P B Sunil Kumar

Inspite of the fluid nature and low elastic modulus, membranes play a crucial role in maintaining the structural integrity of the cell. Recent experiments have challenged the passive nature of the membrane as proposed by the classical fluid mosaic model. Experiments indicate that biomembranes of eukaryotic cells may be laterally organized into small nanoscopic domains, called rafts, which are rich in sphingomyelin and cholesterol. It is largely believed that this in-plane organization is essential for a variety of physiological functions such as signaling, recruitment of specific proteins and endocytosis. However, elucidation of the fundamental issues including the mechanisms leading to the formation of lipid rafts, their stability, and their size remain difficult. This has reiterated the importance of understanding the equilibrium phase behavior and the kinetics of fluid multicomponent lipid membranes before attempts are made to find the effects of more complex mechanisms that may be involved in the formation and stability of lipid rafts. Current increase in interest in the domain formation in multicomponent membranes also stems from the experiments demonstrating fluid-fluid coexistence in mixtures of lipids and cholesterol and the success of several computational models in predicting their behavior. Here we review time dependent Ginzburg Landau model, dynamical triangulation Monte Carlo, and dissipative particle dynamics which are some of the methods that are commonly employed. © 2009 The Physical Society of Japan.

We study the linearized hydrodynamics of a two-component fluid membrane near a repulsive wall, using a model that incorporates curvature-concentration coupling as well as hydrodynamic interactions. This model is a simplified version of a recently proposed one [J.-B. Manneville et al., Phys. Rev. E 64, 021908 (2001)] for nonequilibrium force centers embedded in fluid membranes, such as light-activated bacteriorhodopsin pumps incorporated in phospholipid egg phosphatidyl choline (EPC) bilayers. The pump-membrane system is modeled as an impermeable, two-component bilayer fluid membrane in the presence of an ambient solvent, in which one component, representing active pumps, is described in terms of force dipoles displaced with respect to the bilayer midpoint. We first discuss the case in which such pumps are rendered inactive, computing the mode structure in the bulk as well as the modification of hydrodynamic properties by the presence of a nearby wall. These results should apply, more generally, to equilibrium fluid membranes comprised of two components, in which the effects of curvature-concentration coupling are significant, above the threshold for phase separation. We then discuss the fluctuations and mode structure in the steady state of active two-component membranes near a repulsive wall. We find that proximity to the wall smoothens membrane height fluctuations in the stable regime, resulting in a logarithmic scaling of the roughness even for initially tensionless membranes. This explicitly nonequilibrium result is a consequence of the incorporation of curvature-concentration coupling in our hydrodynamic treatment. This result also indicates that earlier scaling arguments which obtained an increase in the roughness of active membranes near repulsive walls upon neglecting the role played by such couplings may need to be reevaluated. © 2002 The American Physical Society.

We model the stable self-organized patterns obtained in the nonequilibrium steady states of mixtures of molecular motors and microtubules. In experiments [Nédélec, Nature (London) 389, 305 (1997); Surrey, Science 292, 1167 (2001)] performed in a quasi-two-dimensional geometry, microtubules are oriented by complexes of motor proteins. This interaction yields a variety of patterns, including arrangements of asters, vortices, and disordered configurations. We model this system via a two-dimensional vector field describing the local coarse-grained microtubule orientation and two scalar density fields associated to molecular motors. These scalar fields describe motors which either attach to and move along microtubules or diffuse freely within the solvent. Transitions between single aster, spiral, and vortex states are obtained as a consequence of confinement, as parameters in our model are varied. For systems in which the effects of confinement can be neglected, we present a map of nonequilibrium steady states, which includes arrangements of asters and vortices separately as well as aster-vortex mixtures and fully disordered states. We calculate the steady state distribution of bound and free motors in aster and vortex configurations of microtubules and compare these to our simulation results, providing qualitative arguments for the stability of different patterns in various regimes of parameter space. We study the role of crowding or “saturation” effects on the density profiles of motors in asters, discussing the role of such effects in stabilizing single asters. We also comment on the implications of our results for experiments. © 2004 The American Physical Society.

