D’Arcy Thompson at 100: Controlling Cell Shape and Function

Polarization microscopy images of Bacillus subtilis sacculi, with color indicating slow axis orientation. This shows that cell wall material is inserted around the rod width. Image: Ethan Garner

Even though it was published more than a century ago, D’Arcy Thompson’s seminal work, On Growth and Form, continues to fascinate anyone studying living organisms today, especially cell biologists. Thompson’s application of mathematical concepts and formulas to how living things grow and the shapes that they assume has inspired not only biologists, but physicists, mathematicians, and artists to take a more systematic approach to figure out how the structure of living things comes about. The Symposium “D’Arcy Thompson at 100: Controlling cell shape and function,” to be held December 11 at the 2019 ASCB|EMBO Meeting, will explore the latest findings in our understanding of cell growth and developmental biology.

First, let’s learn a bit more about D’Arcy Thompson. Born in 1860, Thompson was a mathematical biologist who became the first chair of biology at what was then called the University of Dundee in Scotland. He amassed a huge collection of biological specimens from around the world, especially aquatic animals, as a scientific adviser to the Fisheries Board of Scotland. Thompson noticed patterns of growth emerging as he studied each animal. Rather than focus on Darwinism in his investigations, Thompson centered his work on physical laws and mechanics. This created the thesis from which Thompson crafted On Growth and Form, published in 1917.¹

Cell Shape and Self-Organizing Systems

Symposium organizer Ethan Garner, professor of Molecular and Cellular Biology at Harvard, studies the molecular mechanisms controlling the spatial and temporal coordination of bacterial growth and division. “Thompson’s work has influenced biologists to reframe their approaches to be more quantitative. Perhaps more importantly, it also attracted a large number of physicists and mathematicians to these problems, bringing in new perspectives,” Garner said. He plans to present the talk “How Cell Shape Arises—The Minimal, Self-Propagating Systems that Create Rod Shaped Cells and Determine Their Width.”

Garner hopes attendees gain an understanding that cell shape, just like all other spatial biological processes, arises from simple self-organizing systems. “These systems need not be complex. In bacteria spatial sensing and formation are accomplished using only a few interacting components, a simplicity that is often obscured when studying similar eukaryotic processes,” he said.

Cells Self-Organizing

Developmental biologist Jennifer Zallen, HHMI investigator and professor at Memorial Sloan Kettering Cancer Center and co-organizer of the Symposium, will present the talk “Signals, Forces, and Cells: Decoding Tissue Morphogenesis.”

Zallen, who uses Drosophila embryos as her model organism, is studying how large populations of cells intercalate and arrange themselves into the complex structures found in a complete organism. “D’Arcy Thompson considered how beautiful shapes and patterns in biology are generated by forces acting at many levels, from the forces that position structures within cells, to the forces that generate cell shape and polarity, to the forces that dynamically organize cells in time and space,” said Zallen. “In my lab, we study how groups of cells self-organize to produce distinct structures during development.”

“Cells not only have different molecular signatures that allow them to recognize each other and assemble to build tissues,” Zallen continued, “they can also directly respond to forces generated by the cells around them—the push and pull of neighboring cells and tissues. This ability of cells to rapidly modulate their behavior in response to force provides a powerful mechanism that allows cells to correct variations during development and to detect and repair tissue damage in the adult.”

If D’Arcy Thompson Were with Us Now

The spirit of Thompson’s ideas has persisted in modern cell biology, whether it is acknowledged or not. What do researchers think Thompson would be studying if he were alive today?

“I’m sure D’Arcy Thompson would be doing what many groups are doing today,” said Garner, “running simulations using our vast computational power to see if mathematics could both describe and recapitulate different biological forms. My guess would be running simulations to see if he could recapitulate the different shapes of diatoms from different interacting rules.”

Garner added that Thompson’s contributions to the realm of cell mechanics help provide a different lens through which cell processes can be elucidated. “Recent and upcoming work is showing that mechanics play a role in smaller organisms. Both bacteria and archaea adjust their shape and gene expression in response to shear flow, tension, or pressure, and this causes changes in how they form into colonies or biofilms,” said Garner. “I’m most excited about how single cells, or groups of them, sense and respond to mechanical forces. I think this will not only be a key to understanding development in eukaryotes but also multicellularity in the other kingdoms.”

“This is an exciting time when we can now really begin to address these questions,” added Zallen, “not only by prodding cells in a dish, but also by using biophysical and live-imaging approaches to visualize and understand how forces affect cell behavior in real time, in response to the physiological pressures that cells experience in living organisms.”

“Personally, I think if Thompson were to see where we are now, he would be excited. Not by us having ‘solved’ or ‘understood’ any of these problems, but rather that we are primed to do so, with a lot of momentum in our interest, tools, and approaches,” Garner remarked. “I think that, like many of us, Thompson would say we do have a long way to go. Even for the simplest, most minimal systems we still don’t really know how they work; we still lack a full understanding of all the parts, how they interact, and their emergent properties. So currently, I think he’d say the mathematical models we make are good starts, but they are lacking and speculative until we further define these systems.”

Footnote

¹www.darcythompson.org.