Constitutive and Regulatory Responses of Arabidopsis thaliana to Harmonically Oscillating Light

1 of 15 Physiologia Plantarum, 2025; 177:e70421 https://doi.org/10.1111/ppl.70421 Physiologia Plantarum ORIGINAL RESEARCH OPEN ACCESS Constitutive and Regulatory Responses of Arabidopsis thaliana to Harmonically Oscillating Light YuxiNiu1,2 | DavidFuente3 | ShizueMatsubara1 | DušanLazár3 | LadislavNedbal1,3 1Institute of Bioand Geosciences/Plant Sciences (IBG2), Jülich, Germany | 2Department of Biophysics, Wageningen University and Research, Wageningen, the Netherlands | 3Department of Biophysics, Faculty of Science, Palacký University, Olomouc,Czech Republic Correspondence: Ladislav Nedbal ([email protected]) Received: 5 February 2025 | Revised: 1 July 2025 | Accepted: 7 July 2025 Handling Editor: A. KriegerLiszkay Funding: The work of D.F., S.M., D.L., and L.N. was funded by HORIZON EUROPE EIC 2021 Pathfinder Open project DREAM, grant agreement no. 101046451. The work of Y.N. and L.N. was supported by the Federal Ministry of Education and Research of Germany in the framework of the YESPVNIGBEN project (03SF0576A). The work of D.L. was supported by the project Interdisciplinary approaches for the development and application of new materials in industrial, agricultural, and medical practice, reg. no. CZ.02.01.01/00/23_021/0008909 of the ERDF Programme Johannes Amos Comenius. Keywords: chlorophyll fluorescence| frequency domain| harmonics| mathematical model| photosynthesis ABSTRACT The rate of net CO2 uptake is proportional to dim light and saturates when the light exceeds the plant's assimilation capacity. This simple relationship between constant light and photosynthesis becomes intriguingly complex when the light oscillates. The rates of photosynthesis may differ between the descending and ascending phases of light oscillation. This hysteresis changes with the frequency and amplitude of the light and reports on the dynamics of the photosynthetic reactions and their regulation. Here, we investigated the chlorophyll fluorescence response of Arabidopsis thaliana to light oscillating with three different amplitudes: 100–200, 100–400, and 100–800 μmol photons m−2 s−1, each with periods ranging from 1 s to 8 min. The light amplitudes and periods were chosen to represent light patterns often appearing in nature. Three genotypes were compared: wildtype Col0 and npq1 and npq4 mutants that are incapacitated in the rapidly reversible energydependent nonphotochemical quenching (qE). The experiments identified two major dynamic patterns. One was found in oscillation periods shorter than 30 s, characterized by constitutive hysteresis and nonlinearity. The other was mainly formed by regulatory hysteresis, occurring when the oscillation periods were longer than 30 s. The mathematical model simulating the chlorophyll fluorescence dynamics qualitatively reproduced the constitutive and regulatory dynamic patterns observed in the experiments. The model simulations illustrated the dynamics of plastoquinone pool reduction and variables affecting nonphotochemical quenching that form the constitutive and regulatory hysteresis types. The model simulations provided mechanistic insights into molecular processes forming the plant response to oscillating light. 1 | Introduction The stimulus–response1 relationship is a fundamental concept in biology, characterizing the extent to which an organism responds to the strength, duration, or dose of a stimulus (Calabrese and Baldwin2003; Mattson2008; Pinheiro and Duffull2009). In plant research, this concept is commonly applied to assess optimal growth conditions or plant resistance to stress (Berry and Bjorkman1980; Idso and Idso1994; Lee etal.2007; Dusenge etal.2019). Another widely used stimulus–response relationship is the photosynthetic light response curve (P–I curve), which describes how the net carbon assimilation rate, P, depends on This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2025 The Author(s). Physiologia Plantarum published by John Wiley & Sons Ltd on behalf of Scandinavian Plant Physiology Society. 2 of 15 Physiologia Plantarum, 2025 the intensity of the photosynthetically active radiation, PAR or I (Evans etal.1993; Ralph and Gademann2005; Hogewoning etal.2010; Flood etal.2011). A typical P–I curve exhibits three distinct phases. Under low light intensities, the rate of photosynthesis is primarily limited by the availability of light, and therefore, it increases as a linear function of light intensity (Kiss etal.2008; Krah and Logan2010; Murchie and Niyogi 2011; Hasan and Cramer 2012). Under high light, photosynthesis is limited by the electron transport and the capacity of the CalvinBensonBassham cycle (Murchie and Niyogi2011; Hasan and Cramer2012; Hoh etal.2023) and therefore, it increases little when PAR is increased. Third, the absorbed light energy that exceeds the assimilation capacity of the plant can cause photodamage and, ultimately, photoinhibition that is manifested by decreasing photosynthesis in increasing light (Krause1988; Aro etal.1993; Allahverdiyeva and Aro2012). The P–I curve of photosynthesis can be determined by measuring steadystate rates of net CO2 uptake or net O2 evolution in different