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

Komarova, Natalia L.; Wu, Lin; Baldi, Pierre

doi:10.1016/j.mbs.2007.04.007

Cited by 28 publications

(32 citation statements)

References 38 publications

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“…We can see that there is a large degree of variation in this number, with a SD that is an order-of-magnitude higher than the mean (please note the logarithmic scale on the horizontal axis). This phenomenon has been previously described (33). On the other hand, the time until the resistant mutant reaches the threshold population size shows a much more narrow distribution and only little variation (Fig.…”

Section: Resistant Mutants Can Have a Selective Advantage In The Absesupporting

confidence: 80%

Evolution of ibrutinib resistance in chronic lymphocytic leukemia (CLL)

Komarova

Burger

Wodarz

2014

Proc. Natl. Acad. Sci. U.S.A.

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The Bruton tyrosine kinase inhibitor (BTKi) ibrutinib is a new targeted therapy for patients with chronic lymphocytic leukemia (CLL). Ibrutinib is given orally on a continuous schedule and induces durable remissions in the majority of CLL patients. However, a small proportion of patients initially responds to the BTKi and then develops resistance. Estimating the frequency, timing, and individual risk of developing resistance to ibrutinib, therefore, would be valuable for long-term management of patients. Computational evolutionary models, based on measured kinetic parameters of patients, allow us to approach these questions and to develop a roadmap for personalized prognosis and treatment management. Our kinetic models predict that BTKi-resistant mutants exist before initiation of ibrutinib therapy, although they only comprise a minority of the overall tumor burden. Furthermore, we can estimate the time required for resistant cells to grow to detectable levels. We predict that this can be highly variable, depending mostly on growth and death rates of the individual CLL cell clone. For a specific patient, this time can be predicted with a high degree of certainty. Our model can thus be used to predict for how long ibrutinib can suppress the disease in individual patients. Furthermore, the model can suggest whether prior debulking of the tumor with chemo-immunotherapy can prolong progression-free survival under ibrutinib. Finally, by applying the models to data that document progression during ibrutinib therapy, we estimated that resistant mutants might have a small (<2%) mean fitness advantage in the absence of treatment, compared with sensitive cells.evolutionary dynamics | drug resistance | personalized medicine | mathematical models | stochastic dynamics

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Section: Resistant Mutants Can Have a Selective Advantage In The Absesupporting

confidence: 80%

Evolution of ibrutinib resistance in chronic lymphocytic leukemia (CLL)

Komarova

Burger

Wodarz

2014

Proc. Natl. Acad. Sci. U.S.A.

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“…Yet, final number data are rarely reported in fluctuation analysis experiments, although exceptions exist such as [17], [18]. Theoretical models considering variations in the population size have previously been proposed by Angerer [19] and Komarova et al [20]. Yet, to the best of our knowledge, Foster's assertion that “there is currently no valid method to correct for different 's” remains true to this date.…”

Section: Introductionmentioning

confidence: 99%

Unbiased Estimation of Mutation Rates under Fluctuating Final Counts

Ycart

Véziris

2014

PLoS ONE

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Estimation methods for mutation rates (or probabilities) in Luria-Delbrück fluctuation analysis usually assume that the final number of cells remains constant from one culture to another. We show that this leads to systematically underestimate the mutation rate. Two levels of information on final numbers are considered: either the coefficient of variation has been independently estimated, or the final number of cells in each culture is known. In both cases, unbiased estimation methods are proposed. Their statistical properties are assessed both theoretically and through Monte-Carlo simulation. As an application, the data from two well known fluctuation analysis studies on Mycobacterium tuberculosis are reexamined.

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“…The authors found that the probability of resistance increases with the detection size and the mutation rate, and that a tumor with larger apoptosis rates has a higher incidence of resistance. Using a similar two-type birth and death process model, Komarova et al studied the dynamics of resistance at the time of detection for the special case of neutral mutations – resistance mutations that do not alter the fitness parameters of cells [55]. They also presented an efficient computational method to estimate the expected number of resistant cells at the time at which the total population reaches a fixed size.…”

Section: Previous Workmentioning

confidence: 99%

Evolution of acquired resistance to anti-cancer therapy

Foo

Michor

2014

Journal of Theoretical Biology

232

178

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Acquired drug resistance is a major limitation for the successful treatment of cancer. Resistance can emerge due to a variety of reasons including host environmental factors as well as genetic or epigenetic alterations in the cancer cells. Evolutionary theory has contributed to the understanding of the dynamics of resistance mutations in a cancer cell population, the risk of resistance pre-existing before the initiation of therapy, the composition of drug cocktails necessary to prevent the emergence of resistance, and optimum drug administration schedules for patient populations at risk of evolving acquired resistance. Here we review recent advances towards elucidating the evolutionary dynamics of acquired drug resistance and outline how evolutionary thinking can contribute to outstanding questions in the field.

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

Cited by 28 publications

References 38 publications

Evolution of ibrutinib resistance in chronic lymphocytic leukemia (CLL)

Evolution of ibrutinib resistance in chronic lymphocytic leukemia (CLL)

Unbiased Estimation of Mutation Rates under Fluctuating Final Counts

Evolution of acquired resistance to anti-cancer therapy

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