Interpreting the folding kinetics of helical proteins (original) (raw)
Related papers
Kinetics and thermodynamics of folding in model proteins
Proceedings of the National …, 1993
Monte Carlo simulations on a class of lattice models are used to probe the thermodynamics and kinetics of protein folding. We find two transition temperatures: one at To, when chains collapse from a coil to a compact phase, and the other at Tf (< TO), when chains adopt a conformation corresponding to their native state. The kinetics are probed by several correlation functions and are interpreted in terms ofthe underlying energy landscape. The transition from the coil to the native state occurs in three distinct stages. The initial stage corresponds to a random collapse of the protein chain. At intermediate times i¢, during which much of the native structure is acquired, there are multiple pathways. For longer times rr (>> r,) the decay is exponential, suggestive of a late transition state. The folding time scale (= rr) varies greatly depending on the model. Implications of our results for in vitro folding of proteins are discussed.
Folding Thermodynamics of a Model Three-Helix-Bundle Protein
Proceedings of The National Academy of Sciences, 1997
The calculated folding thermodynamics of a simple off-lattice three-helix-bundle protein model under equilibrium conditions shows the experimentally observed protein transitions: a collapse transition, a disordered-toordered globule transition, a globule to native-state transition, and the transition from the active native state to a frozen inactive state. The cooperativity and physical origin of the various transitions are explored with a single ''optimization'' parameter and characterized with the Lindemann criterion for liquid versus solid-state dynamics. Below the folding temperature, the model has a simple free energy surface with a single basin near the native state; the surface is similar to that calculated from a simulation of the same three-helixbundle protein with an all-atom representation [Boczko, E. M. & Brooks III, C. L. (1995) Science 269, 393-396].
Folding of a model three-helix bundle protein: a thermodynamic and kinetic analysis1
Journal of Molecular Biology, 1999
The kinetics and thermodynamics of an off-lattice model for a three-helix bundle protein are investigated as a function of a bias gap parameter that determines the energy difference between native and non-native contacts. A simple dihedral potential is used to introduce the tendency to form right-handed helices. For each value of the bias parameter, 100 trajectories of up to one microsecond are performed. Such statistically valid sampling of the kinetics is made possible by the use of the discrete molecular dynamics method with square-well interactions. This permits much faster simulations for off-lattice models than do continuous potentials. It is found that major folding pathways can be de®ned, although ensembles with considerable structural variation are involved. The large gap models generally fold faster than those with a smaller gap. For the large gap models, the kinetic intermediates are non-obligatory, while both obligatory and non-obligatory intermediates are present for small gap models. Certain large gap intermediates have a two-helix microdomain with one helix extended outward (as in domain-swapped dimers); the small gap intermediates have more diverse structures. The importance of studying the kinetic, as well as the thermodynamics, of folding for an understanding of the mechanism is discussed and the relation between kinetic and equilibrium intermediates is examined. It is found that the behavior of this model system has aspects that encompass both the``new'' view and the``old'' view of protein folding.
Proceedings of The National Academy of Sciences, 2011
Quantitative description of how proteins fold under experimental conditions remains a challenging problem. Experiments often use urea and guanidinium chloride to study folding whereas the natural variable in simulations is temperature. To bridge the gap, we use the molecular transfer model that combines measured denaturant-dependent transfer free energies for the peptide group and amino acid residues, and a coarse-grained C α -side chain model for polypeptide chains to simulate the folding of src SH 3 domain. Stability of the native state decreases linearly as ½C (the concentration of guanidinium chloride) increases with the slope, m, that is in excellent agreement with experiments. Remarkably, the calculated folding rate at ½C¼0 is only 16-fold larger than the measured value. Most importantly ln k obs (k obs is the sum of folding and unfolding rates) as a function of ½C has the characteristic V (chevron) shape. In every folding trajectory, the times for reaching the native state, interactions stabilizing all the substructures, and global collapse coincide. The value of m f m (m f is the slope of the folding arm of the chevron plot) is identical to the fraction of buried solvent accessible surface area in the structures of the transition state ensemble. In the dominant transition state, which does not vary significantly at low ½C, the core of the protein and certain loops are structured. Besides solving the long-standing problem of computing the chevron plot, our work lays the foundation for incorporating denaturant effects in a physically transparent manner either in all-atom or coarse-grained simulations.
