The Laguerre polyhedral decomposition: application to protein folds

An extension of the Voronoi tessellation, the Laguerre polyhedral decomposition, is introduced and applied to the analysis of the packing geometry of amino-acids in folded proteins. This method considers an ensemble of points with different weights and therefore it is well suited for a geometrical analysis of a set of objects with a wide size distribution. With this method it is shown that the true volumes occupied by the amino-acids inside a protein is better described than with the standard Voronoi procedure. This method allows defining unambiguously (without cut-off distance) the neighborhood for each amino-acid in a given protein and contact matrices can be established which contain all topological informations on the internal structure. Finally, a statistical analysis of the geometrical characteristics of the polyhedra attached to each amino-acid is done over a collection of 35 proteins. Received 20 November 2002 / Received in final form 26 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: sadoc@lps.u-psud.fr     

Theory of gel point in real polymer solutions

We develop a new theory of gelation which takes into account (i) delay of the gel point and (ii) change of functionality due to ring formation. We show that the problem of finding the gel point in real polymer solutions reduces to the problem of calculating the total ring concentration and the extent of reaction of intermolecular reaction at the gel point. In this paper, we solve a special case of this problem, on the basis of the independence assumption between intermolecular reaction and cyclization which takes into account only (i) the delay of the gel point: making use of the asymptotic equality of the total ring concentration, we acquire an approximate solution for the gel point D_c as a function of the inverse concentration , the relative frequency of cyclization and dimension d. Applying the observed values of in linear polyesters, the theoretical result reproduces well the Wile and the Gordon-Scantlebury observations, showing the existence of a critical dilution beyond which gelation can not occur, and an asymptote . As the classical gel point is approached, the present theory reduces to the linear equation, which makes one-to-one correspondence with the real slope , suggesting the inequality which is just what polymer chemists have quested for so far, with the physical meaning having remained unknown. Receveid: 30 December 1997 / Revised: 28 May 1998 / Accepted: 12 June 1998     

Simple models of proteins with repulsive non-native contacts

The Go model is extended to the case when the non-native contact energies may be either attractive or repulsive. The folding temperature is found to increase with the energy of non-native contacts. The repulsive non-native contact energies may lead to folding at T=0 for some unusual two-dimensional sequences and to reduction in complexity of disconnectivity graphs for local energy minima. Received 10 May 1999 and Received in final form 13 October 1999     

Model of population evolution with and without eugenics

We propose, and solve via Monte-Carlo simulation, a model describing evolution of population subject to harmful mutations. The habitat changes periodically. The evolution of two, initially identical, populations is compared. One without any external ingerence and the second in which we eliminate all individuals which are ill-fitted to the changed environment (eugenics). We show that although in the short run the individuals in the latter are better adapted and live longer, after some more changes of the environment, the populations with eugenics become extinct, while the others live on. Received 8 April 1999     

Recognition games

In this work we propose an evolution model based on the competition between individuals belonging to populations of neural networks, obeying the Hopfield dynamics. The selection rule adopted relies on generalization and natural classification abilities. The results obtained through computer simulation show that these populations self-organize and evolve towards equilibrium states in the region of transition between ordered and disordered phases. Received 28 October 1998 and Received in final form 2 December 1998     

Cooperative diffusion in weakly charged polyelectrolyte gels

A general expression for the cooperative diffusion constant of weakly charged gels is derived as a function of the thermodynamic parameters such as polyelectrolyte concentration, salt concentration, ionic strength, and the degree of crosslinking. In the low concentration range it decreases with the monomer concentration. Received: 30 January 1998 / Revised: 4 May 1998 / Accepted: 6 May 1998     

Characterization of the structure and the size distribution of branched polymers formed by co-polymerization of MMA and EGDMA

Free radical co-polymerization of methyl methacrylate (MMA) and ethyl glycol dimethyl methacrylate (EGDMA) in solution leads to the formation of polydisperse branched PMMA which grows in size until the system gels. The structure and the size distribution of the PMMA aggregates were characterized at infinite dilution using static and dynamic light scattering and size exclusion chromatography (SEC). The reaction extent was measured using SEC and Raman spectroscopy. The results show that the structure and size distribution of PMMA aggregates formed close to the gel point are compatible with those of percolating clusters. The structure factor of semi-dilute solutions of PMMA aggregates is the same as that of dilute solutions at distance scales much smaller than the correlation length of the concentration fluctuations (). However, the cut-off function of the pair correlation function at for semi-dilute solutions is more gradual than the cut-off function at for dilute solutions. Received 11 May 1998 and Received in final form 22 October 1998     

