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.

We investigate the learning performance of the pseudolikelihood maximization method for inverse Ising problems. In the teacher–student scenario under the assumption that the teacher’s couplings are sparse and the student does not know the graphical structure, the learning curve and order parameters are assessed in the typical case using the replica and cavity methods from statistical mechanics. Our formulation is also applicable to a certain class of cost functions having locality; the standard likelihood does not belong to that class. The derived analytical formulas indicate that the perfect inference of the presence/absence of the teacher’s couplings is possible in the thermodynamic limit taking the number of spins N as infinity while keeping the dataset size M proportional to N, as long as α = M/N > 2. Meanwhile, the formulas also show that the estimated coupling values corresponding to the truly existing ones in the teacher tend to be overestimated in the absolute value, manifesting the presence of estimation bias. These results are considered to be exact in the thermodynamic limit on locally tree-like networks, such as the regular random or Erdős–Rényi graphs. Numerical simulation results fully support the theoretical predictions. Additional biases in the estimators on loopy graphs are also discussed.

Abstract. The 1-bit compressed sensing framework enables the recovery of a sparse vector x from the sign information of each entry of its linear transformation. Discarding the amplitude information can significantly reduce the amount of data, which is highly beneficial in practical applications. In this paper, we present a Bayesian approach to signal reconstruction for 1-bit compressed sensing, and analyze its typical performance using statistical mechanics. As a basic setup, we consider the case that the measuring matrix Φ has i.i.d entries, and the measurements y are noiseless. Utilizing the replica method, we show that the Bayesian approach enables better reconstruction than the l 1 -norm minimization approach, asymptotically saturating the performance obtained when the non-zero entries positions of the signal are known, for signals whose nonzero entries follow zero mean Gaussian distributions. We also test a message passing algorithm for signal reconstruction on the basis of belief propagation. The results of numerical experiments are consistent with those of the theoretical analysis.

Covariance-based discovery of polymorphisms under co-selective pressure or epistasis has received considerable recent attention in population genomics. Both statistical modeling of the population level covariation of alleles across the chromosome and model-free testing of dependencies between pairs of polymorphisms have been shown to successfully uncover patterns of selection in bacterial populations. Here we introduce a model-free method, SpydrPick, whose computational efficiency enables analysis at the scale of pan-genomes of many bacteria. SpydrPick incorporates an efficient correction for population structure, which adjusts for the phylogenetic signal in the data without requiring an explicit phylogenetic tree. We also introduce a new type of visualization of the results similar to the Manhattan plots used in genome-wide association studies, which enables rapid exploration of the identified signals of co-evolution. Simulations demonstrate the usefulness of our method and give some insight to when this type of analysis is most likely to be successful. Application of the method to large population genomic datasets of two major human pathogens, Streptococcus pneumoniae and Neisseria meningitidis, revealed both previously identified and novel putative targets of co-selection related to virulence and antibiotic resistance, highlighting the potential of this approach to drive molecular discoveries, even in the absence of phenotypic data.