The AMS sponsored an exhibit at the 22nd annual Coalition for National Science Funding (CNSF) Exhibition & Reception on Capitol Hill held on April 26, 2016. Konstantina Trivisa, University of Maryland, presented her work “On the Movement of Cells, Birds, Fish and Other Agents: Mathematical Modeling in Biology and Ecology.”
Nature and biological systems offer many examples of collective self-organized behavior: ants build colonies, birds fly in flocks, fish swim in schools. Bacteria can behave either as individual single-cell organisms or as multicellular populations. Bacteria exhibit this behavior bychemically "talking" to one another through a process called quorum sensing. Using principles of self-organized dynamics, the work of Prof. Trivisa, in collaboration with the lab of W. Bentley at the University of Maryland and the Ph.D. student H. Ueda, have constructed a new model of Cucker-Smale-type that exhibits such behavior. Quorum sensing involves the production, release and community-wide sensing of molecules called autoinducers that modulate gene expression and ultimately bacterial behavior in response to the density of a bacterial population. The phenomenon of bioluminescence (the production and emission of light by a living organism which occurs widely in marine life) and the construction of antibiotics and proteins are intimately connected to this process. When the number of particles is sufficiently large, it is not economical to keep track of the motion of each particle through a particle system. Instead, one is forced to study the mean field limit of the particle system introducing a kinetic description for flocking analogous to Vlasov equation in plasma and astrophysics. By taking into consideration random effects, this kinetic description yields in certain regimes a macroscopic description governed by Euler-type systems, which are in general more cost-effective for computational purposes.
One of the goals of Trivisa’s research is the construction of numerical algorithms for the approximation of such systems which govern the motion of cells. Numerical algorithms complement the analysis and inform the experiments providing valuable insight on the evolution of cells. Such numerical algorithms have been constructed by Trivisa (in collaboration with Weber) providing information on the effect of drug application on cancerous cells and tumor growth. This research which aims at the prediction of cancer progression based on imaging analysis is in collaboration with S. Lockett and B. Kinders at the National Cancer Institute. Similar analysis is currently under way in the context of models exhibiting quorum sensing.
The CNSF Exhibition was attended by over 250 people viewing 35 exhibits. Professor Trivisa and the other exhibitors were able to present their work, funded by the National Science Foundation, and explain the critical importance of increased, sustained federal investments in basic scientific research.
CNSF is an alliance of over 130 professional societies, universities and corporations (including the AMS) united by a concern for the future vitality of the national science, mathematics and engineering enterprise. CNSF supports the goal of increasing the national investment in the National Science Foundation's research and education programs.
For information on the annual CNSF Exhibition & Reception, please visit the CNSF website.