The presence of macromolecules in cells geometrically restricts the available space for poplypeptide chains. To study the effects of macromolecular crowding on folding thermodynamics and kinetics, we used an off-lattice model of the all-␤-sheet WW domain in the presence of large spherical particles whose interaction with the polypeptide chain is purely repulsive. At all volume fractions, c, of the crowding agents the stability of the native state is enhanced. Remarkably, the refolding rates, which are larger than the value at c ‫؍‬ 0, increase nonmonotonically as c increases, reaching a maximum at c ‫؍‬ * c. At high values of c, the depletion-induced intramolecular attraction produces compact structures with considerable structure in the denatured state. Changes in native state stability and folding kinetics at c can be quantitatively mapped onto confinement in a volume-fraction-dependent spherical pore with radius Rs Ϸ (4͞3c) 1͞3 Rc (Rc is the radius of the crowding particles) as long as c < * c. We show that the extent of native state stabilization at finite c is comparable with that in a spherical pore. In both situations, rate enhancement is due to destabilization of the denatured states with respect to c ‫؍‬ 0.confinement effects ͉ protein folding ͉ depletion-interaction T he interior of cells contains several kinds of macromolecules like lipids, sugars, nucleic acids, and proteins, along with large organized macromolecular arrays, such as cytoskeleton fibers. The volume fraction c , occupied by the macromolecular crowding agents in Escherichia coli, can be as large as 0.4 (1, 2). The large volume occupied by crowding agents can have profound effect on a number of processes of biological importance. For example, biochemical reactions, stability of actin, and amyloid formation are profoundly altered in a crowded environment (3, 4). Folding of globular proteins, which is the focus of this study, in such a crowded environment can be significantly different from that at c ϭ 0. Although systematic studies of the effect of crowding on folding kinetics of well characterized proteins are lacking, several experiments have shown that refolding at finite c is greatly affected. The oxidative refolding of hen lysozyme is changed when crowding agents are present (5). The rate for the molecules that reach the native basin of attraction (NBA) rapidly increases by a factor of Ϸ2-5, whereas the rate for the slow track molecules (i.e., those that are trapped in misfolded states) increases only by Ϸ80% (5). These studies and the need to systematically assess crowding effects on folding of proteins have motivated this work.Because of the complexity of interactions, E pc , between the crowding agents and the protein of interest, it is difficult to predict the effect of macromolecular crowding on refolding of proteins. If E pc is short-ranged and repulsive, then excluded volume interactions, which prevent the polypeptide chain from accessing regions occupied by the crowding particles, are the most important. Typically, the range ...

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.

Multiple long molecular dynamics simulations are used to probe the oligomerization mechanism of Abeta(16-22) (KLVFFAE) peptides. The peptides, in the monomeric form, adopt either compact random-coil or extended beta strand-like structures. The assembly of the low-energy oligomers, in which the peptides form antiparallel beta sheets, occurs by multiple pathways with the formation of an obligatory alpha-helical intermediate. This observation and the experimental results on fibrillogenesis of Abeta(1-40) and Abeta(1-42) peptides suggest that the assembly mechanism (random coil --> alpha helix --> beta strand) is universal for this class of peptides. In Abeta(16-22) oligomers both interpeptide hydrophobic and electrostatic interactions are critical in the formation of the antiparallel beta 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.

Replica exchange molecular dynamics and an all-atom implicit solvent model are used to probe the thermodynamics of deposition of Alzheimer's Abeta monomers on preformed amyloid fibrils. Consistent with the experiments, two deposition stages have been identified. The docking stage occurs over a wide temperature range, starting with the formation of the first peptide-fibril interactions at 500 K. Docking is completed when a peptide fully adsorbs on the fibril edge at the temperature of 380 K. The docking transition appears to be continuous, and occurs without free energy barriers or intermediates. During docking, incoming Abeta monomer adopts a disordered structure on the fibril edge. The locking stage occurs at the temperature of approximately 360 K and is characterized by the rugged free energy landscape. Locking takes place when incoming Abeta peptide forms a parallel beta-sheet structure on the fibril edge. Because the beta-sheets formed by locked Abeta peptides are typically off-registry, the structure of the locked phase differs from the structure of the fibril interior. The study also reports that binding affinities of two distinct fibril edges with respect to incoming Abeta peptides are different. The peptides bound to the concave edge have significantly lower free energy compared to those bound on the convex edge. Comparison with the available experimental data is discussed.

Thermodynamics and kinetics of off-lattice models with side chains for the ␤-hairpin fragment of immunoglobulin-binding protein and its variants are reported. For all properties (except refolding time F) there are no qualitative differences between the full model and the Go version. The validity of the models is established by comparison of the calculated native structure with the Protein Data Bank coordinates and by reproducing the experimental results for the degree of cooperativity and F. For the full model F Ϸ 2 s at the folding temperature (experimental value is 6 s); the Go model folds 50 times faster. Upon refolding, structural changes take place over three time scales. On the collapse time scale compact structures with intact hydrophobic cluster form. Subsequently, hydrogen bonds form, predominantly originating from the turn by a kinetic zipping mechanism. The assembly of the hairpin is complete when most of the interstrand contacts (the rate-limiting step) is formed. The dominant transition state structure (located by using cluster analysis) is compact and structured. We predict that when hydrophobic cluster is moved to the loop F marginally increases, whereas moving the hydrophobic cluster closer to the termini results in significant decrease in F relative to wild type. The mechanism of hairpin formation is predicted to depend on turn stiffness. Fast folding experiments on proteins and their building blocks (␣-helices, ␤-hairpins, and loops) are providing glimpses into the time scales of the early events in the assembly of biomolecules (1, 2). In a recent study, Munoz et al. (3) showed that the 16-residue C-terminal peptide from the protein GB1 forms a ␤-hairpin in about 6 s at the folding transition temperature T F (Ϸ300 K), which is in accord with our earlier theoretical predictions (4, 5). They also proposed a statistical mechanical model to explain the observed thermodynamics and kinetics (6).The key experimental findings of Munoz et al. (3) are (i) Thermodynamically, the formation of ␤-hairpin can be described by a two-state process. The transition to the folded state is broad, which is expected for small finite systems. (ii) In the temperature range 15-55°C the folding kinetics (monitored by tryptophan fluorescence) is exponential. This behavior suggests two-state folding kinetics. (iii) ␤-Hairpins form at rates considerably slower than helices. (iv) The temperature dependence of the measured relaxation rates shows slight curvature and an Arrhenius fit to the data gives negative activation energy.Before these experiments theoretical and computational studies had demonstrated that generically ␤-hairpins can form in microseconds (4, 5). There are large variations in the time scales for ␤-turn formation depending on the underlying sequencedependent characteristic temperatures (4). All-atom simulations in water have shown that many of the characteristics of folding kinetics in proteins (kinetic partitioning, ''mini'' hydrophobic core packing, etc.) are found in ␤-turn forming peptides (7). The expe...