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Intrinsic kinetic model of photoautotrophic microalgae based on chlorophyll fluorescence analysis
Accepted Manuscript
Intrinsic kinetic model of photoautotrophic microalgae based on chlorophyll fluorescence analysis Jiawen Xiong , Linlin Yu , Zhibin Zhang , Ya Wang , Weiying Wang , Huilin Yang , Riming Yan , Du Zhu PII: DOI: Article Number: Reference:
S0025-5564(18)30651-5 https://doi.org/10.1016/j.mbs.2019.108234 108234 MBS 108234
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Mathematical Biosciences
Received date: Revised date: Accepted date:
5 November 2018 19 July 2019 19 July 2019
Please cite this article as: Jiawen Xiong , Linlin Yu , Zhibin Zhang , Ya Wang , Weiying Wang , Huilin Yang , Riming Yan , Du Zhu , Intrinsic kinetic model of photoautotrophic microalgae based on chlorophyll fluorescence analysis, Mathematical Biosciences (2019), doi: https://doi.org/10.1016/j.mbs.2019.108234
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Highlights
A intrinsic kinetic model for microalgae under photoautotrophic condition is proposed.
The model relies on growth kinetics determination and chlorophyll fluorescence analysis which
biotechnological cultivation.
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can effectively monitor the state of the photosynthetic apparatus of microalgae in the process of
The model can model can realistically reflect the light energy utilization efficiency of microalgae
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as well as their intrinsic growth kinetic characteristics.
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Intrinsic kinetic model of photoautotrophic microalgae based on chlorophyll fluorescence analysis Jiawen Xionga, Linlin Yua, Zhibin Zhanga, Ya Wangb, Weiying Wanga, Huilin Yanga, Riming Yana,*, Du Zhua,b,* Key Laboratory of Protection and Utilization of Subtropic Plant Resources of Jiangxi Province, Jiangxi Normal University, Nanchang 330022, Jiangxi, China; b
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Key Laboratory of Bioprocess of Jiangxi Province, Jiangxi Science & Technology Normal University,
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Nanchang 330013, Jiangxi, China
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* Corresponding author: [email protected]; [email protected]
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Abstract: As photoautotrophic microorganisms, microalgae feature complex mechanisms of photosynthesis and light energy transfer and as such studying their intrinsic growth kinetics is fairly difficult. In this article, the quantum yield of photochemical reaction was introduced in a study of microalgal kinetics to establish an intrinsic kinetic model of photoautotrophic microalgal growth. The
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blue-green algae Synechococcus sp. PCC7942 was used to verify the kinetic model developed using chlorophyll fluorescence analysis and growth kinetics determination. Results indicate that the kinetic model can realistically reflect the light energy utilization efficiency of microalgae as well as their
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intrinsic growth kinetic characteristics. The model and method proposed in this article may be utilized in intrinsic kinetics studies of photoautotrophic microorganisms.
Keywords: Microalgae; Chlorophyll fluorescence analysis; Intrinsic kinetic model; Light utilization
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efficiency
Abbreviations
Maximum quantum yield of PS II under dark adaptation
F'v/F'm
Maximum quantum yield of PS II in light-adapted state
PS II
Photosystem II
QA
Primary electron acceptor in PS II
QA−
Reduced QA
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Fv/Fm
Introduction
Most microalgae are photoautotrophic microorganisms that can utilize light as energy and CO2 as a
carbon source to carry out photosynthesis. Light energy exerts a great impact on algal cell growth and relevant product generation. As such, studies on the absorption and utilization of light energy are an important aspect of research in algal growth kinetics[1]. In early 1982, Aiba reported the results of his
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study on the growth kinetics of photosynthetic microbes[2]. Many similar reports have been published since then [3; 4; 5; 6]. For example, a turbidostatic culture was first to perform on Spirulina platensis and found that the maximum light yield (Ymax) of algal cells decreases while the actual maintenance coefficient (m) increases with increasing incident light intensity[7]. Iehana also observed this
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phenomenon by performing continuous and batch cultures on Chlorella vulgaris[8]. The results of these studies, however, conflict with the concepts of classical growth kinetics, which state that Ymax and m, the intrinsic parameters of cell growth kinetics, must be relatively constant.
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Microalgal photosynthesis, which involves the absorption, transmission, and transformation of light, is a process by which light energy is transformed into chemical energy[9]. Besides photochemical reaction, the light energy absorbed by microalgae may be released as fluorescence or consumed as heat
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to some extent[10]. That is to say, the light energy consumed during photosynthesis only accounts for part of the total energy absorbed by microalgae, and the proportion of light energy utilized gradually
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decreases with variations in light intensity. The photoautotrophic growth kinetics parameters of algal
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cells described in these studies were obtained based on the hypothesis that all of the light energy absorbed by algal cells is utilized completely. Thus, the parameters obtained, Ymax and m, are not intrinsic
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kinetic parameters; instead, these values reflect the apparent maximum growth yield and maintenance
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coefficient of algal cells, respectively. Chlorophyll fluorescence reflects primary processes of photosynthesis, including light energy
absorption, excited energy transmission, and photochemical reaction. Chlorophyll fluorescence analysis allows estimation of various photosynthetic parameters, such as quantum efficiency, photosynthetic capacity, and electron transport rate. As a rapid and sensitive photosynthetic probe, this technique has been widely used in studies of photosynthesis in algal cells[11]. In the present article, chlorophyll
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fluorescence and metabolic flux analyses were performed to investigate the energy utilization efficiency of Synechococcus sp. PCC7942, a blue-green algal species, under different culture conditions. Results indicate that light utilization efficiency is closely correlated with light intensity and nutritional type[12; 13].
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Blue-green algae perform critical functions in studies of photosynthetic mechanisms and microalgal light utilization. To reveal the intrinsic growth kinetics of photoautotrophic microalgae and establish an appropriate model describing its growth process, Synechococcus sp. PCC7942 was subjected to
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chlorophyll fluorescence and traditional growth kinetics analyses.
Materials and methods Algae and culture medium
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Synechococcus sp. PCC7942 and Synechocystis sp. PCC6803 were provided by the Freshwater
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Algae Culture Collection of the Institute of Hydrobiology, Chinese Academy of Sciences. Modified
Culture methods
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BG-11 culture medium was used throughout this work[12].
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The algae were cultured in a flat-plate glass photobioreactor with a total volume of 2.5 L; here, the incident light intensity was adjusted by varying the position of the light source outside the
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photobioreactor[12]. The culture temperature was 28 °C, and the air flow rate was set to 0.5 vvm. After inoculation, the initial algal culture concentration was 0.04 g/L (dry cell weight). Batch culture was performed until a stable phase was achieved, after which a two-channel constant flow pump (BT1-200E, Shanghai Qite Analytical Instrument Co., Ltd.) was used to add fresh medium to the culture and pump out appropriate volumes of culture solution at constant velocity. The culture solution was sampled every 12 h to determine thallus concentrations. A stable state was defined as four consecutive measurements 5
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with a variation of <5%.
Analytical methods Cell concentration determination Algal cell culture solutions of different concentrations were collected, and their optical density
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OD730 was detected by a 752 spectrophotometer (Shanghai Analytical Instrument Factory). Algal solutions of equal volume with different OD730 were filtered through a 0.45 μm cellulose acetate membrane filter, and the residual algae were dried at 105 °C to a constant weight. The algal cakes were
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weighed three times, and their average weight was calculated. Results indicated that the OD730 of the algal solutions ranged from 0.18 to 0.85 and linearly correlated with their dry weights. The relation between dry cell weight (X) and OD730 followed the equation X (g/L) = 0.352 × OD730 with R2 = 0.998.
