Frequency-domain identification of photosynthetic regulation under fluctuating light

Plant photosynthesis operates under naturally fluctuating light, yet its dynamic responses across timescales remain incompletely understood. Here, we apply sinusoidal light modulation as a controlled periodic input and analyze the response in the frequency domain, enabling quantitative system identification of photosynthetic dynamics. Using a minimal biochemical model of photosynthetic electron transport and regulation, we show that the system exhibits distinct dynamic regimes separated by a characteristic timescale of approximately 10 s. In the high-frequency domain, the response is governed by constitutive processes and reflects steady-state properties such as the plastoquinone redox state. In the low-frequency domain, regulatory feedback dominates, particularly non-photochemical quenching (NPQ), which modulates both the amplitude and phase of the response. For small-amplitude perturbations, the system behaves linearly and can be characterized using transfer functions and Bode plots. We show that key physiological parameters, including relaxation times and regulatory gains, can be extracted directly from frequency-response features such as phase maxima and gain transitions. In the nonlinear regime, large-amplitude oscillations generate higher-harmonic structure and alter time-averaged photosynthetic performance relative to constant illumination. We further introduce the concept of regulation fingerprints, defined as ratios of transfer functions between regulated and unregulated systems. These fingerprints reveal distinct spectral signatures of fast (PsbS-mediated) and slow (zeaxanthin-dependent) NPQ processes, enabling their quantitative separation. Together, these results establish frequency-domain analysis as a framework for probing and identifying the dynamic regulation of photosynthesis under fluctuating light, with direct applicability to non-invasive measurements in laboratory and field conditions.