混合物的联合毒性评价是毒理学研究的一个重要课题。前期的研究发现，剂量效应曲线（CRC）的特征参数k∙EC_x可以判断浓度加和模型（CA）的适用性，物质的CRCs形态与混合物的联合作用有关。本研究进一步评估了k∙EC_x在联合毒性评价中的可预测性。采用微孔板毒性分析法测定了12种不同来源的环境污染物对费氏弧菌（V. fischeri）的一元、二元急性毒性。利用CA和独立作用模型（IA）进行二元混合物联合作用的评价。研究了二元混合物联合作用（借助修正的偏移百分比模型（rMDR）的计算）与各组分特性参数k∙EC_x关系。由于CA与IA模型存在一定的不足之处，CA模型存在某些预测盲区，而IA模型是一个纯粹的理论构想，因此引入理论非线性联合毒性评价模型（TNL）对部分混合物进行补充评价，对三种模型进行选择优化。

首先，为判断物质的特征参数k∙EC_x是否能够表征物质CRCs的形态以及两种常见加和模型对二元混合物联合毒性的评价能力，本研究采用微孔板毒性分析方法测定了环境常见污染物的一元及二元混合物对V. fischeri的急性生物毒性。通过拟合获得单一物质的CRC，并利用CA、IA模型对二元混合物进行联合作用评价。实验结果表明：十二种物质及其二元混合物的CRCs均可用Hill方程很好的拟合。CRCs的拟合参数n值在一定程度上与其形态具有相关性，12种化学物质的特征参数k∙EC_x与Hill函数拟合参数n值的大小顺序基本一致。由于k∙EC_x对应不同的浓度有其确切值，因此更能反应CRCs在整个浓度区间的形态趋势。依据CA和IA模型的预测结果，由于所选物质的k∙EC_x差异较大，65%的等毒性比二元混合物产生了较强的拮抗或协同作用。同一组合，浓度比不同的二元混合物联合作用强度也不同。CA和IA模型对混合物的联合毒性评价结果差异较大，结合实验结果及文献分析，IA模型为最佳的联合作用评价模型。

其次，为探究各组分的k∙EC_x之间与混合物联合作用的函数关系，本研究利用数学方法对实验数据进行处理。通过数学拟合发现：无论混合物比例如何变化，各组分的k∙EC_x的相对差异与联合作用强度（rMDR_x）都很好的服从指数函数。根据∆(k∙EC_x)%与rMDR_x的变化特征将指数函数分为a₁、a₂、b₁和b₂四种类型混合物，对于a₁型二元混合物，所有函数均为非单调函数，虚线rMDR_x=0和∆(k∙EC_x)%=0与指数函数的交点不重合。虚线rMDR_x=0与指数函数交点对应的混合物浓度较低，即联合作用方式的改变早于CRC形状的转变。随着∣∆(k∙EC_x)%∣增加，联合作用强度先增加后减少再增加，与联合作用的方式无关。对于a₂型二元混合物，当拟合的指数函数为非单调函数并且联合作用为拮抗作用时，随着∣∆(k∙EC_x)%∣增加，联合作用强度先减少再增加；当联合作用是协同作用时，联合作用强度变化趋势相反。对于b₁型二元混合物，当∆(k∙EC_x)%＞0，随着∆(k∙EC_x)%的增加，联合作用强度先减小后增大。当∆(k∙EC_x)%＜0，联合作用强度变化趋势相反。对于b₂型二元混合物拟合的指数函数均为单调函数，且无论作用方式如何，增减函数的概率都是相近的。四种类型的不同浓度比二元混合物的联合作用规律同等毒性研究结果，说明该规律具有普遍适用性。该规律的确定为多元混合物联合毒性的预测奠定基础。

最后，为了对混合物联合毒性评价模型进行选择优化，本研究引入TNL模型并利用三种模型对混合物进行评价。TNL模型源于混合物联合作用的定义，研究者也从生化水平检测验证了其正确性。本研究选择21组等毒性比二元混合物与2种化学物的5组二元混合物的联合毒性进行补充评价。结果表明：CA、IA和TNL模型的评价结果存在较大差异，有8组混合物作用方式评价出现分歧。当各组分CRC的特征参数k·EC_x差异较小时，选用CA模型进行评价。若CA模型出现预测盲点时，直接选用IA模型。当k·EC_x差异较大时，宜使用TNL模型进行评价。

综上所述，本研究确定了CRC的特征参数k∙EC_x，探明了参数∆(k∙EC_x)%与混合物联合作用的函数关系。利用参数k∙EC_x预测二元混合物的联合毒性，在规划实验时可以快速获得非常重要的数据，同时也可以减少实验次数。将混合物分为四种类型，分别研究其联合作用的变化规律，能为二元混合物联合毒性的预测及“有效组合”的确定提供更为详细、具体理论支持。对混合物联合毒性评价模型进行了选择优化，将TNL模型作为补充模型，联合CA、IA模型共同应用于二元混合物联合作用评价，可得到准确的结果。

The evaluation of joint toxicity of mixtures is an important topic in toxicology. Previous studies have found that the characteristic parameter k∙EC_x of concentration response curves (CRCs) can be used to assess the applicability of concentration addition model (CA), and the CRCs of substances are related to the combined effect of the mixture. This study further assesses the predictability of k∙EC_x on the joint toxicity evaluation. The single and binary acute toxicity of 12 kinds of environmental pollutants from different sources to Vibrio fischeri was tested by using the microplate toxicity analysis. The joint toxicity evaluation of mixtures was conducted by CA and independent action model (IA). The relationship between the joint toxicity of binary mixture (measured by the relative model deviation ratio (rMDR)) and the characteristic parameter k∙EC_x of each component was studied. However, the CA and IA models have certain shortcomings. The CA model has some prediction blind spots, and the IA model is a pure theoretical conception. Therefore, the theoretical non-linear combined toxicity assessment model (TNL) is introduced to supplement the evaluation of some mixtures, and the three models are optimally selected.

