Development of Two-Dimensional Model of Photosynthesis in Plant Leaves and Analysis of Induction of Spatial Heterogeneity of CO2 Assimilation Rate under Action of Excess Light and Drought

Abstract

Photosynthesis is a key process in plants that can be strongly affected by the actions of environmental stressors. The stressor-induced photosynthetic responses are based on numerous and interacted processes that can restrict their experimental investigation. The development of mathematical models of photosynthetic processes is an important way of investigating these responses. Our work was devoted to the development of a two-dimensional model of photosynthesis in plant leaves that was based on the Farquhar-von Caemmerer-Berry model of CO₂ assimilation and descriptions of other processes including the stomatal and transmembrane CO₂ fluxes, lateral CO₂ and HCO₃^- fluxes, transmembrane and lateral transport of H⁺ and K⁺, interaction of these ions with buffers in the apoplast and cytoplasm, light-dependent regulation of H⁺-ATPase in the plasma membrane, etc. Verification of the model showed that the simulated light dependences of the CO₂ assimilation rate were similar to the experimental ones and dependences of the CO₂ assimilation rate of an average leaf CO₂ conductance were also similar to the experimental dependences. An analysis of the model showed that a spatial heterogeneity of the CO₂ assimilation rate on a leaf surface should be stimulated under an increase in light intensity and a decrease in the stomatal CO₂ conductance or quantity of the open stomata; this prediction was supported by the experimental verification. Results of the work can be the basis of the development of new methods of the remote sensing of the influence of abiotic stressors (at least, excess light and drought) on plants.

Keywords: CO2 assimilation; drought; excess light; leaf CO2 conductance; spatial heterogeneity; two-dimensional photosynthetic model.

Figure 1

A general scheme of the developed two-dimensional model (a) and main processes described by the model on the cell level (b). Model elements (squares) include both mesophyll cells and stomata or only mesophyll cells (without stomata). Small arrows in the general scheme show transport of carbon dioxide, H⁺, and K⁺ between apoplastic volumes of neighboring cells and across the plasma membrane. PAR is the photosynthetic active radiation. pH_ap, pH_cyt, and pH_str are pH in the apoplast, cytoplasm, and stroma of chloroplasts, respectively. B_cyt⁻ and B_cytH are the free and proton-bound cytoplasmic buffers. B_ap⁻, B_apH, and B_apK are the free, proton-bound, and potassium-bound apoplastic buffers. E_m is the difference of electrical potentials across the plasma membrane. FvCB model is the Farquhar–von Caemmerer–Berry model. The main systems of ion transport at rest, including H⁺-ATP-ases, H⁺/K⁺-antiporters, inwardly rectifying K⁺ channels, and outwardly rectifying K⁺ channels, are described in the two-dimensional photosynthetic model.

Figure 2

Simulated (a) and experimental (b) dependences of the average photosynthetic CO₂ assimilation rate (A_hv) on the intensity of the photosynthetic active radiation (PAR) at the varied average leaf CO₂ conductance (g_S). Simulated dependences were calculated at average g_S = 0.064 mol m⁻²s⁻¹ (the basic g_S) and g_S = 0.023 mol m⁻²s⁻¹ (the decreased g_S). Each stomata in the model was located in the center of square (3 × 3 elements); the average gS was calculated as the CO₂ conductance in the element with stomata divided by 9. In order to obtain experimental dependences, all experimental records in this series were ranged and divided into two groups with the low (g_S < 0.04 mol m⁻²s⁻¹, n = 5) and high (g_S > 0.04 mol m⁻²s⁻¹, n = 9) CO₂ conductance (see Section 5.1). A combination of Dual-PAM-300 and GFS-3000 was used in the experimental measurements of pea seedlings.

