Impact of Hydrophobic Residue Ratio and Hydrophobic Distribution Pattern on Protein Folding in a Two-Dimensional Hydrophobic-Polar Lattice Model: A Simulated Annealing Simulation

The process of protein folding depends on the interaction between sequence composition and conformational search. This study, in detail, the effect of the hydrophobic residue ratio and the spatial distribution pattern on thermodynamic stability and search efficiency by applying minimalistic two-dimensional hydrophobic-polar (HP) lattice model. Four different hydrophobic ratios (30 percent, 40 percent, 50 percent, and 60 percent) and three distribution modes (aggregated, alternating, and random) were used to generate 300 independent sequences of fixed length 30. The folding simulations were done with simulated annealing protocol using corner-flip and end-rotation moves on a square lattice. As results indicate, increasing the hydrophobic content reduces the conformational energy and radius of gyration monotonically, hence establishing the hydrophobic effect as the main driving force of chain compaction. Kinetic accessibility, however, has a different trend: aggregated distributions have the lowest absolute energies but take long convergence times, low success rates and high conformational degeneracies, particularly, at high hydrophobic ratios. On the other hand, alternating distributions have small thermodynamic stability but fast convergence and high success rates. These results show that sequence architecture has a role in controlling the ruggedness of folding energy landscape and underscore the disconnect between thermodynamic optimality and kinetic reliability in simple protein models.