Professor, Mathematics and Statistics
Research area: mathematical biology, neuronal and gene networks, mathematical models of neuromotor control
What do neuroscience, kinesiology, and the study of gene regulation all have in common? They are all medical research fields involving complex biological networks, which increasingly rely on sophisticated mathematics to complement biologists’ lab work. These are also just a few of the diverse topics that Dr. Roderick Edwards of UVic’s Department of Mathematics and Statistics has tackled recently.
Edwards specializes in understanding the patterns produced by networks and feedback loops. He studied artificial neural networks during his PhD, and then for his post-doctoral fellowship, he did something unusual for a mathematician: he joined a neuro-kinetics team and got some hands-on lab experience, measuring the movements of people affected by Parkinson’s disease.
His combined interest in math and biology has made him very in-demand. There is no doubt about it – there is an increasing need for a mathematician’s perspective to find order in the chaos of the staggering volume of biological information that scientists are producing.
UVic biochemist Dr. Vern Paetkau had an age-old question for Edwards: what is the molecular mechanism behind a 24-hour circadian rhythm? Although a vast number of papers have been written on circadian rhythms, it is still not clear how these cellular clocks work as a whole. More specifically, several gene regulation feedback loops (called ultradian oscillators) have been found to play a part in circadian rhythms, yet there are several competing theories for how these loops, which typically repeat every one or two hours, interact to produce a 24-hour rhythm.
Paetkau, Edwards and Dr. Reinhard Illner (another UVic mathematician) reasoned that perhaps several regulation cycles, which seemingly work independently, can combine their effects to create a longer period cycle that we more commonly observe. In mathematical terms, Edwards is proposing a stochastic model rather than a linear deterministic one: “If this prediction is true, you should see superimposed on the 24-hour rhythm a smaller-amplitude fast rhythm”. Edwards, Paetkau and collaborators are seeking these patterns in bean plants, in which circadian rhythm controls such things as the raising of leaves at dawn. They hope to find a general mechanism that will explain how such diverse life forms from cyanobacteria to humans have roughly 24-hour rhythms, despite the fact that the genes involved are not very conserved, and may have evolved independently.
Another topic of interest for Edwards is Parkinson’s disease; he is modelling neuromotor dysfunction, which results in Parkinsonian tremor, to understand how deep brain stimulation works.
Deep brain stimulation (DBS) is a new treatment that is increasingly being used for brain disorders, such as Parkinson's. DBS involves surgically implanting an electrode into the brain, and using it to deliver electrical impulses to a small region of the brain, dampening brain activity. It is unclear how it works, but it has dramatic and immediate effects on Parkinson’s patients: halting tremor, and allowing patients to regain voluntary movement.
Edwards and his collaborators are measuring and modelling neural oscillations, before and after stimulation, in order to fine-tune the method. They have two goals: to create an “adaptive stimulator,” which is an implant that will record brain activity as it stimulates, and can therefore react to modify the stimulation on an ongoing (and on-demand) basis; and to see if they can get similar results by stimulating the cerebral cortex of the brain from the surface of a person’s head, thereby removing the need to operate. This might be possible because, while tremor is generated deep in the basal ganglia, it is propagated through other areas of the brain. By disrupting the oscillations in the motor cortex, the therapy may be able to keep tremor from reaching muscles.
Edwards is also measuring the movement of patients suffering from dyskinesia, the involuntary jerks brought on as a side effect of the Parkinson’s drug levodopa. Dyskinesias are typically thought of as random movements, says Edwards, but he has looked for – and found – underlying patterns not visible to the naked eye. He did this by crunching data collected by hooking patients up to magnetic trackers, and using sensors that are similar to ones used in live animation suits to create 3D renderings of people. He hopes the information will help neuroscientists better understand the mechanism behind the dysfunction. More immediately, it may help physiotherapists devise new therapies to control dyskinesia, based on a better understanding of the involuntary motion.