Combinatorics in biology: From gene regulation to public health

The goal of my research is to find mathematical and statistical models that describe how genes work together in combination to produce various cell types and phenotypes. With the availability high-performance parallel computing, now is an opportune time to study the information hidden in the exponential number of higher-order interactions between genetic and environmental variables. Such information may explain why only a certain fraction of people with a risk-predisposing polymorphism go on to develop disease, and we need new methods and insights to extract it. In my Ph.D. work, I studied how permuting the temporal order of small number of regulatory molecules can give rise to a large number of gene expression states, challenging the traditional combinatorial binding model.¹ With the realization that biology may be noncommutative, I am exploring mathematically the paradox that a single cell with a single DNA blueprint can simultaneously and autonomously differentiate into unique cell types. It is a similar paradox how subjects with the same DNA polymorphisms present with different disease phenotypes. I have developed pattern-mining methods to search for rare, noncontiguous haplotypes of common genetic variants in chromosomes of breast cancer patients from the UK Biobank that confer very high risk for developing disease.² My current research is dedicated to finding combinatorial and noncommutative models that more perfectly distinguish disease cases from controls and deepen our understanding of the relationship between genotype and phenotype. Towards this goal I am using parallel computing to efficiently test different haplotypes for disease association in public datasets.

Selected publications

1. Letsou, W. & Cai, L., Noncommutative biology: sequential regulation of complex networks. PLoS Comput Biol 12, e1005089 (2016).
2. Letsou, W., Wang, F., Moon, W., Im, C., Sapkota, Y., Robison, L. L. & Yasui, Y., Potential misrepresentation of inherited breast cancer risk by common germline alleles. Under revision (2023).