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arxiv: 2606.11080 · v1 · pith:PELTHINYnew · submitted 2026-06-09 · ❄️ cond-mat.soft · physics.bio-ph

How to grow a straight filament

Ludwig A. Hoffmann , L. Mahadevan This is my paper

Pith reviewed 2026-06-27 11:20 UTC · model grok-4.3

classification ❄️ cond-mat.soft physics.bio-ph
keywords growing filamentmorphogenesisfeedback controlelastic stabilitystochastic growthproprioceptionnonlocal feedbacklinear stability analysis
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The pith

Nonlocal feedback stabilizes straight growth of a noisy filament using curvature sensing alone.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets up a minimal model of an elastic filament whose growth rate at each point depends on its strain, curvature, and orientation, with the dependence allowed to be either strictly local or spread over space and time. Linear stability analysis of the straight state shows that additive noise excites long-wavelength bends unless the local feedback rule also senses absolute orientation; a nonlocal rule removes this requirement and stabilizes the filament through curvature sensing only. Attachment to an elastic substrate supplies an extra restoring force that damps the remaining large-scale fluctuations. These results identify the smallest sets of sensory and regulatory rules sufficient for reproducible straight morphogenesis. A reader cares because the same rules could explain how cells and tissues achieve precise linear shapes without central coordination.

Core claim

We formulate a minimal model in which growth responds to the filament's strain, curvature, and orientation through local or nonlocal spatiotemporal feedback laws. Linear stability analysis identifies the conditions under which these feedback mechanisms stabilize a straight configuration. In the presence of noise, we show that purely local feedback requires orientation sensing to suppress long-wavelength instabilities, whereas nonlocal feedback allows stabilization through proprioceptive (curvature) sensing alone. Coupling to an elastic substrate further suppresses large-scale fluctuations.

What carries the argument

Minimal model of growth regulated by local or nonlocal spatiotemporal feedback on strain, curvature, and orientation.

If this is right

  • Straight growth is possible with curvature sensing alone when feedback is nonlocal.
  • Local feedback always needs an extra orientation channel to eliminate long-wavelength instabilities.
  • Elastic coupling to a substrate damps the remaining large-scale fluctuations.
  • The two feedback classes produce distinct experimental signatures that can be used to identify the mechanism in real systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same distinction between local and nonlocal rules may apply to other linear biological structures such as roots or hyphae.
  • Varying the spatial range of feedback experimentally should produce a sharp transition from unstable to stable growth.
  • The model predicts that noise amplitude and feedback range together set a critical wavelength below which bends are suppressed.
  • Nonlinear extensions could reveal whether the straight state remains attracting once large deflections appear.

Load-bearing premise

The growth rate at each point is set by a linear combination of the filament's local strain, curvature, and orientation, with the combination allowed to be local or nonlocal.

What would settle it

Direct observation of a biological filament that grows straight using only local curvature feedback and no orientation sensing would falsify the necessity of orientation input for local rules.

Figures

Figures reproduced from arXiv: 2606.11080 by L. Mahadevan, Ludwig A. Hoffmann.