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Light intensity determination
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A radiometer measuring photosynthetically active radiation (FGH-1; Photoelectric Instrument Factory of Beijing Normal University) was used to determine light intensity.
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Average light intensity Iave and specific absorption rate of light energy Eab I (1 exp[ L K a X ]) L Ka X
Eab I ave Ka I ave
Am B X
(1)
(2)
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I ave
where I, L, Ka, and X respectively indicate the incident light intensity, light path, specific extinction coefficient, and cell concentration of the cultures; Am and B reflect parameters in the hyperbolic model of light attenuation[14]. Light energy-based growth yield calculations According to the model described by Pirt[15], the specific absorption rate of light energy of algal
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cells shows a linear relation with the specific growth rate: Eab
Ymax
m
(3)
where μ is the specific growth rate and Ymax and m are the maximum growth yield coefficient of algal
Chlorophyll fluorescence parameter determinations
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cells based on light energy absorption and light energy maintenance coefficient, respectively.
An AquaPen 100 (AP100) fluorometer (Photon Systems Instruments, Czech Republic) was used to determine various parameters of chlorophyll fluorescence. During detection of the maximum
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fluorescence Fm and Fm' of the algal solutions, the light intensity used to detect basic fluorescence Fo was set to 0.01 μmol•m−2 •s−1 and the light intensity of saturation pulses was set to 3000 μmol•m−2 •s−1 with a duration of 0.8 s. Other chlorophyll fluorescence parameters were automatically detected by the
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fluorometer.
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Experimental replication and statistical treatment All the experiments were performed in triplicate and the results were expressed as mean ± SD (n=3).
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The data were analyzed statistically using IBM® SPSS® Statistics software version 13.0. Data plotting
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were achieved using OriginPro® 8.0724.
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Results and Discussion Establishment of intrinsic kinetic model of microalgal growth Based on photosynthetic theory, quantum yield is related to the state of photosystem II (PS II).
Depending on the illumination history and light intensity, the state of PS II is dynamic[16]. Describing the state of PS II is a key step in establishing a photosynthetic model. Under nonphotoinhibition conditions, PS II exhibits two states: the open state (reactive) and the closed state (activated). After
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photon absorption, PS II in the open state switches to the closed state[17]. The change rate of this switch is directly proportional to the light intensity and effective absorption cross-sectional area of PS II. After photochemical reaction and electron release, the closed PS II switches to the open state. This change rate is directly proportional to the electronic release rate and inversely proportional to the turnover time τ of
d 1 PSII I (1 ) dt
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the electron transport chain. Therefore, the dynamic equation of PS II is as follows [18]: (4)
where υ is the probability of PSUs at the reactive state, or the probability that PSII is in an open state,
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also called the ratio of PS II reaction centers participating in photon capture and photochemical reaction or the quantum yield of photochemical reaction, σPS II is the effective absorption cross-sectional area of PS II, I is the intensity of incident light, and τ is the turnover time of the electron transport chain.
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At stable states,
1
PS II
, then
1 PSII I
(5)
1 1 PS II I
Ik Ik I
(6)
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Let I k
1
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where Ik is the half-saturation irradiance, or is the irradiance at which the photosynthetic rate is
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half-maximum, has been extensively discussed in literatures [16; 19]. As an empirical model, Equation (6) has established the quantitative relationship between υ and Ik.
Unlike the photosynthesis-Irradiance response curve[17], this model presents a quasi-hyperbolic form. The parameter υ in algal cells gradually decreases with increasing light intensity, which means the light energy utilization efficiency of algal cells consistently decreases with increasing light intensity. This result may be explained as follows: under photoautotrophic conditions, light energy increases promote 8
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competition by heat consumption, which limits the photochemical process of PS II; that is, more photoreaction centers are closed. Only the light energy absorbed by open photosynthetic reaction centers can be utilized during photochemical reaction. In particular, under subsaturated light intensity, the photosynthetic rate of microalgae cells reaches half of the maximal level, and at that point about half of
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the photosynthetic center is open, which means that the value of υ is about half. To establish an intrinsic kinetic model of microalgal growth, υ was introduced to the Pirt model (3). Eab Eab
max
Y
m (7)
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where E ab represents the actual amount of light energy used in photosynthesis and Ymax and mΘ
respectively represent the actual maximum growth yield coefficient of algal cells based on light energy absorption and actual light energy maintenance coefficient; here, Ymax and mΘ are intrinsic kinetic
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parameters of photoautotrophic growth. The relationships between Ymax and Ymax and between m and mΘ
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can be determined using Formulas (3) and (7).
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Ymax Ymax /
Ik m Ik I
(9)
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m m
Ik I Ymax (8) Ik
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Microalgal light energy utilization efficiency and verification of the kinetic model Light energy-based growth yield of microalgae under different light intensities Relatively stable μ values were obtained by using a chemostat culture and changing the dilution rate
D during culture. The relation between Eab and μ can be determined according to the Eab equation (Formula 2) and Pirt model (Formula 3; Fig. 1). In the chemostat culture, increases in μ decreased algal cell density, thereby increasing the average light intensity in the reactor. Under the same μ, increases in
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incident light intensity also enhanced the average light intensity in the reactor. The Eab of algal cells was directly proportional to the average light intensity in the reactor. Thus, improving both μ and incident light intensity can increase Eab. The Ymax and m of Synechococcus sp. PCC7942 under different light intensities were subsequently
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calculated. Figs. 2 and 3 demonstrate that the Ymax of Synechococcus sp. PCC7942 constantly declines with increasing light intensity under photoautotrophic conditions. This finding suggests that although μ increases with increasing light intensity, the conversion and utilization rates of light energy consistently
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decline. By contrast, m showed a tendency to increase linearly, which means the energy required for cell maintenance under high light intensity is higher than that required under low light intensity. With increasing light intensity, the energy available for cell maintenance also increases.
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Classical growth kinetic models of heterotrophic microorganisms suggest that the maximum cell yield Ymax and the maintenance coefficient m are intrinsic parameters of the cell and should be kept
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constant. However, the values of these parameters in these conventional models varied with the change
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of light intensity due to the decline of the bioenergy yield for microalgae[7; 8]. Actually, for the complexity of processes of photosynthetic transformation of light energy, absorption of a light quantum
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entails charge separation in the primary photoactive pair and is attended by conformational changes in
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the photosynthetic reaction centers (RC) components that prevent back electron transport and loss of energy through fluorescence[20]. There are various electron transfer models take account of their thermodynamic characteristics and varied-nature mechanisms of attending energy losses during the photosynthesis process[21; 22; 23]. As the solution of maintenance coefficient m, reflects the cost of a cell to survive that expend in the photosynthesis (including losses in the primary process), metabolism and reproduction processes, is rather complicated. Therefore, the classical Pirt model made an important
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simplification that the losses in the photosynthetic apparatus are a constant fraction and thus supposed the maintenance coefficient is also a constant. However, with the increase of the light intensity, especially in the case of exceeding the cell needs, the microalgae will consume a large amount of energy for avoiding photoinhibition, repairing photodamage and heat dissipation[10]. As a consequence, the
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values of Ymax and m based on the apparent absorption energy in above model are varied as well, that is, with the enhancement of light intensity, the Ymax decrease distinctly whereas m increases gradually. In present study the coefficients υ was introduced into the modified model to acquire the intrinsic maximum
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Θ cell yield 𝑌max and maintenance coefficient mΘ that are constant during the growth of autotrophic
microalgae and to be consistent with the expression of the classic model. Fluorescent quantum yield under different light intensities
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Fluorescent quantum yield is an important indicator of photosynthetic efficiency. Among the chlorophyll fluorescence parameters available, Fv/Fm and F′v/F′m are two important parameters that can
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best reflect light energy utilization efficiency. Fv/Fm represents the maximum photochemical yield of
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algal cells in PS II under dark adaptation. As Fv/Fm is stable in common physiological conditions, it is a characteristic value of photosynthetic organisms[24]. F'v/F'm represents the photon capture efficiency in
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open photosynthetic reaction centers[25]. The degree of limitation of the photochemical reaction in PS II
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due to competition by heat consumption can be quantified by F'v/F'm. As such, studying the Fv/Fm and F'v/F'm values of microalgae under different light intensities is of great significance when discussing light energy utilization efficiency. Using the AquaPen 100 fluorometer, the maximum υ of Synechococcus sp. PCC7942 was determined under OJIP mode. Fig. 4 shows that Fv/Fm and F′v/F′m basically remain constant over a large concentration range of algal cells under the same incident light intensity. In particular, Fv/Fm values
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remained stable at about 0.7 under different light intensities; this finding means Fv/Fm is a characteristic parameter of algal cells. As the light intensity increased to 115 μmol•m−2•s−1, the Fv/Fm value declined considerably (P < 0.05), which indicates Synechococcus sp. PCC7942 photoinhibition. At an incident light intensity of 151 μmol•m−2•s−1, the average Fv/Fm was about 0.32, which is only 45% of the normal
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value. Such a finding indicates extensive photoinhibition at the present conditions. The growth status of algal cells demonstrates that cell growth rates constantly increase with increasing light intensity but decrease rapidly at light intensities exceeding115 μmol•m−2•s−1 (P < 0.05). This result demonstrates that
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light is the major factor affecting algal cell growth under low-intensity light conditions; by contrast, photoinhibition is the major inhibiting factor influencing cell growth under high-intensity light conditions.
