Computational Models of Vascularization and Therapy in Tumor Growth - Mechanical and Chemical Signaling in Angiogenesis - page 232

by VEGF binding VEGFR2. It can be also used to theoretically investigate the
effect of different therapeutic compounds acting at different level on the pathway.
As a perspective, this model can be integrated into a multiscale framework
describing tumor growth and angiogenesis such as in [ 38 ]. Indeed, in [ 38 ], three
main processes govern the evolution of endothelial cell: proliferation, migration,
and survival. In consequence, the model of VEGF intra-signaling, which also links
to those three main behaviors, can be ''plugged'' into the endothelial cell equation.
For this, and in order to homogenize the timescales between the two models, we
could assume that at a given VEGF signal, we run the intracellular signaling model
to the steady state and use those values as inputs for the endothelial cell equations.
Alternatively, we could use the maximum values of concentrations downstream
the VEGF signaling as they may better represent the force and amplitude of the
signals towards proliferation, migration and survival. This approach was already
used in a multiscale model for non-small cell lung cancer integrating the EGFR
signaling pathway [ 55 ].
Scianna and coworkers have studied the link with the activation of calcium
channels [ 56 ], a process also called non-store-operated calcium entry (NSOCE),
because it is known that the absorption of calcium from the extracellular envi-
ronment influences cell polarization, motility, and adhesion, all processes that are
fundamental in vascular network formation. In fact, it has been recently demon-
strated that mitogen-induced intracellular calcium signals and the relative path-
ways play a critical role in vascular progression both in vitro and in vivo (see for
instance [ 57 - 61 ]). In this light they could also be in principle potential targets for
anticancer drugs. In particular, different lines of evidence have shown that VEGF,
after binding specific tyrosine kinase receptors with high affinity, triggers their
dimerization and the auto-phosphorylation of critical cytoplasmic tyrosine resi-
dues, resulting in the indirect recruitment of PLA2 and eNOS enzymes. PLA2, in a
single-step reaction, catalyzes the hydrolysis of esterified phospholipids (stored
within the cell membrane), producing free arachidonic acid (AA), while eNOS
releases its endothelium-derived nitric oxide (NO) [ 58 , 61 ]. The complex interplay
between these second messengers modulates the activity of probably more than
one type of plasma-membrane calcium channels [ 62 , 63 ]. The subsequent increase
in intracellular calcium levels mediates cell motility, adhesion and cytoskeletal
reorganization [ 57 , 59 , 60 , 64 ], all cellular behaviors involved in tumor-derived
blood vessel formation. A schematic view of the model is proposed Fig. 5 . The
model proposed by Scianna and coworkers [ 56 , 65 ] introduces such subcellular
mechanisms in a cellular Potts model, a discrete lattice Monte Carlo generalization
of the Ising's model, based on an energy minimization principle. Typically, the
CPM represents a collection of biological cells on a numerical grid, associating an
integer index to each site to identify the space occupied at any instant by a cell or
in a more detailed description by a subcellular compartment. Domains, i.e., col-
lection of lattice sites with the same index, represent then subcellular compart-
ments such as nucleus, cytosol, membrane which then form the considered
individual cells and allow a better reproduction of cell motion and shape changes.
The mathematical model is then a hybrid, because of the need to take care of the