Effect of eugenics on the evolution of populations

We discuss a model of population dynamics under selection pressure from a changing environment. The population, subject to mutations, is composed of diploidal organisms reproducing quasi-sexually (two parents, recombination but no sexes) and with overlapping generations. Two cases are considered - in one we do not influence the dynamics of the population, while in the other we perform eugenics, i.e. we eliminate all individuals which have phenotypes not conforming to the optimal one at the place where the change has been made. We show that eugenics reduces greatly genetic diversity of the population, increases the percentage of homozygotes and therefore leads to a population badly prepared to cope with the next changes of the environment. The present paper is an extension of our previous work (Ref. [9]). Received 16 May 2000     

The Penna model for biological ageing on a lattice: spatial consequences of child-care

We introduce a square lattice into the Penna bit-string model for biological ageing and study the evolution of the spatial distribution of the population considering different strategies of child-care. Two of the strategies are related to the movements of a whole family on the lattice: in one case the mother cannot move if she has any child younger than a given age, and in the other case if she moves, she brings these young children with her. A stronger condition has also been added to the second case, considering that young children die with a higher probability if their mothers die, this probability decreasing with age. We show that a highly non uniform occupation can be obtained when child-care is considered, even for an uniform initial occupation per site. We also compare the standard survival rate of the model with that obtained when the spacial lattice is considered (without any kind of child-care). Received 30 October 1998 and Received in final form 27 November 1998     

New considerations on the role of covalency in ferroelectric niobates and tantalates

We consider the interaction of an homogeneous polyelectrolyte with an obstacle during electrophoretic drift. We explicitly take into account the hydrodynamic interactions generated by this mechanical trapping, and we evaluate their influence on the unhooking process. Important qualitative effects are pointed out in low and moderate field regimes. However, numerical simulations indicate that, in strong field, the existing simpler local force models, which neglect these hydrodynamic interactions, are quantitatively acceptable. Received: 18 March 1998 / Received in final form and accepted: 20 May 1998     

Log-periodic oscillations for biased diffusion of a polymer chain in a porous medium

A coarse-grained off-lattice bead-spring model is used to reveal the complex dynamics of a polymer chain in a quenched porous medium in the presence of an external field B. The behavior of the mean square displacement (MSD) of the center chain bead and that of the center of mass of the chain as a function of time is studied at different values of the barrier concentration C, the field strength B and the chain length N. In a field, important information on the way in which chains move between obstacles and overcome them is gained from the MSD vs. time analysis in the directions parallel and perpendicular to the flow. Instead of a steady approach to uniform drift-like motion at low C, for sufficiently strong field B we observe logarithmic oscillations in the effective exponents describing the time dependence of the MSD along and perpendicular to field. A common nature of this phenomenon with oscillatory behavior, observed earlier for biased diffusion of tracers on random lattices, is suggested. Received 7 August 1998     

Elastic properties of nematoid arrangements formed by amoeboid cells

In culture migrating and interacting amoeboid cells can form nematoid arrangements in analogy to a nematic liquid crystal phase. A nematoid arrangement is formed if the interaction has an apolar symmetry. Different cell types like human melanocytes (= pigment cells of the skin), human fibroblasts (= connective tissue cells), human osteoblasts (= bone cells), human adipocytes (= fat cells) etc., form a nematoid structure. Our hypothesis is that elastic properties of these nematoid structures can be described in analogy to that of classical nematic liquid crystals. The orientational elastic energy is derived and the orientational defects (disclination) of nematoid arrangements are investigated. The existence of half-numbered disclinations shows that the nematoid structure has an apolar symmetry. The density- and order parameter dependence of the orientational elastic constants and their absolute values are estimated. From the defect structure, one finds that the splay elastic constant is smaller than the bend elastic constant (melanocytes). The core of a disclination is either a cell free space or occupied by non oriented cells (isotropic state), by a cell with a different symmetry, or by another cell type. Received 3 May 1999 and Received in final form 29 September 1999     

Quantum-Monte-Carlo simulations of polyethylene

The diffusion Quantum-Monte-Carlo method of solving the Schr?dinger equation is applied to the vibrational ground state of a polyethylene molecule. The results for the ground state energy show good agreement with normal mode analysis. In addition to stretching, bending and torsional interaction van-der-Waals interaction is applied to a single chain showing a decrease of the energy of 5%. The decrease for a polyethylene system of 5 chains with 10 atoms per molecule at the positions of a unit cell is determined to be 4.8% per molecule. Finally first steps towards simulating excited states were performed. Received: 9 February 1998 / Revised: 2 April 1998 / Accepted: 23 April 1998     

