Handan Arkin

Gyration tensor based analysis of the shapes of polymer chains in an attractive spherical cage

In a recent computational study, we found highly structured conformations for the polymer-attractive sphere model system. Those conformations are of highly ordered spherical shape or form two-dimensional planar, compact to extended, random coil structures. The observed conformations range from desorbed to partially or even completely adsorbed. In order to present their shape characteristics, here we calculate the gyration tensor and related shape descriptors.

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.

Searching low-energy conformations of two elastin sequences

The three-dimensional structures of two common repeat motifs Val1-Pro2-Gly3-Val4-Gly5 and Val1-Gly2-Val3-Pro4-Gly5-Val6-Gly7-Val8-Pro9 of tropoelastin are investigated by using the multicanonical simulation procedure. By minimizing the energy structures along the trajectory the thermodynamically most stable low-energy microstates of the molecule are determined. The structural predictions are in good agreement with X-ray diffraction experiments.

Ground-State Properties of a Polymer Chain in an Attractive Sphere

We analyze the structural formation of a polymer chain inside of an attractive sphere depending on the attraction strength. Our model is composed of a coarse-grained polymer and an attractive sphere potential. Within this frame, multicanonical Monte Carlo simulations are employed to identify the global minimum energies for a polymer chain interacting with the attractive inner wall of the sphere. Different compact structures are found with varying attraction strengths, among which are spherical, three/two, or monolayer. The conformational properties of these structures are presented.

STRUCTURE OF ENERGY LANDSCAPE OF SHORT PEPTIDES

We have simulated, as a showcase, the pentapeptide Met-enkephalin (Tyr-Gly-Gly-Phe-Met) to visualize the energy landscape and to investigate the conformational coverage by the multicanonical method. We obtained a three-dimensional topographic picture of the whole energy landscape by plotting the histogram with respect to energy (temperature) and the order parameter, which gives the degree of resemblance of any created conformation with the global energy minimum.

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.

STUDY OF PHASE CONVERSION IN THREE-DIMENSIONAL q = 3 POTTS MODEL

In order to see the phase conversion taking place in a weak first-order phase transition, we have simulated the q = 3 state Potts model in three dimensions and studied the time evolutions of oriented clusters forming after a rapid temperature quench. Our results indicate that the phase conversion mechanism following a deep temperature quench is spinodal decomposition while a rather shallow quench to temperatures near the phase transition point proceeds through usual nucleation.

STUDY OF PHASE SEPARATION IN A FIRST-ORDER PHASE TRANSITION: NUCLEATION VERSUS SPINODAL DECOMPOSITION

Studies of dynamical properties of first-order phase transition for a scalar field theory indicate that the phase conversion mechanism itself depends on the strength of the first-order transition: if the transition is strongly (weakly) first-order, bubble nucleation (spinodal decomposition) are favored conversion mechanisms, respectively. These distinct scenarios are of phenomenological impact. In order to see which phase conversion mechanism takes place depending on the strength of transition, we have simulated the q=5 state Potts model in two dimensions with an external magnetic field. The transition gets weakened in its first-order as the external field increases. Our results indicate that the phase conversion mechanism changes from nucleation to spinodal decomposition.

Nonextensive Statistical Mechanics Application to Vibrational Dynamics of Protein Folding

The vibrational dynamics of protein folding is analyzed in the framework of Tsallis thermostatistics. The generalized partition functions, internal energies, free energies and temperature factor (or Debye-Waller factor) are calculated. It has also been observed that the temperature factor is dependent on the non-extensive parameter q which behaves like a scale parameter in the harmonic oscillator model. As