What thermodynamic features characterize good and bad folders? Results from a simplified off-lattice protein model

The thermodynamics of the small SH3 protein domain is studied by means of a simplified model where each bead-like amino acid interacts with the others through a contact potential controlled by a 20x20 random matrix. Good folding sequences, characterized by a low native energy, display three main thermodynamical phases, namely a coil-like phase, an unfolded globule and a folded phase (plus other two phases, namely frozen and random coil, populated only at extremes temperatures). Interestingly, the unfolded globule has some regions already structured. Poorly designed sequences, on the other hand, display a wide transition from the random coil to a frozen state. The comparison with the analytic theory of heteropolymers is discussed

Mean first passage time analysis reveals rate-limiting steps, parallel pathways and dead ends in a simple model of protein folding

We have analyzed dynamics on the complex free energy landscape of protein folding in the FOLD-X model, by calculating for each state of the system the mean first passage time to the folded state. The resulting kinetic map of the folding process shows that it proceeds in jumps between well-defined, local free energy minima. Closer analysis of the different local minima allows us to reveal secondary, parallel pathways as well as dead ends.Comment: 7 page

Computational redesign of thioredoxin is hypersensitive towards minor conformational changes in the backbone template

Despite the development of powerful computational tools, the full-sequence design of proteins still remains a challenging task. To investigate the limits and capabilities of computational tools, we conducted a study of the ability of the program Rosetta to predict sequences that recreate the authentic fold of thioredoxin. Focusing on the influence of conformational details in the template structures, we based our study on 8 experimentally determined template structures and generated 120 designs from each. For experimental evaluation, we chose six sequences from each of the eight templates by objective criteria. The 48 selected sequences were evaluated based on their progressive ability to (1) produce soluble protein in Escherichia coli and (2) yield stable monomeric protein, and (3) on the ability of the stable, soluble proteins to adopt the target fold. Of the 48 designs, we were able to synthesize 32, 20 of which resulted in soluble protein. Of these, only two were sufficiently stable to be purified. An X-ray crystal structure was solved for one of the designs, revealing a close resemblance to the target structure. We found a significant difference among the eight template structures to realize the above three criteria despite their high structural similarity. Thus, in order to improve the success rate of computational full-sequence design methods, we recommend that multiple template structures are used. Furthermore, this study shows that special care should be taken when optimizing the geometry of a structure prior to computational design when using a method that is based on rigid conformations

Potentials of Mean Force for Protein Structure Prediction Vindicated, Formalized and Generalized

Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge based potentials based on pairwise distances -- so-called "potentials of mean force" (PMFs) -- have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state -- a necessary component of these potentials -- is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities reference ratio distributions deriving from the application of the reference ratio method. This new view is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures

Durability and cycle frequency of smartphone and tablet lithium-ion batteries in the field

The study presents data on the state of health of smartphone and tablet lithium-ion batteries that were used in devices in the field for up to several years. Data was retrieved from the coconutBattery database, which contains thousands of datasets on batteries from several device models from the same manufacturer. The durability of batteries in the sample data was found to be quite high. Even batteries that had been in the field for several years and had endured hundreds of charging cycles were able to retain a relatively high state of health. However, several major limitations in regard to generalizability of the findings were identified. Furthermore, the cycle frequency of smartphone and tablet batteries in the field is presented, which may be useful to support life cycle assessments and carbon footprinting of such product groups

A generative, probabilistic model of local protein structure

Despite significant progress in recent years, protein structure prediction maintains its status as one of the prime unsolved problems in computational biology. One of the key remaining challenges is an efficient probabilistic exploration of the structural space that correctly reflects the relative conformational stabilities. Here, we present a fully probabilistic, continuous model of local protein structure in atomic detail. The generative model makes efficient conformational sampling possible and provides a framework for the rigorous analysis of local sequence–structure correlations in the native state. Our method represents a significant theoretical and practical improvement over the widely used fragment assembly technique by avoiding the drawbacks associated with a discrete and nonprobabilistic approach

Recognizing and Defining True Ras Binding Domains II: In Silico Prediction Based on Homology Modelling and Energy Calculations

Considering the large number of putative Ras effector proteins, it is highly desirable to develop computational methods to be able to identify true Ras binding molecules. Based on a limited sequence homology. among members of the Ras association (RA) and Ras binding (RB) sub-domain families of the ubiquitin super-family, we have built structural homology models of Ras proteins in complex with different RA and RB domains, using the FOLD-X software. A critical step in our approach is to use different templates of Ras complexes, in order to account for the structural variation among the RA and RB domains. The homology models are validated by predicting the effect of mutating hot spot residues in the interface, and residues important for the specificity of interaction with different Ras proteins. The FOLD-X calculated energies of the best-modelled complexes are in good agreement with previously published experimental data and with new data reported here. Based on these results, we can establish energy thresholds above, or below which, we can predict with 96% confidence that a RA/RB domain will or will not interact with Ras. This study shows the importance of in depth structural analysis, high quality force-fields and modelling for correct prediction. Our work opens the possibility of genome-wide prediction for this protein family and for others, where there is enough structural information. (c) 2005 Elsevier Ltd. All rights reserved

Subtle Monte Carlo Updates in Dense Molecular Systems

Although Markov chain Monte Carlo (MC) simulation is a potentially powerful approach for exploring conformational space, it has been unable to compete with molecular dynamics (MD) in the analysis of high density structural states, such as the native state of globular proteins. Here, we introduce a kinetic algorithm, CRISP, that greatly enhances the sampling efficiency in all-atom MC simulations of dense systems. The algorithm is based on an exact analytical solution to the classic chain-closure problem, making it possible to express the interdependencies among degrees of freedom in the molecule as correlations in a multivariate Gaussian distribution. We demonstrate that our method reproduces structural variation in proteins with greater efficiency than current state-of-the-art Monte Carlo methods and has real-time simulation performance on par with molecular dynamics simulations. The presented results suggest our method as a valuable tool in the study of molecules in atomic detail, offering a potential alternative to molecular dynamics for probing long time-scale conformational transitions

Prediction of water and metal binding sites and their affinities by using the Fold-X force field

The empirical force field Fold-X was developed previously to allow rapid free energy calculations in proteins. Here, we present an enhanced version of the force field allowing prediction of the position of structural water molecules and metal ions, together called single atom ligands. Fold-X picks up 76% of water molecules found to interact with two or more polar atoms of proteins in high-resolution crystal structures and predicts their position to within 0.8 Å on average. The prediction of metal ion-binding sites have success rates between 90% and 97% depending on the metal, with an overall standard deviation on the position of binding of 0.3-0.6 Å. The following metals were included in the force field: Mg(2+), Ca(2+), Zn(2+), Mn(2+), and Cu(2+). As a result, the current version of Fold-X can accurately decorate a protein structure with biologically important ions and water molecules. Additionally, the free energy of binding of Ca(2+) and Zn(2+) (i.e., the natural logarithm of the dissociation constant) and its dependence on ionic strength correlate reasonably well with the experimental data available in the literature, allowing one to discriminate between high- and low-affinity binding sites. Importantly, the accuracy of the energy prediction presented here is sufficient to efficiently discriminate between Mg(2+), Ca(2+), and Zn(2+) binding