Concatenative Nonmonotonicity and Optimal Links in HP Protein Folding Models
Abstract
The hydrophobic-polar (HP) model represents proteins as binary strings embedded in lattices, with fold quality measured by an energy score. We prove that the optimal fold energy is not monotonic under concatenation for several standard lattices, including the 2D and 3D rectangular, hexagonal, and triangular lattices. In other words, concatenating two polymers can produce a fold with strictly worse optimal energy than one of the polymers alone. For closed chains, we show that under the levels-of-hydrophobicity model of Agarwala et al. (1997), proper links can arise as uniquely optimal folds, revealing an unexpected connection between HP models and knot/link theory.
Fields of Study & Subjects
Protein Structure and Dynamics
RNA and protein synthesis mechanisms
Geometric and Algebraic Topology
Publication details
- Journal / source
- Journal of Experimental Mathematics
- Volume
- 2
- Issue
- 1
- Pages
- 172–193
- Publication date
- 1 March 2026
- Language
- EN