D. Thirumalai

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

Urea denaturation by stronger dispersion interactions with proteins than water implies a 2-stage unfolding

The mechanism of denaturation of proteins by urea is explored by using all-atom microseconds molecular dynamics simulations of hen lysozyme generated on BlueGene/L. Accumulation of urea around lysozyme shows that water molecules are expelled from the first hydration shell of the protein. We observe a 2-stage penetration of the protein, with urea penetrating the hydrophobic core before water, forming a “dry globule.” The direct dispersion interaction between urea and the protein backbone and side chains is stronger than for water, which gives rise to the intrusion of urea into the protein interior and to ureas preferential binding to all regions of the protein. This is augmented by preferential hydrogen bond formation between the urea carbonyl and the backbone amides that contributes to the breaking of intrabackbone hydrogen bonds. Our study supports the “direct interaction mechanism” whereby urea has a stronger dispersion interaction with protein than water.

Protein folding kinetics: timescales, pathways and energy landscapes in terms of sequence-dependent properties

BACKGROUND Recent experimental and theoretical studies have revealed that protein folding kinetics can be quite complex and diverse depending on various factors such as size of the protein sequence and external conditions. For example, some proteins fold apparently in a kinetically two-state manner, whereas others follow complex routes to the native state. We have set out to provide a theoretical basis for understanding the diverse behavior seen in the refolding kinetics of proteins in terms of properties that are intrinsic to the sequence. RESULTS The folding kinetics of a number of sequences for off-lattice continuum models of proteins is studied using Langevin simulations at two different values of the friction coefficient. We show for these models that there is a remarkable correlation between folding time, tau F, and sigma = (T theta - TF)/T theta, where T theta and TF are the equilibrium collapse and folding transition temperatures, respectively. The microscopic dynamics reveals that several scenarios for the kinetics of refolding arise depending on the range of values of sigma. For relatively small sigma, the chain reaches the native conformation by a direct native conformation nucleation collapse (NCNC) mechanism without being trapped in any detectable intermediates. For moderate and large values of sigma, the kinetics is described by the kinetic partitioning mechanism, according to which a fraction of molecules phi (kinetic partition factor) reach the native conformation via the NCNC mechanism. The remaining fraction attains the native state by off-pathway processes that involve trapping in several misfolded structures. The rate-determining step in the off-pathway processes is the transition from the misfolded structures to the native state. The partition factor phi is also determined by sigma: the smaller the value of sigma, the larger is phi. The qualitative aspects of our results are found to be independent of the friction coefficient. The simulation results and theoretical arguments are used to obtain estimates for timescales for folding via the NCNC mechanism in small proteins, those with less than about 70 amino acid residues. CONCLUSIONS We have shown that the various scenarios for folding of proteins, and possibly other biomolecules, can be classified solely in terms of sigma. Proteins with small values of sigma reach the native conformation via a nucleation collapse mechanism and their energy landscape is characterized by having one dominant native basin of attraction (NBA). On the other hand, proteins with large sigma get trapped in competing basins of attraction (CBAs) in which they adopt misfolded structures. Only a small fraction of molecules access the native state rapidly when sigma is large. For these sequences, the majority of the molecules approach the native state by a three-stage multipathway mechanism in which the rate-determining step involves a transition from one of the CBAs to the NBA.

Emerging ideas on the molecular basis of protein and peptide aggregation.

Several neurodegenerative diseases are associated with the unfolding and subsequent fibrillization of proteins. Although neither the assembly mechanism nor the atomic structures of the amyloid fibrils are known, recent experimental and computational studies suggest that a few general principles that govern protein aggregation may exist. Analysis of the results of several important recent studies has led to a set of tentative ideas concerning the oligomerization of proteins and peptides. General rules have been described that may be useful in predicting regions of known proteins (prions and transthyretin) that are susceptible to fluctuations, which give rise to structures that can aggregate by the nucleation-growth mechanism. Despite large variations in the sequence-dependent polymerization kinetics of several structurally unrelated proteins, there appear to be only a few plausible scenarios for protein and peptide aggregation.

Dissecting the Assembly of Aβ16–22 Amyloid Peptides into Antiparallel β Sheets

Abstract Multiple long molecular dynamics simulations are used to probe the oligomerization mechanism of Aβ 16–22 (KLVFFAE) peptides. The peptides, in the monomeric form, adopt either compact random-coil or extended β strand-like structures. The assembly of the low-energy oligomers, in which the peptides form antiparallel β sheets, occurs by multiple pathways with the formation of an obligatory α-helical intermediate. This observation and the experimental results on fibrillogenesis of Aβ 1–40 and Aβ 1–42 peptides suggest that the assembly mechanism (random coil → α helix → β strand) is universal for this class of peptides. In Aβ 16–22 oligomers both interpeptide hydrophobic and electrostatic interactions are critical in the formation of the antiparallel β sheet structure. Mutations of either hydrophobic or charged residues destabilize the oligomer, which implies that the 16-22 fragments of Arctic (E22G), Dutch (E22Q), and Italian (E22K) mutants are unlikely to form ordered fibrils.

Low-frequency normal modes that describe allosteric transitions in biological nanomachines are robust to sequence variations

By representing the high-resolution crystal structures of a number of enzymes using the elastic network model, it has been shown that only a few low-frequency normal modes are needed to describe the large-scale domain movements that are triggered by ligand binding. Here we explore a link between the nearly invariant nature of the modes that describe functional dynamics at the mesoscopic level and the large evolutionary sequence variations at the residue level. By using a structural perturbation method (SPM), which probes the residue-specific response to perturbations (or mutations), we identify a sparse network of strongly conserved residues that transmit allosteric signals in three structurally unrelated biological nanomachines, namely, DNA polymerase, myosin motor, and the Escherichia coli chaperonin. Based on the response of every mode to perturbations, which are generated by interchanging specific sequence pairs in a multiple sequence alignment, we show that the functionally relevant low-frequency modes are most robust to sequence variations. Our work shows that robustness of dynamical modes at the mesoscopic level is encoded in the structure through a sparse network of residues that transmit allosteric signals.

