A generative, probabilistic model of local protein structure

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 ...

Equilibrium simulations of proteins using molecular fragment replacement and NMR chemical shifts

“…Each hidden node value is associated with a particular conditional distribution over all output nodes: dihedral angles (D), amino acid type (A), secondary structure (S), cis/trans state of the peptide bond (T), and distributions over backbone chemical shift values (C Cα , C Cβ , C C , C N , C Hα , and C H ). This design is an extension of an earlier model of protein local structure (27). A graphical illustration of the model (Fig.…”

“…The sum runs over all possible sequences of hidden nodes, a calculation that can be done efficiently using dynamic programming (27). Although the model is Markovian, it will capture longer range effects up to six residues along the protein chain through allocated paths in the transition matrix (27), and thus contains similar information as that encoded in fragment libraries (SI Appendix).…”

“…The sum runs over all possible sequences of hidden nodes, a calculation that can be done efficiently using dynamic programming (27). Although the model is Markovian, it will capture longer range effects up to six residues along the protein chain through allocated paths in the transition matrix (27), and thus contains similar information as that encoded in fragment libraries (SI Appendix). The symmetry among the output nodes in this type of model provides a convenient flexibility: dihedral angles can be sampled conditionally on an input of amino acid and chemical shift information, but it is also possible to sample chemical shift values or even amino acid types compatible to a given protein structure.…”

“…As described in Materials and Methods, the parameters of CS-TORUS were estimated using a set of 1,349 protein structures with known experimental chemical shifts. ,i ), but it is also possible to sample entire subsequences from the model using the forward-backtrack algorithm (27). Random stretches of dihedral angles can thereby be repeatedly replaced to construct new candidate structures, thus mimicking the traditional fragment replacement strategy, but avoiding the boundary issues associated with the discrete fragments.…”

Maximum likelihood estimation using composite likelihoods for closed exponential families

“…The computational advantages of the full conditional composite likelihood become even more pronounced in this case. Such models have become important in bioinformatics for the modelling of correlated conformational angles in protein structure prediction (Mardia et al, 2007;Boomsma et al, 2008).…”