Mutual information analysis of mutation, nonlinearity and triple
interactions in proteins
Abstract
Mutations are the cause of several diseases as well as the underlying
force of evolution. A thorough understanding of its 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. MI calculated from these
trajectories shows that: (i) the multivariate Gaussian distribution of
joint probabilities characterizes the MI between residue pairs with
sufficient accuracy. Nonlinearities in joint probabilities calculated by
tensor Hermite polynomials up to the fifth order contribute
insignificantly. (ii) Changes in MI between residue pairs show the
characteristic patterns resulting from specific mutations. (iii) Triple
correlations are characterized by evaluating MI between triplets of
residues, certain triplets are strongly affected by mutation. (iv)
Susceptibility of residues to perturbation are obtained by MI and
discussed in terms of linear response theory.