Revisiting the Temperature Dependence of the Photorespiratory CO₂ Compensation Point (Γ*)

Accurate estimation of the photorespiratory CO₂ compensation point (Γ*) is essential for describing the balance between Rubisco carboxylation and oxygenation and for parameterising biochemical models of photosynthesis. Γ* and the rate of CO₂ release in the light (D_L) are commonly estimated using the Laisk method, based on measurements of net CO₂ assimilation rate (A_net) at low chloroplastic CO₂ concentrations (c_c), under several sub-saturating irradiance levels. However, many widely used temperature dependence relationships for Γ* (Γ*(T)) were derived using conventional linear implementations of the Laisk method, despite the intrinsically nonlinear behaviour of the A_net-c_c response predicted by the photosynthetic theory. Here, we revisited the temperature dependence of Γ* and D_L using the improved Laisk-FvCB framework that simultaneously constrains the nonlinear A_net-c_c response across multiple irradiance levels. Gas exchange of sunflower leaves was measured across a wide temperature range from 3.9°C to 42.0°C. The conventional linear implementation generated highly dispersed pairwise intersections and unstable estimates of both Γ* and D_L, including some physiologically unrealistic negative D_L values at low temperatures. In contrast, the mechanistically constrained Laisk-FvCB framework produced physiologically meaningful temperature responses and substantially reduced methodological artefacts associated with linear extrapolation. Using this framework, we derived a revised in vivo Γ*(T) relationship described by an Arrhenius-type function with Γ*(25) = 43.4 μmol mol^-1 and an apparent activation energy of 27.7 kJ mol^-1, such that Γ*(T) = 43.4 exp[11.176 ((T - 25)/(T + 273.15))], where T is leaf temperature in °C. Comparison with other widely used Γ*(T) formulations showed substantial divergence at temperature extremes, often exceeding the variability expected from realistic interspecific differences in Rubisco specificity among C₃ species.