Fitting protein-folding free energy landscape for a certain conformation to an NK fitness landscape

The NK fitness landscape is a mathematical landscape model with a parameter k that governs the degree of ruggedness of the landscape. We presented a procedure to fit a given landscape to the NK fitness landscape by introducing the “apparent k  -value” kappkapp. In this paper, we defined the protein free energy (ΔG)(ΔG) landscape in amino acid sequence space, where ΔGΔG is the folding free energy from a random coil to a “certain conformation”. Applying this landscape to our fitting procedure, we examined the statistical properties of the landscape. For calculation of a conformation energy, amino acid residues are represented by points, and interaction energies among amino acid residues are given as (1+K)(1+K)-body interactions, that is, an unit of interacting (1+K)(1+K) residues cooperatively contribute a single energy value to the conformational energy. Our results suggest that the apparent k  -value of the free energy landscape is kapp≈Kkapp≈K, and that the number of possible interactions among residues is unrelated to the kappkapp value. This leads to the inference that kappkapp takes values about 1–3 in real landscapes, if nature adopts two-body ∼four∼four-body interaction energies.