Mathematical model of heterogeneous cancer growth with an autocrine signalling pathway.
OBJECTIVE
Cancer is a complex biological occurrence which is difficult to describe clearly and explain its growth development. As such, novel concepts, such as of heterogeneity and signalling pathways, grow exponentially and many mathematical models accommodating the latest knowledge have been proposed. Here, we present a simple mathematical model that exhibits many characteristics of experimental data, using prostate carcinoma cell spheroids under treatment.


METHODS
We have modelled cancer as a two-subpopulation system, with one subpopulation representing a cancer stem cell state, and the other a normal cancer cell state. As a first approximation, these follow a logistical growth model with self and competing capacities, but they can transform into each other by using an autocrine signalling pathway.


CONCLUSIONS
By analysing regulation behaviour of each of the system parameters, we show that the model exhibits many characteristics of actual cancer growth curves. Features reproduced in this model include delayed phase of evolving cancer under 17AAG treatment, and bi-stable behaviour under treatment by irradiation. In addition, our interpretation of the system parameters corresponds well with known facts involving 17AAG treatment. This model may thus provide insight into some of the mechanisms behind cancer.
Physics Department, National Taiwan University, Taipei, Taiwan. pipipshu@gmail.com
G-M
GM
Hu
C-Y
CY
Lee
Y-Y
YY
Chen
N-N
NN
Pang
W J
WJ
Tzeng
D019898:Autocrine Communication / Q000187:drug effects / Q000502:physiology* / Q000528:radiation effects; D016227:Benzoquinones / Q000494:pharmacology; D049109:Cell Proliferation / Q000187:drug effects / Q000528:radiation effects; D018841:HSP90 Heat-Shock Proteins / Q000037:antagonists & inhibitors; D006801:Humans; D047029:Lactams, Macrocyclic / Q000494:pharmacology; D016015:Logistic Models; D009369:Neoplasms / Q000378:metabolism* / Q000473:pathology*; D010641:Phenotype; D011829:Radiation Dosage; D015398:Signal Transduction / Q000187:drug effects / Q000502:physiology* / Q000528:radiation effects
D016227:Benzoquinones; D018841:HSP90 Heat-Shock Proteins; D047029:Lactams, Macrocyclic; C112765:tanespimycin