Showing papers on "Contact order published in 1998"
TL;DR: Investigations have revealed statistically significant correlations between the average sequence separation between contacting residues in the native state and the rate and transition state placement of folding for a non-homologous set of simple, single domain proteins, indicating that proteins featuring primarily sequence-local contacts tend to fold more rapidly and exhibit less compact folding transition states than those characterized by more non-local interactions.
1,492 citations
TL;DR: An implementation of classical molecular dynamics on parallel computers of increased efficiency has enabled a simulation of protein folding with explicit representation of water for 1 microsecond, about two orders of magnitude longer than the longest simulation of a protein in water reported to date.
Abstract: An implementation of classical molecular dynamics on parallel computers of increased efficiency has enabled a simulation of protein folding with explicit representation of water for 1 microsecond, about two orders of magnitude longer than the longest simulation of a protein in water reported to date. Starting with an unfolded state of villin headpiece subdomain, hydrophobic collapse and helix formation occur in an initial phase, followed by conformational readjustments. A marginally stable state, which has a lifetime of about 150 nanoseconds, a favorable solvation free energy, and shows significant resemblance to the native structure, is observed; two pathways to this state have been found.
1,351 citations
TL;DR: Using recent studies, can the authors begin to search for trends which may lead to a better understanding of the protein folding process, and stable intermediates are not a prerequisite for the fast, efficient folding of proteins.
895 citations
TL;DR: A hydrogen bond network involving two β-turns and an adjacent hydrophobic cluster appear to be formed in the folding transition state of the src SH3 domain, while the remainder of the polypeptide chain is largely unstructured.
Abstract: Experimental and theoretical studies on the folding of small proteins such as the chymotrypsin inhibitor 2 (CI-2) and the P22 Arc repressor suggest that the folding transition state is an expanded version of the native state with most interactions partially formed. Here we report that this picture does not hold generally: a hydrogen bond network involving two β-turns and an adjacent hydrophobic cluster appear to be formed in the folding transition state of the src SH3 domain, while the remainder of the polypeptide chain is largely unstructured. Comparison with data on other small proteins suggests that this structural polarization is a consequence of the topology of the SH3 domain fold. The non-uniform distribution of structure in the folding transition state provides a challenging test for computational models of the folding process.
311 citations
TL;DR: To fold efficiently and retain robustness to changes in amino acid sequence, proteins may have evolved a native structure situated within a broad basin of low-energy conformations, a feature which could facilitate the prediction of protein structure at low resolution.
Abstract: Recent experimental studies of the denatured state and theoretical analyses of the folding landscape suggest that there are a large multiplicity of low-energy, partially folded conformations near the native state. In this report, we describe a strategy for predicting protein structure based on the working hypothesis that there are a greater number of low-energy conformations surrounding the correct fold than there are surrounding low-energy incorrect folds. To test this idea, 12 ensembles of 500 to 1,000 low-energy structures for 10 small proteins were analyzed by calculating the rms deviation of the Calpha coordinates between each conformation and every other conformation in the ensemble. In all 12 cases, the conformation with the greatest number of conformations within 4-A rms deviation was closer to the native structure than were the majority of conformations in the ensemble, and in most cases it was among the closest 1 to 5%. These results suggest that, to fold efficiently and retain robustness to changes in amino acid sequence, proteins may have evolved a native structure situated within a broad basin of low-energy conformations, a feature which could facilitate the prediction of protein structure at low resolution.
284 citations
TL;DR: Analysis of the existence of obligatory steps in the folding reaction of the α-spectrin SH3 domain by mutating Asp 48 (D48G), which is at position i+3 of an isolated two-residue type II' β-turn, indicates that transition state ensembles in β-sheet proteins could be quite defined and conformationally restricted.
Abstract: We have analyzed the existence of obligatory steps in the folding reaction of the α-spectrin SH3 domain by mutating Asp 48 (D48G), which is at position i+3 of an isolated two-residue type II' β-turn. Calorimetry and X-ray analysis show an entropic stabilizing effect resulting from local changes at the dihedral angles of the β-turn. Kinetic analysis of D48G shows that this β-turn is fully formed in the transition state, while there is no evidence of its formation in an isolated fragment. Introduction of several mutations in the D48G protein reveals that the local stabilization has not significantly altered the transition state ensemble. All these results, together with previous analysis of other α-spectrin and src SH3 mutants, indicate that: (i) in the folding reaction there could be obligatory steps which are not necessarily part of the folding nucleus; (ii) transition state ensembles in β-sheet proteins could be quite defined and conformationally restricted ('mechanic folding nucleus'); and (iii) transition state ensembles in some proteins could be evolutionarily conserved.