light intensities (Evans etal.1993; Ögren and Evans1993). An alternative way of estimating the rate of photosynthesis in relation to light intensity is by measuring the relative electron transport rate (ETR) of photosystem II (PSII). The ETR is calculated from the chlorophyll fluorescence measured by the pulse amplitude modulation (PAM) technique that probes the actinic effects of the applied actinic light, combined with saturation pulses of light that transiently close PSII reaction centers (Schreiber2004). The P–I curve, measured through O2, CO2, or chlorophyll fluorescence, characterizes a steadystate photosynthesis response to constant light exposure. Such a P–I curve represents a fundamental plant stimulus–response, which, however, cannot be used to understand the plant behavior in rapidly changing light that often occurs in nature (Way and Pearcy2012; Smith and Berry2013; Kaiser etal.2018). The light fluctuations in different environments can be roughly classified by their typical frequencies and amplitudes (Table1). This is, however, only a crude characterization, and there is an endless number of light fluctuation patterns that occur in nature, each pattern potentially leading to different plant responses. On a trivial level, this variability can be illustrated by plant responses to diurnal light modulation in a square, on–off form compared with light modulation that gradually increases from morning to noon and decreases toward the evening, as, for example, in Fondy etal.(1989). The plant responses are different, although the period, duty cycle, and total photon energy per day may be the same in both regimes. Plants will also respond differently when light is modulated by a sine function or by a square wave in minutes, seconds, or shorter. The sine harmonic modulation is analogous to monochromatic light in spectroscopy or a pure musical tone. Square, triangle, or other periodic light modulation patterns are analogous to polychromatic light or complex sounds because they consist of multiple harmonics represented by multiple sine functions. This originates from the uniqueness of harmonic functions of sine or cosine among all other periodic stimulus patterns (Williams 1973; Nuij etal.2006). No other modulation pattern can be used to analyze complex periodic or even fluctuating pseudoperiodic TABLE 1 | The phenomena that result in fluctuations in photosynthetically active radiation (PAR) with different characteristic periods T and frequencies f = 1/T in vegetation canopies. Period, T1 s > T ≥ 10 ms 8 min > T ≥ 1 s T ≥ 8 min Frequency, f100 Hz > f ≥ 1 Hz 1 Hz > f ≥ 2.1 × 103 Hz 2.1 × 10−3 Hz > f Fluctuations against a low light background in vegetation understory Leaf flutter (Roden and Pearcy1993) results in very brief sun flecks (Smith and Berry2013). Plant swaying (Pearcy etal.1996) and transient gaps in the canopy (Chazdon and Pearcy1991) cause sun flecks (Pearcy etal.1996). Earth rotation (Pearcy etal.1996) and canopy gaps (Smith and Berry2013) result in longduration sun patches (Smith and Berry2013). Fluctuations against a mediumrange background occurring within canopies Leaf flutter (Roden and Pearcy1993) or plant swaying (de Langre2008) result in brief sun flecks (Pearcy1990). Transient gaps in the upper canopy (Chazdon and Pearcy1991), windinduced canopy movement (Peressotti etal.2001), and intermittent cloudiness (Knapp and Smith1987) give rise to complex light patterns within canopies (Way and Pearcy2012; Kaiser etal.2018). Earth rotation, canopy gaps, and cloud movement result in sun and cloud patches (Smith and Berry2013). Diurnal changes create regular irradiance changes (Chazdon and Pearcy1991) Fluctuations against a highlight background in outer canopies Leaf flutter in canopies creates highintensity sun flecks and shade flecks (Pearcy etal.1996). Effects of plant swaying (de Langre2008) and intermittent cloudiness (Knapp and Smith1987) create sun and cloud flecks (Morales and Kaiser2020). Slowly variable irradiance under overcast skies (Navrátil etal.2007), cloud movement, and diurnal changes (Morales and Kaiser2020). 13993054, 2025, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ppl.70421 by University Palacky, Wiley Online Library on [31/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 3 of 15 light with the clarity of harmonic functions of sine or cosine2. Therefore, the stimulation of plants by harmonically modulated light is a unique probe of plant response to a particular frequency and amplitude. In this study, we used harmonically modulated light that was a sine function with periods 1 s ≤ T ≤ 8 min, that is, of frequencies 1 Hz ≥ f ≥ 2.1 × 10−3 Hz. The respective frequencies dominate natural fluctuating light patterns represented in the middle column of Table1. The dynamics of photosynthesis under harmonically oscillating light were rarely studied in the past. The pioneering work of Lam and Bungay(1986) and the position paper of Lam etal.