Abstract: Guided by the recent success of empirical model predicting the folding rates of small two-state folding proteins from the relative contact order (CO) of their native structures, by a theoretical model of protein folding that predicts that logarithm of the folding rate decreases with the protein chain length L as L(2/3), and by the finding that the folding rates of multistate folding proteins strongly correlate with their sizes and have very bad correlation with CO, we reexamined the dependence of folding rate on CO and L in attempt to find a structural parameter that determines folding rates for the totality of proteins. We show that the Abs_CO = CO x L, is able to predict rather accurately folding rates for both two-state and multistate folding proteins, as well as short peptides, and that this Abs_CO scales with the protein chain length as L(0.70 +/- 0.07) for the totality of studied single-domain proteins and peptides.

Abstract: Theoretical studies of protein folding suggest that multiple folding pathways should exist, but there is little experimental evidence to support this Here we demonstrate changes in the flux between different transition states on parallel folding pathways, resulting in unprecedented upward curvature in the denaturant-dependent unfolding kinetics of a β-sandwich protein As denaturant concentration increases, the highly compact transition state of one pathway becomes destabilized and the dominant flux of protein molecules shifts toward another pathway with a less structured transition state Furthermore, point mutations alter the relative accessibility of the pathways, allowing the structure of two transition states on separate, direct folding pathways to be mapped by systematic Φ-value analysis It has been suggested that pathways with diffuse rather than localized transition states are evolutionarily selected to prevent misfolding, and indeed we find that the transition state favored at high concentrations of denaturant is more polarized than the physiologically relevant one

Abstract: We demonstrate that chain length is the main determinant of the folding rate for proteins with the three-state folding kinetics. The logarithm of their folding rate in water (k(f)) strongly anticorrelates with their chain length L (the correlation coefficient being -0.80). At the same time, the chain length has no correlation with the folding rate for two-state folding proteins (the correlation coefficient is -0.07). Another significant difference of these two groups of proteins is a strong anticorrelation between the folding rate and Baker's "relative contact order" for the two-state folders and the complete absence of such correlation for the three-state folders.

Abstract: Here, we describe the folding/unfolding kinetics of α3D, a small designed three-helix bundle. Both IR temperature jump and ultrafast fluorescence mixing methods reveal a single-exponential process consistent with a minimal folding time of 3.2 ± 1.2 μs (at ≈50°C), indicating that a protein can fold on the 1- to 5-μs time scale. Furthermore, the single-exponential nature of the relaxation indicates that the prefactor for transition state (TS)-folding models is probably ≥1 (μs)–1 for a protein of this size and topology. Molecular dynamics simulations and IR spectroscopy provide a molecular rationale for the rapid, single-exponential folding of this protein. α3D shows a significant bias toward local helical structure in the thermally denatured state. The molecular dynamics-simulated TS ensemble is highly heterogeneous and dynamic, allowing access to the TS via multiple pathways.

Abstract: A microscopic study of functional disorder–order folding transitions coupled to binding is performed for the p27 protein, which derives a kinetic advantage from the intrinsically disordered unbound form on binding with the phosphorylated cyclin A-cyclin-dependent kinase 2 (Cdk2) complex. Hierarchy of structural loss during p27 coupled unfolding and unbinding is simulated by using high-temperature Monte Carlo simulations initiated from the crystal structure of the tertiary complex. Subsequent determination of the transition-state ensemble and the proposed atomic picture of the folding mechanism coupled to binding provide a microscopic rationale that reconciles the initiation recruitment of p27 at the cyclin A docking site with the kinetic benefit for a disordered α-helix in the unbound form of p27. The emerging structural polarization in the ensemble of unfolding/unbinding trajectories and in the computationally determined transition-state ensemble is not determined by the intrinsic folding preferences of p27 but rather is attributed to the topological requirements of the native intermolecular interface to order β-hairpin and β-strand of p27 that could be critical for nucleating rapid folding transition coupled to binding. In agreement with the experimental data, the disorder–order folding transition for p27 is largely determined by the functional requirement to form a specific intermolecular interface that ultimately dictates the folding mechanism and overwhelms any local folding preferences for creating a stable α-helix in the p27 structure before overcoming the major free energy barrier.

