Embedding a native state into a random heteropolymer model: the dynamic approach (original) (raw)
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Physical review. E, Statistical, nonlinear, and soft matter physics, 2001
We study the Langevin dynamics of the standard random heteropolymer model by mapping the problem to a supersymmetric field theory using the Martin-Siggia-Rose formalism. The resulting model is solved nonperturbatively employing a Gaussian variational approach. In constructing the solution, we assume that the chain is very long and impose the translational invariance which is expected to be present in the bulk of the globule by averaging over the center of mass coordinate. In this way we derive equations of motion for the correlation and response functions C(t,t') and R(t,t'). The order parameters are extracted from the asymptotic behavior of these functions. We find a dynamical phase diagram with frozen (glassy) and melted (ergodic) phases. In the glassy phase the system fails to reach equilibrium and exhibits aging of the type found in p-spin glasses. Within the approximations used in this study, the random heteropolymer model can be mapped to the problem of a manifold in a...
Phase Diagram of Random Heteropolymers
Physical Review Letters, 2004
We propose a new analytic approach to study the phase diagram of random heteropolymers, based on the cavity method. For copolymers we analyze the nature and phenomenology of the glass transition as a function of sequence correlations. Depending on these correlations, we find that two different scenarios for the glass transition can occur. We show that, beside the much studied possibility of an abrupt freezing transition at low temperature, the system can exhibit, upon cooling, a first transition to a soft glass phase with fully broken replica symmetry and a continuously growing degree of freezing as the temperature is lowered. PACS numbers: 81.05.Lg, 64.70.Pf, 36.20.Ey
Glassy phases in random heteropolymers with correlated sequences
The Journal of Chemical Physics, 2004
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Self-generated disorder: from spin glasses to the glassy homopolymer globule
Journal of Non-Crystalline Solids, 2002
We have investigated the interrelation between spin glasses and structural glasses. Spin glasses in this case are p-spin interaction spin glasses (at p > 2) or Potts glasses which contain quenched disorder, whereas the structural glasses are here exemplified by the homopolymeric globule, which can be viewed as a liquid of connected units on nanoscales. It is argued that the homopolymeric globule problem can be mapped onto a disorder field theoretical model whose effective Hamiltonian resembles the corresponding one for the spin glass model. In this sense the disorder in the globule is selfgenerated (in contrast to spin glasses) and can be related with competing interactions (virial coefficients of different signs) and the chain connectivity. The work is aimed at giving a quantitative description of this analogy. We have investigated in the mean-field (MF) approximation the phase diagram of the homopolymeric globule where the transition line from the liquid to glassy globule is treated in terms of the replica symmetry breaking paradigm. The configurational entropy temperature dependence is also discussed.
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We discuss various aspects of the randomly interacting directed polymers with emphasis on the phases and phase transition. We also discuss the behaviour of overlaps of directed paths in a random medium.
The behavior of a random AB block copolymer with the same fraction of monomers of each type near the critical point has been studied. In the Brazovski approximation it is shown that thermodynamic fluctuations give rise to a lamellar structure whose period is greater than the size of a block. The structure appears as a result of a first-order phase transition. The parameters of this transition are calculated and the region of coexistence of the disordered and lamellar phases is found.
Dynamic Properties of Random Heteropolymer with Correlations in Sequence
The some dynamic properties of a random heteropolymer in the condensed state are studied in the mode coupling approximation. In agreement with recent report a dynamic friction increasing is predicted for the random heteropolymer with power-law correlations in comparison with exponential correlations. In the case of strong power-law correlations the dynamic friction function diverge in the thermodynamic limit. The qualitative explanation is given for the monomer's dynamics slowing down and diverged energetic barrier between the frozen and random coil states. The possible relations with protein's function and evolution are discussed.
Freezing transition of random heteropolymers consisting of an arbitrary set of monomers
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1995
Mean field replica theory is employed to analyze the freezing transition of random heteropolymers comprised of an arbitrary number (q) of types of monomers. Our formalism assumes that interactions are short range and heterogeneity comes only from pairwise interactions, which are defined by an arbitrary q × q matrix. We show that, in general, there exists a freezing transition from a random globule, in which the thermodynamic equilibrium is comprised of an essentially infinite number polymer conformations, to a frozen globule, in which equilibrium ensemble is dominated by one or very few conformations. We also examine some special cases of interaction matrices to analyze the relationship between the freezing transition and the nature of interactions involved.
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Macromolecules, 1995
It is shown that a general model of athermal random copolymers in an equilibrium state is related to an appropriately generalized n-0 spin vector model, with each spin having 2n components. By adjusting various coupling constants in the model, one can control various densities such as bond densities of each type and copolymer density, average copolymer size, average block size, etc. The model is solved in a mean-field approximation to study the complete phase diagram and to calculate the free energy and the entropy and the entropy of mixing of copolymers in an athermal solution.
Hierarchical Random Energy Model of a Spin Glass
Physical Review Letters, 2010
We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a nonmean field model. Through small coupling series expansion and a direct numerical solution of the model, we provide evidence for a spin glass condensation transition similar to the one occurring in the usual mean field Random Energy Model. At variance with mean field, the high temperature branch of the free-energy is non-analytic at the transition point. PACS numbers: 05.10.-a,05.50.+q,75.10.Nr