(1986) went largely unnoticed. Also, the independently developed line of research using harmonically modulated light (Nedbal and Březina2002; Nedbal etal.2003, 2005; Matous etal.2006; Berger etal.2007) was seldom cited. Recently, the dynamics of photosynthesis in oscillating light and sensing in the frequency domain have become subjects of renewed interest (Shimakawa and Miyake 2018; Samson etal. 2019; Jose 2021; Nedbal and Lazár 2021; Lazár et al. 2022; Niu etal.2023, 2024). Lately, a mathematical model has been developed specifically to support the interpretation of decisive mechanisms for the stimulus–response dynamics in oscillating light (Fuente etal.2024). The model correctly predicted the dispersion, that is, the frequency dependence of the measurable reporter signals, such as the relative chlorophyll fluorescence yield for small amplitudes of light oscillations. However, the model predictions have not yet been confronted with experiments in which large light oscillation amplitudes reach saturation in the P–I curves. Such amplitudes often occur in nature (Table1) and represent a relevant scenario to study. This led us to investigate the dependence of the photosynthetic responses to light that oscillated in a broad range of intensities from subsaturating to saturating levels. We report on the normalized chlorophyll fluorescence yield, further ChlF(t) response of Arabidopsis thaliana wildtype (WT) Columbia (Col0), and its npq1 (Niyogi etal.1998) and npq4 mutants (Li etal.2000) to light that harmonically oscillates between 100 and 200, 100 and 400, and 100 and 800 μmol photons m−2 s−1 with periods ranging between 1 s and 8 min. The results are presented in the stimulus–response form by plotting ChlF(t) against the dynamically changing light intensity, as in Nedbal etal.(2005). Also, the formal concepts of constitutive and regulatory nonlinearity (Bich etal.2016) were already cited in connection with photosynthesis by Nedbal and Lazár(2021). These approaches are further developed here to classify response dynamics of photosynthesis as constitutive and regulatory hysteresis. As argued above, the dynamic responses of photosynthesis to harmonically oscillating light of a large amplitude differ from those observed during transients from darkness to light or reverse that are often used in the laboratory to probe, for example, the activation or relaxation of the nonphotochemical quenching (Nilkens etal.2010; Kress and Jahns2017). Photosynthesis responds differently to abrupt increases and decreases in light intensity, with forward and reverse reactions happening with different rate constants. For example, the conversion of zeaxanthin to violaxanthin during NPQ relaxation is catalyzed by zeaxanthin epoxidase, whose rate constant is smaller than that of violaxanthin deepoxidase (VDE), catalyzing the reverse reactions to convert violaxanthin to zeaxanthin during the NPQ activation (Niyogi et al. 1997; Nilkens et al. 2010; Jahns and Holzwarth 2012; Kress and Jahns2017). While constantlight induction and dark relaxation measurements can be used to characterize specific reactions that predominate in one of these two phases, they cannot capture the dynamic responses of photosynthesis to fluctuating light. Harmonically oscillating light provides a framework to study systemic responses in both directions as a function of frequency, offering valuable information on photosynthesis dynamics. The experimental results were further compared with the simulations obtained by a mathematical model. The original model (Fuente etal.2024) was modified here to simulate the ChlF(t) data obtained in our PAM experiments. This modified model, further called BDM2, reproduced the essential features of the experimental data and explained some of them mechanistically. The residual discrepancy between the experiment and the model simulations is used here to identify knowledge gaps, better understand the regulation of photosynthesis and operational modes in a dynamic light environment, and pave the way for future systems identification. 2 | Materials and Methods 2.1 | Experimental Setups Three genotypes of A. thaliana were grown in a climate chamber under light intensity of approximately 100 μmol photons m˗2 s˗1, including wildtype Col0, the npq1 mutant that cannot convert violaxanthin into zeaxanthin (Niyogi etal.1998), and the npq4 mutant that is deficient in the PsbS protein (Li etal.2000). Plants were cultivated under controlled environmental conditions, with a 12h light/12h dark diurnal regime and a day/ night air temperature of 26°C/20°C. Relative air humidity was maintained at 60%. Measurements were done between 38 and 43 days after sowing. The DualKLASNIR spectrophotometer with a 3010DUAL leaf cuvette (Heinz Walz GmbH) was used to measure the instantaneous relative chlorophyll fluorescence yield F′(t) responding to the actinic light oscillations (Klughammer and Schreiber2016; Schreiber and Klughammer2016). The data were collected every 5 ms, and 20 points were averaged to improve the signaltonoise ratio. The resulting time resolution of 0.1 s was sufficient to capture the plant response in light oscillating with a 1 Hz frequency or slower. Red actinic light (630 nm) was applied to both the abaxial and adaxial sides of the leaf. The measuring light was green (540 nm) with an intensity of 6 μmol photons m−2 s−1, and it was applied only to the abaxial side of the leaf. The plants were collected from the climate chamber before the end of the dark photoperiod