On the observed logarithmic factor in dose-response relationship, illustrated with the effect of some herbicides on photosynthesis

It has been observed that in many processes a logarithmic relation exists between dosage and response. To explain this a simple model is proposed departing from the fact that the occupancy of target molecules by poison molecules depends on the number of effective contacts. The fraction of poisoned target molecules is determined by the equation E(p) = l-e'r/n, where n is the total number of target molecules and r the total number of poison molecules that are in contact with the target molecules. It appears from this model that, within limits, the range of inhibition will be proportional to log dose. This relationship has indeed been observed for the effects of three herbicides on photosynthetic reactions in the alga Scenedesmus, where the gradual degree of inhibition has been measured in various dosage steps. Here also a log dose relation was found. For DCMU and simeton the slope of the lines is in accordance with the model. Differences in sensitivity to the poison under various conditions were discussed. No explanation could be given for the less steep slope in one of the three conditions for both DCMU and simeton. When the poisoning is reversible the line will be less steep when plotting log dose against response on normal scale. When elimination is important, the line will shift to the right when the same method of plotting is used. The model simulates the logarithmic factor in dose-response graphs, except in the region of very high or very low occupancy, where in the model and in the experiments the lines bend.