Overview

This project focuses on quantitative analysis of Atomic Force Microscopy (AFM) force–distance curves acquired from protein samples.
The goal is to extract meaningful interaction parameters by fitting experimental data to the Lennard–Jones (LJ) potential, a standard model for intermolecular forces.

The workflow combines AFM data preprocessing, numerical modeling, and nonlinear curve fitting to study nanoscale protein–surface interactions.

Problem Statement

AFM force–distance measurements often contain:
- noise and instrumental artifacts,
- non-linear interaction regimes,
- difficulty in extracting physical parameters directly.

Interpreting these curves in a physically meaningful way requires:
- a robust preprocessing pipeline,
- a suitable interaction model,
- stable parameter estimation.

Approach

The analysis pipeline:
- Imports and preprocesses AFM force–distance data
- Identifies relevant interaction regions
- Models tip–sample interaction using the Lennard–Jones potential
- Performs curve fitting to estimate interaction parameters
- Visualizes experimental vs fitted curves for validation

The fitting enables estimation of:
- equilibrium distance,
- interaction strength,
- repulsive and attractive force regimes.

Mathematical Model

The Lennard–Jones potential used in this project is given by:

$$
U(r) = 4\epsilon \left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6\right]
$$

Where:
- $r$ is the tip–sample separation
- $\epsilon$ represents interaction strength
- $\sigma$ is the equilibrium distance parameter

Force curves are derived from the gradient of the potential and fitted to experimental AFM data.

Technologies Used

• Python
• NumPy
• SciPy (optimization + curve fitting)
• Matplotlib (visualization)
• Jupyter Notebook

Results

• Successful fitting of AFM force–distance curves using an LJ model
• Clear separation of attractive vs repulsive interaction regimes
• Physically interpretable parameters extracted from experimental data

How to Run

1. Clone the repository:
   bash git clone https://github.com/mohdrafik/Protein-AFM-Analysis-and-Lennard-Jones-potential-fitting