SIAM Life Sciences meeting

By Tim Lewis

Applications of dynamical systems

The 2012 SIAM Conference on the Life Sciences was held in San Diego, CA during the first week in August. Over the past two decades, the application of mathematics to biological problems has seen significant activity and rapid growth. More and more biologists are recognizing that mathematicians can make significant contributions to problems in the life sciences, and mathematicians are recognizing that biology presents not only interesting scientific problems but exciting mathematical challenges as well. This was reflected in the demographics of the participants at the Life Sciences conference, which included M.D.s, experimental biologists from academics, representatives from the pharmaceutical industry, engineers, computer modelers, and applied mathematicians. The applied mathematicians included those from. In terms of mathematics, many areas of traditionally applied mathematics and some areas of traditionally pure mathematics were represented, but the conference was dominated by dynamical systems theory.

In the opening plenary talk, Mike Reed (Duke University) gave several examples that illustrated the difficulties and pleasures of investigating biological systems in which (1) processes occur on multiple space and time scales and (2) stochasticity is ubiquitous and often fundamental to functionality. He asserted that only with mathematics can we discover the mechanisms underlying the bewilderingly complicated and complex behavior of these systems, and he posed the question: What fields of mathematics are necessary and useful for this endeavor, now and in the future? His answer was: almost all, but progress in dynamical systems – both deterministic and stochastic – will be central.

The plenary talks, mini-tutorials, mini-symposia talks and poster presentations included a mix of new and now classical theories in dynamical systems, and most presentations focused on the stochastic and/or multi-scale nature of biological processes. Sam Isaacson (Boston University) organized a mini-tutorial on numerical methods for studying stochastic models, and Tim David (University of Canterbury) organized another mini-tutorial on multi-scale modeling. In the invited plenary talks: L. Mahadevan (Harvard University) used a combination of physical experiments, mathematical models and numerical computations to identify the bifurcations that lead to the morphology of pollen tubes, algal blades and the looping pattern of the vertebrate gut. Artie Sherman (NIH) described the bifurcation structure associated with bursting electrical activity in neurons and pancreatic beta-cells, referring to bifurcations as the dynamical “atoms” upon which biological models are built. John Milton (Claremont College) explained how time-delays and stochasticity make neural systems sit on the edge of stability. He hypothesized that this may be essential for neural systems to function but it also predisposes them to certain pathological behaviors. Similarly, Ary Goldberger (Harvard Medical School) argued that the multi-scale nature of cardiac electrodynamics and cardiovascular control was necessary for healthy cardiac function and that pathologies are often associated with decreased complexity/dimensionality of cardiac dynamics. Charles Taylor showed how his company HeartFlow Inc. is using computational fluid dynamics as part of a safe, inexpensive diagnostic tool for heart disease. Peter Hunter (University of Auckland) described the efforts of the Virtual Physiological Human/Physiome Project to advance multi-scale modeling of integrative physiological processes. Finally, Mariel Vazquez (San Francisco State University) explained how she uses topological methods and computational tools to understand DNA unknotting and unlinking, and she described new work in which she is modeling the dynamics of these processes. You can view all of the invited plenary talks and the mini-tutorials on the SIAM website.

In his plenary talk, Mike Reed praised the efforts and accomplishments of mathematical community in the Life Sciences and pointed out that SIAM has vigorously supported these efforts. He concluded by saying, “Hooray Life Sciences! Hooray SIAM!” … and we should add “Hooray for Dynamical Systems”.

If you are a dynamical system theorist looking for interesting and challenging mathematical problems with important applications, look to the life sciences. If you aren’t already a member of the Life Science SIAG, think about joining … and think about coming to the next SIAM Conference on the Life Sciences in 2014.

As the departing co-chair of the SIAM Life Science Conferences, I would like to take this opportunity to thank my co-chairs Jon Rubin (2010) and Mette Olufsen (2012), the conference organizing committees, the workshop and mini-tutorial organizers, the speakers, Lee Segel Forum and Forward Looking Session panelists, poster presenters, and the NSF for supporting the SIAM-LS conference. Finally, I would like to thank the conference staff at SIAM, especially Nicole Erle – I can’t imagine having had to organize the conferences without them.

Tim Lewis


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