Mathématiques en biologie et médecine
Mardi, 18 juin
Salle Du Manège
Mathematical Modelling of Glioma Growth
Hillen, Thomas
University of Alberta

Glioma are the most aggressive malignant brain tumors. The spread of glioma inside brain tissue is strongly dependent on the white matter tracks and the overall brain geometry. Diffusion Tensor Imaging (DTI) is a rather new method to use MRI measurements to visualize directionalities in the brain and to identify white matter tracks. In my talk I will discuss models that allow to include DTI measurements into equations of reaction-diffusion type. I will show how these might be used for brain tumor growth predictions. Initial results are promising, but it is still a long way to go ….

This is a joint work with K.J. Painter, Heriot-Watt University, Edinburgh.

Ubiquitination feedback during matrix protein import into peroxisomes
Rutenberg, Andrew D.
Dalhousie University
Peroxisomes are membrane-bound organelles in eukaryotic cells that post-translationally import folded proteins into their matrix. Import uses a receptor, usually Pex5, that cycles between the cytosol and the peroxisome membrane through a process of docking, ubiquitination, and export while guiding matrix proteins through the import process. Translocation of the protein across the membrane is not well understood and so we consider both uncoupled translocation and directly coupled translocation, as well as a third model we propose, cooperatively coupled translocation. We develop a stochastic computational model of the Pex5 cycle for all three types of translocation and measure the Pex5 and ubiquitin levels on the peroxisomes. Uncoupled and directly coupled translocation behave identically with respect to Pex5 and ubiquitin, with the ubiquitin signal increasing as the matrix protein traffic increases. Cooperatively coupled translocation behaves differently, and yields a ubiquitin signal that decreases with increasing matrix protein traffic, in contrast to the other translocation types. Recent work has shown that ubiquitin on mammalian peroxisome membranes can induce degradation by autophagy. Therefore, the high ubiquitin level for low protein traffic with cooperatively coupled protein translocation could constitute a disuse signal that mediates degradation. This mechanism may be one way that a cell could indirectly regulate peroxisome numbers.
Transport through the Nuclear Pore Complex: simple physics of a complex biomachine
Zilman, Anton
University of Toronto

Nuclear Pore Complex (NPC) is a biological “nano-machine” that controls the macromolecular transport between the cell nucleus and the cytoplasm. It is a remarkable device that combines selectivity with robustness and speed. Unlike many other biological nano-channels, it functions without direct input of metabolic energy and without transitions of the gate from a ‘closed’ to an ‘open’ state during transport. The key aspect of transport is the interaction of the transported molecules with the meshwork of unfolded, natively unstructured proteins that cover the lumen of the Nuclear Pore Complex. Recently, the Nuclear Pore Complex inspired creation of artificial selective nano-channels that mimic its structure and function for nano-technology applications.

Despite recent advances, mechanistic understanding of transport through the Nuclear Pore Complex, and in particular its selectivity, is still lacking. I will present a theoretical framework that explains the mechanism of selectivity of transport through the Nuclear Pore Complex and related artificial nano-channels. The theory provides a general physical mechanism for selectivity based on the differences in the interaction strength of the transported molecules with the unfolded proteins within the NPC. In particular, the theory explains how such channels can remain selective in the presence of vast amounts of non-specific noise. The theoretical predictions have been verified in experiments with bio-mimetic molecular nano-channels. Finally, I will discuss how the general theory can be tied to the underlying conformational dynamics of the unfolded proteins within the NPC.

Quadratic ODE and PDE Models of Drug Release Kinetics from Biodegradable Polymers
Delfour, Michel (1) and André Garon (2)
(1) Université de Montréal, (2) École Polytechnique de Montréal

In order to achieve prescribed drug release kinetics over long therapeutic periods, bi-phasic and possibly multi-phasic releases from blends of biodegradable polymers are currently envisioned. The modelling of drug release in the presence of degradation of the polymer matrix and surface erosion is quite complex. Yet, simple reliable mathematical models validated against experimental data are now available to help in classifying neat polymers and in predicting the release dynamics from polymer blends. In this paper, we survey a two-parameter quadratic ODE model that has been validated against experimental data for the release of paclitaxel from a broad range of biodegradable polymers and a quadratic semi-permeable membrane PDE model that mimics the ODE model and could readily be extended to drug eluding stents.


Blanchet, G., Delfour, M.C., Garon, A., Quadratic models to fit experimental data of Paclitaxel release kinetics from biodegradable polymers. SIAM J. on Applied Mathematics (Special Issue on Mathematical Modeling of Controlled Drug Delivery) 71(6), 2269–2286 (2011)

Delfour, M.C.,Drug release kinetics from biodegradable polymers via partial differential equations models. Acta Appl. Math. 118, 161–183 (2012)

Lao, L.L., Venkatraman, S.S.,Adjustable paclitaxel release kinetics and its efficacy to inhibit smooth muscle cells proliferation. J. Control. Release 130, 9–14 (2008)

Lao, L.L., Venkatraman, S.S.,Paclitaxel release from single and double layered poly (DL-lactide-co-glycolide)/poly (L-lactide) film for biodegradable coronary stent application. J. Biomed. Mater. Res. A 87A(1), 1–7 (2008)

Lao, L.L., Venkatraman, S.S., Peppas, N.A., Modeling of drug release from biodegradable polymer blends. Eur. J. Pharm. Biopharm. 70, 796–803 (2008)

Lao, L.L., Venkatraman, S.S., Peppas, N.A.,A novel model and experimental analysis of hydrophilic and hydrophobic agent release from biodegradable polymers. J. Biomed. Mater. Res. A 90(4), 1054–1065 (2009)