Mathematical Biology

In this talk I will present a "dynamical paradigm" for modeling networks of interacting genes and proteins that regulate every aspect of cell physiology. The paradigm is based on dynamical systems theory of nonlinear ODEs, especially one- and two-parameter bifurcation diagrams. I will show how we have used this paradigm to unravel the mechanisms controlling "multiple fission" cycles in the photosynthetic green alga Chlamydomonas. While most eukaryotic cells maintain a characteristic size by executing binary division after each mass doubling, Chlamydomonas cells can grow more than eight-fold during daytime before undergoing rapid cycles of DNA replication, mitosis and cell division at night, which produce up to 16 daughter cells. We propose that this unusual strategy of growth and division (which is clearly advantageous for a photosynthetic organism) can be governed by a size-dependent bistable switch that turns on and off a limit cycle oscillator that drives cells through rapid cycles of DNA synthesis and mitosis. We show that this simple ‘sizer-oscillator’ arrangement reproduces the experimentally observed features of multiple-fission cycles and the response of Chlamydomonas cells to different light-dark regimes. Our model makes unexpected predictions about the size-dependence of the time of onset of cell-cycle oscillations after cells are transferred from light to dark conditions, and these predictions are confirmed by single-cell experiments.

Collaborators: Stefan Heldt and Bela Novak (Oxford Univ) on the modeling; Fred Cross (Rockefeller Univ) on the experiments.

In meiosis, DNA is copied from parents to offspring, so that individuals who share common ancestors may have identical DNA copies from those ancestors through repeated meiosis. This identical-by-descent (IBD) DNA underlies the similarities between relatives, at both the family level and at the population level. However, the process of meiosis is quite variable, and DNA is inherited generation-to-generation in large segments. The patterns of IBD genome among relatives are complex, and in remote relatives segments of IBD DNA are rare but not short. Modern genetic data on millions of markers across the genome allows estimation of shared DNA, but accurate estimation requires modelling the processes that give rise to these complex IBD patterns. IBD must be estimated jointly among individuals and across the genome. Pedigree information, if available, provides prior probabilities of IBD patterns. Where inferred IBD is discordant with pedigree information, there is potential to detect selection or other processes distorting the outcomes of the meiotic process.

Speaker Biography: Elizabeth Thompson received her B.A. and Ph.D. in mathematics from Cambridge University, UK. After postdoctoral work in genetics at Stanford University, she joined the mathematics faculty of the University of Cambridge in 1976. She was a Professor of Statistics at the University of Washington from 1985 until her (semi-) retirement in 2018. Her research is in the development of methods for model-based likelihood inference from genetic data on both humans and other species, including inference of relationships among individuals and among populations. Dr. Thompson has received an Sc.D degree from the University of Cambridge, the Jerome Sacks award for cross-disciplinary statistical research, the Weldon Prize for contributions to Biometric Science, and a Guggenheim fellowship. She is an honorary fellow of Newnham College, Cambridge, and an elected member of the International Statistical Institute, the American Academy of Arts and Sciences, and the US National Academy of Sciences.

For the past 40 years the demise of the dinosaurs has been attributed to an asteroid impact on Yucatan, a theory that is imaginative, popular and even sexy. From the very beginning, scientists who doubted this theory were threatened into silence or their careers destroyed by the main theory proponents. Thus began the Dinosaur wars in 1980 – and still continuing. As in any war, there are two sides to the Dinosaur wars. The majority believes an asteroid hit Yucatan and instantaneously wiped out 75% of all life including the dinosaurs in a global firestorm and nuclear type winter. A small minority tested this theory and found contrary evidence that supported Deccan volcanism in India that caused rapid climate warming due to greenhouse gases (CO2), environmental stress, acid rain and ocean acidification culminating in the mass extinctions. This lecture highlights the four decades of the dinosaur wars, the increasing acceptance of volcanism’s catastrophic effects and likely cause of the mass extinction and the resulting ad hoc revisions to accommodate the impact theory. The talk ends with the ongoing 6th mass extinction initiated by rapid fuel burning that is causing the most rapid climate warming in Earth’s history and ocean acidification, which is predicted to reach the 6th mass extinction in as little as 50-75 years and maximum of 250 years. We could be the Dinosaurs of the 6th mass extinction.

