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

众所周知，肿瘤的异质性导致了治疗的局限性和失败，因为面对治疗，表现出一定程度耐药性的癌细胞占了上风，其中突出表现为使用多种酪氨酸酶抑制剂的非小细胞肺癌治疗最终失败。这些抑制剂拮抗许多引起细胞行为全面改变的异常信号通路，包括肿瘤的形成。在信号通路的水平上，细胞缓冲外部扰动引起的变化的能力通常是复杂的，如(部分)抑制酪氨酸激酶，正如在代谢背景下对生化细胞网络中的动态平衡的研究所强调的那样[1，2]。因此，在动态系统的数学建模和模拟中使用不同的技术，以及参数减少、参数估计和模型选择研究，我们的目标将是推广细胞如何为癌症相关的信号通路维持强大的动态平衡的理论研究。特别是，我们的目标将包括探索单个细胞信号通路中的生化基序如何缓冲异常通路的拮抗扰动，并调查这种机制在种群水平的影响，包括种群水平药动-药效学模型的参数化和预测。例如，到目前为止，我们已经改进了一个捕捉EGFR信号通路的数学模型[4]。进行了系统的敏感性分析，以探讨模型输出如何依赖于感兴趣的参数。此外，利用MATCONT(一个图形化的MatLab软件包)对系统的稳态进行了分叉和稳定性分析，并对通过G蛋白偶联受体的信号传递产生了广泛的兴趣[5]。更广泛地说，这类研究的潜在影响在于理解对治疗不敏感，即耐药性，以及由此产生的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，这种方法的新颖性涉及到从动态平衡到癌症相关途径及其扰动的概念的应用。该项目的工业合作伙伴是葛兰素史克(GSK)的詹姆斯·耶茨博士，该项目对相对较大的信号通路的理论研究属于EPSRC数学、生物学和非线性系统研究领域。[1]Reed，M.，Best，J.，Golubitsky，M.，Stewart，I.，&Nijhout，H.F.(2017)。生化网络中的动态平衡机制分析。数学生物学通讯，79(11)，2534-2557。Https://doi.org/10.1007/s11538-017-0340-z[2]Watson，E.，Cappell，M.，Ducrozet，F.，Poucher，S.，&Yates，J.(2009年)。一种新的基于比例-积分-导数控制器的广义葡萄糖稳态模型。IFAC会议论文集，42(12)，79-84。[3]https://doi.org/10.3182/20090812-3-dk-2006.0027[3]张，S.A.，马吉德，O.，叶茨，J.W.，&Aarons，L.(2012年)。心血管反馈模型的结构可辨识性分析和再参数化(参数减少)。欧洲药学杂志，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年)。具有正反馈的自分泌环路允许上下文相关的细胞信号传递。《美国生理学-细胞生理学》，282(3)，C545-C559。Https://doi.org/10.1152/ajpcell.00260.2001[5]Bridge，L.，Mead，J.，Frattini，E.，Winfield，I.，&Lads，G.(2018年)。G蛋白偶联受体偏向激动动力学的建模和模拟。《理论生物学杂志》，第442期，第44-65页。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