Hybrid Monte Carlo simulation of polymer chains

We develop the hybrid Monte Carlo method for simulations of single off-lattice polymer chains. We discuss implementation and choice of simulation parameters in some detail. The performance of the algorithm is tested on models for homopolymers with short- or long-range self-repulsion, using chains with $16\le N\le 512$ monomers. Without excessive fine tuning, we find that the computational cost grows as $N^{2+z^\prime}$ with $0.64<z^\prime<0.84$. In addition, we report results for the scaling of the end-to-end distance, $r_{1N}\sim N^\nu(\ln N)^{-\alpha}$.Comment: 13 pages, single postscript file, uuencoded form, Lund Preprint LU-TP 93-2

Identification of Amino Acid Sequences with Good Folding Properties in an Off-Lattice Model

Folding properties of a two-dimensional toy protein model containing only two amino-acid types, hydrophobic and hydrophilic, respectively, are analyzed. An efficient Monte Carlo procedure is employed to ensure that the ground states are found. The thermodynamic properties are found to be strongly sequence dependent in contrast to the kinetic ones. Hence, criteria for good folders are defined entirely in terms of thermodynamic fluctuations. With these criteria sequence patterns that fold well are isolated. For 300 chains with 20 randomly chosen binary residues approximately 10% meet these criteria. Also, an analysis is performed by means of statistical and artificial neural network methods from which it is concluded that the folding properties can be predicted to a certain degree given the binary numbers characterizing the sequences.Comment: 15 pages, 8 Postscript figures. Minor change

Monte Carlo Procedure for Protein Design

A new method for sequence optimization in protein models is presented. The approach, which has inherited its basic philosophy from recent work by Deutsch and Kurosky [Phys. Rev. Lett. 76, 323 (1996)] by maximizing conditional probabilities rather than minimizing energy functions, is based upon a novel and very efficient multisequence Monte Carlo scheme. By construction, the method ensures that the designed sequences represent good folders thermodynamically. A bootstrap procedure for the sequence space search is devised making very large chains feasible. The algorithm is successfully explored on the two-dimensional HP model with chain lengths N=16, 18 and 32.Comment: 7 pages LaTeX, 4 Postscript figures; minor change

Monte Carlo Update for Chain Molecules: Biased Gaussian Steps in Torsional Space

We develop a new elementary move for simulations of polymer chains in torsion angle space. The method is flexible and easy to implement. Tentative updates are drawn from a (conformation-dependent) Gaussian distribution that favors approximately local deformations of the chain. The degree of bias is controlled by a parameter b. The method is tested on a reduced model protein with 54 amino acids and the Ramachandran torsion angles as its only degrees of freedom, for different b. Without excessive fine tuning, we find that the effective step size can be increased by a factor of three compared to the unbiased b=0 case. The method may be useful for kinetic studies, too.Comment: 14 pages, 4 figure

Finite-Size Scaling on the Ising Coexistence Line

We study the finite-size scaling of moments of the magnetization in the low-temperature phase of the two-dimensional Ising model.Comment: talk at Lattice '92, 4 pages, Latex, needs espcrc2.sty, figures not included, CERN-TH.6724/9

Mechanical resistance in unstructured proteins

Single-molecule pulling experiments on unstructured proteins linked to neurodegenerative diseases have measured rupture forces comparable to those for stable folded proteins. To investigate the structural mechanisms of this unexpected force resistance, we perform pulling simulations of the amyloid {\beta}-peptide (A{\beta}) and {\alpha}-synuclein ({\alpha}S), starting from simulated conformational ensembles for the free monomers. For both proteins, the simulations yield a set of rupture events that agree well with the experimental data. By analyzing the conformations right before rupture in each event, we find that the mechanically resistant structures share a common architecture, with similarities to the folds adopted by A{\beta} and {\alpha}S in amyloid fibrils. The disease-linked Arctic mutation of A{\beta} is found to increase the occurrence of highly force-resistant structures. Our study suggests that the high rupture forces observed in A{\beta} and {\alpha}S pulling experiments are caused by structures that might have a key role in amyloid formation.Comment: v3: Added correct journal reference plus minor correction

Structure optimization in an off-lattice protein model

We study an off-lattice protein toy model with two species of monomers interacting through modified Lennard-Jones interactions. Low energy configurations are optimized using the pruned-enriched-Rosenbluth method (PERM), hitherto employed to native state searches only for off lattice models. For 2 dimensions we found states with lower energy than previously proposed putative ground states, for all chain lengths $\ge 13$. This indicates that PERM has the potential to produce native states also for more realistic protein models. For $d=3$, where no published ground states exist, we present some putative lowest energy states for future comparison with other methods.Comment: 4 pages, 2 figure

An effective all-atom potential for proteins

We describe and test an implicit solvent all-atom potential for simulations of protein folding and aggregation. The potential is developed through studies of structural and thermodynamic properties of 17 peptides with diverse secondary structure. Results obtained using the final form of the potential are presented for all these peptides. The same model, with unchanged parameters, is furthermore applied to a heterodimeric coiled-coil system, a mixed alpha/beta protein and a three-helix-bundle protein, with very good results. The computational efficiency of the potential makes it possible to investigate the free-energy landscape of these 49--67-residue systems with high statistical accuracy, using only modest computational resources by today's standards