Quantitative models characterizing seed germination responses to abscisic acid and osmoticum

Mathematical models were developed to characterize the physiological bases of the responses of tomato (Lycopersicon esculentum Mill. cv T5) seed germination to water potential and abscisic acid (ABA). Using probit analysis, three parameters were derived that can describe the germination time courses of a seed population at different water potential or ABA levels. For the response of seed germination to reduced water potential, these parameters are the mean base water potential, the standard deviation of the base water potential among seeds in the population, and the "hydrotime constant" (MPa.h). For the response to ABA, they are the log of the mean base ABA concentration, the standard deviation of the base ABA concentration among seeds in the population (log[m]), and the "ABA-time constant" (log[M].h). The values of the mean base water potential and the mean base ABA concentration provide quantitative estimates of the mean sensitivity of germination rate to water potential or ABA, whereas standard deviation of the base water potential among seeds in the population and the standard deviation of the base ABA concentration among seeds in the population account for the variation in sensitivity among seeds in the population. The "hydrotime" and "ABA-time" constants indicate the extent to which germination rate will be affected by a given change in water potential or ABA. Using only these parameters, germination time courses can be predicted with reasonable accuracy at any medium water potential according to the equation probit(g) = [water potential - (hydrotime constant divided by t(g)) - mean base water potential] divided by standard deviation of the base water potential among seeds in the population, or at any ABA concentration according to the equation probit(g) = [log[ABA] - (ABA-time constant divided by t(g)) - log[mean base ABA concentration]] divided by standard deviation of the base ABA concentration among seeds in the population, where t(g) 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 water potential, the same parameters can be used to predict seed germination time courses based upon strictly additive effects of water potential, and ABA in delaying the time of radicle emergence. Further analysis indicates that ABA and water potential, can act both independently and interactively to influence physiological processes preparatory for radicle growt