Bending elasticity of macromolecules: analytic predictions from the wormlike chain model

We present a study of the bend angle distribution of semiflexible polymers of short and intermediate lengths within the wormlike chain model. This enables us to calculate the elastic response of a stiff molecule to a bending moment. Our results go beyond the Hookean regime and explore the nonlinear elastic behaviour of a single molecule. We present analytical formulae for the bend angle distribution and for the moment-angle relation. Our analytical study is compared against numerical Monte Carlo simulations. The functional forms derived here can be applied to fluorescence microscopic studies on actin and DNA. Our results are relevant to recent studies in "kinks" and cyclization in short and intermediate length DNA strands.Comment: 4 page

Bilayer registry in a multicomponent asymmetric membrane : dependence on lipid composition and chain length

A question of considerable interest to cell membrane biology is whether phase segregated domains across an asymmetric bilayer are strongly correlated with each other and whether phase segregation in one leaflet can induce segregation in the other. We answer both these questions in the affirmative, using an atomistic molecular dynamics simulation to study the equilibrium statistical properties of a 3-component {\em asymmetric} lipid bilayer comprising an unsaturated POPC (palmitoyl-oleoyl-phosphatidyl-choline), a saturated SM (sphingomyelin) and cholesterol with different composition ratios. Our simulations are done by fixing the composition of the upper leaflet to be at the coexistence of the liquid ordered ($l_o$) - liquid disordered ($l_d$) phases, while the composition of the lower leaflet is varied from the phase coexistence regime to the mixed $l_d$ phase, across a first-order phase boundary. In the regime of phase coexistence in each leaflet, we find strong transbilayer correlations of the $l_o$ domains across the two leaflets, resulting in {\it bilayer registry}. This transbilayer correlation depends sensitively upon the chain length of the participating lipids and possibly other features of lipid chemistry, such as degree of saturation. We find that the $l_o$ domains in the upper leaflet can {\em induce} phase segregation in the lower leaflet, when the latter is nominally in the mixed ($l_d$) phase.Comment: 6 figure

Atomistic simulations of a multicomponent asymmetric lipid bilayer

The cell membrane is inherently asymmetric and heterogeneous in its composition, a feature that is crucial for its function. Using atomistic molecular dynamics simulations, the physical properties of a 3-component asymmetric mixed lipid bilayer system comprising of an unsaturated POPC (palmitoyl-oleoyl-phosphatidyl-choline), a saturated SM (sphingomyelin) and cholesterol are investigated. In these simulations, the initial stages of liquid ordered, $l_o$, domain formation are observed and such domains are found to be highly enriched in cholesterol and SM. The current simulations also suggest that the cholesterol molecules may partition into these SM-dominated regions in the ratio of $3:1$ when compared to POPC-dominated regions. SM molecules exhibit a measurable tilt and long range tilt correlations are observed within the $l_o$ domain as a consequence of the asymmetry of the bilayer, with implications to local membrane deformation and budding. Tagged particle diffusion for SM and cholesterol molecules, which reflects spatial variations in the physical environment encountered by the tagged particle, is computed and compared with recent experimental results obtained from high resolution microscopy.Comment: Manuscript with 5 figures, Supplementary Information, 10 Supplementary Figure

Clustering of lipids driven by integrin

Integrin is an important transmembrane receptor protein which remodels the actin network and anchors the cell membrane towards the extracellular matrix via mechanochemical pathways. The clustering of specific lipids and lipid-anchored proteins, which is essential for a certain type of endocytosis process, is facilitated at integrin-mediated active regions. To study this, we propose a minimal exactly solvable model which includes the interplay of stochastic shuttling between integrin on and off states with the intrinsic dynamics of the membrane. We obtain an analytic expression for the deformation and local membrane velocity, and thereby the evolution of clustering mediated by a single integrin. The deformation, velocity and lipid clustering evolve nonmonotonically and their dependences on the stochastic shuttling timescales and membrane properties are elucidated.Comment: 7 pages, 7 figure

Atomistic Simulations of a Multicomponent Asymmetric Lipid Bilayer

The cell membrane is inherently asymmetric and heterogeneous in its composition, a feature that is crucial for its function. Using atomistic molecular dynamics simulations, the physical properties of a 3-component asymmetric mixed lipid bilayer system comprising an unsaturated POPC (palmitoyloleoylphosphatidylcholine), a saturated PSM (palmitoylsphingomyelin), and cholesterol are investigated. Our simulations explore both the dynamics of coarsening following a quench from the mixed phase and the final phase-segregated regime obtained by equilibrating a fully segregated configuration. Following a quench, the membrane quickly enters a coarsening regime, where the initial stages of liquid ordered, <i>l</i>_o, domain formation are observed. These growing domains are found to be highly enriched in cholesterol and PSM. Consistent with this, the final phase-segregated regime contains large <i>l</i>_o domains at equilibrium, enriched in cholesterol and PSM. Our simulations suggest that the cholesterol molecules may partition into these PSM-dominated regions in the ratio of 3:1 when compared to POPC-dominated regions. PSM molecules exhibit a measurable tilt and long-range tilt correlations within the <i>l</i>_o domain as a consequence of the asymmetry of the bilayer, with implications to local membrane deformation and budding. Tagged particle diffusion for PSM and cholesterol molecules, which reflects spatial variations in the physical environment encountered by the tagged particle, is computed and compared with recent experimental results obtained from high-resolution microscopy