Ensemble refinement produces structural ensembles of flexible and dynamic biomolecules by integrating experimental data and molecular simulations. Here we present two efficient numerical methods to solve the computationally challenging maximum-entropy problem arising from a Bayesian formulation of ensemble refinement. Recasting the resulting constrained weight optimization problem into an unconstrained form enables the use of gradient-based algorithms. In two complementary formulations that differ in their dimensionality, we optimize either the log-weights directly or the generalized forces appearing in the explicit analytical form of the solution. We first demonstrate the robustness, accuracy, and efficiency of the two methods using synthetic data. We then use NMR J -couplings to reweight an all-atom molecular dynamics simulation ensemble of the disordered peptide Ala-5 simulated with the AMBER99SB*-ildn-q force field. After reweighting, we find a consistent increase in the population of the polyproline-II conformations and a decrease of α-helical-like conformations. Ensemble refinement makes it possible to infer detailed structural models for biomolecules exhibiting significant dynamics, such as intrinsically disordered proteins, by combining input from experiment and simulation in a balanced manner.

Blood glucose control, for example, in diabetes mellitus or severe illness, requires strict adherence to a protocol of food, insulin administration and exercise personalized to each patient. An artificial pancreas for automated treatment could boost quality of glucose control and patients' independence. The components required for an artificial pancreas are: i) continuous glucose monitoring (CGM), ii) smart controllers and iii) insulin pumps delivering the optimal amount of insulin. In recent years, medical devices for CGM and insulin administration have undergone rapid progression and are now commercially available. Yet, clinically available devices still require regular patients' or caregivers' attention as they operate in open-loop control with frequent user intervention. Dosage-calculating algorithms are currently being studied in intensive care patients [1] , for short overnight control to supplement conventional insulin delivery [2] , and for short periods where patients rest and follow a prescribed food regime [3] . Fully automated algorithms that can respond to the varying activity levels seen in outpatients, with unpredictable and unreported food intake, and which provide the necessary personalized control for individuals is currently beyond the state-of-the-art. Here, we review and discuss reinforcement learning algorithms, controlling insulin in a closed-loop to provide individual insulin dosing regimens that are reactive to the immediate needs of the patient.

Double electron-electron resonance (DEER) experiments probe nanometer-scale distances in spin-labeled proteins and nucleic acids. Rotamer libraries of the covalently attached spin-labels help reduce position uncertainties. Here we show that rotamer reweighting is essential for precision distance measurements, making it possible to resolve Ångstrom-scale domain motions. We analyze extensive DEER measurements on the three N-terminal polypeptide transport-associated (POTRA) domains of the outer membrane protein Omp85. Using the "Bayesian inference of ensembles" maximum-entropy method, we extract rotamer weights from the DEER measurements. Small weight changes suffice to eliminate otherwise significant discrepancies between experiments and model and unmask 1-3 Å domain motions relative to the crystal structure. Rotamer-weight refinement is a simple yet powerful tool for precision distance measurements that should be broadly applicable to label-based measurements including DEER, paramagnetic relaxation enhancement, and fluorescence resonance energy transfer (FRET).

The SLC26 family of transporters maintains anion equilibria in all kingdoms of life. The family shares a 7 + 7 transmembrane segments inverted repeat architecture with the SLC4 and SLC23 families, but holds a regulatory STAS domain in addition. While the only experimental SLC26 structure is monomeric, SLC26 proteins form structural and functional dimers in the lipid membrane. Here we resolve the structure of an SLC26 dimer embedded in a lipid membrane and characterize its functional relevance by combining PELDOR/DEER distance measurements and biochemical studies with MD simulations and spin-label ensemble refinement. Our structural model reveals a unique interface different from the SLC4 and SLC23 families. The functionally relevant STAS domain is no prerequisite for dimerization. Characterization of heterodimers indicates that protomers in the dimer functionally interact. The combined structural and functional data define the framework for a mechanistic understanding of functional cooperativity in SLC26 dimers.