Figure 1
Figure 1. Figure 1: The most common interoceptive mechanisms in this context are proprioception (sensing one’s own shape) and strain sensing. The former has been shown to be re￾quired for the straight growth of plant shoots and verte￾brate spines [9–13], as well as for posture control [14– 16]; see [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Theoretical model. (a) Sketch of an elastic fila￾ment in two-dimensional space (x, z) described by the coor￾dinate s. The filament’s orientation is described by an angle θ(s) and it can grow in-line (ϵg) and out-of-line (κg). The filament is coupled to a substrate at height w = 0 through “springs” of stiffness k (see Eq. (1)), and there is a preferred orientation θp. (b) Sketch of our framework, in which a… view at source ↗
Figure 3
Figure 3. Figure 3: Local, instantaneous feedback. (a) The real (top) and imaginary (bottom) parts of the eigenvalues for dif￾ferent parameter values, with fϵ = gθ = 1, obtained from the stability matrix given by Eq. (7). The coefficients fi and gi denote feedback from the state variables i ∈ {ϵ, θ, κ} onto axial and curvature growth, respectively. ¯fi ∝ figϵ is the rescaled parameter with “coupling” gϵ. (b) The stability dia… view at source ↗
Figure 4
Figure 4. Figure 4: Nonlocal feedback. (a) Stability diagram for nonlocal feedback in the limit where local feedback is negligi￾ble (fi = gi = 0), with φ¯κ = φκγϵ rescaled by the “coupling” γϵ. We choose φϵ = 1 here; see SM Sec. SIV for a differ￾ent choice. The axes γκ and φ¯κ denote the strengths of the nonlocal feedback by which the system’s curvature regulates the growth fields. (b) Stability diagram assuming equal mag￾nit… view at source ↗
read the original abstract

How can a growing biological filament remain straight despite stochastic fluctuations in growth? Motivated by filamentary structures that develop reproducibly across biological systems, we study the stability of a noisy, growing elastic filament regulated by feedback. We formulate a minimal model in which growth responds to the filament's strain, curvature, and orientation through local or nonlocal spatiotemporal feedback laws. Linear stability analysis identifies the conditions under which these feedback mechanisms stabilize a straight configuration. In the presence of noise, we show that purely local feedback requires orientation sensing to suppress long-wavelength instabilities, whereas nonlocal feedback allows stabilization through proprioceptive (curvature) sensing alone. Coupling to an elastic substrate further suppresses large-scale fluctuations. Our results establish minimal control strategies that ensure robust straight growth and suggest experimental signatures for identifying the feedback mechanisms underlying morphogenesis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The paper claims that a minimal model of a growing elastic filament regulated by local or nonlocal feedback on strain, curvature, and orientation can be analyzed for stability using linear stability analysis. In the presence of noise, purely local feedback requires orientation sensing to suppress long-wavelength instabilities, whereas nonlocal feedback allows stabilization through proprioceptive (curvature) sensing alone. Coupling to an elastic substrate further suppresses large-scale fluctuations. The results establish minimal control strategies for robust straight growth and suggest experimental signatures.

Significance. If the result holds, the paper is significant for providing a theoretical framework to understand how biological filaments maintain straight growth despite stochastic fluctuations. The distinction between local and nonlocal feedback mechanisms offers insights into the role of sensing in morphogenesis. The identification of minimal strategies and experimental signatures is valuable for the field of soft matter and biophysics.

minor comments (1)
  1. [Abstract] The abstract provides a high-level description of the linear stability analysis and noise model but does not include specific equations or the form of the feedback laws, which would help readers assess the claims immediately.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary of our work and for recommending minor revision. The assessment correctly identifies the key distinctions between local and nonlocal feedback mechanisms and their implications for stabilizing straight growth under noise. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; model and analysis are self-contained

full rationale

The paper formulates a minimal model of growth response to strain/curvature/orientation via local or nonlocal feedback, then applies linear stability analysis to derive stabilization conditions under noise. No load-bearing step reduces by construction to its inputs, no self-citation chains justify uniqueness or ansatzes, and no fitted parameters are relabeled as predictions. The derivation chain begins from the stated physical model and proceeds mathematically without circular reduction, consistent with the reader's assessment of score 2.0.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, additional axioms, or invented entities are stated. The central modeling choice is treated as a domain assumption.

axioms (1)
  • domain assumption Growth rate of the elastic filament responds to its strain, curvature, and orientation via local or nonlocal spatiotemporal feedback laws.
    This is the explicit starting formulation of the minimal model given in the abstract.

pith-pipeline@v0.9.1-grok · 5653 in / 1180 out tokens · 30129 ms · 2026-06-27T11:20:18.646003+00:00 · methodology

discussion (0)

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