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

A Density-Dependent Switch Drives Stochastic Clustering and Polarization of Signaling Molecules

Positive feedback plays a key role in the ability of signaling molecules to form highly localized clusters in the membrane or cytosol of cells. Such clustering can occur in the absence of localizing mechanisms such as pre-existing spatial cues, diffusional barriers, or molecular cross-linking. What prevents positive feedback from amplifying inevitable biological noise when an un-clustered “off” state is desired? And, what limits the spread of clusters when an “on” state is desired? Here, we show that a minimal positive feedback circuit provides the general principle for both suppressing and amplifying noise: below a critical density of signaling molecules, clustering switches off; above this threshold, highly localized clusters are recurrently generated. Clustering occurs only in the stochastic regime, suggesting that finite sizes of molecular populations cannot be ignored in signal transduction networks. The emergence of a dominant cluster for finite numbers of molecules is partly a phenomenon of random sampling, analogous to the fixation or loss of neutral mutations in finite populations. We refer to our model as the “neutral drift polarity model.” Regulating the density of signaling molecules provides a simple mechanism for a positive feedback circuit to robustly switch between clustered and un-clustered states. The intrinsic ability of positive feedback both to create and suppress clustering is a general mechanism that could operate within diverse biological networks to create dynamic spatial organization

A Comparison of Mathematical Models for Polarization of Single Eukaryotic Cells in Response to Guided Cues

Polarization, a primary step in the response of an individual eukaryotic cell to a spatial stimulus, has attracted numerous theoretical treatments complementing experimental studies in a variety of cell types. While the phenomenon itself is universal, details differ across cell types, and across classes of models that have been proposed. Most models address how symmetry breaking leads to polarization, some in abstract settings, others based on specific biochemistry. Here, we compare polarization in response to a stimulus (e.g., a chemoattractant) in cells typically used in experiments (yeast, amoebae, leukocytes, keratocytes, fibroblasts, and neurons), and, in parallel, responses of several prototypical models to typical stimulation protocols. We find that the diversity of cell behaviors is reflected by a diversity of models, and that some, but not all models, can account for amplification of stimulus, maintenance of polarity, adaptation, sensitivity to new signals, and robustness

The role of cell location and spatial gradients in the evolutionary dynamics of colon and intestinal crypts

BACKGROUND: Colon and intestinal crypts serve as an important model system for adult stem cell proliferation and differentiation. We develop a spatial stochastic model to study the rate of somatic evolution in a normal crypt, focusing on the production of two-hit mutants that inactivate a tumor suppressor gene. We investigate the effect of cell division pattern along the crypt on mutant production, assuming that the division rate of each cell depends on its location. RESULTS: We find that higher probability of division at the bottom of the crypt, where the stem cells are located, leads to a higher rate of double-hit mutant production. The optimal case for delaying mutations occurs when most of the cell divisions happen at the top of the crypt. We further consider an optimization problem where the “evolutionary” penalty for double-hit mutant generation is complemented with a “functional” penalty that assures that fully differentiated cells at the top of the crypt cannot divide. CONCLUSION: The trade-off between the two types of objectives leads to the selection of an intermediate division pattern, where the cells in the middle of the crypt divide with the highest rate. This matches the pattern of cell divisions obtained experimentally in murine crypts. REVIEWERS: This article was reviewed by David Axelrod (nominated by an Editorial Board member, Marek Kimmel), Yang Kuang and Anna Marciniak-Czochra. For the full reviews, please go to the Reviewers’ comments section. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13062-016-0141-6) contains supplementary material, which is available to authorized users

A wave-pinning mechanism for eukaryotic cell polarization based on Rho GTPase dynamics

In response to chemical stimulation, many eukaryotic cells are able to sense the direction of the stimulus and initiate movement. To do so, the cell must break symmetry and develop a front and back in a process known as polarization. During polarization, members of the Rho GTPase family (Cdc42, Rac, and Rho) are recruited to the plasma membrane and localize to form a front and a back of the polarizing cell. These proteins exist in both active forms (on the inner surface of the membrane of the cell), and inactive forms (in the cytosol). In earlier work, I have shown that the property of membrane-cytosol interconversion, together with appropriate feedbacks, endows the Rho proteins with the ability to initiate cell polarity, resulting in a high Cdc42/Rac region, which will become the front, and a high Rho region, which will become the back of the cell. Here I show that this property of polarizability can be explained using a simplified model system comprising of a single active/inactive protein pair with positive feedback. In this model, a travelling wave of GTPase activation is initiated at one end of the domain, moves across the cell, and eventually stops inside the domain, resulting in a stable polar distribution. The key requirements for the mechanism to work include conservation of total amount of protein, a sufficiently large difference in diffusion rates of the two forms, and nonlinear positive feedback that allows for multiple homogeneous steady states to exist. Using singular perturbation theory, I explain the mathematical basis of wave-pinning behaviour, and discuss its biological and mathematical implications. I show that this mechanism for generating a chemical pattern is distinct from Turing pattern formation. I also analyze the transition from a spatially heterogeneous solution to a spatially homogeneous solution as the diffusion coefficient of the active form is increased, and show the existence of other unstable stationary wavefronts. Finally, I argue that this wave-pinning mechanism can account for a number of features of cell polarization such as spatial amplification, maintenance of polarity, and the sensitivity to new stimuli that is typical of polarization of eukaryotic cells.Science, Faculty ofMathematics, Department ofGraduat

An interlocked feed-forward loop circuit can explain the phenotypic heterogeneity of fat-cell differentiation

Non UBCUnreviewedAuthor affiliation: University of Notre DameFacult

Mathematical study of Rho GTPases in motile cells

Rho family GTPases play an essential role in cell motility, transducing extracellular signal to the actin cytoskeleton. This thesis presents the formulation and analysis of several models concerning three.members of the Rho family: Cdc42, Rac, and Rho. Experimental observations of the spatio-temporal dynamics of these proteins give evidence of spatial polarization and mutual exclusion between Cdc42/Rac and Rho, which suggests that the Rho protein system is bistable. Biochemical evidence shows that there is crosstalk between the Rho proteins. However, current biological literature includes multiple (and often contradictory) hypotheses about these mutual interactions. We idealize the indirect pathways between the Rho proteins as direct effects (positive or negative feedback from one protein to another), and investigate the various proposed interactions to determine which of them can give rise to a bistable " toggle switch", alternating between a high level of Cdc42/Rac, low level of Rho steady state and low level of Cdc42/Rac, high level of Rho steady state. We discuss the biological interpretation of our findings. Next, we investigate a spatial variant of a model with suitable interactions to determine if it can give rise to spatial segregation of Rho proteins. We find that in a suitable parameter regime, a small initial gradient of one of the proteins will become amplified and give rise to long-lasting spatial segregation of Cdc42/Rac and Rho. On a longer timescale, the system eventually reaches a spatially uniform high Cdc42/Rac and low Rho steady state. Finally, a multi-compartment model for the activation of a single Rho family GTPase that includes a greater level of biological detail is developed. Parameter values for this model are obtained from biochemical literature. This compartment model can be used as a subunit in more realistic models of cell polarization and motility when further details of the biochemistry and interactions of the Rho proteins emerge from experimental data.Science, Faculty ofMathematics, Department ofGraduat

Pattern formation in a membrane-bulk model for cell polarity and intracellular oscillations

Non UBCUnreviewedAuthor affiliation: University of Notre DameFacult