Mathematics of Information Technology and Complex Systems


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Research

Type 1 Diabetes:

It is now commonly understood that type 1 diabetes (T1D) is the result of a T cell-dependent autoimmune process that destroys the insulin-producing beta-cells in the pancreatic islets of Langerhans. The specificity of this destruction suggests that autoimmunity is directed at one or more beta-cell specific targets. In addition, several recent findings by members of our group support the contention that beta-cell destruction is the result of direct contact between the target beta-cell and specific effector cytotoxic T lymphocytes (CTL's). These findings include the following: (a) a large fraction of all islet associated CD8+ T-cells in non-obese diabetic (NOD) mice use highly homologous TCR-alpha chains on their T cell-receptors (TCR's); (b) these cells are a significant component of the earliest islet infiltrates (c) their levels in blood are detectable and predictive of subsequent diabetes development (d) they recognize a peptide from an islet specific protein, islet glucose-6-phosphatase catalytic subunit related protein (IGRP). Type 1 diabetes (T1D) results from complex interactions of many organs, cell types, and soluble mediators. To effectively prevent or interrupt the development of T1D we must understand how these systems function in a coordinated manner in vivo. Our team has been working for over two years, combining mathematical and experimental expertise to improve understanding of the dynamic, interacting complex systems involved in the initiation, progression, and cure of T1D.
At the core of T1D pathogenesis is the body's own immune system. The immune system is designed to detect and destroy foreign antigen, but in autoimmune (type 1) diabetes, this defense mechanism becomes destructive. By a complex set of interactions, a battalion of specialized immune system cells called (CD8+) effector T cells is created to target the insulin-producing pancreatic beta-cells. (These T cells recognize a specific feature of the beta-cells called an epitope.) Diabetes results when a large fraction of the beta-cells have been killed. Once this has progressed beyond some level, it is an irreversible condition. Fundamental questions in T1D include: (A) what mechanism leads to the priming of T cells? (If this mechanism could be blocked, it may be possible to envision a cure.) (B) What other effects (cytokines, macrophages) promote autoimmune conditions? (C)Why do some self-proteins become auto-antigens while others do not? (How does the type of protein, its location in the cell, its tendency to get misfolded implicate its role?)

(1) Peptide Therapy: (Maree, Santamaria, Keshet, others) The gradual amplification of increasingly effective killer T cells that bind more avidly to the beta-cell epitope is termed "avidity maturation". Our models have been aimed at understanding (1) what leads to this faulty immune response and avidity maturation, and (2) under what conditions peptide therapy could subdue the deadly T cells. A potential therapy involves injection of artificial peptides that mimic the beta-cell-specific epitope to modulate the observed avidity maturation. (Carried out by Pere Santamaria, U Calgary, using non-obese diabetic (NOD) mice, animals that spontaneously develop diabetes). A carefully selected dose and avidity for the injected peptide leads to magnification of harmless ("low avidity") T cells at the expense of the ("high avidity") killer T cells. Former MITACS PDF, Stan Maree, who continues to be an international team member, has modeled the process, using biologically relevant values of rates and parameters. His model reproduces the experimental data well, and discriminates between several underlying hypotheses, thus providing insight about what causes disease progression and what conflicting effects could result from peptide at the wrong dose or avidity. The model suggests under what conditions APL therapy is promising, and when it can actually be dangerous. The close relationship between experimental and theoretical scientists that characterizes this project would not have been possible without MITACS funding. (This work has been submitted for publication.)

(2) Macrophage clearance: (Maree, Komba, Keshet, Finegood, Dyck) A second model focuses on defective clearance of dead (apoptotic) pancreatic beta-cells as a possible cause of immune system triggering and inflammation leading to T1D. Clearance is usually handled by macrophages, cells that ingest and remove debris to avoid buildup of antigen stimulus. Finegood's group has observed that macrophages derived from diabetes-prone (NOD) mice are poor at clearance. She has also shown in previous work that in early life, there is a naturally occurring wave of programmed cell death of beta cells in experimental animals. The idea of a causative link between the death of beta cells and the buildup of inflammation and autoimmunity is being tested in our models.

