The general aim of my research is to achieve scientific breakthroughs and develop innovative methods, algorithms and technologies using interdisciplinary research in applied mathematics, algorithms, computational theory and biochemistry with applications to protein science, data science and robotics.
As an applied mathematician and computational biologist, my research spans several areas of bioinformatics and discrete applied mathematics, specializing in algorithm development to understand how proteins function. The techniques I use and develop are at the confluence of structural-mathematical rigidity theory, discrete applied mathematics (graph theory, discrete and computational geometry, combinatorial algorithms, matroid theory), and various tools and methods in computational biology and bioinformatics.
The current research is focussed on several projects related to the analysis and prediction of protein function and in synthesis and analysis of mechanical linkages and robots. To understand how proteins function, we need deep knowledge about their flexibility and motions at atomic level, which is critical in medicine and drug design. Experimental techniques are costly and traditional computational approaches, such as molecular dynamics simulations, are still largely impractical. In several studies, I have demonstrated that my algorithms and methods address these critical bottlenecks and provide extremely fast alternate high-throughput computational methods for analysis of protein flexibility and its dynamics. For more details on previous research see publications.
Some of my current research projects:
1. Deciphering a general mechanism of allostery in proteins (multiple collaborations in Japan, Europe, USA and Canada):
Allostery, which has been coined the “second secret of life”, refers to regulation of protein function by transfer of signals between distant sites on protein structure. Modeling allostery is a difficult problem and most questions surrounding allostery are largely unresolved. A key puzzle is to describe the general physical allosteric mechanism of distant coupled conformational change and to detect regions (residues) in the protein that are the most critical for transmission of information. To address this, I have developed a first rigidity theory-based mechanistic model and description of allosteric transmission during my PhD studies known as Rigidity Transmission Allostery (RTA) algorithm. RTA method is a powerful tool and has been experimentally validated for modelling and predicting allostery in enzymes, GPCRs and many other protein structures. We continue to investigate and develop this approach in combination with other computational methods and experimental techniques to better understand allostery. See press release for more info.
2. Allostery in G Protein Coupled Receptors (GPCRs) (see recent study).
3. Fast computational predictions of protein flexibility, ensembles and its dynamics.
4. Validation of NMR protein structures using rigidity theory and NMR chemical shifts (collaboration with Sheffield University, University of Alberta and Osaka Protein Institute).
5. Evolution of Antibody flexibility and mechanism of affinity maturation (collaboration with Jeffrey Gray at John Hopkins University and University of Tokyo) (see recent study).
6. Algorithms and analysis for design of mechanical linkages, robots and metamaterials (collaboration with Andreas Muller at Johannes Kepler University)
7. Impact of symmetry on molecular flexibility and protein motions (continuation of this work).
8. Mathematical inductive constructions of Assur graphs and metamaterials.
For more information on mathematical rigidity theory see here.