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Register a new userLocal contact inhibition leads to universal principles of cell population growth
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Cancer cell population dynamics often exhibit remarkably replicable, universal laws despite their underlying heterogeneity. Mechanistic explanations of universal cell population growth remain partly unresolved to this day, whereby population feedback between the microscopic and mesoscopic configurations can lead to macroscopic growth laws. We here present a unification under density-dependent birth events via contact inhibition. We consider five classical tumor growth laws: exponential, generalized logistic, Gompertz, radial growth, and fractal growth, which can be seen as manifestations of a single microscopic model. Our theory is substantiated by agent based simulations and can explain growth curve differences in experimental data from in vitro cancer cell population growth. Thus, our framework offers a possible explanation for the large number of mean-field laws that can adequately capture seemingly unrelated cancer or microbial growth dynamics.
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In this work, some phenomenological models, those that are based only on the population information (macroscopic level), are deduced in an intuitive way. These models, as for instance Verhulst, Gompertz and Bertalanffy models, are posted in such a manner that all the parameters involved have physical interpretation. A model based on the interaction (distance dependent) between the individuals (microscopic level) is also presented. This microscopic model reachs the phenomenological models presented as particular cases. In this approach, the Verhulst model represents the situation in which all the individuals interact in the same way, regardless of the distance between them. That means Verhulst model is a kind of mean field model. The other phenomenological models are reaching from the microscopic model according to two quantities: i) the relation between the way that the interaction decays with the distance; and ii) the dimension of the spatial structure formed by the population. This microscopic model allows understanding population growth by first principles, because it predicts that some phenomenological models can be seen as a consequence of the same individual level kind of interaction. In this sense, the microscopic model that will be discussed here paves the way to finding universal patterns that are common to all types of growth, even in systems of very different nature.
Many unicellular organisms allocate their key proteins asymmetrically between the mother and daughter cells, especially in a stressed environment. A recent theoretical model is able to predict when the asymmetry in segregation of key proteins enhances the population fitness, extrapolating the solution at two limits where the segregation is perfectly asymmetric (asymmetry $a$ = 1) and when the asymmetry is small ($0 leq a ll 1$). We generalize the model by introducing stochasticity and use a transport equation to obtain a self-consistent equation for the population growth rate and the distribution of the amount of key proteins. We provide two ways of solving the self-consistent equation: numerically by updating the solution for the self-consistent equation iteratively and analytically by expanding moments of the distribution. With these more powerful tools, we can extend the previous model by Lin et al. to include stochasticity to the segregation asymmetry. We show the stochastic model is equivalent to the deterministic one with a modified effective asymmetry parameter ($a_{rm eff}$). We discuss the biological implication of our models and compare with other theoretical models.
A fundamental question in biology is how cell populations evolve into different subtypes based on homogeneous processes at the single cell level. Here we show that population bimodality can emerge even when biological processes are homogenous at the cell level and the environment is kept constant. Our model is based on the stochastic partitioning of a cell component with an optimal copy number. We show that the existence of unimodal or bimodal distributions depends on the variance of partition errors and the growth rate tolerance around the optimal copy number. In particular, our theory provides a consistent explanation for the maintenance of aneuploid states in a population. The proposed model can also be relevant for other cell components such as mitochondria and plasmids, whose abundances affect the growth rate and are subject to stochastic partition at cell division.
We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, like dengue, and the threshold of the disease. The coexistence space is composed by two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice-versa so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible whatever is the death rate of infected mosquito.
We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a sizer-timer model incorporates both demographic and individual cell growth rate stochasticities. Averages taken over the densities obeying the kinetic equations can be used to generate a second order PDE that incorporates the growth rate stochasticity. On the other hand, marginalizing over the densities yields a modified birth-death process that shows how age and size influence demographic stochasticity. Our kinetic framework is thus a more complete model that subsumes both the deterministic PDE and birth-death master equation representations for structured populations.
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