Survival probabilities at spherical frontiers

Theoretical Population Biology
Maxim O Lavrentovich, D R Nelson

Abstract

Motivated by tumor growth and spatial population genetics, we study the interplay between evolutionary and spatial dynamics at the surfaces of three-dimensional, spherical range expansions. We consider range expansion radii that grow with an arbitrary power-law in time: R(t) = R0(1 + t/t(∗))Θ, where Θ is a growth exponent, R0 is the initial radius, and t(∗) is a characteristic time for the growth, to be affected by the inflating geometry. We vary the parameters t(∗) and Θ to capture a variety of possible growth regimes. Guided by recent results for two-dimensional inflating range expansions, we identify key dimensionless parameters that describe the survival probability of a mutant cell with a small selective advantage arising at the population frontier. Using analytical techniques, we calculate this probability for arbitrary Θ. We compare our results to simulations of linearly inflating expansions (Θ = 1 spherical Fisher-Kolmogorov-Petrovsky-Piscunov waves) and treadmilling populations (Θ = 0, with cells in the interior removed by apoptosis or a similar process). We find that mutations at linearly inflating fronts have survival probabilities enhanced by factors of 100 or more relative to mutations at treadmilling population fr...Continue Reading

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Citations

Jun 23, 2016·Biophysical Journal·Maxim O LavrentovichAndrew W Murray
Dec 23, 2016·Scientific Reports·Chay PatersonBartlomiej Waclaw
Apr 11, 2018·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·Jona KayserOskar Hallatschek
Dec 2, 2017·PLoS Computational Biology·Bryan T WeinsteinDavid R Nelson
Oct 26, 2018·Proceedings of the National Academy of Sciences of the United States of America·Andrea GiomettoAndrew W Murray
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Niladri Sarkar
Nov 28, 2019·Physical Review. E·Maxim O Lavrentovich, David R Nelson
Sep 19, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tibor AntalM A Nowak

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