Speaker Biography

Gerta Keller is Professor of Paleontology and Geology in the Geosciences Department of Princeton University since 1984. She was born on March 7, 1945 in Liechtenstein. She grew up on a small farm in Switzerland as the sixth of a dozen children with no prospect for education. At age 14 she entered apprenticeship as dressmaker, at 17 she worked for the DIOR Fashion House in Zurich. With no prospect for advancement she began her adventure travels through North Africa and the Middle East, supporting herself by waitressing. She immigrated to Australia at 21, was shot by a bank robber and nearly died at 22. After recovery, she resumed her adventure travels through Southeast Asia and arrived in San Francisco in 1968. There she found the first opportunity for education and entered City College, continued her undergraduate studies at San Francisco State College majoring in Anthropology and Geology, concentrating on climate and environmental changes and their effects on mass extinctions. She was awarded a Danforth Fellowship for her graduate studies at Stanford University in 1974 and received her PhD in 1978. She continued her work at Stanford University and the U.S. Geological Survey in Menlo Park and steadily researched climatic and environmental effects on life all the way back to the dinosaur mass extinction 66 million years ago. In 1984 she was hired as tenured faculty at Princeton University.

Prof. Gerta Keller’s major research and discoveries ranged from climate change and its effects on ocean circulation, ocean anoxic events, polar warming, Deccan volcanism, comet showers, extraterrestrial impacts, the dinosaur mass extinction, the age of the Chicxulub impact and the 6th mass extinction. Her research frequently challenged accepted scientific dogma and placed her at the center of acrimonious debates fighting for survival of truth-based evidence. All but the cause of the Chicxulub impact were soon accepted by scientists and integrated into new research. After four decades, impact proponents still fiercely defend the impact theory, deny contrary evidence and at best incorporate volcanism as ad hoc revisions, proclaiming the impact triggered volcanism that caused the mass extinction.

Gerta Keller has over 260 scientific publications in international journals and is a leading authority on catastrophes and mass extinctions, and the biotic and environmental effects of impacts and volcanism. She has co-authored and edited several books and she has been featured in many films and documentaries by very popular TV channels and Film Corporations, including BBC, The History Channel, and Hollywood.

The subject of mathematical ecology is one of the oldest and most exciting
in mathematical biology, and has helped in the management of natural
systems and infectious diseases. Though many problems remain in those
areas, we face new challenges today in finding ways to cooperate in
managing our Global Commons. From behavioral and evolutionary
perspectives, our societies display conflict of purpose or fitness across
levels, leading to game-theoretic problems in understanding how
cooperation emerges in Nature, and how it might be realized in dealing with
problems of the Global Commons. This lecture will attempt to weave these
topics together, tracing the evolution from earlier work to challenges for the
future.

Simon Levin is the J.S. McDonnell distinguished university professor in Ecology and Evolutionary Biology at Princeton University. He is a recipient of the National Medal of Science, the Kyoto Prize and a Robert H. MacArthur Award.

How social traits evolve remains an open question in evolutionary biology. Two traits of particular interest are altruism (where an individual incurs a cost to help others) and spite (where an individual incurs a cost to harm others). Both traits should be evolutionarily disadvantageous because any benefits arising from these behaviours are also available to “cheaters” who do not pay the cost of displaying altruism or spite themselves. In this talk I will show how stochasticity can sometimes reverse the direction of evolution and drive the emergence of these behaviours. I will start with an individual-based evolutionary model and then approximate it using a system of stochastic differential equations (SDEs). These SDEs are then be reduced to a single SDE on a “slow manifold” governing the evolutionary dynamics. A rather complete analysis of this SDE is then possible, showing exactly when and how stochasticity can drive the evolution of altruism and spite.

Biography:

Tryo Day is a Professor and former CRC in the Department of Mathematics and Statistics at Queen’s University. His research interests involve evolutionary theory, including the evolution of pathogen virulence, drug resistance, social traits, and epigenetic inheritance.

Dr. Day is coauthor (with James Stewart) of the textbooks “Biocalculus: Calculus, Probability and Statistics for the Life Sciences”, and (with Sarah P. Otto) “A Biologist’s Guide to Mathematical Modeling”. He is an Elected Fellow of the Royal Society of Canada and the AAAS, and is the recipient of a Killam Research Fellowship, a Steacie Fellowship, the CAIMS Research Prize, and the Steacie Prize.