and kept in darkness until measurement. Before the oscillating light measurements, each darkadapted plant was exposed for 10 min to constant red actinic light (630 nm) to induce photosynthesis. The intensity of this constant light was set to the average of the oscillating light that followed. Thus, plants later exposed to light oscillating between 100 and 200 μmol 13993054, 2025, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ppl.70421 by University Palacky, Wiley Online Library on [31/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 4 of 15 Physiologia Plantarum, 2025 photons m−2 s−1 were first acclimated to a constant light intensity of 150 μmol photons m−2 s−1. Those exposed to oscillations ranging from 100 to 400 μmol photons m−2 s−1 were initially subjected to a constant light of 250 μmol photons m−2 s−1 and, similarly, a constant light intensity of 450 μmol photons m−2 s−1 was used for plants that were later exposed to oscillations between 100 and 800 μmol photons m−2 s−1. Following the induction in constant actinic light, plants were exposed to harmonically oscillating light of low, medium, and high amplitudes, as described above. The sequence of oscillating light periods was similar to Niu etal.(2023), consisting of eight different periods that varied continuously from 8 min to 1 s: three oscillation cycles with an 8 min period, five cycles each with 4 min, 2 min, 1 min, 30 s, and 10 s periods, and finally ten cycles with 5 and 1 s periods. The light was controlled by an 8bit digitaltoanalog converter, yielding 256 light levels to cover the amplitude range of the light intensities. This led to light changes in which discrete steps approximated the sine function: the oscillations were approximated by eight light intensity steps for 100–200 μmol photons m−2 s−1, 22 light intensity steps for 100–400 μmol photons m−2 s−1, and 49 light intensity steps for 100–800 μmol photons m−2 s−1. The light oscillation protocol and chlorophyll fluorescence responses are illustrated in Figure1. Three plants of each A. thaliana genotype were measured in three oscillating light conditions as biological replicates. The dynamic patterns of ChlF(t) signals sometimes change during the first one or two cycles following the change of the oscillation period. Therefore, only the steadystate dynamic patterns3 that emerged in later cycles were used for the analysis. Specifically, the first cycle of the T = 8 min oscillation and the first two cycles of the other oscillation periods were excluded from the study to minimize aperiodic transient components. The steadystate ChlF(t) dynamic patterns were then averaged and fitted by the function in Equation (1) as previously done (Nedbal and Lazár2021; Niu etal.2023). The leastsquare fitting was done by Microsoft Excel, yielding the offset A0 as well as the amplitudes (A1, A2, A3, A4) and the phase shifts (τ1/T, τ2/T, τ3/T, τ4/T) of up to the fourth harmonic component. These nine parameters characterizing each of the three biological replicates separately were averaged, and statistical errors were calculated. Figures SI1 to SI5 show that fitting by the analytical function in Equation(1) did not distort the ChlF loops. 2.2 | Mathematical Model BDM2 The model BDM2 used here for the in silico simulations is an upgrade of the parent BDM model (Fuente etal.2024). The BDM2 scheme is shown in Figure2. The most significant modification is the inclusion of the two mechanisms of NPQ regulation in BDM2 instead of the single mechanism considered in BDM. Two separate NPQ mechanisms in BDM2 allowed for representing the different kinetics of the PsbSand zeaxanthinrelated NPQ mechanisms. The added dimension allowed for better simulations of ChlF dynamics with BDM2 than those that one could obtain with BDM. BDM2 consists of six ordinary differential equations representing the redox state of the PQ pool by the PQ(t) variable, the redox state of the photosystem I donors by the PIox(t) variable, the lumen proton concentration by the HL(t) variable, the ATP concentration by the ATP(t) variable, the zeaxanthin by the Zea(t) variable, and the protonated PsbS by the PsbSact(t) variable, all functions of time during light oscillation. The two new independent variables Zea(t) and PsbSact(t) replace in BDM2 the variable FQact(t) of the parent BDM model (Fuente etal.2024). (1) Fit (t)=A0+A1⋅sin [ 1⋅ 2π ( t−𝜏1 ) T ] +A2⋅sin [ 2⋅ 2𝜋 ( t−𝜏2 ) T ] +A3⋅sin [ 3⋅ 2𝜋 ( t−𝜏3 ) T ] +A4⋅sin [ 4⋅ 2𝜋 ( t−𝜏4 ) T ] FIGURE 1 | Examples of the normalized ChlF(t) = F� ( t) F M of the WT strain Col0 to light oscillating with a period T = 8 min at three different amplitudes are shown (A–C). The oscillation ranges were 100–200, 100–400, and 100–800 μmol photons m−2 s−1. The light oscillation (Aa, Ba, Ca) starts at its minimum (red circle), continues with the ascending phase marked by the yellow line to the maximum (black circle), and concludes the period by its descending phase along the blue line to the following minimum (purple circle). The normalized ChlF(t) response is shown with the same marking in panels Ab, Bb, and Cb. The same data are shown in the stimulus–response format in Ac, Bc, and Cc, where the line and marker colors are the same as in the a and b panels. The overlapping light minima are marked by halfpurple, halfred circles in c. 13993054, 2025, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ppl.70421 by University Palacky, Wiley Online Library on [31/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 5 of 15 The activation dynamics of Zea(t) and PsbSact(t) are modeled similarly to eq. (11) and (12) in Fuente etal.