Tarik Çelik

A PERCOLATION APPROACH TO STRONGLY INTERACTING MATTER

Abstract Using percolation theory to determine transition points, we show that strongly interacting bulk systems exhibit hadronic matter behaviour for densities 0.48 n 0 ⩽ n ⩽ 14.0 n 0 and quark matter behavior for n ⩾ 3.84 n 0 , where n 0 = 0.17 fm −3 is nuclear density. For 3.84 n 0 ⩽ n ⩽ 14.0 n 0 , we find a coexistence region of the two phases.

Multicanonical procedure for continuum peptide models

The multicanonical (Muca) Monte Carlo method enables simulating a system over a wide range of temperatures and thus has become an efficient tool for studying spin glasses, first‐order phase transitions, the helix–coil transition of polypeptides, and protein folding. However, implementation of the method requires calculating the multicanonical weights by an iterative procedure that is not straightforward and is a stumbling block for newcomers. A recursive procedure that takes into account the statistical errors of all previous iterations and thus enables an automatic calculation of the weights without the need for human intervention after each iteration has been proposed. This procedure, which has already been tested successfully for lattice systems, is extended here to continuum models of peptides and proteins. The method is examined in detail and tested for models of the pentapeptide Leu‐enkephalin (Tyr‐Gly‐Gly‐Phe‐Leu) described by the potential energy function ECEPP. Because of the great interest in the structural mapping of the low‐energy region of biomolecules, the energy of structures selected from the Muca trajectory is minimized. The extent of conformational coverage provided by the method is examined and found to be very satisfactory.

Ground-state properties of the three-dimensional Ising spin glass.

We study zero-temperature properties of the three-dimensional Edwards-Anderson Ising spin glass on finite lattices up to size 12[sup 3]. Using multicanonical sampling we generate large numbers of ground-state configurations in thermal equilibrium. Finite-size scaling fits of the data are carried out for two hypothetical scenarios: Parisi mean-field theory versus a droplet scaling ansatz. With a zero-temperature scaling exponent [ital y]=0.72[plus minus]0.12 the data are well described by the droplet scaling ansatz. Alternatively, a description in terms of the Parisi mean-field behavior is still possible. The two scenarios give significantly different predictions on lattices of size [ge]12[sup 3].

Efficiency of the multicanonical simulation method as applied to peptides of increasing size: The heptapeptide deltorphin

The advantage of the multicanonical (MUCA) simulation method of Berg and coworkers over the conventional Metropolis method is in its ability to move a system effectively across energy barriers thereby providing results for a wide range of temperatures. However, a MUCA simulation is based on weights (related to the density of states) that should be determined prior to a production run and their calculation is not straightforward. To overcome this difficulty a procedure has been developed by Berg that calculates the MUCA weights automatically. In a previous article (Yaşar et al. J Comput Chem 2000, 14, 1251–1261) we extended this procedure to continuous systems and applied it successfully to the small pentapeptide Leu‐enkephalin. To investigate the performance of the automated MUCA procedure for larger peptides, we apply it here to deltorphin, a linear heptapeptide with bulky side chains (H‐Tyr1‐D‐Met2‐Phe3‐His4‐Leu5‐Met6‐Asp7‐NH2). As for Leu‐enkephalin, deltorphin is modeled in vacuum by the potential energy function ECEPP. MUCA is found to perform well. A weak second peak is seen for the specific heat, which is given a special attention. By minimizing the energy of structures along the trajectory it is found that MUCA provides a good conformational coverage of the low energy region of the molecule. These latter results are compared with conformational coverage obtained by the Monte Carlo minimization method of Li and Scheraga.

STUDY OF CLUSTER FLUCTUATIONS IN THE TWO-DIMENSIONAL Q-STATE POTTS MODEL

The two-dimensional Potts Model with 2 to 10 states is studied using a cluster algorithm to calculate fluctuations in cluster size as well as commonly used quantities like equilibrium averages and the histograms for energy and the order parameter. Results provide information about the variation of cluster sizes depending on the temperature and the number of states. They also give evidence for first-order transition when energy and the order parameter related measurables are inconclusive on small size lattices.

CLUSTER DISTRIBUTIONS IN TWO-DIMENSIONAL Q-STATE POTTS MODEL

Abstract Two-dimensional Potts model with q = 2–10 states is studied using a cluster algorithm to investigate the distributions of cluster sizes. Results concerning the distribution of clusters depending on the temperature and the number of states give supporting evidence for the order of the transition when energy and the order parameter related measurables are inconclusive on small size lattices.

TWO-DIMENSIONAL SEVEN-STATE POTTS MODEL UNDER EXTERNAL MAGNETIC FIELD

The two-dimensional Potts model with seven states under external field is studied using a cluster algorithm. Cluster size distribution and the fluctuations in the average cluster size provide helpful information on the order of phase transitions.

Structural properties of small semiconductor-binding synthetic peptides

We have performed exhaustive multicanonical Monte Carlo simulations of three 12-residue synthetic peptides in order to investigate the thermodynamic and structural properties as well as the characteristic helix-coil transitions. In these studies, we employ a realistic model where the interactions between all atoms are taken into account. Effects of solvation are also simulated by using an implicit-solvent model.

Multicanonical simulations of some peptides

A brief discussion of the multicanonical simulation method is given and the results of our simulations of the peptides Leu-enkephalin and deltorphin (in vacuum) are presented. For Leu-enkephalin the determination of the a priori unknown multicanonical weight factors by a recursion is demonstrated, a comparison to the canonical simulations at fixed temperature is done and the effectiveness of the multicanonical simulation method is discussed. Ramachandran plots are shown for deltorphin and interpreted in favor of a funnel kind of picture.

MULTICANONICAL SIMULATIONS OF FIVE TETRAPEPTIDE SEQUENCES IN THE CENTRAL DOMAIN OF HMW GLUTENIN

The application of the multicanonical simulation method to small proteins and peptides seems to be feasible and should be undertaken. In this work, the three-dimensional structures of five common tetrapeptide sequences (QPGQ, QSGQ, YPTS, SPQQ and QPGY, in one letter code) in the repetitive central domain of HMW glutenin subunits are investigated by using the multicanonical simulation procedure. Ramachandran plots were prepared and analyzed to predict the relative occurrence probabilities of β-turn and γ-turn structures and helical states. Structural predictions of the five tetrapeptide sequences indicated the presence of high level of β-turns and considerable level of γ-turns. It was also possible to distinguish different type of turns and their occurrence probabilities.