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F'v/F'm decreased steadily with increasing light intensity, which means the degree of heat consumption by algal cells constantly increases under the same conditions. Such a phenomenon further
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limits the photochemical reaction. Fv/Fm and F'v/F'm were fairly similar under low-light intensity light,
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which indicates low degrees of heat consumption under this condition. However, increases in incident light intensity gradually increased differences in Fv/Fm and F'v/F'm. This phenomenon reveals that the
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degrees of heat consumption and photoinhibition also increase gradually, whereas the proportion of light
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energy used in photosynthesis decreases. Results further confirm that deducing characteristic parameters by introducing υ to the model of microalgal growth kinetics is reasonable. Derivation and verification of parameters of intrinsic kinetic model of growth Using Formulas (8) and (9) and experimental data, nonlinear regression (Figs. 2 and 3) via the least-squares method was performed to deduce the parameters of the intrinsic kinetic model of Synechococcus sp. PCC7942 growth; here, Ymax 0.0119 0.0025 g/kJ and m 0.705 0.063 kJ/(g h) . Aiba
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indicated that the YG and m of most microalgal cells are 1.4 × 10−3–1.1 × 10−1 g/kJ and 0.08–6.9 kJ/(g•h), respectively[2]. The light intensity (Ik) of Synechococcus sp. PCC7942 under half-saturation conditions was further calculated as 123.7 ± 16 μmol•m−2•s−1. Light energy absorption and utilization by algae is considered to balance out at Ik[18]. Beyond this point, the light energy absorbed by algae will exceed the
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amount of light energy utilized with further increases in light intensity. This surplus light energy cannot be used for photosynthetic oxygen evolution or CO2 fixation and must be consumed through other pathways. In general, when the light intensity is lower than Ik, the degree of light damage is minimal,
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otherwise, the degree of light damage intensifies[26]. Results illustrated in Fig. 4 show that photoinhibition occurs in Synechococcus sp. PCC7942 when the light intensity exceeds 115 μmol•m−2•s−1, which is close to the Ik value calculated by the model.
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In the intrinsic kinetic model of microalgal growth, υ represents the probability of PSUs at the reactive state during photosynthesis. To verify the reliability of υ, chlorophyll fluorescence analysis was
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employed to determine microalgal photosynthetic efficiency under different light intensities. The
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photochemical quenching coefficient qp, as a chlorophyll fluorescence parameter, reflects the proportion of light energy absorbed by PS II antenna pigments and used in photochemical electron transport[27].
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Thus, qp and υ present similar meanings in the model. PS II reaction centers must remain open to achieve
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high qp. Thus, qp can reflect the open degree of PS II reaction centers; in fact, qp reflects the reducing state of primary electron acceptor QA in PS II, which is produced by oxidation of QA−. The larger the qp value, the larger the amount of QA produced by QA−, that is, the higher the activity of PS II electron transport. By contrast, if qp is low, electron flow from PS II oxidation sites to PS II reaction centers is inhibited. This information may be used to verify υ in the proposed model using qp. Fig. 5 shows that the qp values are very close to υ values under low light intensity and that larger
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errors in these parameters may be observed under higher light intensity. Such a finding may be attributed to the complexity of the photosynthetic mechanism. As light intensity increases, interferences by nonphotochemical factors may also increase and the conformations of relevant enzymes in the electron transport chain may be altered[28]; these phenomena may result in slight differences between
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the actual and theoretical open degrees of PS II. Despite this problem, the proposed model can reflect the influence of light intensity on light energy utilization to some extent. In particular, the model is able to predict light energy utilization efficiency under a specific light intensity as long as the half-saturation
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light intensity (Ik) is known. Thus, the model provides an important basis for optimizing illumination conditions for microalgal cultures.
To verify the applicability of the model developed in this work further, the relation between the E ab and μ of another blue-green alga, Synechocystis sp. PCC6803, was studied under different light
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intensities. Fig. 6 demonstrates that E ab shows a linear relationship with μ under incident light of
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different intensities. This result confirms that YG and mΘ remain almost unchanged under different light
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intensities; thus, these properties are parameters of the intrinsic growth kinetics of Synechocystis sp. PCC6803.
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During the microalgal photoautotrophic process, photons are captured by PS II antenna pigments
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and light energy is converted via one of three pathways[29]: (1) some photons may generate activation energy and enter the electron transport chain, where they are eventually utilized in photosynthesis; (2) some light energy may be consumed as heat; and (3) a small proportion of light energy may be lost in the form of fluorescence. Therefore, in the Pirt model of substrate consumption, Eab is based on macroscopic absorption. Ymax and m calculated by Formula (3) are apparent maximum growth yield and apparent light energy maintenance coefficients, respectively, rather than the intrinsic parameters of algal cells. In fact,
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the light energy used in photochemical reactions accounts for only a portion of all of the energy absorbed by algal cells, and only the energy captured by open PS II reaction centers and utilized in photochemical reactions may be effectively processed. The ratio of open to closed PS II reaction centers directly determines photosynthetic efficiency[30]. Here, υ refers to the ratio of light energy used in
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photochemical reactions to the light energy absorbed by cells. As light intensity increases, nonphotochemical processes in algal cells, such as heat consumption, also increase, thereby causing constant reductions in υ. On the one hand, reductions in quantum yield υ
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require algal cells to absorb more light energy to reproduce at an equal rate. That is, the biomass produced per unit light energy decreases. Under these circumstances, the Ymax of algal cells decreases with increasing light intensity. On the other hand, increases in light intensity enhance the degree of heat
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consumption and energy required to maintain algal cells. Thus, m constantly increases with increasing light intensity.
