Flexible polypeptides such as unfolded proteins may access an astronomical number of conformations. The most advanced simulations of such states usually comprise tens of thousands of individual structures. In principle, a comparison of parameters predicted from such ensembles to experimental data provides a measure of their quality. In practice, analyses that go beyond the comparison of unbiased average data have been impossible to carry out on the entirety of such very large ensembles and have, therefore, been restricted to much smaller subensembles and/or nondeterministic algorithms. Here, we show that such very large ensembles, on the order of 10(4) to 10(5) conformations, can be analyzed in full by a maximum entropy fit to experimental average data. Maximizing the entropy of the population weights of individual conformations under experimental χ(2) constraints is a convex optimization problem, which can be solved in a very efficient and robust manner to a unique global solution even for very large ensembles. Since the population weights can be determined reliably, the reweighted full ensemble presents the best model of the combined information from simulation and experiment. Furthermore, since the reduction of entropy due to the experimental constraints is well-defined, its value provides a robust measure of the information content of the experimental data relative to the simulated ensemble and an indication for the density of the sampling of conformational space. The method is applied to the reweighting of a 35,000 frame molecular dynamics trajectory of the nonapeptide EGAAWAASS by extensive NMR (3)J coupling and RDC data. The analysis shows that RDCs provide significantly more information than (3)J couplings and that a discontinuity in the RDC pattern at the central tryptophan is caused by a cluster of helical conformations. Reweighting factors are moderate and consistent with errors in MD force fields of less than 3kT. The required reweighting is larger for an ensemble derived from a statistical coil model, consistent with its coarser nature. We call the method COPER, for convex optimization for ensemble reweighting. Similar advantages of large-scale efficiency and robustness can be obtained for other ensemble analysis methods with convex targets and constraints, such as constrained χ(2) minimization and the maximum occurrence method.

SummaryLymphocyte function-associated antigen 1 (LFA-1) is an integrin that transmits information in two directions across the plasma membrane of leukocytes, in so-called outside-in and inside-out signaling mechanisms. To investigate the structural basis of these mechanisms, we studied the conformational space of the apo I-domain using replica-averaged metadynamics simulations in combination with nuclear magnetic resonance chemical shifts. We thus obtained a free energy landscape that reveals the existence of three conformational substates of this domain. The three substates include conformations similar to existing crystallographic structures of the low-affinity I-domain, the inactive I-domain with an allosteric antagonist inhibitor bound underneath α helix 7, and an intermediate affinity state of the I-domain. The multiple substates were validated with residual dipolar coupling measurements. These results suggest that the presence of three substates in the apo I-domain enables the precise regulation of the binding process that is essential for the physiological function of LFA-1.

The relation between the sequence of a protein and its three-dimensional structure remains largely unknown. A lasting dream is to elucidate the side-chain-dependent driving forces that govern the folding process. Different structural data suggest that aromatic amino acids play a particular role in the stabilization of protein structures. To better understand the underlying mechanism, we studied peptides of the sequence EGAAXAASS (X = Gly, Ile, Tyr, Trp) through comparison of molecular dynamics (MD) trajectories and NMR residual dipolar coupling (RDC) measurements. The RDC data for aromatic substitutions provide evidence for a kink in the peptide backbone. Analysis of the MD simulations shows that the formation of internal hydrogen bonds underlying a helical turn is key to reproduce the experimental RDC values. The simulations further reveal that the driving force leading to such helical-turn conformations arises from the lack of hydration of the peptide chain on either side of the bulky aromatic side chain, which can potentially act as a nucleation point initiating the folding process.