A model for the irradiance responses of photosynthesis

Abstract

The analysis of the irradiance responses of photosynthetic processes, such as the quantum efficiencies of electron transport by photosystems I and II (PSI and PSII) or the rate of carbon dioxide fixation, is limited by the lack of mechanistically based analytical model for these processes. Starting with a model of P700 redox state, we develop a series of analytical functions which can be used to fit the irradiance responses of the quantum yields for electron transport by PSI and PSII, the irradiance responses of electron transport by PSI and PSII, and even the irradiance response of the fixation rate of carbon dioxide. These functions depend on two or three parameters so they can be fit to typical irradiance response data. We illustrate by example the use of these functions in various applications and discuss further use and development of the basic model described in detail here.

Figure 1

The basic physical structures that are reproduced in the models for 0, 1 and 2 donors. ‘P’ is P₇₀₀ while ‘D’ is the lumped donor pool within the high‐potential chain part of the photosynthetic electron transport chain. Oxidation of P₇₀₀ occurs via steps k_x, while electron transfer from the PQH₂ pool to the lumped donor pool occurs via steps k_e, and redox equilibration between P₇₀₀ and the donor pool occurs via steps ‘K’. The oxidized forms of P₇₀₀ are on the right side, and the reduced forms on the left side, of the diagram.

Figure 2

(A) The irradiance dependency of Φ_PSI (the relative quantum yield for PSI electron transport) and k_e – the pseudo‐first order rate constant for reduction of P₇₀₀ ⁺ by electrons derived from the oxidation of PQH₂. These measurements were made on a leaf of Juanulloa aurantiaca. These data are (and other similar data from this leaf) presented to demonstrate the use of the models outlined here. (B) A fit using an n = 0 form (i.e. zero high‐potential chain donors to P₇₀₀) of the Φ_PSI/irradiance model to an experimentally measured Φ_PSI/irradiance response obtained from a leaf of J. aurantiaca.

Figure 3

A fit using an n = 1 form (i.e. one high‐potential chain donor to P₇₀₀) of the Φ_PSI/irradiance model to an experimentally measured Φ_PSI/irradiance response obtained from a leaf of Juanulloa aurantiaca. K_eq is unitless, while k_e/ϵ has units of mol⁻¹ m².

Figure 4

A fit using an n = 2 form (i.e. two high‐potential chain donors to P₇₀₀) of the Φ_PSI/irradiance model to an experimentally measured Φ_PSI/irradiance response obtained from a leaf of Juanulloa aurantiaca.

Figure 5

A fit using an n = 3 form (i.e. three high‐potential chain donors to P₇₀₀) of the Φ_PSI/irradiance model to an experimentally measured Φ_PSI/irradiance response obtained from a leaf of Juanulloa aurantiaca.

Figure 6

Fits using an n = 3 form of the Φ_PSI/irradiance model to experimentally measured Φ_PSI/irradiance responses obtained from leaves of Pisum sativum (A) and Prunus laurocerasus (B).

Figure 7

The effect of varying the k_e/ϵ parameter, while keeping the K_eq parameter fixed, on calculated Φ_PSI/irradiance responses; these responses were calculated using an n = 2 version of the Φ_PSI/irradiance model and the fit shown in Fig. 4 was used as a template, and is included in this figure as a reference.

Figure 8

The effect of varying the K_eq parameter, while keeping the k_e/ϵ parameter fixed, on calculated Φ_PSI/irradiance responses; these responses were calculated using an n = 2 version of the Φ_PSI/irradiance model and the fit shown in Fig. 4 was used as a template, and is included in this figure as a reference.

Figure 9

A fit to an experimentally determined irradiance response of J_I (Φ_PSI times irradiance; derived from the dataset shown in Fig. 2) using a version of the n = 2 form of the Φ_PSI/irradiance model modified to simulate the irradiance response of PSI electron transport.

Figure 10

The effect of varying the k_e/ϵ parameter, while keeping the K_eq parameter fixed, on calculated J_I/irradiance responses; these responses were calculated using an n = 2 version of the J_I/irradiance model and the fit shown in Fig. 9 was used as a template, and is included in this figure as a reference.

Figure 11

The effect of varying the K_eq parameter, while keeping the k_e/ϵ parameter fixed, on calculated J_I/irradiance responses; these responses were calculated using an n = 2 version of the J_I/irradiance model and the fit shown in Fig. 9 was used as a template, and is included in this figure as a reference.

Figure 12

The actual J_I/irradiance responses measured at low irradiances (as shown in Fig. 9 at a larger scale), and the simulated J_I/low irradiance responses calculated using the fitted parameters obtained by fitting the n = 2 J_I/irradiance model to the data shown in Fig. 9. The diagonal line was fit by eye through the linear phase of the response at the lowest irradiances.

Figure 13

A fit using an n = 2 form (i.e. derived from the version with two high‐potential chain donors to P₇₀₀) of the Φ_PSII/irradiance model to an experimentally measured Φ_PSII/irradiance response obtained from a leaf of Juanulloa aurantiaca and using a 660 nm excitation wavelength for chlorophyll fluorescence. In this example, all datapoints (including the dark adapted F_v/F_m) have been fit by the function.

Figure 14

(A) A fit using an n = 2 form (i.e. derived from the version with two high‐potential chain donors to P₇₀₀) of the Φ_PSII/irradiance model to an experimentally measured Φ_PSII/irradiance response obtained from a leaf of Juanulloa aurantiaca. In this example point corresponding to the dark adapted F_v/F_m was excluded from the fit. (B) A closer view of the fits to Φ_PSII/irradiance response at low irradiances in which the dark‐adapted Fv/Fm is included (Fig. 13; dotted line) or excluded from the fit (Fig. 14B; solid line).

Figure 15

A fit using an n = 2 form (i.e. derived from the version with two high‐potential chain donors to P₇₀₀) of the Φ_PSII/irradiance model to an experimentally measured Φ_PSII/irradiance response obtained from a leaf of Juanulloa aurantiaca and using a 560 nm excitation wavelength for chlorophyll fluorescence (open symbols); the values for the estimated parameters shown in the figure are for the 560 nm excitation derived data. The estimated curve for this data can be mapped accurately onto the curve obtained using 660 nm as an excitation wavelength (solid symbols; Fig. 13) by adjusting the value of k_e/ϵ obtained by fitting the 560‐nm dataset.

Figure 16

A fit using an n = 2 form of the Φ_PSI/irradiance model modified to fit carbon dioxide fixation rate/irradiance data to an experimentally measured carbon dioxide/irradiance response obtained from a leaf of Juanulloa aurantiaca. The solid line shows the fit obtained to all datapoints available (solid and open symbols) while the dotted line shows the fit obtained when using a limited subset of the data (solid symbols alone).

Figure 17

The calculated Φ_CO2/irradiance response of the carbon dioxide fixation rate/irradiance relationship shown in Fig. 16.