I work on mathematical modeling for biology. One of the objectives in my work is to develop mathematical models that are "very biological", in the sense of being useful in laboratory and clinical studies. My work partly draws on results from cellular biology, structural biology, dynamical systems, proteins, DNA, enzyme dynamics, spatial-temporal dynamics, reaction-diffusion equations.
Present work includes a project on chemotaxis of microbials with motility. This is collaborative work with faculty members from the biology department (Farone) and computational science (Khaliq). We are working on the spatial-temporal dynamics of microbial aggregates, and therefore the models make some use of systems of partial differential equations (e.g., in some cases reaction-diffusion). Part of what is new in the present work is the strategic use of stochastic terms to better align with experimental conditions. Randomness in dynamics requires stochastic partial differential equations. There is also randomness in initial values. The work is three-fold and interdisciplinary: 1. biological and experimental results; 2. new mathematical and geometric analysis; 3. new computational results.
Recent work (with Z. Sinkala, MTSU) provides a method for the rapid computation of parameters of a Gumbel distribution for gapped alignment of DNA sequences, using mixture distributions.
Previously, our team obtained results on modeling enzymatic transition states. Our approach is based on known primary sequence analysis techniques but includes new features that make the approach significantly more user-friendly. The method reproduces results in the literature and also successfully predicts potential actives sites for ribonucleoside hydrolase of E. coli encoded by RihC.
Other recent work was on the dynamics of prostate cancer stem cells with diffusion and organism response (with Z. Sinkala).