The article 10.1093/bioinformatics/bty340/, published alongside this paper, also addresses the problem of biases in protein stability change predictions.

No abstract

We study the quantum properties of certain BPS Wilson loops in N = 4 supersymmetric Yang-Mills theory. They belong to a general family, introduced recently, in which the addition of particular scalar couplings endows generic loops on S 3 with a fraction of supersymmetry. When restricted to S 2 , their quantum average has been further conjectured to be exactly computed by the matrix model governing the zero-instanton sector of YM 2 on the sphere. We perform a complete two-loop analysis on a class of cusped Wilson loops lying on a two-dimensional sphere, finding perfect agreement with the conjecture. The perturbative computation reproduces the matrix-model expectation through a highly non-trivial interplay between ladder diagrams and self-energies/vertex contributions, suggesting the existence of a localization procedure.

The ability to rationally modify targeted physical and biological features of a protein of interest holds promise in numerous academic and industrial applications and paves the way towards de novo protein design. In particular, bioprocesses that utilize the remarkable properties of enzymes would often benefit from mutants that remain active at temperatures that are either higher or lower than the physiological temperature, while maintaining the biological activity. Many in silico methods have been developed in recent years for predicting the thermodynamic stability of mutant proteins, but very few have focused on thermostability. To bridge this gap, we developed an algorithm for predicting the best descriptor of thermostability, namely the melting temperature , from the protein's sequence and structure. Our method is applicable when the of proteins homologous to the target protein are known. It is based on the design of several temperature-dependent statistical potentials, derived from datasets consisting of either mesostable or thermostable proteins. Linear combinations of these potentials have been shown to yield an estimation of the protein folding free energies at low and high temperatures, and the difference of these energies, a prediction of the melting temperature. This particular construction, that distinguishes between the interactions that contribute more than others to the stability at high temperatures and those that are more stabilizing at low , gives better performances compared to the standard approach based on -independent potentials which predict the thermal resistance from the thermodynamic stability. Our method has been tested on 45 proteins of known that belong to 11 homologous families. The standard deviation between experimental and predicted 's is equal to 13.6°C in cross validation, and decreases to 8.3°C if the 6 worst predicted proteins are excluded. Possible extensions of our approach are discussed.

Bioinformatics tools that predict protein stability changes upon point mutations have made a lot of progress in the last decades and have become accurate and fast enough to make computational mutagenesis experiments feasible, even on a proteome scale. Despite these achievements, they still suffer from important issues that must be solved to allow further improving their performances and utilizing them to deepen our insights into protein folding and stability mechanisms. One of these problems is their bias towards the learning datasets which, being dominated by destabilizing mutations, causes predictions to be better for destabilizing than for stabilizing mutations. We thoroughly analyzed the biases in the prediction of folding free energy changes upon point mutations (∆∆G 0 ) and proposed some unbiased solutions. We started by constructing a dataset S sym of experimentally measured ∆∆G 0 s with an equal number of stabilizing and destabilizing mutations, by collecting mutations for which the structure of both the wild type and mutant protein is available. On this balanced dataset, we assessed the performances of fifteen widely used ∆∆G 0 predictors. After the astonishing observation that almost all these methods are strongly biased towards destabilizing mutations, especially those that use blackbox machine learning, we proposed an elegant way to solve the bias issue by imposing physical symmetries under inverse mutations on the model structure, which we implemented in PoPMuSiC sym . This new predictor constitutes an efficient trade-off between accuracy and absence of biases. Some final considerations and suggestions for further improvement of the predictors are discussed.

We study the correlators of a recently discovered family of BPS Wilson loops in N = 4 supersymmetric U (N ) Yang-Mills theory. When the contours lie on a two-sphere in the space-time, we propose a closed expression that is valid for all values of the coupling constant g and for any rank N , by exploiting the suspected relation with two-dimensional gauge theories. We check this formula perturbatively at order O(g 4 ) for two latitude Wilson loops and we show that, in the limit where one of the loops shrinks to a point, logarithmic corrections in the shrinking radius are absent at O(g 6 ). This last result strongly supports the validity of our general expression and suggests the existence of a peculiar protected local operator arising in the OPE of the Wilson loop. At strong coupling we compare our result to the string dual of the N = 4 SYM correlator in the limit of large separation, presenting some preliminary evidence for the agreement.

A direct connection is proved between the Non-Abelian Bianchi Identities(NABI), and the abelian Bianchi identities for the 't Hooft tensor. As a consequence the existence of a non-zero magnetic current is related to the violation of the NABI's and is a gauge-invariant property. The construction allows to show that not all abelian projections can be used to expose monopoles in lattice configurations: each field configuration with non-zero magnetic charge identifies its natural projection, up to gauge transformations which tend to unity at large distances. It is shown that the so-called maximal-abelian gauge is a legitimate choice. It is also proved, starting from the NABI, that monopole condensation is a physical gauge invariant phenomenon, independent of the choice of the abelian projection.

The accurate prediction of the impact of an amino acid substitution on the thermal stability of a protein is a central issue in protein science, and is of key relevance for the rational optimization of various bioprocesses that use enzymes in unusual conditions. Here we present one of the first computational tools to predict the change in melting temperature ∆T m upon point mutations, given the protein structure and, when available, the melting temperature T m of the wild-type protein.The key ingredients of our model structure are standard and temperature-dependent statistical potentials, which are combined with the help of an artificial neural network. The model structure was chosen on the basis of a detailed thermodynamic analysis of the system. The parameters of the model were identified on a set of more than 1,600 mutations with experimentally measured ∆T m .The performance of our method was tested using a strict 5-fold cross-validation procedure, and was found to be significantly superior to that of competing methods. We obtained a root mean square deviation between predicted and experimental ∆T m values of 4.2°C that reduces to 2.9°C when ten percent outliers are removed. A webserver-based tool is freely available for non-commercial use at soft.dezyme.com. * fapucci@ulb.ac.be † rbourgeas@ulb.ac.be ‡ mrooman@ulb.ac.be 1 not peer-reviewed)