249 citations
TL;DR: These findings indicate that an initial collapse precedes the formation of significant native structure in the folds of streptococcal protein G, and elements of local structure originate in the regions of the protein shown to have higher H/2H exchange protection factors in early stages of folding.
200 citations
TL;DR: It is shown that both the I and fully unfolded states of αLP are lower in free energy than the native state, and Native αLP is thus metastable.
Abstract: α-Lytic protease (αLP), an extracellular bacterial protease, is synthesized with a large amino-terminal pro-region that is essential for its folding in vivo and in vitro1,2. In the absence of the pro-region, the protease folds to an inactive, partially folded state, designated ‘I’. The pro-region catalyses protease folding by directly stabilizing the folding transition state (>26 kcal mol−1) which separates the native state ‘N’ from I1,3. Although a basic tenet of protein folding is that the native state of a protein is at the minimum free energy4, we show here that both the I and fully unfolded states of αLP are lower in free energy than the native state. Native αLP is thus metastable: its apparent stability derives from a large barrier to unfolding. Consequently, the evolution of αLP has been distinct from most other proteins: it has not been constrained by the free-energy difference between the native and unfolded states, but instead by the size of its unfolding barrier.
191 citations
TL;DR: It is suggested that a good strategy to improve folding speed in proteins would be to stabilize the helices that are not folded in the denatured state but are partly present in the transition state.
171 citations
TL;DR: In this paper, it was shown that pairwise contact potentials alone cannot be used to predict the native fold of a protein, and that it is impossible to find a set of contact parameters for which the energy of the native contact map of a single protein (crambin) is lower than that of all possible physically realizable decoy maps.
Abstract: We demonstrate that pairwise contact potentials alone cannot be used to predict the native fold of a protein. Ideally, one would hope that a universal energy function exists, for which the native folds of all proteins are the respective ground states. Here we pose a much more restricted question: Is it possible to find a set of contact parameters for which the energy of the native contact map of a single protein (crambin) is lower than that of all possible physically realizable decoy maps? The set of maps we used was derived by energy minimization (not by threading). We seek such a set of parameters by perceptron learning, a procedure which is guaranteed to find such a set if it exists. We found that it is impossible to fine-tune contact parameters that will assign all alternative conformations higher energy than that of the native map. This finding proves that there is no pairwise contact potential that can be used to fold any given protein. Inclusion of additional energy terms, such as hydrophobic (solv...
154 citations
TL;DR: The mechanism and thermodynamics of small α/β protein folding were characterized at the atomic level in this paper by using the statistical mechanical methods of importance sampling and molecular dynamics, showing that the α-helix forms early and the β-sheet forms concomitantly with the overall topology.
Abstract: We characterize, at the atomic level, the mechanism and thermodynamics of folding of a small α/β protein. The thermodynamically significant states of segment B1 of streptococcal protein G (GB1) are probed by using the statistical mechanical methods of importance sampling and molecular dynamics. From a thermodynamic standpoint, folding commences with overall collapse, accompanied by formation of ∼35% of the native structure. Specific contacts form at the loci experimentally inferred to be structured early in folding kinetics studies. Our study reveals that these initially structured regions are not spatially adjacent. As folding progresses, fluid-like nonlocal native contacts form, with many contacts forming and breaking as the structure searches for the native conformation. Although the α-helix forms early, the β-sheet forms concomitantly with the overall topology. Water is present in the protein core up to a late stage of folding, lubricating conformational transitions during the search process. Once 80% of the native contacts have formed, water is squeezed from the protein interior and the structure descends into the native manifold. Examination of the onset of side-chain mobility within our model indicates side-chain motion is most closely linked to the overall volume of the protein and no sharp order–disorder transition appears to occur. Exploration of models for hydrogen deuterium exchange show qualitative agreement with equilibrium measurement of hydrogen/deuterium protection factors.
TL;DR: In this article, the rate-limiting conformational changes that underlie two-state folding were investigated experimentally on the refolding of the IgG binding domain of protein L. In conjunction with numerical simulations, the results indicated that the rate limiting changes of the folding of this domain are strongly coupled to solvent viscosity and lack any significant internal friction arising from intrachain collisions.
