Geometric Restrictions on Producible Polygonal Protein Chains

Fixed-angle polygonal chains in 3D serve as an interesting model of protein backbones. Here we consider such chains produced inside a “machine” modeled crudely as a cone, and examine the constraints this model places on the producible chains. We call this notion producible, and prove as our main result that a chain whose maximum turn angle is α is producible in a cone of half-angle ≥ α if and only if the chain is flattenable, that is, the chain can be reconfigured without self-intersection to lie flat in a plane. This result establishes that two seemingly disparate classes of chains are in fact identical. Along the way, we discover that all producible configurations of a chain can be moved to a canonical configuration resembling a helix. One consequence is an algorithm that reconfigures between any two flat states of a “nonacute chain” in O(n) “moves,” improving the O(n2 )-move algorithm in [ADD+ 02]. Finally, we prove that the producible chains are rare in the f...

• Type: Conference
• Year: 2003
• Where: ISAAC
• Authors: Erik D. Demaine, Stefan Langerman, Joseph O'Rourke
• Keywords: Chains, Fixed-angle Polygonal Chains, ISAAC 2003, Producible Chains