Kinetic modelling of phototropism in maize coleoptiles

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Abstract
Blue-light-induced phototropism of maize (Zea mays L.) coleoptiles was studied with a view to kinetic models. Red-light-grown plants were used to eliminate complication arising from the activation by blue light of phytochrome-mediated phototropism. In the first part, mathematical models were developed to explain the phototropic fluence-response data, which were obtained for the responses induced by a single unilateral pulse (30 s) and those induced by a unilateral pulse (30 s) given immediately after a bilateral pulse (30 s, fixed fluences). These data showed bell-shaped fluence-response curves, characteristic of “first positive curvature”. Modelling began with the assumptions that the light gradient plays a fundamental role in phototropism and that the magnitude of the response is determined by the gradient, or the concentration difference, in a photoproduct between the irradiated and the shaded sides of the tissue. Minimal mathematical models were then derived, by defining chemical kinetics of the photoreaction and introducing the minimum of parameters needed to correlate the incident fluencerate to the functional fluence-rates within the tissue, the functional fluence-rate to the rate constant of the photoreaction, and the photoproduct concentration difference to the curvature response. The models were tested using a curve-fitting computer program. The model obtained by assigning first-order kinetics to the photoreaction failed to explain the fluence-response data, whereas application of second-order kinetics led to a successful fit of the model to the data. In the second part, temporal aspects of the photosystem were examined. Experimental results showed that a high-fluence bilateral pulse eliminated the bell-shaped fluence-response curve for an immediate unilateral pulse, and that the curve gradually reappeared as the time for unilateral stimulation elapsed after the bilateral pulse. The model based on a second-order photoreaction could be extended to explain the results, with assumed changes in two components: the concentration of the reactant for the photoproduct, and the light-sensitivity of the reaction. The reactant concentration, computed with the curvefitting program, showed a gradual increase from zero to a saturation level. This increase was then modelled in terms of regeneration of the reactant from the photoproduct, with an estimated first-order rate constant of about 0.001·s-1. The computed value for the constant reflecting the light-sensitivity showed a sharp decline after the high-fluence pulse, followed by a gradual return to the initial level. From these analytical results, the appearance of “second positive curvature” was predicted.