MATHEMATICAL BIOLOGY
The Math That Tells Cells What They Are
During development, cells seem to decode their fate through optimal information processing, which could hint at a more general principle of life.
Cells in embryos need to make their way across a “developmental landscape” to their eventual fate. New findings bear on how they may do this so efficiently.
Adrian du Buisson for Quanta Magazine
In 1891, when the German biologist Hans Driesch split two-cell sea urchin embryos in half, he found that each of the separated cells then gave rise to its own complete, albeit smaller, larva. Somehow, the halves “knew” to change their entire developmental program: At that stage, the blueprint for what they would become had apparently not yet been drawn out, at least not in ink.
Since then, scientists have been trying to understand what goes into making this blueprint, and how instructive it is. (Driesch himself, frustrated at his inability to come up with a solution, threw up his hands and left the field entirely.) It’s now known that some form of positional information makes genes variously switch on and off throughout the embryo, giving cells distinct identities based on their location. But the signals carrying that information seem to fluctuate wildly and chaotically — the opposite of what you might expect for an important guiding influence.
“The [embryo] is a noisy environment,” said Robert Brewster, a systems biologist at the University of Massachusetts Medical School. “But somehow it comes together to give you a reproducible, crisp body plan.”
I don’t think optimization is an aesthetic or philosophical idea. It’s a very concrete idea.
William Bialek, Princeton University
The same precision and reproducibility emerge from a sea of noise again and again in a range of cellular processes. That mounting evidence is leading some biologists to a bold hypothesis: that where information is concerned, cells might often find solutions to life’s challenges that are not just good but optimal — that cells extract as much useful information from their complex surroundings as is theoretically possible. Questions about optimal decoding, according to Aleksandra Walczak, a biophysicist at the École Normale Supérieure in Paris, “are everywhere in biology.”
Biologists haven’t traditionally cast analyses of living systems as optimization problems because the complexity of those systems makes them hard to quantify, and because it can be difficult to discern what would be getting optimized. Moreover, while evolutionary theory suggests that evolving systems can improve over time, nothing guarantees that they should be driven to an optimal level.
Yet when researchers have been able to appropriately determine what cells are doing, many have been surprised to see clear indications of optimization. Hints have turned up in how the brain responds to external stimuli and how microbes respond to chemicals in their environments. Now some of the best evidence has emerged from a new study of fly larva development, reported recently in Cell.
Cells That Understand Statistics
For decades, scientists have been studying fruit fly larvae for clues about how development unfolds. Some details became apparent early on: A cascade of genetic signals establishes a pattern along the larva’s head-to-tail axis. Signaling molecules called morphogens then diffuse through the embryonic tissues, eventually defining the formation of body parts.
Particularly important in the fly are four “gap” genes, which are expressed separately in broad, overlapping domains along the axis. The proteins they make in turn help regulate the expression of “pair-rule” genes, which create an extremely precise, periodic striped pattern along the embryo. The stripes establish the groundwork for the later division of the body into segments.
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