Abstract: Small, single-domain proteins typically fold via a compact transition-state ensemble in a process well fitted by a simple, two-state model. To characterize the rate-limiting conformational changes that underlie two-state folding, we have investigated experimentally the effects of changing solvent viscosity on the refolding of the IgG binding domain of protein L. In conjunction with numerical simulations, our results indicate that the rate-limiting conformational changes of the folding of this domain are strongly coupled to solvent viscosity and lack any significant “internal friction” arising from intrachain collisions. When compared with the previously determined solvent viscosity dependencies of other, more restricted conformational changes, our results suggest that the rate-limiting folding transition involves conformational fluctuations that displace considerable amounts of solvent. Reconciling evidence that the folding transition state ensemble is comprised of highly collapsed species with these and similar, previously reported results should provide a significant constraint for theoretical models of the folding process.
01 Jan 1998
TL;DR: This work investigates experimentally the effects of changing solvent viscosity on the refolding of the IgG binding domain of protein L and suggests that the rate-limiting folding transition involves conformational fluctuations that displace considerable amounts of solvent.
Abstract: Small, single-domain proteins typically fold via a compact transition-state ensemble in a process well fitted by a simple, two-state model. To characterize the rate-limiting conformational changes that underlie two-state folding, we have investigated experimentally the effects of changing solvent viscosity on the refolding of the IgG binding domain of protein L. In conjunction with numerical simula- tions, our results indicate that the rate-limiting conforma- tional changes of the folding of this domain are strongly coupled to solvent viscosity and lack any significant ''internal friction'' arising from intrachain collisions. When compared with the previously determined solvent viscosity dependencies of other, more restricted conformational changes, our results suggest that the rate-limiting folding transition involves con- formational f luctuations that displace considerable amounts of solvent. Reconciling evidence that the folding transition state ensemble is comprised of highly collapsed species with these and similar, previously reported results should provide a significant constraint for theoretical models of the folding process.
TL;DR: Results from mutants of CI2 and comparison with other two-state proteins point at the possibility that the barrier for folding is generally broad and that localised transition states result from minor ripples in the free-energy profile.
TL;DR: A microscopic variational theory for the free energy surface of a fast folding protein that allows folding kinetics to be resolved to the residue level using Debye-Waller factors as local order parameters is presented.
Abstract: We present a microscopic variational theory for the free energy surface of a fast folding protein that allows folding kinetics to be resolved to the residue level using Debye-Waller factors as local order parameters. We apply the method to the $\ensuremath{\lambda}$-repressor protein and compare with site directed mutagenesis experiments. The formation of native structure and the free energy profile along the folding route are shown to be well described by the capillarity approximation but with some fine structure due to local folding topology.
TL;DR: The major implication of the MFN model is that, even if the residues whose tertiary interactions are formed nearly completely in the transition state are mutated, it does not disrupt the nature of the nucleation-collapse mechanism.
TL;DR: It was found that even if the folding is under kinetic control, the sequence will evolve so that the native state is most often the state of minimum free energy.
Abstract: The validity of the thermodynamic hypothesis of protein folding was explored by simulating the evolution of protein sequences. Simple models of lattice proteins were allowed to evolve by random point mutations subject to the constraint that they fold into a predetermined native structure with a Monte Carlo folding algorithm. We employed a simple analytical approach to compute the probability of violation of the thermodynamic hypothesis as a function of the size of the protein, the fraction of the total number of possible conformations which are kinetically accessible, and the roughness of the free-energy landscape. It was found that even if the folding is under kinetic control, the sequence will evolve so that the native state is most often the state of minimum free energy.
TL;DR: It emerges from a comparison of the kinetic behaviour of several small model proteins that the free-energy barrier for folding could be generally broad and level, including deviations from classical two-state kinetics determined by free- energy extrapolations.
Abstract: Deviations from classical two-state kinetics in protein folding need not always be explained by the presence of rapidly formed intermediates. In some cases, such deviations are caused by short-lived aggregates whereas in other cases they arise from changes of the position of the transition state. These are two new facets of the mechanism of two-state folding. The first part of this account describes the effect of aggregates which form transiently in the first few milliseconds of the refolding reaction. The aggregates show many similarities with folding intermediates, but may be identified by their disappearance at low concentrations of protein where the two-state conversion of monomeric protein becomes predominant. In the second part, the focus is directed to two-state folding and movements of the transition state ensemble. The movements are used to derive information about the shape of the free-energy profile for folding. It emerges from a comparison of the kinetic behaviour of several small model proteins that the free-energy barrier for folding could be generally broad and level. An attractive feature of broad barriers is that, depending on minor variations in the fine-structure of the free-energy profile, they account for a wide range of seemingly unrelated folding data, including deviations from classical two-state kinetics determined by free-energy extrapolations. (Less)
TL;DR: The study shows that the energetic balance is the dominant factor governing protein sizes and it forces a large protein to break into several domains during folding.
