Relationships between unfolded configurations of proteins and dynamics of folding to the native state (original) (raw)
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Proceedings of the National Academy of Sciences, 2001
Previous experimental and theoretical studies have produced highresolution descriptions of the native and folding transition states of chymotrypsin inhibitor 2 (CI2). In similar fashion, here we use a combination of NMR experiments and molecular dynamics simulations to examine the conformations populated by CI2 in the denatured state. The denatured state is highly unfolded, but there is some residual native helical structure along with hydrophobic clustering in the center of the chain. The lack of persistent nonnative structure in the denatured state reduces barriers that must be overcome, leading to fast folding through a nucleation-condensation mechanism. With the characterization of the denatured state, we have now completed our description of the folding͞ unfolding pathway of CI2 at atomic resolution.
Equilibrium folding pathways for model proteins
Journal of Statistical Physics, 1983
Protein conformations have been generated with both a Monte Carlo scheme and a simpler two-state noninteracting globule-coil model. Conformational energies are taken to consist of intraresidue and interresidue terms. Interresidue energies are taken to be proportional to the number of nativelike contacts. To describe probable folding pathways, either energy or the number of native residues are employed as simple one-dimensional folding-unfolding coordinates. By considering only conformations at each point on these coordinates, it is possible to obtain detailed conformational descriptions of relatively rare intermediates on the folding pathway. This technique of "trapping" intermediates and statistically characterizing them is useful for studying conformational transitions. Equilibrium folding-unfolding pathways have been constructed by connecting most probable conformations in order along the folding coordinate. Calculations with the noninteracting globule-coil model have been performed with details chosen to correspond to those in the Monte Carlo calculation for pancreatic trypsin inhibitor. Both pathways are similar. The a helix appears prior to formation of the central beta sheet; beta sheet formation coincides with a large maximum in the free energy because of the attendant loss of conformational entropy. Subsequently the Monte Carlo method indicates two alternative pathways for growth toward either the amino or the carboxyl terminus, followed by completion of the native form. For the globule-coil model, the growth pattern differs somewhat, with the appearance of the single pathway for folding up to the carboxyl terminus prior to completion of folding. This difference may originate in the Monte Carlo sampling procedures or in the simplifications of the globule-coil model.
Characterization of protein-folding pathways by reduced-space modeling
Proceedings of the National Academy of Sciences, 2007
Ab initio simulations of the folding pathways are currently limited to very small proteins. For larger proteins, some approximations or simplifications in protein models need to be introduced. Protein folding and unfolding are among the basic processes in the cell and are very difficult to characterize in detail by experiment or simulation. Chymotrypsin inhibitor 2 (CI2) and barnase are probably the best characterized experimentally in this respect. For these model systems, initial folding stages were simulated by using CA-CB-side chain (CABS), a reduced-space protein-modeling tool. CABS employs knowledge-based potentials that proved to be very successful in protein structure prediction. With the use of isothermal Monte Carlo (MC) dynamics, initiation sites with a residual structure and weak tertiary interactions were identified. Such structures are essential for the initiation of the folding process through a sequential reduction of the protein conformational space, overcoming the Levinthal paradox in this manner. Furthermore, nucleation sites that initiate a tertiary interactions network were located. The MC simulations correspond perfectly to the results of experimental and theoretical research and bring insights into CI2 folding mechanism: unambiguous sequence of folding events was reported as well as cooperative substructures compatible with those obtained in recent molecular dynamics unfolding studies. The correspondence between the simulation and experiment shows that knowledge-based potentials are not only useful in protein structure predictions but are also capable of reproducing the folding pathways. Thus, the results of this work significantly extend the applicability range of reduced models in the theoretical study of proteins.
Proceedings of The National Academy of Sciences, 2005
We report the application of Langevin dynamics to the physicsbased united-residue (UNRES) force field developed in our laboratory. Ten trajectories were run on seven proteins [PDB ID codes 1BDD (␣; 46 residues), 1GAB (␣; 47 residues), 1LQ7 (␣; 67 residues), 1CLB (␣; 75 residues), 1E0L (; 28 residues), and 1E0G (␣؉; 48 residues), and 1IGD (␣؉; 61 residues)] with the UNRES force field parameterized by using our recently developed method for obtaining a hierarchical structure of the energy landscape. All ␣helical proteins and 1E0G folded to the native-like structures, whereas 1IGD and 1E0L yielded mostly nonnative ␣-helical folds although the native-like structures are lowest in energy for these two proteins, which can be attributed to neglecting the entropy factor in the current parameterization of UNRES. Average folding times for successful folding simulations were of the order of nanoseconds, whereas even the ultrafast-folding proteins fold only in microseconds, which implies that the UNRES time scale is approximately three orders of magnitude larger than the experimental time scale because the fast motions of the secondary degrees of freedom are averaged out. Folding with Langevin dynamics required 2-10 h of CPU time on average with a single AMD Athlon MP 2800؉ processor depending on the size of the protein. With the advantage of parallel processing, this process leads to the possibility to explore thousands of folding pathways and to predict not only the native structure but also the folding scenario of a protein together with its quantitative kinetic and thermodynamic characteristics.
