Mathematics of Information Technology and Complex Systems

Project Highlights
Team Members
Partner Organizations


last updated: Nov 1, 2007


Our team has studied two distinct types of diabetic diseases, with a primary focus on the type 1 autoimmune form. In type 1 diabetes (T1D), immune cells such as CD8+ T-cells target and kill the insulin-secreting pancreatic beta cells. Diabetes results when most of the beta cells have been killed. We have studied several aspects of this disease.

For several years, we investigated the way that dead beta cells are cleared by non- specific scavenger immune cells (macrophages), and quantified the defects in this clearance rate that occur in diabetes-prone Non-Obese Diabetic (NOD) mice (Maree et al, 2005). We then showed (Maree et al 2006) that these defects alone can already account for chronic inflammation in the pancreas that could set the stage for autoimmune diabetes. This year, we revisited this research and improved our quantification of macrophage phagocytosis (in normal and diabetic mice) using redesigned experiments carried out in Finegood's SFU lab (Maree, Komba, Finegood, Keshet, 2007).

In separate work on Type 1 Diabetes, we have explored therapies for prevention and treatment of autoimmune diseases. In earlier year(s), we concentrated on peptide therapy (similar to vaccination), and showed why this therapy is problematic (Maree, Santamaria and Edelstein-Keshet, 2006). In a related work, Mahaffy and Keshet (2006) modeled the cyclic fluctuations observed in levels of T cells circulating in the blood. We showed that these oscillations could result from feedback: killing of beta cells generates peptide that has a differential effect on production of memory vs effector T cells, which in turn, affect the further rate of killing of beta cells. During the last year, Khadra and Keshet have been investigating new hypotheses for competition between low and high avidity T-cells and therapies based on other strategies for manipulating that competition.

In the past year, we have developed a new project that links our expertise in Type 2 diabetes and in amyloid dynamics. Our MSc student Bailey was awarded an internship at the Children's Hospital in Vancouver, in the group of collaborator B. Verchere. (His internship earned an award of excellence, see Awards.) Bailey carried out in vitro experiments on the polymerization and fibrilization of Islet Amyloid Poly-Peptide (IAPP). He used modeling and data fitting to uncover the steps involved in the kinetics of formation of the (toxic) oligomers that occur in the pancreas of Type 2 diabetes patients. The significance is that understanding these kinetics can lead to strategies for treating this symptom.

Alzheimer's Disease:

AD is one of a family of neurodegenerative diseases that are characterized by the aggregation of a pathogenic or misfolded peptide into insoluble aggregates. Its characteristic feature plaques and tangles were described by Alois Alzheimer nearly a century ago. Today some half-million Canadians over 65 have Alzheimer's disease (AD) and related dementias, and 100,000 new cases are diagnosed every year. This burgeoning epidemic is expected to be one of the major health care challenges in the coming years. A better understanding of AD pathogenesis should also lead to insight about other diseases involving aggregated proteins, including Type 2 diabetes.

The leading hypothesis in the field of AD research, dubbed the amyloid cascade hypothesis, assigns the primary pathogenesis of AD to a 42-amino acid protein Amyloid beta (A-beta). Excessive accumulation of A-beta and its resultant aggregation into senile plaques is widely believed to be the precursor to neuronal death and cognitive impairment. A-beta is produced from the amyloid precursor protein (APP) through two sequential cleavages catalyzed by the enzymes beta-secretase and gamma-secretase, respectively. Potential therapeutical strategies to combat AD target various stages of A- beta production and aggregation. Our team members (Das, Coombs, Keshet, Bailey) have been working with Merck scientists (Salzman, Nachbar, Bagchi) to understand a potential drug that inhibits gamma-secretase. We have applied mathematical modeling to determine what could account for the observed time course of the amyloid level measured in blood after this drug is administered. A paper on our results is being submitted for publication.

We have maintained some level of expertise and work on Alzheimer's Disease ever since our first year of operation as a team. See our interactive Alzheimer's In Silico simulation.

Blood Diseases:

Periodic hematological diseases include cyclical neutropenia (CN), periodic leukemia (PL), and cyclical thrombocytopenia (CT). These diseases offer a glimpse into the regulation of the hematopoietic system (i.e. system that produces blood cells). Michael Mackey and McGill University team members are working on a physiologically accurate mathematical model of this control system in humans, to develop eventual strategies for treating hematological diseases. The Mackey group research has confirmed that cyclical neutropenia is due to elevated levels of apoptosis (programmed cell death). Further, it points to the possibility that periodic leukemia is due to decreased levels of apoptosis in the peripheral neutrophil line but an elevation of the rate of apoptosis in the stem cells. Similar insights into the origins of PL and CT have been derived from their extensive mathematical modeling project, and have again highlighted the importance of apoptosis as a control mechanism in normal hematopoiesis. This is currently being extended to a study of aplastic anemia (AA) in conjunction with the University Hospital of Basel who have over 40 years of experience with this interesting stem cell disorder.

To try to understand the molecular control of apoptosis, Mackey's team studies the operation of gene regulatory circuits (operons), which are only partially understood qualitatively and incompletely explored mathematically. Research on the regulation of the lactose and tryptophan operons, as well as the lysis-lysogeny switch in phage lambda, will help this group to develop the necessary expertise to deal with the molecular aspects of apoptosis regulation. Mackey's work on apoptosis regulation will link well with aspects of the T1D diabetes projects centering on beta-cell apoptosis.

