Aharonov-Bohm effects in entangled molecules.

Molecules which are magnetic and conducting, if suitably entangled (e.g., catenanes and knots) could exhibit Aharonov-Bohm effects which can be viewed as particular examples of a Berry phase. The corrections to the quantum energy levels reflect the entangled geometry of the molecules and, while small (they are proportional to the square of the fine structure constant), may be observable. We illustrate these corrections for a number of catenated and knotted structures. For couplings between the components of a catenane (link), the Aharonov-Bohm corrections are determined by integer-valued linking numbers. For knots, the Aharonov-Bohm correction is proportional to the geometric writhe of the knot.

Quantum corrections for the liquid-gas transition of Lennard-Jones particles in two dimensions.

The quantum corrections in first-order perturbation theory are semiquantitatively reproduced in the low temperature behavior of the liquid-gas coexistence curve of the simulations-at least for reduced masses down to m(*)=50.

Stiff polymer in monomer ensemble.

We employ an ordered monomer ensemble formalism in order to develop techniques to investigate a stiff polymer chain which is confined to a certain region. In particular, we calculate the segment density for a given location and segment orientation distribution within the confining geometry. With this method the role of the stiffness can be examined by means of differential equations, integral equations, or recursive relations for both continuum and lattice models. A suitable choice of lattice model permits an exact analytical solution for the segment location and orientation density for a chain between two parallel plates. For the stiff polymer in a spherical cavity we develop an integral equation formalism which is treated numerically, and in the same spherical geometry, a different model of the polymer displays a solution of a differential equation.

Fast Kawasaki spin exchange limit of spin-facilitated kinetic Ising models.

We study a Fock-space operator technique for describing the stochastic kinetics of a spin-facilitated kinetic Ising model. We focus in particular on the diffusion (fast Kawasaki exchange) limit in which the kinetics can be described by a single mean field evolution equation. We derive some general criteria for the approximative validity of mean field theory for the case of a nondiverging diffusion coefficient of the local spin states.

Kinetics in one-dimensional lattice gas and Ising models from time-dependent density-functional theory.

Time-dependent density-functional theory, proposed recently in the context of atomic diffusion and nonequilibrium processes in solids, is tested against Monte Carlo simulation. In order to assess the basic approximation of that theory, the representation of nonequilibrium states by a local equilibrium distribution function, we focus on one-dimensional lattice models, where all equilibrium properties can be worked exactly from the known free energy as a functional of the density. This functional determines the thermodynamic driving forces away from equilibrium. In our studies of the interfacial kinetics of atomic hopping and spin relaxation, we find excellent agreement with simulations, suggesting that the method is also useful for treating more complex problems.

Single homopolymers in the relative density representation.

A single symmetric homopolymer is studied in the grand ensemble of its monomeric units. For an arbitrary external field but next neighbor interactions alone, such a system is represented as a functional of the local density to local fugacity ratio, conjugate to the fugacity, with the excess grand potential as thermodynamic generating function. A sample case in a spherical enclosure is solved, where a complementary exclusion from a spherical volume requires an extension to a grand ensemble of polymers. A preliminary extension is also made in mean field form to non-neighbor interactions, as well as to nonsymmetric interactions.

Kramers potential study of the Rouse-like dynamics of short alkane chains.

In this work we present a Kramers potential study of the orientational dynamics and shear viscosity of short chain alkanes. In this approach the determination of the orientational relaxation time is reduced to the calculation of static moments of single chain conformations. We study a chemically realistic alkane model that asymptotically produces Gaussian chain conformations by means of a Monte Carlo simulation. Our results are applicable to single chain descriptions of polymer melt dynamics and to the intrinsic viscosity of molecules in a Theta solvent. When we map the unknown time unit of our relaxation time result for one particular chain length and temperature to the value obtained for the same parameters from a molecular dynamics simulation of a melt of these chains, we are able to reproduce the experimental data on the chain length dependence of the melt viscosity of alkane chains at this temperature.

High dimensionality as an organizing device for classical fluids.

