Logical analysis of the mechanism of protein folding III. Prediction of the strong long-range interactions.

It has been found that strong long-range interactions occur in regions having large β-structural potentials. As has been described previously (Nagano, 1974), interactions among regions having both helical and β-structural potentials (αβ-gaβ interactions) are also very important. Accordingly, an idea is presented in this paper that the relative stability of a protein conformation could be estimated by a relatively simple mathematical function of sequence and conformation. The function P(p,q) is called the non-energy part of pseudo-free energy, because minimization of the sum of P(p,q) and energy functions (cf. Levitt, 1974; Warme &; Scheraga, 1974) can be expected to lead to a plausible model of a protein. A merit of the function is that it can help us decide which way to go in manipulating a temporarily built model, e.g. towards a helix-rich protein or towards a β-structure-rich protein. The estimation of P(p,q) as an artificial potential does not use much computer time because only the co-ordinates of the β-carbon atoms (α-carbon atoms if the residue is Gly) are used. It is composed of terms of the long-range interactions P_L and short-range interactions P_S. The term P_L represents the relative strength of helix-helix interactions, helix-β-candidate interactions and β-candidate-β-candidate interactions. It is assumed that both helical and β-structural potentials can be measured as the differences between the predicted function for helix and β-structure, respectively, as defined previously (Nagano, 1973), and the corresponding largest values ever found. A hypothesis that two residues distantly separated in the primary sequence contribute less to the stability of the whole molecule is finally discarded because the true conformation of concanavalin A becomes very unstable compared with its false conformation folded like the main part of subtilisin. The parameters thus determined indicate that the helix-β-candidate interactions are almost as important as the β-candidate-β-candidate interactions. Both helix and loop prediction functions are combined to give the short-range interactions term, P_S, according to whether the region is really helical or not, and to whether it is really looped or not. The function P(p,q) can be used as a criterion for judging whether the predicted conformation is realistic or false, because the parameters can be adjusted to give, within limits, reasonable values of −10 kcal/residue for true conformations and higher than −5 kcal/residue for false conformations.As an application of the present theory of protein folding, the tertiary structure of bacteriophage T4 lysozyme is predicted and presented in Figure 1, prior to the X-ray structure becoming available.