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The biomass productivity is an important parameter in microalgal culture. Mathematical analysis
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was conducted in order to predict the rate of microalgal mass production, which is supported by the actual values of photosynthetic productivity per cell. Quantitative photosynthetic productivity of the
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microalgae depends on a balanced contribution between the photosynthesis irradiance and the
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photosynthetic efficiency of the photosystem. At subsaturating irradiance, photosynthesis is limited by light absorption. Despite of the most number of reactive PSUs and with high absorption efficiency in the present model, the efficiency of light energy utilization is considered negligible compared to the energy supply. The cells will grow slowly as a consequence of the photosynthetic production in the situation. Conversely, in light saturation, photosynthesis is limited on the acceptor side of photosystem[17]. The photosynthetic efficiency of the organisms yield to the excitation energy from the light-harvesting
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systems to photosystem I (PSI) and photosystem II (PSII). As a consequence, the production of biomass is not proportional to the increase of radiation because of the gradual reduction of light absorption efficiency. Therefore, the best way to promote photosynthetic production is to improve the light energy utilization efficiency on the basis of sufficient irradiance. As shown in the present model, the Formula (7),
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to improve total light energy supply (Eab) while increasing light efficiency (υ), that is, increasing the Θ effective light energy supply (𝐸ab ), is an effective way to promote the growth and metabolism of
microalgae cells.
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Using the chlorophyll fluorescence parameters Fv/Fm and F'v/F'm, the photosynthetic characteristics of PS II reaction centers of photoautotrophic Synechococcus sp. PCC7942 under different illumination conditions were revealed. The relevant photosynthesis mechanism was then applied to establish an
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accurate model of υ, which reflects light energy utilization. The kinetic characteristics of photoautotrophic growth of other algae under different conditions can be studied using this model.
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Establishment of an intrinsic kinetic model enables researchers to understand the mechanism of light
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energy utilization by microalgae. The maximum biomass of different microalgae can be estimated by chlorophyll fluorescence analysis. Several reports [31; 32; 33; 34] on the application of chlorophyll
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fluorescence analysis in the estimation and monitoring of microalgal primary production show
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satisfactory results.
Studying various concepts of light energy utilization and conversion is fairly difficult because of the
diverse characteristics of photosynthetic reaction centers and the complexity of the photosynthetic mechanisms of algal cells. Most studies explore photosynthetic efficiency only on the basis of macroscopic photosynthesis. Chlorophyll fluorescence induction kinetics is an intrinsically complex phenomenon. As such, further exploration of the essence of light energy utilization efficiency in
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photoautotrophic microalgae is necessary. Although the model obtained in the present work was successfully applied in blue-green algae, such as Synechococcus sp. PCC7942 and Synechocystis sp. PCC6803, further verification using other microalgae belonging to other species and genera is of great importance. Future studies by our group aim to reveal more information regarding this topic.
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Conclusions
Because the microalgal growth kinetics parameters Ymax and m change with the light intensity under photoautotrophic conditions, determining intrinsic kinetic parameters is difficult. Analysis of the
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microalgal photosynthesis mechanism indicated that variations in kinetic parameters correlate well with the light energy utilization efficiency of microalgae. Therefore, υ was introduced to the classical kinetic equation in the present article, and kinetic analysis of microbial growth was performed to establish an
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intrinsic kinetic model reflecting photoautotrophic microalgal growth. The blue-green algae Synechococcus sp. PCC7942 was used to verify the kinetic model by chlorophyll fluorescence analysis.
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Results indicated that the kinetics model can realistically reflect the light energy utilization efficiency of
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microalgae as well as their intrinsic growth kinetics characteristics; it also effectively solves the problem of variations in kinetic parameters. The model and method proposed in this article not only apply to
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studies on the intrinsic kinetics of photoautotrophic microorganisms but also provide a theoretical basis
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for designing photobioreactors and optimizing the culture process of photoautotrophic microorganisms.
Conflicts of interest There are no conflicts to declare.
Acknowledgments This work was supported by the National Natural Science Foundation of China (No. 20506009), the Jiangxi Provincial Science Fund for Distinguished Young Scholars (20171BCB23037) and the Education
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Development Plan of Young and Middle-aged Teachers in College in Jiangxi Province.
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[30] K. Roháček, Chlorophyll fluorescence parameters: the definitions, photosynthetic meaning, and mutual relationships. Photosynthetica 40 (2002) 13-29. [31] F.L. Figueroa, C.G. Jerez, and N. Korbee, Use of in vivo chlorophyll fluorescence to estimate photosynthetic activity and biomass productivity in microalgae grown in different culture systems. Latin American Journal of Aquatic Research 41 (2013) 801-819. [32] C.G. Jerez, J.R. Malapascua, M. Sergejevová, J. Masojídek, and F.L. Figueroa, Chlorella fusca (Chlorophyta) grown in thin-layer cascades: Estimation of biomass productivity by in-vivo chlorophyll a fluorescence monitoring. Algal Research
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Fluorescence in Microalgae Integrating Photoproduction, Photoinhibition and Photoregulation. Journal of Biotechnology
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194 (2015) 91-99.
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Figure legends Fig. 1. Relation between specific absorption rate of light energy and specific growth rate of Synechococcus sp. PCC7942 under incident light of different intensities. Fig. 2. Maximum growth yield of Synechococcus sp. PCC7942 under incident light of different intensities. Data are presented
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as mean of three replicate samples ± SD (n = 3). Fig. 3. Light energy maintenance coefficient of Synechococcus sp. PCC7942 under incident light of different intensities. Data are presented as mean of three replicate samples ± SD (n = 3).
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Fig. 4. Variation in quantum yield of fluorescence of Synechococcus sp. PCC7942 under different light intensities: (A) 6.90 μmol•m−2•s−1, (B) 15.8 μmol•m−2•s−1, (C) 55.2 μmol•m−2•s−1, (D) 78.2 μmol•m−2•s−1, (E) 115 μmol•m−2•s−1, and (F) 151 μmol•m−2•s−1. Data are presented as means ± SD of three biological replicates (n=3).
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Fig. 5. Photochemical quenching coefficient (qp) of Synechococcus sp. PCC7942 under different light intensities. The straight line represents the theoretical quantum yield of photochemical reaction calculated by the light energy utilization model.
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Fig. 6. Relationship between the specific absorption rate of light energy and specific growth rate of Synechocystis sp.
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PCC6803 under different light intensities.
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Fig.1 -2
Eab (kJ/(gh))
8
6
-1
3.55 molm s -2 -1 7.1 molm s -2 -1 11.04 molm s -2 -1 23.66 molm s -2 -1 39.43 molm s -2 -1 55.2 molm s -2 -1 78.85 molm s -2 -1 118.28 molm s
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Fig. 1 Relation between the specific absorption rate of light energy and specific growth rate of Synechococcus sp. PCC7942 under incident
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light of different intensities.
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Fig.2 0.012
Ymax (g/kJ)
0.009
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0.006
0.000 0
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60
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Incident intensity ( molm s )
Fig. 2 Maximum growth yield of Synechococcus sp. PCC7942 under incident light of different intensities. Data are presented as mean of
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three replicate samples ± SD (n = 3).
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Fig.3 1.2
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m (kJg h )
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Incident intensity (molm s )
Fig. 3 Light energy maintenance coefficient of Synechococcus sp. PCC7942 under incident light of different intensities. Data are presented
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as mean of three replicate samples ± SD (n = 3).
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Fig.4 1.0 Cell concentration F'v/F'm Fv/Fm
Cell concentration (g/L)
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Fig. 4 Variation in quantum yield of fluorescence of Synechococcus sp. PCC7942 under different light intensities: −
−
−
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−
−
−
−
−
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A) 6.90 μmol•m 2•s 1, B) 15.8 μmol•m 2•s 1, C) 55.2 μmol•m 2•s 1, D) 78.2 μmol•m 2•s 1, E) 115 μmol•m 2•s 1, and F) 151 μmol•m 2•s 1. Data are presented as means ± SD of three biological replicates (n=3).
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Fig.5 1.0
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Fig. 5 Photochemical quenching coefficient (qp) of Synechococcus sp. PCC7942 under different light intensities. The straight line represents
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the theoretical quantum yield of photochemical reaction calculated by the light energy utilization model.