The Mayer diagrammatic expansion for a classical pair-interacting fluid in thermal equilibrium is cast in a form particularly appropriate to high-dimensional space. At asymptotically high dimensionality, the series, when it converges, is dominated by a single term. Focusing upon repulsive interactions, the dominant term belongs to a ring diagram and can have either sign, but when negative, the series must diverge. The nature of the divergence is found explicitly for hard core interactions, and analytic extension in density obtained by summing up the dominant ring contributions. The result is that a second virial truncation remains valid at densities much higher than that at which the series diverges. Corrections first appear in the vicinity of a particle volume-scaled density of 1 / 2(e/2)(1/2) per dimension, and produce a spinodal in the equation of state. Suggestions are made as to elucidating the resulting phase transition.

Two metric solutions to three-dimensional reconstruction for an eye in pure rotations.

A problem in space perception concerns how a mobile observer acquires information about the structure of objects. Earlier research derived the optic-flow equations for an eye undergoing pure rotations. It was suggested that, by utilizing three points and two views, one can recover the distance of points and the motion parameters. The radius of the eyeball was the metric unit. Yet the common view regards this problem as indeterminate. We derived a unique solution in the discrete case, which required three points and two views. However, when we observed a single bright point, a substantial amount of visual stability existed. We therefore derived a solution in the differential approach for a single point, which is based on a distinction that we made between mathematical and visual points. Both solutions were checked with a computer simulation and were found to be accurate, supporting the space perception in navigation (SPIN) theory.

The effects of lithium, rubidium, cesium and magnesium ions on the close packing of persistence-length DNA fragments.

By application of scaled particle theory to persistence-length DNA fragments in sedimentation-equilibrium at speeds high enough to maintain close packing, the range of interhelical electrostatic repulsion was evaluated with LiCl, RbCl, CsCl, and MgCl2 as supporting electrolytes. Analysis of the data in terms of the Zimm cluster function confirmed that the net interaction between helices is purely repulsive in all cases. At constant ionic strength the electrostatic radius of the rod-like DNA decreases as the counterion changes from Li+ to Rb+ to Cs+. In contrast to univalent counterions, electrostatic radius increases with Mg2+ concentration, except at very low (mM) MgCl2 concentrations. All solutions undergo a reversible transition to a turbid, optically anisotropic phase at a slightly salt-dependent, critical DNA concentration, as observed previously for NaDNA.

Wetting, percolation and morphogenesis in a model tissue system.

Artificial tissues constructed of cells or polystyrene beads suspended in a solution of type I collagen will, under appropriate conditions, protrude into regions of similar matrices lacking particles, but containing the extracellular glycoprotein fibronectin. This phenomenon has been termed "matrix-driven translocation". Conditions required for the effect include the presence of heparin-like molecules on the cell or bead surfaces, appropriate concentrations of particles and collagen, and physiological ionic strength and pH. Here we consider the idea that the driving force for the concerted movement of matrix and suspended particles is the thermodynamically spontaneous spreading or wetting behavior of two immiscible fluids bounded by common substrata. Wetting theory is shown to be capable of accounting for the behavior of this model system, but this analysis requires that the two matrix regions constitute separate phases at thermodynamic coexistence. We show that one plausible mechanism for the generation of separate phases is the formation of a percolation network of collagen fibers on a lattice of cells or beads. It is argued that the concepts of wetting and percolation apply to properties in common between the model system and living tissues, and may therefore be used to provide a physical account of aspects of tissue morphogenesis.

Relaxation effects in the gel electrophoresis of DNA in intermittent fields.

The electrophoretic mobility of restriction fragments of lambda DNA in agarose gels declines if the field is intermittent rather than continuous, with a greater effect on the longer fragments. The changes are compatible with the assumption of two exponential relaxation processes for field-dependent configurational changes, one when the field is turned on and another when it terminates. The length dependence at the extrapolated limit of mobility for short pulses with long intervals corresponds closely to the simple inverse proportionality to length expected from theoretical considerations when the molecular configuration is not affected by the electric field. Simple intermittent fields would allow separation of longer molecules than can ordinarily be resolved. The relaxation times for both the change in conformation imposed by the field and the return to field-free conformation vary as approximately the second power of the length of the molecule, independent of the salt concentration or field strength and varying only slightly with gel density. These relations are not in good agreement with properties expected from reputation theory, and they suggest that a different mechanism must be invoked for the electrophoretic migration of long DNA molecules at ordinary values of field strength.

