Robert B. Best

Simultaneous determination of protein structure and dynamics

We present a protocol for the experimental determination of ensembles of protein conformations that represent simultaneously the native structure and its associated dynamics. The procedure combines the strengths of nuclear magnetic resonance spectroscopy—for obtaining experimental information at the atomic level about the structural and dynamical features of proteins—with the ability of molecular dynamics simulations to explore a wide range of protein conformations. We illustrate the method for human ubiquitin in solution and find that there is considerable conformational heterogeneity throughout the protein structure. The interior atoms of the protein are tightly packed in each individual conformation that contributes to the ensemble but their overall behaviour can be described as having a significant degree of liquid-like character. The protocol is completely general and should lead to significant advances in our ability to understand and utilize the structures of native proteins.

Optimized molecular dynamics force fields applied to the helix-coil transition of polypeptides.

Obtaining the correct balance of secondary structure propensities is a central priority in protein force-field development. Given that current force fields differ significantly in their alpha-helical propensities, a correction to match experimental results would be highly desirable. We have determined simple backbone energy corrections for two force fields to reproduce the fraction of helix measured in short peptides at 300 K. As validation, we show that the optimized force fields produce results in excellent agreement with nuclear magnetic resonance experiments for folded proteins and short peptides not used in the optimization. However, despite the agreement at ambient conditions, the dependence of the helix content on temperature is too weak, a problem shared with other force fields. A fit of the Lifson-Roig helix-coil theory shows that both the enthalpy and entropy of helix formation are too small: the helix extension parameter w agrees well with experiment, but its entropic and enthalpic components are both only about half the respective experimental estimates. Our structural and thermodynamic analyses point toward the physical origins of these shortcomings in current force fields, and suggest ways to address them in future force-field development.

Are Current Molecular Dynamics Force Fields too Helical

Accurate force fields are essential for the success of molecular dynamics simulations. In apparent contrast to the conformational preferences of most force fields, recent NMR experiments suggest that short polyalanine peptides in water populate the polyproline II structure almost exclusively. To investigate this apparent contradiction, with its ramifications for the assessment of molecular force fields and the structure of unfolded proteins, we performed extensive simulations of Ala(5) in water ( approximately 5 micros total time), using twelve different force fields and three different peptide terminal groups. Using either empirical or density-functional-based Karplus relations for the J-couplings, we find that most current force fields do overpopulate the alpha-region, with quantitative results depending on the choice of Karplus relation and on the peptide termini. Even after reweighting to match experiment, we find that Ala(5) retains significant alpha- and beta-populations. In fact, several force fields match the experimental data well before reweighting and have a significant helical population. We conclude that radical changes to the best current force fields are not necessary, based on the NMR data. Nevertheless, experiments on short peptides open the way toward the systematic improvement of current simulation models.

Characterizing the unfolded states of proteins using single-molecule FRET spectroscopy and molecular simulations

To obtain quantitative information on the size and dynamics of unfolded proteins we combined single-molecule lifetime and intensity FRET measurements with molecular simulations. We compared the unfolded states of the 64-residue, α/β protein L and the 66-residue, all-β cold-shock protein CspTm. The average radius of gyration (Rg) calculated from FRET data on freely diffusing molecules was identical for the two unfolded proteins at guanidinium chloride concentrations >3 M, and the FRET-derived Rg of protein L agreed well with the Rg previously measured by equilibrium small-angle x-ray scattering. As the denaturant concentration was lowered, the mean FRET efficiency of the unfolded subpopulation increased, signaling collapse of the polypeptide chain, with protein L being slightly more compact than CspTm. A decrease in Rg with decreasing denaturant was also observed in all-atom molecular dynamics calculations in explicit water/urea solvent, and Langevin simulations of a simplified representation of the polypeptide suggest that collapse can result from either increased interresidue attraction or decreased excluded volume. In contrast to both the FRET and simulation results, previous time-resolved small-angle x-ray scattering experiments showed no collapse for protein L. Analysis of the donor fluorescence decay of the unfolded subpopulation of both proteins gives information about the end-to-end chain distribution and suggests that chain dynamics is slow compared with the donor life-time of ≈2 ns, whereas the bin-size independence of the small excess width above the shot noise for the FRET efficiency distributions may result from incomplete conformational averaging on even the 1-ms time scale.

Hidden complexity in the mechanical properties of titin

Individual molecules of the giant protein titin span the A-bands and I-bands that make up striated muscle. The I-band region of titin is responsible for passive elasticity in such muscle, and contains tandem arrays of immunoglobulin domains. One such domain (I27) has been investigated extensively, using dynamic force spectroscopy and simulation. However, the relevance of these studies to the behaviour of the protein under physiological conditions was not established. Force studies reveal a lengthening of I27 without complete unfolding, forming a stable intermediate that has been suggested to be an important component of titin elasticity. To develop a more complete picture of the forced unfolding pathway, we use mutant titins—certain mutations allow the role of the partly unfolded intermediate to be investigated in more depth. Here we show that, under physiological forces, the partly unfolded intermediate does not contribute to mechanical strength. We also propose a unified forced unfolding model of all I27 analogues studied, and conclude that I27 can withstand higher forces in muscle than was predicted previously.