We study, using dissipative particle dynamics simulations, the effect of active lipid flip-flop on model fluid bilayer membranes. We consider both cases of symmetric as well as asymmetric flip-flops. Symmetric flip-flop leads to a steady state of the membrane with an effective temperature higher than that of the equilibrium membrane and an effective surface tension lower than that of the equilibrium membrane. Asymmetric flip-flop leads to transient conformational changes in the membrane in the form of bud or blister formation, depending on the flip rate. © 2008 American Institute of Physics.

The effect of asymmetry in the transbilayer lipid distribution on the dynamics of phase separation in fluid vesicles is investigated numerically. This asymmetry is shown to set a spontaneous curvature for the domains that alter the morphology and dynamics considerably. For moderate tension, the domains are capped and the spontaneous curvature leads to anomalously slow dynamics, as compared to the case of symmetric bilayers. In contrast, in the limiting cases of high and low tensions, the dynamics proceeds toward full phase separation. © 2006 The American Physical Society.

We investigate the dynamics of a single semiflexible filament under the action of external forces. We show that unlike in stiff elastic rods in the thermally activated semiflexible filaments external forces applied at one extremity of the filament do not propagate to the other end till the filament is fully stretched. This asymmetric tension profile is shown to be the reason for qualitatively different behavior exhibited by semiflexible filaments under external tension. © 2002 Elsevier Science B.V. All rights reserved.

The interaction between equal, uniformly charged flat surfaces, separated by a solution of spheroidal nanoparticles was studied theoretically. The nanoparticles were assumed to have spatially distributed electric charge. The nonlocal Poisson-Boltzmann (PB) theory for the spheroidal nanoparticles, which play the role of counterions, was developed. In the model the center of the spheroidal nanoparticle could not approach the charged surfaces closer than the radius of the nanoparticle. It was shown that for large enough diameters of nanoparticles and large enough surface charge densities of membrane surfaces, the two equally charged surfaces could experience an attractive force due to the spatially distributed charges within the nanoparticles. The results presented in this chapter may add to a better understanding of the coalescence of negatively charged membrane surfaces induced by positively charged nanoparticles (e.g., proteins) which are proposed to play an important role in the complex vital processes such as blood clot formation. © 2009 Elsevier Inc. All rights reserved.

A systematic investigation of the phase-separation dynamics in self-assembled binary fluid vesicles and open membranes is presented. We use large-scale dissipative particle dynamics to explicitly account for solvent, thereby allowing for numerical investigation of the effects of hydrodynamics and area-to-volume constraints. In the case of asymmetric lipid composition, we observed regimes corresponding to coalescence of flat patches, budding, vesiculation, and coalescence of caps. The area-to-volume constraint and hydrodynamics have a strong influence on these regimes and the crossovers between them. In the case of symmetric mixtures, irrespective of the area-to-volume ratio, we observed a growth regime with an exponent of 12. The same exponent is also found in the case of open membranes with symmetric composition. © 2005 American Institute of Physics.

We obtain, using transfer-matrix methods, the distribution function P(R) of the end-to-end distance, the loop formation probability, and force-extension relations in a model for short double-stranded DNA molecules. Accounting for the appearance of "bubbles," localized regions of enhanced flexibility associated with the opening of a few base pairs of double-stranded DNA in thermal equilibrium, leads to dramatic changes in P(R) and unusual force-extension curves. An analytic formula for the loop formation probability in the presence of bubbles is proposed. For short heterogeneous chains, we demonstrate a strong dependence of loop formation probabilities on sequence. © 2005 The American Physical Society.

The dynamics of domain growth in self-assembled fluid vesicles was discussed by using large-scale dissipative particle dynamics. The model allowed the very first numerical investigation of the effects of hydrodynamics and area-to-volume constraints. Regimes corresponding to coalescence of flat patches, budding and vesiculation and coalescence of caps were observed. It was found that between these regimes, the area-to-volume constraint has a strong influence on crossovers.