How many bits of information can be transferred within a protein and how fast?

Amount and rate of information that may be transferred from one residue to another in a protein is quantified using the transfer entropy concept of information theory. Information transfer from one residue to the second is defined as the decrease in the uncertainty in the second residue due to coupling with past values of the first. Three types of information transfer between pairs of residues are defined: transfer between residues that are (i) close in both space and along the primary protein chain, (ii) close in space but distant along the chain, and (iii) distant in space and along the chain may be distinguished. The widely studied third PDZ domain from the synaptic protein PSD-95 is used as an example. The three types of transfer show that residues close in space and chain transfer the largest amount of information. Transfer along the primary chain is also significant. Predictions of the model show that significant amount of transfer may also take place between spatially distant pairs of residues. The latter forms the basis of dynamic allostery in proteins. The role of information transfer between distant pairs in relation to coevolution has been controversial, some works assigning it to near neighbor residue pairs only and others supporting long range coupling. The present paper shows that significant amount of information may be transferred between distant pairs in PSD-95.Transfer rates of the order of gigabytes per second are predicted by the present theory. Information transfer between a specific set of residue pairs exhibit strong directionality, or causality, an observation that may be of use in protein engineering and drug design.