Protein folding using contact maps

We present the development of the idea to use dynamics in the space of contact maps as a computational approach to the protein folding problem. We first introduce two important technical ingredients, the reconstruction of a three dimensional conformation from a contact map and the Monte Carlo dynamics in contact map space. We then discuss two approximations to the free energy of the contact maps and a method to derive energy parameters based on perceptron learning. Finally we present results, first for predictions based on threading and then for energy minimization of crambin and of a set of 6 immunoglobulins. The main result is that we proved that the two simple approximations we studied for the free energy are not suitable for protein folding. Perspectives are discussed in the last section.Comment: 29 pages, 10 figure

ABC likelihood-freee methods for model choice in Gibbs random fields

Gibbs random fields (GRF) are polymorphous statistical models that can be used to analyse different types of dependence, in particular for spatially correlated data. However, when those models are faced with the challenge of selecting a dependence structure from many, the use of standard model choice methods is hampered by the unavailability of the normalising constant in the Gibbs likelihood. In particular, from a Bayesian perspective, the computation of the posterior probabilities of the models under competition requires special likelihood-free simulation techniques like the Approximate Bayesian Computation (ABC) algorithm that is intensively used in population genetics. We show in this paper how to implement an ABC algorithm geared towards model choice in the general setting of Gibbs random fields, demonstrating in particular that there exists a sufficient statistic across models. The accuracy of the approximation to the posterior probabilities can be further improved by importance sampling on the distribution of the models. The practical aspects of the method are detailed through two applications, the test of an iid Bernoulli model versus a first-order Markov chain, and the choice of a folding structure for two proteins.Comment: 19 pages, 5 figures, to appear in Bayesian Analysi

On the optimal contact potential of proteins

We analytically derive the lower bound of the total conformational energy of a protein structure by assuming that the total conformational energy is well approximated by the sum of sequence-dependent pairwise contact energies. The condition for the native structure achieving the lower bound leads to the contact energy matrix that is a scalar multiple of the native contact matrix, i.e., the so-called Go potential. We also derive spectral relations between contact matrix and energy matrix, and approximations related to one-dimensional protein structures. Implications for protein structure prediction are discussed.Comment: 5 pages, text onl

Protein secondary structure: Entropy, correlations and prediction

Is protein secondary structure primarily determined by local interactions between residues closely spaced along the amino acid backbone, or by non-local tertiary interactions? To answer this question we have measured the entropy densities of primary structure and secondary structure sequences, and the local inter-sequence mutual information density. We find that the important inter-sequence interactions are short ranged, that correlations between neighboring amino acids are essentially uninformative, and that only 1/4 of the total information needed to determine the secondary structure is available from local inter-sequence correlations. Since the remaining information must come from non-local interactions, this observation supports the view that the majority of most proteins fold via a cooperative process where secondary and tertiary structure form concurrently. To provide a more direct comparison to existing secondary structure prediction methods, we construct a simple hidden Markov model (HMM) of the sequences. This HMM achieves a prediction accuracy comparable to other single sequence secondary structure prediction algorithms, and can extract almost all of the inter-sequence mutual information. This suggests that these algorithms are almost optimal, and that we should not expect a dramatic improvement in prediction accuracy. However, local correlations between secondary and primary structure are probably of under-appreciated importance in many tertiary structure prediction methods, such as threading.Comment: 8 pages, 5 figure

Through the Eye of the Needle: Recent Advances in Understanding Biopolymer Translocation

In recent years polymer translocation, i.e., transport of polymeric molecules through nanometer-sized pores and channels embedded in membranes, has witnessed strong advances. It is now possible to observe single-molecule polymer dynamics during the motion through channels with unprecedented spatial and temporal resolution. These striking experimental studies have stimulated many theoretical developments. In this short theory-experiment review, we discuss recent progress in this field with a strong focus on non-equilibrium aspects of polymer dynamics during the translocation process.Comment: 29 pages, 6 figures, 3 tables, to appear in J. Phys.: Condens. Matter as a Topical Revie