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

TL;DR

This paper introduces an integrative method for inverse Ising problems that combines equilibrium data with energy measurements, improving inference accuracy especially in biological applications like protein mutational landscapes.

Contribution

The authors develop a novel integrative approach that enhances inverse Ising inference by incorporating heterogeneous data types, including noisy energy measurements.

Findings

Outperforms standard methods using only equilibrium data or energy measurements.

Effective error correction for noisy energy data.

Improves modeling of protein mutational fitness landscapes.

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.