Title: Understanding the role of linker histone in DNA packaging with mathematical modelling

Transcription

1 Gustavo Carrero Araujo, Athabasca University Title: Understanding the role of linker histone in DNA packaging with mathematical modelling Abstract: When we think of the approximate average length of DNA (2 meters) in a human cell and the fact that this DNA is contained in a cell nucleus of approximately 6 micrometers (μm) of diameter, we might not only be amazed by this fact of nature but we might also ask ourselves "how is this possible?". The evolving answer that started with the discovery of histone proteins in the late nineteenth century can be summarized by saying that DNA is packed with the help of proteins called histones. Since then, trying to understand the complete dynamics of this process has been a scientific interest in cell biology. This talk will aim at describing how mathematical modelling of the spatio-temporal dynamics of linker histone or histone H1 (a class of histone proteins) together with fluorescence microscopy experiments can be used to further our understanding of the dynamical aspects of DNA packaging. Elena Braverman, University of Calgary Title: The influence of dispersal strategies on survival in a competition Authors: Elena Braverman, L. Korobenko, Md. Kamrujjaman Abstract: Two competing populations in spatially heterogeneous but temporarily constant environment are investigated: one is subject to regular movements to lower density areas (random diffusion) while the dispersal of the other is in the direction of the highest per capita available resources (carrying capacity driven diffusion). The growth of both species is subject to the same general growth law which involves Gilpin-Ayala, Gompertz and some other equations as particular cases. The growth rate, carrying capacity and dispersal rate are the same for both population types, the only difference is the dispersal strategy. The main result of the paper is that the two species cannot coexist (unless the environment is spatially homogeneous), and the carrying capacity driven diffusion strategy is evolutionarily stable in the sense that the species adopting this strategy cannot be invaded by randomly diffusing population. Moreover, once the invasive species inhabits some open nonempty domain, it would spread over any available area bringing the native species diffusing randomly to extinction. One of important technical results used in the proofs can be interpreted in the form that the limit solution of the equation with a regular diffusion leads to lower total population fitness than the ideal free distribution.

2 Qihua Huang, University of Alberta Title: Homing Fidelity and the Reproductive Rate for Migratory Populations Abstract: Adding spatial structure to a matrix model, we investigated the dependence of the overall population persistence on the strength of connectivity among subpopulations. As an example, we focused on population persistence of migratory salmonids, and examined the effect of migration on persistence. We are interested in both long-term and short-term reproductive rate. The long-term reproductive rate is measured by a classical persistence parameter, net reproductive rate, R 0. By way of contrast, we also introduced two new measures of transient reproductive rate, R l and R u, which predict the lowest and highest single generation population growth rates, respectively, based on the distribution of individuals amongst source and sink patches. The spatially structured population theory developed here shows that homing fidelity may decrease the reproductive rate in the short run while increasing it in the long run. The theory introduces new methods for the management and conservation of migratory species for shortand long-term growth. Jude Kong, University of Alberta Title: Modeling the Spread of Influenza A (H1N1) Abstract: H1N1 is a swine originated influenza A virus, which is responsible for the 2009 pandemic flu that killed more than people. It remains a seasonal flu in North America with annual increase in the number of victims. There is much fear that another outbreak might occur in the future as predicted by many authors after the 2009 pandemic. We constructed a delayed SIR model for influenza A. Using data from laboratory confirmed cases, we estimated the basic reproduction number and the infectious period for the 2009 epidemic in Mexico. Our result matches what happened in 2009, thus our model could be used to predict the spread of the disease and future outbreaks, and to determine the infectious period and the basic reproduction number. We carry out stability and sensitivity analysis. Our findings from the stability analysis reveal a parameter space in which we might have forward or backward Hopf bifurcation when we alter the latent period. It also indicates the range of values for the latent period, within which the flu may be controlled. Out of this range, oscillatory behaviors occur, and it can be difficult to make definite predictions regarding the size of the outbreak. We discover that, to control the intensity of any future outbreak, it is better to focus on the contact rate.

