Michael Andrec

A large data set comparison of protein structures determined by crystallography and NMR: Statistical test for structural differences and the effect of crystal packing

The existence of a large number of proteins for which both nuclear magnetic resonance (NMR) and X‐ray crystallographic coordinates have been deposited into the Protein Data Bank (PDB) makes the statistical comparison of the corresponding crystal and NMR structural models over a large data set possible, and facilitates the study of the effect of the crystal environment and other factors on structure. We present an approach for detecting statistically significant structural differences between crystal and NMR structural models which is based on structural superposition and the analysis of the distributions of atomic positions relative to a mean structure. We apply this to a set of 148 protein structure pairs (crystal vs NMR), and analyze the results in terms of methodological and physical sources of structural difference. For every one of the 148 structure pairs, the backbone root‐mean‐square distance (RMSD) over core atoms of the crystal structure to the mean NMR structure is larger than the average RMSD of the members of the NMR ensemble to the mean, with 76% of the structure pairs having an RMSD of the crystal structure to the mean more than a factor of two larger than the average RMSD of the NMR ensemble. On average, the backbone RMSD over core atoms of crystal structure to the mean NMR is approximately 1 Å. If non‐core atoms are included, this increases to 1.4 Å due to the presence of variability in loops and similar regions of the protein. The observed structural differences are only weakly correlated with the age and quality of the structural model and differences in conditions under which the models were determined. We examine steric clashes when a putative crystalline lattice is constructed using a representative NMR structure, and find that repulsive crystal packing plays a minor role in the observed differences between crystal and NMR structures. The observed structural differences likely have a combination of physical and methodological causes. Stabilizing attractive interactions arising from intermolecular crystal contacts which shift the equilibrium of the crystal structure relative to the NMR structure is a likely physical source which can account for some of the observed differences. Methodological sources of apparent structural difference include insufficient sampling or other issues which could give rise to errors in the estimates of the precision and/or accuracy. Proteins 2007.

Simulating replica exchange simulations of protein folding with a kinetic network model

Replica exchange (RE) is a generalized ensemble simulation method for accelerating the exploration of free-energy landscapes, which define many challenging problems in computational biophysics, including protein folding and binding. Although temperature RE (T-RE) is a parallel simulation technique whose implementation is relatively straightforward, kinetics and the approach to equilibrium in the T-RE ensemble are very complicated; there is much to learn about how to best employ T-RE to protein folding and binding problems. We have constructed a kinetic network model for RE studies of protein folding and used this reduced model to carry out “simulations of simulations” to analyze how the underlying temperature dependence of the conformational kinetics and the basic parameters of RE (e.g., the number of replicas, the RE rate, and the temperature spacing) all interact to affect the number of folding transitions observed. When protein folding follows anti-Arrhenius kinetics, we observe a speed limit for the number of folding transitions observed at the low temperature of interest, which depends on the maximum of the harmonic mean of the folding and unfolding transition rates at high temperature. The results shown here for the network RE model suggest ways to improve atomic-level RE simulations such as the use of “training” simulations to explore some aspects of the temperature dependence for folding of the atomic-level models before performing RE studies.

Protein backbone structure determination using only residual dipolar couplings from one ordering medium.

Residual dipolar couplings provide significant structural information for proteins in the solution state, which makes them attractive for the rapid determination of protein folds. Unfortunately, dipolar couplings contain inherent structural ambiguities which make them difficult to use in the absence of additional information. In this paper, we describe an approach to the construction of protein backbone folds using experimental dipolar couplings based on a bounded tree search through a structural database. We filter out false positives via an overlap similarity measure that insists that protein fragments assigned to overlapping regions of the sequence must have self-consistent structures. This allows us to determine a backbone fold (including the correct Cα-Cβ bond orientations) using only residual dipolar coupling data obtained from one ordering medium. We demonstrate the applicability of the method using experimental data for ubiquitin.

