) is a geometrical function that involves both microscopic and macroscopic scales. The volume and surface area of the simulation region is microscopic, whereas the volume of the surrounding bath is macroscopic. From the analysis, it becomes clear why ions take so long to enter the channel. [Preview Abstract] |
Friday, March 25, 2005 8:48AM - 9:00AM |
X21.00003: Fission in multiphase membrane tubes Cornelis Storm, Jean-Marc Allain, Aurelien Roux, Martine Ben Amar, Jean-Francois Joanny A common mechanism for intracellular transport is the use of controlled deformations of the membrane to create spherical or tubular buds. While the basic physical properties of homogeneous membranes are relatively well-known, the effects of inhomogeneities within membranes are very much an active field of study. Membrane domains enriched in certain lipids in particular are attracting much attention, and in this talk we investigate the effect of such domains on the shape and fate of membrane tubes. Recent experiments have demonstrated that forced lipid phase separation can trigger tube fission, and we demonstrate how this can be understood purely from the difference in elastic constants between the domains. Moreover, the proposed model predicts timescales for fission that agree well with experimental findings. Published as Phys. Rev. Lett. 93 158104 (2004). [Preview Abstract] |
Friday, March 25, 2005 9:00AM - 9:12AM |
X21.00004: Brownian Simulations and Uni-Directional Flux in Diffusion Amit Singer, Zeev Schuss Brownian dynamics simulations of ion permeation in protein channels require the connection of a small discrete simulation volume to large baths that are maintained at fixed concentrations and voltages. Average boundary concentrations have to be maintained at their values in the baths by injecting and removing particles at the boundary of the simulation volume. The particles injected into the simulation volume represent a unidirectional diffusion flux. The classical diffusion equation defines net diffusion flux, but not unidirectional fluxes. The stochastic formulation of classical diffusion in terms of the Wiener process leads to a Wiener path integral, which can split the net flux into unidirectional fluxes. These unidirectional fluxes are infinite, though the net flux is finite and agrees with classical theory. We find that the infinite unidirectional flux is an artifact caused by replacing the Langevin dynamics with its Smoluchowski approximation, which is classical diffusion. We find that the probability of Brownian trajectories that cross an interface in one direction in unit time $\Delta t$ equals that of the probability of the corresponding Langevin trajectories if $\gamma\Delta t=2$. This unidirectional flux is proportional to the concentration and inversely proportional to $\sqrt{\Delta t} $ to leading order. We develop a BD simulation that maintains fixed average boundary concentrations in a manner consistent with the actual physics of the interface and without creating spurious boundary layers. [Preview Abstract] |
Friday, March 25, 2005 9:12AM - 9:24AM |
X21.00005: Langevin Trajectories Between Fixed Concentrations Amit Singer, Zeev Schuss, Boaz Nadler 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 absorbers and sources of outgoing and ingoing trajectories at the boundaries, with specified strengths, velocity and location distributions. We present a simulation scheme that maintains averaged fixed concentrations without creating spurious boundary layers. [Preview Abstract] |
Friday, March 25, 2005 9:24AM - 10:00AM |
X21.00006: Multiscale approach to ions in solution, proteins and channels: from brownian dynamics to continuum equations Invited Speaker: The diffusive motion of ions in solution, near proteins and through protein channels of biological membranes involves many length and time scales. In this talk we'll describe a multiscale averaging procedure, that starting from a Brownian dynamics description for the ionic motion of particles, yields a hierarchy of continuum equations for the averaged concentration profiles in the system. This set of equations is a generalization of the well known BBGKY equations of equilibrium statistical mechanics to non-equilibrium. Therefore, as in the equilibrium theory, closure relations are needed to compute explicit solutions. In the context of ionic permeation through protein channels, we show how an analysis of these continuum equations together with simple closures provides a theoretical explanation for experimentally measured phenomena. [Preview Abstract] |
Friday, March 25, 2005 10:00AM - 10:12AM |