By analyzing data for the numbers of macrophages that have ingested 1, 2, .. N apoptotic cells (in vitro), and using a simple mathematical model for this stage-structured population of macrophages, we were able to quantify the rates of engulfment and the rates of digestion of dead cells by the macrophages. We found that macrophages from diabetes resistant animals were able to engulf apoptotic cells significantly faster than those derived from diabetes-prone animals; digestion rates were relatively similar. We were able to quantify the differences that had been observed. Our model and analysis helped to improve the design of the experiment, so that a second round of data collected was much cleaner and more easily interpreted. New MITACS graduate student Mitsu Komba (started in Finegood's lab at SFU, Sept 2003) will be investigating the consequence of defective macrophage engulfment experimentally, while Stan Maree and Leah Keshet continue modeling work.


(3) Inflammed versus normal states: (Kublik, Komba, Maree, Keshet, Finegood, others) New MSc student Richard Kublik is studying the way that inflammation can be amplified by the wave of apoptosis of beta cells. Starting with the "Copenhagen model", he is determining under what conditions this (normally harmless) process can lead to runaway inflammation and overt disease conditions. His work is based on projects initiated by former PDF Labecki, and is being carried out in close consultation with Finegood's lab. Mitsu Komba's work on the role of defective macrophages described above in (2), and its implications on danger signals and dendritic cell response should provide insight the Copenhagen model extension.

(4) The epitope IGRP and T-Cell priming: (Pere Santamaria, Daniel Coombs, L Keshet) Santamaria's group has discovered an important protein found in beta cells which acts as autoantigen in T1D. Called IGRP, this transmembrane protein resides in a cell compartment in which antigen-MHC complexes are constructed (the endoplasmic reticulum). IGRP is highly hydrophobic, frequently misfolded, and thus often degraded into peptides by the proteosome. This could be one reason why it tends to be presented as a stimulus that primes T-cells. Santamaria, Coombs, and Keshet, plan to investigate the trafficking of IGRP from synthesis (by the ribosomes) through processing, and to rates of presentation. Experimental techniques of Pinciotta et al, Immunity 18:343-354, will be used in the Santamaria lab to provide data from which we will identify the key rate constants governing the major steps of antigen production and presentation, from ribosome to cell surface. Quantitative modeling at this level of detail has not previously been undertaken for a protein relevant to actual disease.

(5) Other potential future work: (Pere Santamaria, Maree, others?) Santamaria is interested in understanding how T-cells compete with one another in vivo. He can experiment with an in vivo reductionist 3-clonal population which he has developed, and we could base future detailed models on the observations. Pur previous models could be modified to include other effects, such as antigen sharing. For example, mature dendritic cells (DC's) are not able to make new peptide/MHC complexes, and cannot down-regulate pre-made complexes. They can also share exogenous antigens with other DC's by packaging them in exosomes. It is interesting to investigate how the small amounts of antigen captured by dendritic cells stimulate so many T-cells (in a TCR-transgenic mouse, for example).
Another possible project concerns cyclic wave of tetramer positive cells seen in peripheral blood in the pre-diabetic state (Trudeau et al, Clin Invest 111:217-23, 2003). Where do these cells come from? Do they represent cells that arise from the pancreatic lymph nodes? This is hard to believe given the few tetramer positive cells that are present there. Or do they represent memory T-cells that are hiding elsewhere and are then induced to migrate through the bloodstream in response to hypothetical stimuli? A mathematical analysis of the problem, together with carefully designed experiments might provide us with clues as to how this works.

Type 2 Diabetes:

Brian Topp (GS), Changting Xiao, Diane Finegood
Type 2 diabetes (T2D) is associated with insulin resistance, insulin secretory defects, and possibly insufficient beta-cell mass. However, it is not clear if these defects have a single causal origin or if they occur independently. Under certain circumstances, experimental induction of insulin resistance has been shown to cause type 2 diabetes. Some individuals who are highly resistant to insulin, nevertheless have normal glucose levels, suggesting that independent defects in insulin sensitivity and beta-cell function are required for T2D. In an attempt to investigate the relationship between insulin resistance and adaptation of insulin secretory capacity Brian Topp (PhD student of Finegood) has developed a mathematical model of coupled beta-cell mass, Insulin, and Glucose (bIG) dynamics. Applying the bIG model to longitudinal data from the Zucker Diabetic Fatty rat has generated the following predictions:

