Case Studies and Project Ideas: Colorectal Cancer

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A Multistage Model for Tumor Progression

Source

Hargrove, James L. Dynamic Modeling in the Health Sciences. Springer-Verlang New York. Harrisonburg, VA. 1998.

Vocabulary

proto-oncogenes

cells involved in control of normal cell growth, can be mutated to cause overproliferation of cell growth

tumor supressor genes

genes which inhibit cell growth and division, when turned off, can lead to an overproliferation of cell growth.

Background

Cancer is one of the leading causes of death in the United States and other developed nations. Millions of dollars each year are dedicated to cancer research-- of the causes of cancer, prevention of cancer, and looking for a cure for cancer. Cancer growth is a result of abnormal cell proliferation, the causes of which are not entirely known, although mutations of some type are involved. The colon is an especially likely place for cancer to occur because of the frequent replacement of cells by cell division. When cells divide frequently, the chance for mutations to arise in so-called "daughter cells" is greater. These mutations can then be passed onto future generations of cells, leading to abnormal cell growth and tumors. Genetics play a large role in cancer risk, with mutations in cell growth regulating genes being the main culprit. Proto-oncogenes, which are involved in control of normal cell growth, can often be mutated to overproliferate cell growth. Tumor Suppressor genes, which function to inhibit cell growth and division, can be "turned off", leading to an overproliferation of cell growth.

Case Study

This model focuses on colorectal cancer, a form of cancer that is found in mucosa of the large bowel. There are several forms of colorectal cancer, a "sporadic" form (no family history of the disease), inherited adenomatous polyposis coli, and hereditary non-polyposis colon cancer. In our model we study the stages of noninherited types of cancer. Colon cancer develops through a series of stages, with each stage being characterized by an increasing loss of cell growth control. Progression from stage to stage is caused by additional gene mutations, the following chart depicts the progression of cancerous cell growth with the genes resposible for mutation.

Molecular events that Correlate with Tumor Progression

Chart of cancer progression

(Diagram from Hargrove 264)

Building the Model

In our model of colorectal cancer, we show a multistage progression in which our cell stocks are: normal colon cells, intermediate cells 1, intermediate cells 2, and malignant cells. Each population of cells has a "birth rate" dependent on the rate at which mutations arise in the prior cell population and the rate of cell division (Mitosis in the intermediate and malignant populations). Cells leave a population by either gaining new mutations and moving onto the next group of cells, or by dying (ususally sloughing off into the stool or apoptosis, programmed cell death). Both the intermediate cells 1 and intermediate cells 2 population affect the polyp size (in grams), the malignant cell population affects the tumor size (in grams).

Equations:

dN/dt = N*a - N*i - N*d

dI/dt = N*i + I*n + I*p - I*f

dJ/dt = I*p + J*q - J*c - J*g

dM/dt = J*c + M*m - M*h

N = Normal cells

I = Intermediate Cells 1

J = Intermediate Cells 2

M = Malignant Cells

a = rate of normal cell division

i = initiation

d = death rate of normal cells

n = Mitosis I rate

p = rate of promotion

f = death rate of intermediate cells 1

g = Mitosis II rate

m = Mitosis rate (malignant cells)

h = death rate of malignant cells

Constant Values:

i = .107

d = 99.893

n = 2

p = .307

f = 1

g = 2

c = .1

g = 2

m = 6

h = 4

Variations to Consider

Can you change the model in order to:

Add a mutation rate?
Show the effects of dietary agents on mutation rate (high intake of fiber, low intake of saturated fat, high intake of crciferous vegetables (broccoli), and an aspirin a day are all though to reduce risk of cancer)?