A Rigorous and Efficient Method To Reweight Very Large Conformational Ensembles Using Average Experimental Data and To Determine Their Relative Information Content.

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.

Backbone hydration determines the folding signature of amino acid residues.

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.

NMR characterization of the conformational fluctuations of the human lymphocyte function-associated antigen-1 I-domain.

Lymphocyte function-associated antigen-1 (LFA-1) is an integrin protein that transmits information across the plasma membrane through the so-called inside-out and outside-in signaling mechanisms. To investigate these mechanisms, we carried out an NMR analysis of the dynamics of the LFA-1 I-domain, which has enabled us to characterize the motions of this domain on a broad range of timescales. We studied first the internal motions on the nanosecond timescale by spin relaxation measurements and model-free analysis. We then extended this analysis to the millisecond timescale motions by measuring (15) N-(1) H residual dipolar couplings of the backbone amide groups. We analyzed these results in the context of the three major conformational states of the I-domain using their corresponding X-ray crystallographic structures. Our results highlight the importance of the low-frequency motions of the LFA-1 I-domain in the inactive apo-state. We found in particular that α-helix 7 is in a position in the apo-closed state that cannot be fully described by any of the existing X-ray structures, as it appears to be in dynamic exchange between different conformations. This type of motion seems to represent an inherent property of the LFA-1 I-domain and might be relevant for controlling the access to the allosteric binding pocket, as well as for the downward displacement of α-helix 7 that is required for the activation of LFA-1.