Spatially proximate amino acids in a protein tend to coevolve. A protein's three-dimensional (3D) structure hence leaves an echo of correlations in the evolutionary record. Reverse engineering 3D structures from such correlations is an open problem in structural biology, pursued with increasing vigor as more and more protein sequences continue to fill the data banks. Within this task lies a statistical inference problem, rooted in the following: correlation between two sites in a protein sequence can arise from firsthand interaction but can also be network-propagated via intermediate sites; observed correlation is not enough to guarantee proximity. To separate direct from indirect interactions is an instance of the general problem of inverse statistical mechanics, where the task is to learn model parameters (fields, couplings) from observables (magnetizations, correlations, samples) in large systems. In the context of protein sequences, the approach has been referred to as direct-coupling analysis. Here we show that the pseudolikelihood method, applied to 21-state Potts models describing the statistical properties of families of evolutionarily related proteins, significantly outperforms existing approaches to the direct-coupling analysis, the latter being based on standard mean-field techniques. This improved performance also relies on a modified score for the coupling strength. The results are verified using known crystal structures of specific sequence instances of various protein families. Code implementing the new method can be found at http://plmdca.csc.kth.se/.

Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation functions, while still computationally feasible for hundreds of nodes. The largest improvement in reconstruction occurs for strong interactions. Using two examples, a diluted Sherrington-Kirkpatrick model and a two-dimensional lattice, we also show that interaction topologies can be recovered from few samples with good accuracy and that the use of l1 regularization is beneficial in this process, pushing inference abilities further into low-temperature regimes.

Correlation patterns in multiple sequence alignments of homologous proteins can be exploited to infer information on the three-dimensional structure of their members. The typical pipeline to address this task, which we in this paper refer to as the three dimensions of contact prediction, is to (i) filter and align the raw sequence data representing the evolutionarily related proteins; (ii) choose a predictive model to describe a sequence alignment; (iii) infer the model parameters and interpret them in terms of structural properties, such as an accurate contact map. We show here that all three dimensions are important for overall prediction success. In particular, we show that it is possible to improve significantly along the second dimension by going beyond the pair-wise Potts models from statistical physics, which have hitherto been the focus of the field. These (simple) extensions are motivated by multiple sequence alignments often containing long stretches of gaps which, as a data feature, would be rather untypical for independent samples drawn from a Potts model. Using a large test set of proteins we show that the combined improvements along the three dimensions are as large as any reported to date. Proteins are large molecules that living cells make by stringing together building blocks called amino acids or peptides, following their blue-prints in the DNA. Freshly made proteins are typically long, structure-less chains of peptides, but shortly afterwards most of them fold into characteristic structures. Proteins execute many functions in the cell, for which they need to have the right structure, which is therefore very important in determining what the proteins can do. The structure of a protein can be determined by X-ray diffraction and other experimental approaches which are all, to this day, somewhat labor-intensive and difficult. On the other hand, the order of the peptides in a protein can be read off from the DNA blue-print, and such protein sequences are today routinely produced in large numbers. In this paper we show that many similar protein sequences can be used to find information about the structure. The basic approach is to construct a probabilistic model for sequence variability, and then to use the parameters of that model to predict structure in three-dimensional space. The main technical novelty compared to previous contributions in the same general direction is that we use models more directly matched to the data.

Recent advances in the scale and diversity of population genomic datasets for bacteria now provide the potential for genome-wide patterns of co-evolution to be studied at the resolution of individual bases. Here we describe a new statistical method, genomeDCA, which uses recent advances in computational structural biology to identify the polymorphic loci under the strongest co-evolutionary pressures. We apply genomeDCA to two large population data sets representing the major human pathogens Streptococcus pneumoniae (pneumococcus) and Streptococcus pyogenes (group A Streptococcus). For pneumococcus we identified 5,199 putative epistatic interactions between 1,936 sites. Over three-quarters of the links were between sites within the pbp2x, pbp1a and pbp2b genes, the sequences of which are critical in determining non-susceptibility to beta-lactam antibiotics. A network-based analysis found these genes were also coupled to that encoding dihydrofolate reductase, changes to which underlie trimethoprim resistance. Distinct from these antibiotic resistance genes, a large network component of 384 protein coding sequences encompassed many genes critical in basic cellular functions, while another distinct component included genes associated with virulence. The group A Streptococcus (GAS) data set population represents a clonal population with relatively little genetic variation and a high level of linkage disequilibrium across the genome. Despite this, we were able to pinpoint two RNA pseudouridine synthases, which were each strongly linked to a separate set of loci across the chromosome, representing biologically plausible targets of co-selection. The population genomic analysis method applied here identifies statistically significantly co-evolving locus pairs, potentially arising from fitness selection interdependence reflecting underlying protein-protein interactions, or genes whose product activities contribute to the same phenotype. This discovery approach greatly enhances the future potential of epistasis analysis for systems biology, and can complement genome-wide association studies as a means of formulating hypotheses for targeted experimental work. Epistatic interactions between polymorphisms in DNA are recognized as important drivers of evolution in numerous organisms. Study of epistasis in bacteria has been hampered by the lack of densely sampled population genomic data, suitable statistical models and inference algorithms sufficiently powered for extremely high-dimensional parameter spaces. We introduce the first model-based method for genome-wide epistasis analysis and use two of the largest available bacterial population genome data sets on Streptococcus pneumoniae (the pneumococcus) and Streptococcus pyogenes (group A Streptococcus) to demonstrate its potential for biological discovery. Our approach reveals interacting networks of resistance, virulence and core machinery genes in the pneumococcus, which highlights putative candidates for novel drug targets. We also discover a number of plausible targets of co-selection in S. pyogenes linked to RNA pseudouridine synthases. Our method significantly enhances the future potential of epistasis analysis for systems biology, and can complement genome-wide association studies as a means of formulating hypotheses for targeted experimental work.

Enterococcus faecalis is the third cause of nosocomial infections. To obtain the first snapshot of transcriptional organizations in this bacterium, we used a modified RNA-seq approach enabling to discriminate primary from processed 5′ RNA ends. We also validated our approach by confirming known features in Escherichia coli. We mapped 559 transcription start sites (TSSs) and 352 processing sites (PSSs) in E. faecalis. A blind motif search retrieved canonical features of SigA- and SigN-dependent promoters preceding transcription start sites mapped. We discovered 85 novel putative regulatory RNAs, small- and antisense RNAs, and 72 transcriptional antisense organizations. Presented data constitute a significant insight into bacterial RNA landscapes and a step toward the inference of regulatory processes at transcriptional and post-transcriptional levels in a comprehensive manner.