Georgia Institute of Technology College of Sciences

The CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) system is a recently discovered immune defense in bacteria and archaea (hosts) that functions via directed incorporation of viral DNA into host genomes. Here, we introduce a multi-scale model of dynamic coevolution between hosts and viruses in an ecological context that incorporates CRISPR immunity principles. We analyze the model to test whether and how CRISPR immunity induces host and viral diversification and maintenance of coexisting strains. We show that hosts and viruses coevolve to form highly diverse communities through punctuated replacement of extant strains. The populations have very low similarity over long time scales. However over short time scales, we observe evolutionary dynamics consistent with incomplete selective sweeps of novel strains, recurrence of previously rare strains, and sweeps of coalitions of dominant host strains with identical phenotypes but different genotypes. Our explicit eco-evolutionary model of CRISPR immunity can help guide efforts to understand the drivers of diversity seen in microbial communities where CRISPR systems are active. 

The paper "Complete probabilistic analysis of RNA shapes" (2006) by Voss, Giegerich, and Rehmsmeier will be discussed.

The concept of "strategic equilibrium," where each player's strategy is optimal against those of the other players, was introduced by John Nash in his Ph.D. thesis in 1950. Throughout the years, Nash equilibrium has had a most significant impact in economics and many other areas. However, more than 60 years later, its dynamic foundations - how are equilibria reached in long-term interactions - are still not well established. In this talk we will overview a body of work of the last decade on dynamical systems in multi-player environments. On the one hand, the natural informational restriction that each participant may not know the payoffs and utilities of the other participants - "uncoupledness" - turns out to severely limit the possibilities to converge to Nash equilibria. On the other hand, there are simple adaptive heuristics - such as "regret matching" - that lead in the long run to correlated equilibria, a concept that embodies full rationality. We will also mention connections to behavioral and neurobiological studies, to computer science concepts, and to engineering applications.

Angiogenesis, growth of new blood vessels from existing ones, is animportant process in normal development, wound healing, and cancer development.  Presented with increasingly complex biological data and observations, the daunting task is to develop a mathematical model that is useful, i.e. can help to answer important and relevant questions, or to test a hypothesis, and/or to cover a novel mechanism. I will present two cell-based multiscale models focusing on biochemical (vescular endothelial growth factors) and biomechanical (extra-cellular matrix) interactions.  Our models consider intracellular signaling pathways, cell dynamics, cell-cell andcell-environment interactions. I will show that they reproduced someexperimental observations, tested some hypotheses, and generated more hypotheses.