Richard Cimino's DIMACS REU Project

Cell Population Dynamics and Cancer Modeling in the Human Colon: An Extension of the Johnston Model


Gyan Bhanot; Rutgers University, Cancer Institute of New Jersey and the Institute for Advanced Study

Kerri-Ann Norton; Rutgers University BioMaPS graduate researcher


Cancer is a disease of uncontrolled cellular proliferation, with various evolutionary mechanisms and myriad different manifestations in the affected individual. One fact that is undeniably clear is that cancer incidence increases exponentially with age, but then something odd seems to occur - once an individual reaches a certain limiting age, cancer incidence plummets. This project focuses on colorectal cancer, one of the most widely studied and well known epithelial cancers. Using computer software and analytic methods, we model a population-time dynamic of colon homeostasis and colorectal cancer incidence, and attempt to reconcile the results with collected data.

Weekly Updates

Week -4 to 0

For the past month I have been reading "Cancer Biology" given to me by Dr.Bhanot as preparation and background for my further study.

Week 1

DIMACS begins. We've all been eating a LOT of pizza. In other news, I met with Dr. Bhanot again and continued to read. I found a generalized cell cycle model online here Using Maple, I whittled down the equations to a 3D system involving Cyclin E, its activity, and CKI. These specific equations were used to model enzymatic activity around the R point gate in late G1 phase.

Week 2

Met with Dr. Bhanot monday and was given an immense pile of reading on colon cancer, aging and crypt biology. Learned about Markov processes. Met with Ms.Norton for the first time. Researched the functions of APC, beta-catenin, the Wnt signaling pathway, and went to the DIMACS workshop on Genotype vs. Phenotype thursday. Project presentation on friday.

Week 3

Website design. Begin delving deep into the background Nowak paper as my base model. I will attempt to add to this model the idea of telomere shortening. Learned to use Simulink, which I will use to model my final project.Completed Transition model chooser in simulink, to be used in concert with solving ODEs.

Week 4

Continued work on final presentation powerpoint. Reproduced Nowak's results using Simulink and Matlab! Now I can move on to extending the model.Moved on to Johnston model, which seems more viable. Begin analysis of biological meaning behind parameter values.

Week 5

Finally a breakthrough! Made several modifications to the Johnston model and prepared all 2D and 3D graphs in preparation to write my paper. Learned LaTeX, which I will use to type my paper on.

Week 6

Spent the week writing the rough drafts of my paper, which I will transfer to LaTeX next week, along with a final powerpoint.

Week 7

Wrote final paper in LaTeX and completed final presentation powepoint. Additionally, I completed a linearization of Johnston's model which reaffirms the behavior of the solutions. The search continues for a possible f(t). We speculate it will most likely have to be piecewise defined. Next week I will meet with Dr.Bhanot, who is returning from abroad, to talk about my results. I begin to work in the microbiology labs at Waksman on Monday. Final presentations are tommorrow.

Week 8

Went to visit Dr. Bhanot at IAS in Princeton to discuss additions to my paper. I am going to add some background on colon cancer to make the paper more readable for people from different areas of study. I intend to submit the paper to a student workshop at some point in the future, and will continue to work with Dr. Bhanot in the coming years. We are looking to possibly transfer this experiment to a full scale stochastic model of colon cancer. Will write final report for DIMACS this week and submit it.

Thank You

To Dr. B, DIMACS, Gene Fiorini, David Duncan, and everyone who has made this experience possible.


Armitage, P. and R. Doll. "The age distribution of cancer and a multi-stage theory of carcinogenosis." International Journal of Epidemiology Advance Access 33(2004)1-6.

Johnston, Matthew D. et al. "Mathematical modeling of cell population dynamics in the colonic crypt and in colorectal cancer" PNAS 104.10 (2007):4008-40013.

Norton, Kerri-ann et al. "Colon Cancer Modeling" Powerpoint Presentation, 2009.

Nowak, Martin A. et al."The role of chromosomal instability in tumor initiation" PNAS 99.25 (2002):16226-16231.

Weinberg, Robert A.Biology of Cancer. New York: Garland Science, 2006.