Heteropolymer Sequence Design and Preferential Solvation of Hydrophilic Monomers: One More Application of Random Energy Model

In this paper, we study the role of surface of the globule and the role of interactions with the solvent for designed sequence heteropolymers using random energy model (REM). We investigate the ground state energy and surface monomer composition distribution. By comparing the freezing transition in random and designed sequence heteropolymers, we discuss the effects of design. Based on our results, we are able to show under which conditions solvation effect improves the quality of sequence design. Finally, we study sequence space entropy and discuss the number of available sequences as a function of imposed requirements for the design quality

Exact enumeration of Hamiltonian circuits, walks, and chains in two and three dimensions

We present an algorithm for enumerating exactly the number of Hamiltonian chains on regular lattices in low dimensions. By definition, these are sets of k disjoint paths whose union visits each lattice vertex exactly once. The well-known Hamiltonian circuits and walks appear as the special cases k=0 and k=1 respectively. In two dimensions, we enumerate chains on L x L square lattices up to L=12, walks up to L=17, and circuits up to L=20. Some results for three dimensions are also given. Using our data we extract several quantities of physical interest

Highly Designable Protein Structures and Inter Monomer Interactions

By exact computer enumeration and combinatorial methods, we have calculated the designability of proteins in a simple lattice H-P model for the protein folding problem. We show that if the strength of the non-additive part of the interaction potential becomes larger than a critical value, the degree of designability of structures will depend on the parameters of potential. We also show that the existence of a unique ground state is highly sensitive to mutation in certain sites.Comment: 14 pages, Latex file, 3 latex and 6 eps figures are include

A possible mechanism for cold denaturation of proteins at high pressure

We study cold denaturation of proteins at high pressures. Using multicanonical Monte Carlo simulations of a model protein in a water bath, we investigate the effect of water density fluctuations on protein stability. We find that above the pressure where water freezes to the dense ice phase ($\approx2$ kbar), the mechanism for cold denaturation with decreasing temperature is the loss of local low-density water structure. We find our results in agreement with data of bovine pancreatic ribonuclease A.Comment: 4 pages for double column and single space. 3 figures Added references Changed conten

One-dimensional Ising ferromagnet frustrated by long-range interactions at finite temperatures

We consider a one-dimensional lattice of Ising-type variables where the ferromagnetic exchange interaction J between neighboring sites is frustrated by a long-ranged anti-ferromagnetic interaction of strength g between the sites i and j, decaying as |i-j|^-alpha, with alpha>1. For alpha smaller than a certain threshold alpha_0, which is larger than 2 and depends on the ratio J/g, the ground state consists of an ordered sequence of segments with equal length and alternating magnetization. The width of the segments depends on both alpha and the ratio J/g. Our Monte Carlo study shows that the on-site magnetization vanishes at finite temperatures and finds no indication of any phase transition. Yet, the modulation present in the ground state is recovered at finite temperatures in the two-point correlation function, which oscillates in space with a characteristic spatial period: The latter depends on alpha and J/g and decreases smoothly from the ground-state value as the temperature is increased. Such an oscillation of the correlation function is exponentially damped over a characteristic spatial scale, the correlation length, which asymptotically diverges roughly as the inverse of the temperature as T=0 is approached. This suggests that the long-range interaction causes the Ising chain to fall into a universality class consistent with an underlying continuous symmetry. The e^(Delta/T)-temperature dependence of the correlation length and the uniform ferromagnetic ground state, characteristic of the g=0 discrete Ising symmetry, are recovered for alpha > alpha_0.Comment: 12 pages, 7 figure

IFN stimulated gene expression in the liver is a better predictor of treatment response in chronic hepatitis c than the IL28b (IFN lambda 3) genotype

