Modelling drug efficacy: capturing the target engagement of heterogeneous cancer cells

肿瘤的异质性是众所周知的，这导致了治疗的局限性和失败，因为癌细胞在面对治疗时表现出一定程度的耐药性，正如使用多种酪氨酸激酶抑制剂治疗非小细胞肺癌的最终失败所突出的那样。这些抑制剂对抗许多异常信号通路，这些信号通路诱导了细胞行为的全面变化，包括肿瘤的形成。在信号通路的水平上，细胞缓冲外部扰动（如酪氨酸激酶的（部分）抑制）引起的变化的能力通常是复杂的，正如代谢背景下生物化学细胞网络中的稳态研究所强调的那样[1,2]。因此，在动态系统的数学建模和模拟中使用各种技术，以及参数约简、参数估计和模型选择研究，我们的目标将是推广细胞如何维持癌症相关信号通路的稳健稳态的理论研究。特别是，我们的目标将包括探索个体细胞信号通路中的生化基元如何缓冲异常通路的拮抗扰动，并研究这种机制在群体水平上的影响，包括群体水平药代动力学-药效学模型的参数化和预测。例如，迄今为止，我们已经完善了一个捕获EGFR信号通路[4]的数学模型。系统的敏感性分析已经实现，以探索模型输出如何依赖于感兴趣的参数。此外，MATCONT（一个图形化的MATLAB软件包）已被用于执行系统稳态的分岔和稳定性分析，并且对通过G蛋白偶联受体[5]的信号传导有广泛的进一步兴趣。更一般地说，这些研究的潜在影响在于理解对治疗的不敏感（即耐药性）是如何产生的，以及对旨在使信号通路反应正常化的单个和多个靶点的预测。此外，这种方法的新颖之处在于将稳态概念应用于癌症相关途径及其扰动。该项目的工业合作伙伴是葛兰素史克公司（GSK）的James Yates博士，其相对较大的信号传导途径的理论研究属于EPSRC数学生物学和非线性系统研究领域的研究范围。[1] Reed， M., Best， J., Golubitsky， M., Stewart， I.和Nijhout， H. F.（2017）。生物化学网络中的稳态机制分析。数学生物学通报，79(11),2534-2557。https://doi.org/10.1007/s11538-017-0340-z [2] Watson， E., Chappell， M., Ducrozet， F., Poucher， S., & Yates， J.（2009）。一种基于比例-积分-导数控制器的通用葡萄糖稳态模型。国际会计联合会论文集，42(12),79-84。https://doi.org/10.3182/20090812-3-dk-2006.0027[3]张，s.a, Majid， O., Yates， J. W., & Aarons， L.（2012）。心血管反馈模型的结构可识别性分析和参数化（参数缩减）。医药科学杂志，46(4),259-271。https://doi.org/10.1016/j.ejps.2011.12.017 [4] Shvartsman, s.y., Hagan, m.p., jacob， A., Dent， P., Wiley, h.s., & Lauffenburger， D. A.（2002）。具有正反馈的自分泌回路使上下文依赖的细胞信号传导成为可能。中国生物医学工程学报，2014(3):545- 559。https://doi.org/10.1152/ajpcell.00260.2001 [5] Bridge， L., Mead， J., Frattini， E., Winfield， I., & Ladds， G.（2018）。G蛋白偶联受体的偏激作用动力学建模和模拟。生物工程学报，42(2):444 - 444。https://doi.org/10.1016/j.jtbi.2018.01.01

Tumour heterogeneity is well known, leading to therapeutic limitations and failure as cancer cells that exhibit some degree of resistance prevail in the face of treatment, as highlighted by the ultimate failure of non-small cell lung carcinoma therapies with multiple tyrosine kinase inhibitors. These inhibitors antagonise numerous aberrant signalling pathways that have induced comprehensive changes in cell behaviour, including tumour formation. At the level of signalling pathways, the capabilities of a cell to buffer changes induced by external perturbations, such as the (partial) inhibition of tyrosine kinases, is generally complex as highlighted by a study of homeostasis in biochemical cellular networks, in the context of metabolism [1,2]. Thus, using diverse techniques in the mathematical modelling and simulation of dynamical systems together with parameter reduction [3], parameter estimation and model selection studies, our aim will be to generalise theoretical investigations of how cells maintain robust homeostasis for cancer relevant signalling pathways. In particular our objectives will include exploring how biochemical motifs within the signalling pathway of an individual cell may buffer antagonistic perturbations of aberrant pathways and investigating the impact of such mechanisms at the population level, including the parameterisation and predictions of population level Pharmacokinetic-Pharmacodynamic models. For example, to date we have refined a mathematical model capturing the EGFR signaling pathway [4]. A systematic sensitivity analysis has been implemented to explore how model outputs depend on parameters that are of interest. In addition, MATCONT (a graphical MATLAB software package) has been utilized to perform bifurcation and stability analysis of the steady states of the system and there is extensive further interest in signalling via the G protein coupled receptor [5]. More generally, the potential impact of such studies lies in understanding how an insensitivity to treatment, that is resistance, may arise together with the resulting predictions for single and multiple targets aimed at normalising signalling pathway responses. In addition, the novelty of this approach concerns the application of concepts from homeostasis to cancer relevant pathways and their perturbation. The industrial partner of this project is Dr James Yates of GlaxoSmithKline (GSK) and its theoretical study of relatively large signalling pathways falls within the remit of the EPSRC Mathematical Biology and Non-linear Systems research areas. [1] Reed, M., Best, J., Golubitsky, M., Stewart, I., & Nijhout, H. F. (2017). Analysis of Homeostatic Mechanisms in Biochemical Networks. Bulletin of Mathematical Biology, 79(11), 2534-2557. https://doi.org/10.1007/s11538-017-0340-z [2] Watson, E., Chappell, M., Ducrozet, F., Poucher, S., & Yates, J. (2009). A New General Glucose Homeostatic Model using a Proportional-Integral-Derivative Controller. IFAC Proceedings Volumes, 42(12), 79-84. https://doi.org/10.3182/20090812-3-dk-2006.0027 [3] Cheung, S. A., Majid, O., Yates, J. W., & Aarons, L. (2012). Structural identifiability analysis and reparameterisation (parameter reduction) of a cardiovascular feedback model. European Journal of Pharmaceutical Sciences, 46(4), 259-271. https://doi.org/10.1016/j.ejps.2011.12.017 [4] Shvartsman, S. Y., Hagan, M. P., Yacoub, A., Dent, P., Wiley, H. S., & Lauffenburger, D. A. (2002). Autocrine loops with positive feedback enable context-dependent cell signaling. American Journal of Physiology-Cell Physiology, 282(3), C545-C559. https://doi.org/10.1152/ajpcell.00260.2001 [5] Bridge, L., Mead, J., Frattini, E., Winfield, I., & Ladds, G. (2018). Modelling and simulation of biased agonism dynamics at a G protein-coupled receptor. Journal of Theoretical Biology, 442, 44-65. https://doi.org/10.1016/j.jtbi.2018.01.01