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Register a new userHidden Structure in Protein Energy Landscapes
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Dengming Ming
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Inherent structure theory is used to discover strong connections between simple characteristics of protein structure and the energy landscape of a Go model. The potential energies and vibrational free energies of inherent structures are highly correlated, and both reflect simple measures of networks of native contacts. These connections have important consequences for models of protein dynamics and thermodynamics.
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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.
Energy landscape theory describes how a full-length protein can attain its native fold after sampling only a tiny fraction of all possible structures. Although protein folding is now understood to be concomitant with synthesis on the ribosome there have been few attempts to modify energy landscape theory by accounting for cotranslational folding. This paper introduces a model for cotranslational folding that leads to a natural definition of a nested energy landscape. By applying concepts drawn from submanifold differential geometry the dynamics of protein folding on the ribosome can be explored in a quantitative manner and conditions on the nested potential energy landscapes for a good cotranslational folder are obtained. A generalisation of diffusion rate theory using van Kampens technique of composite stochastic processes is then used to account for entropic contributions and the effects of variable translation rates on cotranslational folding. This stochastic approach agrees well with experimental results and Hamiltionian formalism in the deterministic limit.
In single molecule laser optical tweezer (LOT) pulling experiments a protein or RNA is juxtaposed between DNA handles that are attached to beads in optical traps. The LOT generates folding trajectories under force in terms of time-dependent changes in the distance between the beads. How to construct the full intrinsic folding landscape (without the handles and the beads) from the measured time series is a major unsolved problem. By using rigorous theoretical methods---which account for fluctuations of the DNA handles, rotation of the optical beads, variations in applied tension due to finite trap stiffness, as well as environmental noise and the limited bandwidth of the apparatus---we provide a tractable method to derive intrinsic free energy profiles. We validate the method by showing that the exactly calculable intrinsic free energy profile for a Generalized Rouse Model, which mimics the two-state behavior in nucleic acid hairpins, can be accurately extracted from simulated time series in a LOT setup regardless of the stiffness of the handles. We next apply the approach to trajectories from coarse grained LOT molecular simulations of a coiled-coil protein based on the GCN4 leucine zipper, and obtain a free energy landscape that is in quantitative agreement with simulations performed without the beads and handles. Finally, we extract the intrinsic free energy landscape from experimental LOT measurements for the leucine zipper, which is independent of the trap parameters.
Coarse-graining is a powerful tool for extending the reach of dynamic models of proteins and other biological macromolecules. Topological coarse-graining, in which biomolecules or sets thereof are represented via graph structures, is a particularly useful way of obtaining highly compressed representations of molecular structure, and simulations operating via such representations can achieve substantial computational savings. A drawback of coarse-graining, however, is the loss of atomistic detail - an effect that is especially acute for topological representations such as protein structure networks (PSNs). Here, we introduce an approach based on a combination of machine learning and physically-guided refinement for inferring atomic coordinates from PSNs. This neural upscaling procedure exploits the constraints implied by PSNs on possible configurations, as well as differences in the likelihood of observing different configurations with the same PSN. Using a 1 $mu$s atomistic molecular dynamics trajectory of A$beta_{1-40}$, we show that neural upscaling is able to effectively recapitulate detailed structural information for intrinsically disordered proteins, being particularly successful in recovering features such as transient secondary structure. These results suggest that scalable network-based models for protein structure and dynamics may be used in settings where atomistic detail is desired, with upscaling employed to impute atomic coordinates from PSNs.
This article introduces a novel protein structure alignment method (named TALI) based on the protein backbone torsion angle instead of the more traditional distance matrix. Because the structural alignment of the two proteins is based on the comparison of two sequences of numbers (backbone torsion angles), we can take advantage of a large number of well-developed methods such as Smith-Waterman or Needleman-Wunsch. Here we report the result of TALI in comparison to other structure alignment methods such as DALI, CE, and SSM ass well as sequence alignment based on PSI-BLAST. TALI demonstrated great success over all other methods in application to challenging proteins. TALI was more successful in recognizing remote structural homology. TALI also demonstrated an ability to identify structural homology between two proteins where the structural difference was due to a rotation of internal domains by nearly 180$^circ$.
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