Kinetic modelling of phototropism in maize coleoptiles

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-me diated phototropism. In the first part, mathemati cal models were developed to explain the photo tropic 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 fun damental role in phototropism and that the magni tude 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 pho toreaction and introducing the minimum of pa rameters needed to correlate the incident fluence rate to the functional fluence-rates within the tis sue, the functional fluence-rate to the rate constant of the photoreaction, and the photoproduct con centration difference to the curvature response. The models were tested using a curve-fitting com puter program. The model obtained by assigning first-order kinetics to the photoreaction failed to explain the fluence-response data, whereas applica tion 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 exam ined. 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 re sults, with assumed changes in two components: the concentration of the reactant for the photopro duct, and the light-sensitivity of the reaction. The reactant concentration, computed with the curve fitting 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 com puted 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 ap pearance of "second positive curvature" was pre dicted. * CIW-DPB publication No. 884 ** Present address, where all correspondence should be di rected: Tokyo Metropolitan Universtiy, Department of Biolo gy, Fukazawa 2-1-1, Setagaya-ku, Tokyo 158, Japan Abbreviations: FPC = first positive curvature; SPC = second positive curvature