Improving landscape inference by integrating heterogeneous data in the inverse Ising problem.

Pierre Barrat-Charlaix,Matteo Figliuzzi,Martin Weigt

doi:10.1038/srep37812

Abstract

The inverse Ising problem and its generalizations to Potts and continuous spin models have recently attracted much attention thanks to their successful applications in the statistical modeling of biological data. In the standard setting, the parameters of an Ising model (couplings and fields) are inferred using a sample of equilibrium configurations drawn from the Boltzmann distribution. However, in the context of biological applications, quantitative information for a limited number of microscopic spins configurations has recently become available. In this paper, we extend the usual setting of the inverse Ising model by developing an integrative approach combining the equilibrium sample with (possibly noisy) measurements of the energy performed for a number of arbitrary configurations. Using simulated data, we show that our integrative approach outperforms standard inference based only on the equilibrium sample or the energy measurements, including error correction of noisy energy measurements. As a biological proof-of-concept application, we show that mutational fitness landscapes in proteins can be better described when combining evolutionary sequence data with complementary structural information about mutant sequences.

Highlights

The inverse Ising problem and its generalizations to Potts and continuous spin models have recently attracted much attention thanks to their successful applications in the statistical modeling of biological data
A paradigmatic example is represented by the Ising model and its generalizations to Potts and continuous spin variables, which have recently become popular for extracting information from large-scale biological datasets
This widespread use is motivated by the observation that the least constrained statistical model reproducing empirical single-variable and pairwise frequencies observed in a list of equilibrium configurations is given by a Boltzmann distribution: P (s) = 1 exp{−H(s)}, Z

Summary

Introduction

The inverse Ising problem and its generalizations to Potts and continuous spin models have recently attracted much attention thanks to their successful applications in the statistical modeling of biological data. Successful examples are as different as multiple-sequence alignments of evolutionary related proteins[1,2,3], gene-expression profiles[4], spiking patterns of neural networks[5,6], or the collective behavior of bird flocks[7] This widespread use is motivated by the observation that the least constrained (i.e. maximum-entropy8) statistical model reproducing empirical single-variable and pairwise frequencies observed in a list of equilibrium configurations is given by a Boltzmann distribution:. Inferring the couplings J ={Jij}1≤i

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Conclusion