Bioinformatics and Mathematical Biology

Our research in mathematical biology employs tools from stochastic processes, differential equations, and statistics. Topics being actively investigated include: bioinformatics, population genetics and evolutionary biology, ecology, and epidemiology. Much of our work is done in close collaboration with biologists at UI and elsewhere, especially involving the evolution and ecology of microorganisms (bacteria and viruses). The majority of this work is supported by interdisciplinary grants from NIH and NSF. Our graduate students have the option of pursuing the Bioinformatics and Computational Biology (BCB) degree option. We are also key players in UI's Initiative for Bioinformatics and Evolutionary Studies (IBEST) which provides a stimulating environment for interactions between mathematicians, biologists, and computer scientists.

• Zaid Abdo
  Professor Abdo's research combines mathematical modeling and statistical analysis using computationally intensive methods and simulation, and stems from current problems in biology. A description of some of his projects follows:

  Barcoding of Life (A decision theoretic approach based on the coalescent):
  Accurate assignment and clustering are crucial for responding effectively and efficiently to newly detected potential disease carriers or disease causing species. Assignment facilitates prediction of the biology of the classified individual(s). Should we identify an insect to belong to a disease-carrying species/group, for example, we could invoke counter measures to eliminate the environmental conditions that help the spread of these insects. Accurate assignment depends on the accurate and correct characterization of groups/species, and, hence, on the accurate and correct clustering. This project works to develop new, model-based, statistical methods to use barcode data to quickly and accurately identify (assign) individual organisms and to distinguish and characterize (cluster) different species and groups. Methods utilize the evolutionary history, inferred from the data, and a measure of similarity or difference, in a decision theoretic framework, to make an informed decision of assignment or clustering.

  Experimental Evolution (Plasmid and phage Evolution):
  Mathematical models provide predictive power to help explain the evolutionary and ecological mechanisms of plasmids and phage. Professor Abdo is interested in developing stochastic models to describe the mechanics of evolution and the interaction between a parasite (a plasmid or phage) and a host (a bacterial cell) and utilize these models in statistical inference of the factors most important in such ecological and evolutionary structure.

  Systematic Biology (A decision theoretic approach to model selection in phylogenetic analysis):
  Likelihood and Bayesian methods in phylogenetic analysis rely on choosing a justifiable stochastic models of evolution based on which researchers infer the relationship between different individuals (taxa) that belong to different species. We developed and continue to refine a decision theoretic approach that takes into account performance, as well as fit in choosing an evolutionary model for phylogenetic inference.

• Frank Gao
  Collaborating with Larry Forney (Biology) and Steve Krone (Mathematics), Professor Gao works on mathematical modeling of microbial biofilms. In particular, he studies properties of diffusion (of nutrients, antibiotics, etc.) within biofilms and analyzes images from confocal microscopy.

  In the natural world, more than 99 percent of all bacteria aggregate as biofilms, glue-like structured slimes adherent to surfaces which behave very differently from the free-floating bacteria growing in many laboratory cultures. A characterization of the biofilm environment is key to a better understanding of biofilm biology. However, due to limitations in current techniques, measurements through direct laboratory experiments are rather limited. A joint effort of laboratory experiments and mathematical modeling is now being undertaken.

  One of the main factors that determine the biofilm environment is the diffusion-reaction process. Rather than uniform layers, biofilms have complicated structures and uneven surfaces; as a consequence, diffusion-reaction processes in biofilms are complicated and species-specific. By analyzing time-lapse confocal images of fluorescent tracers diffusing into biofilms, Professor Gao is currently developing species-specific diffusion models in biofilms.

• Paul Joyce

• Steve Krone
  Professor Krone uses tools from probability and differential equations in the study of biological populations. This work focuses mostly on theoretical population genetics and on the effects of spatial structure in the ecology and evolution of various populations.

  Most populations in natural and clinical settings are spatially structured and this structure impinges heavily upon their ecological and evolutionary dynamics. Microbial populations (bacteria and viruses), in addition to their obvious importance in the health of humans, animals and plants, are ideal for laboratory study since they can be grown in carefully controlled conditions and their generation times are so short that evolution can be observed in real time. In a number of highly interdisciplinary projects with biologists, Krone uses interacting particle systems to create and study stochastic spatial models of microbial ecology and evolution. With Eva Top (Biology), he investigates the spread of plasmids (extrachromosomal pieces of DNA that code for things like antibiotic resistance and can be copied and transmitted from one bacterial cell to anothebreven between different species!) in spatially structured environments. With Holly Wichman (Biology), he studies the competition and evolution of phages (viruses that infect bacteria). With Larry Forney (Biology) and Frank Gao (Mathematics), he considers bacterial biofilms, the highly complex, self-organized spatial structuring that is so common in bacterial communities. In all of these projects, mathematical modeling and laboratory experiments are tightly linked in a way that leads to understanding that could not be achieved by a single approach.

  Krone's work in population genetics deals mostly with various aspects of coalescent theory. Coalescents are mathematical embodiments of the genealogies (or ancestral trees) of populations. Their study, initiated in the early 80s by Kingman, has revolutionized the subject of population genetics. In real populations, many of the simplifying assumptions that led to Kingman's original coalescent do not hold. Krone studies the effects that these factors (selection, spatial structure, fluctuating population size, etc.) on the resulting genealogies. His other work in population genetics has dealt with diffusion approximations.

• Matthew Rudd