Atomistic description of the folding of a dimeric protein
2013
Equilibrium molecular dynamics simulations are increasingly being used to describe the folding of individual proteins and protein domains at an atomic level of detail. Isolated protein domains, however, are rarely observed in vivo, where multidomain proteins and multimeric assemblies are far more common. It is clear that the folding of such proteins is often inextricably coupled with the process of dimerization; indeed, many protein monomers and protein domains are not stable in isolation, and fold to their native structures only when stabilized by interactions with other members of a protein complex. Here, we use equilibrium molecular dynamics simulations with an aggregate simulation length of 4 ms to elucidate key aspects of the folding mechanism, and of the associated free-energy surface, of the Top7-CFr dimer, a 114-amino-acid protein homodimer with a mixed α/β structure. In these simulations, we observed a number of folding and unfolding events. Each folding event was characterized by the assembly of two unfolded Top7-CFr monomers to form a stable, folded dimer. We found that the isolated monomer is unstable but that, early in the folding pathway, nascent native structure is stabilized by contacts between the two monomer subunits. These contacts are in some cases native, as in an induced-folding model, and in other cases non-native, as in a fly-casting mechanism. Occasionally, folding by conformational selection, in which both subunits form independently before dimerization, was also observed. Folding then proceeds through the sequential addition of strands to the protein β sheet. Although the longtime-scale relaxation of the folding process can be well described by a single exponential, these simulations reveal the presence of a number of kinetic traps, characterized by structures in which individual strands are added in an incorrect order.
A Minimal Model of Three-State Folding Dynamics of Helical Proteins
Journal of Physical Chemistry B, 2005
A diffusion-collision-like model is proposed for helical proteins with three-state folding dynamics. The model generalizes a previous scheme based on the dynamics of putatively essential parts of the protein (foldons) that was successfully tested on proteins with two-state folding. We show that the extended model, unlike the original one, allows satisfactory calculation of the folding rate and reconstruction of the salient steps of the folding pathway of two proteins with three-state folding (Im7 and p16). The dramatic reduction of variables achieved by focusing on the foldons makes our model a good candidate for a minimal description of the folding process also for three-state folders. Finally, the applicability of the foldon diffusion-collision model to two-state and three-state folders suggests that different folding mechanisms are amenable to conceptually homogeneous descriptions. The implications for a unification of the variety of folding theories so far proposed for helical proteins are discussed in the final discussion.
An experimental survey of the transition between two-state and downhill protein folding scenarios
2008
A kinetic and thermodynamic survey of 35 WW domain sequences is used in combination with a model to discern the energetic requirements for the transition from two-state folding to downhill folding. The sequences used exhibit a 600-fold range of folding rates at the temperature of maximum folding rate. Very stable proteins can achieve complete downhill folding when the temperature is lowered sufficiently below the melting temperature, and then at even lower temperatures they become two-state folders again because of cold denaturation. Less stable proteins never achieve a sufficient bias to fold downhill because of the onset of cold denaturation. The model, considering both heat and cold denaturation, reveals that to achieve incipient downhill folding (barrier <3 RT) or downhill folding (no barrier), the WW domain average melting temperatures have to be >50°C for incipient downhill folding and >90°C for downhill folding.
Protein model exhibiting three folding transitions
Physica A: Statistical Mechanics and its Applications, 2001
We explain the physical basis of a model for small globular proteins with water interactions. The water is supposed to access the protein interior in an "all-or-none" manner during the unfolding of the protein chain. As a consequence of this mechanism (somewhat speculative), the model exhibits fundamental aspects of protein thermodynamics, as cold, and warm unfolding of the polypeptide chain, and hence decreasing the temperature below the cold unfolding the protein folds again, accordingly the heat capacity has three characteristic peaks. The cold and warm unfolding has a sharpness close to a two-state system, while the cold folding is a transition where the intermediate states in the folding is energetical close to the folded/unfolded states, yielding a less sharp transition. The entropy of the protein chain causes both the cold folding and the warm unfolding.
Journal of Molecular Biology, 2002
To what extent do general features of folding/unfolding kinetics of small globular proteins follow from their thermodynamic properties? To address this question, we investigate a new simplifed protein chain model that embodies a cooperative interplay between local conformational preferences and hydrophobic burial. The present four-helix-bundle 55mer model exhibits proteinlike calorimetric two-state cooperativity. It rationalizes native-state hydrogen exchange observations. Our analysis indicates that a coherent, self-consistent physical account of both the thermodynamic and kinetic properties of the model leads naturally to the concept of a native state ensemble that encompasses considerable confomational fluctuations. Such a multiple-conformation native state is seen to involve conformational states similar to those revealed by native-state hydrogen exchange. Many of these conformational states are predicted to lie below native baselines commonly used in interpreting calorimetric data. Folding and unfolding kinetics are studied under a range of intrachain interaction strengths as in experimental chevron plots. Kinetically determined transition midpoints match well with their thermodynamic counterparts. Kinetic relaxations are found to be essentially single exponential over an extended range of model interaction strengths. This includes the entire unfolding regime and a significant part of a folding regime with a chevron rollover, as has been observed for real proteins that fold with non-two-state kinetics. The transition state picture of protein folding and unfolding is evaluated by comparing thermodynamic free energy profiles with actual kinetic rates. These analyses suggest that some chevron rollovers may arise from an internal frictional effect that increasingly impedes chain motions with more native conditions, rather than being caused by discrete deadtime folding intermediates or shifts of the transition state peak as previously posited.