A Minimal Model of Three-State Folding Dynamics of Helical Proteins (original) (raw)
Related papers
Proteins-structure Function and Bioinformatics, 2006
In this article we use mutation studies as a benchmark for a minimal model of the folding process of helical proteins. The model ascribes a pivotal role to the collisional dynamics of a few crucial residues (foldons) and predicts the folding rates by exploiting information drawn from the protein sequence. We show that our model rationalizes the effects of point mutations on the kinetics of folding. The folding times of two proteins and their mutants are predicted. Stability and location of foldons have a critical role as the determinants of protein folding. This allows us to elucidate two main mechanisms for the kinetic effects of mutations. First, it turns out that the mutations eliciting the most notable effects alter protein stability through stabilization or destabilization of the foldons. Secondly, the folding rate is affected via a modification of the foldon topology by those mutations that lead to the birth or death of foldons. The few mispredicted folding rates of some mutants hint at the limits of the current version of the folding model proposed in the present article. The performance of our folding model declines in case the mutated residues are subject to strong long-range forces. That foldons are the critical targets of mutation studies has notable implications for design strategies and is of particular interest to address the issue of the kinetic regulation of single proteins in the general context of the overall dynamics of the interactome. Proteins 2006. © 2006 Wiley-Liss, Inc.
Interpreting the folding kinetics of helical proteins
Nature, 1999
The detailed mechanism of protein folding is one of the major problems in structural biology 1,2 . Its solution is of practical as well as fundamental interest because of its possible role in utilizing the many sequences becoming available from genomic analysis 3 . Although the Levinthal paradox 4 (namely, that a polypeptide chain can ®nd its unique native state in spite of the astronomical number of con®gurations in the denatured state) has been resolved 4±7 , the reasons for the differences in the folding behaviour of individual proteins remain to be elucidated. Here a C abased three-helix-bundle-like protein model with a realistic thermodynamic phase diagram is used to calculate several hundred folding trajectories. By varying a single parameter, the difference between the strength of native and non-native contacts, folding is changed from a diffusion±collision mechanism 8 to one that involves simultaneous collapse and partial secondary-structure formation, followed by reorganization to the native structure. Non-obligatory intermediates are important in the former, whereas there is an obligatory on-pathway intermediate in the latter. Our results provide a basis for understanding the range of folding behaviour that is observed in helical proteins.
Protein folding: search for basic physical models
2003
How a unique three-dimensional structure is rapidly formed from the linear sequence of a polypeptide is one of the important questions in contemporary science. Apart from biological context of in vivo protein folding (which has been studied only for a few proteins), the roles of the fundamental physical forces in the in vitro folding remain largely unstudied. Despite a degree of success in using descriptions based on statistical and/or thermodynamic approaches, few of the current models explicitly include more basic physical forces (such as electrostatics and Van Der Waals forces). Moreover, the present-day models rarely take into account that the protein folding is, essentially, a rapid process that produces a highly specific architecture. This review considers several physical models that may provide more direct links between sequence and tertiary structure in terms of the physical forces. In particular, elaboration of such simple models is likely to produce extremely effective computational techniques with value for modern genomics.
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.
Biochemistry, 2001
This paper presents a new method for calculating the folding-unfolding rates of globular proteins. The method is based on solution of kinetic equations for a network of folding-unfolding pathways of the proteins. The rates are calculated in the point of thermodynamic equilibrium between the native and completely unfolded states. The method has been applied to all the proteins listed by Jackson [Jackson, S. E. (1998) Folding Des. 3, R81-R91] and some peptides. Although the studied protein chains differ by more than 1 order of magnitude in size and exhibit two-as well as three-state kinetics in water, and their folding rates cover more than 11 orders of magnitude, the theoretical estimates are reasonable close to the experimentally measured folding rates in midtransition (the correlation coefficient being as high as 0.78). This means that the presented theory (having no adjustable parameters at all) is consistent with the experimental observations.
Fast folding of a helical protein initiated by the collision of unstructured chains
Proceedings of the National Academy of Sciences, 2004
To examine whether helix formation necessarily precedes chain collision, we have measured the folding of a fully helical coiled coil that has been specially engineered to have negligible intrinsic helical propensity but high overall stability. The folding rate approaches the diffusion-limited value and is much faster than possible if folding is contingent on precollision helix formation. Therefore, the collision of two unstructured chains is the initial step of the dominant kinetic pathway, whereas helicity exerts its influence only at a later step. Folding from an unstructured encounter complex may be efficient and robust, which has implications for any biological process that couples folding to binding.