Figure 3

Simulated (a) and experimental (b) scatter plots between the average photosynthetic CO₂ assimilation rate (A_hv) and the average leaf CO₂ conductance (g_S) under high intensity of the photosynthetic active radiation (758 µmol m⁻²s⁻¹). Simulated Ahv were calculated at the average g_S equaling 0.007, 0.012, 0.023, 0.064, and 0.096 mol m⁻²s⁻¹. Each stomata in the model was located in the center of square (3 × 3 elements); the average g_S was calculated as the CO₂ conductance in the element with stomata divided by 9. Pea seedlings were experimentally investigated; all g_S and A_hv (under the 758 µmol m⁻²s⁻¹ PAR intensity) were used (n = 14). R² is the determination coefficient.

Figure 4

Dependences of parameters of the simulated spatial heterogeneity of the photosynthetic CO₂ assimilation rate (A_hv) on the intensity of the photosynthetic active radiation (PAR). (a) Dependence of the standard deviation of Ahv (SD(A_hv)) on the PAR intensity. There were three variants of parameters. (i) The average g_S of the leaf was 0.064 mol m⁻²s⁻¹, each stomata was located in the center of the 3 × 3 elements square. This variant was assumed as the control. (ii) The average g_S of the leaf was decreased to 0.023 mol m⁻²s⁻¹. The CO₂ conductance in individual stomata was decreased; each stomata was located in the center of the 3 × 3 elements square. (iii) The average g_S of the leaf was decreased to 0.023 mol m⁻²s⁻¹. The CO₂ conductance in individual stomata was not changed; each stomata was located in the center of the 5 × 5 elements square. (b) Dependence of the coefficient of variation of A_hv (CV(A_hv)) on the PAR intensity. (c) Dependence of the ratio of the SD(Ahv) at g_S = 0.023 mol m⁻²s⁻¹ (3 × 3 elements) to the SD(Ahv) at g_S = 0.064 mol m⁻²s⁻¹ (3 × 3 elements) on the PAR intensity and the analogical dependence for CV(A_hv).

Figure 5

The dependence of average photosynthetic CO₂ assimilation rate (A_hv) on the average linear electron flow (LEF) at 34, 108, 239, 425, and 758 µmol m⁻²s⁻¹ intensities of actinic light (n = 5–7) and the linear calibration Equation (a), the dependence of individual A_hv on individual LEF at 34, 108, 239, and 425 µmol m⁻²s⁻¹ light intensities (n = 25) and the linear calibration Equation (b), dependences of LEF and A_hv (calculated) on the PAR intensity (n = 6) (c), and dependences of parameters of the spatial heterogeneity of Ahv (calculated) (SD(Ahv) and CV(A_hv)) on the PAR intensity (n = 6) (d). R² is the determination coefficient. Ahv (calculated) was calculated based on LEF and the calibration Equation. A combination of Dual-PAM-300 and GFS-3000 was used for development of the calibration Equation. IMAGING-PAM M-Series MINI Version was used for analysis of the spatial heterogeneity of A_hv. Pea seedlings were used in all variants of experiments.

Figure 6

Influence of the short-term drought (1 day) on the leaf CO₂ conductance (g_S) (a) and the coefficient of variation of A_hv (CV(A_hv)) showing the relative spatial heterogeneity of this parameter in the leaf (b) (n = 6). GFS-3000 was used for the gS measurement (averaged in the investigated area of the leaf) and IMAGING-PAM M-Series MINI Version was used for the analysis of the spatial heterogeneity of A_hv (based on the spatial heterogeneity of LEF and the calibration Equation). The moderate light intensity (249 µmol m⁻²s⁻¹) was used in this experiment. Pea seedlings were irrigated in the control and were not irrigated under drought conditions. *, difference with the control was significant.

Figure 7

A scheme of potential ways the excess light and drought influencing the heterogeneity of the spatial distribution of photosynthetic parameters and the hypothetical importance of this heterogeneity for the plant tolerance and remote sensing of plant stress changes. The scheme is based on analysis of the developed model and experimental results (see Section 4 for details).