This year’s BAMM! (Biology and Medicine Through Mathematics) Conference featured interesting research on dynamics in the context of mathematical biology. Held at Virginia Commonwealth University in Richmond, VA, USA on May 20–22, 2016, BAMM! brought together researchers in biological mathematics for a long weekend of plenary talks, contributed presentations, posters, and numerous networking opportunities.
Four renowned invited speakers spoke about topics that intersect with dynamics.
- Bard Ermentrout (University of Pittsburgh) spoke about chemical sensing and olfaction in a talk entitled “Scent and Sensibility: Navigating a Chemical Trail.” In one example, he modeled bacterial chemotaxis using the Keller–Segel equations and discussed a mean-field model to explain three distinct behaviors: moving to the center of the chemoattractant and remaining there, moving to the center and then returning to the original location, and moving to the center and then relocating depending on system parameters like population density. He also discussed approaches that animals use for extracting directional cues from olfactory signals from (often-turblent) fluids. One example is casting, in which an animal sweeps from side to side and compares environmental inputs to detect odor gradients. This approach can be analyzed as a dynamical system involving sensor position, which moves in response to what is sensed, and the direction of motion, which is proportional to the difference in the sensed odor concentrations on each side.
- “Mathematical models of molecular motors and other cellular processes” were the topic of Leah Edelstein-Keshet’s (University of British Columbia) plenary talk. She focused on microtubules, which are large polarized biopolymers that transport materials from neuronal cell bodies to and from the dendrites. The microtubules, which function as “tracks,” use molecular motors to move materials actively rather than relying on diffusion, which generally is insufficient for this purpose. Modeling approaches include particle-based (Lagrangian) methods; continuum (Eulerian) approaches, which are valid if there are many identical objects or interpreted as an average over an ensemble; and stochastic techniques, which together with a quasi-steady state approximation can be reduced to a Fokker–Plank equation. Edelstein-Keshet and her collaborators found this last approach to be useful for explaining behavior of filamentous hyphae of a fungus, an experimental system, with a structure similar to microtubules, that is easier to study than single neurons.
- In his plenary talk, James Keener (University of Utah) discussed “Cell Biology: Making Diffusion Your Friend.” He suggested that diffusion with positive feedback enables living organisms to survive and flourish—specifically by allowing them to signal, form structures and patterns, make measurements, and make decisions. Essentially, biological entities can use energy to concentrate molecules and then accomplish useful activities by relying on the fact that molecules move down their concentration gradients. For example, flux is inversely proportional to length, so information about a flux also provides information about length. Some of the discussed examples included maintenance of glucose concentrations in cells, Turing patterns in activator–inhibitor systems, quorum sensing in bacterial colonies, cell-size measurement, and flagellar-length detection.
Jim Keener (University of Utah) explains how cells can measure lengths through fluxes.
- Jim Cushing (University of Arizona) gave the final plenary talk, which was about “Matrix Models for Population & Evolutionary Dynamics: Climate Change Studies on Protection Island Wildlife Refuge.” He discussed how behaviors of a population of glaucous-winged gulls living on a refuge island near Seattle vary with mean sea-surface temperature, which can increase in the short term due to warming effects of the El Niño weather pattern. The gulls are considered sentinels of climate change in the region, and they change feeding strategies in response to temperature changes. Warmer waters make fish and plankton move to greater water depths, and the decreased availability of these food sources increases the rate of cannibalism of other gulls’ eggs as a feeding practice. Adaptations to prevent significant egg loss include a longer breeding season and egg-laying synchrony, in which gulls, who normally lay eggs approximately every other day, synchronize to limit opportunities for cannibalism. Several discrete matrix models were used to represent the population dynamics, and Cushing and his collaborators studied the bifurcations that occur when the population’s inherent net reproduction number increases through the value 1, corresponding to destabilization of the extinction equilibrium.
Along with the plenary talks, the conference included dozens of posters and contributed presentations. One highlight was a live demonstration of electric current strength: Flavio Fenton (Georgia Institute of Technology) applied electrode patches to Bard Ermentrout’s arm to demonstrate how even small electric currents—of lower magnitude than those given to terminate ventricular fibrillation and other cardiac arrhythmias—can have noticeable effects. Bard’s arm and hand twitched involuntarily in response to the applied current. Rosalyn Rael (Tulane University) provided another highlight in her creative study of the movement and dynamics of Norway rats in New Orleans post-Hurricane Katrina. Her modeling work included using both a movement network and population dynamics to predict rodent movement and to develop strategies to control the population.
Flavio Fenton (Georgia Institute of Technology) motivates the need for lower-energy defibrillation approaches by using human guinea pig Bard Ermentrout (University of Pittsburgh) to demonstrate the effects of even relatively weak electric currents.
Meals, coffee breaks, and the poster session provided many opportunities to talk about mathematics with other attendees. Conference-goers hope that this meeting becomes an annual event!