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Fig.6 2.4 y=44.45 x +0.306 2 r = 0.958
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(h )
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6.33 molm s -2 -1 11.03 molm s -2 -1 15.76 molm s -2 -1 23.64 molm s -2 -1 39.45 molm s -2 -1 55.16 molm s -2 -1 70.92 molm s
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Fig. 6 Relationship between the specific absorption rate of light energy and specific growth rate of Synechocystis sp. PCC6803 under
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Intrinsic kinetic model of photoautotrophic microalgae based on chlorophyll fluorescence analysis Jiawen Xiong , Linlin Yu , Zhibin Zhang , Ya Wang , Weiying Wang , Huilin Yang , Riming Yan , Du Zhu PII: DOI: Article Number: Reference:
S0025-5564(18)30651-5 https://doi.org/10.1016/j.mbs.2019.108234 108234 MBS 108234
To appear in:
Mathematical Biosciences
Received date: Revised date: Accepted date:
5 November 2018 19 July 2019 19 July 2019
Please cite this article as: Jiawen Xiong , Linlin Yu , Zhibin Zhang , Ya Wang , Weiying Wang , Huilin Yang , Riming Yan , Du Zhu , Intrinsic kinetic model of photoautotrophic microalgae based on chlorophyll fluorescence analysis, Mathematical Biosciences (2019), doi: https://doi.org/10.1016/j.mbs.2019.108234
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Highlights
A intrinsic kinetic model for microalgae under photoautotrophic condition is proposed.
The model relies on growth kinetics determination and chlorophyll fluorescence analysis which
biotechnological cultivation.
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can effectively monitor the state of the photosynthetic apparatus of microalgae in the process of
The model can model can realistically reflect the light energy utilization efficiency of microalgae
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as well as their intrinsic growth kinetic characteristics.
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Intrinsic kinetic model of photoautotrophic microalgae based on chlorophyll fluorescence analysis Jiawen Xionga, Linlin Yua, Zhibin Zhanga, Ya Wangb, Weiying Wanga, Huilin Yanga, Riming Yana,*, Du Zhua,b,* Key Laboratory of Protection and Utilization of Subtropic Plant Resources of Jiangxi Province, Jiangxi Normal University, Nanchang 330022, Jiangxi, China; b
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a
Key Laboratory of Bioprocess of Jiangxi Province, Jiangxi Science & Technology Normal University,
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Nanchang 330013, Jiangxi, China
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* Corresponding author: [email protected]; [email protected]
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Abstract: As photoautotrophic microorganisms, microalgae feature complex mechanisms of photosynthesis and light energy transfer and as such studying their intrinsic growth kinetics is fairly difficult. In this article, the quantum yield of photochemical reaction was introduced in a study of microalgal kinetics to establish an intrinsic kinetic model of photoautotrophic microalgal growth. The
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blue-green algae Synechococcus sp. PCC7942 was used to verify the kinetic model developed using chlorophyll fluorescence analysis and growth kinetics determination. Results indicate that the kinetic model can realistically reflect the light energy utilization efficiency of microalgae as well as their
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intrinsic growth kinetic characteristics. The model and method proposed in this article may be utilized in intrinsic kinetics studies of photoautotrophic microorganisms.
Keywords: Microalgae; Chlorophyll fluorescence analysis; Intrinsic kinetic model; Light utilization
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efficiency
Abbreviations
Maximum quantum yield of PS II under dark adaptation
F'v/F'm
Maximum quantum yield of PS II in light-adapted state
PS II
Photosystem II
QA
Primary electron acceptor in PS II
QA−
Reduced QA
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Fv/Fm
Introduction
Most microalgae are photoautotrophic microorganisms that can utilize light as energy and CO2 as a
carbon source to carry out photosynthesis. Light energy exerts a great impact on algal cell growth and relevant product generation. As such, studies on the absorption and utilization of light energy are an important aspect of research in algal growth kinetics[1]. In early 1982, Aiba reported the results of his
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study on the growth kinetics of photosynthetic microbes[2]. Many similar reports have been published since then [3; 4; 5; 6]. For example, a turbidostatic culture was first to perform on Spirulina platensis and found that the maximum light yield (Ymax) of algal cells decreases while the actual maintenance coefficient (m) increases with increasing incident light intensity[7]. Iehana also observed this
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phenomenon by performing continuous and batch cultures on Chlorella vulgaris[8]. The results of these studies, however, conflict with the concepts of classical growth kinetics, which state that Ymax and m, the intrinsic parameters of cell growth kinetics, must be relatively constant.
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Microalgal photosynthesis, which involves the absorption, transmission, and transformation of light, is a process by which light energy is transformed into chemical energy[9]. Besides photochemical reaction, the light energy absorbed by microalgae may be released as fluorescence or consumed as heat
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to some extent[10]. That is to say, the light energy consumed during photosynthesis only accounts for part of the total energy absorbed by microalgae, and the proportion of light energy utilized gradually
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decreases with variations in light intensity. The photoautotrophic growth kinetics parameters of algal
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cells described in these studies were obtained based on the hypothesis that all of the light energy absorbed by algal cells is utilized completely. Thus, the parameters obtained, Ymax and m, are not intrinsic
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kinetic parameters; instead, these values reflect the apparent maximum growth yield and maintenance
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coefficient of algal cells, respectively. Chlorophyll fluorescence reflects primary processes of photosynthesis, including light energy
absorption, excited energy transmission, and photochemical reaction. Chlorophyll fluorescence analysis allows estimation of various photosynthetic parameters, such as quantum efficiency, photosynthetic capacity, and electron transport rate. As a rapid and sensitive photosynthetic probe, this technique has been widely used in studies of photosynthesis in algal cells[11]. In the present article, chlorophyll
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fluorescence and metabolic flux analyses were performed to investigate the energy utilization efficiency of Synechococcus sp. PCC7942, a blue-green algal species, under different culture conditions. Results indicate that light utilization efficiency is closely correlated with light intensity and nutritional type[12; 13].
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Blue-green algae perform critical functions in studies of photosynthetic mechanisms and microalgal light utilization. To reveal the intrinsic growth kinetics of photoautotrophic microalgae and establish an appropriate model describing its growth process, Synechococcus sp. PCC7942 was subjected to
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chlorophyll fluorescence and traditional growth kinetics analyses.
Materials and methods Algae and culture medium
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Synechococcus sp. PCC7942 and Synechocystis sp. PCC6803 were provided by the Freshwater
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Algae Culture Collection of the Institute of Hydrobiology, Chinese Academy of Sciences. Modified
Culture methods
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BG-11 culture medium was used throughout this work[12].
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The algae were cultured in a flat-plate glass photobioreactor with a total volume of 2.5 L; here, the incident light intensity was adjusted by varying the position of the light source outside the
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photobioreactor[12]. The culture temperature was 28 °C, and the air flow rate was set to 0.5 vvm. After inoculation, the initial algal culture concentration was 0.04 g/L (dry cell weight). Batch culture was performed until a stable phase was achieved, after which a two-channel constant flow pump (BT1-200E, Shanghai Qite Analytical Instrument Co., Ltd.) was used to add fresh medium to the culture and pump out appropriate volumes of culture solution at constant velocity. The culture solution was sampled every 12 h to determine thallus concentrations. A stable state was defined as four consecutive measurements 5
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with a variation of <5%.
Analytical methods Cell concentration determination Algal cell culture solutions of different concentrations were collected, and their optical density
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OD730 was detected by a 752 spectrophotometer (Shanghai Analytical Instrument Factory). Algal solutions of equal volume with different OD730 were filtered through a 0.45 μm cellulose acetate membrane filter, and the residual algae were dried at 105 °C to a constant weight. The algal cakes were
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weighed three times, and their average weight was calculated. Results indicated that the OD730 of the algal solutions ranged from 0.18 to 0.85 and linearly correlated with their dry weights. The relation between dry cell weight (X) and OD730 followed the equation X (g/L) = 0.352 × OD730 with R2 = 0.998.
