Howard Gregory J, Webster Thomas F
Department of Environmental Health, Boston University School of Public Health, 715 Albany Street, Boston, MA 02118, USA.
J Theor Biol. 2009 Aug 7;259(3):469-77. doi: 10.1016/j.jtbi.2009.03.030. Epub 2009 Apr 5.
Environmentally relevant toxic exposures often consist of simultaneous exposure to multiple agents. Methods to predict the expected outcome of such combinations are critical both to risk assessment and to an accurate judgment of whether combinations are synergistic or antagonistic. Concentration addition (CA) has commonly been used to assess the presence of synergy or antagonism in combinations of similarly acting chemicals, and to predict effects of combinations of such agents. CA has the advantage of clear graphical interpretation: Curves of constant joint effect (isoboles) must be negatively sloped straight lines if the mixture is concentration additive. However, CA cannot be directly used to assess combinations that include partial agonists, although such agents are of considerable interest. Here, we propose a natural extension of CA to a functional form that may be applied to mixtures including full agonists and partial agonists. This extended definition, for which we suggest the term "generalized concentration addition," encompasses linear isoboles with slopes of any sign. We apply this approach to the simple example of agents with dose-response relationships described by Hill functions with slope parameter n=1. The resulting isoboles are in all cases linear, with negative, zero and positive slopes. Using simple mechanistic models of ligand-receptor systems, we show that the same isobole pattern and joint effects are generated by modeled combinations of full and partial agonists. Special cases include combinations of two full agonists and a full agonist plus a competitive antagonist.
与环境相关的有毒暴露通常包括同时接触多种化学物质。预测此类混合物预期结果的方法对于风险评估以及准确判断混合物是否具有协同或拮抗作用至关重要。浓度相加法（CA）通常用于评估作用相似的化学物质混合物中协同或拮抗作用的存在，并预测此类物质混合物的效应。CA具有清晰的图形解释优势：如果混合物是浓度相加性的，恒定联合效应曲线（等效应线）必须是负斜率的直线。然而，CA不能直接用于评估包含部分激动剂的混合物，尽管此类物质备受关注。在此，我们提出将CA自然扩展为一种函数形式，可应用于包含完全激动剂和部分激动剂的混合物。我们建议将这个扩展定义称为“广义浓度相加”，它涵盖了具有任何符号斜率的线性等效应线。我们将此方法应用于由斜率参数n = 1的希尔函数描述剂量 - 反应关系的简单化学物质示例。所得的等效应线在所有情况下都是线性的，具有负、零和正斜率。使用配体 - 受体系统的简单机理模型，我们表明完全激动剂和部分激动剂的模拟混合物会产生相同的等效应线模式和联合效应。特殊情况包括两种完全激动剂的组合以及一种完全激动剂加一种竞争性拮抗剂的组合。