Viscosity Dependence of the Folding Rates of Proteins

The viscosity shd dependence of the folding rates for four sequences (the native state of three sequences is a b sheet, while the fourth forms an a helix) is calculated for off-lattice models of proteins. Assuming that the dynamics is given by the Langevin equation, we show that the folding rates increase linearly at low viscosities h, decrease as 1yh at large h, and have a maximum at intermediate values. The Kramers’ theory of barrier crossing provides a quantitative fit of the numerical results. By mapping the simulation results to real proteins we estimate that for optimized sequences the time scale for forming a four turn a-helix topology is about 500 ns, whereas for b sheet it is about 10 ms. [S0031-9007(97)03573-4]

Role of water in protein aggregation and amyloid polymorphism.

A variety of neurodegenerative diseases are associated with amyloid plaques, which begin as soluble protein oligomers but develop into amyloid fibrils. Our incomplete understanding of this process underscores the need to decipher the principles governing protein aggregation. Mechanisms of in vivo amyloid formation involve a number of coconspirators and complex interactions with membranes. Nevertheless, understanding the biophysical basis of simpler in vitro amyloid formation is considered important for discovering ligands that preferentially bind regions harboring amyloidogenic tendencies. The determination of the fibril structure of many peptides has set the stage for probing the dynamics of oligomer formation and amyloid growth through computer simulations. Most experimental and simulation studies, however, have been interpreted largely from the perspective of proteins: the role of solvent has been relatively overlooked in oligomer formation and assembly to protofilaments and amyloid fibrils. In this Account, we provide a perspective on how interactions with water affect folding landscapes of amyloid beta (Aβ) monomers, oligomer formation in the Aβ16-22 fragment, and protofilament formation in a peptide from yeast prion Sup35. Explicit molecular dynamics simulations illustrate how water controls the self-assembly of higher order structures, providing a structural basis for understanding the kinetics of oligomer and fibril growth. Simulations show that monomers of Aβ peptides sample a number of compact conformations. The formation of aggregation-prone structures (N*) with a salt bridge, strikingly similar to the structure in the fibril, requires overcoming a high desolvation barrier. In general, sequences for which N* structures are not significantly populated are unlikely to aggregate. Oligomers and fibrils generally form in two steps. First, water is expelled from the region between peptides rich in hydrophobic residues (for example, Aβ16-22), resulting in disordered oligomers. Then the peptides align along a preferred axis to form ordered structures with anti-parallel β-strand arrangement. The rate-limiting step in the ordered assembly is the rearrangement of the peptides within a confining volume. The mechanism of protofilament formation in a polar peptide fragment from the yeast prion, in which the two sheets are packed against each other and create a dry interface, illustrates that water dramatically slows self-assembly. As the sheets approach each other, two perfectly ordered one-dimensional water wires form. They are stabilized by hydrogen bonds to the amide groups of the polar side chains, resulting in the formation of long-lived metastable structures. Release of trapped water from the pore creates a helically twisted protofilament with a dry interface. Similarly, the driving force for addition of a solvated monomer to a preformed fibril is water release; the entropy gain and favorable interpeptide hydrogen bond formation compensate for entropy loss in the peptides. We conclude by offering evidence that a two-step model, similar to that postulated for protein crystallization, must also hold for higher order amyloid structure formation starting from N*. Distinct water-laden polymorphic structures result from multiple N* structures. Water plays multifarious roles in all of these protein aggregations. In predominantly hydrophobic sequences, water accelerates fibril formation. In contrast, water-stabilized metastable intermediates dramatically slow fibril growth rates in hydrophilic sequences.

Simulations of β-hairpin folding confined to spherical pores using distributed computing

We report the thermodynamics and kinetics of an off-lattice Go model β-hairpin from Ig-binding protein confined to an inert spherical pore. Confinement enhances the stability of the hairpin due to the decrease in the entropy of the unfolded state. Compared with their values in the bulk, the rates of hairpin formation increase in the spherical pore. Surprisingly, the dependence of the rates on the pore radius, Rs, is nonmonotonic. The rates reach a maximum at Rs/R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{g,{\mathit{N}}}^{b}}}\end{equation*}\end{document} ≃ 1.5, where R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{g,{\mathit{N}}}^{b}}}\end{equation*}\end{document} is the radius of gyration of the folded β-hairpin in the bulk. The denatured state ensemble of the encapsulated β-hairpin is highly structured even at substantially elevated temperatures. Remarkably, a profound effect of confinement is evident even when the β-hairpin occupies less than a 10th of the sphere volume. Our calculations show that the emergence of substantial structure in the denatured state of proteins in inert pores is a consequence of confinement. In contrast, the structure of the bulk denatured state ensemble depends dramatically on the extent of denaturation.

Capturing the essence of folding and functions of biomolecules using coarse-grained models

The distances over which biological molecules and their complexes can function range from a few nanometres, in the case of folded structures, to millimetres, for example, during chromosome organization. Describing phenomena that cover such diverse length, and also time, scales requires models that capture the underlying physics for the particular length scale of interest. Theoretical ideas, in particular, concepts from polymer physics, have guided the development of coarse-grained models to study folding of DNA, RNA and proteins. More recently, such models and their variants have been applied to the functions of biological nanomachines. Simulations using coarse-grained models are now poised to address a wide range of problems in biology.