A Better Look at How Cells Move

computer simulations
A collection of soft, deformable cells as represented in the computational model. (Image courtesy of Corey O’Hern)

A new computational model clarifies the structure and mechanics of soft, shape-changing cells, potentially giving scientists a better understanding of cancerous tumor growth, wound healing, and embryonic development.

Led by Corey O’Hern, a Yale professor of mechanical engineering and materials science, physics, and applied physics, the researchers developed an efficient computational model that allows simulated particles to realistically change shape during interactions with other particles. Their results are published Dec. 11 in the journal Physical Review Letters.

Particles such as sand grains and ball bearings are rigid and don’t readily change shape, so developing computer simulations of them is fairly straightforward. Doing the same for cells and other soft particles is more difficult, and the computational models researchers currently use don’t accurately capture how soft particles deform.

The computational model developed by O’Hern and collaborators tracks many points on the surfaces of polygonal cells. Each surface point can move independently, in accordance with its surroundings and neighboring particles, allowing the shape of the particle to change. It’s a more computationally demanding simulation than those currently used, but necessary to correctly model particle deformation, O’Hern said.

“We now have a computational model that can investigate packing in systems containing discrete, deformable particles,” O’Hern said. It also allows researchers to easily adjust cell-cell interactions, consider directed motion, and it can be used for both 2D and 3D systems.

One unexpected result the model produced shows that deformable particles must deviate from a sphere by more than 15% to completely fill a space, O’Hern added.

“In our new model, if no external pressure is applied to the system, the particles are spherical,” O’Hern said. “As the pressure increases, the particles deform and increase the fraction of space they occupy. When the particles completely fill the space, they will be 15% deformed. Whether it’s bubbles, droplets, or cells, it’s a universal result for soft particle systems.”

Among other applications, this technology potentially gives researchers a new tool to examine how cancerous tumors metastasize. “We can now create realistic models of the packing of cells in tumors using computer simulations and ask important questions, such as whether a cell in a tumor needs to change its shape to become more capable of motion and eventually leave the tumor.”

O’Hern is also using the new computational model in collaboration with Scott Holley, a Yale professor of molecular, cellular and developmental biology, to study how the zebrafish spinal column forms. Specifically, they’re examining how cells move during the elongation phase in the embryo in such a way to ensure spinal column symmetry. These studies could explain the mechanisms that lead to spinal column disorders such as scoliosis and spina bifida.