---
title: "Contractile cortex and feedback Interactive Lab | Sandbox Physics"
description: "How can contraction gather more material, and what happens when one region stops pulling?"
canonical_url: "https://sandboxphysics.com/labs/mechanochemical-cortex/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/mechanochemical-cortex/"
last_modified: "2026-10-28"
---

FR21 · Active material

# Contractile cortex and feedback

**How can contraction gather more material, and what happens when one region stops pulling?** A denser patch can pull the surrounding cortex inward and carry more material into itself. Diffusion and turnover oppose this feedback; locally suppressing active stress changes the flow and density together.

Watch a cortex gather into dense bands. Move a local inhibitor around the ring and compare the response with an untouched copy.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

This is a dimensionless one-dimensional active viscous layer on a fixed periodic ring, with density transport and turnover. Ring thickness indicates density; the ring does not deform. Inhibition reduces active stress and does not sever the material. Elastic storage, anisotropy and biochemical oscillators are omitted.

Cyan: material density Amber: inhibition location

Fixed ring · thickness represents density · arrows show calculated flow

Time $4.00$

Density variation $0.200$

Peak flow speed $0.100$

Mean density $1.00$

### Density around the ring

Cyan is the current ring. Dashed gray is an untouched copy advanced from the same state. Amber marks the inhibited region.

### Does a local release change the pattern?

Both curves are computed trajectories. A change in active pulling can alter the density even though local reaction rates stay the same.

Physics tutorial

## Contractile cortex and feedback

**Background** A dense patch of active material pulls more strongly. Its pull creates a flow, and that flow can bring still more material into the patch.

**Why it matters** Changing the pulling force gives a direct test of this feedback. Compare the same evolving density with and without local inhibition.

Start with the essentials

- **Focus question**: How can contraction gather more material, and what happens when one region stops pulling?
- **One-sentence intuition**: Contractile feedback can amplify a density variation even with simple local turnover. Diffusion and renewal compete with the gathering flow.

### Core mathematical model

#### Stress drives an overdamped flow

$$
\sigma=\eta\,\partial_x v+\zeta I(x)\frac{c}{1+c},\qquad\partial_x\sigma=\xi v
$$

The density, time and coordinate are dimensionless. Viscous stress and saturating active stress add. Friction balances their spatial gradient; inertia is omitted.

#### Density moves, diffuses and renews

$$
\partial_t c=-\partial_x(cv)+D\partial_x^2c+k(1-c)
$$

The ring is periodic. Transport conserves total material; turnover exchanges material with a uniform reservoir. With turnover off, the mean density is conserved even during inhibition.

#### Growth of a small density wave

$$
\lambda(q)=\frac{\zeta q^2}{4(\xi+\eta q^2)}-Dq^2-k
$$

This expression follows by linearizing about unit density with no inhibition. It predicts whether a small spatial ripple grows before nonlinear saturation matters.

### Common difficulties

#### Inhibition leaves the ring connected

**Typical misconception** The amber mark is a cut in the material.

**Better mental model** The marker multiplies local active stress by a smooth suppression profile. Material can still flow across it. A real cut would need new free-edge conditions.

#### The ring thickness is a density scale

**Typical misconception** A thicker patch means the whole cell has deformed by that amount.

**Better mental model** The periodic coordinate and radius stay fixed. Thickness encodes density, and the arrows show computed tangential flow. Cell shape is outside this one-dimensional model.

### Run the experiment

1. 01

   #### Release one region

   Choose Release one region. Move the amber handle and compare the cyan profile with the dashed reference.

   **What to observe:** The two trajectories separate because only one ring has its local active stress reduced. No reaction parameter has changed.

2. 02

   #### Make a prediction at stronger friction

   Reset, choose Stronger friction, then inhibit the highlighted region with the same strength and width.

   **What to observe:** Friction changes the flow that redistributes density. This second condition tests a mechanical prediction beyond a single final pattern.

Physical conclusion

This is a dimensionless one-dimensional active viscous layer on a fixed periodic ring, with density transport and turnover. Ring thickness indicates density; the ring does not deform. Inhibition reduces active stress and does not sever the material. Elastic storage, anisotropy and biochemical oscillators are omitted.

## Related experiments and articles

Morphogenesis and reaction–diffusion · Reading path

### Reaction, diffusion, growth and active stress

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **How contraction draws more material together**](https://sandboxphysics.com/stories/morphogenesis/contractile-cortex/)
2. [Article **Test a pattern mechanism with an intervention**](https://sandboxphysics.com/stories/morphogenesis/testing-mechanisms/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)