X21.00007: Spreadsheet analysis of ion channel data using a linearized permeation model Peter Hugo Nelson, Ashley Rink A linearization of a recent ion channel permeation model [Nelson, \textit{J. Chem. Phys.} \textbf{177} (2002) 11396-11403] is proposed. The linearization enables rapid visual screening of current-voltage-concentration data sets to determine whether they can be successfully modeled using the permeation theory. To test this approach, we compared an extensive set of permeation data published by the Busath group [Cole \textit{et al}., \textit{Biophys. J.} \textbf{83}, 1974 (2002)] for both native and fluorinated variants of gramicidin A in diphytanoylphosphatidylcholine and glyceryl monoolein bilayers. Using the linearized model, we were able to show that both the electrical dissociation distance and the association rate constant were independent of fluorination, being determined by the composition of the bilayer and the identity of the permeant ion. We found that the electrostatic modulation of current flow by fluorination could be accounted for by varying only the dissociation rate constant, in agreement with electrostatic predictions. As a result, we conclude that modification of permeant ion binding affinity is the primary effect of fluorination. In contrast, when Cole \textit{et al.} analyzed their data, with a traditional site-based model, they concluded that a reduced translocation barrier was required for three of the eight channel analogs. Sample spreadsheet(s) illustrating how the linearized model can be used to rapidly screen permeation data are available online at http://circle4.com/rink-nelson/ [Preview Abstract] |
Friday, March 25, 2005 10:12AM - 10:24AM |
X21.00008: How Water Meets a Hydrophobic Surface Adel\'e Poynor, Wina Tjen, Steve Granick, Paul Fenter, Zhan Zhang The details of how water meets a hydrophobic surface are still hotly debated. Here we use two independent methods, ellipsometry in the time-resolved phase-modulated mode, and x-ray reflectivity, to investigate the view that thermodynamics causes a nanometer-sized low-density layer to form adjacent to the hydrophobic solid. Strong evidence in favor of the hypothesis is found. This ``vapor'' layer shows large fluctuations even with the spatial (over a beam size of 10 $\mu $m) and temporal (with a time constant of 30 ms) averaging inherent in the ellipsometry measurement. The very presence of the vapor layer shows hitherto-unsuspected dependence not only on pH of the water phase but also on chemical makeup and quality of the organic hydrophobic surface itself. [Preview Abstract] |
Friday, March 25, 2005 10:24AM - 10:36AM |
X21.00009: Competition and spatial distribution of ions diffusively bound to DNA Kurt Andresen, Rhiju Das, Hye Yoon Park, Heather Smith, Lisa Kwok, Jessica S. Lamb, Earl Kirkland, Daniel J. Herschlag, Kenneth D. Finkelstein, Lois Pollack Anomalous small angle x-ray scattering (ASAXS) has been employed to study the spatial distribution of diffusively bound counterions around DNA. Solutions containing pure monovalent and pure divalent cations have been examined. Measurements probing the competition of monovalent and divalent ions will also be reported and allow for further tests of basic predictions of current electrostatic models, such as the insensitivity of the normalized ion distribution to the competitive environment. In addition, measurements of competitive binding allow determination of a critical surface concentration parameter. Comparison of the competition data to the Poisson-Boltzmann (PB) model suggests that ion size effects are important when modeling ion atmospheres around polyelectrolytes such as nucleic acids using mean field theories. [Preview Abstract] |
Friday, March 25, 2005 10:36AM - 10:48AM |
X21.00010: Counterion Liquid Dynamics in F-Actin Bundles: A High Resolution Inelastic X-Ray Scattering Study Thomas Angelini, Robert Coridan, John Butler, Lori Sanders, Alexandre Beraud, Michael Krisch, Harald Sinn, Gerard Wong The behavior of counterions plays a pivotal role in the interaction between charged polyelectrolytes. Previously, we observed the counterion distribution in bundles of the polyelectrolyte F-actin using small angle x-ray scattering (SAXS) and found that the ions take on a periodic arrangement in the form of 1D counterion density waves (CDW), coupling to twist deformations of the F-actin helix [Angelini, et. al., PNAS 100 (2003)]. To probe the \textbf{\textit{dynamics}} of the CDW ions, we carried out a series of $\sim $meV resolution inelastic x-ray scattering (IXS) experiments on F-actin bundles condensed by different ion species. We find a new acoustic-like mode associated with the CDW, which has dispersive properties sensitive to ion species as well as ion density. [Preview Abstract] |
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