4,248 research outputs found
Effect of Dedifferentiation on Time to Mutation Acquisition in Stem Cell-Driven Cancers
Accumulating evidence suggests that many tumors have a hierarchical
organization, with the bulk of the tumor composed of relatively differentiated
short-lived progenitor cells that are maintained by a small population of
undifferentiated long-lived cancer stem cells. It is unclear, however, whether
cancer stem cells originate from normal stem cells or from dedifferentiated
progenitor cells. To address this, we mathematically modeled the effect of
dedifferentiation on carcinogenesis. We considered a hybrid
stochastic-deterministic model of mutation accumulation in both stem cells and
progenitors, including dedifferentiation of progenitor cells to a stem
cell-like state. We performed exact computer simulations of the emergence of
tumor subpopulations with two mutations, and we derived semi-analytical
estimates for the waiting time distribution to fixation. Our results suggest
that dedifferentiation may play an important role in carcinogenesis, depending
on how stem cell homeostasis is maintained. If the stem cell population size is
held strictly constant (due to all divisions being asymmetric), we found that
dedifferentiation acts like a positive selective force in the stem cell
population and thus speeds carcinogenesis. If the stem cell population size is
allowed to vary stochastically with density-dependent reproduction rates
(allowing both symmetric and asymmetric divisions), we found that
dedifferentiation beyond a critical threshold leads to exponential growth of
the stem cell population. Thus, dedifferentiation may play a crucial role, the
common modeling assumption of constant stem cell population size may not be
adequate, and further progress in understanding carcinogenesis demands a more
detailed mechanistic understanding of stem cell homeostasis
Stochastic tunneling and metastable states during the somatic evolution of cancer
Tumors initiate when a population of proliferating cells accumulates a
certain number and type of genetic and/or epigenetic alterations. The
population dynamics of such sequential acquisition of (epi)genetic alterations
has been the topic of much investigation. The phenomenon of stochastic
tunneling, where an intermediate mutant in a sequence does not reach fixation
in a population before generating a double mutant, has been studied using a
variety of computational and mathematical methods. However, the field still
lacks a comprehensive analytical description since theoretical predictions of
fixation times are only available for cases in which the second mutant is
advantageous. Here, we study stochastic tunneling in a Moran model. Analyzing
the deterministic dynamics of large populations we systematically identify the
parameter regimes captured by existing approaches. Our analysis also reveals
fitness landscapes and mutation rates for which finite populations are found in
long-lived metastable states. These are landscapes in which the final mutant is
not the most advantageous in the sequence, and resulting metastable states are
a consequence of a mutation-selection balance. The escape from these states is
driven by intrinsic noise, and their location affects the probability of
tunneling. Existing methods no longer apply. In these regimes it is the escape
from the metastable states that is the key bottleneck; fixation is no longer
limited by the emergence of a successful mutant lineage. We used the so-called
Wentzel-Kramers-Brillouin method to compute fixation times in these parameter
regimes, successfully validated by stochastic simulations. Our work fills a gap
left by previous approaches and provides a more comprehensive description of
the acquisition of multiple mutations in populations of somatic cells.Comment: 33 pages, 7 figure
A tug-of-war between driver and passenger mutations in cancer and other adaptive processes
Cancer progression is an example of a rapid adaptive process where evolving
new traits is essential for survival and requires a high mutation rate.
Precancerous cells acquire a few key mutations that drive rapid population
growth and carcinogenesis. Cancer genomics demonstrates that these few 'driver'
mutations occur alongside thousands of random 'passenger' mutations-a natural
consequence of cancer's elevated mutation rate. Some passengers can be
deleterious to cancer cells, yet have been largely ignored in cancer research.
In population genetics, however, the accumulation of mildly deleterious
mutations has been shown to cause population meltdown. Here we develop a
stochastic population model where beneficial drivers engage in a tug-of-war
with frequent mildly deleterious passengers. These passengers present a barrier
to cancer progression that is described by a critical population size, below
which most lesions fail to progress, and a critical mutation rate, above which
cancers meltdown. We find support for the model in cancer age-incidence and
cancer genomics data that also allow us to estimate the fitness advantage of
drivers and fitness costs of passengers. We identify two regimes of adaptive
evolutionary dynamics and use these regimes to rationalize successes and
failures of different treatment strategies. We find that a tumor's load of
deleterious passengers can explain previously paradoxical treatment outcomes
and suggest that it could potentially serve as a biomarker of response to
mutagenic therapies. Collective deleterious effect of passengers is currently
an unexploited therapeutic target. We discuss how their effects might be
exacerbated by both current and future therapies
Mean field mutation dynamics and the continuous Luria-Delbr\"uck distribution
The Luria-Delbr\"uck mutation model has a long history and has been
mathematically formulated in several different ways. Here we tackle the problem
in the case of a continuous distribution using some mathematical tools from
nonlinear statistical physics. Starting from the classical formulations we
derive the corresponding differential models and show that under a suitable
mean field scaling they correspond to generalized Fokker-Planck equations for
the mutants distribution whose solutions are given by the corresponding
Luria-Delbr\"uck distribution. Numerical results confirming the theoretical
analysis are also presented
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