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An analytical expression is derived for the transition path time distribution for a one-dimensional particle crossing of a parabolic barrier. Two cases are analyzed: (i) A non-Markovian process described by a generalized Langevin equation with a power-law memory kernel and (ii) a Markovian process with a noise violating the fluctuation-dissipation theorem, modeling the stochastic dynamics generated by active forces. In the case (i) we show that the anomalous dynamics strongly affecting the short time behavior of the distributions, but this happens only for very rare events not influencing the overall statistics. At long times the decay is always exponential, in disagreement with a recent study suggesting a stretched exponential decay. In the case (ii) the active forces do not substantially modify the short time behavior of the distribution, but lead to an overall decrease of the average transition path time. These findings offer some novel insights, useful for the analysis of experiments of transition path times in (bio)molecular systems., Comment: 13 pages, 5 figures

Biomolecular folding, at least in simple systems, can be described as a two state transition in a free energy landscape with two deep wells separated by a high barrier. Transition paths are the short part of the trajectories that cross the barrier. Average transition path times and, recently, their full probability distribution have been measured for several biomolecular systems, e.g. in the folding of nucleic acids or proteins. Motivated by these experiments, we have calculated the full transition path time distribution for a single stochastic particle crossing a parabolic barrier, focusing on the underdamped regime. Our analysis thus includes inertial terms, which were neglected in previous studies. These terms influence the short time scale dynamics of a stochastic system, and can be of experimental relevance in view of the short duration of transition paths. We derive the full transition path time distribution in the underdamped case and discuss the similarities and differences with the high friction (overdamped) limit., Comment: 16 pages, 5 figures

We present McGenus, an algorithm to predict RNA secondary structures with pseudoknots. The method is based on a classification of RNA structures according to their topological genus. McGenus can treat sequences of up to 1000 bases and performs an advanced stochastic search of their minimum free energy structure allowing for non trivial pseudoknot topologies. Specifically, McGenus employs a multiple Markov chain scheme for minimizing a general scoring function which includes not only free energy contributions for pair stacking, loop penalties, etc. but also a phenomenological penalty for the genus of the pairing graph. The good performance of the stochastic search strategy was successfully validated against TT2NE which uses the same free energy parametrization and performs exhaustive or partially exhaustive structure search, albeit for much shorter sequences (up to 200 bases). Next, the method was applied to other RNA sets, including an extensive tmRNA database, yielding results that are competitive with existing algorithms. Finally, it is shown that McGenus highlights possible limitations in the free energy scoring function. The algorithm is available as a web-server at http://ipht.cea.fr/rna/mcgenus.php ., Comment: 6 pages, 1 figure

The dominant reaction pathway (DRP) is a rigorous framework to microscopically compute the most probable trajectories, in non-equilibrium transitions. In the low-temperature regime, such dominant pathways encode the information about the reaction mechanism and can be used to estimate non-equilibrium averages of arbitrary observables. On the other hand, at sufficiently high temperatures, the stochastic fluctuations around the dominant paths become important and have to be taken into account. In this work, we develop a technique to systematically include the effects of such stochastic fluctuations, to order k_B T. This method is used to compute the probability for a transition to take place through a specific reaction channel and to evaluate the reaction rate.

Using the Dominant Reaction Pathways method, we perform an ab-initio quantum-mechanical simulation of a conformational transition of a peptide chain. The method we propose makes it possible to investigate the out-of-equilibrium dynamics of these systems, without resorting to an empirical representation of the molecular force field. It also allows to study rare transitions involving rearrangements in the electronic structure. By comparing the results of the ab-initio simulation with those obtained employing a standard force field, we discuss its capability to describe the non-equilibrium dynamics of conformational transitions., Comment: 9 pages, 5 figures