Pairwise and higher-order correlations among drug-resistance mutations in HIV-1 subtype B protease

BackgroundThe reaction of HIV protease to inhibitor therapy is characterized by the emergence of complex mutational patterns which confer drug resistance. The response of HIV protease to drugs often involves both primary mutations that directly inhibit the action of the drug, and a host of accessory resistance mutations that may occur far from the active site but may contribute to restoring the fitness or stability of the enzyme. Here we develop a probabilistic approach based on connected information that allows us to study residue, pair level and higher-order correlations within the same framework.ResultsWe apply our methodology to a database of approximately 13,000 sequences which have been annotated by the treatment history of the patients from which the samples were obtained. We show that including pair interactions is essential for agreement with the mutational data, since neglect of these interactions results in order-of-magnitude errors in the probabilities of the simultaneous occurence of many mutations. The magnitude of these pair correlations changes dramatically between sequences obtained from patients that were or were not exposed to drugs. Higher-order effects make a contribution of as much as 10% for residues taken three at a time, but increase to more than twice that for 10 to 15-residue groups. The sequence data is insufficient to determine the higher-order effects for larger groups. We find that higher-order interactions have a significant effect on the predicted frequencies of sequences with large numbers of mutations. While relatively rare, such sequences are more prevalent after multi-drug therapy. The relative importance of these higher-order interactions increases with the number of drugs the patient had been exposed to.ConclusionCorrelations are critical for the understanding of mutation patterns in HIV protease. Pair interactions have substantial qualitative effects, while higher-order interactions are individually smaller but may have a collective effect. Together they lead to correlations which could have an important impact on the dynamics of the evolution of cross-resistance, by allowing the virus to pass through otherwise unlikely mutational states. These findings also indicate that pairwise and possibly higher-order effects should be included in the models of protein evolution, instead of assuming that all residues mutate independently of one another.

Complete protein structure determination using backbone residual dipolar couplings and sidechain rotamer prediction

Residual dipolar couplings provide significant structural information for proteins in the solution state, which makes them attractive for the rapid determination of protein structures. While dipolar couplings contain inherent structural ambiguities, these can be reduced via an overlap similarity measure that insists that protein fragments assigned to overlapping regions of the sequence must have self-consistent structures. This allows us to determine a backbone fold (including the correct Cα–Cβ bond orientations) using only residual dipolar coupling data from one ordering medium. The resulting backbone structures are of sufficient quality to allow for modeling of sidechain rotamer states using a rotamer prediction algorithm and a force field employing the Surface Generalized Born continuum solvation model. We demonstrate the applicability of the method using experimental data for ubiquitin. These results illustrate the synergies that are possible between protein structural database and molecular modeling methods and NMR spectroscopy, and we expect that the further development of these methods will lead to the extraction of high resolution structural information from minimal NMR data.

Recovering Kinetics from a Simplified Protein Folding Model Using Replica Exchange Simulations: A Kinetic Network and Effective Stochastic Dynamics

We present an approach to recover kinetics from a simplified protein folding model at different temperatures using the combined power of replica exchange (RE), a kinetic network, and effective stochastic dynamics. While RE simulations generate a large set of discrete states with the correct thermodynamics, kinetic information is lost due to the random exchange of temperatures. We show how we can recover the kinetics of a 2D continuous potential with an entropic barrier by using RE-generated discrete states as nodes of a kinetic network. By choosing the neighbors and the microscopic rates between the neighbors appropriately, the correct kinetics of the system can be recovered by running a kinetic simulation on the network. We fine-tune the parameters of the network by comparison with the effective drift velocities and diffusion coefficients of the system determined from short-time stochastic trajectories. One of the advantages of the kinetic network model is that the network can be built on a high-dimensional discretized state space, which can consist of multiple paths not consistent with a single reaction coordinate.

