A ubiquitous feature of living cells is their growth over time followed by division into daughter cells. How isogenic cell populations maintain size homeostasis, i.e., a narrow distribution of cell size, is an intriguing fundamental problem. We model cell size using a stochastic hybrid system, where a cell grows exponentially in size (volume) over time and probabilistic division events are triggered at discrete time intervals. Moreover, whenever division events occur, size is randomly partitioned among daughter cells. We first consider a scenario, where a timer (i.e., cell-cycle clock) that measures the time since the last division event regulates both the cellular growth and division rates. Analysis reveals that such a timer-controlled system cannot achieve size homeostasis, in the sense that, the cell-to-cell size variation grows unboundedly with time. To explore biologically meaningful mechanisms for controlling size we consider two classes of regulation: a size-dependent growth rate and a size-dependent division rate. Our results show that these strategies can provide bounded intercellular variation in cell size, and exact mathematical conditions on the form of regulation needed for size homeostasis are derived. Different known forms of size control strategies, such as, the adder and the sizer are shown to be consistent with these results. Interestingly, for timer-based division mechanisms, the mean cell size depends on the noise in the cell-cycle duration but independent of errors incurred in partitioning of volume among daughter cells. In contrast, the mean cell size decreases with increasing partitioning errors for size-based division mechanisms. Finally, we discuss how organisms ranging from bacteria to mammalian cells have adopted different control approaches for maintaining size homeostasis.
Maintenance of plasma IgM levels is critical for immune system function and homeostasis in humans and mice. However, the mechanisms that control homeostasis of the activated IgM-secreting B cells are unknown. After adoptive transfer into immune-deficient hosts, B-lymphocytes expand poorly but fully reconstitute the pool of natural IgM-secreting cells and circulating IgM levels. By using sequential cell transfers and B cell populations from several mutant mice, we were able to identify novel mechanisms regulating the size of the IgM-secreting B cell pool. Contrary to previous mechanisms describ…
Microbial growth and division are fundamental processes relevant to many areas of life science. Of particular interest are homeostasis mechanisms, which buffer growth and division from accumulating fluctuations over multiple cycles. These mechanisms operate within single cells, possibly extending over several division cycles. However, all experimental studies to date have relied on measurements pooled from many distinct cells. Here, we disentangle long-term measured traces of individual cells from one another, revealing subtle differences between temporal and pooled statistics. By analyzing co…
Pancreatic islets, controlling glucose homeostasis, consist of α, β, and δ cells. It has been observed that α and β cells generate out-of-phase synchronization in the release of glucagon and insulin, counter-regulatory hormones for increasing and decreasing glucose levels, while β and δ cells produce in-phase synchronization in the release of the insulin and somatostatin. Pieces of interactions between the islet cells have been observed for a long time, although their physiological role as a whole has not been explored yet. We model the synchronized hormone pulses of islets with coupled phase …
Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a recent work [Tzur et al., Science, 2009, 325:167-171], size distributions in an exponentially growing population of mammalian cells were used to infer the growth rate in size. The results suggest that cell growth is neither linear nor exponential, but subject to size-dependent regulation. To explain their data, we build a model in which the cell growth rate is controlled by the relative amount of mRNA and ribosomes in a cell. Plus a stochastic division rule, the evolutionary process of a populatio…
Stem cells maintain tissues by generating differentiated cell types while simultaneously self-renewing their own population. The mechanisms that allow stem cell populations to function collectively to control their density, maintain robust homeostasis and recover from injury remain elusive. Motivated by recent experimental advances, here we develop a generic and robust mechanism of stem cell self-renewal based on competition for diffusible fate determinants, which exert fate control. Using both analytical methods and stochastic simulations, we show that the mechanism is characterized by signat…
Feedback loops are essential for regulating cell proliferation and maintaining the delicate balance between cell division and cell death. Thanks to the exact solution of a few simple models of cell growth it is by now clear that stochastic fluctuations play a central role in this process and that cell growth (and in particular the robustness and stability of homeostasis) can be properly addressed only as a stochastic process. Using epidermal homeostasis as a prototypical example, we show that it is possible to discriminate among different feedback strategies which turn out to be characterized …
We present a computational model to study the spatiotemporal dynamics of the epidermis homeostasis under normal and pathological conditions. The model consists of a population kinetics model of the central transition pathway of keratinocyte proliferation, differentiation and loss and an agent-based model that propagates cell movements and generates the stratified epidermis. The model recapitulates observed homeostatic cell density distribution, the epidermal turnover time and the multilayered tissue structure. We extend the model to study the onset, recurrence and phototherapy-induced remissio…
