A mechanistic model of winter stem diameter dynamics reveals the time constant of diameter changes and the elastic modulus across tissues and species

Abstract

When freezing occurs in trees in the autumn living cells are able to withstand the rapid dehydration that they experience due to the chemical properties of ice that fills apoplastic spaces. Elasticity and hydraulic permeability of living tissue are important properties influencing the frost tolerance of trees, because of their effects on how rapidly the dehydration occurs. Stem diameter change measurements have been used to quantify these tissue properties during the summer, but no such attempt has yet been made during winter when the apoplast is frozen. Here the dynamics of xylem, phloem and whole stem diameter changes for three tree species were simulated by formulating a mechanistic model using temperature of ice as a driver for water exchange between symplast and apoplast in accordance with theory of extracellular freezing. Hence in our model formulation, a decrease in the temperature of the apoplastic ice leads to a decrease in the apoplastic water potential drawing water from the living cells, which could be also observed in diameter change measurements in the field. The model was successful in explaining diameter changes in the case of all tree species when modelled diameter changes were fitted against measured diameter changes. Estimates for the elastic modulus, the time constant of diameter changes and the hydraulic permeability at tissue level were obtained by the fitting of three model parameters. The elastic modulus of the living tissue was found to exhibit a negative temperature dependency, while the time constant of diameter changes was found to exhibit a positive temperature dependency. Overall, this modelling approach offers an easy and non-destructive way of gaining valuable information about physiological properties of trees and their tissues in the winter. However, a complete understanding of the parameters estimated by the model requires further investigation into the physical processes that result in winter diameter changes.