Examining Go-or-Grow Using Fluorescent Cell-Cycle Indicators and Cell-Cycle-Inhibiting Drugs

Phenotypic switching mechanisms determine the structure of cell migration into extracellular matrix under the 'go-or-grow' hypothesis

A fundamental feature of collective cell migration is phenotypic heterogeneity which, for example, influences tumour progression and relapse. While current mathematical models often consider discrete phenotypic structuring of the cell population, in-line with the 'go-or-grow' hypothesis (Hatzikirou et al., 2012; Stepien et al., 2018), they regularly overlook the role that the environment may play in determining the cells' phenotype during migration. Comparing a previously studied volume-filling model for a homogeneous population of generalist cells that can proliferate, move and degrade extracellular matrix (ECM) (Crossley et al., 2023) to a novel model for a heterogeneous population comprising two distinct sub-populations of specialist cells that can either move and degrade ECM or proliferate, this study explores how different hypothetical phenotypic switching mechanisms affect the speed and structure of the invading cell populations. Through a continuum model derived from its individual-based counterpart, insights into the influence of the ECM and the impact of phenotypic switching on migrating cell populations emerge. Notably, specialist cell populations that cannot switch phenotype show reduced invasiveness compared to generalist cell populations, while implementing different forms of switching significantly alters the structure of migrating cell fronts. This key result suggests that the structure of an invading cell population could be used to infer the underlying mechanisms governing phenotypic switching.

Quantifying cell cycle regulation by tissue crowding

The spatiotemporal coordination and regulation of cell proliferation is fundamental in many aspects of development and tissue maintenance. Cells have the ability to adapt their division rates in response to mechanical constraints, yet we do not fully understand how cell proliferation regulation impacts cell migration phenomena. Here, we present a minimal continuum model of cell migration with cell cycle dynamics, which includes density-dependent effects and hence can account for cell proliferation regulation. By combining minimal mathematical modeling, Bayesian inference, and recent experimental data, we quantify the impact of tissue crowding across different cell cycle stages in epithelial tissue expansion experiments. Our model suggests that cells sense local density and adapt cell cycle progression in response, during G1 and the combined S/G2/M phases, providing an explicit relationship between each cell-cycle-stage duration and local tissue density, which is consistent with several experimental observations. Finally, we compare our mathematical model's predictions to different experiments studying cell cycle regulation and present a quantitative analysis on the impact of density-dependent regulation on cell migration patterns. Our work presents a systematic approach for investigating and analyzing cell cycle data, providing mechanistic insights into how individual cells regulate proliferation, based on population-based experimental measurements.

Cell cycle perturbation uncouples mitotic progression and invasive behavior in a post-mitotic cell

The acquisition of the post-mitotic state is crucial for the execution of many terminally differentiated cell behaviors during organismal development. However, the mechanisms that maintain the post-mitotic state in this context remain poorly understood. To gain insight into these mechanisms, we used the genetically and visually accessible model of C. elegans anchor cell (AC) invasion into the vulval epithelium. The AC is a terminally differentiated uterine cell that normally exits the cell cycle and enters a post-mitotic state before initiating contact between the uterus and vulva through a cell invasion event. Here, we set out to identify the set of negative cell cycle regulators that maintain the AC in this post-mitotic, invasive state. Our findings revealed a critical role for CKI-1 (p21CIP1/p27KIP1) in redundantly maintaining the post-mitotic state of the AC, as loss of CKI-1 in combination with other negative cell cycle regulators-including CKI-2 (p21CIP1/p27KIP1), LIN-35 (pRb/p107/p130), FZR-1 (Cdh1/Hct1), and LIN-23 (β-TrCP)-resulted in proliferating ACs. Remarkably, time-lapse imaging revealed that these ACs retain their ability to invade. Upon examination of a node in the gene regulatory network controlling AC invasion, we determined that proliferating, invasive ACs do so by maintaining aspects of pro-invasive gene expression. We therefore report that the requirement for a post-mitotic state for invasive cell behavior can be bypassed following direct cell cycle perturbation.

