Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe

Shelling the Voronoi interface of protein-protein complexes predicts residue activity and conservation

The accurate description of protein-protein interfaces remains a challenging task. Traditional criteria, based on atomic contacts or changes in solvent accessibility, tend to over or underpredict the interface itself and cannot discriminate active from less relevant parts. A recent simulation study by Mihalek and co-authors (2007, JMB 369, 584-95) concluded that active residues tend to be `dry', that is, insulated from water fluctuations. We show that patterns of `dry' residues can, to a large extent, be predicted by a fast, parameter-free and purely geometric analysis of protein interfaces. We introduce the shelling order of Voronoi facets as a straightforward quantitative measure of an atom's depth inside an interface. We analyze the correlation between Voronoi shelling order, dryness, and conservation on a set of 54 protein-protein complexes. Residues with high shelling order tend to be dry; evolutionary conservation also correlates with dryness and shelling order but, perhaps not surprisingly, is a much less accurate predictor of either property. Voronoi shelling order thus seems a meaningful and efficient descriptor of protein interfaces. Moreover, the strong correlation with dryness suggests that water dynamics within protein interfaces may, in first approximation, be described by simple diffusion models

Analysis and Manipulation of Repetitive Structures of Varying Shape

Self-similarity and repetitions are ubiquitous in man-made and natural objects. Such structural regularities often relate to form, function, aesthetics, and design considerations. Discovering structural redundancies along with their dominant variations from 3D geometry not only allows us to better understand the underlying objects, but is also beneficial for several geometry processing tasks including compact representation, shape completion, and intuitive shape manipulation. To identify these repetitions, we present a novel detection algorithm based on analyzing a graph of surface features. We combine general feature detection schemes with a RANSAC-based randomized subgraph searching algorithm in order to reliably detect recurring patterns of locally unique structures. A subsequent segmentation step based on a simultaneous region growing is applied to verify that the actual data supports the patterns detected in the feature graphs. We introduce our graph based detection algorithm on the example of rigid repetitive structure detection. Then we extend the approach to allow more general deformations between the detected parts. We introduce subspace symmetries whereby we characterize similarity by requiring the set of repeating structures to form a low dimensional shape space. We discover these structures based on detecting linearly correlated correspondences among graphs of invariant features. The found symmetries along with the modeled variations are useful for a variety of applications including non-local and non-rigid denoising. Employing subspace symmetries for shape editing, we introduce a morphable part model for smart shape manipulation. The input geometry is converted to an assembly of deformable parts with appropriate boundary conditions. Our method uses self-similarities from a single model or corresponding parts of shape collections as training input and allows the user also to reassemble the identified parts in new configurations, thus exploiting both the discrete and continuous learned variations while ensuring appropriate boundary conditions across part boundaries. We obtain an interactive yet intuitive shape deformation framework producing realistic deformations on classes of objects that are difficult to edit using repetition-unaware deformation techniques

Visual Tracking and Motion Estimation for an On-orbit Servicing of a Satellite

This thesis addresses visual tracking of a non-cooperative as well as a partially cooperative satellite, to enable close-range rendezvous between a servicer and a target satellite. Visual tracking and estimation of relative motion between a servicer and a target satellite are critical abilities for rendezvous and proximity operation such as repairing and deorbiting. For this purpose, Lidar has been widely employed in cooperative rendezvous and docking missions. Despite its robustness to harsh space illumination, Lidar has high weight and rotating parts and consumes more power, thus undermines the stringent requirements of a satellite design. On the other hand, inexpensive on-board cameras can provide an effective solution, working at a wide range of distances. However, conditions of space lighting are particularly challenging for image based tracking algorithms, because of the direct sunlight exposure, and due to the glossy surface of the satellite that creates strong reflection and image saturation, which leads to difficulties in tracking procedures. In order to address these difficulties, the relevant literature is examined in the fields of computer vision, and satellite rendezvous and docking. Two classes of problems are identified and relevant solutions, implemented on a standard computer are provided. Firstly, in the absence of a geometric model of the satellite, the thesis presents a robust feature-based method with prediction capability in case of insufficient features, relying on a point-wise motion model. Secondly, we employ a robust model-based hierarchical position localization method to handle change of image features along a range of distances, and localize an attitude-controlled (partially cooperative) satellite. Moreover, the thesis presents a pose tracking method addressing ambiguities in edge-matching, and a pose detection algorithm based on appearance model learning. For the validation of the methods, real camera images and ground truth data, generated with a laboratory tet bed similar to space conditions are used. The experimental results indicate that camera based methods provide robust and accurate tracking for the approach of malfunctioning satellites in spite of the difficulties associated with specularities and direct sunlight. Also exceptional lighting conditions associated to the sun angle are discussed, aimed at achieving fully reliable localization system in a certain mission