We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and long time scales and both Molecular Dynamics (MD) or Monte Carlo (MC) simulations are generally inefficient. Using a field theoretic approach, we perform analytically the average over the short-time stochastic fluctuations. This way, we obtain an effective theory, which generates the same long-time dynamics of the original theory, but has a lower time resolution power. Such an approach is used to develop an improved version of the MC algorithm, which is particularly suitable to investigate the dynamics of rare conformational transitions. In the specific case of molecular systems at room temperature, we show that elementary integration time steps used to simulate the effective theory can be chosen a factor ~100 larger than those used in the original theory. Our results are illustrated and tested on a simple system, characterized by a rugged energy landscape., Comment: 17 pager, 7 figures

This paper is devoted to the development of a theoretical and computational framework to efficiently sample the statistically significant thermally activated reaction pathways, in multi-dimensional systems obeying Langevin dynamics. We show how to obtain the set of most probable reaction pathways and compute the corrections due to quadratic thermal fluctuations around such trajectories. We discuss how to obtain predictions for the evolution of arbitrary observables and how to generate conformations which are representative of the transition state ensemble. We present an illustrative implementation of our method by studying the diffusion of a point particle in a 2-dimensional funneled external potential., Comment: 18 pages, 7 figures. Improvement in the text and in the figures. Version submitted for publication

We formulate a self-consistent field theory for polyelectrolyte brushes in the presence of counterions. We numerically solve the self-consistent field equations and study the monomer density profile, the distribution of counterions, and the total charge distribution. We study the scaling relations for the brush height and compare them to the prediction of other theories. We find a weak dependence of the brush height on the grafting density.We fit the counterion distribution outside the brush by the Gouy-Chapman solution for a virtual charged wall. We calculate the amount of counterions outside the brush and find that it saturates as the charge of the polyelectrolytes increases.

We develop a theoretical approach to the protein folding problem based on out-of-equilibrium stochastic dynamics. Within this framework, the computational difficulties related to the existence of large time scale gaps in the protein folding problem are removed and simulating the entire reaction in atomistic details using existing computers becomes feasible. In addition, this formalism provides a natural framework to investigate the relationships between thermodynamical and kinetic aspects of the folding. For example, it is possible to show that, in order to have a large probability to remain unchanged under Langevin diffusion, the native state has to be characterized by a small conformational entropy. We discuss how to determine the most probable folding pathway, to identify configurations representative of the transition state and to compute the most probable transition time. We perform an illustrative application of these ideas, studying the conformational evolution of alanine di-peptide, within an all-atom model based on the empiric GROMOS96 force field., Comment: 4 pages, 1 figure

The near-native free energy landscape of protein G is investigated through 0.4 microseconds-long atomistic molecular dynamics simulations in explicit solvent. A theoretical and computational framework is used to assess the time-dependence of salient thermodynamical features. While the quasi-harmonic character of the free energy is found to degrade in a few ns, the slow modes display a very mild dependence on the trajectory duration. This property originates from a striking self-similarity of the free energy landscape embodied by the consistency of the principal directions of the local minima, where the system dwells for several ns, and of the virtual jumps connecting them., Comment: revtex, 6 pages, 5 figures

We present a method to investigate the kinetics of protein folding on a long time-scale and the dynamics underlying the formation of secondary and tertiary structures during the entire reaction. The approach is based on the formal analogy between thermal and quantum diffusion: by writing the solution of the Fokker-Planck equation for the time-evolution of a protein in a viscous heat-bath in terms of a path integral, we derive a Hamilton-Jacobi variational principle from which we are able to compute the most probable pathway of folding. The method is applied to the folding of the Villin Headpiece Subdomain, in the framework of a Go-model. We have found that, in this model, the transition occurs through an initial collapsing phase driven by the starting coil configuration and a later rearrangement phase, in which secondary structures are formed and all computed paths display strong similarities. This method is completely general, does not require the prior knowledge of any reaction coordinate and represents an efficient tool to perfom ab-initio simulations of the entire folding process with available computers., Comment: Final version, accepted for publication in Phys. Rev. Lett

