Are there Unfoldable Proteins in Dimension Three?

TL;DR

This paper demonstrates the existence of rigid, unfoldable lattice conformations in three dimensions, providing computer-assisted proof and explaining the complexity of protein folding in 3D.

Contribution

It proves the existence of three-dimensional rigid lattice structures, extending prior 2D results and addressing a specific open question.

Findings

Existence of 3D rigid lattice conformations with 450+ bonds

Computer-assisted proof of such structures

Rigid structures explain folding complexity in 3D

Abstract

In this paper we show the existence of three dimensional rigid, and thus unfoldable, lattice conformations. The structure we found has 450+ bonds, and we provide a computer assisted proof of the existence of such structures. The existence of such rigid structures illustrates why protein folding problems are hard also in dimension three. The existence of two rigid two dimensional structures was shown earlier. This work answers question 8 in \cite{2D} in the affirmative: rigid self avoiding walks exist in three dimensional lattice configurations.