My main research interests lie in computational biology (a.k.a. bioinformatics). My work has focussed on applying computational techniques to study biopolymer systems, specifically protein folding, and to a lesser degree protein/ligand binding sometimes called drug docking. Throughout my doctoral research, my background in statistical physics (which governs polymers) and computer science have come together in synergy in this interdisciplinary field. Our work has attracted great attention and has been featured in the news.

My other research interests include the algorithmic aspects of motion planning and their applications in CAD (Computer Aided Design) and virtual prototyping, where we have designed a framework for integrating automatic motion planning and user input through a haptic device. I am also actively working in quantum computing, which is another interdisciplinary field bridging physics and computer science.
 

Protein Folding: Energy Landscape and Folding Pathways and Kinetics

We have developed a novel framework for studying protein folding pathways, energy landscapes and folding kinetics.  Our work uses Probabilistic Roadmap (PRM) motion planning techniques which have proven successful for problems involving high-dimensional configuration spaces. A strength of these methods is their efficiency in rapidly covering the planning space without becoming trapped in local minima.  Our work in protein folding was motivated by our success in paper folding, where we provide folding sequences for high degrees of freedom paper folding models in a few seconds.  Our  approach, by constructing a roadmap that approximates the protein's potential landscape, computes multiple folding pathways in a single run and provides a natural way to study protein folding kinetics at the pathway level.  What we sacrifice is path quality, which can be improved through bigger roadmaps, oversampling, or other techniques.

One of folding pathways found with our method for Protein A which clearly show the three helice form about the same time, agreeing with experimental observations. Folding movies of more proteins can be found here.

We have recently applied our technique to Protein G (B1 immunoglobulin-binding domain of streptococcal protein G) and protein L (B1 immunoglobulin-binding domain of peptostreptococcal protein L). Protein G and L are known to fold differently although they have great structural similarity (they have only 15 sequence similarity). Both are composed of one -helix and a 4-stranded -sheet with two strands forming an N-terminal hairpin and two strands forming a C-terminal hairpin. Experimental results show that the N-terminal hairpin forms first in protein L, while the C-terminal hairpin forms first in protein G. Our results  were in strong agreement with experimental observations, which demonstrates that our approach is able to capture subtle folding differences.
 

Drug Docking (or Ligand Binding)

Efficiency of a drug molecule is measured by its ability to find a specific position and orientation inside a protein (or the receptor molecule).  This process is called docking and the drug molecule is often referred to as a ligand. We applied our obstacle-based PRM method (OBPRM) to generate potential binding conformations since  has proven strengths in generating near contact configurations, which are good starting points in the search for possible binding sites (which are usually local potential minima). We were able to generate conformations close to the binding site, within 1-2  in many cases  in a study of 15 different protein-ligand complexes obtained from the Protein Data Bank.
 

Algorithmic Aspects of Motion Planning: Probabilistic Roadmap Methods

In this area, we have proposed a new approach for building and querying probabilistic roadmaps.  An important benefit of our approach is that it gives one the ability to customize the same roadmap in accordance with multiple, variable, query preferences. Coarse roadmaps are constructed first and then the roadmap is validated and refined only in the area of interest for the query, and moreover, is customized in accordance with any specified query preferences.  The framework is general enough to encompass all previously proposed lazy evaluation  variants.  Our results on problems drawn from diverse application domains show that it dramatically improves performance, and shows remarkable flexibility when adapting to different query requirements.  Specifically, based on this approach, we develop an algorithm for motion planning for nonholonomic car-like robots, where we introduce the use of a 'control roadmap' during both roadmap construction and path smoothing.
 

Virtual Prototyping enhanced by Haptic Input

In this work, we investigated methods for enabling a human operator and an automatic motion planner to cooperatively solve a motion planning query.  Our work was motivated by our experience that automatic motion planners sometimes fail due to the difficulty of discovering `critical' configurations of the robot that are often naturally apparent to a human observer. We developed techniques by which the automatic planner can utilize user-input, and determine `natural' ways to inform the user of the progress made by the motion planner.  We showed that simple randomized techniques inspired by probabilistic roadmap methods were useful for transforming approximate, user-generated paths into collision-free paths, and described an iterative transformation method which enables one to transform a solution for an easier version of the problem into a solution for the original problem.  We illustrated the utility of our methods on difficult problems involving complex 3D CAD Models.
 

Quantum Computing

In this field, I am especially interested in lower bound proofs for quantum circuit and gate implementation.  The controlled-not gate and the single qubit gates are considered elementary gates in quantum computing. It is natural to ask how many such elementary gates are needed to implement more elaborate gates or circuits.  In one work, we provided optimal realizations for any controlled unitary gate. The results showed that the well-known realization with two controlled-not gates and four single qubit gates is only optimal under certain conditions. We also derived optimal implementations for the remaining non-generic cases. In other work, we have proved the optimality of the Margolus' simplified Toffoli gate (we are currently preparing this result for publication).
 

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