with central chargeN

We study representations of the central extension of the Lie algebra of differential operators on the circle, the algebra. We obtain complete and specialized character formulas for a large class of representations, which we call primitive; these include all quasi-finite irreducible unitary representations. We show that any primitive representation with central chargeN has a canonical structure of an irreducible representation of the with the same central charge and that all irreducible representations of with central chargeN arise in this way. We also establish a duality between integral modules of and finite-dimensional irreducible modules ofgl _N , and conjecture their fusion rules.Supported by a Junior Fellowship from Harvard Society of Fellows and in part by NSF grant DMS-9205303.Supported in part by NSF grant DMS-9103792.     

Quantum affine algebras and deformations of the Virasoro and 237-1237-1237-1

Using the Wakimoto realization of quantum affine algebras we define new Poisson algebras, which areq-deformations of the classicalW. We also define their free field realizations, i.e. homomorphisms into some Heisenberg-Poisson algebras. The formulas for these homomorphisms coincide with formulas for spectra of transfer-matrices in the corresponding quantum integrable models derived by the Bethe-Ansatz method.Partially supported by NSF grants DMS-9205303 and DMS-9296120.     

Scaling models of thermodynamic properties on the coexistence curve: Problems and some solutions

Models consistent with the scaling theory of critical phenomena and capable of describing the thermodynamic properties F of substances on the coexistence curve, such as the density of the liquid ρ _l , density of the gas ρ _g , order parameter f _s , mean coexistence curve diameter f _d , and saturation pressure P _s are discussed. The models are presented in the form of equations F = (τ, D, C), where τ = (T _c ? T)/T _c , and D = (α, β, T _c , ρ _c , P _c , ...) are the critical characteristics, such as T _c , ρ _c , and P _c (temperature, density, and pressure, respectively), α and β are the scaling exponents, and C are adjustable coefficients. The authors developed combined models f(τ, D, C) for describing the indicated properties of a number of compounds (CH₄, NH₃, SF₆, water, methanol, ethanol, diethyl ether, and freons R134a, R143a, and R236ea). The coefficients C were determined based on experimental data over a wide temperature range, including the critical point. The equations derived are used to perform practical calculations, including estimates of the first and second derivatives of the saturation pressure with respect to the temperature in the critical region.     

The sensitivity of the results of molecular docking to induced fit effects: Application to thrombin, thermolysin and neuraminidase

This paper describes the application of PRO_–LEADS to the flexible docking of ligands into crystallographically derived enzyme structures that are assumed to be rigid. PRO_–LEADS uses a Tabu search methodology to perform the flexible search and an empirically derived estimate of the binding affinity to drive the docking process. The paper tests the extent to which the assumption of a rigid enzyme compromises the accuracy of the results. All-pairs docking experiments are performed for three enzymes (thrombin, thermolysin and influenza virus neuraminidase) based on six or more ligand-enzyme crystal structures for each enzyme. In 76% of the cases, PRO_–LEADS can successfully identify the correct ligand conformation as the lowest energy configuration when the enzyme structure is derived from that ligand's crystal structure, but the methodology only docks 49% of the cases successfully when the ligand is docked against enzyme crystal structures derived from other ligands. Small movements in the enzyme structure lead to an under-prediction in the energy of the correct binding mode by up to 14 kJ/mol and in some cases this under-prediction can lead to the native mode not being recognised as the lowest energy solution. The type of movements responsible for mis-docking are: the movement of sidechains as a result of changes in C position; the movement of sidechains without changes in C position; the movement of flexible portions of main chains to facilitate the formation of hydrogen bonds; and the movement of metal atoms bound to the enzyme active site. The work illustrates that the assumption of a rigid active site can lead to errors in identification of the correct binding mode and the assessment of binding affinity, even for enzymes which show relatively small shift in atomic positions from one ligand to the next. A good docking code, such as PRO_–LEADS, can usually dock successfully if there is induced fit in relatively rigid enzymes but there remains the need to develop improved strategies for dealing with enzyme flexibility. The work implies that treatments of enzyme flexibility which focus only on sidechain rotations will not deal with the critical shifts responsible for mis-docking of ligands in thrombin, thermolysin and neuraminidase. The paper demonstrates the utility of all pairs docking experiments as a method of assessing the effectiveness of docking methodologies in dealing with enzyme flexibility.     

Modeling flexible amphiphilic bilayers: a solvent-free off-lattice Monte Carlo study

We present a simple, implicit-solvent model for fluid bilayer membranes. The model was designed to reproduce the elastic properties of real bilayer membranes. For this model, we observed the solid-fluid transition and studied the in-plane diffusivity of the fluid phase. As a test, we compute the elastic-bending and area-compressing moduli of fluid bilayer membranes. We find that the computed elastic properties are consistent with the available experimental data.     

Deviations from Fick's law in Lorentz gases

We have calculated the self-dynamic structure factorF(k,t) for tagged particle motion in hopping Lorentz gases. We find evidence that, even at long times, the probability distribution function for the displacement of the particles is highly non-Gaussian. At very small values of the wave vector this manifests itself as the divergence of the Burnett coefficient (the fourth moment of the distribution never approaching a value characteristic of a Gaussian). At somewhat larger wave vectors we find thatF(k,t) decays algebraically, rather than exponentially as one would expect for a Gaussian. The precise form of this power-law decay depends on the nature of the scatterers making up the Lorentz gas. We find different power-law exponents for scatterers which exclude certain sites and scatterers which do not.