Background: Therapy of chronic hepatitis C (CHC) with pegIFNa/ribavirin achieves sustained virologic response (SVR) in ~55%. Pre-activation of the endogenous interferon system in the liver is associated non-response (NR). Recently, genome-wide association studies described associations of allelic variants near the IL28B (IFNλ3) gene with treatment response and with spontaneous clearance of the virus. We investigated if the IL28B genotype determines the constitutive expression of IFN stimulated genes (ISGs) in the liver of patients with CHC. Methods: We genotyped 93 patients with CHC for 3 IL28B single nucleotide polymorphisms (SNPs, rs12979860, rs8099917, rs12980275), extracted RNA from their liver biopsies and quantified the expression of IL28B and of 8 previously identified classifier genes which discriminate between SVR and NR (IFI44L, RSAD2, ISG15, IFI22, LAMP3, OAS3, LGALS3BP and HTATIP2). Decision tree ensembles in the form of a random forest classifier were used to calculate the relative predictive power of these different variables in a multivariate analysis. Results: The minor IL28B allele (bad risk for treatment response) was significantly associated with increased expression of ISGs, and, unexpectedly, with decreased expression of IL28B. Stratification of the patients into SVR and NR revealed that ISG expression was conditionally independent from the IL28B genotype, i.e. there was an increased expression of ISGs in NR compared to SVR irrespective of the IL28B genotype. The random forest feature score (RFFS) identified IFI27 (RFFS = 2.93), RSAD2 (1.88) and HTATIP2 (1.50) expression and the HCV genotype (1.62) as the strongest predictors of treatment response. ROC curves of the IL28B SNPs showed an AUC of 0.66 with an error rate (ERR) of 0.38. A classifier with the 3 best classifying genes showed an excellent test performance with an AUC of 0.94 and ERR of 0.15. The addition of IL28B genotype information did not improve the predictive power of the 3-gene classifier. Conclusions: IL28B genotype and hepatic ISG expression are conditionally independent predictors of treatment response in CHC. There is no direct link between altered IFNλ3 expression and pre-activation of the endogenous system in the liver. Hepatic ISG expression is by far the better predictor for treatment response than IL28B genotype

Theta-point universality of polyampholytes with screened interactions

By an efficient algorithm we evaluate exactly the disorder-averaged statistics of globally neutral self-avoiding chains with quenched random charge $q_i=\pm 1$ in monomer i and nearest neighbor interactions $\propto q_i q_j$ on square (22 monomers) and cubic (16 monomers) lattices. At the theta transition in 2D, radius of gyration, entropic and crossover exponents are well compatible with the universality class of the corresponding transition of homopolymers. Further strong indication of such class comes from direct comparison with the corresponding annealed problem. In 3D classical exponents are recovered. The percentage of charge sequences leading to folding in a unique ground state approaches zero exponentially with the chain length.Comment: 15 REVTEX pages. 4 eps-figures . 1 tabl

Statistical properties of contact vectors

We study the statistical properties of contact vectors, a construct to characterize a protein's structure. The contact vector of an N-residue protein is a list of N integers n_i, representing the number of residues in contact with residue i. We study analytically (at mean-field level) and numerically the amount of structural information contained in a contact vector. Analytical calculations reveal that a large variance in the contact numbers reduces the degeneracy of the mapping between contact vectors and structures. Exact enumeration for lengths up to N=16 on the three dimensional cubic lattice indicates that the growth rate of number of contact vectors as a function of N is only 3% less than that for contact maps. In particular, for compact structures we present numerical evidence that, practically, each contact vector corresponds to only a handful of structures. We discuss how this information can be used for better structure prediction.Comment: 20 pages, 6 figure

Molecular dynamics simulation of polymer helix formation using rigid-link methods

Molecular dynamics simulations are used to study structure formation in simple model polymer chains that are subject to excluded volume and torsional interactions. The changing conformations exhibited by chains of different lengths under gradual cooling are followed until each reaches a state from which no further change is possible. The interactions are chosen so that the true ground state is a helix, and a high proportion of simulation runs succeed in reaching this state; the fraction that manage to form defect-free helices is a function of both chain length and cooling rate. In order to demonstrate behavior analogous to the formation of protein tertiary structure, additional attractive interactions are introduced into the model, leading to the appearance of aligned, antiparallel helix pairs. The simulations employ a computational approach that deals directly with the internal coordinates in a recursive manner; this representation is able to maintain constant bond lengths and angles without the necessity of treating them as an algebraic constraint problem supplementary to the equations of motion.Comment: 15 pages, 14 figure

Energetic Components of Cooperative Protein Folding

A new lattice protein model with a four-helix bundle ground state is analyzed by a parameter-space Monte Carlo histogram technique to evaluate the effects of an extensive variety of model potentials on folding thermodynamics. Cooperative helical formation and contact energies based on a 5-letter alphabet are found to be insufficient to satisfy calorimetric and other experimental criteria for two-state folding. Such proteinlike behaviors are predicted, however, by models with polypeptide-like local conformational restrictions and environment-dependent hydrogen bonding-like interactions.Comment: 11 pages, 4 postscripts figures, Phys. Rev. Lett. (in press