40 research outputs found
Measuring subdiffusion parameters
We propose a method to extract from experimental data the subdiffusion
parameter and subdiffusion coefficient which are defined by
means of the relation where
denotes a mean square displacement of a random walker starting from
at the initial time . The method exploits a membrane system where a
substance of interest is transported in a solvent from one vessel to another
across a thin membrane which plays here only an auxiliary role. Using such a
system, we experimentally study a diffusion of glucose and sucrose in a gel
solvent. We find a fully analytic solution of the fractional subdiffusion
equation with the initial and boundary conditions representing the system under
study. Confronting the experimental data with the derived formulas, we show a
subdiffusive character of the sugar transport in gel solvent. We precisely
determine the parameter , which is smaller than 1, and the subdiffusion
coefficient .Comment: 17 pages, 9 figures, revised, to appear in Phys. Rev.
Variational Methods for Biomolecular Modeling
Structure, function and dynamics of many biomolecular systems can be
characterized by the energetic variational principle and the corresponding
systems of partial differential equations (PDEs). This principle allows us to
focus on the identification of essential energetic components, the optimal
parametrization of energies, and the efficient computational implementation of
energy variation or minimization. Given the fact that complex biomolecular
systems are structurally non-uniform and their interactions occur through
contact interfaces, their free energies are associated with various interfaces
as well, such as solute-solvent interface, molecular binding interface, lipid
domain interface, and membrane surfaces. This fact motivates the inclusion of
interface geometry, particular its curvatures, to the parametrization of free
energies. Applications of such interface geometry based energetic variational
principles are illustrated through three concrete topics: the multiscale
modeling of biomolecular electrostatics and solvation that includes the
curvature energy of the molecular surface, the formation of microdomains on
lipid membrane due to the geometric and molecular mechanics at the lipid
interface, and the mean curvature driven protein localization on membrane
surfaces. By further implicitly representing the interface using a phase field
function over the entire domain, one can simulate the dynamics of the interface
and the corresponding energy variation by evolving the phase field function,
achieving significant reduction of the number of degrees of freedom and
computational complexity. Strategies for improving the efficiency of
computational implementations and for extending applications to coarse-graining
or multiscale molecular simulations are outlined.Comment: 36 page