Transcript Modeling of Tumor Induced Angiogenesis

Modeling of Tumor
Induced Angiogenesis
Heather Harrington, Marc Maier &
Lé Santha Naidoo
Faculty Advisors: Panayotis Kevrekidis & Nathaniel Whitaker
Biological Background
Important terms

Angiogenesis: The process of formation of capillary sprouts in response to
external chemical stimuli which leads to the formation of blood vessels.
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Tumor Angiogenic Factors (TAFs): Stimuli secreted by Tumors
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Extra Cellular Matrix (ECM): The area in which cells interact with the
Fibronectin(F).
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Haptotaxis: The attraction of cells to ECM.
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Proteases (P): Secreted by tumor to attract cells and
destroy Inhibitors. Promotes Angiogenesis.
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Inhibitors: Prevent Cells from getting to tumor. Generated by fibronectin
cells in the ECM to inactivate proteases.
More Bio

Cells: Diffuse in the ECM,
get generated and die. They
are driven to the TAF
gradient (chemotaxis), as well
as the ECM concentration
gradient and are “repelled”
from inhibitor gradients

TAFs: We assume TAF
gradient is fixed

ECM: Secretion of Proteases
by the tumor gradually
degrades the ECM; proteases
involved in the angiogenic
process bind to the
Fibronectin depleting it
allowing the cells to be driven
to the tumor

Proteases: Neutralized by
inhibitors

Inhibitor: Mutually
Neutralizes with Protease.
5 “Species” Dynamical Evolution
Model

(1) Ct = DcΔC – ∂/∂x(fF* ∂F/∂x)
- ∂/∂x(fT* ∂T/∂x)
+ ∂/∂x(fI* ∂I/∂x) + k1C(1-C)
²

(2) T = e(-(x-L) /ε)

(3) Ft = -k2PF

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(4) Pt = -k3PI + k4TC + k5T – k6P
(5) It = -k3PI

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fT term represents chemotactic
attraction of cells to tumor
fF term represents haptotactic
response to the Fibronectin
fI term represents the “repulsive”
effect of inhibitor gradients

Dc = Diffusion Coefficient

fF = a1C

fT = a2C/(1 + a3T)

fI = a4C
What’s Next?
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1-Dimensional Model with “random walker
cells”
2-Dimensional Model of Angiogenesis
Modelling Angiogenesis in the Cornea (ignoring
inhibitors)
(If Time Permits) Angiogenesis in the Cornea
with Inhibitors