# Restriction enzymes use a 24 dimensional coding space to recognize 6 base long DNA sequences

## TL;DR

This paper uses information theory and high-dimensional sphere packing concepts to explain how restriction enzymes recognize DNA sequences, revealing that EcoRI operates in a 24-dimensional space aligned with the Leech lattice, which explains the prevalence of 6-base recognition sites.

## Contribution

It introduces a novel application of 24-dimensional sphere packing to model restriction enzyme-DNA interactions, linking biological recognition to optimal coding theory.

## Key findings

- EcoRI functions in 24-dimensional space.
- Leech lattice provides optimal sphere packing for enzyme recognition.
- 6-base restriction enzymes are common due to optimal packing density.

## Abstract

Restriction enzymes recognize and bind to specific sequences on invading bacteriophage DNA. Like a key in a lock, these proteins require many contacts to specify the correct DNA sequence. Using information theory we develop an equation that defines the number of independent contacts, which is the dimensionality of the binding. We show that EcoRI, which binds to the sequence GAATTC, functions in 24 dimensions. Information theory represents messages as spheres in high dimensional spaces. Better sphere packing leads to better communications systems. The densest known packing of hyperspheres occurs on the Leech lattice in 24 dimensions. We suggest that the single protein EcoRI molecule employs a Leech lattice in its operation. Optimizing density of sphere packing explains why 6 base restriction enzymes are so common.