José N. Onuchic

Navigating the folding routes.

To fold, a protein navigates with remarkable ease through a complicated energy landscape as it explores many possible physical configurations. This feat is beginning to be quantitatively understood by means of statistical mechanics and simplified computer models (1). Folded proteins are marvels of molecular engineering and it is hard to avoid thinking that all of their complex structural features play a role in their folding through an obligate En multistep mechanism. A unique folding pathway, if it exists, could be elucidated with classical chemical experiments. A newer view holds that in the earlier stages a protein possesses a large ensemble of structures. The problem is not to find a single route but to characterE ize the dynamics of the ensemble n through a statistical description of 2 the topography of the free-energy landscape. Folding is easy if the landscape resembles a many-dimensional funnel leading through a myriad of pathways to the native structure. Only a few parameters should be needed to characterize statistically the topography of and routes down the folding funnel. Using experimental data, Onuchic et al. have estimated the extent, ruggedness, and slope of the folding funnel (2). Similar parameters characterize the energy landscape Enat of simple computer models of pron teins. These models of self-interacting necklaces of beads, often on Fig. 1. lattices, lack most of the details of helical real proteins, but establishing a represE quantitative correspondence bethrougt tween the landscapes of computer emerg models and real proteins makes it Q, is in possible to use simulations to understand folding kinetics. The extent of a protein energy landscape is huge. Before folding, each residue can take on about 10 different conformations; thus, a 60-residue protein can be in any of 1060 states. An unguided search, like a

Direct-coupling analysis of residue coevolution captures native contacts across many protein families

The similarity in the three-dimensional structures of homologous proteins imposes strong constraints on their sequence variability. It has long been suggested that the resulting correlations among amino acid compositions at different sequence positions can be exploited to infer spatial contacts within the tertiary protein structure. Crucial to this inference is the ability to disentangle direct and indirect correlations, as accomplished by the recently introduced direct-coupling analysis (DCA). Here we develop a computationally efficient implementation of DCA, which allows us to evaluate the accuracy of contact prediction by DCA for a large number of protein domains, based purely on sequence information. DCA is shown to yield a large number of correctly predicted contacts, recapitulating the global structure of the contact map for the majority of the protein domains examined. Furthermore, our analysis captures clear signals beyond intradomain residue contacts, arising, e.g., from alternative protein conformations, ligand-mediated residue couplings, and interdomain interactions in protein oligomers. Our findings suggest that contacts predicted by DCA can be used as a reliable guide to facilitate computational predictions of alternative protein conformations, protein complex formation, and even the de novo prediction of protein domain structures, contingent on the existence of a large number of homologous sequences which are being rapidly made available due to advances in genome sequencing.

Effect of friction on electron transfer in biomolecules

In biological and chemical electron transfer, a nuclear reaction coordinate is coupled to other nuclear and/or ‘‘solvent’’ coordinates. This coupling, or friction, if strong enough, may substantially slow down motion along the reaction coordinate, and thus vitiate the assumption of electron transfer being nonadiabatic with respect to the nuclei. Here, a simple, fully quantum mechanical model for electron transfer using a one mode treatment which incorporates this coupling is studied. Path integral methods are used to study the dependence of the reaction rate on friction, and the limits of the moderate and the high friction are analyzed in detail. The first limit will prevail if the reaction coordinate is, e.g., an underdamped nuclear vibration, whereas the second limit will prevail if it corresponds to a slow or diffusive degree of freedom. In the high‐friction limit, the reaction rate is explicitly shown to vary between the nonadiabatic and adiabatic expressions as the tunneling matrix element and/or the friction are varied. Starting from a path integral expression for the time evolution of the reduced density matrix for the electron and reaction coordinate, a Fokker–Planck equation is obtained which reduces in the high‐friction limit to a Smoluchowski equation similar to one solved by Zusman.

Nonlinear elasticity, proteinquakes, and the energy landscapes of functional transitions in proteins

Large-scale motions of biomolecules involve linear elastic deformations along low-frequency normal modes, but for function nonlinearity is essential. In addition, unlike macroscopic machines, biological machines can locally break and then reassemble during function. We present a model for global structural transformations, such as allostery, that involve large-scale motion and possible partial unfolding, illustrating the method with the conformational transition of adenylate kinase. Structural deformation between open and closed states occurs via low-frequency modes on separate reactant and product surfaces, switching from one state to the other when energetically favorable. The switching model is the most straightforward anharmonic interpolation, which allows the barrier for a process to be estimated from a linear normal mode calculation, which by itself cannot be used for activated events. Local unfolding, or cracking, occurs in regions where the elastic stress becomes too high during the transition. Cracking leads to a counterintuitive catalytic effect of added denaturant on allosteric enzyme function. It also leads to unusual relationships between equilibrium constant and rate like those seen recently in single-molecule experiments of motor proteins.

Protein folding mediated by solvation: Water expulsion and formation of the hydrophobic core occur after the structural collapse

The interplay between structure-search of the native structure and desolvation in protein folding has been explored using a minimalist model. These results support a folding mechanism where most of the structural formation of the protein is achieved before water is expelled from the hydrophobic core. This view integrates water expulsion effects into the funnel energy landscape theory of protein folding. Comparisons to experimental results are shown for the SH3 protein. After the folding transition, a near-native intermediate with partially solvated hydrophobic core is found. This transition is followed by a final step that cooperatively squeezes out water molecules from the partially hydrated protein core.