We consider the folding of a self-avoiding homopolymer on a lattice, with saturating hydrogen bond interactions. Our goal is to numerically evaluate the statistical distribution of the topological genus of pseudoknotted configurations. The genus has been recently proposed for classifying pseudoknots (and their topological complexity) in the context of RNA folding. We compare our results on the distribution of the genus of pseudoknots, with the theoretical predictions of an existing combinatorial model for an infinitely flexible and stretchable homopolymer. We thus obtain that steric and geometric constraints considerably limit the topological complexity of pseudoknotted configurations, as it occurs for instance in real RNA molecules. We also analyze the scaling properties at large homopolymer length, and the genus distributions above and below the critical temperature between the swollen phase and the compact-globule phase, both in two and three dimensions., Comment: RevTeX 4 pages, 6 figures, minor typos fixed

We enumerate the number of RNA contact structures according to their genus, i.e. the topological character of their pseudoknots. By using a recently proposed matrix model formulation for the RNA folding problem, we obtain exact results for the simple case of an RNA molecule with an infinitely flexible backbone, in which any arbitrary pair of bases is allowed. We analyze the distribution of the genus of pseudoknots as a function of the total number of nucleotides along the phosphate-sugar backbone., Comment: RevTeX, 4 pages, 2 figures

In this paper we consider the problem of RNA folding with pseudoknots. We use a graphical representation in which the secondary structures are described by planar diagrams. Pseudoknots are identified as non-planar diagrams. We analyze the non-planar topologies of RNA structures and propose a classification of RNA pseudoknots according to the minimal genus of the surface on which the RNA structure can be embedded. This classification provides a simple and natural way to tackle the problem of RNA folding prediction in presence of pseudoknots. Based on that approach, we describe a Monte Carlo algorithm for the prediction of pseudoknots in an RNA molecule., Comment: 22 pages, 14 figures

We present a model for the ion distribution near a charged surface, based on the response of the ions to the presence of a single test particle. Near an infinite planar surface this model produces the exact density profile in the limits of weak and strong coupling, which correspond to zero and infinite values of the dimensionless coupling parameter. At intermediate values of the coupling parameter our approach leads to approximate density profiles that agree qualitatively with Monte-Carlo simulation. For large values of the coupling parameter our model predicts a crossover from exponential to algebraic decay at large distance from the charged plate. Based on the test charge approach we argue that the exact density profile is described, in this regime, by a modified mean field equation, which takes into account the interaction of an ion with the ions close to the charged plate., Comment: 19 pages, 12 figures

We further develop the large $ N $ formalism presented by some of us in earlier works in order to recursively calculate the partition function of a singly pseudoknotted RNA. We demonstrate that this calculation takes time proportional to the sixth power of the length of the RNA. The algorithm itself is presented in a self-contained form for the convenience of readers interested in implementing it., Comment: 21 pages, 14 figures

In the framework of the Poland Scheraga model of DNA denaturation, we derive a recursion relation for the partition function of double stranded DNA, allowing for mismatches between the two strands. This relation is studied numerically using standard parameters for the stacking energies and loop entropies. For complementary strands (of length 1000), we find that mismatches are significant only when the cooperativity parameter $\sigma$ is of order one. Since $\sigma \sim O(10^{-5})$ in DNA, entropic gains from mismatches are overwhelmed by the energetic cost of opening a loop: mismatches are therefore irrelevant (and molecular recognition of the strands is perfect). Generating random mutations with probability $p$ on one strand, we find that large values of $\sigma$ are rather tolerant to mutations. For realistic (small) values of $\sigma$, the two strands do not recombine, even for small mutation fractions. Thus, molecular recognition is extremely selective., Comment: 7 pages, uses epl.cls (included), a few typos corrected

We enumerate possible topologies of pseudoknots in single-stranded RNA molecules. We use a steepest-descent approximation in the large N matrix field theory, and a Feynman diagram formalism to describe the resulting pseudoknot structure.

