Nonextensive Statistical Mechanics Application to Vibrational Dynamics of Protein Folding

The vibrational dynamics of protein folding is analyzed in the framework of Tsallis statistics. We employ exact expressions for classical harmonic oscillators by considering the unnormalized constraints. As q→1, we show that these approximations agree with the result of Gaussian network model.     

Quadratic transformations of the sixth Painlevé equation with application to algebraic solutions

In 1991, one of the authors showed the existence of quadratic transformations between the Painlevé VI equations with local monodromy differences (1/2, a, b, ±1/2) and (a, a, b, b). In the present paper we give concise forms of these transformations. They are related to the quadratic transformations obtained by Manin and Ramani–Grammaticos–Tamizhmani via Okamoto transformations. To avoid cumbersome expressions with differentiation, we use contiguous relations instead of the Okamoto transformations. The 1991 transformation is particularly important as it can be realized as a quadratic‐pull back transformation of isomonodromic Fuchsian equations. The new formulas are illustrated by derivation of explicit expressions for several complicated algebraic Painlevé VI functions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

遗传算法在构象搜寻中的应用

遗传算法是一种模仿自然进化进程的新颖的启发式优化方法。通过它，人们可以在计算机上对所需的各种问题实施进化操作，最终产生理想的结果。遗传算法现已被广泛于计算机辅助设计、工程设计、系统模拟等领域并取得了极大的成功。本文拟对遗传算法在对大、中、小分子的构象搜寻中的应用作一较全面的综述。     

Relative stability of major types of beta-turns as a function of amino acid composition: a study based on Ab initio energetic and natural abundance data

Folding properties of small globular proteins are determined by their amino acid sequence (primary structure). This holds both for local (secondary structure) and for global conformational features of linear polypeptides and proteins composed from natural amino acid derivatives. It thus provides the rational basis of structure prediction algorithms. The shortest secondary structure element, the beta-turn, most typically adopts either a type I or a type II form, depending on the amino acid composition. Herein we investigate the sequence-dependent folding stability of both major types of beta-turns using simple dipeptide models (-Xxx-Yyy-). Gas-phase ab initio properties of 16 carefully selected and suitably protected dipeptide models (for example Val-Ser, Ala-Gly, Ser-Ser) were studied. For each backbone fold most probable side-chain conformers were considered. Fully optimized 321G RHF molecular structures were employed in medium level [B3LYP/6-311++G(d,p)//RHF/3-21G] energy calculations to estimate relative populations of the different backbone conformers. Our results show that the preference for beta-turn forms as calculated by quantum mechanics and observed in Xray determined proteins correlates significantly.     

Protein fold recognition

Summary An important, yet seemingly unattainable, goal in structural molecular biology is to be able to predict the native three-dimensional structure of a protein entirely from its amino acid sequence. Prediction methods based on rigorous energy calculations have not yet been successful, and best results have been obtained from homology modelling and statistical secondary structure prediction. Homology modelling is limited to cases where significant sequence similarity is shared between a protein of known structure and the unknown. Secondary structure prediction methods are not only unreliable, but also do not offer any obvious route to the full tertiary structure. Recently, methods have been developed whereby entire protein folds are recognized from sequence, even where little or no sequence similarity is shared between the proteins under consideration. In this paper we review the current methods, including our own, and in particular offer a historical background to their development. In addition, we also discuss the future of these methods and outline the developments under investigation in our laboratory.     

Fast folding and comparison of RNA secondary structures

Summary Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions and base pairing probabilities.An efficient heuristic for the inverse folding problem of RNA is introduced. In addition we present compact and efficient programs for the comparison of RNA secondary structures based on tree editing and alignment.All computer codes are written in ANSI C. They include implementations of modified algorithms on parallel computers with distributed memory. Performance analysis carried out on an Intel Hypercube shows that parallel computing becomes gradually more and more efficient the longer the sequences are.

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Schnelle Faltung und Vergleich von Sekundärstrukturen von RNA

Zusammenfassung Die im Vienna RNA package enthaltenen Computer Programme für die Berechnung und den Vergleich von RNA Sekundärstrukturen werden präsentiert. Ihren Kern bilden Algorithmen zur Vorhersage von Strukturen minimaler Energie sowie zur Berechnung von Zustandssumme und Basenpaarungswahrscheinlichkeiten mittels dynamischer Programmierung.Ein effizienter heuristischer Algorithmus für das inverse Faltungsproblem wird vorgestellt. Darüberhinaus präsentieren wir kompakte und effiziente Programme zum Vergleich von RNA Sekundärstrukturen durch Baum-Editierung und Alignierung.Alle Programme sind in ANSI C geschrieben, darunter auch eine Implementation des Faltungs-algorithmus für Parallelrechner mit verteiltem Speicher. Wie Tests auf einem Intel Hypercube zeigen, wird das Parallelrechnen umso effizienter je länger die Sequenzen sind.

     

Positivity of entropy production in nonequilibrium statistical mechanics

We analyze different mechanisms of entropy production in statistical mechanics, and propose formulas for the entropy production ratee() in a state . When is steady state describing the long term behavior of a system we show thate()0, and sometimes we can provee()>0.     

The application of the genetic algorithm to the minimization of potential energy functions

We adapted the genetic algorithm to minimize the AMBER potential energy function. We describe specific recombination and mutation operators for this task. Next we use our algorithm to locate low energy conformation of three polypeptides (AGAGAGAGA, A9, and [Met]-enkephalin) which are probably the global minimum conformations. Our potential energy minima are –94.71, –98.50, and –48.94 kcal/mol respectively. Next, we applied our algorithm to the 46 amino acid protein crambin and located a non-native conformation which had an AMBER potential energy 150 kcal/mol lower than the native conformation. This is not necessarily the global minimum conformation, but it does illustrate problems with the AMBER potential energy function. We believe this occurred because the AMBER potential energy function does not account for hydration.