Large population solution of the stochastic Luria-Delbruck evolution model.

The fixed-size Luria-Delbruck model with a nonzero death rate.

What is the expected number of mutants in a stochastically growing colony once it reaches a given size, N? This is a variant of the famous Luria-Delbruck model which studies the distribution of mutants after a given time-lapse. Instead of fixing the time-lapse, we assume that the colony size is a measurable quantity, which is the case in many in-vivo oncological and other applications. We study...

The Dynamics of Adaptive Genetic Diversity during the Early Stages of Clonal Evolution

The dynamics of genetic diversity in large clonally-evolving cell populations are poorly understood, despite having implications for the treatment of cancer and microbial infections. Here, we combine barcode lineage tracking, sequencing of adaptive clones, and mathematical modelling of mutational dynamics to understand diversity changes during experimental evolution. We find that, despite diffe...

Scaling solution in the large population limit of the general asymmetric stochastic Luria-Delbrück evolution process.

One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size N is...

Continuous dependence on coefficients for stochastic evolution equations with multiplicative Levy Noise and monotone nonlinearity

Semilinear stochastic evolution equations with multiplicative L'evy noise are considered‎. ‎The drift term is assumed to be monotone nonlinear and with linear growth‎. ‎Unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎As corollaries of ...

Luria-Delbruck Fluctuation Test