Window functions and sigmoidal behaviour of memristive systems

Summary: A common approach to model memristive systems is to include empirical window functions to describe edge effects and nonlinearities in the change of the memristance. We demonstrate that under quite general conditions, each window function can be associated with a sigmoidal curve relating the normalised time-dependent memristance to the time integral of the input. Conversely, this explicit relation allows us to derive window functions suitable for the mesoscopic modelling of memristive systems from a variety of well-known sigmoidals. Such sigmoidal curves are defined in terms of measured variables and can thus be extracted from input and output signals of a device and then transformed to its corresponding window. We also introduce a new generalised window function that allows the flexible modelling of asymmetric edge effects in a simple manner

Prediction of allosteric sites and signalling: insights from benchmarking datasets

Allostery is a pervasive mechanism that regulates protein activity through ligand binding at a site different from the orthosteric site. The universality of allosteric regulation complemented by the benefits of highly specific and potentially non-toxic allosteric drugs makes uncovering allosteric sites invaluable. However, there are few computational methods to effectively predict them. Bond-to-bond propensity analysis has successfully predicted allosteric sites in 19 of 20 cases using an energy-weighted atomistic graph. We here extended the analysis onto 432 structures of 146 proteins from two benchmarking datasets for allosteric proteins: ASBench and CASBench. We further introduced two statistical measures to account for the cumulative effect of high-propensity residues and the crucial residues in a given site. The allosteric site is recovered for 127 of 146 proteins (407 of 432 structures) knowing only the orthosteric sites or ligands. The quantitative analysis using a range of statistical measures enables better characterization of potential allosteric sites and mechanisms involved

Proteins across scales through graph partitioning: application to the major peanut allergen Ara h 1

The analysis of community structure in complex networks has been given much attention recently, as it is hoped that the communities at various scales can affect or explain the global behaviour of the system. A plethora of community detection algorithms have been proposed, insightful yet often restricted by certain inherent resolutions. Proteins are multi-scale biomolecular machines with coupled structural organization across scales, which is linked to their function. To reveal this organization, we applied a recently developed multi-resolution method, Markov Stability, which is based on atomistic graph partitioning, along with theoretical mutagenesis that further allows for hot spot identification using Gaussian process regression. The methodology finds partitions of a graph without imposing a particular scale a priori and analyses the network in a computationally efficient way. Here, we show an application on peanut allergenicity, which despite extensive experimental studies that focus on epitopes, groups of atoms associated with allergenic reactions, remains poorly understood. We compare our results against available experiment data, and we further predict distal regulatory sites that may significantly alter protein dynamics

An edge-based formulation of elastic network models

We present an edge-based framework for the study of geometric elastic network models to model mechanical interactions in physical systems. We use a formulation in the edge space, instead of the usual node-centric approach, to characterise edge fluctuations of geometric networks defined in d- dimensional space and define the edge mechanical embeddedness, an edge mechanical susceptibility measuring the force felt on each edge given a force applied on the whole system. We further show that this formulation can be directly related to the infinitesimal rigidity of the network, which additionally permits three- and four-centre forces to be included in the network description. We exemplify the approach in protein systems, at both the residue and atomistic levels of description

Community detection and role identification in directed networks: understanding the Twitter network of the care.data debate

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 Englands 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

Repurposed floxacins targeting RSK4 prevent chemoresistance and metastasis in lung and bladder cancer

Lung and bladder cancers are mostly incurable because of the early development of drug resistance and metastatic dissemination. Hence, improved therapies that tackle these two processes are urgently needed to improve clinical outcome. We have identified RSK4 as a promoter of drug resistance and metastasis in lung and bladder cancer cells. Silencing this kinase, through either RNA interference or CRISPR, sensitized tumor cells to chemotherapy and hindered metastasis in vitro and in vivo in a tail vein injection model. Drug screening revealed several floxacin antibiotics as potent RSK4 activation inhibitors, and trovafloxacin reproduced all effects of RSK4 silencing in vitro and in/ex vivo using lung cancer xenograft and genetically engineered mouse models and bladder tumor explants. Through x-ray structure determination and Markov transient and Deuterium exchange analyses, we identified the allosteric binding site and revealed how this compound blocks RSK4 kinase activation through binding to an allosteric site and mimicking a kinase autoinhibitory mechanism involving the RSK4’s hydrophobic motif. Last, we show that patients undergoing chemotherapy and adhering to prophylactic levofloxacin in the large placebo-controlled randomized phase 3 SIGNIFICANT trial had significantly increased (P = 0.048) long-term overall survival times. Hence, we suggest that RSK4 inhibition may represent an effective therapeutic strategy for treating lung and bladder cancer

Severability of mesoscale components and local time scales in dynamical networks

A major goal of dynamical systems theory is the search for simplified descriptions of the dynamics of a large number of interacting states. For overwhelmingly complex dynamical systems, the derivation of a reduced description on the entire dynamics at once is computationally infeasible. Other complex systems are so expansive that despite the continual onslaught of new data only partial information is available. To address this challenge, we define and optimise for a local quality function severability for measuring the dynamical coherency of a set of states over time. The theoretical underpinnings of severability lie in our local adaptation of the Simon-Ando-Fisher time-scale separation theorem, which formalises the intuition of local wells in the Markov landscape of a dynamical process, or the separation between a microscopic and a macroscopic dynamics. Finally, we demonstrate the practical relevance of severability by applying it to examples drawn from power networks, image segmentation, social networks, metabolic networks, and word association

Towards precision healthcare: context and mathematical challenges

Precision medicine refers to the idea of delivering the right treatment to the right patient at the right time, usually with a focus on a data-centred approach to this task. In this perspective piece, we use the term "precision healthcare" to describe the development of precision approaches that bridge from the individual to the population, taking advantage of individual-level data, but also taking the social context into account. These problems give rise to a broad spectrum of technical, scientific, policy, ethical and social challenges, and new mathematical techniques will be required to meet them. To ensure that the science underpin-ning "precision" is robust, interpretable and well-suited to meet the policy, ethical and social questions that such approaches raise, the mathematical methods for data analysis should be transparent, robust and able to adapt to errors and uncertainties. In particular, precision methodologies should capture the complexity of data, yet produce tractable descriptions at the relevant resolution while preserving intelligibility and traceability, so that they can be used by practitioners to aid decision-making. Through several case studies in this domain of precision healthcare, we argue that this vision requires the development of new mathematical frameworks, both in modelling and in data analysis and interpretation