Modeling Disordered Regions in Proteins Using Rosetta

Protein structure prediction methods such as Rosetta search for the lowest energy conformation of the polypeptide chain. However, the experimentally observed native state is at a minimum of the free energy, rather than the energy. The neglect of the missing configurational entropy contribution to the free energy can be partially justified by the assumption that the entropies of alternative folded states, while very much less than unfolded states, are not too different from one another, and hence can be to a first approximation neglected when searching for the lowest free energy state. The shortcomings of current structure prediction methods may be due in part to the breakdown of this assumption. Particularly problematic are proteins with significant disordered regions which do not populate single low energy conformations even in the native state. We describe two approaches within the Rosetta structure modeling methodology for treating such regions. The first does not require advance knowledge of the regions likely to be disordered; instead these are identified by minimizing a simple free energy function used previously to model protein folding landscapes and transition states. In this model, residues can be either completely ordered or completely disordered; they are considered disordered if the gain in entropy outweighs the loss of favorable energetic interactions with the rest of the protein chain. The second approach requires identification in advance of the disordered regions either from sequence alone using for example the DISOPRED server or from experimental data such as NMR chemical shifts. During Rosetta structure prediction calculations the disordered regions make only unfavorable repulsive contributions to the total energy. We find that the second approach has greater practical utility and illustrate this with examples from de novo structure prediction, NMR structure calculation, and comparative modeling

Combining Experiments and Simulations Using the Maximum Entropy Principle

A key component of computational biology is to compare the results of computer modelling with experimental measurements. Despite substantial progress in the models and algorithms used in many areas of computational biology, such comparisons sometimes reveal that the computations are not in quantitative agreement with experimental data. The principle of maximum entropy is a general procedure for constructing probability distributions in the light of new data, making it a natural tool in cases when an initial model provides results that are at odds with experiments. The number of maximum entropy applications in our field has grown steadily in recent years, in areas as diverse as sequence analysis, structural modelling, and neurobiology. In this Perspectives article, we give a broad introduction to the method, in an attempt to encourage its further adoption. The general procedure is explained in the context of a simple example, after which we proceed with a real-world application in the field of molecular simulations, where the maximum entropy procedure has recently provided new insight. Given the limited accuracy of force fields, macromolecular simulations sometimes produce results that are at not in complete and quantitative accordance with experiments. A common solution to this problem is to explicitly ensure agreement between the two by perturbing the potential energy function towards the experimental data. So far, a general consensus for how such perturbations should be implemented has been lacking. Three very recent papers have explored this problem using the maximum entropy approach, providing both new theoretical and practical insights to the problem. We highlight each of these contributions in turn and conclude with a discussion on remaining challenges

Absolute free energy calculations for biomolecular systems

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Limits and CO2 equilibration of near-coast alkalinity enhancement

Ocean alkalinity enhancement (OAE) has recently gained attention as a potential method for carbon dioxide removal (CDR) at gigatonne (Gt) scale, with near-coast OAE operations being economically favorable due to proximity to mineral and energy sources. In this paper we study critical questions which determine the scale and viability of OAE. Which coastal locations are able to sustain a large flux of alkalinity at minimal pH and omega(Arag )(aragonite saturation) changes? What is the interference distance between adjacent OAE projects? How much CO2 is absorbed per unit of alkalinity added? How quickly does the induced CO2 deficiency equilibrate with the atmosphere? Choosing relatively conservative constraints on delta pH or delta Omega, we examine the limits of OAE using the ECCO LLC270 (0.3 degrees) global circulation model. We find that the sustainable OAE rate varies over 1-2 orders of magnitude between different coasts and exhibits complex patterns and non-local dependencies which vary from region to region. In general, OAE in areas of strong coastal currents enables the largest fluxes and depending on the direction of these currents, neighboring OAE sites can exhibit dependencies as far as 400 km or more. At these steady state fluxes most regional stretches of coastline are able to accommodate on the order of 10s to 100s of megatonnes of negative emissions within 300 km of the coast. We conclude that near-coastal OAE has the potential to scale globally to several Gt CO2 yr(-1) of drawdown with conservative pH constraints, if the effort is spread over the majority of available coastlines. Depending on the location, we find a diverse set of equilibration kinetics, determined by the interplay of gas exchange and surface residence time. Most locations reach an uptake efficiency plateau of 0.6-0.8 mol CO2 per mol of alkalinity after 3-4 years, after which there is only slow additional CO2 uptake. Regions of significant downwelling (e.g., around Iceland) should be avoided by OAE deployments, as in such locations up to half of the CDR potential of OAE can be lost to bottom waters. The most ideal locations, reaching a molar uptake ratio of around 0.8, include North Madagascar, California, Brazil, Peru and locations close to the Southern Ocean such as Tasmania, Kerguelen and Patagonia, where the gas exchange appears to occur faster than the surface residence time. However, some locations (e.g., Hawaii) take significantly longer to equilibrate (up to 8-10 years) but can still eventually achieve high uptake ratios

Alternate States of Proteins Revealed by Detailed Energy Landscape Mapping

What conformations do protein molecules populate in solution? Crystallography provides a high-resolution description of protein structure in the crystal environment, while NMR describes structure in solution but using less data. NMR structures display more variability, but is this because crystal contacts are absent or because of fewer data constraints? Here we report unexpected insight into this issue obtained through analysis of de tailed protein energy landscapes generated by large-scale, native-enhanced sampling of conformational space with Rosetta@home for 111 protein domains. In the absence of tightly associating binding partners or ligands, the lowest-energy Rosetta models were nearly all <2.5 angstrom C alpha RMSD from the experimental structure; this result demonstrates that structure prediction accuracy for globular proteins is limited mainly by the ability to sample close to the native structure. While the lowest-energy models are similar to deposited structures, they are not identical; the largest deviations are most often in regions involved in ligand, quaternary, or crystal contacts. For ligand binding proteins, the low energy models may resemble the apo structures, and for oligomeric proteins, the monomeric assembly intermediates. The deviations between the low energy models and crystal structures largely disappear when landscapes are computed in the context of the crystal lattice or multimer. The computed low-energy ensembles, with tight crystal-structure-like packing in the core, but more NMR-structure-like variability in loops, may in some cases resemble the native state ensembles of proteins better than individual crystal or NMR structures, and can suggest experimentally testable hypotheses relating alternative states and structural heterogeneity to function. (C) 2010 Elsevier Ltd. All rights reserved

Results of disordered internal loop predictions.

<p>(<b>A</b>) Comparisons of prediction accuracy using the free energy function with optimized parameters (<i>β</i> = 1.5 and <i>L₀</i> = 0.3) with that of a null model. The y-axis shows disorder prediction accuracy over the benchmark set using Eq. (2). The x-axis shows the prediction of the null model, which assumes all residues are ordered. (<b>B</b>) Examples of successful prediction of disordered internal loops. Blue line: the actual disordered regions assessed from the residue deviations in the NMR structure. Red line: frequency of disorder assignment by optimization of Eq. (1) over decoy population.</p