Effect of single-site mutations on hydrophobic-polar lattice proteins

We developed a heuristic method for determining the ground-state degeneracy of hydrophobic-polar (HP) lattice proteins, based on Wang-Landau and multicanonical sampling. It is applied during comprehensive studies of single-site mutations in specific HP proteins with different sequences. The effects in which we are interested include structural changes in ground states, changes of ground-state energy, degeneracy, and thermodynamic properties of the system. With respect to mutations, both extremely sensitive and insensitive positions in the HP sequence have been found. That is, ground-state energies and degeneracies, as well as other thermodynamic and structural quantities, may be either largely unaffected or may change significantly due to mutation.

Figure 1

A 3D structure of a HP protein with eight hydrophobic (H: small, silver beads) and six polar (P: large, orange beads) residues.

Figure 2

Number of different ground states found over time for HP sequences 48.1 fitted to the corresponding curve of protein 48.3. $g^{\prime }(E_0,\lambda )$ is the actual estimator of ground-state degeneracy and $\lambda =1/\left(10000\text{MC}\text{steps}\right)$ is the inverse Monte Carlo time. For clarity, only selected data points and error bars are shown. See text for details.

Figure 3

Ground-state energy $E_0$ (top) and ground-state degeneracy $g\left(E_0\right)$ (bottom) of mutated Seq3D42. The $X$-axis value indicates the position which has been affected by the single-site mutation. Properties of the original, unmutated sequence are marked by horizontal lines.

Figure 4

Ground-state energy $E_0$ and ground-state degeneracy $g\left(E_0\right)$ of mutated Seq3D67 (cf. Fig. 3). Each of the bottom pictures shows the result of two overlapping ground-state structures of Seq3D67. Overlapped monomers are shown in faint color. Monomers pointed to by arrows belong to the same structure, while the rest belong to different structures.

Figure 5

Examples of thermal stability of the ground state: (a) comparison between Seq3D42s13 and Seq3D42 based on specific heat (top curves, left-hand scale) and ground-state population (bottom curves, right-hand scale) and (b) comparison between Seq3D67s28 and Seq3D67 based on specific heat and ground-state population. In both figures, error bars smaller than data points are not shown.

Figure 6

Effect of mutations on folding behavior: (a, b) two cases where the mutations do not affect the folding behavior and (c, d) examples of changed thermodynamic quantities under mutation. In all panels above, error bars smaller than data points are not shown.

Figure 7

Three different ground-state structures for the 67mer studied in this paper. Residues 2–10 form a lattice helix, and residues 12–16 form a lattice strand [60]. Hydrophobic monomers are represented by small, silver beads, while polar monomers are represented by big beads which are either orange (light gray) or green (dark). Green monomers are those for which the ground-state degeneracy remains the same under single-site mutations; they are located at the joints connecting lattice strands and lattice helices.

Figure 8

Four different ground-state structures for the 42mer studied in this paper. Each ground-state structure is sliced into three layers. The top layer is shared by all the ground-state structures, while there are two different structures for the middle and bottom layers, respectively. Arrows in the figure point to the bonded monomer in the next layer. Hydrophobic monomers are represented by small, silver beads, while polar monomers are represented by big beads which are either orange (light gray) or green (dark). Green colored monomers are those for which the ground-state degeneracy remains the same under single-site mutation.