First of all, in order to determine whether the characteristic parameter k∙EC_x of the substance can characterize the form of the substance CRCs and to verify the evaluation ability of two common additive models for the joint toxicity of binary mixtures, the acute toxicities of the single and binary mixtures of common pollutants in the environment to Vibrio fischeri were determined by using the microplate toxicity analysis. The CRC of a single substance was obtained by fitting, and the combined effect of the binary mixture was evaluated using CA and IA models. The result shows that the CRCs of 12 substances and their binary mixtures can be well fitted by Hill equation. The fitting parameter n value of CRCs is correlated with their morphology to some extent. The arrangement of the characteristic parameter k∙EC_x of 12 chemical substances and the n value of Hill function fitting parameter is basically the same. Because k∙EC_x has its exact value in different concentrations, and the k∙EC_x could reflect the shape of CRCs in the whole concentration range. According to the prediction results CA and IA models, due to the large difference in k∙EC_x of the selected substances, 65% of the mixtures with equal toxicity ratio produce strong antagonism or synergism. For the same combination, the combined action intensity of binary mixture with different concentration ratio is also different. The joint toxicity evaluation results of the mixture of CA and IA models are quite different. Combined with the experimental results and literature analysis, IA model is the best evaluation model.

Secondly, in order to determine the functional relationship between the k∙EC_x of each component and the joint action of the mixture, the experimental data were processed by mathematical methods in this study. Through mathematical fitting, it is found that no matter how the mixture ratio changes, the relative difference of k∙EC_x of components and the rMDR_x can be fitted by an exponential function. According to the change of ∆(k∙EC_x)% and rMDR_x, the exponential function is divided into four types of mixtures. For a₁ type binary mixtures, all functions are non-monotonic functions. The intersection points of the dotted lines rMDR_x=0 and ∆(k∙EC_x)%=0 and the exponential function do not coincide. The concentration of the mixture corresponding to the intersection of the dotted line rMDR_x=0 and the exponential function is lower. In other words, the change of the combined mode of action precedes the change of CRC shape. With the increase of∣∆(k∙EC_x)%∣, the intensity of combined action first increases, then decreases and then increases, This law has nothing to do with the way of joint action. For a₂ type binary mixtures, when the fitting exponential functions are non-monotonic and the joint action is antagonistic, with the increase of∣∆(k∙EC_x)%∣, the intensity of the combined action first decreases and then increases. When the joint action is synergetic, the intensity of the combined effect changes in the opposite direction. For b₁ type binary mixtures, when ∆(k∙EC_x)% > 0, with the increase of ∆(k∙EC_x)% , the joint action strength first decreases and then increases. When ∆(k∙EC_x)% < 0, the intensity of the combined effect changes in the opposite direction. For b₂ type binary mixtures, the fitting exponential functions are all monotone functions. Regardless of the mode of action, the probability of increasing or decreasing functions is similar. The combined action law of the four types of binary mixtures with different concentration ratios has the same toxicity study results, indicating that the law has universal applicability. This rule does provide a basis for predicting the combined toxicity of multiple mixtures.

Finally, in order to select and optimize the joint toxicity evaluation model of the mixture, this study introduces the TNL model and uses three models to evaluate the mixture. This model is derived from the definition of mixture combined action, and its correctness has also been verified by biochemical tests. In this study, 21 groups of binary mixtures with equal toxicity ratio and 5 sets of binary mixtures of 2 chemicals were selected for supplementary evaluation. The evaluation results of CA, IA and TNL models were quite different, the action mode of eight groups by the three models was different. When the difference of characteristic parameter k‧EC_x value was small, the CA model was used for evaluation. If the CA model has a prediction blind spot, the IA model was directly selected. When the difference of k‧EC_x was big, the TNL model should be used.

In summary, the characteristic parameter k∙EC_x of CRC was determined, and the functional relationship between the parameter ∆(k∙EC_x)% and the combined action of the mixture was explored. The parameter k∙EC_x is used to predict the joint toxicity of binary mixtures, which can quickly obtain very important data when planning experiments and the number of experiments can also be reduced. By studying the changing law of the combined action of the four types of mixtures, it can provide more detailed and specific theoretical support for the prediction of the joint toxicity of the binary mixture and the determination of the “effective combination”. The joint toxicity evaluation model of the mixture was selected and optimized. As a supplementary model, the TNL model can be combined with CA and IA models to evaluate the combined effects of binary mixtures, and accurate results can be obtained.

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