Modeling Anisotropic Elasticity of Fluid Membranes

Abstract

The biological membrane, which compartmentalizes the cell and its organelles, exhibit wide variety of macroscopic shapes of varying morphology and topology.s A systematic understanding of the relation of membrane shapes to composition, external field, environmental conditions etc. have important biological relevance. Here we review the triangulated surface model, used in the macroscopic simulation of membranes and the associated Monte Carlo (DTMC) methods. New techniques to calculate surface quantifiers, that will facilitate the study of additional in-plane orientational degrees of freedom, has been introduced. The mere presence of a polar and nematic fields in the ordered phase drives the ground state conformations of the membrane to a cylinder and tetrahedron respectively.

Numerical insights into the phase diagram of p-atic membranes with spherical topology

“…In this section we analyse the buckling instability of the membrane in the ordered phase by use of the discretised model. We have previously shown configurations with disclinations bound to curvature singularity for p = 1 and p = 2 [35,38]. Similarly, the equilibrium configurations for all combinations of p = 1, 2, 3, 4, 5, ε = 5, 10, 15, where certain combinations show disclinations with associated curvature singularity in the membrane configurations.…”

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

“…Ramakrishnan et al [101, 305] considered the vertices of the triangulated surface (introduced in section 3.6) by additionally decorating them with a nematic in-plane field m̂ , of unit length, defined on the tangent plane at each vertex. Fig.22(a) shows the neighbourhood of a vertex with an in-plane field and fig.22(b) shows a vesicular membrane with in-plane order defined at all vertices; the surface coverage can be set to the desired concentration.…”

“…The form of this interaction potential differs with the value of p . For example, the self-interaction between the in-plane field with polar symmetry ( p = 1) can be represented by the standard XY -like interactions [68], $${ℌ}_{1-\text{atic}}=-J_1\sum _{false\langle \upsilon ,\upsilon \prime false\rangle }\text{cos}({\theta }_{\upsilon \upsilon \prime }),$$ For a nematic field, the Lebwohl-Lasher interaction potential [306], $${ℌ}_{2-\text{atic}}=-\frac{J_2}{2}\sum _{false\langle \upsilon ,\upsilon \prime false\rangle }false\{3{\text{cos}}^{2}false({\theta }_{\upsilon \upsilon \prime }false)-1false\},$$ has been used by Ramakrishnan et al [101, 305] to model the self-interaction of the nematic in-plane field defined on the vertices of the membrane. J 1 and J 2 are the interaction strengths of the polar and nematic fields, respectively.…”

“…As described by Ramakrishnan et al [101, 305], the Monte Carlo techniques for a fluid random surface can be extended to a field-decorated membrane when the contributions arising from field orientations are accounted for in the phase space integral. The total partition function of the membrane with the in-plane field has the form, $$Zfalse(N,\kappa ,\mathrm{normal\Delta }p,J_{p}false)=\frac{1}{N!}\sum _{false\{𝔗false\}}\prod _{\upsilon =1}^{N}true\int d\phi false(\upsilon false)true\int d\overrightarrow{x}false(\upsilon false)\text{exp}false\{-\beta {ℌ}_{\text{tot}}false\},$$ where ℌ tot = ℌ sur + ℌ 2−atic + V SA , and the integral is performed over all possible in-plane orientations, in addition to the phase space of the random surface in eqn.(41).…”

Novel Simulation Approaches for Polymeric and Soft Matter Systems

“…The first article by Ramakrishnan et al [9] is a review that focuses on the current Monte Carlo techniques available to describe fluid membranes via the dynamically triangulated surface approach. In a subsequent feature article, Engin et al [10] discuss the different approaches one can follow to coarse-grain peptides while highlighting the importance of transferability of the coarse-grained force field.…”