Quasi-quantization of writhe in ideal knots

The values of writhe of the tightest conformations, found by the SONO algorithm, of all alternating prime knots with up to 10 crossings are analysed. The distribution of the writhe values is shown to be concentrated around the equally spaced levels. The “writhe quantum” is shown to be close to the rational 4/7 value. The deviation of the writhe values from the n(4/7) writhe levels scheme is analysed quantitatively. Received 29 February 2001 and Received in final form 17 August 2001     

Protein folding simulations in a deformed energy landscape

A modified version of stochastic tunneling, a recently introduced global optimization technique, is introduced as a new generalized-ensemble technique and tested for a benchmark peptide, Met-enkephalin. It is demonstrated that the new technique allows to evaluate folding properties and especially the glass temperature of this peptide. Received 2 September 1999     

Simulation study of lateral diffusion in lipid-sterol bilayer mixtures

We employ off-lattice Monte Carlo simulations to study lateral diffusion in lipid-sterol bilayers using a two-dimensional model system which has been designed to simulate the experimental phase diagrams of both lipid-cholesterol and lipid-lanosterol systems. We focus on the effects of varying sterol concentration and temperature on the tracer diffusion coefficient, D, which characterizes the lateral motion of single tagged lipids in a bilayer. Generally, we find that increasing the cholesterol concentration suppresses D due to an increased conformational ordering of lipid chains. We argue that this effect competes with an increase in the average free area per lipid, which favours an increase in D. At temperatures close to the main transition temperature, the competition between the two effects leads to intriguing behavior of D. Overall, the model results are in excellent qualitative agreement with available experimental results for lipid-cholesterol mixtures. Additional studies of a model lipid-lanosterol system, for which experimental diffusion results are not available, predict that the presence of lanosterol has a smaller effect than cholesterol on reducing D relative to the pure lipid system. We conclude that the molecular model employed contains the essential features required to describe many of the qualitative features of the lateral diffusion behavior in lipid-sterol systems. Received 24 November 2000 and Received in final form 30 April 2001     

Deformation in cooperative molecular motors

We implement a model to represent the effect of the deformation of the backbone of a system of motor proteins while sliding on a track filament. This model incorporates a nearest neighbor interaction term among the motors for the deformation energy. Correlations induced by this term result in increased motor force for inter-particle distances small compared to the ratchet period. Received 20 February 2001 and Received in final form 31 May 2001     

Self-averaging in complex brain neuron signals

Nonlinear statistical properties of Ventral Tegmental Area (VTA) of limbic brain are studied in vivo. VTA plays key role in generation of pleasure and in development of psychological drug addiction. It is shown that spiking time-series of the VTA dopaminergic neurons exhibit long-range correlations with self-averaging behavior. This specific VTA phenomenon has no relation to VTA rewarding function. Last result reveals complex role of VTA in limbic brain. Received 17 April 2002 / Received in final form 30 September 2002 Published online 31 December 2002     

Probabilistic properties of neuron spiking time-series obtained in vivo

Probabilistic properties of spiking time-series obtained in vivo from singular neurons belonging to Red Nucleus of brain are analyzed for two groups of rats: genetically defined rat model of depression (Flinders Sensitive Rat Line - FSL) and a control (healthy) group. The FSL group shows a distribution of interspike intervals with a much longer tail than that found for normal rats. The former distribution (for the FSL group) indicates a power-law with exponent α = - 1±0.1. A simple thermodynamic (noise) model is elaborated to explain obtained results. Received 13 May 2001 and Received in final form 20 September 2001     

Tomographic-probability description of solitons in Bose-Einstein condensates

The influence of a weight-dependent spike-timing dependent plasticity (STDP) rule on the temporal evolution and equilibrium state of a certain synapse is investigated. We show that under certain conditions, a spike-induced rate-learning scheme could be achieved. Through studying the situation when a single Hodgkin-Huxley neuron is driven by a large ensemble of input neurons, we find that synchronized firing of a sub population of input neurons may be important to information processing in the nervous system. Using simulations, we show that the temporal structure of the spike trains of these synchronized input neurons can be transmitted reliably; further, synapses from these neurons will increase stably due to the STDP rule and this may provide a mechanism for learning and information storage in biologically plausible network models. Received 12 September 2002 / Received in final form 12 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: huang_yue@netease.com     

