Mechanical stress can strongly influence the capability of a protein to aggregate and the kinetics of aggregation, but there is little insight into the underlying mechanism. Here we study the effect of different mechanical stress conditions on the fibrillation of the peptide hormone glucagon, which forms different fibrils depending on temperature, pH, ionic strength, and concentration. A combination of spectroscopic and microscopic data shows that fibrillar polymorphism can also be induced by mechanical stress. We observed two classes of fibrils: a low-stress and a high-stress class, which differ in their kinetic profiles, secondary structure as well as morphology and that are able to self-propagate in a template-dependent fashion. The bending rigidity of the low-stress fibrils is sensitive to the degree of mechanical perturbation. We propose a fibrillation model, where interfaces play a fundamental role in the switch between the two fibrillar classes. Our work also raises the cautionary note that mechanical perturbation is a potential source of variability in the study of fibrillation mechanisms and fibril structures.

Knowledge-based potentials are energy functions derived from the analysis of databases of protein structures and sequences. They can be divided into two classes. Potentials from the first class are based on a direct conversion of the distributions of some geometric properties observed in native protein structures into energy values, while potentials from the second class are trained to mimic quantitatively the geometric differences between incorrectly folded models and native structures. In this paper, we focus on the relationship between energy and geometry when training the second class of knowledge-based potentials. We assume that the difference in energy between a decoy structure and the corresponding native structure is linearly related to the distance between the two structures. We trained two distance-based knowledge-based potentials accordingly, one based on all inter-residue distances (PPD), while the other had the set of all distances filtered to reflect consistency in an ensemble of decoys (PPE). We tested four types of metric to characterize the distance between the decoy and the native structure, two based on extrinsic geometry (RMSD and GTD-TS*), and two based on intrinsic geometry (Q* and MT). The corresponding eight potentials were tested on a large collection of decoy sets. We found that it is usually better to train a potential using an intrinsic distance measure. We also found that PPE outperforms PPD, emphasizing the benefits of capturing consistent information in an ensemble. The relevance of these results for the design of knowledge-based potentials is discussed.

SummaryProteins are the main active elements of life whose chemical activities regulate cellular activities. A protein is characterized by having a sequence of amino acids and a three dimensional structure. The three-dimensional structure has only been determined experimentally for 50000 of the seven million sequences that are known. Determining the protein structure from its sequence of amino acids is therefore a major problem in computational structural biology and is referred to as the protein folding problem. The folding problem is solved using de novo methods or comparative methods depending on whether the three-dimensional structure of a homologous sequence is known. Whether or not a protein model can be used for industrial purposes depends on the quality of the predicted structure. A model can be used to design a drug when the quality is high.The overall goal of this project is to assess and improve the quality of a predicted structure. The starting point of this work is a technique called metric training where a knowledge-based protein potential, for a fixed set of native protein structures and a set of deformed decoys for each native structure, is designed to have native-decoy energy gabs that correlates maximally to a native-decoy distance. The main contribution of this thesis is methods developed for analyzing the performance of metrically trained knowledge-based potentials and for optimizing their performance while making them less dependent on the decoy set used to define them. We focus on using the gradient and the Hessian in the analysis and present a novel smooth solvation potential but otherwise the studied potential is kept close to standard coarse grained potentials.We analyze the importance of the choice of metric both when used in metric training and when used in the evaluation of the performance of the resulting potential and find a significant improvement by using a metric based on intrinsic geometry. It is well-known that energy minimization of a potential that is efficient in ordering a fixed set of decoys need not bring the decoys closer to the native state. The next part of the work is focused on improving the convergence of decoy structures and we present a method that significantly improves the results of shorter energy minimizations of a metrically trained potential and discuss its limitations. In an ideal potential all nearnative decoys will converge toward the native structure being at-least a local minimum of the potential. To address how far the current functional form of the potential is from an ideal potential we present two methods for finding the optimal metrically trained potential that simultaneous has a number of native structures as a local minimum. Our results generally indicate that a more fine-grained potential is needed to meet desired model accuracies but even with our coarse-grained model we obtain good results and there is an unexplored possibility to combine it with comparative modeling.To allow fast energy minimization in Matlab a new set of more sparse formulas...

We derive compact expressions of the second-order derivatives of bond length, bond angle, and proper and improper torsion angle potentials, in terms of operators represented in two orthonormal bases. Hereby, simple rules to generate the Hessian of an internal coordinate or a molecular potential can be formulated. The algorithms we provide can be implemented efficiently in high-level programming languages using vectorization. Finally, the method leads to compact expressions for a second-order expansion of an internal coordinate or a molecular potential.