Mutual information analysis of mutation, nonlinearity, and triple interactions in proteins

Mutations are the cause of several diseases as well as the underlying force of evolution. A thorough understanding of their biophysical consequences is essential. We present a computational framework for evaluating different levels of mutual information (MI) and its dependence on mutation. We used molecular dynamics trajectories of the third PDZ domain and its different mutations. Nonlinear MI between all residue pairs are calculated by tensor Hermite polynomials up to the fifth order and compared with results from multivariate Gaussian distribution of joint probabilities. We show that MI is written as the sum of a Gaussian and a nonlinear component. Results for the PDZ domain show that the Gaussian term gives a sufficiently accurate representation of MI when compared with nonlinear terms up to the fifth order. Changes in MI between residue pairs show the characteristic patterns resulting from specific mutations. Emergence of new peaks in the MI versus residue index plots of mutated PDZ shows how mutation may change allosteric pathways. Triple correlations are characterized by evaluating MI between triplets of residues. We observed that certain triplets are strongly affected by mutation. Susceptibility of residues to perturbation is obtained by MI and discussed in terms of linear response theory.