HP Protein Lattice Constructor

• Neil Virani, Biological Sciences,

• John Jungck, Biological Sciences and Mathematical Sciences, University of Delaware

The HP Protein Lattice Constructor is a software environment that folds a linear protein sequence uploaded from the Protein Data Base into a compact lattice known as a self-avoiding walk, space filling curve. Proteins mediate virtually every biological process: enzymes catalyze chemical reactions, receptors transmit signals across membranes, chaperones assist in protein maturation, and structural proteins provide mechanical support. In every case, function is inseparable from shape. The process by which a disordered polypeptide chain spontaneously collapses into a precise, reproducible structure occurs on timescales of microseconds to seconds and is governed primarily by thermodynamics. The dominant driving force is the hydrophobic effect: nonpolar (hydrophobic) amino acid residues are thermodynamically penalized when exposed to aqueous solvent, because their presence disrupts the hydrogen-bonding network of water. This entropic cost drives hydrophobic residues to cluster in the protein’s interior, forming a stable hydrophobic core. Simultaneously, hydrophilic (polar and charged) residues occur more frequently on the the protein surface, where they can form electrostatic interactions with water. The net result is a thermodynamically stable, compact structure with a nonpolar interior and a polar exterior — a pattern conserved across virtually all globular and membrane proteins.The shapes that the HP Protein Lattice Constructor produces are lattices known as Hilbert curves and are fractals. Our algorithm works by packing as many hydrophobic amino acid residues in close contact in the central region of the lattice as possible. While the Noble Prize AI software entitled AlphaFold has made a revolutionary difference in predicting the three-dimensional structure of a protein from its primary sequence, there is still a need to build models of the secondary structure of proteins that help students comprehend that most globular proteins have a concentrated region of hydrophobic (H) residues in their interior with many of the polar (P) residues on their exterior. Our simulator extends classical binary HP models in three important ways: (1) Continuous hydrophobicity values from 9 different validated biochemical scales, provides a richer energetic landscape than binary H/P assignment; (2) Sliding window smoothing (window 3–21) computes an effective hydrophobicity at each position that reflects the local sequence context — capturing the amphipathic character of α-helices and β-strands; and (3) Quantitative burial metrics including radial distance analysis, Pearson correlation, and surface exposure counts, enabling rigorous comparison of fold quality across sequences and scales.