The energy landscape, folding pathways and the kinetics of a knotted protein.

The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N or C terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N terminus portion of the knot and a rate-determining step where the C terminus is incorporated. The low-lying minima with the N terminus knotted and the C terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N and C termini into the knot occurs late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly.

Protein structure prediction using basin-hopping.

Associative memory Hamiltonian structure prediction potentials are not overly rugged, thereby suggesting their landscapes are like those of actual proteins. In the present contribution we show how basin-hopping global optimization can identify low-lying minima for the corresponding mildly frustrated energy landscapes. For small systems the basin-hopping algorithm succeeds in locating both lower minima and conformations closer to the experimental structure than does molecular dynamics with simulated annealing. For large systems the efficiency of basin-hopping decreases for our initial implementation, where the steps consist of random perturbations to the Cartesian coordinates. We implemented umbrella sampling using basin-hopping to further confirm when the global minima are reached. We have also improved the energy surface by employing bioinformatic techniques for reducing the roughness or variance of the energy surface. Finally, the basin-hopping calculations have guided improvements in the excluded volume of the Hamiltonian, producing better structures. These results suggest a novel and transferable optimization scheme for future energy function development.

Induced fit, folding, and recognition of the NF-kappaB-nuclear localization signals by IkappaBalpha and IkappaBbeta.

Protein structure prediction codes based on the associative memory Hamiltonian were used to probe the binding modes between the nuclear localization signal (NLS) polypeptide of NF-kappaB and the inhibitors IkappaBalpha and IkappaBbeta. Experimentally, it is known that the NLS polypeptide is unstructured in the NF-kappaB complex with DNA but it forms an extended helical structure with the NLS (residues 301-304) between the two helices in the NF-kappaB/IkappaBalpha complex. The simulations included the NF-kappaB(p65) and (p50) NLS polypeptides and various mutants alone and in the presence of IkappaBalpha and IkappaBbeta. The simulations predict that the NLS polypeptide by itself binds tightly to IkappaBalpha and IkappaBbeta. In the NF-kappaB (p50/p65) heterodimer, the p50 NLS is predicted to remain free to bind to importin alpha. In the interaction with IkappaBalpha, both p65 NLSs are predicted to be bound. In IkappaBbeta, the NLS polypeptide binds to two binding sites, as seen in the crystal structure, with one site heavily favored for stable binding.

Protein Structure Prediction: The Next Generation.

Over the last 10-15 years a general understanding of the chemical reaction of protein folding has emerged from statistical mechanics. The lessons learned from protein folding kinetics based on energy landscape ideas have benefited protein structure prediction, in particular the development of coarse grained models. We survey results from blind structure prediction. We explore how second generation prediction energy functions can be developed by introducing information from an ensemble of previously simulated structures. This procedure relies on the assumption of a funneled energy landscape keeping with the principle of minimal frustration. First generation simulated structures provide an improved input for associative memory energy functions in comparison to the experimental protein structures chosen on the basis of sequence alignment.

Associative memory Hamiltonians for structure prediction without homology: alpha/beta proteins.

We describe a method for predicting the structure of alpha beta class proteins in the absence of information from homologous structures. The method is based on an associative memory model for short to intermediate range in sequence contacts and a contact potential for long range in sequence contacts. The coefficients in the energy function are chosen to maximize the ratio of the folding temperature to the glass transition temperature. We use the resulting optimized model to predict the structure of three alpha beta protein domains ranging in length from 81 to 115 residues. The resulting predictions align with low rms deviations to large portions of the native state. We have also calculated the free energy as a function of similarity to the native state for one of these three domains, and we show that, as expected from the optimization criteria, the free energy surface resembles a rough funnel to the native state. Finally, we briefly demonstrate the effect of roughness in the energy landscape on the dynamics.