With the completion of a consensus human genome, much attention has turned to the small differences that typically distinguish one individual from another. These can take many forms, although the predominant one is the single nucleotide polymorphism (SNP). Understanding the nature of these differences and determining how they relate to phenotype promises to become a powerful approach for locating disease-related genome regions and developing diagnostic and therapeutic methods, provided the meaningful differences can be distinguished from random noise. Part of my research involves developing models and algorithms for interpreting genetic data to locate and characterize polymorphisms. My most recent work in this area has focused on recombination and haplotype patterns in the human genome. I am also interested in applying these data and methods to the study of genetic predictors of disease.

My other major research focus is modeling and simulation of biological systems, particularly self-assembly systems. Mathematical models and simulations complement experimental work by providing a means to test and refine theories about the behaviors of biological systems, suggest laboratory experiments, and observe aspects of those systems that are not apparent through either experimental or purely theoretical analyses. Two recent trends - vast increases in quantities of data available to many disciplines of biology and similarly vast increases in available computing power - have simultaneously made biological simulations far more valuable and far more feasible than they were only a few years ago. Self-assembly systems provide an ideal subject for the development of such methodologies. They generally consist of simple sub-units that can be characterized and individually modeled, yet the overall systems can exhibit emergent behaviors that are not apparent given even detailed knowledge about their isolated components. In addition, naturally-occurring self-assembly systems can have substantial practical importance in themselves. My research in this direction has focused primarily on virus assembly, examining models for the capsid assembly process and hypotheses about how it might be influenced. In addition, I have been developing models and simulations at multiple abstraction levels for studying protein aggregates and amyloids.

T. Zhang and R. Schwartz. “Simulation study of the contribution of oligomer/oligomer binding to capsid assembly kinetics.” Biophysical Journal, 90:57-64, 2006.

S. Sridhar, K. Dhamdhere, G. E. Blelloch, E. Halperin, R. Ravi, and R. Schwartz. “Fixed parameter tractability of binary near-perfect phylogenetic tree reconstruction.” Proceedings of the International Colloquium on Automata, Languages, and Computability (ICALP), 2006.

N. Castellana, K. Dhamdhere, S. Sridhar, and R. Schwartz. “Relaxing haplotype block models for association testing.” Proceedings of the Pacific Symposium on Biocomputing (PSB06), 2006.

G. Pennington, C. A. Smith, S. Shackney, and R. Schwartz. “Expectation-maximization method for the reconstruction of tumor phylogenies from single-cell data.” Proceedings of the Computational Systems Bioinformatics Conference (CSB06), pp. 371-380, 2006.

F. Jamalyaria, R. Rohlfs, and R. Schwartz. “Queue-based method for efficient simulation of biological self-assembly systems.” Journal of Computational Physics, 204(1):100-120, 2005.