32 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
Minimal Mesoscale Model for Protein-Mediated Vesiculation in Clathrin-Dependent Endocytosis
In eukaryotic cells, the internalization of extracellular cargo via the endocytic machinery is an important regulatory process required for many essential cellular functions. The role of cooperative protein-protein and protein-membrane interactions in the ubiquitous endocytic pathway in mammalian cells, namely the clathrin-dependent endocytosis, remains unresolved. We employ the Helfrich membrane Hamiltonian together with surface evolution methodology to address how the shapes and energetics of vesicular-bud formation in a planar membrane are stabilized by presence of the clathrin-coat assembly. Our results identify a unique dual role for the tubulating protein epsin: multiple epsins localized spatially and orientationally collectively play the role of a curvature inducing capsid; in addition, epsin serves the role of an adapter in binding the clathrin coat to the membrane. Our results also suggest an important role for the clathrin lattice, namely in the spatial- and orientational-templating of epsins. We suggest that there exists a critical size of the coat above which a vesicular bud with a constricted neck resembling a mature vesicle is stabilized. Based on the observed strong dependence of the vesicle diameter on the bending rigidity, we suggest that the variability in bending stiffness due to variations in membrane composition with cell type can explain the experimentally observed variability on the size of clathrin-coated vesicles, which typically range 50â100 nm. Our model also provides estimates for the number of epsins involved in stabilizing a coated vesicle, and without any direct fitting reproduces the experimentally observed shapes of vesicular intermediates as well as their probability distributions quantitatively, in wildtype as well as CLAP IgG injected neuronal cell experiments. We have presented a minimal mesoscale model which quantitatively explains several experimental observations on the process of vesicle nucleation induced by the clathrin-coated assembly prior to vesicle scission in clathrin dependent endocytosis
Membrane-mediated interactions
Interactions mediated by the cell membrane between inclusions, such as
membrane proteins or antimicrobial peptides, play important roles in their
biological activity. They also constitute a fascinating challenge for
physicists, since they test the boundaries of our understanding of
self-assembled lipid membranes, which are remarkable examples of
two-dimensional complex fluids. Inclusions can couple to various degrees of
freedom of the membrane, resulting in different types of interactions. In this
chapter, we review the membrane-mediated interactions that arise from direct
constraints imposed by inclusions on the shape of the membrane. These effects
are generic and do not depend on specific chemical interactions. Hence, they
can be studied using coarse-grained soft matter descriptions. We deal with
long-range membrane-mediated interactions due to the constraints imposed by
inclusions on membrane curvature and on its fluctuations. We also discuss the
shorter-range interactions that arise from the constraints on membrane
thickness imposed by inclusions presenting a hydrophobic mismatch with the
membrane.Comment: 38 pages, 10 figures, pre-submission version. In: Bassereau P., Sens
P. (eds) Physics of Biological Membranes. Springer, Cha
Mechanical factors affecting the mobility of membrane proteins
To appear as a Chapter in "Physics of Biological Membranes", edited by Dr. Patricia Bassereau & Dr. Pierre Sens, Springer Nature SwitzerlandThe mobility of membrane proteins controls many biological functions. The application of the model of Saffman and Delbr\"uck to the diffusion of membrane proteins does not account for all the experimental measurements. These discrepancies have triggered a lot of studies on the role of the mechanical factors in the mobility. After a short review of the Saffman and Delbr\"uck model and of some key experiments, we explore the various ways to incorporate the effects of the different mechanical factors. Our approach focuses on the coupling of the protein to the membrane, which is the central element in the modelling. We present a general, polaron-like model, its recent application to the mobility of a curvature sensitive protein, and its various extensions to other couplings that may be relevant in future experiments