Basic Immunology and Infectious Disease Modelling:

A central theme in the adaptive immune system is the signaling between antigen-presenting-cells (APCs) and T cells. Coombs and Dushek are working in close collaboration with the laboratory of Valitutti (Toulouse, France) to elucidate molecular mechanisms of T cell stimulation by carefully screened APCs. A major part of this project involves interpreting fluorescence recovery after photo-bleaching (FRAP) data. This experimental technique involves fluorescently labeling a protein of interest on the T cell surface. The labels are then removed from a small area on the cell surface. Protein motion allows fluorescence to return to this area. Mathematical analysis of the rate of recovery of fluorescence is then performed, yielding the diffusion coefficient of the labeled protein. Two papers on this topic have been completed (Dushek & Coombs, 2007, and Dushek, Das & Coombs, submitted 2007). In a related project, Coombs, Das (PDF), Cortes and Simpson (BSc students) have begun work on modeling single-particle tracking data, where a single protein is labeled and followed. The goal is to understand protein mobility on a cell surface.

The threat of emergent diseases and pandemics has made infectious diseases caused by viruses of great current interest. Investigator Coombs and trainees have been studying the selective pressures on viruses at multiple scales: viruses compete for cell resources within a single infected cell, for cells to infect within a host, and for hosts to infect within a population. To understand how viral behaviour at the level of an individual virus translates to population-scale dynamics of virus evolution (that can have public-health consequences), we need to nest mathematical models drawn from each level of selection. At UBC, investigator Coombs, (former MSc student) Ball, and (BSc student) Mehta have combined mathematical models for chronic viral infections (such as human immunodeficiency virus and hepatitis C virus) within a single host with simple epidemic models, to understand how selective pressure may act on such viruses.

Stem Cell Cultures:

Stem cells have the potential to develop into heart muscle cells, bone cells, nerve cells, skin cells, blood cells. They could be used, therefore, to repair or replace damaged tissues in Parkinson's disease, stroke, cardiac diseases, diabetes, etc. One of our investigators, Piret, and his trainees (former PhD student Glover, PDF Chaudhry) have been studing the influence of the culture environment on stem cell gene expression.

Optimizing the culture conditions for embryonic stem cells is ongoing, combining knowledge of the cells' response to process variables in conjunction with the gene expression. The ultimate goal is to develop robust culture techniques for large-scale expansion. Knowledge of the molecular determinants of stem-cell fate (self-renewal, differentiation or apoptosis) as well as a greater understanding of the influence of culture variables will significantly aid in the development of these protocols.

Dynamics of Reproductive Hormone Secretion:

Hormonal regulation of mammalian reproduction occurs at three different levels. The gonadotropin-releasing hormone (GnRH), secreted by GnRH neurons in the hypothalamus, is at the highest level of this hierarchical control. GnRH plays an essential role in reproductive maturation, and in regulating hormonal changes in menstrual and estrous cycles. GnRH is carried by local blood circulation to the pituitary, where it triggers the release of two intermediate hormones, the luteinizing hormone (LH) and the follicle- stimulating hormone (FSH), from gland cells called the gonadotrophs. It has been found that the temporal profile of the GnRH signal must be pulsatile to be effective (i.e., sharp pulses separated by intervals of near-zero baseline levels), with a species-specific frequency (e.g., 1 pulse per hour in primates).

Although the underlying mechanism remains obscure, it is well-known that GnRH neurons exhibit intrinsic pulsatile secretion of GnRH. Further, as the GnRH neurons have receptors for GnRH, it was suggested that autocrine regulation of the neurons by the hormone was responsible for the pulsatility. In recent work, it was proposed that high levels of GnRH inhibit GnRH secretion though a G-protein coupled process. Based on such new evidence, investigator Li and (PDF) Khadra have been assembling and studying models for mechanisms of the pulsatile signal. These models provide some predictions and crucial answers to some of the experimental observations made in vivo and in vitro. In this work, it has been shown recently that synchrony between different neurons through sharing a common pool of GnRH is extremely robust. In a diversely heterogeneous population of neurons, the pulsatile rhythm is often maintained when only a small fraction of the neurons are active oscillators. These active oscillators are capable of recruiting nonoscillatory neurons into a group of recruited oscillators while forcing the non-recruitable neurons to oscillate passively. In addition, this work predicts that the same mechanism revealed by experiments in vitro could also operate in vivo. This is done by elucidating some of the apparent inconsistencies obtained in vivo when different doses of GnRH are injected into the population at different frequencies. In other words, our models provide a plausible explanation of the controversial effects of the negative and positive feedback loops of GnRH on its own release observed in vivo. This work is of clinical and fundamental value for understanding the normal reproductive system as well as certain pathologies.

Cellular and Molecular Biology:

Several team members have been working on problems at the level of the cell. Investigator Cytrynbaum studies dynamics of the eukaryotic cytoskeleton, including microtubules, actin and a host of regulatory proteins and molecular motors. Cytrynbaum explores bacterial cell division and models for the unique bacterial cytoskeletal polymers.

Our previous work on modelling the biochemistry of signalling proteins in cell polarity gave rise to an interesting phenomenon we termed "wave-pinning", where a travelling wave solution is initiated, slows down and eventually stalls forming a stable stationary front. To understand the mechanism behind wave-pinning we (Mori, Jilkine, Keshet) are considering a simplified model of two components that has the same behaviour and can be analyzed analytically. We determined the necessary conditions under which a reaction diffusion system will undergo wave-pinning and in one spatial dimension and used the method of matched asymptotic expansions to predict the location of the pinned wave based on model parameters and initial conditions. We are currently working on extending the model to higher dimensions.