Information flow and allosteric communication in proteins.

Based on Schreiber's work on transfer entropy, a molecular theory of nonlinear information transfer between residue pairs in proteins is developed. The joint distribution function for residue fluctuations required by the theory is expressed in terms of tensor Hermite polynomials that conveniently separate harmonic and nonlinear contributions to information transfer. The harmonic part of information transfer is expressed as the difference between time dependent and independent mutual information. Third order nonlinearities are discussed in detail. The amount and speed of information transfer between residues, which are important for understanding allosteric activity in proteins, are discussed. Mutual information between two residues is commonly used for information transfer. While mutual information shows the maximum amount of information that may be transferred between two residues, it does not explain the actual amount of transfer nor the transfer rate of information. For this, dynamic equations of the system are needed. The solution of the Langevin equation and molecular dynamics trajectories are used in the present work for this purpose. Allosteric communication in human NAD-dependent isocitrate dehydrogenase is studied as an example. Calculations show that several paths contribute collectively to information transfer. Important residues on these paths are identified. Time resolved information transfer between these residues, their amplitudes, and transfer rates, which are in agreement with time resolved ultraviolet resonance Raman measurements in general, are estimated. Peak values of calculated information transfer, ∼0.01-0.04 bits, are about two orders of magnitude smaller than the information content of residues. They are comparable to mutual information values, however. Estimated transfer rates are in the order of 1-20 megabits per second, and sustained transfer during the activity time-span of proteins may be significant. Information transfer from third order contributions is one to two orders of magnitude smaller than the harmonic terms, showing that harmonic analysis is a good approximation to information transfer.