Helix vs. Sheet Formation in a Small Peptide

Segments with the amino acid sequence EKAYLRT appear in natural occurring proteins both in $\alpha$-helices and $\beta$-sheets. For this reason, we have use this peptide to study how secondary structure formation in proteins depends on the local environment. Our data rely on multicanonical Monte Carlo simulations where the interactions among all atoms are taken into account. Results in gas phase are compared with that in an implicit solvent. We find that both in gas phase and solvated EKAYLRT forms an $\alpha$-helix when not interacting with other molecules. However, in the vicinity of a $\beta$-strand, the peptide forms a $\beta$-strand. Because of this change in secondary structure our peptide may provide a simple model for the $\alpha \to \beta$ transition that is supposedly related to the outbreak of Prion diseases and similar illnesses.Comment: to appear in Physical Review

Proteinlike behavior of a spin system near the transition between ferromagnet and spin glass

A simple spin system is studied as an analog for proteins. We investigate how the introduction of randomness and frustration into the system effects the designability and stability of ground state configurations. We observe that the spin system exhibits protein-like behavior in the vicinity of the transition between ferromagnet and spin glass. Our results illuminate some guiding principles in protein evolution.Comment: 12 pages, 4 figure

Numerical comparison of two approaches for the study of phase transitions in small systems

We compare two recently proposed methods for the characterization of phase transitions in small systems. The validity and usefulness of these approaches are studied for the case of the q=4 and q=5 Potts model, i.e. systems where a thermodynamic limit and exact results exist. Guided by this analysis we discuss then the helix-coil transition in polyalanine, an example of structural transitions in biological molecules.Comment: 16 pages and 7 figure

Compact phases of polymers with hydrogen bonding

We propose an off-lattice model for a self-avoiding homopolymer chain with two different competing attractive interactions, mimicking the hydrophobic effect and the hydrogen bond formation respectively. By means of Monte Carlo simulations, we are able to trace out the complete phase diagram for different values of the relative strength of the two competing interactions. For strong enough hydrogen bonding, the ground state is a helical conformation, whereas with decreasing hydrogen bonding strength, helices get eventually destabilized at low temperature in favor of more compact conformations resembling $\beta$-sheets appearing in native structures of proteins. For weaker hydrogen bonding helices are not thermodynamically relevant anymore.Comment: 5 pages, 3 figures; revised version published in PR

Monte Carlo Methods for Rough Free Energy Landscapes: Population Annealing and Parallel Tempering

Parallel tempering and population annealing are both effective methods for simulating equilibrium systems with rough free energy landscapes. Parallel tempering, also known as replica exchange Monte Carlo, is a Markov chain Monte Carlo method while population annealing is a sequential Monte Carlo method. Both methods overcome the exponential slowing associated with high free energy barriers. The convergence properties and efficiency of the two methods are compared. For large systems, population annealing initially converges to equilibrium more rapidly than parallel tempering for the same amount of computational work. However, parallel tempering converges exponentially and population annealing inversely in the computational work so that ultimately parallel tempering approaches equilibrium more rapidly than population annealing.Comment: 10 pages, 3 figure

Microcanonical Replica Exchange Molecular Dynamics Simulation of Proteins

We present microcanonical replica exchange molecular dynamics simulations as an alternative to canonical ones. Its advantage is the easily tunable high acceptance rate for replica exchange. We present the theory, comment on its actual implementation, and demonstrate its application for a common test case, the trp-cage protein