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We present an approach to the study of protein folding that uses the combined power of replica exchange simulations and a network model for the kinetics. We carry out replica exchange simulations to generate a large (Ϸ10 6 ) set of states with an all-atom effective potential function and construct a kinetic model for folding, using an ansatz that allows kinetic transitions between states based on structural similarity. We use this network to perform random walks in the state space and examine the overall network structure. Results are presented for the C-terminal peptide from the B1 domain of protein G. The kinetics is two-state after small temperature perturbations. However, the coil-to-hairpin folding is dominated by pathways that visit metastable helical conformations. We propose possible mechanisms for the ␣-helix͞ ␤-hairpin interconversion.graph ͉ master equation ͉ protein G P rotein folding is a fundamental problem in modern structural biology, and recent advances in experimental techniques have helped to elucidate some of the thermodynamic and kinetic features that underlie different stages of the folding process (1-3). Computer simulations using reduced (4-11) and atomistic molecular models (12-21) have played a central role in the interpretation of experimental studies. Although reduced models have provided considerable insight into the overall mechanisms of protein folding, especially in helping to clarify the nature of folding funnels, intermediates, and kinetic bottlenecks, they are limited in their ability to explore the detailed molecular aspects of folding. However, because of the large number of degrees of freedom and the rarity of folding events even in small model systems, all-atom simulations require both considerable computational resources and ingenuity to obtain meaningful results; a variety of methods have been developed to increase simulation efficiency.A particularly powerful technique for the calculation of free energy surfaces and other thermodynamic properties of complex systems is replica exchange molecular dynamics (REMD) (22), in which a generalized ensemble of the system is simulated in parallel over a range of temperatures. Periodically, coordinates are exchanged by using a Metropolis criterion that ensures that at any given temperature a canonical distribution is realized and allows for more efficient barrier crossing than could be obtained with conventional simulation methods. Although REMD is a powerful method for exploring free energy landscapes, it does not provide direct information about kinetics. To study folding by using all-atom effective potentials, heterogeneous distributed computing (16,19) and transition path sampling (23, 24) techniques have been used. Although the former can enhance sampling by combining information from a large number of short MD trajectories ''steered'' by rare events, these techniques can introduce a bias toward fast events in the ensemble average of the reactive trajectories (25). Transition path sampling (23,24) can yield quantitative estimat...

Section: Discussionmentioning

confidence: 94%

Protein folding pathways from replica exchange simulations and a kinetic network model

Andrec

Felts

Gallicchio

et al. 2005

138

167

“…in experimental (13)(14)(15) as well as computational studies using simplified approaches (16,17). Our results are obtained using first-principle all-atom Monte Carlo simulations.…”

Section: Resultsmentioning

confidence: 99%

Simulation of Top7-CFr: A transient helix extension guides folding

Mohanty

Meinke

Zimmermann

et al. 2008

Protein structures often feature β-sheets in which adjacent β-strands have large sequence separation. How the folding process orchestrates the formation and correct arrangement of these strands is not comprehensively understood. Particularly challenging are proteins in which β-strands at the N and C termini are neighbors in a β-sheet. The N-terminal β-strand is synthesized early on, but it can not bind to the C terminus before the chain is fully synthesized. During this time, there is a danger that the β-strand at the N terminus interacts with nearby molecules, leading to potentially harmful aggregates of incompletely folded proteins. Simulations of the C-terminal fragment of Top7 show that this risk of misfolding and aggregation can be avoided by a "caching" mechanism that relies on the "chameleon" behavior of certain segments.protein folding | all-atom simulation | folding mechanism | chameleon segment | nonnative intermediates S tructure and function of proteins are determined by their amino acid sequence. How proteins find their functional native form is a long-standing question (1-3). Protein synthesis is directional from the N to the C terminus. In proteins with end-toend β-sheets, there is a danger that the N-terminal strand binds to nearby molecules or other parts of the chain, as the strand cannot bind to the C-terminal strand until the molecule is fully synthesized. Misfolding and aggregation may be the consequence. In our simulations, the N terminus of fragment Glu-2-Leu-50 of the 59-residue CFr (Protein Data Bank ID code 2GJH) (4) avoids the risk of misfolding by growing first into a non-native extension of an existing α-helix. Only after the other structural elements have formed and correctly assembled, does the N terminus unfold and attach to the C-terminal β-sheet as its last closing strand. We speculate that such a temporary caching of β-strands is a common mechanism that eases folding and hinders aggregation.The C-terminal fragment (CFr) (5) of the designed protein Top7 (6) forms a stable homodimer, whose secondary structure remains nearly unchanged up to 98 • C and high concentrations of denaturant (4). It is a model for small fast-folding proteins with complex topology and diverse secondary structure elements (see Fig. 1). Such proteins often have long-distance (in sequence) contacts between β-strands. Unlike helix contacts, these depend on the conformation of a large segment between the strands. It is unlikely that these contacts form before the intermediate segment has folded, as this would lead to a large entropic cost, or even interfere with the folding of the connecting segment. For slowfolding proteins, one can conjecture a "backtracking" mechanism (7) where folding succeeds only after breaking of prematurely formed β-contacts. In this study, we explore in silico the behavior of fast-folding proteins, as computational approaches (8, 9) can resolve details of folding that are beyond the reach of experiments. Results and DiscussionWe find that the CFr monomer folds to a native-like conform...

