QAP14抑制4T1乳腺癌肺转移的群体药效学随机模型

doi:10.5246/jcps.2021.10.067

中国药学(英文版) ›› 2021, Vol. 30 ›› Issue (10): 794-805.DOI: 10.5246/jcps.2021.10.067

QAP14抑制4T1乳腺癌肺转移的群体药效学随机模型

韩梦仪¹, 雍灵¹, 郭昱辰¹, 严晓雪², 陈国术², 孔大明¹, 周田彦¹^,^*()

1. 北京大学药学院药剂学系, 分子药剂学与新释药系统北京市重点实验室, 北京 100191
2. 广州大学化学化工学院化学基础实验室, 广东广州 510006

收稿日期:2021-04-18 修回日期:2021-05-20 接受日期:2021-06-19 出版日期:2021-10-24 发布日期:2021-10-24
通讯作者: 周田彦
作者简介:
+ Tel.: +86-10-82801717, E-mail: tianyanzhou@bjmu.edu.cn
基金资助:
Natural Science Foundation of Beijing Municipality (Grant No. 7192100).

A stochastic population pharmacodynamic model of QAP14 in the treatment of lung metastases of 4T1 breast cancer

Mengyi Han¹, Ling Yong¹, Yuchen Guo¹, Xiaoxue Yan², Guoshu Chen², Daming Kong¹, Tianyan Zhou¹^,^*()

1 Beijing Key Laboratory of Molecular Pharmaceutics and New Drug Delivery System, Department of Pharmaceutics, School of Pharmaceutical Sciences, Peking University, Beijing 100191, China
2 Chemical Basic Laboratory, School of Chemistry and Chemical Engineering, Guangzhou University, Guangzhou 510006, China

Received:2021-04-18 Revised:2021-05-20 Accepted:2021-06-19 Online:2021-10-24 Published:2021-10-24
Contact: Tianyan Zhou

摘要/Abstract

摘要：

肿瘤转移是一个多步骤的复杂过程, 具有明显的随机性。本研究旨在建立一种随机数学模型来描述肿瘤转移的随机过程, 预测新化合物QAP14对小鼠肿瘤转移的抑制作用。4T1细胞植入BALB/c小鼠22天后, 收集QAP14治疗组与对照组的肺转移数据, 基于原发肿瘤和转移灶指数生长的特点和以上数据, 建立转移大小和数量的联合分布模型, 进而模拟疾病进展和QAP14的临床前药效。参数M和m分别代表转移灶体积的最大值和最小值, 估计值分别为3.24和0.0184 mm³, 转移生长速率γ和促转移时间ρ的估计值分别为0.0216/天和7.8天并在药效模型中固定, QAP14对促转移时间和转移生长速率常数的作用以指数的形式加入到模型中, 药效参数Effect_ρ和Effect_γ的估计值分别为16.6和0.327 g/mg。本研究系统描述了肿瘤转移的疾病进程以及QAP14抑制4T1乳腺癌小鼠肺转移的药效, 为临床上建立肿瘤转移的群体模型提供了有价值的参考。

关键词: 随机群体模型, PD模型, 高通量4T1, 肺转移, 乳腺癌

Abstract:

Cancer metastasis is a process with multi-step complexity and apparent randomness. In this study, we aimed to establish a stochastic mathematical model to describe the random process of cancer metastasis and predict the drug effect of QAP14 on metastasis in a mouse model. The data of lung metastases on the 22^nd day after cancer cell implantation with or without the treatment of QAP14, a new chemical compound, were collected in 4T1 breast cancer BALB/c mice. Based on the exponential growth of the primary tumor and metastatic loci, a joint distribution model of metastasis size and number was developed. Disease progression of metastasis and preclinical efficacy of QAP14 were modeled. Parameters M and m representing maximum and minimum of metastasis volume were 3.24 and 0.0184 mm³, respectively. The metastasis growth rate γ and metastasis promotion time ρ were estimated and fixed to be 0.0216 d^–1 and 7.8 d, respectively. The efficacy of QAP14 acted on metastasis promotion time and metastasis growth rate constant in an exponential term, and the effect parameter Effect_ρ and Effect_γ were 16.6 and 0.327 g/mg, respectively. In the present study, we comprehensively characterized the random process of lung metastasis and efficacy of QAP14 in 4T1 breast cancer mice, which might provide a useful reference for the establishment of a clinical population model of cancer metastasis.

Key words: Stochastic population model, PD model, 4T1, Lung metastasis, Breast cancer

Supporting:

Supplement Figure 1. Individual fit plots of instantaneous seeding model on the 22^nd day. Abscissa is metastasis volume and ordinate is cumulative density function value (cdf). The dotted lines, dashed and solid lines represent observed values, population predicted values and individual population predicted values, respectively.

Supplement Figure 2.Individual fit plots of two types of models in reference article. Abscissa is metastasis volume and ordinate is cumulative density function value (cdf). The dotted lines and dashed lines represent observed values and population predicted values respectively.a. The individual fit plot of instantaneous seeding model;b. The individual fit plot of homogeneous model.

Supplementary Table 1. Metastasis volume-cdf data of ID 1 on the 22^nd day.

韩梦仪, 雍灵, 郭昱辰, 严晓雪, 陈国术, 孔大明, 周田彦. QAP14抑制4T1乳腺癌肺转移的群体药效学随机模型[J]. 中国药学(英文版), 2021, 30(10): 794-805.

Mengyi Han, Ling Yong, Yuchen Guo, Xiaoxue Yan, Guoshu Chen, Daming Kong, Tianyan Zhou. A stochastic population pharmacodynamic model of QAP14 in the treatment of lung metastases of 4T1 breast cancer[J]. Journal of Chinese Pharmaceutical Sciences, 2021, 30(10): 794-805.

图/表 6

Figure 1. Scheme of QAP14 PD model.

Table 1. Descriptions and estimates of parameters and functions.

Figure 2. Diagnostic graphs of the primary tumor growth model. The dot represents the observed value, and the line is y = x or y = 0 line. The diagnostic graphs including DV versus PRED or IPRED, CWRES versus PRED, or metastasis volume.

Figure 3. Histograms of the metastasis number-size distribution in 4T1 allograft mice of the control and treatment groups. Each panel represents the data of one mouse, and one mouse can provide multi-point data in 1 d.

Figure 4. Diagnostic graphs of the PD model on the 22nd day. The dot represents the observed value, and the line is y = x or y = 0 line. The diagnostic graphs including DV versus PRED or IPRED, CWRES versus PRED, or metastasis volume.

Figure 5. Individual fit plots of PD model. The abscissa is metastasis volume, and ordinate is cdf value. The dotted lines, dashed and solid lines represent observed values, population predicted values, and individual population predicted values, respectively. (a) The individual fit plots in the control group; (b) The individual fit plots in QAP14 20 mg/kg group; (c) The individual fit plots in QAP14 40 mg/kg group.

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QAP14抑制4T1乳腺癌肺转移的群体药效学随机模型

A stochastic population pharmacodynamic model of QAP14 in the treatment of lung metastases of 4T1 breast cancer

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