While using mathematical models to investigate the behavior of signaling networks is hardly new, understanding a complex biosystem, such as a tumor, by focusing on the analysis of its molecular or cellular level separately or exclusively is insufficient, particularly if it excludes the interaction with the surrounding tissue. Recent analyses of signaling pathways in mammalian systems have revealed that highly connected sub-cellular networks generate signals in a context dependent manner [53
]. That is, biological processes take place in heterogeneous and highly structured environments [54
] and such extrinsic conditions alone can induce the transformation of cells independent of genetic mutations as has been shown for the case of melanoma [55
]. Taken together, modeling of cancer systems requires the analysis and use of signaling pathways in a simulated cancer environment (context) across
different spatial-temporal scales.
Our group has been focusing on the development of such multiscale models for studying highly malignant brain tumors [27
]. Here, on the basis of these previous works, we presented a 2D multiscale agent-based model to simulate NSCLC. Specifically, we monitored how, dependent on microenvironmental stimuli, molecular profiles dynamically change, and how they affect a single NSCLC cell's phenotype and, eventually, the resulting multicellular patterns.
in our analysis, we first evaluated the multicellular readout of molecular 'decision' rules A and B (versus general rules; Fig. ). The patterns of a more stationary, concentrically growing cancer system (following rule B) are quite different from the rapid, chemotactically-guided, spatial expansion that can be seen in the tumor regulated by rule A (Fig. ). Not surprisingly, the latter also operates with many more migratory albeit overall less [total] cells (Fig. ). Furthermore, examining in more detail the influence of the two distinct rules on their respective phenotypic yield, we found that the impact of rule A on increasing cell migration is more substantial than rule B's influence on furthering proliferation (Fig. ). This finding suggests that the migratory rule A can operate the cancer system through incrementally smaller changes (while the simulation system is more robust for rule B). Such sensitivity
to migratory cues corresponds well with experimental data on the response of human breast cancer cells, which showed that a spatially successful expansive system reacts rather quickly to even miniscule changes in chemotactic directionality [57
Continuing therefore with rule A, our effort was then geared to gain insights into tumor expansion dynamics not only with regards to extrinsic stimuli but also to cell geography, i.e. a cell's location relative to the replenished nutrient source. Most interestingly, we found a phase transition
in the cancer cell closest to the nutrient source (i.e. Cell No 48, while none of the other three corner cells showed similar behavior). Specifically, for a tumor cell at this location, i.e., facing nutrient abundance, proliferation is completely abolished
once the extrinsic EGF concentration exceeds a certain level. While this at first may seems rather unexpected, this finding however only confirms the experimentally sound notion that EGF stimulates the spatial expansion of a cancer system [5
]. Moreover, with increasing EGF concentrations, the maxima of ROCPLC
(Fig. ) gradually occur earlier
which seems to indicate that, under these conditions, the downstream signal is processed faster
. Interestingly, such a 'no proliferation, just migration' behavior in the presence of chemo-attractant has indeed already been reported in several in vitro
studies using a variety of cancer cell lines [59
] as well as in non-cancerous human cells [61
]. (While admittedly, for the reasons stated, rule B did not receive similar attention in our analysis), we nonetheless argue that, on the basis of our results and the experimental reports they seem to correspond with, rule A and thus a migratory
decision prompted by a [ROCPLC
] condition is a reasonable outcome for the signaling process taking place in NSCLC also in vitro
and in vivo
However, moving the model closer to reality will require a multitude of adjustments, one of which is its ability to account for up- or down-regulation in key molecules as a result of tumorigenesis. As a first step, and since experimental data on over-expression of EGFR in a variety of cancer types, including NSCLC, are ample [62
] we have begun to simulate the impact of an increasing number of receptors on the cancer system (Fig. ; simulations conducted with an EGFR concentration of 800 nM (per system)). Comparing this preliminary data with those reported in Fig. (simulations conducted with an EGFR concentration of 80 nM (per system)), we find that an EGFR-overexpressing NSCLC tumor seems to operate with even more
migration and does so earlier
on. The result is a spatially even more aggressive cancer system, which seems to correspond well with the aforementioned experimental studies. And, intriguingly, while the phase transition itself is preserved, it however occurs already at a smaller EGF concentration, hence indicating that the increase in receptor density leads to an amplification
of the downstream signal, which again corresponds well with experimental results in examining signaling activities generated by different EGFR family members [66
]. Taken together, while preliminary, this finding demonstrates applicability and confirms flexibility of this multiscale platform, hence warrants its further expansion.
Figure 7 Changes at the molecular level for Cell No 48 with an increasing extrinsic EGF concentration (rule A), at an EGFR concentration of 800 nM. Three simulation runs are depicted where (from left to right) the EGF concentration increases from 2.65 × (more ...)
There are a number of research tracks that can and should be pursued in future works. First, it will be intriguing to see if, in the presence of a non
-replenished nutrient source, the proliferative phenotype eventually can be recovered once extrinsic ligand concentrations fall beyond the phase-transition threshold. More generally, while most of the pathway's parameters, including rate constants and initial component concentrations were obtained from the experimental literature, this data naturally originated from a variety of often stationary experimental settings and different cell types. It therefore represents a less desirable and reliable input than time series data that come from one
experimental setting only. Also, some parameters had to be estimated, much like in other well-established pathway models [11
]. Taken together, future works will have to include not only proper experimental verification of the estimated parameters and evaluation of the simulation results but also, on the in silico
side, techniques such as sensitivity analysis to help determine the effects of parameter uncertainties on model outcome [67
] and to identify control points for experiment design [68
]. While a pathway model cannot be a biological representation in every detail [38
] we plan on adding, in incremental steps, other pathways of relevance for NSCLC such as e.g. PI3K/PTEN/AKT [69
]. Moreover, simulating a more heterogeneous biochemical environment and implementing both cell-cell and cell-matrix interactions [70
] are planned steps at the cellular level that should help representing the cancer system of interest in more detail.
Regardless, we believe that the current model already provides useful insights into NSCLC from a systematic view in terms of quantitatively understanding the relationship between extrinsic chemotactic stimuli, the underlying properties of signaling networks, and the cellular biological responses they trigger. Our results yield several experimentally testable hypotheses and thus further support the use of multiscale models in interdisciplinary cancer research. To our knowledge, this presents the first multiscale computational model of Non-Small Cell Lung Cancer and is thus potentially a significant first step towards realizing a fully validated in silico model for this devastating disease.