1. Over-Expression of HER2 Causes Cancer: A Mathematical Model
Wafa Veljeec , Hassan Bukharib , Junaid Amina, Kanwal Rizvic , Mehr-un-Nisa Shahidb, Muhammad Fahad
School of Science and Engineering, Lahore University of Management Sciences
a Department of Engineering b Department of Physics c Department of Mathematics
Based on the paper by Amina Eladdadi and David Isaacson*
School of Science and Engineering
INTRODUCTION
THE SYSTEM OF EQUATIONS
The differential equation for each stage is arrived at using the law of mass action.
HYPOTHESIS
Over-expressed HER2 on the cell surface promotes excessive proliferation
OBJECTIVES
Create graphical simulations which concur with experimental data
Demonstrate the effect of various parameters taken into account in the model
METHODS
Biology behind stimulation of cell division
Kinetic equations that describe binding of receptors and ligands
Mathematically Modeling Cell Division
dN/dt, is derived using the Monod model of proliferation and its dependence on the variables in the other three equations.
Figure1a: Structure of HER2, a cell surface receptor.
Figure1b: Various cellular processes occur due to ligand binging.
Figure1c: Cell function goes haywire when HER2 is over-expressed.
Figure1d: Dividing human breast cancer cells
RESULTS
RESULTS AND CONCLUSIONS
The model quantitatively predicts the increased proliferation rate of Cancer cells compared to normal cells.
NON-DIMENSIONALIZING
BIOLOGY BEHIND HER2
We removed all the units from the equations by equating:
Removal of units from very complex equations to make them simple
Normal
Cell
Ligand binds to EGF receptor, this complex then heterodimerizes with HER2 receptor to initiate a signal cascade (the ERK pathway)
One function of the ERK pathway is to stimulate mitotic cell cycles.
It further predicts that there is a threshold quantity of bound receptors required before proliferation starts.
Our results predict that cancer cells have a lower threshold level so are more likely to proliferate even in low concentrations of signaling ligands.
Previous models4 predict the same threshold for cancer and normal cells
Result of the simulation with parameters:
EGFR per cell = A1=A2=0.5; Cell proliferation rate = µ1max=µ2max
Normal cells: HER2 per cell = 10,000 µ1max=2.391x10-4min-1
Cancer Cells: HER2 =100,000 µ1max=2.50x10-4min-1
We were then left with the following set of equations which contain only dimensionless values:
Figure2a: HER2 signaling. EGFR and HER2 are cell surface proteins.
Breast Cancer Cells
15-20 percent of cancers have an amplification of the HER2/neu gene.
Over-expression of HER2 produces more dimers that initiate ERK.
Excessive proliferation results in these cells.
A1 shows the dependence of cell proliferation on the ligand-receptor complex.
With A1 = 0 all dependence is now on the HER2-complex dimer.
Cancer cells which have over-expressed HER2 proliferate faster than the normal cells.
EXPERIMENTAL DATA OF CELL GROWTH3
TIME(MINUTES)
Hb4a is the normal cell line with 10,000 HER2 receptors
C3.6 cells have 100,000 HER2 receptors
BIBLIOGRAPHY
EGFR receptor = 10000
This will result in the formation of fewer dimers hence slower proliferation of normal cells
* A Mathematical Model for the Effects of HER2 Overexpression on Cell Proliferation in Breast Cancer. Bulletin of Mathematical Biology (2008) 1. 2. 3.
3. Timms et. al Effects of ErbB-2 overexpression on mitogenic signalling and cell cycle progression in human breast luminal epithelial cells . Oncogene (2002)
Figures
Background picture
System of equations
Figure2b: Over-expression of HER2 in cancer cells.