A mathematical model to simulate the dynamics of photosynthetic light reactions under harmonically oscillating light

Alternating electric current and alternating electromagnetic fields revolutionized physics and engineering and led to many technologies that shape modern life. Despite these undisputable achievements that have been reached using stimulation by harmonic oscillations over centuries, applications in biology remain rare. Photosynthesis research is uniquely suited to unleash this potential because light can be modulated as a harmonic function, here sinus. Understanding the response of photosynthetic organisms to sinusoidal light is hindered by the complexity of dynamics that such light elicits, and by the mathematical apparatus required for understanding the signals in the frequency domain which, although well-established and simple, is outside typical curricula in biology. Here, we approach these challenges by presenting a mathematical model that was designed specifically to simulate the response of photosynthetic light reactions to light which oscillates with periods that often occur in nature. The independent variables of the model are the plastoquinone pool, the photosystem I donors, lumen pH, ATP, and the chlorophyll fluorescence (ChlF) quencher that is responsible for the qE non-photochemical quenching. Dynamics of ChlF emission, rate of oxygen evolution, and non-photochemical quenching are approximated by dependent model variables. The model is used to explain the essentials of the frequency-domain approaches up to the level of presenting Bode plots of frequency-dependence of ChlF. The model simulations were found satisfactory when compared with the Bode plots of ChlF response of the green alga Chlamydomonas reinhardtii to light that was oscillating with a small amplitude and frequencies between 7.8 mHz and 64 Hz.