Thermal fluctuations in shape, thickness, and molecular orientation in lipid bilayers. II. Finite surface tensions.

We investigate the role of lipid chemical potential on the shape, thickness, and molecular orientation (lipid tilting relative to the monolayer surface normal) of lipid bilayers via a continuum-level model. We predict that decreasing the chemical potential at constant temperature, which is associated with an increase in surface tension via the Gibbs-Duhem relation, leads both to the well known reduction in thermal membrane undulations and also to increasing fluctuation amplitudes for bilayer thickness and molecular orientation. These trends are shown to be in good agreement with molecular simulations, however it is impossible to achieve full quantitative agreement between theory and simulation within the confines of the present model. We suggest that the assumption of lipid volume incompressibility, common to our theoretical treatment and other continuum models in the literature, may be partially responsible for the quantitative discrepancies between theory and simulation.

Determining biomembrane bending rigidities from simulations of modest size.

Thermal fluctuations of lipid orientation are analyzed to infer the bending rigidity of lipid bilayers directly from molecular simulations. Compared to the traditional analysis of thermal membrane undulations, the proposed method is reliable down to shorter wavelengths and allows for determination of the bending rigidity using smaller simulation boxes. The requisite theoretical arguments behind this analysis are presented and verified by simulations spanning a diverse range of lipid models from the literature.

Thermal fluctuations in shape, thickness, and molecular orientation in lipid bilayers.

We present a unified continuum-level model for bilayer energetics that includes the effects of bending, compression, lipid orientation (tilting relative to the monolayer surface normal), and microscopic noise (protrusions). Expressions for thermal fluctuation amplitudes of several physical quantities are derived. These predictions are shown to be in good agreement with molecular simulations.

The effects of crowding in dendronized polymers.

We present a comprehensive numerical study of the effect of degree of polymerization, generation of dendron growth, length of dendron tether, and dendron grafting density on the conformational statistics of dendronized polymers. This class of supramolecular assembly promises to find application in a number of nanotechnological devices in which their dimensions and conformations are key. We find that the radius of gyration estimates obtained from Brownian dynamics simulations yield to a "Flory" scaling argument in the high degree of polymerization regime and that these data from a range of topologically distinct molecules collapse onto a single curve in this limit. The size of the tethered dendrons serve as the key parameter in the scaling theory. Close examination of the dendrons also reveals some curious trends. In particular, we observe that as the grafting density is increased, spatial packing constraints around the main chain backbone force the dendrons further away from the backbone and compress them, significantly affecting the spatial distribution and accessibility of terminal groups; in contrast to dendrimers, the terminal groups of these molecules display a tendency to partition near the surface at high dendron grafting densities.

A tunable dendritic molecular actuator.

I present an electroresponsive molecular actuator based upon a diblock copolymer of a positively charged dendrimer and a negatively charged linear chain. Brownian dynamics simulations demonstrate the hybrid polyampholyte's ability to apply a force or assume an equilibrium molecular strain tunable with an applied electric field. The free energy as a function of molecular strain at differing electric field strengths, as obtained via the Jarzynski identity, suggests a phase transition in the hybrid.

Influence of supercoiling on the disruption of dsDNA.

We propose that supercoiling energizes double-stranded DNA (dsDNA) so as to facilitate thermal fluctuations to an unzipped state. We support this with a model of two elastic rods coupled via forces that represent base-pair interactions. Supercoiling is shown to lead to a distention of base pairs over a short span of dsDNA. This enhances the thermal probability for their disruption. The localized region of distention is analogous to a soliton. Our theory permits the development of an analogy between the unzipping transition and a second-order phase transition, for which the possibility of a new set of critical exponents is identified.