My area of research is mathematical biology. The main objective
of my research program is to understand and explain physiological
processes through the development and analysis of mathematical models.
We have applied our results in the
analysis of FRAP data of both
actin and histone H1. We showed that the FRAP data for actin is
consistent with the hypothesis that nuclear actin exists in both
and filamentous forms (this is a highly controversial topic in cell
and although many researchers believe this to be the case, there is not
yet definitive proof), and obtained estimates of binding and unbinding
rates (of monomeric actin to and from filamentous actin). The
second application was in
the context of histone H1 dynamics. Histone H1 molecules are
bound to a spatially homogeneously distributed chromatin structure, or
unbound and free to diffuse. Fluorescence recovery data suggest
almost all of the histone H1 population is bound to the chromatin
and only a very small proportion of the histone H1 molecules are free
diffuse. This small proportion allows histone molecules to move
from one binding site to another, which we believe is crucial for the
dynamics of histone (in particular, if histone H1 proteins were
associated with chromatin, it would be more difficult for chromatin
factors to gain access to chromatin).
This research advances knowledge in the area of spatial pattern formation. Specifically, it addresses the origin of nuclear architecture, which ultimately affects nuclear function. Successful outcomes of this research puts us in a better position to predict outcomes of changes in nuclear architecture, such as seen with cancer.This research is in collaboration with PhD student Gustavo Carrero and Dr. Michael Hendzel from the Cross Cancer Institute, Department of Oncology, University of Alberta.
In my earlier research, I have focussed attention on mathematical
models of electrical activity in pancreatic beta-cells. These
cells produce and secrete the hormone insulin, which is the principal
hormone regulating the blood glucose level. In the presence of
glucose, these cells exhibit a complex pattern of oscillations called
bursting. Pancreatic beta-cells are organized in clusters, called
islets of Langerhans, and bursting is synchronized within islets.
The synchronization is due to coupling between neighbouring cells,
through low-resistance electrical pathways called gap junctions.
Modelling efforts related to the electrical activity of beta-cells can be divided broadly into two categories, single-cell models and coupled-cell models. Single-cell models typically include much biophysical detail, and are used to explain specific experimental observations. These models represent bursting as observed in an islet, and a single-cell model can be viewed as a model of the behaviour of an average cell within an islet. Coupled-cell models typically include less biophysical detail, so that attention can be focussed on the role of coupling in the generation of synchronized oscillations.
During the last few years, my attention has been concentrated on coupled-cell models for pancreatic beta cells. Through mathematical and computational analyses of these models, I have obtained a broad and deep understanding of the role of coupling, and its interaction with system noise and parameter variability, in the generation of network behaviour. A recent discovery is bursting as an emergent phenomenon (bursting obtained in a network of cells, each of which is incapable of bursting individually).
Research on bursting oscillations continues within a broadened
context. In particular, attention is focussed on a comparison of
coupling mechanisms, and their effect on different classes of bursting
models, as well as on the behaviour of discrete-time models that
generate bursting oscillations.
Bursting oscillations are observed in many electrically excitable cells other than pancreatic beta cells, such as thalamic neurons and hippocampal pyramidal neurons. This research therefore has strong reciprocal connections with mathematical neurophysiology.
Development and analysis of an integro-differential equation that
describes the re-seeding of ovarian cancer in the peritoneal cavity.
This research is in collaboration with Dr. Thomas Hillen.
Motoneurons are the
neurons controlling muscle contractions. The electrical activity
of these neurons is characterized by tonic firing, the frequency of
which depends on synaptic activation or the strength of current applied
to the soma. Under certain experimental conditions, vertebrate
motoneurons exhibit bistability between firing patterns. It is thought
that the bistability is the result of an interaction between L-type
calcium currents in the dendrites and spike-generating currents in the
soma. Experimentally and theoretically, it has been observed that
the attenuation of a signal travelling from the soma to the dendrites
is less than the attenuation of a signal travelling in the opposite
direction. The Booth-Rinzel model (a popular mathematical model
for the electrical activity in motoneurons exhibiting bistability) does
not reproduce this property, possibly because it uses a constant
coupling conductance between the somatic and dendritic compartments.
This means that the predictions of the model on the experimental
conditions that give rise to bistability likely are inaccurate.
The goal of this project is to determine modifications to the model so
that it exhibits the correct voltage attenuation properties while
maintaining bistability. Successful completion of this project
will provide insight into the relationship between voltage attenuation
This research is carried
out in collaboration with Dr. Kelvin Jones
from the Department of Biomedical Engineering at the University of
Vasomotion refers to the spontaneous oscillatory constriction of
blood vessels. Vasomotion is observed to be enhanced in states of
high resistance such as hypertension, and decreased in states of low
such as pregnancy. However, the functional significance of
remains controversial. In collaboration with Dr.
Sandra Davidge from the Departments of Obstetrics/Gynaecology and
MSc student Chris Meyer and I have resolved a controversy existing in
literature regarding the effect of vasomotion on vascular
We currently are using mathematical models to investigate mechanisms
to underlie the phenomenon of vasomotion. Another issue of
is to determine the influence of the stiffness of the blood vessels on
the amplitude of the vasomotion.
Diabetes is a disease of the glucose regulatory
by hyperglycemia. Type 2 diabetes (also known as adult-onset or
diabetes) is associated with a deficit in the mass of beta cells,
insulin secretion, and resistance to the action of insulin.
the relative contribution and interaction of these defects remains to
clarified. Models are used to study the dynamics of the
interaction between beta cell
mass, insulin and glucose.
This research is in collaboration with Dr. Diane Finegood from Simon Fraser University and her PhD student Brian Topp.