Mathematics in Developmental Biology
On a recent trip to New Zealand, a caravan park in the South Island town of Haast had a book swap, where travellers could leave a book they had finished reading and pick up another left by a fellow guest. Having just finished my novel, on a whim I picked up The Gene: An Intimate History, by Siddhartha Mukherjee, an eye-opening book that proceeded to develop an interest in developmental biology that I never knew lay in wait.
Mukherjee’s book is a timeline of gene research. It chronicles significant milestones in the hypothesising, discovery and understanding of the gene: the base unit of hereditary information, passed from generation to generation. It begins with Aristotle’s ideas in 350BC, to Darwin’s On the Origin of Species in 1859, to the modern sequencing of the entire human genome and our still increasing understanding of the exact process of human and animal development. I was immediately fascinated, and my travel companions were soon sick of hearing my newly-acquired facts about fruit fly embryos and hereditary illness.
I wasn’t just fascinated by the impact of genes and gene research on human history, and the potential of the near future. I was intrigued, and somewhat validated, by the necessity of mathematics in this field. As a final year Bachelor of Mathematics student, I had always understood the importance of maths, and its prevalence in every field from physics and chemistry to sports and music. That was the reason I started the degree, as well as the reason I’d stuck through 3 years of it. Throughout my education, we had applied mathematical concepts to finance, fluid dynamics and even basketball, but this was the first time I truly understood just how much impact mathematics coupled with other sciences could have on tackling real-world issues and answering deeper, ancient scientific questions.
I returned from my holiday and prepared to begin my AMSI Vacation Research project. Attending my first meeting with my supervisors Dr. Pascal Buenzli and Prof. Mat Simpson, I was surprised to be offered a research topic different to the one I had originally accepted. Funding had recently been granted to a project that Dr. Buenzli was collaborating on, researching the inhibitory cascade, a simple rule that governed segmental growth in animals. Basically, the idea was that things like teeth, vertebrae and limbs grew in a very linear fashion: a big molar grows, which inhibits the growth of the next tooth so that it’s smaller, which inhibits the next, and so on. It was hypothesised that behind this process were Turing patterns, a specific chemical reaction that causes patterns to form within a domain. First discussed by famous mathematician/code-breaker Alan Turing, these patterns have been applied to other biological systems, like animal coat patterns and alligator tooth eruptions. The research proposed to validate the Turing-like hypothesis, determine the chemicals involved in the process and identify the genes that regulated it.
In a strange coincidence, my new interest in developmental biology was immediately matched with a mathematical application, and an opportunity, no matter how small, to have an impact on a research area that I felt was significant. Using computer simulations, I was able to validate the assumption of Turing-like reactions in the Inhibitory Cascade, hopefully opening the door for further, more crucial results. I would like to thank AMSI, QUT, Pascal and Mat for the amazing learning experience the AMSI Vacation Research program has been.
Joel Rutten was one of the recipients of a 2017/18 AMSI Vacation Research Scholarship.