Credit: Timothe Vignaud and Colleagues, CEA, France

When I was nine, biology gave me my first existential crisis. If I am built out of trillions of tiny cells, I worried, what’s to keep me from crumbling into a pile like a dried-out sandcastle? Almost two decades later, as a Ph.D. student in mathematics at the University of California, Davis, I’m still trying to figure out how cells cohere together, such as in arterial linings, or move around, such as when immune cells hunt down invaders in the body. And I use a mix of biology, physics and mathematics to do it.

Moving and staying put might seem totally different, but they have one key thing in common: force. It takes force for a cell to grab onto a given surface and pull its way through the body, and also to hang on tight against the everyday strains of gravity, blood flow or simple physical movements.

The machinery that cells use to generate such force is a sophisticated mix of “cables,” made of a protein called actin that crisscross and link into a kind of sturdy mesh, dotted with molecular “motors,” a second protein, called myosin. Myosin grabs onto actin and pulls hard. That force spreads across the interconnected mesh and out into the surrounding world, letting cells grasp the world around them.

Cells have a dizzying array of options for how to lay out their cable networks and where to stick their molecular motors. Various arrangements are responsible for why muscle cells produce force differently than skin cells, and why some cells are good at hanging on for dear life whereas others are better at crawling around.

That’s where math comes in. It’s really hard to just look at a cell under a microscope and know exactly how much force it produces and what it can do with that force. Will it move? Change shape? Just sit there?

The job of us mathematicians is to come up with equations that help explain how those cables and motors (and some other bits of biological machinery) assemble into a cell’s driving engine. With any luck, our equations can help biologists understand what they’re seeing in the lab, and maybe even to make better choices about what kinds of experiments to perform.

The video below, from a September 2013 paper in The Journal of Cell Biology by some of the members of our lab, shows a computer simulation of myosin motors (red dots) grabbing onto and pulling on a few actin cables. This kind of simulation helps biologists understand how force from motors influences the arrangement of cables inside the cell.

Now that you’ve seen a simulation of a specific area, check out this video, by another member of our lab, which simulates how a whole cell might move. This video is part of a current project researching how cells physically turn—as you can see, this hapless wanderer gets stuck spinning in circles.

What about cells that need to stay put? Right now, I’m working with a group of very talented French biologists who want to understand how stationary cells produce force. You can check out their website for an amazing science-meets-art video of cells crawling over Parisian buildings.

Different-size cells grab onto a surface: on the left in white are all the actin “cables” running across the length of the cell, and in red is where the cells are grabbing onto—and pulling—on the surface. Graphs at right show exactly how hard each cell is tugging on the exterior.

Credit: Timothe Vignaud and Colleagues, CEA, France

Experiments such as in the image above are a dream come true for a mathematician like me. With such pictures—in which you can see exactly how those cables are laid out and exactly how much force the cell produces—it’s not so hard to write out mathematical equations that precisely describe how those cables translate into the force the cell exerts on the world around it.

In a few months, I might just be able to help answer nine-year-old me’s question about why we don’t all fall apart.