  Intra-tumour phenotypic heterogeneity limits accuracy of clinical diagnostics
and hampers the efficiency of anti-cancer therapies. Dealing with this cellular
heterogeneity requires adequate understanding of its sources, which is
extremely difficult, as phenotypes of tumour cells integrate hardwired
(epi)mutational differences with the dynamic responses to microenvironmental
cues. The later come in form of both direct physical interactions, as well as
inputs from gradients of secreted signalling molecules. Furthermore, tumour
cells can not only receive microenvironmental cues, but also produce them.
Despite high biological and clinical importance of understanding spatial
aspects of paracrine signaling, adequate research tools are largely lacking.
Here, a partial differential equation (PDE) based mathematical model is
developed that mimics the process of cell ablation. This model suggests how
each cell might contribute to the microenvironment by either absorbing or
secreting diffusible factors, and quantifies the extent to which observed
intensities can be explained via diffusion mediated signalling. The model
allows for the separation of phenotypic responses to signalling gradients
within tumour microenvironments from the combined influence of responses
mediated by direct physical contact and hardwired (epi)genetic differences. The
differential equation is solved around cell membrane outlines using a finite
element method (FEM). The method is applied to a multi-channel
immunofluorescence in situ hybridization (iFISH) stained breast cancer
histological specimen and correlations are investigated between: HER2 gene
amplification; HER2 protein expression; and cell interaction with the
diffusible microenvironment. This approach allows partial deconvolution of the
complex inputs...
