A minimal mathematical model of nonphotochemical quenching of chlorophyll fluorescence

Under natural conditions, plants are exposed to rapidly changing light intensities. To acclimate to such fluctuations, plants have evolved adaptive mechanisms that optimally exploit available light energy and simultaneously minimise damage of the photosynthetic apparatus through excess light. An important mechanism is the dissipation of excess excitation energy as heat which can be measured as nonphotochemical quenching of chlorophyll fluorescence (NPQ). In this paper, we present a highly simplified mathematical model that captures essential experimentally observed features of the short term adaptive quenching dynamics. We investigate the stationary and dynamic behaviour of the model and systematically analyse the dependence of characteristic system properties on key parameters such as rate constants and pool sizes. Comparing simulations with experimental data allows to derive conclusions about the validity of the simplifying assumptions and we further propose hypotheses regarding the role of the xanthophyll cycle in NPQ. We envisage that the presented theoretical description of the light reactions in conjunction with short term adaptive processes serves as a basis for the development of more detailed mechanistic models by which the molecular mechanisms of NPQ can be theoretically studied.