The temperature dependence of dormancy breaking in plants: Mathematical analysis of a two-step model involving a cooperative transition

A two-step model describing the thermal dependence of the dormancy breaking phenomenon is developed. The model assumes that the level of dormancy completion is proportional to the amount of a certain dormancy breaking factor which accumulates in plants by a two-step process. The first step represents a reversible process of formation of a precursor for the dormancy breaking factor at low temperatures and its destruction at high temperatures. The rate constants of this process are assumed to be dependent upon the temperature according to the Arrhenius law. The second step is an irreversible cooperative transition from the unstable precursor to a stable dormancy breaking factor. The transition is assumed to occur when a critical level of the precursor is accumulated. The two-step scheme is analysed mathematically. This model explains qualitatively the main observations on dormancy completion made under controlled temperature conditions and relates the parameters of the theory to the measurable characteristics of the system.