%0 Journal Article
%T A simple algebraic cancer equation: calculating how cancers may arise with normal mutation rates
%A Peter Calabrese
%A Darryl Shibata
%J BMC Cancer
%D 2010
%I BioMed Central
%R 10.1186/1471-2407-10-3
%X The equation [p = 1 - (1 - (1 - (1 - u)d)k)Nm ] calculates the probability of cancer (p) and contains five parameters: the number of divisions (d), the number of stem cells (N กม m), the number of critical rate-limiting pathway driver mutations (k), and the mutation rate (u). In this model progression to cancer "starts" at conception and mutations accumulate with cell division. Transformation occurs when a critical number of rate-limiting pathway mutations first accumulates within a single stem cell.When applied to several colorectal cancer data sets, parameter values consistent with crypt stem cell biology and normal mutation rates were able to match the increase in cancer with aging, and the mutation frequencies found in cancer genomes. The equation can help explain how cancer risks may vary with age, height, germline mutations, and aspirin use. APC mutations may shorten pathways to cancer by effectively increasing the numbers of stem cells at risk.The equation illustrates that age-related increases in cancer frequencies may result from relatively normal division and mutation rates. Although this equation does not encompass all of the known complexity of cancer, it may be useful, especially in a teaching setting, to help illustrate relationships between small and large cancer features.The motivation for this article is to present an easy to understand equation that illustrates how cancers can arise within a lifetime from relatively normal mutation and division rates. Given the multiplicity and greater sophistication of many other cancer models, it is primarily presented as a teaching tool to demonstrate how cancers may result as mutations accumulate in stem cells under a very simple scenario. The goal is to illustrate to a wider audience (an average college graduate) that many numerical aspects of cancer biology may be described mathematically. (A short slide presentation summarizing the major points is provided as Additional file 1.)A more formal analysis of this
%U http://www.biomedcentral.com/1471-2407/10/3