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Light intensity determination
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A radiometer measuring photosynthetically active radiation (FGH-1; Photoelectric Instrument Factory of Beijing Normal University) was used to determine light intensity.
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Average light intensity Iave and specific absorption rate of light energy Eab I (1 exp[ L K a X ]) L Ka X
Eab I ave Ka I ave
Am B X
(1)
(2)
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I ave
where I, L, Ka, and X respectively indicate the incident light intensity, light path, specific extinction coefficient, and cell concentration of the cultures; Am and B reflect parameters in the hyperbolic model of light attenuation[14]. Light energy-based growth yield calculations According to the model described by Pirt[15], the specific absorption rate of light energy of algal
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cells shows a linear relation with the specific growth rate: Eab
Ymax
m
(3)
where μ is the specific growth rate and Ymax and m are the maximum growth yield coefficient of algal
Chlorophyll fluorescence parameter determinations
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cells based on light energy absorption and light energy maintenance coefficient, respectively.
An AquaPen 100 (AP100) fluorometer (Photon Systems Instruments, Czech Republic) was used to determine various parameters of chlorophyll fluorescence. During detection of the maximum
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fluorescence Fm and Fm' of the algal solutions, the light intensity used to detect basic fluorescence Fo was set to 0.01 μmol•m−2 •s−1 and the light intensity of saturation pulses was set to 3000 μmol•m−2 •s−1 with a duration of 0.8 s. Other chlorophyll fluorescence parameters were automatically detected by the
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fluorometer.
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Experimental replication and statistical treatment All the experiments were performed in triplicate and the results were expressed as mean ± SD (n=3).
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The data were analyzed statistically using IBM® SPSS® Statistics software version 13.0. Data plotting
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were achieved using OriginPro® 8.0724.
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Results and Discussion Establishment of intrinsic kinetic model of microalgal growth Based on photosynthetic theory, quantum yield is related to the state of photosystem II (PS II).
Depending on the illumination history and light intensity, the state of PS II is dynamic[16]. Describing the state of PS II is a key step in establishing a photosynthetic model. Under nonphotoinhibition conditions, PS II exhibits two states: the open state (reactive) and the closed state (activated). After
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photon absorption, PS II in the open state switches to the closed state[17]. The change rate of this switch is directly proportional to the light intensity and effective absorption cross-sectional area of PS II. After photochemical reaction and electron release, the closed PS II switches to the open state. This change rate is directly proportional to the electronic release rate and inversely proportional to the turnover time τ of
d 1 PSII I (1 ) dt
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the electron transport chain. Therefore, the dynamic equation of PS II is as follows [18]: (4)
where υ is the probability of PSUs at the reactive state, or the probability that PSII is in an open state,
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also called the ratio of PS II reaction centers participating in photon capture and photochemical reaction or the quantum yield of photochemical reaction, σPS II is the effective absorption cross-sectional area of PS II, I is the intensity of incident light, and τ is the turnover time of the electron transport chain.
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At stable states,
1
PS II
, then
1 PSII I
(5)
1 1 PS II I
Ik Ik I
(6)
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Let I k
1
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where Ik is the half-saturation irradiance, or is the irradiance at which the photosynthetic rate is
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half-maximum, has been extensively discussed in literatures [16; 19]. As an empirical model, Equation (6) has established the quantitative relationship between υ and Ik.
Unlike the photosynthesis-Irradiance response curve[17], this model presents a quasi-hyperbolic form. The parameter υ in algal cells gradually decreases with increasing light intensity, which means the light energy utilization efficiency of algal cells consistently decreases with increasing light intensity. This result may be explained as follows: under photoautotrophic conditions, light energy increases promote 8
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competition by heat consumption, which limits the photochemical process of PS II; that is, more photoreaction centers are closed. Only the light energy absorbed by open photosynthetic reaction centers can be utilized during photochemical reaction. In particular, under subsaturated light intensity, the photosynthetic rate of microalgae cells reaches half of the maximal level, and at that point about half of
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the photosynthetic center is open, which means that the value of υ is about half. To establish an intrinsic kinetic model of microalgal growth, υ was introduced to the Pirt model (3). Eab Eab
max
Y
m (7)
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where E ab represents the actual amount of light energy used in photosynthesis and Ymax and mΘ
respectively represent the actual maximum growth yield coefficient of algal cells based on light energy absorption and actual light energy maintenance coefficient; here, Ymax and mΘ are intrinsic kinetic
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parameters of photoautotrophic growth. The relationships between Ymax and Ymax and between m and mΘ
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can be determined using Formulas (3) and (7).
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Ymax Ymax /
Ik m Ik I
(9)
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m m
Ik I Ymax (8) Ik
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Microalgal light energy utilization efficiency and verification of the kinetic model Light energy-based growth yield of microalgae under different light intensities Relatively stable μ values were obtained by using a chemostat culture and changing the dilution rate
D during culture. The relation between Eab and μ can be determined according to the Eab equation (Formula 2) and Pirt model (Formula 3; Fig. 1). In the chemostat culture, increases in μ decreased algal cell density, thereby increasing the average light intensity in the reactor. Under the same μ, increases in
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incident light intensity also enhanced the average light intensity in the reactor. The Eab of algal cells was directly proportional to the average light intensity in the reactor. Thus, improving both μ and incident light intensity can increase Eab. The Ymax and m of Synechococcus sp. PCC7942 under different light intensities were subsequently
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calculated. Figs. 2 and 3 demonstrate that the Ymax of Synechococcus sp. PCC7942 constantly declines with increasing light intensity under photoautotrophic conditions. This finding suggests that although μ increases with increasing light intensity, the conversion and utilization rates of light energy consistently
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decline. By contrast, m showed a tendency to increase linearly, which means the energy required for cell maintenance under high light intensity is higher than that required under low light intensity. With increasing light intensity, the energy available for cell maintenance also increases.