We formulate the RNA folding problem as an $N\times N$ matrix field theory. This matrix formalism allows us to give a systematic classification of the terms in the partition function according to their topological character. The theory is set up in such a way that the limit $N\to \infty$ yields the so-called secondary structure (Hartree theory). Tertiary structure and pseudo-knots are obtained by calculating the $1/N^2$ corrections to the partition function. We propose a generalization of the Hartree recursion relation to generate the tertiary structure., Comment: 29 pages (LaTex), 13 figures (eps). Missing paragraph and figure added

Following Poland and Scheraga, we consider a simplified model for the denaturation transition of DNA. The two strands are modeled as interacting polymer chains. The attractive interactions, which mimic the pairing between the four bases, are reduced to a single short range binding term. Furthermore, base-pair misalignments are forbidden, implying that this binding term exists only for corresponding (same curvilinear abscissae) monomers of the two chains. We take into account the excluded volume repulsion between monomers of the two chains, but neglect intra-chain repulsion. We find that the excluded volume term generates an effective repulsive interaction between the chains, which decays as $1/r^{d-2}$. Due to this long-range repulsion between the chains, the denaturation transition is first order in any dimension, in agreement with previous studies., Comment: 10 pages

Titration of methacrylic acid / ethyl-acrylate copolymers is studied experimentally and theoretically. At low salt concentrations, this polyacid exhibits a plateau in the titration curve below the neutralization point. The plateau has been often attributed to a first-order phase transition associated with polymer conformational changes. We argue that the specific shape of titration curves of hydrophobic polyelectrolytes is due to electrostatics and does not necessarily require a conformation change of the polyelectrolyte chains. We calculate the free energy at the mean-field level and its first-order (one loop) correction using a loop expansion. The latter is dominated by Debye-Huckel--like charge-charge correlations as well as by correlations between dissociation sites along the polymer chain. We show that the one-loop corrections to the free energy lead to titration curves that agree with experiments. In particular, the model explains the decrease of the pH at the plateau when the polymer concentration is increased or when salt is added to the solution., Comment: 13 pages including 7 postscript figures. Submitted to J. Phys. Chem. B

We consider two different problems involving the localization of a single polymer chain: (i) a periodic $AB$ copolymer at a selective fluid-fluid interface, with the upper (resp. lower) fluid attracting $A$ (resp. $B$) monomers (ii) a homopolymer chain attracted to a hard wall (wetting). Self avoidance is neglected in both models, which enables us to study their localization transition in a grand canonical approach. We recover the results obtained in previous studies via transfer matrix methods. Moreover, we calculate in this way the loop length distribution functions in the localized phase. Some finite size effects are also determined and tested numerically., Comment: 27 pages, 3 eps figures. Some misprints corrected

The behavior of electrolyte solutions close to a charged surface is studied theoretically. A modified Poisson-Boltzmann equation which takes into account the volume excluded by the ions in addition to the electrostatic interactions is presented. In a formal lattice gas formalism the modified Poisson-Boltzmann equation can be obtained from a mean-field approximation of the partition function. In an alternative phenomenological approach, the same equation can be derived by including the entropy of the solvent molecules in the free energy. In order to visualize the effect of the steric repulsion, a simple case of a single, highly charged, flat surface is discussed. This situation resembles recent adsorption experiments of large ions onto a charged monolayer. A simple criterion for the importance of the steric effects is expressed in terms of the surface charge density and the size of the ions. It is shown that when these effects are important a saturated layer is formed near the surface. A modified Grahame equation relating the ion concentration at the surface to the surface charge density is obtained., Comment: 18 pages, 7 postscript figures included. Submitted to Electrochimica Acta

A field theory is presented for particles which interact via Coulomb and hard-core potentials. We apply the method to the one-component plasma (OCP) with hard cores, consisting of identical particles of fixed charge and diameter in a neutralizing background, and the symmetric two-component plasma (TCP) with hard cores, consisting of equal numbers of positively and negatively charged particles of identical size. We obtain exactly the first few coefficients of a systematic low-density expansion of the free energy for both models. The OCP coefficients go over to the classical Abe result in the high-charge (or small hard-core diameter) limit. The TCP, on the other hand, exhibits diverging coefficients in the high-charge limit, which is due to the formation of strongly bound ion-pairs., Comment: 8 pages, 6 postscript figures

