Cancer is caused by dysfunctional signaling pathways which lead to uncontrolled cell proliferation and tumor growth. Understanding the molecular nature of cancer calls for study of the mechanisms of these pathways. Dynamical mechanistic models describe the pathways in terms of molecular and protein-protein interactions through a system of ordinary differential equations. Due to their inherent complexity, large number of parameters, and a limited set of experimental data, the models are usually vastly underdetermined. To obtain non-trivial novel predictions from such models researchers traditionally use single point parameter estimates derived from literature or obtained by various optimization techniques. However, such single point estimates poorly represent models operating in a large multidimensional parameter space, thus casting doubt on validity of model predictions.

Probabilistic simulations of dynamical mechanistic models allow an alternative and principled approach to address parameter uncertainties. We develop a Bayesian formalism of parameter estimation and apply it to the mechanistic model of signaling pathways initiated through epidermal growth factor receptors (EGFR). These pathways most frequently mutate in cancer and thus form a natural target of anti-cancer therapies.

With the probabilistic simulations, we fit the model to a series of dynamic experimental measurements of EGFR phosphorylation. From these simulations, we obtain probabilistic parameter distributions which then serve as a basis for generating predictions, such as predicting long-term system behavior based on initial response, predicting degradation of EGFR at the end of simulations, predicting strengths of the EGFR phosphaptases, and others.  

Next, we analyze the distribution of predicted combinations of signal decay mechanisms (such as receptor degradation, and action of phosphatases) employed in the simulations to fit the long term signal decay in the data. The distribution predicts that the signal is most likely to be decayed exclusively by one of the mechanisms, as opposed to using a combination of the two, which nevertheless has a non-zero likelihood. 

We then experimentally validate our prediction in real cells by measuring levels of degradation of EGFR and strength of their phosphatases. Here, we find that the cells use both mechanisms together, rather then just one of them.

Finally, we use our model to understand the above apparent discrepancy between the predicted and actual mechanisms of signal decay. We hypothesize possible advantages to the cell’s use of both mechanisms, receptor degradation and dephosphorylation by phosphatses, in the context of EGFR signal habituation — a phenomenon in which cells decrease their response to a prolonged exposure to the same level of stimuli. We find that having EGFR phosphatases allows EGFR signal to be sensitive to stimuli removal, whereas receptor degradation ensures that the amplitude of a repeated response is lower then the original signal.