Can Non-Mechanical Proteins Withstand Force? Stretching Barnase by Atomic Force Microscopy and Molecular Dynamics Simulation

Atomic force microscopy (AFM) experiments have provided intriguing insights into the mechanical unfolding of proteins such as titin I27 from muscle, but will the same be possible for proteins that are not physiologically required to resist force? We report the results of AFM experiments on the forced unfolding of barnase in a chimeric construct with I27. Both modules are independently folded and stable in this construct and have the same thermodynamic and kinetic properties as the isolated proteins. I27 can be identified in the AFM traces based on its previous characterization, and distinct, irregular low-force peaks are observed for barnase. Molecular dynamics simulations of barnase unfolding also show that it unfolds at lower forces than proteins with mechanical function. The unfolding pathway involves the unraveling of the protein from the termini, with much more native-like secondary and tertiary structure being retained in the transition state than is observed in simulations of thermal unfolding or experimentally, using chemical denaturant. Our results suggest that proteins that are not selected for tensile strength may not resist force in the same way as those that are, and that proteins with similar unfolding rates in solution need not have comparable unfolding properties under force.

Mechanical Unfolding of a Titin Ig Domain: Structure of Unfolding Intermediate Revealed by Combining AFM, Molecular Dynamics Simulations, NMR and Protein Engineering

The mechanical unfolding of an immunoglobulin domain from the human muscle protein titin (TI I27) has been shown to proceed via a metastable intermediate in which the A-strand is detached. The structure and properties of this intermediate are characterised in this study. A conservative destabilising mutation in the A-strand has no effect on the unfolding force, nor the dependence of the unfolding force on the pulling speed, indicating that the unfolding forces measured in an AFM experiment are those required for the unfolding of the intermediate and not the native state. A mutant of TI I27 with the A-strand deleted (TI I27-A) is studied by NMR and standard biophysical techniques, combined with protein engineering. Molecular dynamics simulations show TI I27-A to be a good model for the intermediate. It has a structure very similar to the native state, and is surprisingly stable. Comparison with a Phi-value analysis of the unfolding pathway clearly shows that the protein unfolds by a different pathway under an applied force than on addition of denaturant.

Coordinate-dependent diffusion in protein folding

Diffusion on a low-dimensional free-energy surface is a remarkably successful model for the folding dynamics of small single-domain proteins. Complicating the interpretation of both simulations and experiments is the expectation that the effective diffusion coefficient D will in general depend on the position along the folding coordinate, and this dependence may vary for different coordinates. Here we explore the position dependence of D, its connection to protein internal friction, and the consequences for the interpretation of single-molecule experiments. We find a large decrease in D from unfolded to folded, for reaction coordinates that directly measure fluctuations in Cartesian configuration space, including those probed in single-molecule experiments. In contrast, D is almost independent of Q, the fraction of native amino acid contacts: Near the folded state, small fluctuations in position cause large fluctuations in Q, and vice versa for the unfolded state. In general, position-dependent free energies and diffusion coefficients for any two good reaction coordinates that separate reactant, product, and transition states, are related by a simple transformation, as we demonstrate. With this transformation, we obtain reaction coordinates with position-invariant D. The corresponding free-energy surfaces allow us to justify the assumptions used in estimating the speed limit for protein folding from experimental measurements of the reconfiguration time in the unfolded state, and also reveal intermediates hidden in the original free-energy projection. Lastly, we comment on the design of future single-molecule experiments that probe the position dependence of D directly.

Native contacts determine protein folding mechanisms in atomistic simulations

Significance Understanding the mechanism by which proteins fold to their native structure is a central problem in protein science. Clearly, interactions between residues that are in contact in the folded state (native interactions) are likely to be important for folding, but, in principle, nonnative interactions may play a role. Here, we use recently published microsecond to millisecond all-atom molecular dynamics simulations of proteins folding and unfolding to show, remarkably, that nonnative contacts are irrelevant to the mechanism of folding in most cases. This statistical analysis would be very difficult to perform by experiment. Although this is a limited set of proteins, the results nonetheless strongly support coarse-grained theoretical and simulation models of folding in which only native contacts are energetically favorable. The recent availability of long equilibrium simulations of protein folding in atomistic detail for more than 10 proteins allows us to identify the key interactions driving folding. We find that the collective fraction of native amino acid contacts, Q, captures remarkably well the transition states for all the proteins with a folding free energy barrier. Going beyond this global picture, we devise two different measures to quantify the importance of individual interresidue contacts in the folding mechanism: (i) the log-ratio of lifetimes of contacts during folding transition paths and in the unfolded state and (ii) a Bayesian measure of how predictive the formation of each contact is for being on a transition path. Both of these measures indicate that native, or near-native, contacts are important for determining mechanism, as might be expected. More remarkably, however, we found that for almost all the proteins, with the designed protein α3D being a notable exception, nonnative contacts play no significant part in determining folding mechanisms.

Balanced Protein–Water Interactions Improve Properties of Disordered Proteins and Non-Specific Protein Association

Some frequently encountered deficiencies in all-atom molecular simulations, such as nonspecific protein–protein interactions being too strong, and unfolded or disordered states being too collapsed, suggest that proteins are insufficiently well solvated in simulations using current state-of-the-art force fields. To address these issues, we make the simplest possible change, by modifying the short-range protein–water pair interactions, and leaving all the water–water and protein–protein parameters unchanged. We find that a modest strengthening of protein–water interactions is sufficient to recover the correct dimensions of intrinsically disordered or unfolded proteins, as determined by direct comparison with small-angle X-ray scattering (SAXS) and Förster resonance energy transfer (FRET) data. The modification also results in more realistic protein-protein affinities, and average solvation free energies of model compounds which are more consistent with experiment. Most importantly, we show that this scaling is small enough not to affect adversely the stability of the folded state, with only a modest effect on the stability of model peptides forming α-helix and β-sheet structures. The proposed adjustment opens the way to more accurate atomistic simulations of proteins, particularly for intrinsically disordered proteins, protein–protein association, and crowded cellular environments.