No abstract

Despite significant progress in recent years, protein structure prediction maintains its status as one of the prime unsolved problems in computational biology. One of the key remaining challenges is an efficient probabilistic exploration of the structural space that correctly reflects the relative conformational stabilities. Here, we present a fully probabilistic, continuous model of local protein structure in atomic detail. The generative model makes efficient conformational sampling possible and provides a framework for the rigorous analysis of local sequence-structure correlations in the native state. Our method represents a significant theoretical and practical improvement over the widely used fragment assembly technique by avoiding the drawbacks associated with a discrete and nonprobabilistic approach.conformational sampling ͉ directional statistics ͉ probabilistic model ͉ TorusDBN ͉ Bayesian network P rotein structure prediction remains one of the greatest challenges in computational biology. The problem itself is easily posed: predict the three-dimensional structure of a protein given its amino acid sequence. Significant progress has been made in the last decade, and, especially, knowledge-based methods are becoming increasingly accurate in predicting structures of small globular proteins (1). In such methods, an explicit treatment of local structure has proven to be an important ingredient. The search through conformational space can be greatly simplified through the restriction of the angular degrees of freedom in the protein backbone by allowing only angles that are known to appear in the native structures of real proteins. In practice, the angular preferences are typically enforced by using a technique called fragment assembly. The idea is to select a set of small structural fragments with strong sequence-structure relationships from the database of solved structures and subsequently assemble these building blocks to form complete structures. Although the idea was originally conceived in crystallography (2), it had a great impact on the protein structureprediction field when it was first introduced a decade ago (3). Today, fragment assembly stands as one of the most important single steps forward in tertiary structure prediction, contributing significantly to the progress we have seen in this field in recent years (4, 5).Despite their success, fragment-assembly approaches generally lack a proper statistical foundation, or equivalently, a consistent way to evaluate their contributions to the global free energy. When a fragment-assembly method is used, structure prediction normally proceeds by a Markov Chain Monte Carlo (MCMC) algorithm, where candidate structures are proposed by the fragment assembler and then accepted or rejected based on an energy function. The theoretical basis of MCMC is the existence of a stationary probability distribution dictating the transition probabilities of the Markov chain. In the context of statistical physics, this stationary distribution is given by the conformational ...

A fundamental problem in bioinformatics is to characterize the secondary structure of a protein, which has traditionally been carried out by examining a scatterplot (Ramachandran plot) of the conformational angles. We examine two natural bivariate von Mises distributions--referred to as Sine and Cosine models--which have five parameters and, for concentrated data, tend to a bivariate normal distribution. These are analyzed and their main properties derived. Conditions on the parameters are established which result in bimodal behavior for the joint density and the marginal distribution, and we note an interesting situation in which the joint density is bimodal but the marginal distributions are unimodal. We carry out comparisons of the two models, and it is seen that the Cosine model may be preferred. Mixture distributions of the Cosine model are fitted to two representative protein datasets using the expectation maximization algorithm, which results in an objective partition of the scatterplot into a number of components. Our results are consistent with empirical observations; new insights are discussed.

The methods are applied to real protein data of conformational angles.

The mechanisms underlying the increase in volume of muscle tissue, and the functional development of muscle fibers from childhood through adolescence to adult age, have been studied. Cross sections of autopsied whole vastus lateralis muscle from 22 previously physically healthy males, 5 to 37 years of age, were prepared enzyme histochemically (myofibrillar ATPase) and examined morphometrically. The data obtained on muscle cross-sectional area, size, total number, and proportion of type 1 (slow-twitch) and type 2 (fast-twitch) fibers were analyzed using linear regression techniques. The results show that the increase in muscle cross-sectional area from childhood to adult age is caused by an increase in mean fiber size. This is accompanied by a functional development of the fiber population: the proportion of type 2 fibers increases significantly from the age of 5 (approx. 35%) to the age of 20 (approx. 50%), which, in the absence of any discernible effect on the total number of fibers, is most likely caused by a transformation of type 1 to type 2 fibers.