Abstract: Chevron rollovers of some proteins imply that their logarithmic folding rates are nonlinear in native stability. This is predicted by lattice and continuum Go models to arise from diminished accessibilities of the ground state from transiently populated compact conformations under strongly native conditions. Despite these models' native-centric interactions, the slowdown is due partly to kinetic trapping caused by some of the folding intermediates' non-native topologies. Notably, simple two-state folding kinetics of small single-domain proteins are not reproduced by common Go-like schemes.

Abstract: Structures of intermediates and transition states in protein folding are usually characterized by amide hydrogen exchange and protein engineering methods and interpreted on the basis of the assumption that they have native-like conformations. We were able to stabilize and determine the high-resolution structure of a partially unfolded intermediate that exists after the rate-limiting step of a four-helix bundle protein, Rd-apocyt b(562), by multidimensional NMR methods. The intermediate has partial native-like secondary structure and backbone topology, consistent with our earlier native state hydrogen exchange results. However, non-native hydrophobic interactions exist throughout the structure. These and other results in the literature suggest that non-native hydrophobic interactions may occur generally in partially folded states. This can alter the interpretation of mutational protein engineering results in terms of native-like side chain interactions. In addition, since the intermediate exists after the rate-limiting step and Rd-apocyt b(562) folds very rapidly (k(f) approximately 10(4) s(-1)), these results suggest that non-native hydrophobic interactions, in the absence of topological misfolding, are repaired too rapidly to slow folding and cause the accumulation of folding intermediates. More generally, these results illustrate an approach for determining the high-resolution structure of folding intermediates.

Abstract: In the recently proposed distributed computing approach to protein folding a very large number of short independent simulations is performed Using this method, folding events on a time scale orders of magnitude shorter than the experimental one have been reported However, it has also been observed that the folding process is not an elementary kinetic step and that the presence of initial lag phases can bias short simulations toward atypical pathways We study here a 20-residue three-stranded antiparallel β-sheet peptide whose equilibrium properties can be characterized by atomistic molecular dynamics simulations We found that the folding rate of this peptide is estimated correctly by the distributed computing approach when trajectories >≈1/100 of the equilibrium folding time are considered We also found that the fastest folding events occur through high-energy pathways, which are unlikely under equilibrium conditions These very fast folding pathways do not relax within the equilibrium denatured state that is stabilized by the transient presence of both native and nonnative interactions, and they are characterized by the nearly simultaneous formation of the two β-hairpins and a very small number of non-native contacts

Abstract: Delineation of the structural properties of transition states is key to deriving models for protein folding. Here we describe the structures of the transition states of the bacterial immunity proteins Im7 and Im9 obtained by all-atom molecular dynamics simulations with phi value restraints derived from protein engineering experiments. This pair of proteins is of special interest because, at pH 7 and 10 degrees C, Im7 folds via an intermediate while Im9 folds with a two-state transition. The structures of the transition states for Im7 and Im9, together with their radii of gyration and distances from the native state, are similar. The typical distance between any two members of the transition state ensemble of both proteins is large, with that of Im9 nearly twice that of Im7. Thus, a broad range of structures make up the transition state ensembles of these proteins. The ensembles satisfy the set of rather low phi values and yet are consistent with high beta(T) values (> 0.85 for both proteins). For both Im7 and Im9 the inter-helical angles are highly variable in the transition state ensembles, although the native contacts between helices I and IV are well conserved. By measuring the distribution of the accessible surface area for each residue we show that the hydrophobic residues that are buried in the native state remain buried in the transition state, corresponding to a hydrophobic collapse to a relatively ordered globule. The data provide new insights into the structural properties of the transition states of these proteins at an atomic level of detail and show that molecular dynamics simulations with phi value restraints can significantly enhance the knowledge of the transition state ensembles (TSE) provided by the experimental phi values alone.

