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The heterogeneous nucleation of hen-egg-white lysozyme (HEWL) crystals has been repeatedly investigated using a double-(thermal)-pulse technique, thus detaching nucleation from growth stage. n(t) dependencies of the nucleus number n, on templates of poly-L-lysine, vs time, t were plotted and the steady-state nucleation rates I were determined. They were compared with the results obtained earlier for surfaces rendered hydrophobic (by means of hexamethyl-disilazane) as well as for bare glass surfaces. In the present paper we determine the number of HEWL molecules in the (heterogeneously formed) critical nucleus. It turned out that it is build of 3 (to 4) HEWL molecules on glass substrate and 8 molecules for both hexamethyl-disilazane and poly-L-lysine templates. The energy A k required for heterogeneous formation of a critical nucleus on poly-L-lysine has been calculated, on the basis of the steady-state nucleation rates I. Intermolecular binding energy in the HEWL crystal lattice has been estimated again (approximately 10 -9 erg/molecule). This time the basis was the adhesion of HEWL crystals to poly-L-lysine substrate (compare D. TZEKOVA, S. DIMITROVA, C.N. NANEV, J. Cryst. Growth, 196 (2), 226 (1999)).