Mathematical description, optimization and prediction of synergistic interaction of fluoride and xylitol

The potential ability of various physical or chemical agents to enhance their effect when they are applied simultaneously with each other is well-known. The purpose of this study was to adjust a simple mathematical model to describe, optimize and predict a synergistic interaction between fluoride and xylitol on acid production by mutans streptococci. The model suggests that the synergism is caused by the additional effective damage arising from an interaction of sublesions induced by each agent. These sublesions are considered to be ineffective when each agent is used individually. The predictions of the model were verified by comparison with experimental data published by other researchers. It was shown that the model describes the experimental data, predicts the greatest value of the synergistic effect and the condition under which it can be achieved. The synergistic effect appeared to decline with any deviation from the optimal value of the ratio of effective damages produced by each agent alone.