On exceptional groups of order p^5

A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient. The smallest examples of exceptional p-groups have order p^5. For an odd prime p, we classify all pairs (G,Q) where G has order p^5 and Q is a distinguished quotient. (The case p=2 has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order p^5 with at least one exceptional quotient tends to 1/2.Comment: 23 page

On exceptional groups of order p⁵

A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient. The smallest examples of exceptional p-groups have order p5. For an odd prime p, we classify all pairs (G, Q)where G has order p5 and Q is a distinguished quotient. (The case p = 2 has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order p5 with at least one exceptional quotient tends to 1/2

Learnt representations of proteins can be used for accurate prediction of small molecule binding sites on experimentally determined and predicted protein structures

Protein-ligand binding site prediction is a useful tool for understanding the functional behaviour and potential drug-target interactions of a novel protein of interest. However, most binding site prediction methods are tested by providing crystallised ligand-bound (holo) structures as input. This testing regime is insufficient to understand the performance on novel protein targets where experimental structures are not available. An alternative option is to provide computationally predicted protein structures, but this is not commonly tested. However, due to the training data used, computationally-predicted protein structures tend to be extremely accurate, and are often biased toward a holo conformation. In this study we describe and benchmark IF-SitePred, a protein-ligand binding site prediction method which is based on the labelling of ESM-IF1 protein language model embeddings combined with point cloud annotation and clustering. We show that not only is IF-SitePred competitive with state-of-the-art methods when predicting binding sites on experimental structures, but it performs better on proxies for novel proteins where low accuracy has been simulated by molecular dynamics. Finally, IF-SitePred outperforms other methods if ensembles of predicted protein structures are generated

Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

The influence of solid state information and descriptor selection on statistical models of temperature dependent aqueous solubility.

Predicting the equilibrium solubility of organic, crystalline materials at all relevant temperatures is crucial to the digital design of manufacturing unit operations in the chemical industries. The work reported in our current publication builds upon the limited number of recently published quantitative structure-property relationship studies which modelled the temperature dependence of aqueous solubility. One set of models was built to directly predict temperature dependent solubility, including for materials with no solubility data at any temperature. We propose that a modified cross-validation protocol is required to evaluate these models. Another set of models was built to predict the related enthalpy of solution term, which can be used to estimate solubility at one temperature based upon solubility data for the same material at another temperature. We investigated whether various kinds of solid state descriptors improved the models obtained with a variety of molecular descriptor combinations: lattice energies or 3D descriptors calculated from crystal structures or melting point data. We found that none of these greatly improved the best direct predictions of temperature dependent solubility or the related enthalpy of solution endpoint. This finding is surprising because the importance of the solid state contribution to both endpoints is clear. We suggest our findings may, in part, reflect limitations in the descriptors calculated from crystal structures and, more generally, the limited availability of polymorph specific data. We present curated temperature dependent solubility and enthalpy of solution datasets, integrated with molecular and crystal structures, for future investigations

Prediction of bioconcentration factors in fish and invertebrates using machine learning

© 2018 The Authors The application of machine learning has recently gained interest from ecotoxicological fields for its ability to model and predict chemical and/or biological processes, such as the prediction of bioconcentration. However, comparison of different models and the prediction of bioconcentration in invertebrates has not been previously evaluated. A comparison of 24 linear and machine learning models is presented herein for the prediction of bioconcentration in fish and important factors that influenced accumulation identified. R2 and root mean square error (RMSE) for the test data (n = 110 cases) ranged from 0.23–0.73 and 0.34–1.20, respectively. Model performance was critically assessed with neural networks and tree-based learners showing the best performance. An optimised 4-layer multi-layer perceptron (14 descriptors) was selected for further testing. The model was applied for cross-species prediction of bioconcentration in a freshwater invertebrate, Gammarus pulex. The model for G. pulex showed good performance with R2 of 0.99 and 0.93 for the verification and test data, respectively. Important molecular descriptors determined to influence bioconcentration were molecular mass (MW), octanol-water distribution coefficient (logD), topological polar surface area (TPSA) and number of nitrogen atoms (nN) among others. Modelling of hazard criteria such as PBT, showed potential to replace the need for animal testing. However, the use of machine learning models in the regulatory context has been minimal to date and is critically discussed herein. The movement away from experimental estimations of accumulation to in silico modelling would enable rapid prioritisation of contaminants that may pose a risk to environmental health and the food chain.Biotechnology and Biological Sciences Research Council (BBSRC) CASE industrial scholarship scheme (Reference BB/K501177/1), iNVERTOX project (Reference BB/P005187/1) and AstraZeneca Global SHE research programme. This work was additionally supported by the Francis Crick Institute which receives its core funding from Cancer Research UK (FC001999), the UK Medical Research Council (FC001999), and the Wellcome Trust (FC001999)

SARS-CoV-2 infects the human kidney and drives fibrosis in kidney organoids

Kidney failure is frequently observed during and after COVID-19, but it remains elusive whether this is a direct effect of the virus. Here, we report that SARS-CoV-2 directly infects kidney cells and is associated with increased tubule-interstitial kidney fibrosis in patient autopsy samples. To study direct effects of the virus on the kidney independent of systemic effects of COVID-19, we infected human-induced pluripotent stem-cell-derived kidney organoids with SARS-CoV-2. Single-cell RNA sequencing indicated injury and dedifferentiation of infected cells with activation of profibrotic signaling pathways. Importantly, SARS-CoV-2 infection also led to increased collagen 1 protein expression in organoids. A SARS-CoV-2 protease inhibitor was able to ameliorate the infection of kidney cells by SARS-CoV-2. Our results suggest that SARS-CoV-2 can directly infect kidney cells and induce cell injury with subsequent fibrosis. These data could explain both acute kidney injury in COVID-19 patients and the development of chronic kidney disease in long COVID

A review of methods for the calculation of solution free energies and the modelling of systems in solution

JLMcD and JBOM are grateful to SULSA for funding; RES and JBOM thank the University of St Andrews, EPSRC (grant EP/L505079/1) and CCDC for funding.Over the past decade, pharmaceutical companies have seen a decline in the number of drug candidates successfully passing through clinical trials, though billions are still spent on drug development. Poor aqueous solubility leads to low bio-availability, reducing pharmaceutical effectiveness. The human cost of inefficient drug candidate testing is of great medical concern, with fewer drugs making it to the production line, slowing the development of new treatments. In biochemistry and biophysics, water mediated reactions and interactions within active sites and protein pockets are an active area of research, in which methods for modelling solvated systems are continually pushed to their limits. Here, we discuss a multitude of methods aimed towards solvent modelling and solubility prediction, aiming to inform the reader of the options available, and outlining the various advantages and disadvantages of each approach.Publisher PDFPeer reviewe

A review of methods for the calculation of solution free energies and the modelling of systems in solution

Over the past decade, pharmaceutical companies have seen a decline in the number of drug candidates successfully passing through clinical trials, though billions are still spent on drug development. Poor aqueous solubility leads to low bio-availability, reducing pharmaceutical effectiveness. The human cost of inefficient drug candidate testing is of great medical concern, with fewer drugs making it to the production line, slowing the development of new treatments. In biochemistry and biophysics, water mediated reactions and interactions within active sites and protein pockets are an active area of research, in which methods for modelling solvated systems are continually pushed to their limits. Here, we discuss a multitude of methods aimed towards solvent modelling and solubility prediction, aiming to inform the reader of the options available, and outlining the various advantages and disadvantages of each approach