In search for the optimal strategy in population dynamics

A unification of recently proposed models describing population dynamics is presented. We study the effect of different factors, like environmental conditions, concentration of individuals in a given area and migration strategies, on population dynamics. Moreover, we show that a population occupying a smaller area is more susceptible to extinction, which is a well known biological fact. We solve the model using Monte Carlo simulations and the mean-field approach. Constructing flow diagrams we find the optimal strategy in population dynamics. Received 10 June 2001 and Received in final form 22 November 2001     

High reproduction rate versus sexual fidelity

We introduce fidelity into the bit-string Penna model for biological ageing and study the advantage of this fidelity when it produces a higher survival probability of the offspring due to paternal care. We attribute a lower reproduction rate to the faithful males but a higher death probability to the offspring of non-faithful males that abandon the pups to mate other females. The fidelity state of the father is transmitted to the male offspring (with or without error). We show that nature may prefer a lower reproduction rate to warrant the survival of the offspring already born. Received 18 February 1999     

Dynamic and static light scattering study of the formation of cross-linked PMMA gels

Free radical co-polymerization of methyl methacrylate (MMA) and ethyl glycol dimethyl metacrylate (EGDMA) was investigated in solution at different molar ratios R = [EGDMA]/[MMA] between 0 and 0.05. Initially mainly linear PMMA was formed with weight average molar mass 7.5 g/mol independent of R. At larger reaction extents branched polymers were formed and the systems gelled. The scattering intensity rose initially with the reaction extent, but reached a plateau value at larger reaction extents. The plateau value increased strongly with R. Dynamic light scattering showed the appearance of a slow relaxation not observed in linear PMMA solutions. The data can be interpreted by assuming that the excess scattering originates from the branching points and relaxes through self diffusion of the branched particles. The results agree with predictions of the percolation model for gelation and Rouse dynamics. Viscosity measurements corroborate this interpretation. Measurements on a progressively diluted sample quenched close to the gel point again showed quantitative agreement with the percolation model for gelation. Received 11 May 1998 and Received in final form 22 October 1998     

A new simulation method for the determination of forces in polymer/colloid systems

We introduce a new simulation method, which we call the contact-distribution method, for the determination of the Helmholtz potential for polymer/colloid systems from lattice Monte-Carlo simulations. This method allows one to obtain forces between finite or semi-infinite objects of any arbitrary shape and dimensions in the presence of polymer chains in solution or physisorbed or chemisorbed at interfaces. We illustrate the application of the method using two examples: (i) the interaction between the tip of an atomic force microscope (AFM) and a single, end-grafted polymer chain and (ii) the interaction between an AFM tip and a polymer brush. Numerical results for the first two cases illustrate how the method can be used to confirm and extend scaling laws for forces and Helmholtz potentials, to examine the effects of the shapes and sizes of the objects and to examine conformational transitions in the polymer chains. Received: 15 May 1998 / Revised: 11 June 1998 / Accepted: 12 June 1998     

Instabilities in population dynamics

Biologists have long known that the smaller the population, the more susceptible it is to extinction from various causes. Biologists define minimum viable population size (MVP), which is the critical population size, below which the population has a very small chance to survive. There are several theoretical models for predicting the probability that a small population will become extinct. But these models either embody unrealistic assumptions or lead to currently unresolved mathematical problems. In other popular models of population dynamics, like the logistic model, MVP does not exist. In this paper we find the existence of such a critical concentration in a simple model of evolution. We solve this model by a mean field theory and show, in one and two dimensions, the existence of the critical adaptation and concentration below which a population dies out. We also show that, like in the logistic model, above the critical value a population reaches its carrying capacity. Moreover, in the two-dimensional case we find - the so common in biological models - periodic solutions and their biffurcations. Received 15 February 2000     

Pattern formation in reaction diffusion systems: a Galerkin model

Reaction diffusion systems are extremely useful for studying pattern formation in biological systems. We carry out a Lorenz like few mode truncation of a reaction diffusion system and show that it not only gives the same qualitative behaviour as the more complicated systems but also indicates of the existence of a Hopf-bifurcation in the turing region. Received 10 May 2000 and Received in final form 14 March 2001