alexa A Fast Analytic Simulation of Stochastic Mutation and i
ISSN: 2168-9679

Journal of Applied & Computational Mathematics
Open Access

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Research Article

A Fast Analytic Simulation of Stochastic Mutation and its Application to Modeling Cancer Drug Resistance

Colborn JA*

Protocol Intelligence, Inc., 7667 Circulo Sequoia, Carlsbad, CA 92009, USA

*Corresponding Author:
Colborn JA
Protocol Intelligence, Inc.
7667 Ci rculo Sequoia
Carlsbad, CA 92009, USA
Tel: 7604979718
E-mail: [email protected]

Received Date: February 16, 2016; Accepted Date: March 14, 2016; Published Date: March 18, 2016

Citation: Colborn JA (2016) A Fast Analytic Simulation of Stochastic Mutation and its Application to Modeling Cancer Drug Resistance. J Appl Computat Math 5: 293. doi:10.4172/2168-9679.1000293

Copyright: © 2016 Colborn JA. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 

Abstract

Random “Darwinian” mutation is a primary mechanism by which cancer and pathogens develop resistance to drugs, and this process has been mathematically modeled extensively. Analytic models employ simple equations and allow for very fast computation, but do not accurately predict mutation times or survival probabilities of resistant populations. Stochastic models provide a distribution of probable outcomes but involve more complex mathematics. We present here an analytic method that simulates stochastic mutation with much better accuracy than that of the standard analytic equations. This method is based on an observation that the median stochastic solution emerges at a time close to when the cumulative probability of a first mutant birth approaches unity, which can be calculated analytically. We compare our model to the median stochastic resistant population versus time for varying rates of cell division, natural death, mutation, and drug kill. Generally we find at least an order-of-magnitude reduction in the error of the birth time and the RMS normalized error relative to the standard analytic solution. This method’s speed, accuracy, and simple results make it well-suited as a tool in software and mutation models to survey the resistant heterogeneity of cancers under various treatment plans or to guide a probabilistic analysis with a stochastic model. Such models could advance progress toward a better understanding of the dynamics of resistant subpopulations, better personalized treatment plans, and longer patient survival given the complex and ever-changing sets of drugs, doses, schedules, and cancer genomics of each patient in the clinical setting.

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