SIAM News Blog

Modeling Collective Cancer Cell Invasion

By Karthika Swamy Cohen

What makes cancer a serious and hard to control disease is its ability to spread to different parts of the body. Cancer cells can spread out from a tumor via the vascular and lymphatic systems to distant organs, giving rise to new cancer colonies and more tumors over time.

At the SIAM Conference of Computational Science and Engineering being held in Atlanta, GA this week, Yi Jiang of Georgia State University described a mathematical model to study tumor invasion as part of the minisymposium on “Recent Advances of Modeling and Computational Techniques in Biological Engineering”. Jiang’s method is based on the Cellular Potts model, a lattice-based computational technique that can simulate the collective behavior of cellular structures. 

Jiang began by explaining the major contributors to cancer growth and metastasis in the human body with a seemingly unrelated question. “If I asked you what makes airplanes fly, you would probably say air drag, thrust, mechanics, and dynamics,” she said. “If I asked a three-year-old—my son—he will say it's the pilot that makes the airplane fly.”

With that, she emphasized the role of decision making and regulation in not only making a plane fly, but also in how cancer invades and spreads in the human body. The focus in cancer study has been on signaling, cell behavior, and cell decision-making processes, Jiang said. But how do biomechanics and biophysics play a role?

“For almost a half century since Nixon declared war on cancer, the search for a magic bullet has largely failed,” Jiang said. This is partly because too much focus has been on certain aspects of cancer and not on others.

In culture, leader cells grow out in different directions (left) while follower cells grow and expand (right). Photo credit: Karthika Swamy Cohen.
In the healthy condition, the human body is in homeostasis, which insures that the body’s internal environment—including body temperature, blood pressure, pH and chemical concentrations—is in a stable state. When an invasive species attacks the body, the chances of its survival are very low. The invading cells need to have just the right composition to adapt to the body’s internal environment.

Cell migration plays a crucial role in the spread of cancer. There are two types of migration: collective invasion where a pack of cells starts to invade out as a single unit, and single cell invasion. The chance of metastatic success is much higher with collective invasion. Heterogeneity among different cells in the tumor contributes to metastasis and promotes invasion.

Recent work suggests that two cell phenotypes with a symbiotic relationship are crucial to migration: “Leader” cells at the edge of colonies and “follower” cells, led by leader cells.

Jiang's group uses a method called spatiotemporal genomic and cellular analysis (SaGA) to study cell migration and metastasis. Based on empirical observations, her group has shown that leader cell migration outward from the tumor leads a stream of follower cells, each stream with one leader and each leader leading a stream. Disconnecting the leader leads to retraction of the stream. Leader cells blaze the trail for followers, leading via finger-like protrusions.

While leader cells are highly migratory and non-proliferative, follower cells are non-migratory and highly proliferative. Follower cells benefit from the nutrient-rich atmosphere outside the cell pack and leader cells gain an advantage from supportive chemicals secreted by follower cells.

The pack of cells functions as an ecosystem and exhibits many characteristics of ecosystems, such as social interactions, division of labor, symbiosis, and collective decision making.

Jiang’s study revealed that leader cells are only capable of giving rise to more leader cells - they can be cloned in the lab to produce more leader cells. Leader and follower cells are seen to behave differently when separated from each other, showing that the cell-to-cell interaction is essential for behaviors seen in cell packs.

When grown in cell cultures, leader cells are seen to spread out as they would in a pack; they do not exhibit growth. In fact, leader cells have mitotic defects, which prevents growth. Follower cells, on the other hand, can grow in cell cultures.

If leader cells are transferred to the growth medium of follower cells, these defects correct, and leader cells begin to grow. Follower cells, however, die when transferred to the medium of leader cells.

It's still not known why leader cells lead at the expense of their own cell growth, and it’s almost tempting to suggest that the cells are altruistic, not caring about growth but contributing to collective cell invasion by leading follower cells, said Jiang. 

Jiang's group uses the Cellular Potts model, which models cells as domains of same numbers on a lattice. The model allows the team to characterize the adhesion properties of cells, which are seen to be type dependent. All cells are seen to respond to a chemical gradient by chemotaxis.

Collective invasion seems to emerge from both differential adhesion between cells and chemotactaxis exhibited by the leaders.

If a leader cell breaks off, the growth of that finger becomes stunted, and follower cells cease to migrate. As expected, leader cells in culture migrate in different directions, and follower cells grow out. But in one case, Jiang and her team found two leader cells, which—instead of forming two fingers—formed just a single protrusion, until one of the leader cells fell off.  The reason for the leader cell breakoff is unknown, but one possible explanation for the presence of a single leader in each pack is that leader-leader cell adhesions are weaker than leader-follower adhesions.

Jiang and her group then looked at interactions among cells as well as interactions between cells and their environment. As cells migrate, they change structure locally and align fibers. To look at interactions, the researchers extracted the fibers and made local alignment measurements, measuring the angle locally for a desirable area size. With these measurements, they calculated the direction of local alignment. The amplitude is given by the sum of all alignments, which in turn gives the alignment distribution field.

The team discovered that cells exhibiting the most local alignment displayed the most invasiveness, since alignment leads to more migration. 

Jiang and her team found that a surprisingly small number of features—including biased migration, adhesion, and proliferation—need to be fulfilled in order to accomplish the leader-follower stream resulting in tumor invasion. 

   Karthika Swamy Cohen is the managing editor of SIAM News.
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