3 Jonathan Potts, University of Alberta Title: Generalizing residual analysis for complex, stochastic animal movement models Authors: Jonathan Potts, Marie Auger-Méthé, Mark Lewis Abstract: The movements and interactions of individual animals in an ecological system form an immensely complex evolving structure. Predicting the time-evolution of such a system requires a model that mimics it with sufficient accuracy, while accounting for its inherent stochasticity. Though many tools exist to determine which of a set of candidate models is best relative to the others, there is currently no generic goodness-of-fit framework for testing the absolute fit of the best model to the data. We propose such a framework that is specifically designed to cope with complex systems of moving and interacting animals using a novel application of the Earth mover's distance. It generalizes the concept of a residual, often used to analyze 1D summary statistics, to situations where the complexity of the underlying model's probability distribution makes standard residual analysis too imprecise for practical use. We give a scheme for testing the hypothesis that a model is an accurate description of a data set. We detail methods for visualizing results and extracting a variety of information on a given model's quality, such as whether there is any inherent bias in the model, or in which situations it is most accurate. We apply our technique to example models of animal movement in complex, heterogeneous environments. Amanda Swan, University of Alberta Title: Modelling brain tumor spread using an anisotropic PDE model Abstract: Current treatment of glioblastoma brain tumors offers lots of room for improvement, with the current expected survival being about a year with treatment. A model which describes the distribution of cancer cells within the brain tissue would offer potential for improved treatment regions, and subsequently improved survival and quality of life. I will present a model which makes use of brain architecture to predict the patterns of invasion. This is done by assuming that the cancer cells migrate preferentially along the white matter tracts of the brain, and adjusting the diffusion coefficient both spatially and directionally. We refer to this as anisotropic diffusion. We make use of Diffusion Tensor Imaging (DTI) to measure the diffusion tensors at each location within the brain and show simulations using real patient data.

4 Silogini Thanarajah, University of Alberta Title: Phage-bacteria petri dish model in different types of media nutrient-limited growth, movement and predation Abstract: To study the role of bacteriophage in controlling the bacterial population, we consider the spread and interaction of bacteria and phage in a petri dish and construct a group of bacteriabacteriophage petri dish models. We present rigorous mathematical results such as steady states, traveling-wave solutions, and asymptotic behavior of solutions. We also obtain insightful numerical results such as population dynamics, effect of burst size, extinction time of bacteria, and threshold value of burst size for bacterial extinction. Our results can potentially provide some guidance for future phage therapy. Hao Wang, University of Alberta Title: The Criterion for Stability and Bifurcation Analysis of DDEs with Two Discrete Delays Abstract: In the talk, I will first present general criteria for determining stability of equilibria in DDEs via Hopf bifurcation and crossing direction, and then present our novel stability criterion for models with two discrete delays using an algebraic method. I will provide some properties of stability switching curves and switching directions. Chuang Xu, University of Alberta Title: A Paradox on Strong Allee Effect Abstract: We propose a stochastic Logistic model with mate limitation and stochastic immigration. Incorporating stochastic immigration into a continuous time Markov chain model, we derive and analyze the associated master equation and prove that a unique globally stable positive stationary distribution with a bimodal profile exists, which implies that strong Allee effect exists in the stochastic model. Such strong Allee effect disappears and threshold phenomenon emerges as the total population size goes to infinity. Stochasticity vanishes and the model becomes deterministic as the total population size goes to infinity. This implies that there is only one possible fate (either to die out or survive) for a species constrained to a specific community and whether population eventually goes extinct or persists does not depend on initial population density but on a critical inherent parameter determined by birth, death and mate limitation. Such a conclusion interprets differently from the classical ordinary differential equation model and thus a paradox on strong Allee effect occurs.

5 Cole Zmurchok, University of Alberta Title: Direction-dependent communication mechanisms enrich pattern formation in an individual-based model of animal movement Abstract: In this presentation, direction-dependent communication mechanisms will be incorporated into a one-dimensional individual-based model of collective behaviour. Previously, direction-dependent communication mechanisms were incorporated into a non-local hyperbolic PDE model for collective behaviour, recreating numerous spatial patterns observed in nature. Like the PDE model, the IBM is formulated in terms of the three social interaction forces: repulsion, alignment, and attraction, and includes information regarding conspecifics' direction of travel. The IBM produces a variety of complex spatial patterns such as stationary groups, traveling groups, zigzagging aggregations, feathers, and ripple-like patterns, matching the rich behaviour of the PDE model. This not only demonstrates that the complex spatial patterns formed are not unique to the PDE model, but also suggests the importance of directiondependent communication in collective behaviour.