Integration of Molecular Signaling into Multiscale Modeling of Cancer - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 377

effectively ground and foster future models incorporating multiple scales from the
molecular up to the cellular level and beyond.

2.1.1 EGFR Signaling

The epidermal growth factor receptor (EGFR) is mutated and overexpressed in
many cancers, including brain cancer and lung cancer [ 25 ]. Epidermal growth
factor (EGF) binds EGFR and promotes dimerization and subsequent autophos-
phorylation, resulting in the downstream activation of a number of key cell deci-
sion-making proteins such as phospholipase Cc (PLCc), extracellular signal-
regulated kinase (ERK), and many others [ 26 ]. A number of EGFR-related pathway
kinetic models have been developed [ 27 - 29 ], but regardless of differences in their
complexity and scale (i.e., the number of molecular entities or molecular events),
all of these models use mathematical kinetic equations to describe molecular
interactions. The change in concentration of a certain protein pathway component
over time is determined based on the following ordinary differential equation form:

¼ X v Production X v Consumption ;

d ð X i Þ
dt

ð 1 Þ

where X i represents one of the pathway components; the change in concentration
of X i is the result of the reaction rates producing X i minus the reaction rates
consuming it. If the initial concentrations of pathway components or reaction rate
constants are not yet available in the literature, their values either have to be
investigated experimentally or are fitted to published time-dependent quantitative
(or sometimes even qualitative) observations.

2.1.2 Microenvironment

A two-dimensional (2D) environment made up of a discrete lattice or a three-
dimensional (3D) environment composed of a discrete cube are constructed to
investigate tumor growth dynamics. Each grid point is occupied by a single cell or
is empty. Heterogeneous environments are attained by distributing external dif-
fusive chemical cues (such as growth factors, glucose, and oxygen) throughout the
computational domain. Throughout a simulation run, the concentrations of the
chemical cues are continuously diffused and updated at a fixed rate with partial
differential equations (PDEs). Each cell has a self-maintained EGFR signaling
network. As a simulation progresses, cells in distinct locations are likely to
experience different external microenvironmental conditions. Thus, even though
their internal states (including cell phenotype and concentrations of pathway
components) are set to be identical initially, they will exhibit different phenotypes
after a certain lapse of time due to their respective molecular changes.