(1) Insulin resistance stimulates adaptation of b-cell mass and function via changes in blood glucose concentrations. (2) Hyperglycemia occurs when adaptation is slow relative to the progression of insulin resistance. (3) A nonlinear relationship between glucose concentration and both replication and death rates can account for beta-cell adaptation and the 'toxic' effects of hyperglycemia on beta-cell mass. However, current understanding of beta-cell mass dynamics is based on in vitro data and unpublished longitudinal in vivo studies. Also, it is unclear whether insufficient adaptation is due to an abnormally fast progression of insulin resistance or to abnormally slow adaptation of beta-cell mass and function. Topp plans to quantify the relationship between blood glucose levels and beta-cell replication rates, beta-cell death rates, and beta-cell function in animals (the 7 wk old Zucker Diabetic Fatty (ZDF), Zucker Fatty (ZF), and Sprague Dawley (SD) rat). In addition to this, he plans to measure the progression of insulin resistance in the ZDF and ZF rats from 6 to 12 wks of age.

The bIG model will be used to estimate the dynamics of insulin sensitivity and beta-cell function from an existing longitudinal data set of glucose, insulin and beta-cell mass levels in the diabetes prone male ZDF rat. Topp will gather similar longitudinal data in two obese control animals (the male ZF rat and the female ZDf rat) as well as another animal model of T2D (the high fat fed female ZDF rat). In a separate experiment, Topp will use a 24 hour clamp protocol to quantify the effects of glycemia on beta-cell replication, death and neogenic rates. Together these experiments will provide insight into the relative contributions of beta-cell mass dynamics to the pathogenesis of type 2 diabetes as well as provide insight into the mechanisms regulating beta-cell mass dynamics.

Changting Xiao, a new MITACS Postdoctoral Fellow, in Finegoods' Diabetes Research Lab, (SFU) will be involved in characterizing factors involved in regulating beta-cell mass (including plasma glucose levels and the immune system) and understanding beta-cell adaptation defects in animal model of type 2 diabetes. These studies will be facilitated by the use of the bIG model and may also lead to refinements or extensions of that model.

REMARK: The modeling and experiments on T2D have been our main direction of impact on the biomedical industries, and earned us support by Bayer, and Glaxo-SmithKline over many years. We are pursuing new industrial funding along these avenues, which are of clear interest to pharmacological companies.

Stem Cells:
Project C: Investigating Gene Expression of Stem Cells in Culture


Clive Glover (GS), Jamie Piret, Jenny Bryan
The Piret lab develops processes for growing stem cells in culture. Partially supported by the Stem Cell NCE (www.stemcellnetwork.ca), this project is exploring the use of gene expression profiling to monitor the performance of stem cell cultures. The identification of a stem cell gene expression signature would be a useful surrogate assay when optimizing the culture conditions. Also, specific changes in gene expression could provide a means to detect unknown culture limitations. Such an approach would replace the mainly trial and error methods currently used and thereby accelerate stem cell culture process development and scale-up. An ultimate goal is to design, test and optimize protocols for the production of stem cells for use in cellular therapy.
Murine embryonic stem cells (mES) provide a useful model system for this research. They are more readily available than adult stem cells and grow rapidly. Ultimately, these studies should contribute to more efficiently optimizing the culture of human ES cells that could lead to major advances in cellular therapy, such as providing cures for Alzheimer's disease or diabetes.

Stem Cells:
Project D: Treatment Strategies for Acute Myelogenous Leukemia and Diseases of the Regulatory Systems for White Blood Cells and Platelets

Michael C. Mackey, Laurent Pujo-Menjouet (PDF), Samuel Bernard (GS)

