Inverse folding models have proven to be highly effective zero-shot predictors of protein stability. Despite this success, the link between the amino acid preferences of an inverse folding model and the free-energy considerations underlying thermodynamic stability remains incompletely understood. A better understanding would be of interest not only from a theoretical perspective, but also potentially provide the basis for stronger zero-shot stability prediction. In this paper, we take steps to clarify the free-energy foundations of inverse folding models. Our derivation reveals the standard practice of likelihood ratios as a simplistic approximation and suggests several paths towards better estimates of the relative stability. We empirically assess these approaches and demonstrate that considerable gains in zero-shot performance can be achieved with fairly simple means.

Bayesian optimization (BO) is an attractive machine learning framework for performing sample-efficient global optimization of black-box functions. The optimization process is guided by an acquisition function that selects points to acquire in each round of BO. In batched BO, when multiple points are acquired in parallel, commonly used acquisition functions are often high-dimensional and intractable, leading to the use of sampling-based alternatives. We propose a statistical physics inspired acquisition function that can natively handle batches. Batched Energy-Entropy acquisition for BO (BEEBO) enables tight control of the explore-exploit trade-off of the optimization process and generalizes to heteroskedastic black-box problems. We demonstrate the applicability of BEEBO on a range of problems, showing competitive performance to existing acquisition functions.

Cell migration is a central biological process that requires fine coordination of molecular events in time and space. A deregulation of the migratory phenotype is also associated with pathological conditions including cancer where cell motility has a causal role in tumor spreading and metastasis formation. Thus cell migration is of critical and strategic importance across the complex disease spectrum as well as for the basic understanding of cell phenotype. Experimental studies of the migration of cells in monolayers are often conducted with 'wound healing' assays. Analysis of these assays has traditionally relied on how the wound area changes over time. However this method does not take into account the shape of the wound. Given the many options for creating a wound healing assay and the fact that wound shape invariably changes as cells migrate this is a significant flaw. Here we present a novel software package for analyzing concerted cell velocity in wound healing assays. Our method encompasses a wound detection algorithm based on cell confluency thresholding and employs a Bayesian approach in order to estimate concerted cell velocity with an associated likelihood. We have applied this method to study the effect of siRNA knockdown on the migration of a breast cancer cell line and demonstrate that cell velocity can track wound healing independently of wound shape and provides a more robust quantification with significantly higher signal to noise ratios than conventional analyses of wound area. The software presented here will enable other researchers in any field of cell biology to quantitatively analyze and track live cell migratory processes and is therefore expected to have a significant impact on the study of cell migration, including cancer relevant processes. Installation instructions, documentation and source code can be found at http://bowhead.lindinglab.science licensed under GPLv3.

Bayesian generalised ensemble (BayesGE) is a new method that addresses two major drawbacks of standard Markov chain Monte Carlo algorithms for inference in high-dimensional probability models: inapplicability to estimate the partition function and poor mixing properties. BayesGE uses a Bayesian approach to iteratively update the belief about the density of states (distribution of the log likelihood under the prior) for the model, with the dual purpose of enhancing the sampling efficiency and making the estimation of the partition function tractable. We benchmark BayesGE on Ising and Potts systems and show that it compares favourably to existing state-of-the-art methods.

A key component of computational biology is to compare the results of computer modelling with experimental measurements. Despite substantial progress in the models and algorithms used in many areas of computational biology, such comparisons sometimes reveal that the computations are not in quantitative agreement with experimental data. The principle of maximum entropy is a general procedure for constructing probability distributions in the light of new data, making it a natural tool in cases when an initial model provides results that are at odds with experiments. The number of maximum entropy applications in our field has grown steadily in recent years, in areas as diverse as sequence analysis, structural modelling, and neurobiology. In this Perspectives article, we give a broad introduction to the method, in an attempt to encourage its further adoption. The general procedure is explained in the context of a simple example, after which we proceed with a real-world application in the field of molecular simulations, where the maximum entropy procedure has recently provided new insight. Given the limited accuracy of force fields, macromolecular simulations sometimes produce results that are at not in complete and quantitative accordance with experiments. A common solution to this problem is to explicitly ensure agreement between the two by perturbing the potential energy function towards the experimental data. So far, a general consensus for how such perturbations should be implemented has been lacking. Three very recent papers have explored this problem using the maximum entropy approach, providing both new theoretical and practical insights to the problem. We highlight each of these contributions in turn and conclude with a discussion on remaining challenges.

