Fluorescence decays in protein-ligand complexes are described by a new efficient model of continuous distribution of fluorescence lifetimes, and compared with multi-exponential models. Resulted analytical power-like decay function provides good fits to highly complex fluorescence kinetics. Moreover, this is a manifestation of so-called Tsallis q-exponential function, which is suitable for description of the systems with long-range interactions, memory effect, as well as with fluctuations of the characteristic lifetime of fluorescence. The proposed decay function was used to study effect of the interaction of E. coli purine nucleoside phosphorylase (PNP-I, the product of the deoD gene) with its specific inhibitor, viz. formycin A (FA), on fluorescence decays of ligand and enzyme tyrosine residues, in the presence of orthophosphate (P(i), a natural co-substrate). The power-like function provides new information about enzyme-ligand complex formation based on the excited state mean lifetime, heterogeneity parameter (q) and a number (N) of decay channels obtained from the variance of gamma distribution of fluorescence decay rates. With FA, which exists as a 85:15 mixture of the N(1)-H and N(2)-H tautomeric forms in aqueous solution, fluorescence intensity decay (lambda(exc)/lambda(em) 270/335 nm) is described by q approximately 1 and N approximately 200. Consequently power-like decay function converges to the single-exponential form, and lifetime distribution to the Dirac delta function. In contrast, selective excitation of the N(2)-H tautomer at higher wavelength led to a highly heterogenic fluorescence decay characterized by q>1 and 10-fold lower number of decay channels. Heterogeneity of fluorescence decays of both PNP-I and FA is enhanced by PNP-FA-P(i) complex formation, reflecting a shift of the tautomeric equilibrium of FA in favor of the N(2)-H species, and fluorescence resonance energy transfer (FRET) from protein tyrosine residue (Tyr160) to the bound N(2)-H tautomer. Moreover, proposed model is simple, and objectively describes heterogeneous nature of studied systems.