(2024) by and In addition to the two independent quenching mechanisms, we also modified some model parameters in BDM2. The complete list of model parameters used here in the simulations is in Table SI1. Most significantly, the values of the lumped rate constants k1+ and k1 − that approximately represent the forward and backward steadystate electron transfer between PSII and the PQ pool in (Fuente etal.2024) were too high, which led to predictions of unrealistically high rates of electron transport in saturating light. In BDM2, the values used for the simulations here are: k1+ = 250 s−1 and k1 − = 100 s−1. With these parameters, BDM2 predicts the rate of the steadystate O2 evolution by the water splitting in PSII in saturating light (1000 μmol photons m−2 s−1) to be ≈ 60 O2 PSII−1 s−1, which is within the range of 27–67 O2 PSII−1 s−1 reported in the literature for saturating light (reviewed in Vinyard etal.2013). The rate of ATP formation, v5(t), described in Fuente etal.(2024) by Equation (16), was in BDM2 defined as where a = 9.202 × 10−2 is an empirical proportionality constant, with which the rate of steadystate ATP production in saturating light (1000 μmol photons m−2 s−1) is ≈ 93 ATP ATPsynthase−1 s−1. Considering the ATPsynthase/PSII stoichiometry of 1/2 (Antal et al. 2013) and the fact that BDM2 includes only the linear electron transport, the rate is close to the maximal rate of 375 ATP ATPsynthase−1 s−1 reported in the literature (Kocks and Ross1995). Further, the effective rate constants approximating violaxanthin deepoxidation to zeaxanthin and the reverse process were set to k3 = 0.01 s−1 and k4 = 0.001 s−1. The rate constants characterizing the activation and deactivation of the PsbS were set to k9 = 0.05 s−1 and k10 = 0.004 s−1. The pK values of the quencher activation were KQ,VDE and KQ,PsbS were both set to 1 μM. The Hill dependence of the quencher activation was assumed to be slightly steeper for zeaxanthin nVDE = 6 and slightly flatter for PsbS nPsbS = 4 than assumed in the earlier model version, where n = 5.3 was used. The used values of the rate constants, pKs, and Hill coefficients are within the range reported in the literature (Jahns etal.2001; Zaks etal.2012; Matuszyńska etal.2016; Steen etal.2020; Short etal.2022). The maximal extent of quenching was assumed in the model calculations for the WT to be Zeamax = 0.3 and PsbSmax = 0.3, for the npq1 mutant to be Zeamax = 0 and PsbSmax = 0.3, and for the npq4 mutant to be Zeamax = 0.3 and PsbSmax = 0. These values were used to get values of the NPQ parameter simulated for saturating light by BDM2 similar to the experimentally measured values. The rate constant of ATP consumption, k6, was set to 8 s−1. As shown below in the Results section, these model parameters led to a good qualitative agreement between the modelsimulated ChlF dynamics and those obtained in the experiments with the WT plants. It is important to note that the parameter values can be further modified to reach even better agreement between the experiment and the simulations but this would not change any of our conclusions here. We preferred conserving most of the parameters of the parent BDM for the sake of an easier comparison. The inactive violaxanthin deepoxidation in npq1 was simulated by reducing the rate constant k3 by a factor of 1000 relative to WT. Similarly, the inactive PsbSdependent quenching in npq4 was simulated by decreasing the rate constant k9 by a factor of 1000 relative to WT. (2) v 3(t)=k3⋅[1−Zea(t)]⋅ 1 1+ [ KQ,VDE H L (t) ] nVDE (3) v 9(t)=k9⋅ [ 1−PsbSact(t) ] ⋅ 1 1+ [ KQ,PsbS H L (t) ] nPsbS (4) v 5(t)=k5⋅ ⎧ ⎪ ⎨ ⎪ ⎩� Atot −ATP(t) � −a⋅ ATP(t) � HL(t) � 14 3 ⎫ ⎪ ⎬ ⎪ ⎭ FIGURE 2 | A scheme of the new version of the DREAM model (BDM2) that, in contrast to the parent version BDM (Fuente etal.2024) differentiates between PsbSand VDEdependent mechanisms of qE. The magentacolored sinusoidal curve represents harmonic light modulation. The oscillations of amplitude u1 and period T = 1/f (f is the frequency) are superimposed on the constant light level u0. The green color marks the independent variables. The black color is used for dependent variables and model parameters. The purple color marks the model variables assumed to be constant in time. 13993054, 2025, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ppl.70421 by University Palacky, Wiley Online Library on [31/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 6 of 15 Physiologia Plantarum, 2025 To compare the BDM2 simulations with experiments, we normalized the instantaneous chlorophyll fluorescence signal measured by the PAM method, F′(t), to the maximum FM attained in a multipleturnover saturating flash in a darkadapted plant. With these modifications, one obtains for the normalized instantaneous chlorophyll fluorescence yield ChlF(t) the following expression: where RCIIclosed(t) is the dependent variable in BDM2 that represents the fraction of the closed reaction centers of PSII, and Zea(t) and PsbSact(t) are two of the six independent variables that represent fractions of the respective quenchers. Zeamax and PsbSmax are model parameters corresponding to the maximal NPQ when the respective quenchers are fully active. ФIImax ( ≝ F V FM ) is the maximum quantum yield of PSII photochemistry determined in the darkadapted state, where FV = FM − F0 is the maximal variable chlorophyll fluorescence yield in the darkadapted state (reviewed in Lazár2015). The details of the Equation(5) derivation, using the approximation for F0′(t) (Oxborough and Baker1997) are provided in the Supporting Information. 