---
title: "ATP Molecular Motor Interactive Lab | Sandbox Physics"
description: "How does ATP drive a molecular motor against a load? ATP reactions maintain a chemical imbalance that favors forward cycles."
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---

FR19-C · Chemistry takes a step

# ATP Molecular Motor

**How does ATP drive a molecular motor against a load?** ATP reactions maintain a chemical imbalance that favors forward cycles. An opposing load makes each forward step cost mechanical work and increases the relative chance of backward motion. At stall, forward and backward steps can continue even when their average motion cancels.

Pull back on a motor carrying a bead in an ideal force clamp. Watch its random steps slow, reverse near stall, or disappear into a narrow-band detector trace.

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

Model assumptions

A reversible two-state teaching network couples one ATP reaction to an eight-nanometer period. Rates and the equilibrium ATP concentration are illustrative, with fixed ADP and phosphate reservoirs. An ideal external force clamp sets the motor load; a passive bead and sampled one-pole detector model observation. The motor rates use that imposed load rather than fluctuating linker tension. Detachment, futile cycles, head mechanics and feedback errors are omitted. All records are simulated.

Synthetic four-second record

## Which steps reach the detector?

Hidden motor position Sampled thermal bead Detector output

Chemical state A Before / after load step $v_{\rm ss}=100\,\mathrm{nm\,s^{-1}}$

How the speed was inferred

The primary fitted speed is a straight-line least-squares fit to detector positions, excluding the first tenth of a second and, for a force step, the first tenth after that step. The two segment fits and both stationary network predictions are saved. A single short trajectory has stochastic uncertainty; agreement is judged across repeated records.

The cyan trajectory and step counts are simulation truth. They are not inferred from the detector. The saved record includes all reversible reaction events, raw bead samples, filtered samples, seed, rate constants, protocol and model version.

$\mathcal A=6.29$

[Continue the single-molecule course](https://sandboxphysics.com/stories/single-molecule/)

Physics tutorial

## ATP Molecular Motor

**Background** A motor attached to a bead can advance along a molecular track even when a force pulls the bead backward. Its individual steps occur at irregular times.

**Why it matters** A smooth bead trace can hide many molecular steps. To connect chemistry to motion, follow both a reversible reaction cycle and the detector that observes it.

Start with the essentials

- **Focus question**: How does ATP drive a molecular motor against a load?
- **One-sentence intuition**: ATP biases a reversible cycle forward; an opposing load biases it backward.

### Core mathematical model

#### The two reactions in one spatial period

$$
A_n\mathop{\rightleftharpoons}^{u_0}_{w_0}B_n\mathop{\rightleftharpoons}^{u_1}_{w_1}A_{n+1}
$$

The first reaction exchanges chemical free energy with ATP, ADP and phosphate reservoirs. The second moves the motor by eight nanometers. Both have reverse reactions. The drawn lobes mark the motor; they do not resolve a two-head gait.

#### How chemistry and force compete

$$
\ln\frac{u_0u_1}{w_0w_1}=\ln\frac{c_{\rm ATP}}{c_{\rm eq}}-\frac{Fd}{k_{\rm B}T}
$$

Load is positive when it opposes motion to the right. The chemical reservoirs set the ATP equilibrium concentration to the illustrative value 0.01 micromolar. A positive cycle affinity favors forward cycles; a zero affinity balances their long-time currents.

#### Stall in a tightly coupled teaching network

$$
F_{\rm stall}=\frac{k_{\rm B}T}{d}\ln\frac{c_{\rm ATP}}{c_{\rm eq}}
$$

At stall, net speed and output power vanish, but individual forward and backward steps continue. Real motors may keep hydrolyzing ATP at stall through additional reaction cycles; those cycles are absent here.

### Common difficulties

#### A stalled motor still fluctuates

**Typical misconception** Zero speed means that every chemical reaction and every molecular step has stopped.

**Better mental model** Zero speed is a statement about the difference between forward and backward step currents. The network can keep making steps in both directions. At equilibrium each edge balances separately; a finite record still fluctuates.

### Run the experiment

1. 01

   #### Predict the effect of pulling harder

   Start with Clear forward steps. Drag the gold force-clamp ring to the left, or increase Opposing load. Keep ATP concentration fixed.

   **What to observe:** The model stall load stays fixed while forward motion slows. Near that load, a finite trace can drift either way because the two random step currents nearly cancel.

2. 02

   #### Let the detector hide the steps

   Compare Clear forward steps and Blurred steps. They share the same seed, ATP concentration and load; only Detector bandwidth changes.

   **What to observe:** The cyan motor trajectory is unchanged. The gold detector trace smooths short plateaus and lags behind sudden jumps. The fitted speed uses only the saved gold samples.

3. 03

   #### Test a new load protocol

   Choose A sudden heavier load. Predict the direction of motion after two seconds, then compare both halves of the saved record with the two steady-load predictions.

   **What to observe:** The reaction rates change at the load step. The bead also shifts backward as its elastic linker takes up the larger force, so the short mechanical transient should be excluded from a long-time drift fit.

Physical conclusion

Compare chemical driving, applied load and detector bandwidth before interpreting a bead trace as a motor trajectory.

## Related experiments and articles

Single-molecule forces and motors · Reading path

### Thermal motion, molecular elasticity, unfolding and motors

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

1. [Article **How ATP gives random transitions a direction**](https://sandboxphysics.com/stories/single-molecule/chemical-motor/)
2. [Article **What remains measurable when steps blur together?**](https://sandboxphysics.com/stories/single-molecule/hidden-steps/)
3. [Article **Can a motor model predict a new load protocol?**](https://sandboxphysics.com/stories/single-molecule/predicting-protocols/)
4. [Lab **Stochastic Unfolding Force Spectroscopy** Transfer the prediction test to unfolding](https://sandboxphysics.com/labs/stochastic-unfolding-force/)

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)