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 (ΔG) landscape in amino acid sequence space, where ΔG 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.