Mathematical Model Explains How Biological Filaments Grow Straight Despite Random Fluctuations
Researchers have developed a mathematical model explaining how growing biological filaments — such as those found in cells and tissues — maintain straight trajectories despite stochastic noise. The study uses linear stability analysis to evaluate how feedback based on strain, curvature, and orientation can stabilize filament growth, finding that local feedback requires orientation sensing while nonlocal feedback can work through curvature sensing alone. The findings offer a minimal theoretical framework for understanding morphogenesis and suggest experimental tests to identify which feedback mechanisms operate in real biological systems.
A new preprint posted to arXiv investigates how biological filaments achieve reproducibly straight growth in the presence of inherent stochastic fluctuations. The authors construct a minimal elastic filament model in which growth rates respond to local or nonlocal feedback signals — specifically the filament's strain, curvature, and orientation. Linear stability analysis reveals that purely local feedback is insufficient to suppress long-wavelength instabilities unless the filament can sense its own orientation, whereas nonlocal feedback enables stabilization through proprioceptive curvature sensing alone. Coupling the filament to an elastic substrate provides an additional mechanism for damping large-scale deviations. The work establishes a set of minimal control strategies sufficient for robust straight growth and proposes experimental signatures — observable differences in fluctuation spectra or growth patterns — that could help biologists determine which feedback mechanisms are active during morphogenesis in specific organisms or cell types.
What's missing
The model is theoretical and has not yet been validated against specific experimental biological systems. The study also does not address how the model performs in three dimensions.
What different sources said
- arXiv physicsCenter
How to grow a straight filament
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