Phase Diagram of Random Heteropolymers (original) (raw)
Related papers
Glassy phases in random heteropolymers with correlated sequences
The Journal of Chemical Physics, 2004
We develop a new analytic approach for the study of lattice heteropolymers, and apply it to copolymers with correlated Markovian sequences. According to our analysis, heteropolymers present three different dense phases depending upon the temperature, the nature of the monomer interactions, and the sequence correlations: (i) a liquid phase, (ii) a "soft glass" phase, and (iii) a "frozen glass" phase. The presence of the new intermediate "soft glass" phase is predicted for instance in the case of polyampholytes with sequences that favor the alternation of monomers.
Freezing of compact random heteropolymers with correlated sequence fluctuations
1998
Random heteropolymers (RHPs) with uncorrelated sequence fluctuations on the segmental scale can undergo a transition wherein, below a certain temperature, the thermodynamics is determined by a few dominant conformations. We study this “freezing” transition for RHPs with correlated sequence fluctuations. Specifically, we apply our theory to the case where the correlations decay with a single correlation length; a pragmatically realizable example is provided by random block copolymers.
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...
Is Heteropolymer Freezing Well Described by the Random Energy Model?
Physical Review Letters, 1996
It is widely held that the Random Energy Model (REM) describes the freezing transition of a variety of types of heteropolymers. We demonstrate that the hallmark property of REM, statistical independence of the energies of states over disorder, is violated in different ways for models commonly employed in heteropolymer freezing studies. The implications for proteins are also 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.
Freezing and folding behavior in simple off-lattice heteropolymers
The Journal of Chemical Physics, 2004
We have performed parallel tempering Monte Carlo simulations using a simple continuum heteropolymer model for proteins. All ten heteropolymer sequences which we have studied have shown first-order transitions at low temperature to ordered states dominated by single chain conformations. These results are in contrast with the theoretical predictions of the random energy model for heteropolymers, from which we would expect continuous transitions to glassy behavior at low temperatures.
Heteropolymer freezing and design: towards physical models of protein folding
2000
Protein folding has become one of the most actively studied problems in modern molecular biophysics. Approaches to the problem combine ideas from the physics of disordered systems, polymer physics, and molecular biology. Much can be learned from the statistical properties of model heteropolymers, the chain molecules having different monomers in irregular sequences.
Polymers
Structural relaxation in polymers occurs at temperatures in the glass transition range and below. At these temperatures, crystallization is controlled by diffusion and nucleation. A sequential occurrence of structural relaxation, nucleation, and crystallization was observed for several homopolymers during annealing in the range of the glass transition. It is known from the literature that all of these processes are strongly influenced by geometrical confinements. The focus of our work is copolymers, in which the confinements are caused by the random sequence of monomer units in the polymer chain. We characterize the influence of these confinements on structure formation and relaxation in the vicinity of the glass transition. The measurements were performed with a hydrogenated nitrile-butadiene copolymer (HNBR). The kinetics of the structural relaxation and the crystallization was measured using fast differential scanning calorimetry (FDSC). This technique was selected because of the...
Statistical mechanics of heteropolymer folding
Physica A: Statistical Mechanics and its Applications, 1992
We investigate by Monte Carlo simulation the thermodynamic behavior of a linear heteropolymer in which the interaction between different monomers contains a quenched random component. We show the existence, along with the usual coil and globule ones, of a new phase, the folded phase, characterized by long relaxation times and by the existence of few stable states.
Glassy correlations and microstructures in randomly cross-linked homopolymer blends
The Journal of Chemical Physics, 2006
We consider a microscopic model of a polymer blend that is prone to phase separation. Permanent crosslinks are introduced between randomly chosen pairs of monomers, drawn from the Deam-Edwards distribution. Thereby, not only density but also concentration fluctuations of the melt are quenched-in in the gel state, which emerges upon sufficient crosslinking. We derive a Landau expansion in terms of the order parameters for gelation and phase separation, and analyze it on the mean-field level, including Gaussian fluctuations. The mixed gel is characterized by thermal as well as time-persistent (glassy) concentration fluctuations. Whereas the former are independent of the preparation state, the latter reflect the concentration fluctuations at the instant of crosslinking, provided the mesh size is smaller than the correlation length of phase separation. The mixed gel becomes unstable to microphase separation upon lowering the temperature in the gel phase. Whereas the length scale of microphase separation is given by the mesh size, at least close to the transition, the emergent microstructure depends on the composition and compressibility of the melt. Hexagonal structures, as well as lamellae or random structures with a unique wavelength, can be energetically favorable.