Zhengping Zhang

Phase transition and director fluctuations in the three-dimensional Lebwohl-Lasher model of liquid crystals

Monte Carlo computer simulation techniques are used to study the orientational phase transition in the three-dimensional Lebwohl-Lasher model which couples molecular rotors placed on a cubic lattice by the potential P 2(cos ϑ ij ). The orientational transition is a model of the nematic-isotropic phase transition in liquid crystals. The simulations involve the determination of energy and order parameter distribution functions which permit free energy functions to be derived. The data have been analysed by finite size scaling methods to reveal the nature of the phase transition which is found to be weakly first order with stability limits of the nematic and isotropic phases being extremely close to the equilibrium transition temperature, in good agreement with experimental studies of room temperature nematogens. Results are reported for the specific heat, the axial and biaxial susceptibilities, as well as the enthalpy and nematic order parameter discontinuity at the transition. It is shown that the inclusio...

A microscopic model for lipid/protein bilayers with critical mixing

A statistical mechanical lattice model is proposed to describe the phase diagram of phospholipid bilayers with small transmembrane proteins or polypeptides. The model is based on the extended Pink-Green-Chapman model (Zhang et al. (1992) Phys. Rev. A 45, 7560-7567) for pure lipid bilayers which undergo a first-order gel-fluid phase transition. The interaction between the lipid bilayer and the protein or polypeptide is modelled using the concept of hydrophobic matching. The phase diagram has been derived by computer-simulation techniques which fully account for thermal density fluctuations and which operate on the level of the free-energy thereby permitting an accurate identification of the phase boundaries. The calculations predict a closed loop of gel-fluid coexistence with a lower critical mixing point. Specific-heat traces across the phase diagram are also presented. The theoretical results for the phase diagram, the specific-heat function, and the transition enthalpy are related to recent experimental measurements on phospholipid bilayers mixed with synthetic transmembrane amphiphilic polypeptides or with gramicidin A.

Computational Approach to Lipid-Protein Interactions in Membranes

Publisher Summary Most biological activity takes place at organized templates and surfaces or near highly structured molecular assemblies. The biological membrane is one such template or interface, which mediates a very large number of different biochemical and physiological processes on both the intra- and intercellular level. Considering the very small amount of free water present in biological tissues, it is reasonable to postulate that most enzymatic reactions take place in close association with structured water and structured molecular interfaces, such as membranes. The biological membrane is a highly stratified composite material consisting of several components: a fluid lipid bilayer, polymeric scaffolding network on the intracellular side (the cytoskeleton in eukaryotes), and a carbohydrate-based glycocalyx on the extracellular side. The lipid bilayer provides the membrane with a permeability barrier, while the other structures maintain the cell shape and provide the proper interaction and communication with its environment.

DETECTING PHASE EQUILIBRIA IN MODELS OF THERMOTROPIC AND LYOTROPIC LIQUID CRYSTALS

New ways are discussed of numerically detecting the nature of phase transitions and the position of phase equilibria in models of thermotropic and lyotropic liquid crystals where the phase transitions are dominated by strong fluctuations. The cases of continuous transitions (critical points), first-order transitions, as well as the absence of transitions, are considered. It is shown how computer-simulation techniques, which operate on a free-energy level by using reweighting (histogram) techniques in combination with finite-size scaling theory, provide an effective tool for unambiguously determining the nature of the transition and the position of associated phase equilibria. Three specific models are considered: the Lebwohl–Lasher model of the nematic–isotropic transition in thermotropic liquid crystals, the mismatch model of the main chain-melting phase transition in lipid-bilayer lyotropic liquid crystals, and a model for critical mixing in a lipid-bilayer lyotropic liquid crystal incorporated with trans-bilayer polypeptides.

Neural Networks with Constrained Inputs as Models for Pattern Formation in Primate Visual Cortex

We present a neural network model for the formation of ocular dominance stripes on primate visual cortex and examine the generic phase behavior and dynamics of the model. The dynamical equation of ocular dominance development can be identified with a class of Langevin equations with a nonconserved order parameter. We first set up and examine an Ising model with long-range interactions in an external field, which is equivalent to the model described by the Langevin equation. We use both mean-field theory and Monte-Carlo simulations to study the equilibrium phase diagram of this equivalent Ising model. The phase diagram comprises three phases: a striped phase, a hexagonal ‘bubble’ phase, and a uniform paramagnetic phase. We then examine the dynamics of the striped phase by solving the Langevin equation both numerically and by singular perturbation theory. Finally, we compare the results of the model with physiological data. The typical striped structure of the ocular dominance columns corresponds to the zero-field configurations of the model. Monocular deprivation can be simulated by allowing the system to evolve in the absence of an external field at early times and then continuing the simulation in the presence of an external field. The physical and physiological applications of our model are discussed in the conclusion.

Modelling Pattern Formation on Primate Visual Cortex

We begin this chapter by giving an overview of the types of theoretical model used to describe pattern formation related to ocular dominance on the visual cortex. We then present a new neural network model for the formation of ocular dominance stripes on primate visual cortex and examine the generic phase behavior and dynamics of the model. The dynamical equation of ocular dominance development can be identified with a class of Langevin equations with a non-conserved order parameter. We find that the phase diagram for our model comprises three phases: a striped phase, a hexagonal “bubble” phase and a uniform paramagnetic phase. We then examine the dynamics of the striped phase by solving the Langevin equation both numerically and by singular perturbation theory. Finally, we compare the results of the model with physiological data. The typical striped structure of the ocular dominance columns corresponds to the zero-field configurations of the model. We also use our model to simulate mononuclear deprivation.