Benchmarking inverse statistical approaches for protein structure and design with exactly solvable models

Abstract

Inverse statistical approaches to determine protein structure and function from Multiple Sequence Alignments (MSA) are emerging as powerful tools in computational biology. However the underlying assumptions of the relationship between the inferred effective Potts Hamiltonian and real protein structure and energetics remain untested so far. Here we use lattice protein model (LP) to benchmark those inverse statistical approaches. We build MSA of highly stable sequences in target LP structures, and infer the effective pairwise Potts Hamiltonians from those MSA. We find that inferred Potts Hamiltonians reproduce many important aspects of 'true' LP structures and energetics. Careful analysis reveals that effective pairwise couplings in inferred Potts Hamiltonians depend not only on the energetics of the native structure but also on competing folds; in particular, the coupling values reflect both positive design (stabilization of native conformation) and negative design (destabilization of competing folds). In addition to providing detailed structural information, the inferred Potts models used as protein Hamiltonian for design of new sequences are able to generate with high probability completely new sequences with the desired folds, which is not possible using independent-site models. Those are remarkable results as the effective LP Hamiltonians used to generate MSA are not simple pairwise models due to the competition between the folds. Our findings elucidate the reasons of the power of inverse approaches to the modelling of proteins from sequence data, and their limitations; we show, in particular, that their success crucially depend on the accurate inference of the Potts pairwise couplings. Author SummaryInverse statistical approaches, modeling pairwise correlations between amino acids in the sequences of similar proteins across many different organisms, can successfully extract protein structure (contact) information. Here, we benchmark those statistical approaches on exactly solvable models of proteins, folding on a 3D lattice, to assess the reasons underlying their success and their limitations. We show that the inferred parameters (effective pairwise interactions) of the statistical models have clear and quantitative interpretations in terms of positive (favoring the native fold) and negative (disfavoring competing folds) protein sequence design. New sequences randomly drawn from the statistical models are likely to fold into the native structures when effective pairwise interactions are accurately inferred, a performance which cannot be achieved with independent-site models.

Inference of epistatic effects in a key mitochondrial protein

“…Here, B is the number of sequences in the MSA, δ(a, b) = 1 if states a and b are the same, and δ(a, b) = 0 otherwise. To solve the inference problem, we use the adaptive cluster expansion (ACE) and Boltzmann machine learning algorithms developed by Barton et al, which avoid over-fitting by constructing a sparse network of interactions sufficient to reproduce the observed frequencies to within errors due to finite sampling [15] (see Jacquin et al [16] for a comparison different methods).…”

“…Explicit sampling of fitness and epistatic effects by mutagenesis is costly, and is limited to proteins that can be expressed and evolved in the laboratory. However, for certain proteins [14], the number of known sequences is sufficient to infer the fitness effects of mutations by machine learning methods -for example, by adjusting the parameters of a Potts spin model to recover the frequencies of amino acids in a protein alignment [14][15][16][17].…”

Inferring interaction partners from protein sequences

“…We calculate the interaction energy for every possible protein pair within each species by summing the interprotein couplings assigned by the model. Such "energies" capture evolutionary correlations, and correlate to physical energies for lattice proteins (30). Using these interaction energies, we predict protein pairs [assuming one-to-one specific HK−RR interactions (28), Fig.…”

Inference of epistatic effects leading to entrenchment and drug resistance in HIV-1 protease

“…Recently, probabilistic models, called Potts models, have been used to assign scores to individual protein sequences which correlate with experimental measures of fitness (Haq et al 2012;Ferguson et al 2013;Mann et al 2014;Figliuzzi et al 2015;Hopf et al 2017). These advances build upon previous and ongoing work in which Potts models have been used to extract information from sequence data regarding tertiary and quaternary structure of protein families (Weigt et al 2009;Morcos et al 2011Morcos et al , 2014Marks et al 2012;Sulkowska et al 2012;Sutto et al 2015;Barton et al 2016a;Haldane et al 2016;Jacquin et al 2016) and sequencespecific quantitative predictions of viral protein stability and fitness (Haq et al 2012;Shekhar et al 2013;Barton et al 2016b;Butler et al 2016).…”