Similarity reasoning for local surface analysis and recognition

This thesis addresses the similarity assessment of digital shapes, contributing to the analysis of surface characteristics that are independent of the global shape but are crucial to identify a model as belonging to the same manufacture, the same origin/culture or the same typology (color, common decorations, common feature elements, compatible style elements, etc.). To face this problem, the interpretation of the local surface properties is crucial. We go beyond the retrieval of models or surface patches in a collection of models, facing the recognition of geometric patterns across digital models with different overall shape. To address this challenging problem, the use of both engineered and learning-based descriptions are investigated, building one of the first contributions towards the localization and identification of geometric patterns on digital surfaces. Finally, the recognition of patterns adds a further perspective in the exploration of (large) 3D data collections, especially in the cultural heritage domain. Our work contributes to the definition of methods able to locally characterize the geometric and colorimetric surface decorations. Moreover, we showcase our benchmarking activity carried out in recent years on the identification of geometric features and the retrieval of digital models completely characterized by geometric or colorimetric patterns

Graphics Technology in Space Applications (GTSA 1989)

This document represents the proceedings of the Graphics Technology in Space Applications, which was held at NASA Lyndon B. Johnson Space Center on April 12 to 14, 1989 in Houston, Texas. The papers included in these proceedings were published in general as received from the authors with minimum modifications and editing. Information contained in the individual papers is not to be construed as being officially endorsed by NASA

Characterizing the Morphology of Protein Binding Patches

International audienceLet the patch of a partner in a protein complex be the collection of atoms accounting for the interaction. To improve our understanding of the structure-function relationship, we present a patch model decoupling the topological and geometric properties. While the geometry is classically encoded by the atomic positions, the topology is recorded in a graph encoding the relative position of concentric shells partitioning the interface atoms. The topological-geometric duality provides the basis of a generic dynamic programming-based algorithm comparing patches at the shell level, which may favor topological or geometric features. On the biological side, we address four questions, using 249 cocrystallized heterodimers organized in biological families. First, we dissect the morphology of binding patches and show that Nature enjoyed the topological and geometric degrees of freedom independently while retaining a finite set of qualitatively distinct topological signatures. Second, we argue that our shell-based comparison is effective to perform atomic-level comparisons and show that topological similarity is a less stringent than geometric similarity. We also use the topological versus geometric duality to exhibit topo-rigid patches, whose topology (but not geometry) remains stable upon docking. Third, we use our comparison algorithms to infer specificity-related information amidst a database of complexes. Finally, we exhibit a descriptor outperforming its contenders to predict the binding affinities of the affinity benchmark. The softwares developed with this article are available from http://team.inria.fr/abs/vorpatch_compatch/

Predicting multibody assembly of proteins

textThis thesis addresses the multi-body assembly (MBA) problem in the context of protein assemblies. [...] In this thesis, we chose the protein assembly domain because accurate and reliable computational modeling, simulation and prediction of such assemblies would clearly accelerate discoveries in understanding of the complexities of metabolic pathways, identifying the molecular basis for normal health and diseases, and in the designing of new drugs and other therapeutics. [...] [We developed] F²Dock (Fast Fourier Docking) which includes a multi-term function which includes both a statistical thermodynamic approximation of molecular free energy as well as several of knowledge-based terms. Parameters of the scoring model were learned based on a large set of positive/negative examples, and when tested on 176 protein complexes of various types, showed excellent accuracy in ranking correct configurations higher (F² Dock ranks the correcti solution as the top ranked one in 22/176 cases, which is better than other unsupervised prediction software on the same benchmark). Most of the protein-protein interaction scoring terms can be expressed as integrals over the occupied volume, boundary, or a set of discrete points (atom locations), of distance dependent decaying kernels. We developed a dynamic adaptive grid (DAG) data structure which computes smooth surface and volumetric representations of a protein complex in O(m log m) time, where m is the number of atoms assuming that the smallest feature size h is [theta](r[subscript max]) where r[subscript max] is the radius of the largest atom; updates in O(log m) time; and uses O(m)memory. We also developed the dynamic packing grids (DPG) data structure which supports quasi-constant time updates (O(log w)) and spherical neighborhood queries (O(log log w)), where w is the word-size in the RAM. DPG and DAG together results in O(k) time approximation of scoring terms where k << m is the size of the contact region between proteins. [...] [W]e consider the symmetric spherical shell assembly case, where multiple copies of identical proteins tile the surface of a sphere. Though this is a restricted subclass of MBA, it is an important one since it would accelerate development of drugs and antibodies to prevent viruses from forming capsids, which have such spherical symmetry in nature. We proved that it is possible to characterize the space of possible symmetric spherical layouts using a small number of representative local arrangements (called tiles), and their global configurations (tiling). We further show that the tilings, and the mapping of proteins to tilings on arbitrary sized shells is parameterized by 3 discrete parameters and 6 continuous degrees of freedom; and the 3 discrete DOF can be restricted to a constant number of cases if the size of the shell is known (in terms of the number of protein n). We also consider the case where a coarse model of the whole complex of proteins are available. We show that even when such coarse models do not show atomic positions, they can be sufficient to identify a general location for each protein and its neighbors, and thereby restricts the configurational space. We developed an iterative refinement search protocol that leverages such multi-resolution structural data to predict accurate high resolution model of protein complexes, and successfully applied the protocol to model gp120, a protein on the spike of HIV and currently the most feasible target for anti-HIV drug design.Computer Science