Quantitation of chemical exchange rates using pulsed-field-gradient diffusion measurements

A new approach to the quantitation of chemical exchange rates is presented, and its utility isillustrated with application to the exchange of protein amide protons with bulk water. Theapproach consists of a selective-inversion exchange HMQC experiment in which a short spinecho diffusion filter has been inserted into the exchange period. In this way, the kinetics ofexchange are encoded directly in an apparent diffusion coefficient which is a function of theposition of the diffusion filter in the pulse sequence. A detailed theoretical analysis of thisexperiment indicates that, in addition to the measurement of simple exchange rates, theexperiment is capable of measuring the effect of mediated exchange, e.g. the transfer ofmagnetization from bulk water to an amide site mediated by an internal bound water moleculeor a labile protein side-chain proton in fast exchange with bulk water. Experimental resultsfor rapid water/amide exchange in acyl carrier protein are shown to be quantitativelyconsistent with the exchange rates measured using a selective-inversion exchange experiment.

Correlated Electrostatic Mutations Provide a Reservoir of Stability in HIV Protease

HIV protease, an aspartyl protease crucial to the life cycle of HIV, is the target of many drug development programs. Though many protease inhibitors are on the market, protease eventually evades these drugs by mutating at a rapid pace and building drug resistance. The drug resistance mutations, called primary mutations, are often destabilizing to the enzyme and this loss of stability has to be compensated for. Using a coarse-grained biophysical energy model together with statistical inference methods, we observe that accessory mutations of charged residues increase protein stability, playing a key role in compensating for destabilizing primary drug resistance mutations. Increased stability is intimately related to correlations between electrostatic mutations – uncorrelated mutations would strongly destabilize the enzyme. Additionally, statistical modeling indicates that the network of correlated electrostatic mutations has a simple topology and has evolved to minimize frustrated interactions. The models statistical coupling parameters reflect this lack of frustration and strongly distinguish like-charge electrostatic interactions from unlike-charge interactions for of the most significantly correlated double mutants. Finally, we demonstrate that our model has considerable predictive power and can be used to predict complex mutation patterns, that have not yet been observed due to finite sample size effects, and which are likely to exist within the larger patient population whose virus has not yet been sequenced.

Protein sequential resonance assignments by combinatorial enumeration using 13C alpha chemical shifts and their (i, i-1) sequential connectivities.

The need for the structural characterization of proteins on a genomic scale has brought with it demands for new technology to speed the structure determination process. In NMR, one bottleneck is the sequential assignment of backbone resonances. In this paper, we explore the computational complexity of the sequential assignment problem using only 13Cα chemical shift data and Cα (i,i−1) sequential connectivity information, all of which can potentially be obtained from a single three-dimensional NMR spectrum. Although it is generally believed that there is too much ambiguity in such data to provide sufficient information for sequential assignment, we show that a straightforward combinatorial search algorithm can be used to find correct and unambiguous sequential assignments in a reasonable amount of CPU time for small proteins (approximately 80 residues or smaller) when there is little missing data. The deleterious effect of missing or spurious peaks and the dependence on match tolerances is also explored. This simple algorithm could be used as part of a semi-automated, interactive assignment procedure, e.g., to test partial manually determined solutions fo uniqueness and to extend these solutions.

Performance of a neural-network-based determination of amino acid class and secondary structure from 1H-15N NMR data

A neural network which can determine both amino acid class andsecondary structure using NMR data from 15N-labeled proteinsis described. We have included nitrogen chemical shifts,3JHNHα coupling constants, α-protonchemical shifts, and side-chain proton chemical shifts as input to athree-layer feed-forward network. The network was trained with 456 spinsystems from several proteins containing various types of secondarystructure, and tested on human ubiquitin, which has no sequence homologywith any of the proteins in the training set. A very limited set of data,representative of those from a TOCSY-HSQC and HNHA experiment, was used.Nevertheless, in 60% of the spin systems the correct amino acid classwas among the top two choices given by the network, while in 96% ofthe spin systems the secondary structure was correctly identified. Theperformance of this network clearly shows the potential of the neuralnetwork algorithm in the automation of NMR spectral analysis.