3 | Results 3.1 | The ChlF(t) Dynamics in the WT A. thaliana Col0 The experimental results obtained with the WT A. thaliana Col0 are shown in Figure 3. The plots were obtained by calculating A0, A1, A2, A3, A4, and τ1/T, τ2/T, τ3/T, τ4/T in Equation(1) for each experimental dataset, followed by averaging and computing standard errors based on measurements on three plants. The average values of the parameters were used in Equation(1) to find the analytical representation of the data plotted by thesolid lines in Figure3. The error bars in Figure3 show the variability of the analytical functions that originated from the experimental errors. The details of raw data, averages, and standard errors are shown in Figure SI1. The individual panels in Figure3 represent the normalized steadystate dynamic ChlF(t) response pattern of the plants exposed to actinic light oscillating with periods T = 1 s (A), 5 s (B), 10 s (C), 30 s (D), 1 min (E), 2 min (F), 4 min (G), and 8 min (H). Each panel shows three curves corresponding to light oscillating between 100 and 200, 100 and 400, and 100 and 800 μmol photons m−2 s−1 of PAR. As in Figure2, each plotted curve consists of two phases: the first one when the light intensity oscillation starts at 100 μmol photons m−2 s−1 and gradually increases (ascending phase, yellow line) up to the maximum value (200, 400, or 800 μmol photons m−2 s−1) and the second one when the light intensity decreases back to 100 μmol photons m−2 s−1 (descending phase, blue line). The orientation of the loop is further emphasized by the purple, counterclockwise, and orange, clockwise arrows in Figure3. The results demonstrate that ChlF(t) responses strongly depend on the oscillating light's period and amplitude. The signal loops in Figure3 mostly show two ChlF(t) values for the same incident light intensity, depending on the illumination history; such behavior is called hysteresis. The term hysteresis is derived from the ancient Greek expression for “lagging behind”. The hysteresis loops in Figure3 differ depending on whether the delay arises from constitutive photosynthetic processes or the regulatory responses. These two types of hysteresis will be categorized as constitutive and regulatory, respectively. The ChlF(t) response lagged the oscillating light when the periods were shorter than 30 s, that is, ChlF(t) was lower in the ascending light oscillation phase than in the descending phase for the same light intensity (Figure3A–C). Such a delayed response is observed in many biological, chemical, and physical systems (Mayergoyz2003; Strogatz2018). We shall show further that this type of hysteresis occurs in all investigated plants, regardless of whether their NPQ mechanisms are fully intact, as in the WT, or compromised, as in the mutants. Such constitutive, regulationindependent hysteresis occurs due to the delays in the primary photosynthetic reactions relative to rapidly changing light. The constitutive hysteresis of photosynthesis is ratedependent and, as such, decreases when the light oscillations are slower than the characteristic times of photosynthetic reactions. The loops representing the constitutive hysteresis in Figure3A–C were nearly elliptical for the lowand mediumamplitude oscillations (100– 200 and 100–400 μmol photons m−2 s−1) and exhibited signs of saturation in the highamplitude oscillations (100–800 μmol photons m−2 s−1, Nedbal and Lazár2021). The orientation of the constitutive hysteresis loops in Figure3 is counterclockwise. The ChlF(t) dynamics changed strikingly when the oscillation periods increased from T = 10 to 30 s (Figure3D). The loop directions changed from counterclockwise, which were observed with shorter periods (Figure 3A–C), to clockwise orientation in the mediumand highamplitude oscillations of the 30s period (Figure3D). This dynamic feature was observed in all light oscillation amplitudes, also with periods longer than 30 s (Figure3E–H). In this case, ChlF(t) was higher in the light ascending phase than in the descending phase, and ChlF(t) started to decrease already in the light ascending phase, that is, the ChlF(t) maxima were reached before the light intensity peaked. This results from a delay in the regulatory response of NPQ, that is, from regulatory hysteresis. In our experiments with the highamplitude light oscillations, the regulatory hysteresis dominated in the period T = 1 min and decreased as the period further increased (Figure3G,H). Thus, the ChlF(t) dynamics under