Todd, M. J. ; Lorimer, G. H. ; Thirumalai, D. Chaperonin-facilitated protein folding: optimization of rate and yield by an iterative annealing mechanism. Proc Natl Acad Sci U S A 93, 4030-5.
AbstractWe develop a heuristic model for chaperonin-facilitated protein folding, the iterative annealing mechanism, based on theoretical descriptions of "rugged" conformational free energy landscapes for protein folding, and on experimental evidence that (i) folding proceeds by a nucleation mechanism whereby correct and incorrect nucleation lead to fast and slow folding kinetics, respectively, and (ii) chaperonins optimize the rate and yield of protein folding by an active ATP-dependent process. The chaperonins GroEL and GroES catalyze the folding of ribulose bisphosphate carboxylase at a rate proportional to the GroEL concentration. Kinetically trapped folding-incompetent conformers of ribulose bisphosphate carboxylase are converted to the native state in a reaction involving multiple rounds of quantized ATP hydrolysis by GroEL. We propose that chaperonins optimize protein folding by an iterative annealing mechanism; they repeatedly bind kinetically trapped conformers, randomly disrupt their structure, and release them in less folded states, allowing substrate proteins multiple opportunities to find pathways leading to the most thermodynamically stable state. By this mechanism, chaperonins greatly expand the range of environmental conditions in which folding to the native state is possible. We suggest that the development of this device for optimizing protein folding was an early and significant evolutionary event.
chaperonin-facilitated-protein-folding-optimization-of-rate-and-yield-by-an-iterative-annealing-mechanism.pdf Camacho, C. J. ; Thirumalai, D. Denaturants can accelerate folding rates in a class of globular proteins. Protein Sci 5 1826-32.
AbstractWe present a lattice Monte Carlo study to examine the effect of denaturants on the folding rates of simplified models of proteins. The two-dimensional model is made from a three-letter code mimicking the presence of hydrophobic, hydrophilic, and cysteine residues. We show that the rate of folding is maximum when the effective hydrophobic interaction epsilon H is approximately equal to the free energy gain epsilon S upon forming disulfide bonds. In the range 1 < or = epsilon H/ epsilon S < or = 3, multiple paths that connect several intermediates to the native state lead to fast folding. It is shown that at a fixed temperature and epsilon S the folding rate increases as epsilon H decreases. An approximate model is used to show that epsilon H should decrease as a function of the concentration of denaturants such as urea or guanidine hydrochloride. Our simulation results, in conjunction with this model, are used to show that increasing the concentration of denaturants can lead to an increase in folding rates. This occurs because denaturants can destabilize the intermediates without significantly altering the energy of the native conformation. Our findings are compared with experiments on the effects of denaturants on the refolding of bovine pancreatic trypsin inhibitor and ribonuclease T1. We also argue that the phenomenon of denaturant-enhanced folding of proteins should be general.
denaturants-can-accelerate-folding-rates-in-a-class-of-globular-proteins.pdf Klimov, D. K. ; Thirumalai, D. Factors governing the foldability of proteins. Proteins 26, 411-41.
AbstractWe use a three-dimensional lattice model of proteins to investigate systematically the global properties of the polypeptide chains that determine the folding to the native conformation starting from an ensemble of denatured conformations. In the coarse-grained description, the polypeptide chain is modeled as a heteropolymer consisting of N beads confined to the vertices of a simple cubic lattice. The interactions between the beads are taken from a random gaussian distribution of energies, with a mean value B0 < 0 that corresponds to the overall average hydrophobic interaction energy. We studied 56 sequences all with a unique ground state (native conformation) covering two values of N (15 and 27) and two values of B0. The smaller value of magnitude of B0 was chosen so that the average fraction of hydrophobic residues corresponds to that found in natural proteins. The higher value of magnitude of B0 was selected with the expectation that only the fully compact conformations would contribute to the thermodynamic behavior. For N = 15 the entire conformation space (compact as well as noncompact structures) can be exhaustively enumerated so that the thermodynamic properties can be exactly computed at all temperatures. The thermodynamic properties for the 27-mer chain were calculated using the slow cooling technique together with standard Monte Carlo simulations. The kinetics of approach to the native state for all the sequences was obtained using Monte Carlo simulations. For all sequences we find that there are two intrinsic characteristic temperatures, namely, T theta and Tf. At the temperature T theta the polypeptide chain makes a transition to a collapsed structure, while at Tf the chain undergoes a transition to the native conformation. We show that foldability of sequences can be characterized entirely in terms of these two temperatures. It is shown that fast folding sequences have small values of sigma = (T theta - Tf)/T theta whereas slow folders have larger values of sigma (the range of sigma is 0 < sigma < 1). The calculated values of the folding times correlate extremely well with sigma. An increase in sigma from 0.1 to 0.7 can result in an increase of 5-6 orders of magnitudes in folding times. In contrast, we demonstrate that there is no useful correlation between folding times and the energy gap between the native conformation and the first excited state at any N for any value of B0. In particular, in the parameter space of the model, many sequences with varying energy gaps, all with roughly the same folding time, can be easily engineered. Folding sequences in this model, therefore, can be classified based solely on the value of sigma. Fast folders have small values of sigma (typically less than about 0.1), moderate folders have values of sigma in the approximate range between 0.1 and 0.6, while for slow folders sigma exceeds 0.6. The precise boundary between these categories depends crucially on N and on the model. The range of sigma for fast folders decreases with the length of the chain. At temperatures close to Tf fast folders reach the native conformation via a native conformation nucleation collapse mechanism without forming any detectable intermediates, whereas only a fraction of molecule phi (T) reaches the native conformation by this process for moderate folders. The remaining fraction reaches the native state via three-stage multipathway process. For slow folders phi (T) is close to zero at all temperatures. The simultaneous requirement of native state stability and kinetic accessibility can be achieved at high enough temperatures for those sequences with small values of sigma. The utility of these results for de novo design of proteins is briefly discussed.
factors-governing-the-foldability-of-proteins.pdf Guo, Z. ; Thirumalai, D. Kinetics and thermodynamics of folding of a de novo designed four-helix bundle protein. J Mol Biol 263, 323-43.
AbstractA simple continuum model of a de novo designed model of a four-helix bundle is presented. The thermodynamics and kinetics of the model are studied using Langevin simulations. We use a three-letter minimal off-lattice representation of a de novo designed four-helix bundle protein. The native state of the model, which can be thought of as an alpha-carbon representation of the peptide chain, is a caricature of the sequence designed by Ho and Degrado and shows several characteristics found in the naturally occurring four-helix bundles. These include the structural aspects and the relative stability of the native conformation. The model four-helix bundle shows two characteristic temperatures T theta and Tf. The former is the temperature above which the structure resembles that of the random coil. Below the first-order folding transition temperature Tf the chain adopts the native conformation corresponding to the four-helix bundle. It is shown that in order to obtain a unique native structure a proper free energy balance between secondary and tertiary interactions is needed. The thermal denaturation starting from the unique native conformation indicates that at least a three-state analysis is required. The intermediates in the equilibrium thermal denaturation are all found to be native-like. The kinetics of refolding starting from an ensemble of denatured states shows that the acquisition of the native conformation takes place via a kinetic partitioning mechanism. A fraction of molecules, phi, reaches the native state by a topology inducing nucleation collapse mechanism, while the remainder (1-phi) follows a complex three-stage multipathway process. We suggest, in accord with our earlier studies, that phi is essentially determined by the intrinsic temperature scales T theta and Tf. Our studies indicate that better design of proteins can be achieved by making T theta as close to Tf as possible. Experimental implications for de novo design of proteins are briefly discussed.