We consider polymers made of magnetic monomers (Ising or Heisenberg-like) in a good solvent. These polymers are modeled as self-avoiding walks on a cubic lattice, and the ferromagnetic interaction between the spins carried by the monomers is short-ranged in space. At low temperature, these polymers undergo a magnetic induced first order collapse transition, that we study at the mean field level. Contrasting with an ordinary $\Theta$ point, there is a strong jump in the polymer density, as well as in its magnetization. In the presence of a magnetic field, the collapse temperature increases, while the discontinuities decrease. Beyond a multicritical point, the transition becomes second order and $\Theta$-like. Monte Carlo simulations for the Ising case are in qualitative agreement with these results., Comment: 29 pages, 15 eps figures (one color figure). Submitted for publication to Eur.Phys.J. B

We consider a model of two (fully) compact polymer chains, coupled through an attractive interaction. These compact chains are represented by Hamiltonian paths (HP), and the coupling favors the existence of common bonds between the chains. Using a ($n=0$ component) spin representation for these paths, we show the existence of a phase transition for strong coupling (i.e. at low temperature) towards a ``frozen'' phase where one chain is completely adsorbed onto the other. By performing a Legendre transform, we obtain the probability distribution of overlaps. The fraction of common bonds between two HP, i.e. their overlap $q$, has both lower ($q_m$) and upper ($q_M$) bounds. This means in particuliar that two HP with overlap greater than $q_M$ coincide. These results may be of interest in (bio)polymers and in optimization problems., Comment: 13 pages, 2 figures

The behavior of polyelectrolytes and polyampholytes in semi-dilute solutions is investigated theoretically. Various statistical charge distributions along the polyelectrolyte chains are considered: smeared, annealed, permuted and quenched. Annealed polyampholytes are also considered. Path integral formulation was used to derive mean field free energies for the different models. Self-consistent field equation is obtained for the polymer order parameter and a Poisson-Boltzmann like equation for the electrostatic potential. The random phase approximation is used to calculate the monomer-monomer structure factor S(q) for the different statistical charge distribution models. We show that in the annealed model, fluctuations of the the monomer charges contribute to the electrostatic screening in addition to the free ions in the solution. The strength of this screening depends on the variance of the monomer charge distribution and is especially important for polyampholytes in bad solvent conditions where the mesophase separation is enhanced. The ratio between the variance and the net average charge determines whether polyampholytes behave as polyelectrolytes or as neutral chains., Comment: 18 pages, 5 figures, submitted to Eur. Phys. J. B

The behavior of polyelectrolytes between charged surfaces immersed in semi-dilute solutions is investigated theoretically. A continuum mean field approach is used for calculating numerically concentration profiles between two electrodes held at a constant potential. A generalized contact theorem relates the inter-surface forces to the concentration profiles. The numerical results show that over-compensation of the surface charges by adsorbing polyelectrolytes can lead to effective attraction between equally charged surfaces. Simple scaling arguments enable us to characterize qualitatively the inter-surface interactions as function of the fraction of charged monomers p and the salt concentration c_b. In the low salt regime we find strong repulsion at short distances, where the polymers are depleted from the inter-surface gap, followed by strong attraction when the two adsorbed layers overlap. The magnitude of this attraction scales as p^{1/2} and its dominant length scale is proportional to a/p^{1/2}, where a is the monomer size. At larger distances the two adsorbing surfaces interact via a weak electrostatic repulsion. For strong polyelectrolytes at high salt concentration the polymer contribution to attraction at short distances scales as p/c_b^{1/2} and the length scale is proportional to kappa*a^2/p, where kappa^{-1} is the Debye-Huckel screening length. For weak polyelectrolytes at high salt concentration the interaction is repulsive for all surface separations and decays exponentially with a decay length equal to kappa^{-1}. The effect of irreversible adsorption is discussed as well and it is shown that inter-surface attraction can be obtained in this case as well., Comment: 35 pages, 16 figures, submitted to J. Phys. Chem. B

