In this blog post, we feature an Interview with Dr. Duncan Martinson, a Postdoctoral Research Fellow at the Isaac Newton Institute (Cambridge, UK).

*Photo credit: Duncan Martinson*

**When did you first become interested in mathematics and biology?**

I knew when I finished high school that I wanted to pursue something related to mathematics, since I loved classes like physics and engineering where I could use mathematical tools to understand the world better. My interest in biology developed a bit later: I didn’t know until my second year as an undergraduate that there were even mathematical models for biology besides those describing population growth. Learning about how mathematics has been used to understand pattern formation and collective behavior in my coursework astounded me — I had no idea that such complicated phenomena could be even modeled. What was even more exciting to me was that there were so many open questions in biology and medicine to which mathematical analysis could bring unique perspectives and insights. This is what drove me to pursue graduate studies in mathematical biology.

**Was the decision to do a Ph.D. an obvious and easy choice?**

I think that going to graduate school was a straightforward decision because I wanted to delve into more detail on mathematics and its applications in biology. Entering a Ph.D. program wasn’t obvious for me, though. I actually began graduate school aiming only to obtain a Master degree, since I didn’t have enough funding at that time to complete a Ph.D. and I was considering applying to medical school in the US (I didn’t know what career paths were available to people pursuing mathematical biology at the time). I also wasn’t that confident in my ability to pursue a long-term research project because I didn’t have much experience at that time conducting mathematical research. After my first term, though, I had enjoyed my experiences so much that I knew that mathematical modeling and analysis was something I wanted to pursue full time. I was very blessed to have extremely supportive supervisors, who not only encouraged me in my projects but also pointed me towards additional funding sources that let me transfer to the Ph.D. program.

**What are the main biological research questions that you are interested in?**

I’m interested in understanding how simple interactions between individual organisms such as cells lead to the emergence of complicated behaviors, such as coordinated movement or pattern formation, at the level of the whole population. These kinds of collective phenomena frequently occur in cell and developmental biology, from the growth of new vascular networks to stem cell migration to zebrafish stripe pattern formation. One of the main themes of my research involves using mathematical modeling to bring relevant insights for experimental collaborators, for example by making predictions that can guide the design of future experiments. Another aim of my research involves understanding the links between different modeling frameworks, in particular those between individual-based descriptions that explicitly track every member of a group versus coarser “continuous” descriptions in which the entire population is represented as a density that varies over time and/or space. I’m especially interested in examining differences between the solutions of these frameworks when the number of cells may be in a biologically relevant “intermediate” zone, in which they are too numerous to represent efficiently with an agent-based model but not so numerous that all the assumptions underlying the continuous description can be necessarily satisfied.

**What types of questions do you think will be important to answer in the future in your field?**

I think one of the major future questions in the field is how to connect the behavior of cells and their groups to the high-resolution genetic data that experimentalists can currently collect. Many models of collective behavior and pattern formation focus on what happens at the level of individual cells or their populations, but experimental biologists working in these areas tend to collect data on the sub-cellular scale. From my point of view as a modeler, it is unclear in many circumstances how to incorporate that detailed information to establish the parameters or rules of my frameworks and this can lead to a disconnect. I think that understanding the connection between genes and phenotype would go a long way in closing this gap and making more accurate and experimentally relevant mathematical descriptions of biological behavior.

**What mathematical and computational tools do you find useful in your work?**

My research involves studying partial differential equations and agent-based models, so techniques involving calculus and probability/statistics are extremely relevant to my work. Additionally, I have found that techniques from asymptotic analysis (e.g., matched expansions and homogenization theory) have been helpful in linking continuous models to individual-based ones, as well as in deriving useful biological conclusions from very nonlinear models. For my new projects involving parameter estimation, I’ve found that techniques from Bayesian inference, such as Approximate Bayesian Computation and Markov Chain Monte Carlo sampling are extremely useful in connecting parameters of my mathematical models to actual experimental datasets.

**What makes you passionate about your work?**

I like how the projects that I work on, even if they’re conducted entirely on a computer, really can make a difference for biologists and how they perceive and interpret their research. I remember one project that I worked on with neurologists that involved creating a simple model of immune cell development in the brain and matching it to experimental data. By analyzing solutions of this model (which was a system of ordinary differential equations), I was able to make a prediction about the role of different cell types that our collaborators had not considered before but which they later confirmed by conducting a new experiment. Successfully developing and analyzing an accurate mathematical model also appeals to me, because I feel in those moments that I’m uncovering a solution to an extremely challenging puzzle.

**What do you like to do in your spare time outside of work?**

I enjoy running and have raced in a few 10k and half-marathon races; I’m about to begin training for my first marathon. I’ve also done triathlons in the past and used to be a competitive swimmer in high school and undergrad. I also really enjoy the challenges of doing crossword puzzles.