Tautomery and H-bonding characteristics of 2-aminopurine: a combined experimental and theoretical study

An experimental and theoretical RHF, MP2 and DFT/6-31++G^** study is described of the matrix FT-IR spectra of monomer 2-aminopurine and H-bonded complexes of 2-aminopurine with water. 2-aminopurine occurs in Ar predominantly as the amino-N9H tautomer, but small amounts of the amino-N7H tautomer are also present. An approximate K_T value for this tautomeric equilibrium is found to be 0.016 (RHF) and 0.015 (DFT) using the infrared intensity measurement. Four H-bonded complexes of the abundant amino-N9H form with water are detected in the experimental FT-IR spectrum by their characteristic predicted absorptions, i.e. the three closed complexes N3 ^... H-O ^... H-N9, N1 ^... H-O ^... H-NH, N3 ^... H-O ^... H-NH and the open complex N7 ^... H-OH. From the experimental results, the proton affinity of the N7 atom in 2-aminopurine can be estimated. The dependence of the H-bond strength on the H-bond linearity is demonstrated by a correlation between the N ^... H distance and the N ^... H-O angle in closed N ^... H-O ^... H-N complexes. Received 10 December 2001 Published online 13 September 2002     

Connecting cluster dynamics and protein folding

The relaxation dynamics of clusters can be interpreted in terms of the topographies of their potential surfaces. Systems with short-range potentials have sawtooth-like potential surfaces with small drops in energy from one local minimum to the next and few-body motions as the clusters move from one minimum to another; such systems readily take on amorphous structures. These are called “glass-formers". Systems with long-range forces have potentials whose topographies are like rough staircases, with some large drops in energy from one minimum to the next; their well-to-well passages involve very collective motions and such systems are excellent structure-seekers. They find their way to well-ordered, highly selective structures under almost all circumstances. These characteristics generalize to describe the potential surfaces and folding behavior of polypeptides and proteins. The forces are effective long-range forces due to the polymer chain. Staircase topographies emerge both from direct sampling of potential surfaces and from the inversion of the kinetics generated by a much more aaabstract topological model, from which folding pathways can be inferred. Received 4 December 2000     

Folding of lattice protein chains with modified Gō potential

We propose a modified Gō model in which the pairwise interaction energies vary as local environment changes. The stability difference between the surface and the core is also well considered in this model. Thermodynamic and kinetic studies suggest that this model has improved folding cooperativity and foldability in contrast with the Gō model. The free energy landscape of this model has broad barriers and narrow denatured states, which is consistent with that of the two-state folding proteins and is lacked for the Gō model. The role of non-native interactions in protein folding is also studied. We find that appropriate consideration of the contribution of the non-native interactions may increase the folding rate around the transition temperature. Our results show that conformation-dependent interaction between the residues is a realistic representation of potential functions in protein folding. Received 10 April 2002 / Received in final form 20 August 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: wangwei@nju.edu.cn     

Topological and geometrical entanglement in a model of circular DNA undergoing denaturation

The linking number (topological entanglement) and the writhe (geometrical entanglement) of a model of circular double stranded DNA undergoing a thermal denaturation transition are investigated by Monte Carlo simulations. By allowing the linking number to fluctuate freely in equilibrium we see that the linking probability undergoes an abrupt variation (first-order) at the denaturation transition, and stays close to 1 in the whole native phase. The average linking number is almost zero in the denatured phase and grows as the square root of the chain length, N, in the native phase. The writhe of the two strands grows as in both phases. Received 8 May 2002 Published online 13 August 2002     

The osmotic coefficient of rod-like polyelectrolytes: Computer simulation, analytical theory, and experiment

The osmotic coefficient of solutions of rod-like polyelectrolytes is considered by comparing current theoretical treatments and simulations to recent experimental data. The discussion is restricted to the case of monovalent counterions and dilute, salt-free solutions. The classical Poisson-Boltzmann solution of the cell model correctly predicts a strong decrease in the osmotic coefficient, but upon closer look systematically overestimates its value. The contribution of ion-ion-correlations are quantitatively studied by MD simulations and the recently proposed DHHC theory. However, our comparison with experimental data obtained on synthetic, stiff-chain polyelectrolytes shows that correlation effects can only partly explain the discrepancy. A quantitative understanding thus requires theoretical efforts beyond the restricted primitive model of electrolytes. Received 25 July 2000 and Received in final form 4 December 2000     

