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” k app . In this paper, we defined the protein free energy ( Δ G ) landscape in amino acid sequence space, where Δ G 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 ) -body interactions, that is, an unit of interacting ( 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 k app ≈ K , and that the number of possible interactions among residues is unrelated to the k app value. This leads to the inference that k app takes values about 1–3 in real landscapes, if nature adopts two-body ∼ four -body interaction energies.