Quantitative Models Characterizing Seed Germination Responses to Abscisic Acid and Osmoticum

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Abstract
Mathematical models were developed to characterize the physiological bases of the responses of tomato (Lycopersicon esculentum Mill. cv T5) seed germination to water potential (ψ) and abscisic acid (ABA). Using probit analysis, three parameters were derived that can describe the germination time courses of a seed population at different ψ or ABA levels. For the response of seed germination to reduced ψ, these parameters are the mean base water potential (¯ψb, MPa), the standard deviation of the base water potential among seeds in the population (σψb, MPa), and the “hydrotime constant” (θH, MPa·h). For the response to ABA, they are the log of the mean base ABA concentration ([unk]ABAb, m), the standard deviation of the base ABA concentration among seeds in the population (σABAb, log[m]), and the “ABA-time constant” (θABA, log[m]·h). The values of ¯ψb and [unk]ABAb provide quantitative estimates of the mean sensitivity of germination rate to ψ or ABA, whereas σψb and σABAb account for the variation in sensitivity among seeds in the population. The time constants, θH and θABA, indicate the extent to which germination rate will be affected by a given change in ψ or ABA. Using only these parameters, germination time courses can be predicted with reasonable accuracy at any medium ψ according to the equation probit(g) = [ψ - (θH/tg) - ¯ψb]/σψb, or at any ABA concentration according to the equation probit(g) = [log[ABA] - (θABA/tg) - log[[unk]ABAb]]/σABAb, where tg is the time to radicle emergence of percentage g, and ABA is the ABA concentration (m) in the incubation solution. In the presence of both ABA and reduced ψ, the same parameters can be used to predict seed germination time courses based upon strictly additive effects of ψ and ABA in delaying the time of radicle emergence. Further analysis indicates that ABA and ψ can act both independently and interactively to influence physiological processes preparatory for radicle growth, such as the accumulation of osmotic solutes in the embryo. The models provide quantitative values for the sensitivity of germination to ABA or ψ, allow evaluation of independent and interactive effects of the two factors, and have implications for understanding how ABA and ψ may regulate growth and development.