A simple model of DNA denaturation and mutually avoiding walks statistics

Recently Garel, Monthus and Orland [Europhys. Lett. 55, 132 (2001)] considered a model of DNA denaturation in which excluded volume effects within each strand are neglected, while mutual avoidance is included. Using an approximate scheme they found a first order denaturation. We show that a first order transition for this model follows from exact results for the statistics of two mutually avoiding random walks, whose reunion exponent is c > 2, both in two and three dimensions. Analytical estimates of c due to the interactions with other denaturated loops, as well as numerical calculations, indicate that the transition is even sharper than in models where excluded volume effects are fully incorporated. The probability distribution of distances between homologous base pairs decays as a power law at the transition. Received 8 July 2002 / Received in final form 25 July 2002 Published online 17 September 2002     

A simple atomistic model for the simulation of the gel phase of lipid bilayers

In this paper we present the results of a large-scale numerical investigation of structural properties of a model of cell membrane, simulated as a bilayer of flexible molecules in vacuum. The study was performed by carrying out extensive Molecular Dynamics simulations, in the (NVE) micro-canonical ensemble, of two systems of different sizes ( 2×32 and 2×256 molecules), over a fairly large set of temperatures and densities, using parallel platforms and more standard serial computers. Depending on the dimension of the system, the dynamics was followed for physical times that go from few hundred picoseconds for the largest system to 5-10 nanoseconds for the smallest one. We find that the bilayer remains stable even in the absence of water and neglecting Coulomb interactions in the whole range of temperatures and densities we have investigated. The extension of the region of physical parameters that we have explored has allowed us to study significant points in the phase diagram of the bilayer and to expose marked structural changes as density and temperature are varied, which are interpreted as the system passing from a crystal to a gel phase. Received 6 July 2000 and Received in final form 28 December 2000     

solitons in quantum Hall systems

We present here an elementary pedagogical introduction to CP_N solitons in quantum Hall systems. We begin with a brief introduction to both CP_N models and to quantum Hall (QH) physics. We then focus on spin and layer-spin degrees of freedom in QH systems and point out that these are in fact CP_N fields for N = 1 and N = 3. Excitations in these degrees of freedom will be shown to be topologically non-trivial soliton solutions of the corresponding CP_N field equations. We conclude with a brief summary of our own recent work in this area, done with Sankalpa Ghosh. Received 17 November 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: doug0700@mail.jnu.ac.in     

Dynamical effects of a one-dimensional multibarrier potential of finite range

We discuss the properties of a large number N of one-dimensional (bounded) locally periodic potential barriers in a finite interval. We show that the transmission coefficient, the scattering cross section σ, and the resonances of σ depend sensitively upon the ratio of the total spacing to the total barrier width. We also show that a time dependent wave packet passing through the system of potential barriers rapidly spreads and deforms, a criterion suggested by Zaslavsky for chaotic behaviour. Computing the spectrum by imposing (large) periodic boundary conditions we find a Wigner type distribution. We investigate also the S-matrix poles; many resonances occur for certain values of the relative spacing between the barriers in the potential. Received 1st August 2001 and Received in final form 18 November 2001     

Shapes of nearly cylindrical, axisymmetric bilayer membranes

Shapes of nearly cylindrical sections of axisymmetric phospholipid membranes are studied theoretically. Describing the shape of such sections by their deviation from a reference cylinder, the well-established shape equation for axisymmetric bilayer membranes is expanded in terms of this deviation, and it is then solved analytically. The phase diagram shows the resulting stationary shapes as functions of system parameters and external conditions, i.e., the pressure difference across the membrane, the membrane tension, the difference between the tensions of the two monolayers, and the axial force acting on the vesicle. The accuracy of the approximate analytical solution is demonstrated by comparison with numerical results. The obtained analytical solution allows to extend the analysis to include shapes where numerical methods have failed. Received 27 September 2000 and Received in final form 26 March 2001