Just as how fast your car moves depends on how well your wheels grip the road, the speed at which a cell moves depends on how well it attaches to the surface it moves on. Deciphering the specific mechanics of the complex interplay between surface and speed in cell movement can lead to a better understanding of basic biological processes, such as how cells move during development to form a full-sized organism, as well as pathological processes, such as how cancer cells radiate from an origin to metastasize.

Theoretical physicists at the Max Delbrück Center for Molecular Medicine in the Helmholtz Association (MDC) and experimental physicists at Ludwig Maximilians Universität München (LMU), have collaborated to develop a mathematical model that captures the precise mechanics involved in cell movement.

These findings are reported in the journal Proceedings of the National Academy of Sciences (PNAS), in an article titled “On the adhesion-velocity relation and length adaptation of motile cells on stepped Fibronectin lanes,” and provide new insight for developmental biology and potential cancer treatment.

“The mathematical model we developed can now be used by researchers to predict how different cells will behave on various substrates,” says Professor Martin Falcke, PhD, who heads MDC’s Mathematical Cell Physiology Lab and has co-led the research. “Understanding these basic movements in precise detail could provide new targets to interrupt tumor metastasis.”

Movement is a basic homeostatic tenet of maintaining unicellular and multicellular life, but it is especially important when newly born cells need to simultaneously educate themselves on their specialized roles (differentiation) and find their home in the correct tissues and organs (specification). Cells move for a variety of reasons. Immune cells move to a site of injury to repair wounds. Cancer cells infiltrate blood vessels to metastasize.

The experimental physicists, led by Joachim Rädler, PhD, have tracked the speed at which more than 15,000 cancer cells move along narrow fibronectin coated lanes where the stickiness alternates between low and high. The scientists then observe as the cells transition between stickiness levels, which represents the dynamic biological environment.

Behnam Amiri, a student in Falcke’s lab and co-first author on the paper, together with Falcke, have developed an equation that captures the dynamicity of all factors involved in cellular motility based on the large dataset of parameters measured as cells moved on the narrow lanes of alternating stickiness.

“Previous mathematical models trying to explain cell migration and motility are very specific, they only work for one feature or cell type,” Amiri says. “What we tried to do here is keep it as simple and general as possible.”

Cancer cells moving on glycoprotein coated strips (Source: Rädler Lab, Ludwig Maximilians Universität München)

The validity of this mathematical model is demonstrated by the fact that it not only matched the recent cell motility data gathered at LMU but also held true for motility measurements of several cell types taken over the past three decades.

“This is exciting,” Falcke says. “It’s rare that you find a theory explaining such a large spectrum of experimental results.”

Friction is key in any movement. When a cell moves, it simultaneously extends its membrane in the direction of movement and pulls forward while pushing off its membranes at the rear end. This dynamic wave of directed cellular motion is made possible through the orchestration of membrane cell-adhesion proteins that attach to the surface and internal actin cytoskeletal scaffolds that expand and contract accordingly. Without attachments to the surface the cell can neither pull forward not push off, and motion becomes impossible.

“When you are on ice skates you cannot push a car, only when there is enough friction between your shoes and the ground can you push a car,” Falcke says.

Martin Falcke, PhD, heads MDC’s Mathematical Cell Physiology Lab and has co-led this research (Source: David Ausserhofer / MDC)

Up to a certain point, the more the number of attachments a cell has to the surface, the easier it is to pull forward and push off, thereby increasing cellular velocity. However, as the surface becomes stickier, and the number of attachments increase, cells find it harder to push off at the rear end and their movement slows down and ultimately comes to a halt.

Employing strips of high and low stickiness, the authors were able to investigate cellular motion under the specific and biologically relevant condition when the surface at the front end of the cell is stickier than the rear end, and vice versa. The authors report that even when the stickiness of the surface is greater at the rear end, cells are still able to peel themselves off and move forward albeit at a slower pace.

“For me, the most challenging part was to wrap my mind around this mechanism working only with friction forces,” Falcke says, because there is nothing for the cell to firmly latch onto. But it is the friction-like forces that allow the cell to keep moving, even when bonds are stronger in the back than the front, slowly peeling itself off like scotch tape. “Even if you pull just a little with a weak force, you are still able to peel the tape off – very slowly, but it comes off,” Falcke says. “This is how the cell keeps itself from getting stuck.”

Future research efforts of the collaborative team are directed at investigating the dynamics of cell motility in two dimensions, including how cells turn right, left or around.

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