From face to interface recognition: a differential geometric approach to distinguish DNA from RNA binding surfaces.

Protein nucleic acid interactions play a critical role in all steps of the gene expression pathway. Nucleic acid (NA) binding proteins interact with their partners, DNA or RNA, via distinct regions on their surface that are characterized by an ensemble of chemical, physical and geometrical properties. In this study, we introduce a novel methodology based on differential geometry, commonly used in face recognition, to characterize and predict NA binding surfaces on proteins. Applying the method on experimentally solved three-dimensional structures of proteins we successfully classify double-stranded DNA (dsDNA) from single-stranded RNA (ssRNA) binding proteins, with 83% accuracy. We show that the method is insensitive to conformational changes that occur upon binding and can be applicable for de novo protein-function prediction. Remarkably, when concentrating on the zinc finger motif, we distinguish successfully between RNA and DNA binding interfaces possessing the same binding motif even within the same protein, as demonstrated for the RNA polymerase transcription-factor, TFIIIA. In conclusion, we present a novel methodology to characterize protein surfaces, which can accurately tell apart dsDNA from an ssRNA binding interfaces. The strength of our method in recognizing fine-tuned differences on NA binding interfaces make it applicable for many other molecular recognition problems, with potential implications for drug design.

Performing efficient NURBS modeling operations on the GPU.

We present algorithms for evaluating and performing modeling operations on NURBS surfaces using the programmable fragment processor on the Graphics Processing Unit (GPU). We extend our GPU-based NURBS evaluator that evaluates NURBS surfaces to compute exact normals for either standard or rational B-spline surfaces for use in rendering and geometric modeling. We build on these calculations in our new GPU algorithms to perform standard modeling operations such as inverse evaluations, ray intersections, and surface-surface intersections on the GPU. Our modeling algorithms run in real time, enabling the user to sketch on the actual surface to create new features. In addition, the designer can edit the surface by interactively trimming it without the need for retessellation. Our GPU-accelerated algorithm to perform surface-surface intersection operations with NURBS surfaces can output intersection curves in the model space as well as in the parametric spaces of both the intersecting surfaces at interactive rates. We also extend our surface-surface intersection algorithm to evaluate self-intersections in NURBS surfaces.

An efficient solution to systems of multivariate polynomial using expression trees.

In recent years, several quite successful attempts have been made to solve systems of polynomial constraints, using geometric design tools, exploiting the availability of subdivision-based solvers [7], [11], [12], [15]. This broad range of methods includes both binary domain subdivision as well as the projected polyhedron method of Sherbrooke and Patrikalakis [15]. A prime obstacle in using subdivision solvers is their scalability. When the given constraint is represented as a tensor product of all its independent variables, it grows exponentially in size as a function of the number of variables. In this work, we show that for many applications, especially geometric ones, the exponential complexity of the constraints can be reduced to a polynomial by representing the underlying structure of the problem in the form of expression trees that represent the constraints. We demonstrate the applicability and scalability of this representation and compare its performance to that of tensor product constraint representation through several examples.

Continuous collision detection for ellipsoids.

We present an accurate and efficient algorithm for continuous collision detection between two moving ellipsoids under rational Euclidean or affine motion. We start with a highly optimized implementation of interference testing between two stationary ellipsoids based on an algebraic condition described in terms of the signs of roots of the characteristic equation of two ellipsoids. Then we derive a time-dependent characteristic equation for two moving ellipsoids, which enables us to develop an efficient algorithm for computing the time intervals in which two moving ellipsoids collide. The effectiveness of our approach is demonstrated with several practical examples.

Global segmentation and curvature analysis of volumetric data sets using trivariate B-spline functions.

This paper presents a method to globally segment volumetric images into regions that contain convex or concave (elliptic) iso-surfaces, planar or cylindrical (parabolic) iso-surfaces, and volumetric regions with saddle-like (hyperbolic) iso-surfaces, regardless of the value of the iso-surface level. The proposed scheme relies on a novel approach to globally compute, bound, and analyze the Gaussian and mean curvatures of an entire volumetric data set, using a trivariate B-spline volumetric representation. This scheme derives a new differential scalar field for a given volumetric scalar field, which could easily be adapted to other differential properties. Moreover, this scheme can set the basis for more precise and accurate segmentation of data sets targeting the identification of primitive parts. Since the proposed scheme employs piecewise continuous functions, it is precise and insensitive to aliasing.