BACKGROUND: Genome sequencing projects have expanded the gap between the amount of known protein sequences and structures. The limitations of current high resolution structure determination methods make it unlikely that this gap will disappear in the near future. Small angle X-ray scattering (SAXS) is an established low resolution method for routinely determining the structure of proteins in solution. The purpose of this study is to develop a method for the efficient calculation of accurate SAXS curves from coarse-grained protein models. Such a method can for example be used to construct a likelihood function, which is paramount for structure determination based on statistical inference. RESULTS: We present a method for the efficient calculation of accurate SAXS curves based on the Debye formula and a set of scattering form factors for dummy atom representations of amino acids. Such a method avoids the computationally costly iteration over all atoms. We estimated the form factors using generated data from a set of high quality protein structures. No ad hoc scaling or correction factors are applied in the calculation of the curves. Two coarse-grained representations of protein structure were investigated; two scattering bodies per amino acid led to significantly better results than a single scattering body. CONCLUSION: We show that the obtained point estimates allow the calculation of accurate SAXS curves from coarse-grained protein models. The resulting curves are on par with the current state-of-the-art program CRYSOL, which requires full atomic detail. Our method was also comparable to CRYSOL in recognizing native structures among native-like decoys. As a proof-of-concept, we combined the coarse-grained Debye calculation with a previously described probabilistic model of protein structure, TorusDBN. This resulted in a significant improvement in the decoy recognition performance. In conclusion, the presented method shows great promise for use in statistical inference of protein structures from SAXS data.

The increasing importance of non-coding RNA in biology and medicine has led to a growing interest in the problem of RNA 3-D structure prediction. As is the case for proteins, RNA 3-D structure prediction methods require two key ingredients: an accurate energy function and a conformational sampling procedure. Both are only partly solved problems. Here, we focus on the problem of conformational sampling. The current state of the art solution is based on fragment assembly methods, which construct plausible conformations by stringing together short fragments obtained from experimental structures. However, the discrete nature of the fragments necessitates the use of carefully tuned, unphysical energy functions, and their non-probabilistic nature impairs unbiased sampling. We offer a solution to the sampling problem that removes these important limitations: a probabilistic model of RNA structure that allows efficient sampling of RNA conformations in continuous space, and with associated probabilities. We show that the model captures several key features of RNA structure, such as its rotameric nature and the distribution of the helix lengths. Furthermore, the model readily generates native-like 3-D conformations for 9 out of 10 test structures, solely using coarse-grained base-pairing information. In conclusion, the method provides a theoretical and practical solution for a major bottleneck on the way to routine prediction and simulation of RNA structure and dynamics in atomic detail.

Current experiments likely cover only a fraction of all protein-protein interactions. Here, we developed a method to predict SH2-mediated protein-protein interactions using the structure of SH2-phosphopeptide complexes and the FoldX algorithm. We show that our approach performs similarly to experimentally derived consensus sequences and substitution matrices at predicting known in vitro and in vivo targets of SH2 domains. We use our method to provide a set of high-confidence interactions for human SH2 domains with known structure filtered on secondary structure and phosphorylation state. We validated the predictions using literature-derived SH2 interactions and a probabilistic score obtained from a naive Bayes integration of information on coexpression, conservation of the interaction in other species, shared interaction partners, and functions. We show how our predictions lead to a new hypothesis for the role of SH2 domains in signaling.