Research in the Graphics and Visual Informatics Laboratory deals with a range of issues in 3D molecular graphics ranging from the theoretical to the applied. Our research is driven by the applications of biological visualization and computer-aided drug design. Here we give an overview of our ongoing and recent research in graphics software systems and algorithms.

Researchers: Amitabh Varshney, Chang Ha Lee , and Xuejun Hao .

We have developed an algorithm for rapid computation of the smooth molecular surface. Our algorithm is analytical, easily parallelizable, and generates triangulated molecular surface. One of the important factors that influences the position and orientation of the protein with respect to the substrate in protein-substrate docking is the geometric fit or surface complementarity. Traditionally, the interface has been studied by using a clipping plane that is moved along the z-axis in the screen space. This does not readily convey the three-dimensional structure of the interface to the biochemist. We have defined the molecular interface surfaces between two molecular units, as a family of surfaces parametrized by the probe-radius α and interface radius β. The molecular interface surfaces are derived from approximations to the power-diagrams over the participating molecular units. Molecular surfaces provide biochemists with a powerful tool to study surface complementarity and to efficiently characterize the interactions during a protein-substrate docking.

The top images show Crambin and its molecular surface (probe radius 1.4 Angstroms) and the bottom images show Trasthyretin domains and their molecular interface surface (α = 1.0 Angstrom, β = 2.4 Angstroms).

• Defining, Computing, and Visualizing Molecular Interfaces A. Varshney, F. P. Brooks, Jr., D. C. Richardson, W. V. Wright, and D. Manocha Proceedings of the IEEE Visualization '95 Oct 29 - Nov 3, 1995, Atlanta, GA, pp 36 - 43
  
  
• Linearly Scalable Computation of Smooth Molecular Surfaces A. Varshney, F. P. Brooks, Jr., and W. V. Wright IEEE Computer Graphics and Applications Sept 1994, Vol. 14, No. 5, pp 19 - 25
  
  
• Interactive Visualization of Weighted Three-dimensional Alpha Hulls A. Varshney, F. P. Brooks, Jr., and W. V. Wright Third Annual Video Review of Computational Geometry in Proceedings of the Tenth Annual Symposium on Computational Geometry Stony Brook, NY, June 6 - 8, 1994, pp 395 - 396
  
  
• Fast Analytical Computation of Richards's Smooth Molecular Surface A. Varshney and F. P. Brooks, Jr. Proceedings of the IEEE Visualization '93 Oct 25 - 29, 1993, San Jose, CA, pp 300 - 307.
  
  

Participants: Chang Ha Lee and Amitabh Varshney

The previous methods to compute smooth molecular surface assumed that each atom in a molecule has a fixed position without thermal motion or uncertainty. In real world, the position of an atom in a molecule is probabilistic because of its uncertainty in protein structure determination and thermal energy of the atom. Therefore, for more realistic and informative visualization of molecular surfaces, we need to represent the probabilistic positions of atoms.

For representing thermal vibrations and uncertainty of atoms, we have proposed a method to compute probabilistic molecular surfaces. We have also implemented a program for interactively visualizing three-dimensional molecular structures including the probabilistic molecular surface using multi-layered transparent surfaces, where the surface of each layer has a different confidence level and the transparency is associated with the confidence level.

• Representing Thermal Vibrations and Uncertainty in Molecular Surfaces C.H. Lee and A. Varshney SPIE Conference on Visualization and Data Analysis 2002, Jan 20-25, 2002, San Jose, CA
  
  

Further details of our work on probabilistic molecular surfaces can be found here.

