---
title: "Pulling a Membrane Tether Interactive Lab | Sandbox Physics"
description: "Why does a long membrane tube resist pulling with nearly constant force? A long tube settles at the radius where bending and membrane tension balance."
canonical_url: "https://sandboxphysics.com/labs/membrane-tether/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/membrane-tether/"
last_modified: "2026-10-28"
---

FR20 · Bending and pulling

# Pulling a Membrane Tether

**Why does a long membrane tube resist pulling with nearly constant force?** A long tube settles at the radius where bending and membrane tension balance. Adding another length then costs the same energy, so the static pulling force stays constant. Pulling at finite speed adds a drag force that relaxes when the trap stops.

Drag an optical trap to extend a preformed membrane tube. Watch the bead lag behind the trap, then let the pulling force settle as the tube grows.

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

Model assumptions

A preformed long cylindrical tether exchanges lipid with a flat reservoir at fixed tension. Bending rigidity and tension set its radius and static force. A linear trap and specified effective drag set the pulling dynamics. Pressure difference, spontaneous curvature, tube nucleation, neck mechanics, finite reservoir depletion and bead Brownian motion are omitted. Tube and bead dimensions share one length scale; the neck and reservoir edge are schematic. All traces are model simulations.

## Pulling faster costs extra force

Cyan: simulated trap force. Dashed amber: static cylinder force. The force falls back when the trap stops. The marker follows the frame above.

Force in piconewtons over time in seconds

How the pulling record is calculated

An exact linear propagator advances the bead under a stationary trap, a constant-speed pull and a final hold. Export includes all times, positions, forces, units and model version. The bead drag is a chosen teaching parameter, not a calibration of a specific instrument.

Physics tutorial

## A tube trades bending for area

**Background** An optical trap can hold a bead attached to a membrane tube. Moving the trap pulls membrane out of a much larger reservoir.

**Why it matters** The tube radius reveals a balance of bending and tension. The bead displacement measures the force needed to keep that tube growing.

Start with the essentials

- **Focus question**: Why does a long membrane tube resist pulling with nearly constant force?
- **One-sentence intuition**: Once a tube has a fixed radius, each extra length costs the same membrane energy.

### Core mathematical model

#### Energy per tube length

$$
E/L=\pi\kappa/r+2\pi\sigma r
$$

The first term penalizes a narrow, strongly curved tube. The second charges tension for the membrane area added to it.

#### Radius and static pulling force

$$
r_0=\sqrt{\kappa/(2\sigma)},\qquad f_0=2\pi\sqrt{2\kappa\sigma}
$$

Minimize the energy with respect to radius, then differentiate it with respect to length. These are the long-cylinder, zero-pressure results.

#### What the trap measures

$$
F=k_{\mathrm{trap}}(X-L),\qquad\zeta\dot L=F-f_0
$$

Trap position and tube end position use the same axial origin; a constant bead-radius offset is suppressed in both. The specified drag turns excess trap force into tube motion.

### Common difficulties

#### A plateau and a moving bead

**Typical misconception** The optical force must always equal the static tube force.

**Better mental model** During a finite-speed pull, the bead needs extra force to overcome drag. When the trap stops, the bead catches up and the force relaxes.

### Run the experiment

1. 01

   #### Watch the bead lag

   Watch A growing tube, then pause during the pull.

   **What to observe:** The amber trap centre sits ahead of the cyan bead. Their separation sets the force in the trace below.

2. 02

   #### Change tension

   Choose Tension makes a thin tube.

   **What to observe:** The tube becomes thinner and its static pulling force rises.

3. 03

   #### Move the trap yourself

   Drag the amber trap handle, then release it.

   **What to observe:** The bead follows with a delay, then settles at the displacement required by the static force.

Physical conclusion

Membrane mechanics sets the plateau; the trap and dissipation shape the approach to it.

## Related experiments and articles

Membranes and vesicles · Reading path

### From curvature to active membrane measurements

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

1. [Article **The force needed to pull a membrane tube**](https://sandboxphysics.com/stories/membrane-mechanics/membrane-tethers/)
2. [Lab **Optical Tweezers: Brownian Calibration** Study an independent probe calibration](https://sandboxphysics.com/labs/optical-tweezers-calibration/)
3. [Article **Reading from a tube formula to an active-membrane paper**](https://sandboxphysics.com/stories/membrane-mechanics/paper-reading/)
4. [Lab **Measuring a Flickering Membrane** Preserve a reproducible observation](https://sandboxphysics.com/labs/membrane-fluctuations/)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

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