Abstract: The biologically active (native) state of most proteins is characterised by a tightly folded and highly ordered conformation. Denaturants are chemical or physical agents that can induce unfolding of the polypeptide chain. Examples include urea, heat, extremes of pH, as well as some detergents. Unfolded proteins adopt a largely disordered structure. Denaturants can interact directly with the protein, or they can alter the properties of the surrounding aqueous environment. Despite the routine use of denaturants in the biochemical laboratory, the mechanisms whereby these agents destabilise the native state remain poorly understood. Folded protein structures are only marginally stable. As a result, relatively subtle alterations in the physical and chemical properties of the solvent can cause major changes in position of the unfolding equilibrium. This review briefly discusses the most commonly used denaturants, their likely mechanisms of action, as well as some thermodynamic aspects. Key Concepts: The biologically active (native) state N of proteins represents a highly ordered and tightly folded structure. N is in equilibrium with an extensively disordered (unfolded) state U. Denaturing agents (e.g. urea, extremes of pH and temperature) shift the unfolding equilibrium from N to U. The exact mechanism of action remains unclear for most denaturants. The position of the unfolding equilibrium is governed by an interplay of enthalpic and entropic contributions that affect the free energy of unfolding according to ΔG0=ΔH0–TΔS0. The sign and magnitude of ΔG0 represents the thermodynamic stability of N; N is stable when ΔG0>0. Unfolding can be triggered by increasing the temperature T, because U has a higher entropy than N (ΔS0>0). Protein stability measurements are commonly carried out by employing urea or guanidinium chloride-induced unfolding in conjunction with optical detection. Some proteins adopt semiunfolded structures (intermediates) under mildly denaturing conditions. Protein (un)folding can be studied under equilibrium conditions and in kinetic experiments. Keywords: protein folding; protein denaturation; protein conformation; folding intermediate; thermodynamics

Abstract: The folding of cutinase, an enzyme displaying lipolytic activity, has been studied in the presence of trehalose. Equilibrium unfolding data show that trehalose increases the free energy change between folded and unfolded states. Unfolding kinetics reveal the presence of an intermediate which is ca. 60% folded in terms of solvent exposure. Trehalose stabilizes this intermediate relative to the folded state. In contrast, the intermediate revealed by folding kinetics is more compact than the transition state, as shown by the positive slope observed at low denaturant concentration in the chevron plot, as well as the decrease in the observable rate constant for folding with the increase in trehalose concentration. This intermediate displays more than 50% of area buried from the solvent (relative to the native state) compared to around 40% for the transition state for folding and therefore appears to be off the folding pathway. Trehalose stabilizes and guanidine hydrochloride destabilizes this compact intermediate. Both unfolding and folding kinetics show that compact conformational states are stabilized by trehalose, in agreement with current models on the effect of compatible solutes. This effect occurs even for compact states that decelerate the folding as in the case of the intermediate revealed by folding kinetics.

Abstract: NMR spectroscopy is the method of choice for determining the structural details of unfolded and partially folded states of proteins. Here, the utility of NMR spectroscopy in characterizing such disordered states which populate protein folding pathways, is discussed. The relevance of the structural information obtained to protein folding mechanisms is examined critically. NMR spectroscopy can not only be applied directly for characterizing disordered states of proteins populated at equilibrium, but can also be applied indirectly, in concert with hydrogen exchange, for characterizing equilibrium as well as kinetic intermediate states of proteins. Structural and dynamic characterization by NMR spectroscopy of protein conformations in the unfolded and intermediate state ensembles are important for elucidating the early events in protein folding, and for determining how folding is channelled along specific routes to attain the unique three-dimensional native protein structure.

Abstract: A F45W mutant of yeast ubiquitin has been used as a model system to examine the effects of nonnative local interactions on protein folding and stability Mutating the native TLTGK G-bulged type I turn in the N-terminal beta-hairpin to NPDG stabilizes a nonnative beta-strand alignment in the isolated peptide fragment However, NMR structural analysis of the native and mutant proteins shows that the NPDG mutant is forced to adopt the native beta-strand alignment and an unfavorable type I NPDG turn The mutant is significantly less stable (approximately 9 kJ mol(-1)) and folds 30 times slower than the native sequence, demonstrating that local interactions can modulate protein stability and that attainment of a nativelike beta-hairpin conformation in the transition state ensemble is frustrated by the turn mutations Surprising, alcoholic cosolvents [5-10% (v/v) TFE] are shown to accelerate the folding rate of the NPDG mutant We conclude, backed-up by NMR data on the peptide fragments, that even though nonnative states in the denatured ensemble are highly populated and their stability further enhanced in the presence of cosolvents, the simultaneous increase in the proportion of nativelike secondary structure (hairpin or helix), in rapid equilibrium with nonnative states, is sufficient to accelerate the folding process It is evident that modulating local interactions and increasing nonnative secondary structure propensities can change protein stability and folding kinetics However, nonlocal contacts formed in the global cooperative folding event appear to determine structural specificity