Coupling the folding of homologous proteins

The empirical observation that homologous proteins fold to similar structures is used to enhance the capabilities of an ab initio algorithm to predict protein conformations. A penalty function that forces homologous proteins to look alike is added to the potential and is employed in the coupled energy optimization of several homologous proteins. Significant improvement in the quality of the computed structures (as compared with the computational folding of a single protein) is demonstrated and discussed.

Recent improvements in prediction of protein structure by global optimization of a potential energy function

Recent improvements of a hierarchical ab initio or de novo approach for predicting both α and β structures of proteins are described. The united-residue energy function used in this procedure includes multibody interactions from a cumulant expansion of the free energy of polypeptide chains, with their relative weights determined by Z-score optimization. The critical initial stage of the hierarchical procedure involves a search of conformational space by the conformational space annealing (CSA) method, followed by optimization of an all-atom model. The procedure was assessed in a recent blind test of protein structure prediction (CASP4). The resulting lowest-energy structures of the target proteins (ranging in size from 70 to 244 residues) agreed with the experimental structures in many respects. The entire experimental structure of a cyclic α-helical protein of 70 residues was predicted to within 4.3 Å α-carbon (Cα) rms deviation (rmsd) whereas, for other α-helical proteins, fragments of roughly 60 residues were predicted to within 6.0 Å Cα rmsd. Whereas β structures can now be predicted with the new procedure, the success rate for α/β- and β-proteins is lower than that for α-proteins at present. For the β portions of α/β structures, the Cα rmsd's are less than 6.0 Å for contiguous fragments of 30–40 residues; for one target, three fragments (of length 10, 23, and 28 residues, respectively) formed a compact part of the tertiary structure with a Cα rmsd less than 6.0 Å. Overall, these results constitute an important step toward the ab initio prediction of protein structure solely from the amino acid sequence.

Molecular dynamics and free-energy calculations applied to affinity maturation in antibody 48G7

We investigated the relative free energies of hapten binding to the germ line and mature forms of the 48G7 antibody Fab fragments by applying a continuum model to structures sampled from molecular dynamics simulations in explicit solvent. Reasonable absolute and very good relative free energies were obtained. As a result of nine somatic mutations that do not contact the hapten, the affinity-matured antibody binds the hapten >104 tighter than the germ line antibody. Energetic analysis reveals that van der Waals interactions and nonpolar contributions to solvation are similar and drive the formations of both the germ line and mature antibody–hapten complexes. Affinity maturation of the 48G7 antibody therefore appears to occur through reorganization of the combining site geometry in a manner that optimizes the balance of gaining favorable electrostatic interactions with the hapten and losing those with solvent during the binding process. As reflected by lower rms fluctuations in the antibody–hapten complex, the mature complex undergoes more restricted fluctuations than the germ line complex. The dramatically increased affinity of the 48G7 antibody over its germ line precursor is thus made possible by electrostatic optimization.

Dynamic weighting in Monte Carlo and optimization

Dynamic importance weighting is proposed as a Monte Carlo method that has the capability to sample relevant parts of the configuration space even in the presence of many steep energy minima. The method relies on an additional dynamic variable (the importance weight) to help the system overcome steep barriers. A non-Metropolis theory is developed for the construction of such weighted samplers. Algorithms based on this method are designed for simulation and global optimization tasks arising from multimodal sampling, neural network training, and the traveling salesman problem. Numerical tests on these problems confirm the effectiveness of the method.

Energy-based de novo protein folding by conformational space annealing and an off-lattice united-residue force field: Application to the 10-55 fragment of staphylococcal protein A and to apo calbindin D9K

The conformational space annealing (CSA) method for global optimization has been applied to the 10-55 fragment of the B-domain of staphylococcal protein A (protein A) and to a 75-residue protein, apo calbindin D9K (PDB ID code 1CLB), by using the UNRES off-lattice united-residue force field. Although the potential was not calibrated with these two proteins, the native-like structures were found among the low-energy conformations, without the use of threading or secondary-structure predictions. This is because the CSA method can find many distinct families of low-energy conformations. Starting from random conformations, the CSA method found that there are two families of low-energy conformations for each of the two proteins, the native-like fold and its mirror image. The CSA method converged to the same low-energy folds in all cases studied, as opposed to other optimization methods. It appears that the CSA method with the UNRES force field, which is based on the thermodynamic hypothesis, can be used in prediction of protein structures in real time.

How optimization of potential functions affects protein folding.

The relationship between the optimization of the potential function and the foldability of theoretical protein models is studied based on investigations of a 27-mer cubic-lattice protein model and a more realistic lattice model for the protein crambin. In both the simple and the more complicated systems, optimization of the energy parameters achieves significant improvements in the statistical-mechanical characteristics of the systems and leads to foldable protein models in simulation experiments. The foldability of the protein models is characterized by their statistical-mechanical properties--e.g., by the density of states and by Monte Carlo folding simulations of the models. With optimized energy parameters, a high level of consistency exists among different interactions in the native structures of the protein models, as revealed by a correlation function between the optimized energy parameters and the native structure of the model proteins. The results of this work are relevant to the design of a general potential function for folding proteins by theoretical simulations.

Chaperonin-facilitated protein folding: optimization of rate and yield by an iterative annealing mechanism.

We 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.

Optimization of rates of protein folding: the nucleation-condensation mechanism and its implications.

Small, single-module proteins that fold in a single cooperative step may be paradigms for understanding early events in protein-folding pathways generally. Recent experimental studies of the 64-residue chymotrypsin inhibitor 2 (CI2) support a nucleation mechanism for folding, as do some computer stimulations. CI2 has a nucleation site that develops only in the transition state for folding. The nucleus is composed of a set of adjacent residues (an alpha-helix), stabilized by long-range interactions that are formed as the rest of the protein collapses around it. A simple analysis of the optimization of the rate of protein folding predicts that rates are highest when the denatured state has little residual structure under physiological conditions and no intermediates accumulate. This implies that any potential nucleation site that is composed mainly of adjacent residues should be just weakly populated in the denatured state and become structured only in a high-energy intermediate or transition state when it is stabilized by interactions elsewhere in the protein. Hierarchical mechanisms of folding in which stable elements of structure accrete are unfavorable. The nucleation-condensation mechanism of CI2 fulfills the criteria for fast folding. On the other hand, stable intermediates do form in the folding of more complex proteins, and this may be an unavoidable consequence of increasing size and nucleation at more than one site.