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Classical growth kinetic models of heterotrophic microorganisms suggest that the maximum cell yield Ymax and the maintenance coefficient m are intrinsic parameters of the cell and should be kept
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constant. However, the values of these parameters in these conventional models varied with the change
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of light intensity due to the decline of the bioenergy yield for microalgae[7; 8]. Actually, for the complexity of processes of photosynthetic transformation of light energy, absorption of a light quantum
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entails charge separation in the primary photoactive pair and is attended by conformational changes in
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the photosynthetic reaction centers (RC) components that prevent back electron transport and loss of energy through fluorescence[20]. There are various electron transfer models take account of their thermodynamic characteristics and varied-nature mechanisms of attending energy losses during the photosynthesis process[21; 22; 23]. As the solution of maintenance coefficient m, reflects the cost of a cell to survive that expend in the photosynthesis (including losses in the primary process), metabolism and reproduction processes, is rather complicated. Therefore, the classical Pirt model made an important
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simplification that the losses in the photosynthetic apparatus are a constant fraction and thus supposed the maintenance coefficient is also a constant. However, with the increase of the light intensity, especially in the case of exceeding the cell needs, the microalgae will consume a large amount of energy for avoiding photoinhibition, repairing photodamage and heat dissipation[10]. As a consequence, the
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values of Ymax and m based on the apparent absorption energy in above model are varied as well, that is, with the enhancement of light intensity, the Ymax decrease distinctly whereas m increases gradually. In present study the coefficients υ was introduced into the modified model to acquire the intrinsic maximum
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Θ cell yield 𝑌max and maintenance coefficient mΘ that are constant during the growth of autotrophic
microalgae and to be consistent with the expression of the classic model. Fluorescent quantum yield under different light intensities
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Fluorescent quantum yield is an important indicator of photosynthetic efficiency. Among the chlorophyll fluorescence parameters available, Fv/Fm and F′v/F′m are two important parameters that can
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best reflect light energy utilization efficiency. Fv/Fm represents the maximum photochemical yield of
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algal cells in PS II under dark adaptation. As Fv/Fm is stable in common physiological conditions, it is a characteristic value of photosynthetic organisms[24]. F'v/F'm represents the photon capture efficiency in
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open photosynthetic reaction centers[25]. The degree of limitation of the photochemical reaction in PS II
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due to competition by heat consumption can be quantified by F'v/F'm. As such, studying the Fv/Fm and F'v/F'm values of microalgae under different light intensities is of great significance when discussing light energy utilization efficiency. Using the AquaPen 100 fluorometer, the maximum υ of Synechococcus sp. PCC7942 was determined under OJIP mode. Fig. 4 shows that Fv/Fm and F′v/F′m basically remain constant over a large concentration range of algal cells under the same incident light intensity. In particular, Fv/Fm values
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remained stable at about 0.7 under different light intensities; this finding means Fv/Fm is a characteristic parameter of algal cells. As the light intensity increased to 115 μmol•m−2•s−1, the Fv/Fm value declined considerably (P < 0.05), which indicates Synechococcus sp. PCC7942 photoinhibition. At an incident light intensity of 151 μmol•m−2•s−1, the average Fv/Fm was about 0.32, which is only 45% of the normal
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value. Such a finding indicates extensive photoinhibition at the present conditions. The growth status of algal cells demonstrates that cell growth rates constantly increase with increasing light intensity but decrease rapidly at light intensities exceeding115 μmol•m−2•s−1 (P < 0.05). This result demonstrates that
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light is the major factor affecting algal cell growth under low-intensity light conditions; by contrast, photoinhibition is the major inhibiting factor influencing cell growth under high-intensity light conditions.
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F'v/F'm decreased steadily with increasing light intensity, which means the degree of heat consumption by algal cells constantly increases under the same conditions. Such a phenomenon further
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limits the photochemical reaction. Fv/Fm and F'v/F'm were fairly similar under low-light intensity light,
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which indicates low degrees of heat consumption under this condition. However, increases in incident light intensity gradually increased differences in Fv/Fm and F'v/F'm. This phenomenon reveals that the
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degrees of heat consumption and photoinhibition also increase gradually, whereas the proportion of light
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energy used in photosynthesis decreases. Results further confirm that deducing characteristic parameters by introducing υ to the model of microalgal growth kinetics is reasonable. Derivation and verification of parameters of intrinsic kinetic model of growth Using Formulas (8) and (9) and experimental data, nonlinear regression (Figs. 2 and 3) via the least-squares method was performed to deduce the parameters of the intrinsic kinetic model of Synechococcus sp. PCC7942 growth; here, Ymax 0.0119 0.0025 g/kJ and m 0.705 0.063 kJ/(g h) . Aiba
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indicated that the YG and m of most microalgal cells are 1.4 × 10−3–1.1 × 10−1 g/kJ and 0.08–6.9 kJ/(g•h), respectively[2]. The light intensity (Ik) of Synechococcus sp. PCC7942 under half-saturation conditions was further calculated as 123.7 ± 16 μmol•m−2•s−1. Light energy absorption and utilization by algae is considered to balance out at Ik[18]. Beyond this point, the light energy absorbed by algae will exceed the
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amount of light energy utilized with further increases in light intensity. This surplus light energy cannot be used for photosynthetic oxygen evolution or CO2 fixation and must be consumed through other pathways. In general, when the light intensity is lower than Ik, the degree of light damage is minimal,
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otherwise, the degree of light damage intensifies[26]. Results illustrated in Fig. 4 show that photoinhibition occurs in Synechococcus sp. PCC7942 when the light intensity exceeds 115 μmol•m−2•s−1, which is close to the Ik value calculated by the model.
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In the intrinsic kinetic model of microalgal growth, υ represents the probability of PSUs at the reactive state during photosynthesis. To verify the reliability of υ, chlorophyll fluorescence analysis was
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employed to determine microalgal photosynthetic efficiency under different light intensities. The
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photochemical quenching coefficient qp, as a chlorophyll fluorescence parameter, reflects the proportion of light energy absorbed by PS II antenna pigments and used in photochemical electron transport[27].
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Thus, qp and υ present similar meanings in the model. PS II reaction centers must remain open to achieve
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high qp. Thus, qp can reflect the open degree of PS II reaction centers; in fact, qp reflects the reducing state of primary electron acceptor QA in PS II, which is produced by oxidation of QA−. The larger the qp value, the larger the amount of QA produced by QA−, that is, the higher the activity of PS II electron transport. By contrast, if qp is low, electron flow from PS II oxidation sites to PS II reaction centers is inhibited. This information may be used to verify υ in the proposed model using qp. Fig. 5 shows that the qp values are very close to υ values under low light intensity and that larger
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errors in these parameters may be observed under higher light intensity. Such a finding may be attributed to the complexity of the photosynthetic mechanism. As light intensity increases, interferences by nonphotochemical factors may also increase and the conformations of relevant enzymes in the electron transport chain may be altered[28]; these phenomena may result in slight differences between
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the actual and theoretical open degrees of PS II. Despite this problem, the proposed model can reflect the influence of light intensity on light energy utilization to some extent. In particular, the model is able to predict light energy utilization efficiency under a specific light intensity as long as the half-saturation
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light intensity (Ik) is known. Thus, the model provides an important basis for optimizing illumination conditions for microalgal cultures.
To verify the applicability of the model developed in this work further, the relation between the E ab and μ of another blue-green alga, Synechocystis sp. PCC6803, was studied under different light
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intensities. Fig. 6 demonstrates that E ab shows a linear relationship with μ under incident light of
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different intensities. This result confirms that YG and mΘ remain almost unchanged under different light
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intensities; thus, these properties are parameters of the intrinsic growth kinetics of Synechocystis sp. PCC6803.
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During the microalgal photoautotrophic process, photons are captured by PS II antenna pigments
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and light energy is converted via one of three pathways[29]: (1) some photons may generate activation energy and enter the electron transport chain, where they are eventually utilized in photosynthesis; (2) some light energy may be consumed as heat; and (3) a small proportion of light energy may be lost in the form of fluorescence. Therefore, in the Pirt model of substrate consumption, Eab is based on macroscopic absorption. Ymax and m calculated by Formula (3) are apparent maximum growth yield and apparent light energy maintenance coefficients, respectively, rather than the intrinsic parameters of algal cells. In fact,
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the light energy used in photochemical reactions accounts for only a portion of all of the energy absorbed by algal cells, and only the energy captured by open PS II reaction centers and utilized in photochemical reactions may be effectively processed. The ratio of open to closed PS II reaction centers directly determines photosynthetic efficiency[30]. Here, υ refers to the ratio of light energy used in
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photochemical reactions to the light energy absorbed by cells. As light intensity increases, nonphotochemical processes in algal cells, such as heat consumption, also increase, thereby causing constant reductions in υ. On the one hand, reductions in quantum yield υ
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require algal cells to absorb more light energy to reproduce at an equal rate. That is, the biomass produced per unit light energy decreases. Under these circumstances, the Ymax of algal cells decreases with increasing light intensity. On the other hand, increases in light intensity enhance the degree of heat
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consumption and energy required to maintain algal cells. Thus, m constantly increases with increasing light intensity.
