Theoretical search for the growth-temperature relationship in plants

In this article we deal with the definition of a new phenomenological model with physical bases for the response of short-term cell expansion growth to temperature. Although the interest on both the biomechanical bases of elongation growth and on temperature responses has a long lasting development in plant biology and biophysics, yet the question of the mode of actions of temperature is a very relevant and still open one. The purpose of our paper was not to deal with all the complexity of the possible effects of temperature on a growing cell but to concentrate on two more focused questions: i) whether it is possible to specify an optimal temperature for growth responses all along development by defining some phenomenological equations for temperature response, ii) can we learn something from that on the temperature dependence of the cell wall expansion process using a minimal analytical modelling? To answer both questions we introduce (by extending Lockhart approach) the notion of temperature by simple thermodynamical reasoning. Assuming incompressibility of water (by the constant molar density n/V ) we also accounted for the role of osmosis and consequently - the role of water uptake in growing cell. This approach allowed us (by comparing theoretical solutions and experimental results) not only to determine the specific (resonance) temperature (or corresponding absorption energy kBT*) of the optimal growth but also draw conclusions about the cell wall extensibility dependence on temperature and its evolution in time. A straightforward application of our method to determine optimum growth temperature for different plant species in a greenhouse practice (as its simple implication) can also be recommended.