Our group uses mathematical modelling tools from systems and control theory to aid in the study and manipulation of biological systems. Our focus is on intracellular networks (metabolism, signal transduction, gene regulatory networks) and on heterogeneous microbial communities.

Natural biological systems have been selected (through evolution) to perform specific functions. As a result, the study of these systems can be framed as a reverse engineering endeavor. This work is known as systems biology. Our work in this area involves the development, validation, and analysis of mechanistic mathematical models. These models (typically formulated as systems of nonlinear differential equations or as stochastic processes) represent working hypotheses that generate predictions about the behavior of systems of interest. These predictions can then be used to refine our understanding and to guide further experimental investigations. In addition to model construction, we are also engaged in the development of new theoretical techniques for model analysis.


The forward-engineering of biological systems with specified behaviours is referred to as synthetic biology. Our work in this area focuses on model-based design -- prototyping by computer simulation  -- which complements construction and testing in the lab. Our focus here is largely on the design and construction of gene regulatory networks.

Much of our work involves experimental data, acquired either in our own laboratory or in the labs of our collaborators.

A primer on mathematical modelling in systems and synthetic biology is posted here.

Our work has been supported by

  • NSERC (Natural Sciences and Engineering Research Council of Canada)
  • CIHR (Canadian Institutes of Health Research)
  • CFI (Canada Foundation for Innovation)
  • MRI (Ontario Ministry of Research and Innovation)

Some on-going projects are described below.

In situ plasmid curing by bioaugmentation

Antibiotic resistant bacteria are a growing health concern. In many instances, antibiotic resistance is conferred by genes housed on a plasmid -- a DNA molecule that resides in a cell but is not part of the cell's genome. We are investigating strategies by which such plasmids could be eliminated from populations of pathogens, rendering them antibiotic-sensitive. Our proposed approach involves bioaugmentation: the delivery of genetic material to the offending population. To that end, we are characterizing the dynamics of plasmid conjugation in a population. We have engineered "competitor" plasmids that take advantage of incompatibility mechanisms to displace undesirable target plasmids once delivered to a population; development of mathematical models of these mechanisms allows model-based design of potential environmental implementations.

Model reduction for stoichiometric networks

An understanding of cellular metabolism is crucial to a wide range of biotechnology and health-related activities, such as biofuel production and drug design. However, cell-level (whole-genome) metabolic networks are highly complex, and so many analytic tools, such as elementary flux mode analysis, cannot be applied. Using a recently developed reduction method, we are able to reduce large metabolic models to more manageable steady state equivalent networks. This reduction minimizes the number of elementary flux modes and hence facilitates flux mode analysis. In addition, we are addressing links between elementary flux mode analysis and signaling pathways. This involves generating a stoichiometric network with the same dynamics as a given signaling network, thus allowing computational tools such as elementary flux mode analysis to be applied in a new context.

Stochastic models of biochemical reaction networks: sensitivity analysis and model reduction

To account for the variability that dominates the dynamics of small-scale reactions networks (as often occur in the cell), stochastic mathematical models are required. In comparison with deterministic models (such as differential equations), there are relatively few tools for analysis and simulation of stochastic models. We are developing computational tools for sensitivity analysis of such models, as well as techniques for model reduction. Sensitivity analysis provides information about how a system's behaviour depends on the characteristics of its environment and internal configuration. Model reduction allows for construction of models of reduced size whose behaviour closely approximates the original model. This is joint work with Silvana Ilie (Mathematics, Ryerson) and Marc Roussel (Chemistry, U. Lethbridge).

Dynamics of heterogeneous microbial communities


In collaboration with Tao Dong (U. Calgary) we are investigating the behaviour of mixed microbial communities. Such communities play important roles both in the environment and in association with human hosts (i.e. the human microbiome). Our analysis involves observation of community behaviour by fluorescence microscopy, and the development and analysis of corresponding spatial models (using both agent-based and differential equation frameworks).

Projects in development address heterogeneity of microbial populations in the transition to stationary phase and analysis of control schemes that regulate ion currents in excitable cells (such as neurons).