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The biomass productivity is an important parameter in microalgal culture. Mathematical analysis
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was conducted in order to predict the rate of microalgal mass production, which is supported by the actual values of photosynthetic productivity per cell. Quantitative photosynthetic productivity of the
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microalgae depends on a balanced contribution between the photosynthesis irradiance and the
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photosynthetic efficiency of the photosystem. At subsaturating irradiance, photosynthesis is limited by light absorption. Despite of the most number of reactive PSUs and with high absorption efficiency in the present model, the efficiency of light energy utilization is considered negligible compared to the energy supply. The cells will grow slowly as a consequence of the photosynthetic production in the situation. Conversely, in light saturation, photosynthesis is limited on the acceptor side of photosystem[17]. The photosynthetic efficiency of the organisms yield to the excitation energy from the light-harvesting
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systems to photosystem I (PSI) and photosystem II (PSII). As a consequence, the production of biomass is not proportional to the increase of radiation because of the gradual reduction of light absorption efficiency. Therefore, the best way to promote photosynthetic production is to improve the light energy utilization efficiency on the basis of sufficient irradiance. As shown in the present model, the Formula (7),
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to improve total light energy supply (Eab) while increasing light efficiency (υ), that is, increasing the Θ effective light energy supply (𝐸ab ), is an effective way to promote the growth and metabolism of
microalgae cells.
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Using the chlorophyll fluorescence parameters Fv/Fm and F'v/F'm, the photosynthetic characteristics of PS II reaction centers of photoautotrophic Synechococcus sp. PCC7942 under different illumination conditions were revealed. The relevant photosynthesis mechanism was then applied to establish an
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accurate model of υ, which reflects light energy utilization. The kinetic characteristics of photoautotrophic growth of other algae under different conditions can be studied using this model.
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Establishment of an intrinsic kinetic model enables researchers to understand the mechanism of light
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energy utilization by microalgae. The maximum biomass of different microalgae can be estimated by chlorophyll fluorescence analysis. Several reports [31; 32; 33; 34] on the application of chlorophyll
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fluorescence analysis in the estimation and monitoring of microalgal primary production show
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satisfactory results.
Studying various concepts of light energy utilization and conversion is fairly difficult because of the
diverse characteristics of photosynthetic reaction centers and the complexity of the photosynthetic mechanisms of algal cells. Most studies explore photosynthetic efficiency only on the basis of macroscopic photosynthesis. Chlorophyll fluorescence induction kinetics is an intrinsically complex phenomenon. As such, further exploration of the essence of light energy utilization efficiency in
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photoautotrophic microalgae is necessary. Although the model obtained in the present work was successfully applied in blue-green algae, such as Synechococcus sp. PCC7942 and Synechocystis sp. PCC6803, further verification using other microalgae belonging to other species and genera is of great importance. Future studies by our group aim to reveal more information regarding this topic.
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Conclusions
Because the microalgal growth kinetics parameters Ymax and m change with the light intensity under photoautotrophic conditions, determining intrinsic kinetic parameters is difficult. Analysis of the
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microalgal photosynthesis mechanism indicated that variations in kinetic parameters correlate well with the light energy utilization efficiency of microalgae. Therefore, υ was introduced to the classical kinetic equation in the present article, and kinetic analysis of microbial growth was performed to establish an
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intrinsic kinetic model reflecting photoautotrophic microalgal growth. The blue-green algae Synechococcus sp. PCC7942 was used to verify the kinetic model by chlorophyll fluorescence analysis.
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Results indicated that the kinetics model can realistically reflect the light energy utilization efficiency of
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microalgae as well as their intrinsic growth kinetics characteristics; it also effectively solves the problem of variations in kinetic parameters. The model and method proposed in this article not only apply to
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studies on the intrinsic kinetics of photoautotrophic microorganisms but also provide a theoretical basis
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for designing photobioreactors and optimizing the culture process of photoautotrophic microorganisms.
Conflicts of interest There are no conflicts to declare.
Acknowledgments This work was supported by the National Natural Science Foundation of China (No. 20506009), the Jiangxi Provincial Science Fund for Distinguished Young Scholars (20171BCB23037) and the Education
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Development Plan of Young and Middle-aged Teachers in College in Jiangxi Province.
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Figure legends Fig. 1. Relation between specific absorption rate of light energy and specific growth rate of Synechococcus sp. PCC7942 under incident light of different intensities. Fig. 2. Maximum growth yield of Synechococcus sp. PCC7942 under incident light of different intensities. Data are presented
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as mean of three replicate samples ± SD (n = 3). Fig. 3. Light energy maintenance coefficient of Synechococcus sp. PCC7942 under incident light of different intensities. Data are presented as mean of three replicate samples ± SD (n = 3).
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Fig. 4. Variation in quantum yield of fluorescence of Synechococcus sp. PCC7942 under different light intensities: (A) 6.90 μmol•m−2•s−1, (B) 15.8 μmol•m−2•s−1, (C) 55.2 μmol•m−2•s−1, (D) 78.2 μmol•m−2•s−1, (E) 115 μmol•m−2•s−1, and (F) 151 μmol•m−2•s−1. Data are presented as means ± SD of three biological replicates (n=3).
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Fig. 5. Photochemical quenching coefficient (qp) of Synechococcus sp. PCC7942 under different light intensities. The straight line represents the theoretical quantum yield of photochemical reaction calculated by the light energy utilization model.
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Fig. 6. Relationship between the specific absorption rate of light energy and specific growth rate of Synechocystis sp.
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PCC6803 under different light intensities.
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Fig.1 -2
Eab (kJ/(gh))
8
6
-1
3.55 molm s -2 -1 7.1 molm s -2 -1 11.04 molm s -2 -1 23.66 molm s -2 -1 39.43 molm s -2 -1 55.2 molm s -2 -1 78.85 molm s -2 -1 118.28 molm s
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Specific growth rate (h )
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2
0.05
Fig. 1 Relation between the specific absorption rate of light energy and specific growth rate of Synechococcus sp. PCC7942 under incident
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light of different intensities.
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Fig.2 0.012
Ymax (g/kJ)
0.009
y = 1.472 / (123.7+ x ) 2 r = 0.972
0.006
0.000 0
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90 -2
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0.003
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Incident intensity ( molm s )
Fig. 2 Maximum growth yield of Synechococcus sp. PCC7942 under incident light of different intensities. Data are presented as mean of
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three replicate samples ± SD (n = 3).
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Fig.3 1.2
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m (kJg h )
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Incident intensity (molm s )
Fig. 3 Light energy maintenance coefficient of Synechococcus sp. PCC7942 under incident light of different intensities. Data are presented
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as mean of three replicate samples ± SD (n = 3).
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Fig.4 1.0 Cell concentration F'v/F'm Fv/Fm
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Fig. 4 Variation in quantum yield of fluorescence of Synechococcus sp. PCC7942 under different light intensities: −
−
−
−
−
−
−
−
−
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−
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A) 6.90 μmol•m 2•s 1, B) 15.8 μmol•m 2•s 1, C) 55.2 μmol•m 2•s 1, D) 78.2 μmol•m 2•s 1, E) 115 μmol•m 2•s 1, and F) 151 μmol•m 2•s 1. Data are presented as means ± SD of three biological replicates (n=3).
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Fig.5 1.0
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Fig. 5 Photochemical quenching coefficient (qp) of Synechococcus sp. PCC7942 under different light intensities. The straight line represents
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Fig.6 2.4 y=44.45 x +0.306 2 r = 0.958
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(h )
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6.33 molm s -2 -1 11.03 molm s -2 -1 15.76 molm s -2 -1 23.64 molm s -2 -1 39.45 molm s -2 -1 55.16 molm s -2 -1 70.92 molm s
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Fig. 6 Relationship between the specific absorption rate of light energy and specific growth rate of Synechocystis sp. PCC6803 under
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