Extracellular Ca2+ and Zn2+ influence many aspects of retinal function. Here, we examined the effect of external Ca2+ and Zn2+ on potassium channels of retinal horizontal cells. When extracellular Ca2+ was lowered from 3 mM to 0.3 mM, horizontal cell transient outward currents elicited by voltage steps from resting membrane potential (−70 mV) were decreased by approximately 50%, whereas the sustained currents remained unchanged. This effect was due to a hyperpolarizing shift in the steady-state inactivation curve of A-type K+ currents when extracellular Ca2+ concentration was lowered. The mean half inactivation potential of the steady-state inactivation curves was hyperpolarized from −56.3 ± 4.7 mV in 3 mM Ca2+ to −76.4 ± 3.9 mV in 0.3 mM Ca2+. Neither the state-steady activation curve nor the kinetics of inactivation was significantly changed in low extracellular Ca2+. The addition of 30 μM Zn2+ restored peak outward currents in 0.3 mM Ca2+. The half inactivation voltages were depolarized from −70 ± 2.8 mV in 0.3 mM Ca2+ to −56 ± 2.6 mV in 0.3 mM Ca2+ plus 30 μM Zn2+. Taken together, the results indicate that external Ca2+ and Zn2+ maintain the activity of A-type potassium channels in retinal horizontal cells by influencing the voltage dependence of steady-state inactivation.

The assumption that the mushroom stem has the ability to undergo autonomic straightening enables a mathematical model to be written that accurately mimics the gravitropic reaction of the stems of Coprinus cinereus. The straightening mechanism is called curvature compensation here, but is equivalent to the ‘autotropism’ that often accompanies the gravitropic reactions of axial organs in plants. In the consequently revised local curvature distribution model, local bending rate is determined by the difference between the ‘bending signal’ (generated by gravitropic signal perception systems) and the ‘straightening signal’ (proportional to the local curvature at the given point). The model describes gravitropic stem bending in the standard assay with great accuracy but has the virtue of operating well outside the experimental data set used in its derivation. It is shown, for example, that the mathematical model can be fitted to the gravitropic reactions of stems treated with metabolic inhibitors by a change of parameters that parallel the independently derived physiological interpretation of inhibitor action. The revised local curvature distribution model promises to be a predictive tool in the further analysis of gravitropism in mushrooms.

The revised local curvature distribution model, which provides accurate computer simulations of the gravitropic response of mushroom stems, was found to produce accurate simulations of the gravitropic reaction of wheat (Triticum aestivum) coleoptiles. The key feature of the mathematical model that enables it to approach universality of application is the assumption that the stem has an autonomic straightening reaction (curvature compensation or ‘autotropism’). In the model, the local bending rate for any segment of the organ is determined by the difference between the ‘bending signal’ (generated by the gravitropic signal perception system) and a ‘straightening signal’ (which is proportional to the local curvature of the segment). The model reveals three major differences between the gravitropic reactions of wheat coleoptiles and Coprinus mushroom stems. First, in Coprinus, the capacity for autonomic straightening is much more concentrated in the apical region of the stem. Second, local perception of the gravitropic signal, which is necessary for exact simulation in Coprinus, is not needed in wheat coleoptiles (the corresponding constant in the model can be set to zero). Third, the transmission rate of the gravitropic signal is about seven times faster in wheat coleoptiles than in the mushroom stem. Thus, we demonstrate that a single model, depending on the values given to its parameters, is able to simulate the spatial organization of the gravitropic reaction of wheat coleoptiles and Coprinus mushroom stems. The model promises to be a valuable predictive tool in guiding future research into the gravitropic reaction of axial organs of all types.

The purpose of this work was to establish how the distribution of local curvatures changed during the mushroom stem gravitropic reaction and to suggest a suitable mathematical model based on these new data.

The gravitropic bending of base- and apex-pinned Coprinus cinereus (Fries) S. F. Gray stems was recorded on videotapes. The images were captured from the tapes after each 10 min, rotated by 45° and transformed into tables of changing co-ordinates of points for each stem. The non-linear regression of these points was performed using Legendre polynomials. From the resulting equations the patterns of changing local curvature for 50 subsections per stem during 400 min of gravitropic reaction were calculated.

It was observed that base-pinned stems first bent from the apex, but later the curvature of this part decreased, and in the late stages the apex became nearly completely straight again. Subsections, located about one third of stem length from the base determined the main part of the final curvature. The free basal part of the apex-pinned stems bent upward and after a certain bending time also began to straighten. However, this process started significantly later and was weaker. Bending of the subsections close to the pinned apex did not stop when they reached the vertical position, and the final angle of gravitropic curvature could exceed 180°.

Plotting various functions of local bending speed and its derivatives against each other and against local angle indicated that, if the hypothetical signal about reorientation arises in the apex, its propagation towards the base did not follow simple wave or simple diffusion laws. The importance of the local angle of all subsections both for signal origin and transmission was established and a signal transmission equation, involving local angle of each subsection, was derived. After creating a suitable program this partial differential equation was solved numerically. The generated shapes of the bending stem coincided in high degree with experimentally observed images.