(130f) Modelling Photoacclimation

The minimal requirement from a mathematical model of photosynthesis is the prediction of the P-I curve. That is the dependence of the photosynthesis rate on irradiance. The models using the concept of Photosynthetic Unit (PSU), called also Photosynthetic Factories (PSF) are the most relevant from the engineering point of view. These models have as central aim representing the dynamics of the photobioreactors, and consider as main variable the light intensity, which is usually the limiting substrate in dense cultures as those focused for industrial production. While the P-I curve gives the variation of the steady state, or photoadapted photosynthesis rate with irradiance, it does not provide any information on the dynamics of the process, i.e. the path followed by a system in passing from one steady state to another, which implies depicting the changes in chlorophyll content of the cell as it adapts to new irradiance conditions.A novel model including this phenomenon will be presented. Photoadaptation: The changes in the quantity of Chla in response to the changes in light may respond to one of two strategies: (i) either a change in the size of the PSU, q mol [Chla/mol PSU], without an alteration in their number, a, [mole PSU/cell], In any case the product of these two variables, will deliver the concentration of Chla in the cell. Both the total concentration of Chla in a light- adapted cell and consequently the number of PSUs in it can vary only within finite limits, the higher provided by the cell structure and the lower one by the requirement of Chla in order the have photosynthesis take place We will assume here that both Chla concentration and the number of PSUs will depend on the illumination following an inverse hyperbolic function: A first approximation may be a linear feedback on K1 as c(t) approaches cad(If), and a similar expression can be written for a(t) as well. This kinetic model is mathematically the same as the logistic model of population growth. Observations reported by others authors for different microalgae have been acceptably modelled by means for changes in illumination from high light to low light and vice versa. This element has been added to a new PSU model, Conclusion: The photoadaptation model can be combined with the PSU model and the fluid dynamics of the bioreactor, which gives the light history of the culture, to produce a predictive model of a photobioreactor operating under changing irradiance conditions.