Institute of Applied Materials, Department of Chemical Engineering, University of Pretoria, Pretoria, South Africa.
Department of Statistics, University of Pretoria, Pretoria, South Africa.
Sci Rep. 2017 May 22;7(1):2234. doi: 10.1038/s41598-017-02474-w.
A Hill-type time-response curve was derived using a single-step chemical kinetics approximation. The rate expression for the transformation is a differential equation that provides an interpolation formula between the logistic growth curve and second order kinetics. The solution is equivalent to the log-logistic cumulative distribution function with the time constant expressed in terms of a kinetic rate constant. This expression was extended to a full dose-time-response equation by postulating a concentration dependence for the rate constant. This was achieved by invoking a modified form of Haber's law that connects an observed toxic effect with the concentration of the active agent and the elapsed exposure time. Analysis showed that the concept of Concentration Addition corresponds to a special case where the rate constant for the overall transformation rate is proportional to the sum of the rate constants that apply when the agents act individually. Biodiesel "survival" curves were measured and used to test the applicability of the empirical model to describe the effects of inhibitor dosage and binary inhibitor mixtures. Positive results suggest that the proposed dose-response relationship for the toxicity of agents to organisms can be extended to inanimate systems especially in cases where accurate mechanistic models are lacking.
采用单步化学动力学近似法推导出 Hill 型时间响应曲线。该转化的速率表达式是一个微分方程，在逻辑增长曲线和二级动力学之间提供了一个插值公式。该解等同于对数逻辑累积分布函数，其中时变常数用动力学速率常数表示。通过假设速率常数与浓度有关，将该表达式扩展为完整的剂量-时间响应方程。这是通过调用哈伯定律的一种修正形式来实现的，该定律将观察到的毒性效应与有效药剂的浓度和暴露时间联系起来。分析表明，浓度加和的概念对应于一种特殊情况，即整体转化速率的速率常数与当药剂单独作用时适用的速率常数之和成正比。测量了生物柴油的“存活”曲线，并将其用于测试经验模型对描述抑制剂剂量和二元抑制剂混合物的影响的适用性。阳性结果表明，拟议的用于描述药剂对生物体毒性的剂量反应关系可以扩展到无生命系统，特别是在缺乏准确的机械模型的情况下。
