Abstract 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 PL and short-range interactions PS. The term PL 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, PS, 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.