Allostery is a fundamental mechanism of biological regulation, in which binding of a molecule at a distant location affects the active site of a protein. Allosteric sites provide targets to fine-tune protein activity, yet we lack computational methodologies to predict them. Here we present an efficient graph-theoretical framework to reveal allosteric interactions (atoms and communication pathways strongly coupled to the active site) without a priori information of their location. Using an atomistic graph with energy-weighted covalent and weak bonds, we define a bond-to-bond propensity quantifying the non-local effect of instantaneous bond fluctuations propagating through the protein. Significant interactions are then identified using quantile regression. We exemplify our method with three biologically important proteins: caspase-1, CheY, and h-Ras, correctly predicting key allosteric interactions, whose significance is additionally confirmed against a reference set of 100 proteins. The almost-linear scaling of our method renders it suitable for high-throughput searches for candidate allosteric sites.

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.

With the rise of social media as an important channel for the debate and discussion of public affairs, online social networks such as Twitter have become important platforms for public information and engagement by policy makers. To communicate effectively through Twitter, policy makers need to understand how influence and interest propagate within its network of users. In this chapter we use graph-theoretic methods to analyse the Twitter debate surrounding NHS England's controversial care.data scheme. Directionality is a crucial feature of the Twitter social graph -information flows from the followed to the followers -but is often ignored in social network analyses; our methods are based on the behaviour of dynamic processes on the network and can be applied naturally to directed networks. We uncover robust communities of users and show that these communities reflect how information flows through the Twitter network. We are also able to classify users by their differing roles in directing the flow of information through the network. Our methods and results will be useful to policy makers who would like to use Twitter effectively as a communication medium.

Allostery is a fundamental mechanism of biological regulation, in which binding of a molecule at a distant location affects the active site of a protein. Allosteric sites provide targets to finetune protein activity, yet we lack computational methodologies to predict them. Here we present an efficient graph-theoretical framework to reveal allosteric interactions (atoms and communication pathways strongly coupled to the active site) without a priori information of their location. Using an atomistic graph with energy-weighted covalent and weak bonds, we define a bond-to-bond propensity quantifying the non-local effect of instantaneous bond fluctuations propagating through the protein. Significant interactions are then identified using quantile regression. We exemplify our method with three biologically important proteins: caspase-1, CheY, and h-Ras, correctly predicting key allosteric interactions, whose significance is additionally confirmed against a reference set of 100 proteins. The almost-linear scaling of our method renders it suitable for high-throughput searches for candidate allosteric sites.

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