high-amplitude and slow oscillations converged to the typical steadystate P–I curves, in which hysteresis is negligible because the photosynthesis apparatus has enough time to settle to the dynamic homeostasis for each light level, and little effect of the light history is therefore expected. Significant hysteresis remained even in the long periods (Figure3G,H) when the low and medium oscillation amplitudes were applied. This may indicate that the mechanisms reducing hysteresis in the highamplitude oscillations and, therefore, the convergence to the steady-state P–I, require high light. The shape of the dynamic pattern in the high-light oscillations also supports this hypothesis. (5) ChlF (t)≝ F�(t) FM = � 1−Zeamax ⋅Zea(t) � ⋅ � 1−PsbSmax ⋅PsbSact(t) � ⋅ ⎡⎢⎢⎣ 1−RCIIclosed(t) 1+ΦIImax 1−Φ IImax ⋅ � 1−Zeamax ⋅Zea(t) � ⋅ � 1−PsbSmax ⋅PsbSact(t) � +RCIIclosed(t) ⎤⎥⎥⎦ 13993054, 2025, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ppl.70421 by University Palacky, Wiley Online Library on [31/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 7 of 15 3.2 | The ChlF(t) Dynamics in the A. thaliana npq1 and npq4 Mutants The npq4 mutant, which does not have the PsbS protein (Li et al. 2000), and the npq1 mutant, which cannot convert violaxanthin into zeaxanthin (Niyogi etal.1998), both exhibit ChlF(t) dynamic responses that differ from those of the Col0 WT (Figure 4). The top row of stimulus–response plots in Figure4A–C shows the differences for the period T = 1 s that was associated with constitutive hysteresis in Figure 3. The FIGURE 3 | The ChlF(t) = F′(t)/FM dynamics in the WT A. thaliana Col0. The steadystate dynamics of ChlF(t) is shown as a function of light intensity, PAR. The light oscillated with eight different periods and three amplitudes (three different yellow–blue loops in each of the eight panels). The dynamics represent the means of three independent biological replicates, with error bars indicating standard errors (n = 3). The oscillation periods are noted in the legend of each panel, while the oscillating light intensity range for each loop is seen in the abscissa axis. The yellow–blue color code is the same as in Figure1, and the loop arrows at the bottom right corner of each panel indicate the orientation of the loops. 13993054, 2025, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ppl.70421 by University Palacky, Wiley Online Library on [31/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 8 of 15 Physiologia Plantarum, 2025 dynamic patterns in the two lower rows (panels D–I), with T = 1 and 4 min, were dominantly formed by the regulatory hysteresis. The raw data and further details are shown in Figures SI3 and SI5. The light oscillations with the short period of T = 1 s (Figure4A–C) elicited ChlF(t) responses that were qualitatively similar in all three genotypes except for the average ChlF(t) levels, which were lower in the WT compared to the mutants. The WT plants were responding by NPQ that was partially incapacitated in the mutants, and therefore, the average ChlF(t) yield in the mutants was higher than that in the WT. As NPQ responded to the average light levels, the ChlF(t) in WT plants was the lowest in highamplitude oscillations. The opposite was the case for lowamplitude oscillations. Except for this difference in the average ChlF(t) levels, the steadystate dynamic patterns found in rapidly oscillating light in the WT and mutant plants were similar. This suggests that the T = 1 s loop is formed by constitutive rather than regulatory hysteresis. In contrast to T = 1 s, it was the regulation that essentially formed the hysteresis found in the oscillations T = 1 and 4 min in the WT (Figure 4D,G) and in the npq1 mutant (Figure4E,H), a feature that was largely absent in the npq4 mutant (Figure4F,I). The experiment shows that regulatory hysteresis occurs due to the PsbSdependent qE that is active in the WT and npq1, but not in npq4 plants. Regulatory hysteresis was weaker in T = 4 min than in T = 1 min, presumably because ChlF(t) was already approaching steadystate in the long oscillation period, and, thus, the relative effects of regulations were less apparent with T = 4 min than with T = 1 min. The absence of zeaxanthindependent qE in the npq1 mutant and PsbSdependent qE in the npq4 mutant led to higher amplitudes of the ChlF(t) patterns in Figure4E,H, and Figure4F,I compared to those in Figure4D,G that represent the WT. This shows that both types of qE are required for dynamic homeostasis, which decides the stable levels of NPQ. Overall, ChlF(t) in WT plants was much less sensitive to light oscillations than in the mutants: The stimulus–response patterns of the WT were nearly flat even when the oscillations reached high light levels (Figure4G). This indicates that in the WT plants, the efficient pHdependent qE quenching balanced the light fluctuations and responded to the mean irradiance, enabling the system to maintain energetic homeostasis despite large changes in light intensity. 