6,074 research outputs found
From Brownian Dynamics to Markov Chain: an Ion Channel Example
A discrete rate theory for general multi-ion channels is presented, in which
the continuous dynamics of ion diffusion is reduced to transitions between
Markovian discrete states. In an open channel, the ion permeation process
involves three types of events: an ion entering the channel, an ion escaping
from the channel, or an ion hopping between different energy minima in the
channel. The continuous dynamics leads to a hierarchy of Fokker-Planck
equations, indexed by channel occupancy. From these the mean escape times and
splitting probabilities (denoting from which side an ion has escaped) can be
calculated. By equating these with the corresponding expressions from the
Markov model the Markovian transition rates can be determined. The theory is
illustrated with a two-ion one-well channel. The stationary probability of
states is compared with that from both Brownian dynamics simulation and the
hierarchical Fokker-Planck equations. The conductivity of the channel is also
studied, and the optimal geometry maximizing ion flux is computed.Comment: submitted to SIAM Journal on Applied Mathematic
Range separation: The divide between local structures and field theories
This work presents parallel histories of the development of two modern
theories of condensed matter: the theory of electron structure in quantum
mechanics, and the theory of liquid structure in statistical mechanics.
Comparison shows that key revelations in both are not only remarkably similar,
but even follow along a common thread of controversy that marks progress from
antiquity through to the present. This theme appears as a creative tension
between two competing philosophies, that of short range structure (atomistic
models) on the one hand, and long range structure (continuum or density
functional models) on the other. The timeline and technical content are
designed to build up a set of key relations as guideposts for using density
functional theories together with atomistic simulation.Comment: Expanded version of a 30 minute talk delivered at the 2018 TSRC
workshop on Ions in Solution, to appear in the March, 2019 issue of
Substantia (https://riviste.fupress.net/index.php/subs/index
Numerical electrokinetics
A new lattice method is presented in order to efficiently solve the
electrokinetic equations, which describe the structure and dynamics of the
charge cloud and the flow field surrounding a single charged colloidal sphere,
or a fixed array of such objects. We focus on calculating the electrophoretic
mobility in the limit of small driving field, and systematically linearise the
equations with respect to the latter. This gives rise to several subproblems,
each of which is solved by a specialised numerical algorithm. For the total
problem we combine these solvers in an iterative procedure. Applying this
method, we study the effect of the screening mechanism (salt screening vs.
counterion screening) on the electrophoretic mobility, and find a weak
non-trivial dependence, as expected from scaling theory. Furthermore, we find
that the orientation of the charge cloud (i. e. its dipole moment) depends on
the value of the colloid charge, as a result of a competition between
electrostatic and hydrodynamic effects.Comment: accepted for publication in Journal of Physics Condensed Matter
(proceedings of the 2012 CODEF conference
Dehydration as a Universal Mechanism for Ion Selectivity in Graphene and Other Atomically Thin Pores
Ion channels play a key role in regulating cell behavior and in electrical
signaling. In these settings, polar and charged functional groups -- as well as
protein response -- compensate for dehydration in an ion-dependent way, giving
rise to the ion selective transport critical to the operation of cells.
Dehydration, though, yields ion-dependent free-energy barriers and thus is
predicted to give rise to selectivity by itself. However, these barriers are
typically so large that they will suppress the ion currents to undetectable
levels. Here, we establish that graphene displays a measurable dehydration-only
mechanism for selectivity of over . This
fundamental mechanism -- one that depends only on the geometry and hydration --
is the starting point for selectivity for all channels and pores. Moreover,
while we study selectivity of over , we find that
dehydration-based selectivity functions for all ions, i.e., cation over cation
selectivity (e.g., over ). Its likely detection
in graphene pores resolves conflicting experimental results, as well as
presents a new paradigm for characterizing the operation of ion channels and
engineering molecular/ionic selectivity in filtration and other applications.Comment: 27 page
A Multidomain Model for Ionic Electrodiffusion and Osmosis with an Application to Cortical Spreading Depression
Ionic electrodiffusion and osmotic water flow are central processes in many
physiological systems. We formulate a system of partial differential equations
that governs ion movement and water flow in biological tissue. A salient
feature of this model is that it satisfies a free energy identity, ensuring the
thermodynamic consistency of the model. A numerical scheme is developed for the
model in one spatial dimension and is applied to a model of cortical spreading
depression, a propagating breakdown of ionic and cell volume homeostasis in the
brain.Comment: submitted for publication, Aug. 28, 201
Discrete solution of the electrokinetic equations
We present a robust scheme for solving the electrokinetic equations. This
goal is achieved by combining the lattice-Boltzmann method (LB) with a discrete
solution of the convection-diffusion equation for the different charged and
neutral species that compose the fluid. The method is based on identifying the
elementary fluxes between nodes, which ensures the absence of spurious fluxes
in equilibrium. We show how the model is suitable to study electro-osmotic
flows. As an illustration, we show that, by introducing appropriate dynamic
rules in the presence of solid interfaces, we can compute the sedimentation
velocity (and hence the sedimentation potential) of a charged sphere. Our
approach does not assume linearization of the Poisson-Boltzmann equation and
allows us for a wide variation of the Peclet number.Comment: 24 pages, 7 figure
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
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