This year’s SIAM Conference on the Life Sciences, which took place August 4-7 in Charlotte, NC, USA, focused more generally on biology but was not short on dynamics. Interesting dynamics-related problems from physiology, ecology, and epidemiology were presented. In fact, the meeting contained so much dynamics than one person could not possibly experience it all! Below I give some of my own personal impressions about dynamics topics from the meeting, so it is unfortunately but necessarily biased toward areas of personal interest.
John Rinzel (New York University) gave an engaging plenary talk on bistable dynamics of perceiving ambiguous visual and auditory stimuli. Examples include the cube drawing that can appear inward or outward. How such ambiguous stimuli are perceived can change over time and can jump back and forth between different interpretations. Rinzel’s main focus was on bistability in visual stimuli, especially visual plaids, and in auditory stimuli involving two different tones played at different rates. One mathematical model discussed used two stimulated populations that served as inhibitors to each other; over time, the inhibition weaked to allow a switch. Fast-slow analysis and phase space analysis showed nullclines that changed as the system evolved over time, thereby altering the existence and stability of fixed points. Noise played an important role in the system in promoting switching between percepts.
In another plenary talk, James Collins (Boston University) spoke about the relatively new field of synthetic biology. This area includes developing “programmable cells” by designing and implementing biological switches. RNA switches have been developed and used to count up to three; the time frames involved are currently on the order of hours, so biocomputation currently is not close to competing with traditional computational technology. In response to concerns over intellectual property as well as safety, a programmable kill switch also has been developed for microbes used in this line of research as an unstable toggle switch.
Other plenary talks ranged from epidemiology to ecology to biomedical applications. Linda Allen (Texas Tech University) spoke about deterministic and stochastic thresholds for disease extinction in models of infectious diseases. She showed a relation between the next generation matrix and the reproduction parameter from deterministic theory and expectation from stochastic theory and proceeded to apply branching process theory to compute, for example, the probability of disease extinction when the reproductive parameter exceeded 1. Alan Hastings (University of California, Davis) presented work about early warning signs in ecology. Because of stochastic effects, it is difficult to predict when critical transitions from one behavior to another occur. He suggested approaches for addressing this problem. Norm Mazur (F. Hoffmann-La Roche, Ltd.) spoke about whether so-called “good” cholesterol is always good, motivated by clinical findings that raising the levels of “good” cholesterol does not always slow deposition of cholesterol ester in arterial walls. He asked the question of whether the tested therapies actually altered other dynamics of cholesterol transport that may have counteracted the effects raising levels of “good” cholesterol would be expected to have.
Several talks explored incorporating data into models through methods such as data assimilation. Henry Abarbanel (University of California, San Diego) used data assimilation to infer biophysical properties of birdsong production network nodes and their connections. Timothy Sauer (George Mason University) applied data assimilation using the ensemble Kalman filter to infer the network structure of neural cultures from spike trains and time series. In this same category, and at the risk of self-promotion, my colleague Matthew Hoffman (Rochester Institute of Technology) and I also presented our recent efforts toward applying data assimilation using the local transform ensemble Kalman filter to reconstructing quantitatively accurate estimates of times series of cardiac tissue preparations during complex states like fibrillation.
Other talks addressed issues related to the role of dynamics in living systems. Dan Wilson (University of California, Santa Barbara) spoke about terminating cardiac alternans using isostable response curves. In this approach, a cardiac system can be targeted for defibrillation so as to minimize the energy required to effect defibrillation. Timothy O’Leary (Brandeis University) postulated that neuronal conductances can vary as a consequence of ion concentration fluctuations as the cell tries to maintain homeostasis because of feedback control of ion channel expression in cells. Margaret Watts (National Institutes of Health) presented a more complete model of pancreatic secretions by modeling glucagon and somatostatin along with insulin; the three secretions are interrelated and each may enhance or inhibit the effects of the others.
In a particularly fascinating application, Patrick Fletcher (Florida State University) described a novel “dynamic clamp” protocol in which a model current is introduced to a live cell to facilitate model calibration and testing of predictions. In this approach, a current is determined computationally using a model and then fed directly to a cell as a digital current. He and his collaborators used this method to explore feature space (aspects such as amplitude, period, active phase duration, number of peaks in a burst, etc.) for a pituitary lactotroph model.
The conference included many more dynamics-related talks and poster presentations than can be summarized effectively in a short review. Perhaps the main take-away message is that for anyone looking for biological applications of dynamics, the SIAM Conference on the Life Sciences has plenty to offer!
Elizabeth Cherry