A simple analytical formula for the free-energy of ligand-receptor mediated interactions

TL;DR

This paper derives a simple analytical formula for ligand-receptor mediated interaction free energy, reducing computational effort and enhancing understanding of colloidal interactions, especially in DNA-coated colloids.

Contribution

The authors present a new, simplified analytical expression for the interaction free energy, making calculations more efficient and transparent compared to previous numerical methods.

Findings

Analytical formula reduces computational cost

Provides insight into limiting cases of interactions

Connects general theory to previous approaches

Abstract

Recently \1, we presented a general theory for calculat- ing the strength and properties of colloidal interactions mediated by ligand-receptor bonds (such as those that bind DNA-coated colloids). In this communication, we derive a surprisingly simple analytical form for the inter- action free energy, which was previously obtainable only via a costly numerical thermodynamic integration. As a result, the computational effort to obtain potentials of in- teraction is significantly reduced. Moreover, we can gain insight from this analytic expression for the free energy in limiting cases. In particular, the connection of our general theory to other previous specialised approaches is now made transparent. This important simplification will significantly broaden the scope of our theory.