I am a translator. I translate from biology into mathematics and vice versa. I write mathematical models which, in my case, are systems of differential equations, to describe biological mechanisms, such as cell growth. Essentially, it works like this.
First, I identify the key elements that I believe may be driving behavior over time of a particular mechanism. Then, I formulate assumptions about how these elements interact with each other and with their environment.
It may look something like this. Then, I translate these assumptions into equations, which may look something like this. Finally, I analyze my equations and translate the results back into the language of biology.
Let me give you an example. What do foxes and immune cells have in common? They're both predators, except foxes feed on rabbits, and immune cells feed on invaders, such as cancer cells. But from a mathematical point of view, a qualitatively same system of predator-prey type equations will describe interactions between foxes and rabbits and cancer and immune cells.
This predator-prey-shared resource type model is something I've worked on in my own research. And it was recently shown experimentally that restoring the metabolic balance in the tumor microenvironment -- that is, making sure immune cells get their food -- can give them, the predators, back their edge in fighting cancer, the prey.
This means that if you abstract a bit, you can think about cancer itself as an ecosystem, where heterogeneous populations of cells compete and cooperate for space and nutrients, interact with predators -- the immune system -- migrate -- metastases -- all within the ecosystem of the human body.
And so, once we have identified the key components of the tumor environment, we can propose hypotheses and simulate scenarios and therapeutic interventions all in a completely safe and affordable way and target different components of the microenvironment in such a way as to kill the cancer without harming the host, such as me or you.
And that's what I try to do through mathematical modeling applied to biology, and in particular, to the development of drugs.
It's a field that until relatively recently has remained somewhat marginal, but it has matured. And there are now very well-developed mathematical methods, a lot of preprogrammed tools, including free ones, and an ever-increasing amount of computational power available to us.
The power and beauty of mathematical modeling lies in the fact that it makes you formalize, in a very rigorous way, what we think we know.
We make assumptions, translate them into equations, run simulations, all to answer the question: In a world where my assumptions are true, what do I expect to see? It's a pretty simple conceptual framework.
Luckily, since this is a model, we control all the assumptions.
So we can go through them, one by one, identifying which one or ones are causing the discrepancy. And then we can fill this newly identified gap in knowledge using both experimental and theoretical approaches.
Of course, this isn't the work of a modeler alone.
It has to happen in close collaboration with biologists. And it does demand some capacity of translation on both sides. But starting with a theoretical formulation of a problem can unleash numerous opportunities for testing hypotheses and simulating scenarios and therapeutic interventions, all in a completely safe way.
In other words: mathematical modeling can help us answer questions that directly affect people's health -- that affect each person's health, actually -- because mathematical modeling will be key to propelling personalized medicine.