Kinetics of voltage-induced conductance increases in the outer mitochondrial membrane.

The kinetics of the increase in conductance in the outer mitochondrial membrane induced by patch-clamping at various negative potentials (pipette inside negative) are reported. The changes are biphasic, a rapid increase is followed by a slowly developing larger change. The results can be predicted by a model in which an initial activation of channels is followed by their assembly into highly conducting channels. The model suggests that five to seven activated subunits form each high-conductance channel.

Monte Carlo simulation of DNA electrophoresis.

This paper describes an attempt to study the electrophoresis mobility of a DNA molecule in a gel by means of a Monte Carlo simulation. We find that the electrophoresis mobility mu can be well described by the empirical equation mu v kappa 1/N + kappa 2E2 with N being the number of monomers of the model chain and E being the applied field. For small E the data can merge into the linear response result mu = kappa 1/N. The paper also discusses necessary extensions of the present approach.

On the stationary state analysis of reaction-diffusion mechanisms for biological pattern formation.

We present a biologically plausible two-variable reaction-diffusion model for the developing vertebrate limb, for which we postulate the existence of a stationary solution. A consequence of this assumption is that the stationary state depends on only a single concentration-variable. Under these circumstances, features of potential biological significance, such as the dependence of the steady-state concentration profile of this variable on parameters such as tissue size and shape, can be studied without detailed information about the rate functions. As the existence and stability of stationary solutions, which must be assumed for any biochemical system governing morphogenesis, cannot be investigated without such information, an analysis is made of the minimal requirements for stable, stationary non-uniform solutions in a general class of reaction-diffusion systems. We discuss the strategy of studying stationary-state properties of systems that are incompletely specified. Where abrupt transitions between successive compartment-sizes occur, as in the developing limb, we argue that it is reasonable to model pattern reorganization as a sequence of independent stationary states.

Theory of the intermediate rippled phase of phospholipid bilayers.

A mathematical model of the periodic, rippled P beta' phase of phosphatidylcholine is described. In this model the P beta' phase shows a periodic variation in membrane properties corresponding to a lateral periodic variation between fluid-like and crystal-like states. The model is based on a curvature-dependent Landau-de Gennes free-energy functional. Our proposed form of the curvature-dependent free energy remedies a subtle mathematical flaw in an earlier model having similar physical content [Falkovitz, M. F., Seul, M., Frisch, H. L. & McConnell, H. M. (1982) Proc. Natl. Acad. Sci. USA 79, 3918-3921].

Scaling of the equilibrium sedimentation distribution in dense DNA solutions.

DNA molecules, several persistence lengths long in sedimentation equilibrium at speeds high enough to maintain fairly close packing, show a dense, sharply-bounded turbid phase and an isotropic phase (as with shorter fragments) and also an intermediate, somewhat turbid region. The concentration distribution in the isotropic phase is in satisfactory agreement with a simple extension of scaled particle theory in which semiflexible chains are equivalent to straight rods of the same length. The net intermolecular interactions, as inferred from the Zimm cluster integral, are purely repulsive. As in our previous study with short fragments, the results are compatible with a hard-core electrostatic radius, decreasing with increasing salt concentration. However, for the longer fragments it is necessary to infer either a slightly greater mass per unit length or a slightly smaller electrostatic radius for closest agreement with scaled particle theory. The properties of the solution at the boundary with the turbid, presumably strongly ordered phase are consistent with those found for shorter fragments and with theoretical scaling expectation for a hard, asymmetric particle.

Theory of periodic structures in lipid bilayer membranes.

An approximate, new model for the structure of the periodic, undulated P(beta'), phase of phosphatidylcholine bilayers is proposed. The properties of this phase are deduced by minimizing a Landau-de Gennes expression for the bilayer free energy when this free energy contains a term favoring a spontaneous curvature of the membrane. The theoretical calculation leads to a model for the P(beta') phase of phosphatidylcholine bilayers having a number of novel physical properties, including periodic variations in membrane "fluidity."