Growth and remodeling control shape memory in morphogenetic rods

Imagine trying to build a sandcastle on a beach where the tide is constantly rising and the wind is blowing sand grains in every direction. This is the daily reality for living things trying to grow. From the way a fruit fly embryo twists into its final shape to how a plant stem curls toward the sun, nature is constantly trying to build complex, 3D structures out of soft, squishy materials. But there's a catch: these materials are messy. They are full of tiny, random jitters—like static on a radio or the chaotic bumping of molecules—that can easily ruin a delicate design. Scientists have long wondered how living things manage to build such precise, reproducible shapes when their building blocks are so noisy and prone to collapsing into the simplest, boring shapes possible. It's a bit like trying to fold a piece of paper into an origami crane while someone is shaking the table and the paper is slowly turning into water.

To solve this puzzle, researchers often look at "rods"—long, thin structures that act like the skeletons of organs or stems. These rods have a natural tendency to buckle or bend when they get too long, much like a wet noodle or a long piece of spaghetti. Usually, if you let a buckled noodle sit, it just relaxes into a simple curve, forgetting any fancy twists you tried to give it. This paper asks a big question: How do living systems keep their complex, wiggly shapes from smoothing out into boring curves, even when they are being shaken by random noise? The answer lies in a delicate dance between three things: how fast the rod grows, how "squishy" or adaptable the material is (a property called plasticity), and how much random noise is trying to mess things up.

The authors of this study, Nicolas Romeo, David B. Brückner, and Noah P. Mitchell, built a mathematical model to simulate these growing, wiggly rods. They treated the rod like a special kind of "morphodynamic" material that can change its own memory. Imagine a piece of clay that, if you leave it alone, slowly forgets the shape you just molded it into and settles into its own default, relaxed state. The researchers wanted to see if they could use this "forgetting" ability to their advantage. They found that the answer is a bit of a Goldilocks story: too little "forgetting," and the rod snaps back to a simple shape; too much "forgetting," and the random noise gets baked into the shape, turning it into a messy blob. But, they discovered a magic trick: if the rod grows fast enough, it can break this rule.

Here is what they found. First, they looked at what happens when a rod just sits there without growing. If the material is perfectly stiff (like hard plastic), any complex shape you give it will eventually relax into the simplest possible curve. They call this "elastic coarsening." It's like a crumpled piece of paper slowly smoothing itself out until it's just a flat sheet. To stop this, the material needs to be a little bit "plastic"—meaning it needs to be able to slowly remodel itself to match its current shape. If the remodeling happens at just the right speed, it freezes the complex shape in place before it can smooth out. This is the "just right" zone where the shape is preserved.

However, there is a second problem. If the material is too plastic (like very runny honey), it becomes too sensitive to the random noise. The tiny, random jitters get trapped in the material's memory, turning the rod into a chaotic, disordered mess. The authors showed through their simulations that there is a trade-off: you need enough plasticity to stop the shape from smoothing out, but not so much that the noise ruins the pattern. This creates a narrow window where a shape can be remembered, but only if the shape isn't too complicated.

The real breakthrough comes when you add growth. The authors simulated the rod getting longer, like a plant stem stretching toward the sun. They found that growth acts like a superpower that solves both problems at once. As the rod grows, it naturally suppresses the tendency to smooth out into a simple curve. At the same time, growth dilutes the effect of the random noise, making the noise less likely to ruin the pattern. In their simulations, they found that if you combine fast growth with a high rate of remodeling, you can create complex, reproducible shapes that would otherwise be impossible.

In short, the paper suggests that living systems don't just rely on being stiff or being soft; they rely on a specific combination of growing fast and remodeling their structure at an optimal rate. This allows them to "remember" their initial patterned instructions despite the chaos of noise and the tendency to collapse into simple shapes. The authors used computer simulations to show that this works, and they even derived mathematical formulas to predict exactly how fast the growth and remodeling need to be to keep a specific shape. While this is currently a model of a single rod, the authors suggest this principle could explain how complex organs, like the loops in a gut or the folds in a brain, manage to form so reliably in the messy, noisy world of a developing embryo. It turns out that to build something complex, you sometimes have to grow fast and be willing to change your mind just enough to hold onto the shape, but not so much that you forget it entirely.