Diffusive dynamics of the reaction coordinate for protein folding funnels

The quantitative description of model protein folding kinetics using a diffusive collective reaction coordinate is examined. Direct folding kinetics, diffusional coefficients and free energy profiles are determined from Monte Carlo simulations of a 27‐mer, 3 letter code lattice model, which corresponds roughly to a small helical protein. Analytic folding calculations, using simple diffusive rate theory, agree extremely well with the full simulation results. Folding in this system is best seen as a diffusive, funnel‐like process.

Folding a protein in a computer: An atomic description of the folding/unfolding of protein A

We study the folding mechanism of a three-helix bundle protein at atomic resolution, including effects of explicit water. Using replica exchange molecular dynamics we perform enough sampling over a wide range of temperatures to obtain the free energy, entropy, and enthalpy surfaces as a function of structural reaction coordinates. Simulations were started from different configurations covering the folded and unfolded states. Because many transitions between all minima at the free energy surface are observed, a quantitative determination of the free energy barriers and the ensemble of configurations associated with them is now possible. The kinetic bottlenecks for folding can be determined from the thermal ensembles of structures on the free energy barriers, provided the kinetically determined transition-state ensembles are similar to those determined from free energy barriers. A mechanism incorporating the interplay among backbone ordering, sidechain packing, and desolvation arises from these calculations. Large Φ values arise not only from native contacts, which mostly form at the transition state, but also from contacts already present in the unfolded state that are partially destroyed at the transition.

Protein folding funnels: The nature of the transition state ensemble

BACKGROUND Energy landscape theory predicts that the folding funnel for a small fast-folding alpha-helical protein will have a transition state half-way to the native state. Estimates of the position of the transition state along an appropriate reaction coordinate can be obtained from linear free energy relationships observed for folding and unfolding rate constants as a function of denaturant concentration. The experimental results of Huang and Oas for lambda repressor, Fersht and collaborators for C12, and Gray and collaborators for cytochrome c indicate a free energy barrier midway between the folded and unfolded regions. This barrier arises from an entropic bottleneck for the folding process. RESULTS In keeping with the experimental results, lattice simulations based on the folding funnel description show that the transition state is not just a single conformation, but rather an ensemble of a relatively large number of configurations that can be described by specific values of one or a few order parameters (e.g. the fraction of native contacts). Analysis of this transition state or bottleneck region from our lattice simulations and from atomistic models for small alpha-helical proteins by Boczko and Brooks indicates a broad distribution for native contact participation in the transition state ensemble centered around 50%. Importantly, however, the lattice-simulated transition state ensemble does include some particularly hot contacts, as seen in the experiments, which have been termed by others a folding nucleus. CONCLUSIONS Linear free energy relations provide a crude spectroscopy of the transition state, allowing us to infer the values of a reaction coordinate based on the fraction of native contacts. This bottleneck may be thought of as a collection of delocalized nuclei where different native contacts will have different degrees of participation. The agreement between the experimental results and the theoretical predictions provides strong support for the landscape analysis.

Folding kinetics of proteinlike heteropolymers

Using a simple three‐dimensional lattice copolymer model and Monte Carlo dynamics, we study the collapse and folding of proteinlike heteropolymers. The polymers are 27 monomers long and consist of two monomer types. Although these chains are too long for exhaustive enumeration of all conformations, it is possible to enumerate all the maximally compact conformations, which are 3 ×3×3 cubes. This allows us to select sequences that have a unique global minimum. We then explore the kinetics of collapse and folding and examine what features determine the various rates. The folding time has a plateau over a broad range of temperatures and diverges at both high and low temperatures. The folding time depends on sequence and is related to the amount of energetic frustration in the native state. The collapse times of the chains are sequence independent and are a few orders of magnitude faster than the folding times, indicating a two‐phase folding process. Below a certain temperature the chains exhibit glasslike beh...

Head swivel on the ribosome facilitates translocation by means of intra-subunit tRNA hybrid sites

The elongation cycle of protein synthesis involves the delivery of aminoacyl-transfer RNAs to the aminoacyl-tRNA-binding site (A site) of the ribosome, followed by peptide-bond formation and translocation of the tRNAs through the ribosome to reopen the A site. The translocation reaction is catalysed by elongation factor G (EF-G) in a GTP-dependent manner. Despite the availability of structures of various EF-G–ribosome complexes, the precise mechanism by which tRNAs move through the ribosome still remains unclear. Here we use multiparticle cryoelectron microscopy analysis to resolve two previously unseen subpopulations within Thermus thermophilus EF-G–ribosome complexes at subnanometre resolution, one of them with a partly translocated tRNA. Comparison of these substates reveals that translocation of tRNA on the 30S subunit parallels the swivelling of the 30S head and is coupled to unratcheting of the 30S body. Because the tRNA maintains contact with the peptidyl-tRNA-binding site (P site) on the 30S head and simultaneously establishes interaction with the exit site (E site) on the 30S platform, a novel intra-subunit ‘pe/E’ hybrid state is formed. This state is stabilized by domain IV of EF-G, which interacts with the swivelled 30S-head conformation. These findings provide direct structural and mechanistic insight into the ‘missing link’ in terms of tRNA intermediates involved in the universally conserved translocation process.