Mathematics of Information Technology and Complex Systems

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Biomedical Models of Cellular and Physiological Systems and Disease

last updated: Nov 1, 2007

Project Leader: Leah Keshet (Professor), Mathematics, UBC
Phone Number:604-822-5889
Fax Number: 604-822-6074
E-mail Address:
Web Page:

Project Description

Over the past years, our team has been working on deciphering the causes, and investigating interventions for diseases such as Alzheimer's Disease, Diabetes, and blood disorders such as leukemia, in addition to our effort in modelling and understanding the mechanisms of certain hormonal rhythms such as GnRH secretion. Our research spans molecular, cell, tissue, and population levels. It is characterized by application of mathematical and physical (quantitative) methods to biological and biomedical areas. Most of our projects are driven by experimental data generated by collaborators of this team. Some projects involve gaining a better understanding of basic scientific problems at the foundation of cell and molecular biology.

In partnership with MERCK, we (Keshet, Coombs, Das, Bailey) have been analysing the dynamics of a potential inhibitor of amyloid-beta for treatment of Alzheimer's Disease. This year, we prepared our results for publication, joint with Merck scientists. In previous years, we designed a simulation model that incorporated some of the cellular and molecular components of this disease. See online simulation of neuroinflammation and senile plaque formation.

We have continued modelling type 1 diabetes (T1D), a disease in which the insulin-producing beta cells are targeted and killed by the body's own defense system. We (Khadra, Keshet) have investigated several aspects of T1D, including (a) the role of macrophages (scavanger cells that clear dead cells) and defects in their function, (b) the proliferation of T cell clones that kill the insulin-producing beta cells, and (c) processing of self-antigen and its presentation by antigen presenting cells. In a previous year, with J. Mahaffy, we were able to use mathematical analysis to understand why cycles of T-cell levels are seen in circulation before the onset of diabetes in experimental animals (non-obese diabetic mice). This year, we have analyzed new potential therapies studied experimentally by our collaborator Pere Santamaria (U Calgary). In Type 2 diabetes, MSc student James Bailey completed an award-winning internship (see Awards) at the Children's Hospital in Vancouver, with Dr. B. Verchere. Bailey investigated the formation of fibers of a kind of toxic protein, Islet Amyloid Poly-Peptide (IAPP) that occurs in the pancreas of Type 2 diabetes patients. His combined laboratory experiments and modelling led to better understanding of the growth of these fibers, with a view to possible treatments.

We are also developing other immunology projects. We (Coombs, Das, Dushek, Bailey) perform research into basic immunological questions concerning T cell activation by antigen-presenting-cells. We are particularly interested in understanding polarization of T cell receptors towards stimuli of varying strength and specificity. This work finds applications in understanding the action of monoclonal-antibody like drugs, as well as in the disease mechanisms of immune disorders.

Our team carries out two projects related to stem cells. One of the challenges being addressed is how to grow and maintain stem cells in culture. The first project is the development of robust culture techniques for cultivation and expansion of stem cells. A second project related to the hematopoietic system (i.e. the system that produces red blood cells, white blood cells and platelets). Ongoing mathematical modeling by our Montreal branch (Mackey and team members, McGill U.) is aimed at understanding blood disorders such as cyclical neutropenia, periodic leukemia, and cyclical thrombocytopenia so as to suggest novel strategies for treatment. A new facet of this project is the link between the Montreal group and a clinical group in Basel to study and analyze cyclicity in blood cell counts of aplastic anemia patients. Part of this project also relates to how programmed cell death (apoptosis) is regulated by genetic regulatory circuits in the cell.

The team is also interested in modelling and studying the rhythmic secretion of a hormone called GnRH in the hypothalamus (Khadra, Li). This hormone is important in regulating the reproductive system. Although it is known that GnRH neurons can secrete this hormone rhythmically, the underlying mechanism for the pulse generation remains obscure. Experiments revealed that GnRH neurons express receptors allowing GnRH to activate its own release. A biochemical mechanism based on G-proteins, Calcium, and cAMP was proposed recently. We have build mathematical models based on this mechanism to describe a single neuron as well as a population of neurons coupled through a common pool of hormone. These models illustrate the mechanistic process which leads to the synchronization of the rhythmic secretion. We have been also able to elucidate some of the puzzling experimental observations made in vivo and in vitro.

In a more mathematical direction, our team member Mori (PDF, UBC) has been obtaining important results on the immersed boundary method, a widely used numerical method to handle problems in biofluid mechanics. Despite its popularity and the impact it has had on the development of many numerical schemes dealing with internal interfaces, a theoretical understanding was lacking. Mori has given the first proof that the immersed boundary method converges to the true solution in a sufficiently simple setting. We expect this work to be the first step toward a satisfactory theory on the convergence properties of the immersed boundary method and related methods.