Participants: Zhiyun Li, Chang Ha Lee, and Amitabh Varshney

The recent growth of interest in virtual environments has been accompanied by a corresponding increase in the types of devices for sensory feedback, especially visual feedback. Our target application is collaborative visualization-assisted computational steering for problems in computational biology. The head-coupled displays are ill suited to applications in which the goal is to interact with other people or for tasks that take several hours (due to eye and neck fatigue). Spatially immersive displays, such as wall-sized tiled displays, allow long work periods, offer a high field of view and resolution, and afford a strong self-presence. Wall-sized tiled displays are more supportive to collaboration and learning than regular monitors. Users prefer to stay longer in such displays, they prefer to move and discuss the datasets more, and repeatedly inspect, walk around and see the displayed datasets from different viewpoints. We have designed and built high-resolution, wall-sized displays that can be quickly assembled and geometrically aligned using software and algorithms.

We have also incorporated interactive ultrasonic trackers to manipulate the molecular structures directly on such displays. Using such electronic sensors, the researchers can explore 3D molecular structures directly on large-area displays.

• A Real-Time Seamless Tiled Display for 3D Graphics Z. Li and A. Varshney Proceedings, Seventh Annual Symposium on Immersive Projection Technology (IPT 2002), March 24-25, 2002, Orlando, FL
  
  

Participants: Xuejun Hao and Amitabh Varshney

We have recently proposed variable-precision geometry transformations and lighting to accelerate 3D molecular surface display. Multiresolution approaches reduce the number of primitives to be rendered; our approach complements the multiresolution techniques as it reduces the precision of each graphics primitive. Our method relates the minimum number of bits of accuracy required in the input data to achieve a desired accuracy in the display output. We achieve speedup by taking advantage of the SIMD parallelism for arithmetic operations, now increasingly common on modern processors. In our research we have derived the mathematical groundwork for performing variable-precision geometry transformations and lighting for 3D graphics. In particular, we explore the relationship between the distance of a given sample from the viewpoint, its location in the view-frustum, to the required accuracy with which it needs to be transformed and lighted to yield a given screen-space error bound.

The left image of the Dihydrofolate Reductase Molecular Surface (145K triangles) shows rendering by conventional floating-point transformation and lighting, whereas the right image shows variable-precision rendering. The latter is a factor of three faster (Pentium III, 933 MHz, 512MB RDRAM).

• Variable-Precision Rendering, X. Hao and A. Varshney Proceedings, ACM Symposium on Interactive 3D Graphics , March 2001, Research Triangle Park, NC, pp 149 - 158
  
  

Participants: Xuejun Hao and Amitabh Varshney

Electrostatic interactions are of central importance for many biological processes. Experiments have shown that electrostatics influence various aspects of nearly all biochemical reactions, such as macromolecular folding and conformational stability. Electrostatics also determine the structural and functional properties of biological samples, such as their 3D shapes, binding energies, and association rates. Electrostatic interactions are one of the only two kinds of long-range interactions involved in biological reactions (the other interaction is van der Waals', which fall off much faster in space than the electrostatic). The successful modeling and computation of electrostatics has great practical importance for applications such as structure-based drug design and protein folding.

We have used the classical electrostatics theory to model the protein electrostatics by numerically solving the non-linearized Poisson-Boltzmann equation on 3D grids and displaying the electrostatic potential on the solvent-accessible surfaces of proteins. The left image shows the solvent-accessible surface of the SOD protein, while the right image shows the potential mapped onto this surface. Blue color represents the positive potential, red color represents the negative potential, and white represents neutral potential.

Participants: Chang Ha Lee, Amitabh Varshney, and Ron Unger

Many drug development process so far have begun with large scale random screening of candidate inhibitors. These initial discoveries are improved through well-defined approaches to find new drugs. As molecular structure determination techniques and computational methods progress, protein docking methods using structure-based molecular complementarity have become a feasible substitution for random screening in the drug design process.

Among many factors involved in protein-protein interactions such as electrostatics, hydrophobicity, and hydrogen bonding, shape complementarity is of major concern. A complete search of all possible geometric fits of two flexible molecules takes too much time because of the extremely large degrees of freedom. Our goal of ongoing research in shape complementarity is to develop fast and reliable methods for finding docking sites and corresponding transformations to align the two molecules into complementary fits.

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