Open AccessMathematical model of heterogeneous cancer growth with an autocrine signalling pathway
Author(s) -
Hu G.M.,
Lee C.Y.,
Chen Y.Y.,
Pang N.N.,
Tzeng W. J.
Publication year - 2012
Publication title -
cell proliferation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.647
H-Index - 74
eISSN - 1365-2184
pISSN - 0960-7722
DOI - 10.1111/j.1365-2184.2012.00835.x
Subject(s) - autocrine signalling , cancer , signalling , cancer cell , prostate cancer , biology , interpretation (philosophy) , mathematical model , biological system , computational biology , computer science , microbiology and biotechnology , mathematics , cell culture , genetics , statistics , programming language
Objectives 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. Materials and 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. Results and conclusion 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 17 AAG treatment, and bi‐stable behaviour under treatment by irradiation. In addition, our interpretation of the system parameters corresponds well with known facts involving 17 AAG treatment. This model may thus provide insight into some of the mechanisms behind cancer.