We investigate theoretically the behavior of proteins as well as other large macromolecules which are incorporated into amphiphilic monolayers at the air-water interface. We assume the monolayer to be in the coexistence region of the ``main'' transition, where domains of the liquid condensed phase coexist with the liquid expanded background. Using a simple mean-field free energy accounting for the interactions between proteins and amphiphilic molecules, we obtain the spatial protein distribution with the following characteristics. When the proteins preferentially interact with either the liquid condensed or liquid expanded domains, they will be dissolved in the respective phase. When the proteins are energetically rather indifferent to the density of the amphiphiles, they will be localized at the line boundary between the (two-dimensional) liquid expanded and condensed phases. In between these two limiting cases, a delocalization transition of the proteins takes place. This transition is accessible by changing the temperature or the amount of incorporated protein. These findings are in agreement with recent fluorescence microscopy experiments. Our results also apply to lipid multicomponent membranes showing coexistence of distinct fluid phases., Comment: 19 pages, 7 figures, Latex2.09 only

The adsorption of large ions from solution to a charged surface is investigated theoretically. A generalized Poisson--Boltzmann equation, which takes into account the finite size of the ions is presented. We obtain analytical expressions for the electrostatic potential and ion concentrations at the surface, leading to a modified Grahame equation. At high surface charge densities the ionic concentration saturates to its maximum value. Our results are in agreement with recent experiments., Comment: 4 pages, 2 figures

An exact calculation of the phase diagram for a loop gas model on the brickwork lattice is presented. The model includes a bending energy. In the dense limit, where all the lattice sites are occupied, a phase transition occuring at an asymmetric Lifshitz tricritical point is observed as the temperature associated with the bending energy is varied. Various critical exponents are calculated. At lower densities, two lines of transitions (in the Ising universality class) are observed, terminated by a tricritical point, where there is a change in the modulation of the correlation function. To each tricritical point an associated disorder line is found., Comment: 19 pages, 6 figures. to appear in J. Phys. A : Math. & Gen

We present a statistical mechanics approach to the protein folding problem. We first review some of the basic properties of proteins, and introduce some physical models to describe their thermodynamics. These models rely on a random heteropolymeric description of these non random biomolecules. Various kinds of randomness are investigated, and the connection with disordered systems is discussed. We conclude by a brief study of the dynamics of proteins., Comment: 57 pages, 7 figures. Uses lprocl.sty (included). To appear in " Spin glasses and random fields ", A.P. Young (ed.), World Scientific

We study a homopolymer model of a protein chain, where each monomer carries a dipole moment. To mimic the geometry of the peptidic bond, these dipoles are constrained to be locally perpendicular to the chain. The tensorial character of the dipolar interaction leads naturally to a (tensorial) liquid crystal-like order parameter. For non chiral chains, a mean field study of this model shows that a classical $\theta$ collapse transition occurs first; at lower temperature, nematic order sets in. For chiral chains, an anisotropic (tensorial) collapse transition may occur before the $\theta$ temperature is reached: the ordered phase can be described as a ``compact phase of secondary structures'', and possesses great similarities with the liquid crystal blue phases., Comment: 17 pages, one ps figure; accepted for publication in J. de Phys (I)

Adsorption of charged polymers (polyelectrolytes) from a semi-dilute solution to a charged surface is investigated theoretically. We obtain simple scaling laws for (i) the amount of polymer adsorbed to the surface, Gamma, and (ii) the width of the adsorbed layer D, as function of the fractional charge per monomer p and the salt concentration c_b. For strongly charged polyelectrolytes (p<1) in a low-salt solution, both Gamma and D scale as p^{-1/2}. In salt-rich solutions D~c_b^{1/2}/p whereas the scaling behavior of Gamma depends on the strength of the polymer charge. For weak polyelectrolytes (p<<1) we find that Gamma~p/c_b^{1/2} while for strong polyelectrolytes Gamma~c_b^{1/2}/p. Our results are in good agreement with adsorption experiments and with numerical solutions of mean-field equations., Comment: 13 pages, RevTex + epsf, 9 postscript figures; minor corrections

