  Allosteric regulation at distant sites is central to many cellular processes.
In particular, allosteric sites in proteins are a major target to increase the
range and selectivity of new drugs, and there is a need for methods capable of
identifying intra-molecular signalling pathways leading to allosteric effects.
Here, we use an atomistic graph-theoretical approach that exploits Markov
transients to extract such pathways and exemplify our results in an important
allosteric protein, caspase-1. Firstly, we use Markov Stability community
detection to perform a multiscale analysis of the structure of caspase-1 which
reveals that the active conformation has a weaker, less compartmentalised
large-scale structure as compared to the inactive conformation, resulting in
greater intra-protein coherence and signal propagation. We also carry out a
full computational point mutagenesis and identify that only a few residues are
critical to such structural coherence. Secondly, we characterise explicitly the
transients of random walks originating at the active site and predict the
location of a known allosteric site in this protein quantifying the
contribution of individual bonds to the communication pathway between the
active and allosteric sites. Several of the bonds we find have been shown
experimentally to be functionally critical, but we also predict a number of as
yet unidentified bonds which may contribute to the pathway. Our approach offers
a computationally inexpensive method for the identification of allosteric sites
and communication pathways in proteins using a fully atomistic description.