TL;DR: The single helix in protein L appears to be largely disrupted at the rate-limiting step in folding and unfolding, in contrast to the predictions of models of folding involving the coalescence of well-formed secondary structure elements.
TL;DR: The impact of folding funnels and folding simulations on the way experimentalists interpret results is examined, and alpha-Helix formation is currently the fastest known process in protein folding, and incipient helices are present at the start of folding.
TL;DR: Results are broadly consistent with models of the transition states for folding of other small proteins derived from mutagenesis studies, and suggest that solvent perturbation methods can provide complementary information about the transition region of the energy surfaces for protein folding.
TL;DR: The analysis helps to interpret the results of protein engineering and allows observed φ values to be directly related to structural features of the unfolded state, the transition state and the native state.
TL;DR: The pH-dependence of hydrogen-exchange, in native conditions, is used to probe the formation of secondary structure in the folding of an immunoglobulin domain (CD2.d1) and shows the highest sequence conservation within the family of folds to which this domain belongs.
Abstract: The pH-dependence of hydrogen-exchange, in native conditions, is used to probe the formation of secondary structure in the folding of an immunoglobulin domain (CD2.d1). The intermediate and transition states in the reaction are insensitive to pH, a simplification that allows us to equate structure formation and folding kinetics. The crucial residues in the folding reaction are grouped in the B, C, E and F strands which constitute a ‘crossover’ nucleus in the β-sandwich. These residues show the highest sequence conservation within the family of folds to which this domain belongs and are located in a unit of structure that is the most consistent topo-logical feature of the immunoglobulin family.
TL;DR: The guanidine hydrochloride concentration dependence of the folding and unfolding rate constants of a derivative of α‐lactalbumin, in which the 6‐120 disulfide bond is selectively reduced and S‐carboxymethylated, supported the multiple‐pathway folding model and the molten globule state that accumulates at an early stage of fold is not an obligatory intermediate.
Abstract: The guanidine hydrochloride concentration dependence of the folding and unfolding rate constants of a derivative of alpha-lactalbumin, in which the 6-120 disulfide bond is selectively reduced and S-carboxymethylated, was measured and compared with that of disulfide-intact alpha-lactalbumin. The concentration dependence of the folding and unfolding rate constants was analyzed on the basis of the two alternative models, the intermediate-controlled folding model and the multiple-pathway folding model, that we had proposed previously. All of the data supported the multiple-pathway folding model. Therefore, the molten globule state that accumulates at an early stage of folding of alpha-lactalbumin is not an obligatory intermediate. The cleavage of the 6-120 disulfide bond resulted in acceleration of unfolding without changing the refolding rate, indicating that the loop closed by the 6-120 disulfide bond is unfolded in the transition state. It is theoretically shown that the chain entropy gain on removing the cross-link from a random coil chain with helical stretches can be comparable to that from an entirely random chain. Therefore, the present result is not inconsistent with the known structure in the molten globule intermediate. Based on this result and other knowledge obtained so far, the structure in the transition state of the folding reaction of alpha-lactalbumin is discussed.
TL;DR: The results suggest that efficient search for the core is dependent on both the native state's overall stability and its amount of kinetically accessible, cooperative structure, whereas rearrangement from the intermediate is facilitated by destabilization of contacts between surface monomers.
Abstract: We investigate the folding of a 125-bead heteropolymer model for proteins subject to Monte Carlo dynamics on a simple cubic lattice. Detailed study of a few sequences revealed a folding mechanism consisting of a rapid collapse followed by a slow search for a stable core that served as the transition state for folding to a near-native intermediate. Rearrangement from the intermediate to the native state slowed folding further because it required breaking native-like local structure between surface monomers so that those residues could condense onto the core. We demonstrate here the generality of this mechanism by a statistical analysis of a 200 sequence database using a method that employs a genetic algorithm to pick the sequence attributes that are most important for folding and an artificial neural network to derive the corresponding functional dependence of folding ability on the chosen sequence attributes [quantitative structure-property relationships (QSPRs)]. QSPRs that use three sequence attributes yielded substantially more accurate predictions than those that use only one. The results suggest that efficient search for the core is dependent on both the native state's overall stability and its amount of kinetically accessible, cooperative structure, whereas rearrangement from the intermediate is facilitated by destabilization of contacts between surface monomers. Implications for folding and design are discussed. Proteins 33:177–203, 1998. © 1998 Wiley-Liss, Inc.