“…ignificant advances in theory and experiment are producing an increasingly detailed description of how a polypeptide self-assembles into the native structure of a protein (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11). Energy landscape theories (1,(12)(13)(14)(15), in particular, have provided a framework for interpreting experimental investigations of protein folding kinetics.…”

mentioning

confidence: 99%

Using deeply trapped intermediates to map the cytochrome c folding landscape

Tezcan

Findley

Crane

et al. 2002

Replacement of iron with cobalt(III) selectively introduces a deep trap in the folding-energy landscape of the heme protein cytochrome c. Remarkably, neither the protein structure nor the folding thermodynamics is perturbed by this metal-ion substitution, as shown by data from spectroscopic and x-ray diffraction experiments. Through kinetics measurements, we have found parallel folding pathways involving several different misligated Co(III) species, and, as these folding intermediates persist for several hours under certain conditions, we have been able to elucidate fully their spectroscopic properties. The results, along with an analysis of the fluorescence energy-transfer kinetics during refolding, show that rapidly equilibrating populations of compact and extended polypeptide conformations are present until all molecules have reached the native structure. These measurements provide direct evidence that collapsed denatured structures are not substantially more stable than extended conformations of cytochrome c. Significant advances in theory and experiment are producing an increasingly detailed description of how a polypeptide self-assembles into the native structure of a protein (1-11). Energy landscape theories (1, 12-15), in particular, have provided a framework for interpreting experimental investigations of protein folding kinetics. Despite this progress, many fundamental questions about protein folding dynamics remain to be answered.Years of experimental work on the energetics and dynamics of self-assembly of cytochrome c (Cyt c) have failed to resolve whether unfolded polypeptides undergo global collapse to compact conformations on dilution or laser triggering to solution conditions that strongly favor the native structure (11,(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26). Indeed, recent kinetics experiments suggest that comparable populations of compact and extended polypeptides are formed rapidly (Ͻ1 ms), and these two populations disappear in parallel as the protein folds (27,28). To test this energy landscape model rigorously, we have isolated the structures that comprise the submillisecond (or ''burst'') phase by replacing the native iron center with cobalt(III) (29): because of very high ligand substitution barriers, the final step of cobalt(III)-Cyt c (Co-Cyt c) folding is well separated in time from all early events, and, in this kinetically stabilized system, the early folding intermediates can be examined carefully over a period of hours by an entire armamentarium of physical methods. Materials and MethodsUV-visible and CD and fluorescence spectra were collected with Hewlett-Packard 8452A, Aviv (Lakewood, NJ) 62A DS, and Hitachi (Tokyo) F-4500 spectrometers, respectively. Fluorescence decay kinetics were measured as described previously (27). Horse, tuna, and yeast Co-Cyt were prepared according to established protocols (30, 31) with minor modifications. For the modification of yeast-Co-Cyt c with a dansyl fluorophore at Cys-102 (DNS-Co-Cyt c), FPLC-purified yeast Co-Cyt c was treated with exce...