Model for the Nucleation Mechanism of Protein Folding
The Journal of Physical Chemistry B, 2007
A nucleation-like pathway of protein folding involves the formation of a cluster containing native residues that grows by including residues from the unfolded part of the protein. This pathway is examined by using a heteropolymer as a protein model. The model heteropolymer consists of hydrophobic and hydrophilic beads with fixed bond lengths and bond angles. The total energy of the heteropolymer is determined by the pairwise repulsive/attractive interactions between nonlinked beads and by the contribution from the dihedral angles involved. The parameters of these interactions can be rigorously defined, unlike the ill-defined surface tension of a cluster of protein residues that constitutes the basis of a previous nucleation model. The main idea underlying the new model consists of averaging the dihedral potential of a selected residue over all possible configurations of all neighboring residues along the protein chain. The resulting average dihedral potential depends on the distance between the selected residue and the cluster center. Its combination with the average pairwise potential of the selected residue and with a confining potential caused by the bonds between the residues leads to an overall potential around the cluster that has a double-well shape. Residues in the inner (closer to the cluster) well are considered as belonging to the folded cluster, whereas those in the outer well are treated as belonging to the unfolded part of the protein. Transitions of residues from the inner well into the outer one and vice versa are considered as elementary emission and absorption events, respectively. The double-well character of the potential well around the cluster allows one to determine the rates of both emission and absorption of residues by the cluster using a first passage time analysis. Once these rates are found as functions of the cluster size, one can develop a self-consistent kinetic theory for the nucleation mechanism of folding of a protein. The model allows one to evaluate the size of the nucleus and the protein folding time. The latter is evaluated as the sum of the times necessary for the first nucleation event to occur and for the nucleus to grow to the maximum size (of the folded protein). Depending on the diffusion coefficients of the native residues in the range from 10 -6 to 10 -8 cm 2 /s, numerical calculations for a protein of 2500 residues suggest that the folding time ranges from several seconds to several hundreds of seconds.
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.
Simple Physical Models Connect Theory and Experiment in Protein Folding Kinetics
Our understanding of the principles underlying the protein-folding problem can be tested by developing and characterizing simple models that make predictions which can be compared to experimental data. Here we extend our earlier model of folding free energy landscapes, in which each residue is considered to be either folded as in the native state or completely disordered, by investigating the role of additional factors representing hydrogen bonding and backbone torsion strain, and by using a hybrid between the master equation approach and the simple transition state theory to evaluate kinetics near the free energy barrier in greater detail. Model calculations of folding f-values are compared to experimental data for 19 proteins, and for more than half of these, experimental data are reproduced with correlation coefficients between r ¼ 0.41 and 0.88; calculations of transition state free energy barriers correlate with rates measured for 37 single domain proteins (r ¼ 0.69). The model provides insight into the contribution of alternative-folding pathways, the validity of quasi-equilibrium treatments of the folding landscape, and the magnitude of the Arrhenius prefactor for protein folding. Finally, we discuss the limitations of simple native-state-based models, and as a more general test of such models, provide predictions of folding rates and mechanisms for a comprehensive set of over 400 small protein domains of known structure.
Physical Review E, 2004
In this paper we aim at determining the key residues of small helical proteins in order to build up reduced models of the folding dynamics. We start by arguing that the folding process can be dissected into concurrent fast and slow dynamics. The fast events are the quasiautonomous coil-to-helix transitions occurring in the minimally frustrated initiation sites of folding in the early stages of the process. The slow processes consist in the docking of the fluctuating helices formed in these critical sites. We show that a neural network devised to predict native secondary structures from sequence can be used to estimate the probabilities of formation of these helical traits as they are embedded in the protein. The resulting probabilities are shown to correlate well with the experimental helicities measured in the same isolated peptides. The relevance of this finding to the hierarchical character of folding is confirmed within the framework of a diffusion-collision-like mechanism. We demonstrate that thermodynamic and topological features of these critical helices allow accurate estimation of the folding times of five proteins that have been kinetically studied. This suggests that these critical helices determine the fundamental events of the whole folding process. A remarkable feature of our model is that not all of the native helices are eligible as critical helices, whereas the whole set of the native helices has been used so far in other reconstructions of the folding mechanism. This stresses that the minimally frustrated helices of these helical proteins comprise the minimal set of determinants of the folding process.