TL;DR: Results indicate that the quasi‐chemical approximation can be used to connect quantitatively the occurrence of various residue–residue contacts in an ensemble of native structures with the energies of the contacts, and suggest that the extracted contact energies do contain information on structural stability and can beused to estimate actual structural energetics.
Abstract: In this study, we exploited an elementary 2-dimensional square lattice model of HP polymers to test the premise of extracting contact energies from protein structures. Given a set of prespecified energies for H–H, H–P, and P–P contacts, all possible sequences of various lengths were exhaustively enumerated to find sequences that have unique lowest-energy conformations. The lowest-energy structures (or native structures) of such (native) sequences were used to extract contact energies using the Miyazawa-Jernigan procedure and here-defined reference state. The relative magnitudes of the original energies were restored reasonably well, but the extracted contact energies were independent of the absolute magnitudes of the initial energies. We turned to a more detailed characterization of the energy landscapes of the native sequences in light of a new theoretical framework on protein folding. Foldability of such sequences imposes two limits on the absolute value of the prespecified energies: a lower bound entailed by the minimum requirement for thermodynamic stability and an upper bound associated with the entrapment of the chain to local minima. We found that these two limits confine the prespecified energy values to a rather narrow range which, surprisingly, also contains the extracted energies in all the cases examined. These results indicate that the quasi-chemical approximation can be used to connect quantitatively the occurrence of various residue–residue contacts in an ensemble of native structures with the energies of the contacts. More importantly, they suggest that the extracted contact energies do contain information on structural stability and can be used to estimate actual structural energetics. This study also encourages the use of structure-derived contact energies in threading. The finding that there is a rather narrow range of energies that are optimal for folding a sequence also cautions the use of arbitrary energy Hamiltonion in minimal folding models. Proteins 31:299–308, 1998. © 1998 Wiley-Liss, Inc.
TL;DR: In this paper, the authors consider the energy landscape roughness in protein sequence design and find that mutations that reduce the energetic roughness at the expense of increasing the native-state energy generally lead to a fast folding and stable protein at lower temperatures.
Abstract: This work addresses the consideration of the energy landscape roughness in protein sequence design. The proteins are modeled by 2D lattice chains, initially designed to maximize the energy gap between the folded and unfolded states. Additional optimization and control of the folding properties is achieved by specific sequence mutations that alter the energetic and geometric roughness of the landscape. It is found that mutations that reduce the energetic roughness at the expense of increasing the native-state energy generally lead to a fast folding and stable protein at lower temperatures. Such mutations are also found to modify the geometric roughness (related to nucleation effects) creating variations in the folding time that depends specifically on each sequence and can lead in many cases to a reduction of the total landscape roughness. An additional reduction of the geometric roughness is achieved by adding local bond-angle propensities to selected sequence sites.
TL;DR: In this article, the results of 3D lattice Monte Carlo simulations of protein folding were presented in the framework of a model taking into account the dependence of the energy of interaction of amino acid residues on their orientation and the rigidity of the polypeptide chain.
Abstract: We present the results of 3D lattice Monte Carlo simulations of protein folding in the framework of a model taking into account the dependence of the energy of interaction of amino acid residues on their orientation and the rigidity of the polypeptide chain. For the model parameters corresponding to the formation of ideal β sheets (such flat fragments of proteins are stabilized by hydrogen bonds), the folding time of chains of length n is found to scale as tf nα with α = 6.8 ± 0.6.
TL;DR: From comparisons performed on a domain of the family sharing 24% identity with FKBP, it appears that the number of fragments, and therefore their location, are sequence dependent.
Abstract: Monte-Carlo simulations of folding of the human protein FKBP are presented. The protein is confined in a simple cubic lattice and only nearest-neighbour interactions are considered. The evolution of protein structure, energy and diameter is followed over time. Starting from different extended conformations, compact globular forms with a hydrophobic core are reached above a critical temperature Tc, while below Tc the protein 'freezes' into high-energy, non-compact states. In the temperature range of folding, all the recorded intermediate states belong to two structural groups, where the process spends most of its time, separated by relatively fast transitions. During folding, the protein is successively composed of three and two compact fragments, whose separation occurs at loop positions. From comparisons performed on a domain of the family sharing 24% identity with FKBP, it appears that the number of fragments, and therefore their location, are sequence dependent.