Nonlinear dependance of the delayed luminescence yield on the intensity of irradiation in the framework of a correlated soliton model

We generalize the correlated soliton model in order to describe the delayed luminescence arising from biological systems after their exposition to the irradiation by relatively high dose (high intensity and/or long duration of irradiation). The quantum yield of the delayed luminescence is calculated as a function of the irradiation and is shown to depend nonlinearly on the intensity and dose of the irradiation. At relatively low intensity, the yield of luminescence increases with increasing dose, and monotonously reaches saturation. At high intensity of the irradiation, the yield of the photosystem under study is restricted from above by the concentration of photosystem units. As a result, the total yield of the delayed luminescence first increases with the dose till the maximum value that, in the general case, is less than the maximum number of available photosystem units. With further increase of the dose, the yield gradually decreases, reaching the saturation value at large dose of illumination. These results are obtained within the steady state approximation in the description of the luminescence kinetics. To check the applicability of this approximation at high levels and large time of illumination, the corrections to the steady state solution have been calculated, and shown to decrease exponentially with increase in time till the small finite constant value. The results of the theoretical model are shown to describe well the experimental data on the dose dependence of the quantum yield of the luminescence of algae Acetabularia acetabulum, for which the correlated soliton model describes well the kinetics of the delayed luminescence at low levels of irradiation.