math shines a light on competition between cells

I am so excited to FINALLY kick off the #mathematicalmodels blog: women in STEM sharing their stories of how they use math in their work. I am overwhelmed by the amount of support I’ve received for this blog and can’t wait to share the lineup of engineers, astronomers, quantum physicists, entrepreneurs, software developers, and PhD students coming down the pipeline. Please stay tuned for their math stories, and please share with anyone who may be interested!

My very first #mathematicalmodel feature is Nika, who has recently completed her PhD in biomedical engineering from the University of Toronto, where she studied stem cells. When she's not in the lab, writing code, or creating mathematical models, Nika likes to spend time encouraging youth to explore their curiosity for science and she is involved with numerous science outreach and communications initiatives. Read more about how she uses #mathematicalmodels to understand the behavior of #stemcells:


Look up at the sky and what do you see? Well, if you're lucky enough you may come upon some stars, maybe even the bright glow of Jupiter. Our collective human curiosity for the universe has encouraged generations of star gazers to ponder the movement of these celestial bodies and predict their behavior, all in an attempt to advance our understanding of our world. After all, "we are all made of stars" and understanding the stars brings us a step closer to understanding ourselves. Names like Galileo and Copernicus come to mind -- key figures that proposed mathematical models to so elegantly capture the movement of the planets and stars around us. At the macro scale, we now have the math we need to make key predictions about planetary orbits, potential collisions, etc.

Now I challenge you to direct your gaze a little closer to home. Perhaps a quick look at your skin, the pupils of your eyes, or your hair follicles. You're probably squinting at this point and may even be tempted to grab a magnifying glass. I don't blame you -- the cells that make up your body are not as accessible as laying outside on a warm summer night and searching for the Big Dipper as you sip hot chocolate. But nevertheless, generations of curious minds have been looking at the universe that is our body: a complex world composed of cells that have specific jobs to do (like carry oxygen or remove bacterial intruders) and work together to allow you to stay alive, to think, to speak… to be you.

You might wonder whether our understanding of our bodies and the behavior of the cells that compose it is as advanced as our grasp of the stars and planets in the sky. Do we know what our cells are doing in there? Can we predict their movement, their fate? The truth is that the field of biology is working on this. With the advance of technologies like the microscope, genetic engineering, tissue culture, live imaging, and cell tracking it is becoming easier to watch cells, to make hypotheses about how these cells make decisions about what to be and how to behave, and to test our ability to predict their next move.


Now that's where I come in: trying to use mathematical models to predict cellular decision making. I'm not the only curious mind of my kind -- there are whole groups of mathematical and computational biologists trying to develop models to explain why cells, tissues, and animals behave the way they do. It's quite exciting actually, to write some lines of computer code, jot down some equations, and let the math carry you away on a journey into the mind of a cell. For me, I'm most interested in understand stem cells. You may have heard the words "stem cell" thrown around in the news or online. They have received a lot of excitement and some hype recently. But before I can tell you more, let me tell you just what defines a stem cell.

Stem cells have two key characteristics. First, they are unspecialized; that is, they haven't committed themselves to becoming a specific type of cell. And second, they can divide and divide -- theoretically, an infinite number of times -- to make copies of themselves. So why are stem cells so special and what am I doing to better understand them? Well, for one thing, stem cells go on to make all of the cells that make up our tissues and organs. In fact, we all started as a single stem cell which formed by the joining of a sperm and egg: the moment we were conceived. The fertilized egg that results from this union is, in fact, a type of stem cell known as "totipotent". That means that it has complete and total potential to form all of the types of cells that make up our bodies (that's about 200 different cell types!) as well as the cells that make up the tissues that support our growth as a fetus (like the umbilical cord and placenta).

Now that's an incredible thought: one single cell without a specific identity goes on to divide and divide to give rise to a complicated, complete human body composed of trillions of cells with 200 different identities (like heart cells, skin cells, red blood cells, kidney cells, etc). You might imagine that if we could harness the power of the stem cell, if we could control it and make as many copies as we need and turn these stem cells into specific types of cells, then maybe we could cure a lot of diseases. What if we could use stem cells to build organs and tissues for transplantation into patients eagerly waiting for donors?

The potential and promise of stem cells has captured my curiosity and it is for this reason that I've devoted years of my PhD to trying to understand how stem cells make decisions about whether to divide, what to become, and how to interact with each other. And while I spend most of my time huddled in front of a biosafety cabinet, doing experiments with stem cells from mice, I also spend some of my time typing up computer code, trying to find the mathematical basis for the behavior of these cells. Specifically, I am interested in understanding how the stem cells I grow in a dish may compete with one other and how this might influence the outcome of the stem cell population as a whole.

Click the photo to read  @itslikepudding 's Instagram post featuring Nika and the stem cell research she does.

Click the photo to read @itslikepudding's Instagram post featuring Nika and the stem cell research she does.

Now when I hear the word "compete", my imagination takes me to a boxing ring and I visualize two cells duking it out with a crowd of other cells huddled around, cheering them on. While this is not quite the scene I see in the dish of stem cells I have growing in the lab right now, the idea is close. In fact, cells in our bodies and those we grow in the lab are constantly competing with one another for nutrients and space. And sometimes they will even take it a step further and eliminate their less-fit or "weaker" neighbors. Who knew that our cells could be so aggressive? But it's true, scientists have found survival-of-the-fittest happening at the cellular level. So what I wanted to know was whether the cells I study were engaging in this behavior and killing their neighbors.

I enlisted the help of my biophysics colleagues and we worked together to develop the math needed to answer this question. I am a big believer in interdisciplinary collaboration and while I myself am a biomedical engineer -- so I do both experimental and computational/mathematical work -- I was eager to join forces with biophysicists who have an expertise in developing these types of cellular models. Together we made a model -- a series of probabilities and differential equations -- that could predict what we would expect to happen in a population of stem cells that were getting along, not engaging in competition. This competition-free cellular society had a regular stream of births and deaths, occurring probabilistically and not as a result of direct cell-killing. But after comparing the predictions of our model to what I observed in my dish of cells, it became clear that my cells were not living in harmony after all. The reality is that the society of cells I have growing in the lab are engaging in a battle to the death that allows only a few of the stem cells and their progeny to take over the population and claim the cellular resources: nutrients and space in the dish on which to grow. Almost sounds like the escapades of ancient civilizations, battling for a claim to the throne!

As we speak, I'm working on sharing what I learned about the competitive behavior of my cells in a scientific publication. Granted, this will be a story intended for other curious scientists, but perhaps one day my cells could star in their very own TV series documenting their battles, triumphs and deaths! Who knew that a bit of math could teach me so much about my society of cells and the competition and death lurking beneath their peaceful exterior. Now we are working on using the math we developed together with some more experiments to find out what exactly makes some cells survive the competition and others banish… stay tuned for part two of the story in the future!

For more from Nika, follow her stem cell adventures on Twitter at @nika_shakiba.