24,506 research outputs found
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
Interplay of packing and flip-flop in local bilayer deformation. How phosphatidylglycerol could rescue mitochondrial function in a cardiolipin-deficient yeast mutant
In a previous work, we have shown that a spatially localized transmembrane pH
gradient, produced by acid micro-injection near the external side of
cardiolipin-containing giant unilamellar vesicles, leads to the formation of
tubules that retract after the dissipation of this gradient. These tubules have
morphologies similar to mitochondrial cristae. The tubulation effect is due to
direct phospholipid packing modification in the outer leaflet that is promoted
by protonation of cardiolipin headgroups. Here we compare the case of
cardiolipin-containing giant unilamellar vesicles with that of
phosphatidylglycerol-containing giant unilamellar vesicles. Local acidification
also promotes formation of tubules in the latter. However, compared to
cardiolipin-containing giant unilamellar vesicles the tubules are longer,
exhibit a visible pearling and have a much longer lifetime after acid
micro-injection is stopped. We attribute these differences to an additional
mechanism that increases monolayer surface imbalance, namely inward PG
flip-flop promoted by the local transmembrane pH-gradient. Simulations using a
fully non-linear membrane model as well as geometrical calculations are in
agreement with this hypothesis. Interestingly, among yeast mutants deficient in
cardiolipin biosynthesis, only the crd1-null mutant, which accumulates
phosphatidylglycerol, displays significant mitochondrial activity. Our work
provides a possible explanation of such a property and further emphasizes the
salient role of specific lipids in mitochondrial function.Comment: 28 pages, 10 figure
Dynamics of membranes driven by actin polymerization
A motile cell, when stimulated, shows a dramatic increase in the activity of
its membrane, manifested by the appearance of dynamic membrane structures such
as lamellipodia, filopodia and membrane ruffles. The external stimulus turns on
membrane bound activators, like Cdc42 and PIP2, which cause increased branching
and polymerization of the actin cytoskeleton in their vicinity leading to a
local protrusive force on the membrane. The emergence of the complex membrane
structures is a result of the coupling between the dynamics of the membrane,
the activators and the protrusive forces. We present a simple model that treats
the dynamics of a membrane under the action of actin polymerization forces that
depend on the local density of freely diffusing activators on the membrane. We
show that, depending on the spontaneous membrane curvature associated with the
activators, the resulting membrane motion can be wave-like, corresponding to
membrane ruffling and actin-waves, or unstable, indicating the tendency of
filopodia to form. Our model also quantitatively explains a variety of related
experimental observations and makes several testable predictions.Comment: 37 pages, 8 figures, revte
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