Cross-scale sensitivity analysis of a non-small cell lung cancer model: linking molecular signaling properties to cellular behavior

Abstract

Sensitivity analysis is an effective tool for systematically identifying specific perturbations in parameters that have significant effects on the behavior of a given biosystem, at the scale investigated. In this work, using a two-dimensional, multiscale non-small cell lung cancer (NSCLC) model, we examine the effects of perturbations in system parameters which span both molecular and cellular levels, i.e. across scales of interest. This is achieved by first linking molecular and cellular activities and then assessing the influence of parameters at the molecular level on the tumor's spatio-temporal expansion rate, which serves as the output behavior at the cellular level. Overall, the algorithm operated reliably over relatively large variations of most parameters, hence confirming the robustness of the model. However, three pathway components (proteins PKC, MEK, and ERK) and eleven reaction steps were determined to be of critical importance by employing a sensitivity coefficient as an evaluation index. Each of these sensitive parameters exhibited a similar changing pattern in that a relatively larger increase or decrease in its value resulted in a lesser influence on the system's cellular performance. This study provides a novel cross-scaled approach to analyzing sensitivities of computational model parameters and proposes its application to interdisciplinary biomarker studies.

Figure 1

Phenotypic decision process for a cancer cell between two time steps.

Figure 2

A typical cell expansion pattern in the NSCLC model. Proliferative cells are labeled in dark blue, migratory cells in red, quiescent cells in green and dead cells in grey.

Figure 3

The sensitivity coefficients of each selected pathway component with respect to the variations listed in Table 1.

Figure 4

The sensitivity coefficients of the most sensitive pathway components (PKC, MEK and ERK) with respect to the variations from 1.0- to 1.2-fold by an incremental increase of 0.01 (left panel) and from 1.2- to 2.0-fold by an incremental increase of 0.1 (right panel).

Figure 5

Plots of sensitivity coefficients for sensitive rate constants. In (a), seven rate constants are shown for which the critical area is between 1.0- and 2.0-fold; their values varied from 1.0- to 1.2-fold by an incremental increase of 0.01 (first and third columns) and from 1.2- to 2.0-fold by an incremental increase of 0.1 (second and fourth columns). In (b), five rate constants are shown for which the critical area is between 0.1 and 1.0; their values varied from 0.1- to 0.8-fold by an incremental increase of 0.1 (first and third columns) and from 0.8- to 1.0-fold by an incremental increase of 0.01 (second and fourth columns).

Figure 5

Plots of sensitivity coefficients for sensitive rate constants. In (a), seven rate constants are shown for which the critical area is between 1.0- and 2.0-fold; their values varied from 1.0- to 1.2-fold by an incremental increase of 0.01 (first and third columns) and from 1.2- to 2.0-fold by an incremental increase of 0.1 (second and fourth columns). In (b), five rate constants are shown for which the critical area is between 0.1 and 1.0; their values varied from 0.1- to 0.8-fold by an incremental increase of 0.1 (first and third columns) and from 0.8- to 1.0-fold by an incremental increase of 0.01 (second and fourth columns).

Figure 6

Schematic illustration of how perturbations (a, b, c, …, n) in one or more sub-cellular parameter(s), p, can yield the same dynamic response at the molecular level, yet may lead to distinct responses at the cellular level dependent on the microenvironment.