Temperature coefficient (Q10) and its applications in biological systems: Beyond the Arrhenius theory

The Q(10) temperature coefficient, which is widely used in scientific literature, is a measure of the temperature sensitivity of chemical reaction rates or biological processes. However, the conclusions drawn from applying this coefficient to experimental data obtained from biological processes are not universal. In many biological processes, Q(10) values are often discordant with the results predicted by the Arrhenius law. The hypothesis tested in the present study is that this problem arises mainly from the fact that the Q(10) coefficient is defined by the ratio between rates described by exponential laws instead of power laws. Considering this hypothesis and the need to review the mathematical laws and models currently used to describe rates and Q(10) coefficients, we propose a model beyond the usual Arrhenius theory or exponential decay law herein. The proposed mathematical model is based on the theory of deformed exponential functions, with the ordinary Q(10) model representing the conventional exponential function. Therefore, all results following the standard model remain valid. Moreover, we include a Q(10) free open-source code, written in Python, and compatible with Windows, Linux and macOS platforms. The validation of the proposed model and confirmation of the given hypothesis were performed based on the following temperature-dependent biological processes: soil organic carbon (SOC) decomposition (which is essential to forecast the impact of climate change on terrestrial ecosystems); the metabolism of Arctic zooplankton; physiological processes of the respiratory and cardiovascular systems; rate of oxygen consumption in mitochondria of the eurythermal killifish Eundulus heteroclitus, and leaf respiration.