Thermodynamics of hydrophobic-polar model proteins on the face-centered cubic lattice

The HP model, a coarse-grained protein representation with only hydrophobic (H) and polar (P) amino acids, has already been extensively studied on the simple cubic (SC) lattice. However, this geometry severely restricts possible bond angles, and a simple improvement is to instead use the face-centered cubic (fcc) lattice. In this paper, the density of states and ground state energies are calculated for several benchmark HP sequences on the fcc lattice using the replica-exchange Wang-Landau algorithm and a powerful set of Monte Carlo trial moves. Results from the fcc lattice proteins are directly compared with those obtained from a previous lattice protein folding study with a similar methodology on the SC lattice. A thermodynamic analysis shows comparable folding behavior between the two lattice geometries, but with a greater rate of hydrophobic-core formation persisting into lower temperatures on the fcc lattice.

Figure 1

HP model on the simple cubic lattice: The six nearest neighbors are shown on the left; a typical lattice configuration of the BPTI protein is shown on the right. Black residues are polar (P) and white are hydrophobic (H).

Figure 2

HP model on the face-centered cubic lattice: The 12 nearest neighbors are shown on the left; a typical lattice configuration of the BPTI protein is shown on the right. Black residues are polar (P) and white are hydrophobic (H).

Figure 3

Two types of rebridging moves. The example configuration has residues arranged in two parallel planes, where the four larger, slightly shaded residues are in plane and in the foreground. The new (broken) bonds need not be parallel, as shown in steps (a). For clarity, the images show configurations without HP sequences; otherwise, a trivial relabeling would be performed.

Figure 4

Natural log of $g\left(E\right)$ [shifted so that $max\left\{g\right(E\left)\right\}=1$] for seq_103 on the SC (gray triangles) and fcc (black circles) lattices. The $x$ axis is normalized by $N_{\text{nn}}$, and results for fcc have approximately twice as many points as SC. Error bars are smaller than the symbol sizes.

Figure 5

Thermodynamic comparison of benchmark sequences folding on SC (dashed with triangles) and fcc (solid with black circles) lattices. Reduced temperature is given on the $x$ axis, and normalized by $N_{\text{nn}}$. Ground state structures and energies are shown in the top left of each plot. The black residues are polar (P), and the white are hydrophobic (H). Error bars for the fcc results are calculated from 20 independent trials. Where not shown, the error bars are smaller than the symbol sizes.