RT Journal Article
SR Electronic
T1 Evolution of Resistance During Clonal Expansion
JF Genetics
JO Genetics
FD Genetics Society of America
SP 2557
OP 2566
DO 10.1534/genetics.105.049791
VO 172
IS 4
A1 Iwasa, Yoh
A1 Nowak, Martin A.
A1 Michor, Franziska
YR 2006
UL http://www.genetics.org/content/172/4/2557.abstract
AB Acquired drug resistance is a major limitation for cancer therapy. Often, one genetic alteration suffices to confer resistance to an otherwise successful therapy. However, little is known about the dynamics of the emergence of resistant tumor cells. In this article, we consider an exponentially growing population starting from one cancer cell that is sensitive to therapy. Sensitive cancer cells can mutate into resistant ones, which have relative fitness α prior to therapy. In the special case of no cell death, our model converges to the one investigated by Luria and Delbrück. We calculate the probability of resistance and the mean number of resistant cells once the cancer has reached detection size M. The probability of resistance is an increasing function of the detection size M times the mutation rate u. If Mu ≪ 1, then the expected number of resistant cells in cancers with resistance is independent of the mutation rate u and increases with M in proportion to \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(M^{1{-}1/\mathrm{{\alpha}}}\) \end{document} for advantageous mutants with relative fitness \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(\mathrm{{\alpha}}{>}1\) \end{document}, to \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(\mathrm{ln}M\) \end{document} for neutral mutants (α = 1), but converges to an upper limit for deleterious mutants (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(\mathrm{{\alpha}}{<}1\) \end{document}). Further, the probability of resistance and the average number of resistant cells increase with the number of cell divisions in the history of the tumor. Hence a tumor subject to high rates of apoptosis will show a higher incidence of resistance than expected on its detection size only.