Abstract: This talk will discuss the use of mathematical models to analyze how cells behave based on the activation of intracellular signalling pathways. Specifically, the mitogen activated protein (MAP) kinase pathway is one of the best understood cellular signal transduction pathways and functions in promoting cell survival, growth and division. The first part of the talk will detail a kinetic analysis of this pathway that could predict the behavior of embryonic stem cell derived neural progenitor cells in response to treatment with the growth factor neurotrophin-3. The second part of the talk will focus on reprogramming cancer cells to chose cell death instead of proliferation through the use of chimeric proteins that manipulate the MAP kinase pathway.

Pathogen transmission between domesticated animals and wildlife presents a challenge for both wildlife conservation and farming.  Mathematical models of transmission dynamics can be used to better understand the sources of pathogens and optimize treatments of domestic animals to reduce the spill-over and spill-back of pathogens between domesticated and wild populations of animals.

In Pacific Canada, the expansion of open-net salmon farming has brought concern about pathogen transmission between farm and wild salmon. In particular, the spill-over of parasitic sea lice from farm salmon to out-migrating juvenile wild salmon has been implicated in declines of wild salmon populations in regions of salmon farming.  Over the past decade, political and scientific controversy has brought attention to the issue and spurred better management of parasites on farm salmon. We present a mechanistic model of sea louse transmission dynamics between farm and wild salmon that considers parasiticide treatments on salmon farms. The model was fit to data (with some challenges!) and used to evaluate farm management scenarios that reduce sea lice on wild juvenile salmon.  The model predicts that locating farms distal to salmon rivers greatly reduces infections of wild juvenile salmon. Treating farm salmon with parasiticides before outbreaks occur also reduces louse transmission, although frequent treatments may accelerate the evolution of parasiticide resistance in sea lice. These results may help inform management of salmon farms in regions with sympatric wild fish populations.

One of the difficulties in studying the intitiation and spacing of organs is finding tractable eukaryotic systems. We investigated phenotypic variation of physiological and morphological traits in cloned embryos of Larix x marschlinsii (hybrid larch)and Pseudotsuga menziesii (Douglas-fir). Embryos are multiplied in vitro and then matured in a stepwise controlled manner. By raising the embryos in different expermimental conditions their physiology, biochemistry and morphology can be altered. Since genotypic variation has been eliminated in such cloned systems, the variation we see is almost entirely phenotypic. We focused on the initiation and differentiation of cotyledons, which are the first lateral organs in the plant embryo. These appear simultaneously as a whorl of organs. We established treatments that reliably varied the number of lateral organs per whorl. By focusing on phenotype, we can use these studies to test physico-chemical models for the spatial patterning underlying morphogenesis. Our data indicate that cotyledon spacing is controlled by a wave-forming mechanism. We discuss the experimental results in terms of our ongoing mathematical and computational work on reaction-diffusion dynamics in growing systems.

Abstract: Local field potentials recorded from groups of neurons often
display prominent oscillations in various frequency ranges. The amplitude of
oscillations in the gamma band (30-80 Hz) is modulated by perception and
cognition and is the object of many modeling and experimental studies. Here
we present and analyze a simple stochastic model of the interactions of
populations of excitatory and inhibitory neurons, which may explain gamma
oscillations. We show how the irregularly changing amplitude of such
oscillations, called "gamma bursts" may arise from the intrinsic dynamics of
the model. This is joint work with Mark McDonnell of Dept of Communications
Engineering, UniSA, Adelaide, and Lawrence Ward of Dept of Psychology, UBC,
Vancouver.