3.3 | Comparing the ChlF(t) Dynamics Observed in Experiments With the BDM2 Model Simulations The experimentally measured ChlF(t) responses are compared with those simulated by BDM2 in Figure5. Dashed lines represent the experimental data, and the simulations are shown by full lines. The comparison is done for short, T = 1 s, and long, FIGURE 4 | The dynamics of ChlF(t) = F′(t)/FM in the A. thaliana Col0 WT (left panels A, D, G), npq1 mutant (central panels B, E, H), and npq4 mutant (right panels C, F, I). The top row panels (A–C) represent ChlF(t) dynamic patterns obtained with light oscillating with period T = 1 s, the middle row (D–F) with T = 1 min, and the bottom row (G–I) with T = 4 min. The yellow–blue color code is the same as in Figure1. The loop arrows at the bottom right corner of each panel indicate the orientations of the loops. 13993054, 2025, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ppl.70421 by University Palacky, Wiley Online Library on [31/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 9 of 15 T = 4 min periods of the light oscillations that lead to constitutive and regulatory types of hysteresis, respectively. The ChlF dynamics of WT in the rapidly oscillating light (T = 1 s) are delayed relative to the forcing light phase. This delay originates in the primary photosynthetic processes. It is, therefore, called constitutive hysteresis with a counterclockwise orientation of the stimulus–response loops (Figure5A). The same was also observed in the npq1 (Figure5B) and npq4 (Figure5C) mutants, confirming that constitutive hysteresis occurs irrespective of the qE mutations, irrespective of regulation. The constitutive hysteresis was found in the experiments (dashed lines in Figure5) and confirmed by the BDM2 simulations (solid lines in Figure5). The model simulations were obtained by including both the Zea(t) and PsbSact(t) model variables for WT (Figure5A), or by setting very small values of the rate constants of formation of Zea in the npq1 mutant or of PsbSact in the npq4 mutant, leading practically to no formation of Zea(t) (Figure5B) or PsbSact(t) (Figure5C) for the npq1 or npq4 mutants, respectively. The ChlF(t) dynamics of WT in the slowly oscillating light (T = 4 min) were formed primarily by the delay of the qE regulation response relative to the forcing light phase. The delayed response of the qE regulation resulted in ChlF(t) pattern that was influenced by increasing quenching only later in the ascending phase of the light (yellow color line segments). Analogous regulatory delays formed the ChlF(t) response during the descending light phase (blue color line segments). The regulatory hysteresis was strongly expressed in the WT data as well as simulations (Figure5D). It led to the clockwise orientation of the stimulus– response loops. Regulatory hysteresis was also observed and simulated with the npq1 mutant that was competent in the PsbSdependent quenching but lacked the VDE mechanism (Figure 5E). The regulatory hysteresis can, therefore, be linked to the PsbSdependent quenching. The absence of VDEdependent regulation was expressed by the ChlF(t) levels that were significantly higher in the npq1 mutant (Figure5E) than in WT (Figure5D). This suggests that the VDEdependent quenching acts in the WT on average ChlF yield over periods much longer than 4 min. Regulatory hysteresis was barely seen in the ChlF(t) responses to the slowly oscillating light in the npq4 mutant that lacks the PsbS quenching capacity (Figure5F). Also, the average ChlF(t) levels were higher in the npq4 mutant than in the npq1 mutant and in the WT plants. This suggests that regulatory protection against oscillating light is largely incapacitated in the npq4 mutant. 3.4 | Molecular Mechanisms Shaping the ChlF(t) Responses to Oscillating Light The dynamics of the inactive forms of the quenchers, violaxanthin (1 − Zea(t)) and the inactive form of PsbS (1 − PsbSact(t)), and reduced PQ (PQtot − PQ(t)), which are expected to be largely positively correlated with ChlF(t), were simulated and are shown together with the concentration of H+ in the lumen in Figure6. The dynamics in WT are distinctly different in the fast and slow light oscillations. The differences can be used to understand the molecular mechanisms forming the constitutive (T = 1 s) and regulatory (T = 4 min) hysteresis types. The analogous simulations for the npq1 and npq4 mutants are compared with the WT simulations in Figure SI6. The simulations confirm that the PsbSand VDEresponses were too slow to follow the rapid light oscillations (T = 1 s). The FIGURE 5 | The experimentally measured ChlF(t) dynamics (dashed lines) presented in Figure4 of WT A. thaliana Col0 (panels A and D) and of the npq1 (panels B and E) and npq4 (panels C and F) mutants are compared with simulations (solid lines) obtained with the BDM2, in which both the Zea(t) and PsbSact(t) quenchers were included (panels A and D) or the Zea(t) (panels B and E) or PsbSact(t) (panels C and F) quenchers were set to zero. The data and simulations were obtained with the short and long light oscillation periods, which have been shown to lead to the constitutive (T = 1 s) and regulatory (T = 4 min) hysteresis. The color code and symbols are the same as in the previous figures. 13993054, 2025, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ppl.70421 by University Palacky, Wiley Online Library on [31/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License