We study the dynamics of a polymer when it is quenched from a $\theta$ solvent into a good or bad solvent by means of a Langevin equation. The variation of the radius of gyration is studied as a function of time. For the first stage of collapse or swelling, the characteristic time-scale is found to be independent of the number of monomers. Other scaling laws are derived for the diffusion regime at larger times. Although the present model is solved only for homopolymers and doesn't include hydrodynamic interactions, these results may be a first step towards the understanding of the early stages of protein folding.

A disorder-dependent Gaussian variational approach is applied to the problem of a $d$ dimensional polymer chain in a random medium (or potential). Two classes of variational solutions are obtained. For $d<2$, these two classes may be interpreted as domain and domain wall. The critical exponent $\nu$ describing the polymer width is $\nu={1\over (4-d)}$ (domain solution) or $\nu={3\over (d+4)}$ (domain wall solution). The domain wall solution is equivalent to the (full) replica symmetry breaking variational result. For $d>2$, we find $\nu={1\over 2}$. No evidence of a phase transition is found for $2< d< 4$: one of the variational solutions suggests that the polymer chain breaks into Imry-Ma segments, whose probability distribution is calculated. For $d>4$, the other variational solution undergoes a phase transition, which has some similarity with B. Derrida's random energy models., Comment: Plain latex file

We consider a lattice model of a semiflexible homopolymer chain in a bad solvent. Beside the temperature $T$, this model is described by (i) a curvature energy $\varepsilon_h$, representing the stiffness of the chain (ii) a nearest-neighbour attractive energy $\varepsilon_v$, representing the solvent (iii) the monomer density $\rho={N \over \Omega}$, where $N$ and $\Omega$ denote respectively the number of monomers and the number of lattice sites. This model is a simplified view of the protein folding problem, which encompasses the geometrical competition between secondary structures (the curvature term modelling helix formation) and the global compactness (modeled here by the attractive energy), but contains no side chain information..., Comment: 17 pages, plain tex, 2 figures available upon request

A disorder-dependent Gaussian variational approach is applied to the $d$-dimensional ferromagnetic XY model in a random field. The randomness yields a non extensive contribution to the variational free energy, implying a random mass term in correlation functions. The Imry-Ma low temperature result, concerning the existence ($d>4$) or absence ($d < 4$) of long-range order is obtained in a transparent way. The physical picture which emerges below $d=4$ is that of a marginally stable mixture of domains. We also calculate within this variational scheme, disorder dependent correlation functions, as well as the probability distribution of the Imry-Ma domain size., Comment: 14 pages, latex file

The stability of the random field Ising model (RFIM) against spin glass (SG) fluctuations, as investigated by M\'ezard and Young, is naturally expressed via Legendre transforms, stability being then associated with the non-negativeness of eigenvalues of the inverse of a generalized SG susceptibility matrix. It is found that the signal for the occurrence of the SG transition will manifest itself in free-energy {\sl fluctuations\/} only, and not in the free energy itself. Eigenvalues of the inverse SG susceptibility matrix is then approached by the Rayleigh Ritz method which provides an upper bound. Coming from the paramagnetic phase {\sl on the Curie line,\/} one is able to use a virial-like relationship generated by scaling the {\sl single\/} unit length $ (D<6; $ in higher dimension a new length sets in, the inverse momentum cut off). Instability towards a SG phase being probed on pairs of {\sl distinct\/} replicas, it follows that, despite the repulsive coupling of the RFIM the effective pair coupling is {\sl attractive\/} (at least for small values of the parameter $ g\bar \Delta , $ $ g $ the coupling and $ \bar \Delta $ the effective random field fluctuation). As a result, \lq\lq bound states\rq\rq\ associated with replica pairs (negative eigenvalues) provide the instability signature. {\sl Away from the Curie line\/}, the attraction is damped out till the SG transition line is reached and paramagnetism restored. In $ D<6, $ the SG transition always precedes the ferromagnetic one, thus the domain in dimension where standard dimensional reduction would apply (on the Curie line) shrinks to zero., Comment: tex