The “first in-last out” hypothesis on protein folding revisited
Proteins: Structure, Function, and Bioinformatics, 2005
We calculated profiles for mean residue depth, contact order, and number of contacts in the native structure of a series of proteins for which folding has been studied extensively, the chymotrypsin inhibitor 2, the SH3 module from the src tyrosine kinase, the small ribonuclease barnase, the bacterial immunity protein Im7, and apomyoglobin. We compared these profiles with experimental data from equilibrium or pulse labeling hydrogendeuterium exchange obtained from NMR and values obtained from the protein engineering approach. We find a good qualitative agreement between the hierarchy of formation of topological elements during the folding process and the ranking of secondary structure elements in terms of residue depth. Residues that are most deeply buried in the core of the native protein usually belong to stretches of secondary structure elements that are formed early in the folding pathway. Residue depth can thus provide a useful and simple tool for the design of folding experiments.
Protein Science, 2011
The pathway which proteins take to fold can be influenced from the earliest events of structure formation. In this light, it was both predicted and confirmed that increasing the stiffness of a beta hairpin turn decreased the size of the transition state ensemble (TSE), while increasing the folding rate. Thus, there appears to be a relationship between conformationally restricting the TSE and increasing the folding rate, at least for beta hairpin turns. In this study, we hypothesize that the enormous sampling necessary to fold even two-state folding proteins in silico could be reduced if local structure constraints were used to restrict structural heterogeneity by polarizing folding pathways or forcing folding into preferred routes. Using a Gō model, we fold Chymotrypsin Inhibitor 2 (CI-2) and the src SH3 domain after constraining local sequence windows to their native structure by rigid body dynamics (RBD). Trajectories were monitored for any changes to the folding pathway and differences in the kinetics compared with unconstrained simulations. Constraining local structure decreases folding time twofold for 41% of src SH3 windows and 45% of CI-2 windows. For both proteins, folding times are never significantly increased after constraining any window. Structural polarization of the folding pathway appears to explain these rate increases. Folding rate enhancements are consistent with the goal to reduce sampling time necessary to reach native structures during folding simulations. As anticipated, not all constrained windows showed an equal decrease in folding time. We conclude by analyzing these differences and explain why RBD may be the preferred way to constrain structure.
Molecular Dynamics Simulations of Protein Folding
Protein Structure Prediction, 2008
Putative transition-state ensemble (TSE) conformations of src SH3 were identified by monitoring the deviation from the experimental values along molecular dynamics (MD) simulations of unfolding. Sixty MD trajectories (for a total of about 7 s) were then started from the putative TSE. About one-half of the 60 runs reached the folded state while unfolding was observed in the remaining half of the runs. This result validates -value analysis as an approach to obtain structural information on the transition state. It also demonstrates that an atomic resolution description of the TSE can be extracted from MD simulations. All conformations in the TSE have the central three-stranded -sheet formed in agreement with experimental data. An elongation of strand 2 as well as nonnative side-chain interactions between the diverging turn and the distal hairpin are observed. The simulation results indicate that the tight packing of the side chains between the diverging turn and the distal hairpin is a necessary condition for rapid folding. Contacts between residues in the most structured element of the TSE, the central -sheet, are kinetically more important than those between the N-and C-terminal strands.
Monte Carlo simulation of protein folding in the presence of residue-specific binding sites
Biopolymers, 2005
Ensemble growth Monte Carlo (EGMC) and dynamic Monte Carlo (DMC) simulations are used to study sequential folding and thermodynamic stability of hydrophobic-polar (HP) chains that fold to a compact structure. Molecularly imprinted cavities are modeled as hard walls having sites that are attractive to specific polar residues on the chain. Using EGMC simulation, we find that the folded conformation can be stabilized using a small number of carefully selected residuespecific sites while a random selection of surface-bound residues may only slightly contribute toward stabilizing the folded conformation, and in some cases may hinder the folding of the chain. DMC simulations of the surface-bound chain confirm increased stability of the folded conformation over a free chain. However, a different trend of the equilibrium population of folded chains as a function of residue-external site interactions is predicted with the two simulation methods.