Some anesthetics bind and potentiate gamma-aminobutyric-acid-type receptors, but no universal mechanism for general anesthesia is known. Furthermore, often encountered complications such as anesthesia induced amnesia are not understood. General anesthetics are hydrophobic molecules easily dissolving into lipid bilayers. Recently, it was shown that general anesthetics perturb phase separation in vesicles extracted from fixed cells. Unclear is whether under physiological conditions general anesthetics induce perturbation of the lipid bilayer, and whether this contributes to the transient loss of…
We study the asymptotic behaviors of stochastic cell fate decision between proliferation and differentiation. We propose a model of a self-replicating Langevin system, where cells choose their fate (i.e. proliferation or differentiation) depending on local cell density. Based on this model, we propose a scenario for multi-cellular organisms to maintain the density of cells (i.e., homeostasis) through finite-ranged cell-cell interactions. Furthermore, we numerically show that the distribution of the number of descendant cells changes over time, thus unifying the previously proposed two models r…
Fundamental mechanisms governing cell size control and homeostasis are still poorly understood. The relationship between sizes at division and birth in single cells is used as a metric to categorize the basis of size homeostasis [1-3]. Cells dividing at a fixed size regardless of birth size (sizer) are expected to show a division-birth slope of 0, whereas cells dividing after growing for a fixed size increment (adder) have an expected slope of +1 [4]. These two theoretical values are, however, rarely experimentally observed. For example, rod-shaped fission yeast $\it{Schizosaccharomyces}$ $\it…
Cells within living soft biological tissues seem to promote the maintenance of a mechanical state within a defined range near a so-called set-point. This mechanobiological process is often referred to as mechanical homeostasis. During this process, cells intimately interact with the fibers of the surrounding extracellular matrix (ECM). It remains poorly understood, however, what individual cells actually regulate during these interactions, and how these micromechanical regulations are translated to tissue level to lead to what we macroscopically call mechanical homeostasis. Herein, we examine …
A recently proposed single progenitor cell model for skin cell proliferation [Clayton et al., Nature v446, 185 (2007)] is extended to incorporate homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can be viewed as a paradigm for the onset of cancer. A novel way in which this can arise is if the homeostatic fixed point becomes metastable, so that the cell populations can escape from the homeostatic basin of attraction by a large but rare stochastic fluctuation. Such an event can be viewed as the final step in a multi-stage model of carcinogenesis. This of…
Many illnesses are associated with an alteration of the immune system homeostasis due to any combination of factors, including exogenous bacterial insult, endogenous breakdown (e.g., development of a disease that results in immuno suppression), or an exogenous hit like surgery that simultaneously alters immune responsiveness and provides access to bacteria, or genetic disorder. We conjecture that, as a consequence of the co-evolution of the immune system of individuals with the ecology of pathogens, the homeostasis of the immune system requires the influx of pathogens. This allows the immune s…
We present a hybrid vertex/cell-centred model for mechanically simulating planar cellular monolayers undergoing cell reorganisation. Cell centres are represented by a triangular nodal network, while the cell boundaries are formed by an associated vertex network. The two networks are coupled through a kinematic constraint which we allow to relax progressively. Special attention is paid to the change of cell-cell connectivity due to cell reorganisation or remodelling events. We handle these situations by using a variable resting length and applying an Equilibrium-Preserving Mapping (EPM) on the …
The mechanism of bacterial cell size control has been a mystery for decades, which involves the well-coordinated growth and division in the cell cycle. The revolutionary modern techniques of microfluidics and the advanced live imaging analysis techniques allow long term observations and high-throughput analysis of bacterial growth on single cell level, promoting a new wave of quantitative investigations on this puzzle. Taking the opportunity, this theoretical study aims to clarify the stochastic nature of bacterial cell size control under the assumption of the accumulation mechanism, which is …
Traditionally, it has been held that a central characteristic of stem cells is their ability to divide asymmetrically. Recent advances in inducible genetic labeling provided ample evidence that symmetric stem cell divisions play an important role in adult mammalian homeostasis. It is well understood that the two types of cell divisions differ in terms of the stem cells' flexibility to expand when needed. On the contrary, the implications of symmetric and asymmetric divisions for mutation accumulation are still poorly understood. In this paper we study a stochastic model of a renewing tissue, a…
In this paper we propose a "discrete in continuous" mathematical model for the morphogenesis of the posterior lateral line system in zebrafishes. Our model follows closely the results obtained in recent biological experiments. We rely on a hybrid description: discrete for the cellular level and continuous for the molecular level. We prove the existence of steady solutions consistent with the formation of particular biological structure, the neuromasts. Dynamical numerical simulations are performed to show the behavior of the model and its qualitative and quantitative accuracy to describe the e…
Understanding cell-fate decisions during tumorigenesis and metastasis is a major challenge in modern cancer biology. One canonical cell-fate decision that cancer cells undergo is Epithelial-to-Mesenchymal Transition (EMT) and its reverse Mesenchymal-to-Epithelial Transition (MET). While transitioning between these two phenotypes - epithelial and mesenchymal - cells can also attain a hybrid epithelial/mesenchymal (i.e. partial or intermediate EMT) phenotype. Cells in this phenotype have mixed epithelial (e.g. adhesion) and mesenchymal (e.g. migration) properties, thereby allowing them to move c…
