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

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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