Mackey's group focuses on modeling periodic hematological through a combination of experimental/clinical investigation and mathematical modeling. The interrelated aspects include: (1) A project on periodic chronic myelogenous leukemia: in this condition, there are oscillations of leukocytes with periods from 30 to 100 days. Experimental observations have led to the conclusion that the hematopoietic stem cells govern this dynamic instability. Mathematical models for the cell cycle (so called G0 models) are under study. (2) Mackey has developed mathematical techniques to analyze flow cytometric data for stem cells of chronic myelogenous leukemia patients. The data is collected by Dr. Burthem, Department of Biomolecular Science, University of Manchester Institute of Science & Technology, Manchester. (3) M. Samuel Bernard GS, (Universite de Montreal) is modeling interactive dynamics of a G0 model of the hematopoietic stem cell with the network controlling the peripheral regulation of neutrophil production in humans. (4) A hypothesis is being investigated that a strong dynamic link exists between the properties of cyclical neutropenia (caused by an abnormal elevation of the rates of apoptosis) and the dynamics of periodic leukemia. Finally, (5) Mackey is investigating the dynamics of erythropoietin production and utilization, incorporating what is known about pharmacokinetics of the hormone EPO, in conjunction with a previously published model for the regulation of erythrocyte production to examine the existing guidelines for doping testing by sports regulatory agencies. More details of all five projects are presented in the Results section.

First Project: We study long period oscillations observed during periodic myelogenous leukemia. Leukemia is a progressive, malignant disease of the blood-forming organs, characterized by uncontrolled proliferation of immature and abnormal white blood cells in the bone marrow, the blood, the spleen, and the liver. It is difficult to get human experimental data. The challenge of this study is then to estimate the parameters involved in the cell cycle (death rates, proliferation rate, cell cycle duration) for this specific form of leukemia and to understand the mechanism of the oscillations in the blood cell population. Although the average division cycle of a cell is about 1-2 days, the oscillation period can be very large (~ 40-80 days). We are trying to explain this phenomenon. Moreover, it seems that the amplitude of the oscillations changes when some parameters of the cycle are modified. We are analyzing the link between the period and the amplitude of the oscillations when the parameters change.


Representation of the Cell cycle

Second Project: The second project is related to the study of a specific cell division marker Carboxyfluorescein diacetate succinimidyl ester (CFSE). This relatively new cell marker is very useful in experimental biology for following a cohort of cells for up to 8 generations, making it possible to analyze some cell cycle data over long periods of time. This cell marker can be used for various cell types, both in vivo and in vitro. We have obtained experimental data from the literature and assembled a mathematical model that includes the CFSE marker data. Our objective was to prove that this approach was consistent with the experimental data. The second objective is to provide a useful software tool that could be used in the laboratory as an interface between our mathematical analysis and future experimental data. (The biologist could enter experimental data and the software would be then able to produce an estimates for parameters such as the death rate, proliferation rate, or cell cycle time). Our software can also be used to predict the cell population age distribution over time.


An example of the agreement between the experimental data and our model


Amplitude and period of the oscillations during periodic myelogenous leukaemia

Actin Dynamics and Cell Motility


Adriana Dawes (GS), Stan Maree, Leah Keshet, A. Carlsson

The actin cytoskeleton is responsible for a large array of cellular functions, including mechanical sensing, signal transduction, motion of cells, cell division, and many others. The dynamics of this structure hold many clues to the fate of the cell in both health and disease.
We have established a working partnership with Anders Carlsson (Washington University, St. Louis) which provides matching NSF funds for this project. Here we focus on how cells respond to signals through their actin cytoskeleton dynamics. One of our goals is to understand how the small G-proteins Rac, Rho, and Cdc42 which act downstream of chemical signals received by a cell, influence the activity, function and motility of the cell, by signaling to its actin cytoskeleton network. Keshet has worked on actin dynamics for over a decade. The recent study of signal transduction (by former MSc student Norris) has provided a base of knowledge from which this project has grown, though the goal is quite distinct. PhD student Adriana Dawes (UBC) has been working with supervision and help from Maree and Keshet to develop differential equation models and simulations of cell motility, in which the effect of signals on the nucleation, polymerization, depolymerization, capping and uncapping of actin filaments is taken into account. Maree has been developing a whole-cell motility model based on actin filament density, and branching by Arp2/3 to generate new "barbed ends" at which the filaments can grow. The model is based on signaling by the small G-proteins to the cytoskeleton. New MSc student Alexandra Jilkine is investigating the temporal and spatial dynamics of the small G-proteins to determine how those interactions can account for cell polarization in response to signals.