Age-dependent stochastic models for understanding population fluctuations in continuously cultured cells

Abstract

For symmetrically dividing cells, large variations in the cell cycle time are typical, even among clonal cells. The consequence of this variation is important in stem cell differentiation, tissue and organ size control, and cancer development, where cell division rates ultimately determine the cell population. We explore the connection between cell cycle time variation and populationlevel fluctuations using simple stochastic models. We find that standard population models with constant division and death rates fail to predict the level of population fluctuation. Instead, variations in the cell division time contribute to population fluctuations. An age-dependent birth and death model allows us to compute the mean squared fluctuation or the population dispersion as a function of time. This dispersion grows exponentially with time, but scales with the population. We also find a relationship between the dispersion and the cell cycle time distribution for synchronized cell populations. The model can easily be generalized to study populations involving cell differentiation and competitive growth situations.

Quantifying gene expression variability arising from randomness in cell division times

“…Living cells grow and divide, at which point the quantities of mRNAs and proteins are approximately divided equally between daughter cells. Since cell division times can vary from cell-to-cell (Roeder et al 2010;Zilman et al 2010;Hawkins et al 2009;Stukalin et al 2013), we investigate its role in driving variability in the level of a given mRNA or protein.…”

To grow is not enough: impact of noise on cell environmental response and fitness

“…Experiments conducted in constant environments maintained in microfluidic devices (so called “Mother Machines”) show that the cell cycle duration 6 is stochastic and exhibits large variations for both prokaryotes and eukaryotes. 7 Thus one should consider a statistical distribution of cell cycle durations P ( τ ), where τ is the time between 2 successive cell divisions (septum formations). Owing to the fact that synthesis of new proteins and replication of DNA require finite time, there is perhaps a physical lower limit for the cell cycle duration, τ * (dependent on the environment), below which no intact cells can divide.…”

Kinetic theory of age-structured stochastic birth-death processes

“…Processes such as birth, death, and mutation are typically highly dependent upon an organism's chronological age. Age-dependent population dynamics, where birth and death probabilities depend on an organism's age, arise across diverse research areas such as demography [1], biofilm formation [2], and stem cell proliferation and differentiation [3,4]. In this latter application, not only does a the cell cycle give rise to age-dependent processes [5,6], but the often small number of cells requires a stochastic interpretation of the population.…”

“…However, such models do not account for the intrinsic stochasticity of the underlying birth-death process that acts differently on individuals at each different age. One alternative approach might be to extend the mean-field, age-structured McKendrick-von Foerster theory into the stochastic domain by considering the evolution of P (n(a); t), the probability density that there are n individuals within age window [a, a + da] at time t [3,32]. This approach is meaningful only if a large number of individuals exist in each age window, in which case a large system size van Kampen expansion within each age window can be applied [15].…”

“…A number of approaches attempt to incorporate ideas of stochasticity and noise into age-dependent population models, [3,18,[24][25][26][27][28][29]. For example, stochasticity can be implemented by assuming a random rate of advancing to the next age window (by e.g., stochastic harvesting [26,27] or a fluctuating environment [30,31]).…”