We study the adsorption of polymer chains on a fluctuating surface. Physical examples are provided by polymer adsorption at the rough interface between two non-miscible liquids, or on a membrane. In a mean-field approach, we find that the self--avoiding chains undergo an adsorption transition, accompanied by a stiffening of the fluctuating surface. In particular, adsorption of polymers on a membrane induces a surface tension and leads to a strong suppression of roughness., Comment: REVTEX, 9 pages, no figures

We study a single statistical amphiphilic copolymer chain AB in a selective solvent (e.g.water). Two situations are considered. In the annealed case, hydrophilic (A) and hydrophobic (B) monomers are at local chemical equilibrium and both the fraction of A monomers and their location along the chain can vary, whereas in the quenched case (which is relevant to proteins), the chemical sequence along the chain is fixed by synthesis. In both cases, the physical behaviour depends on the average hydrophobicity of the polymer chain. For a strongly hydrophobic chain (large fraction of B), we find an ordinary continuous $\theta$ collapse, with a large conformational entropy in the collapsed phase. For a weakly hydrophobic, or a hydrophilic chain, there is an unusual first-order collapse transition. In particular, for the case of Gaussian disorder, this discontinuous transition is driven by a change of sign of the third virial coefficient. The entropy of this collapsed phase is strongly reduced with respect to the $\theta$ collapsed phase. Email contact: orland@amoco.saclay.cea.fr, Comment: Saclay-T94/077 Email: orland@amoco.saclay.cea.fr

The Flory theory for a single polymer chain is derived as the lowest order of a cumulant expansion. In this approach, the full original Flory free energy (including the logarithmic term), is recovered. %This term does not change the wandering exponent $ \nu $ but turns out to %be responsible for the crossover from Brownian $ (d>4) $ to swollen $ %(d\leq4) $ %regime. The prefactors of the elastic and repulsive energy are calculated from the microscopic parameters. The method can be applied to other types of monomer-monomer interactions, and the case of a single chain in a bad solvent is discussed . The method is easily generalized to many chain systems (polymers in solutions), yielding the usual crossovers with chain concentration. Finally, this method is suitable for a systematic expansion around the Flory theory. The corrections to Flory theory consist of extensive terms (proportional to the number $N$ of monomers) and powers of $N^{2-\nu d}$ . These last terms diverge in the thermodynamic limit, but less rapidly than the usual Fixman expansion in $N^{2- d/2}$., Comment: Email contact: orland@amoco.saclay.cea.fr

We study local energy minima of twenty(L-alanine). The minima are generated using high-temperature Molecular Dynamics and Chain-Growth Monte Carlo simulations, with subsequent minimization. We find that the lower-energy configurations are $ \alpha $-helices for a wide range of dielectric constant values $ (\epsilon = 1,10,80), $ and that there is no noticeable difference between the distribution of energy minima in $ \phi \psi $ space for different values of $ \epsilon . $ Ultrametricity tests show that lower-energy $ (\alpha $ -helical) $ \epsilon =1 $ configurations form a set which is ultrametric to a certain degree, providing evidence for the presence of fine structure among those minima. We put forward a heuristic argument for this fine structure. We also find evidence for ultrametricity of a different kind among $ \epsilon =10 $ and $ \epsilon =80 $ energy minima. We analyze the distribution of lengths of $ \alpha $-helical portions among the minimized configurations and find a persistence phenomenon for the $ \epsilon =1 $ ones, in qualitative agreement with previous studies of critical lengths. Email contact: bascle@amoco.saclay.cea.fr, Comment: Saclay-T93/025 Email: bascle@amoco.saclay.cea.fr