Cell cycle perturbation uncouples mitotic progression and invasive behavior in a post-mitotic cell

The acquisition of the post-mitotic state is crucial for the execution of many terminally differentiated cell behaviors during organismal development. However, the mechanisms that maintain the post-mitotic state in this context remain poorly understood. To gain insight into these mechanisms, we used the genetically and visually accessible model of C. elegans anchor cell (AC) invasion into the vulval epithelium. The AC is a terminally differentiated uterine cell that normally exits the cell cycle and enters a post-mitotic state, initiating contact between the uterus and vulva through a cell invasion event. Here, we set out to identify the set of negative cell cycle regulators that maintain the AC in this post-mitotic, invasive state. Our findings revealed a critical role for CKI-1 (p21CIP1/p27KIP1) in redundantly maintaining the post-mitotic state of the AC, as loss of CKI-1 in combination with other negative cell cycle regulators-including CKI-2 (p21CIP1/p27KIP1), LIN-35 (pRb/p107/p130), FZR-1 (Cdh1/Hct1), and LIN-23 (β-TrCP)-resulted in proliferating ACs. Remarkably, time-lapse imaging revealed that these ACs retain their ability to invade. Upon examination of a node in the gene regulatory network controlling AC invasion, we determined that proliferating, invasive ACs do so by maintaining aspects of pro-invasive gene expression. We therefore report that the requirement for a post-mitotic state for invasive cell behavior can be bypassed following direct cell cycle perturbation.

Iron inhibits glioblastoma cell migration and polarization

Glioblastoma is one of the deadliest malignancies facing modern oncology today. The ability of glioblastoma cells to diffusely spread into neighboring healthy brain makes complete surgical resection nearly impossible and contributes to the recurrent disease faced by most patients. Although research into the impact of iron on glioblastoma has addressed proliferation, there has been little investigation into how cellular iron impacts the ability of glioblastoma cells to migrate-a key question, especially in the context of the diffuse spread observed in these tumors. Herein, we show that increasing cellular iron content results in decreased migratory capacity of human glioblastoma cells. The decrease in migratory capacity was accompanied by a decrease in cellular polarization in the direction of movement. Expression of CDC42, a Rho GTPase that is essential for both cellular migration and establishment of polarity in the direction of cell movement, was reduced upon iron treatment. We then analyzed a single-cell RNA-seq dataset of human glioblastoma samples and found that cells at the tumor periphery had a gene signature that is consistent with having lower levels of cellular iron. Altogether, our results suggest that cellular iron content is impacting glioblastoma cell migratory capacity and that cells with higher iron levels exhibit reduced motility.

Modelling microtube driven invasion of glioma

Malignant gliomas are notoriously invasive, a major impediment against their successful treatment. This invasive growth has motivated the use of predictive partial differential equation models, formulated at varying levels of detail, and including (i) "proliferation-infiltration" models, (ii) "go-or-grow" models, and (iii) anisotropic diffusion models. Often, these models use macroscopic observations of a diffuse tumour interface to motivate a phenomenological description of invasion, rather than performing a detailed and mechanistic modelling of glioma cell invasion processes. Here we close this gap. Based on experiments that support an important role played by long cellular protrusions, termed tumour microtubes, we formulate a new model for microtube-driven glioma invasion. In particular, we model a population of tumour cells that extend tissue-infiltrating microtubes. Mitosis leads to new nuclei that migrate along the microtubes and settle elsewhere. A combination of steady state analysis and numerical simulation is employed to show that the model can predict an expanding tumour, with travelling wave solutions led by microtube dynamics. A sequence of scaling arguments allows us reduce the detailed model into simpler formulations, including models falling into each of the general classes (i), (ii), and (iii) above. This analysis allows us to clearly identify the assumptions under which these various models can be a posteriori justified in the context of microtube-driven glioma invasion. Numerical simulations are used to compare the various model classes and we discuss their advantages and disadvantages.

The Impact of Phenotypic Heterogeneity on Chemotactic Self-Organisation

The capacity to aggregate through chemosensitive movement forms a paradigm of self-organisation, with examples spanning cellular and animal systems. A basic mechanism assumes a phenotypically homogeneous population that secretes its own attractant, with the well known system introduced more than five decades ago by Keller and Segel proving resolutely popular in modelling studies. The typical assumption of population phenotypic homogeneity, however, often lies at odds with the heterogeneity of natural systems, where populations may comprise distinct phenotypes that vary according to their chemotactic ability, attractant secretion, etc. To initiate an understanding into how this diversity can impact on autoaggregation, we propose a simple extension to the classical Keller and Segel model, in which the population is divided into two distinct phenotypes: those performing chemotaxis and those producing attractant. Using a combination of linear stability analysis and numerical simulations, we demonstrate that switching between these phenotypic states alters the capacity of a population to self-aggregate. Further, we show that switching based on the local environment (population density or chemoattractant level) leads to diverse patterning and provides a route through which a population can effectively curb the size and density of an aggregate. We discuss the results in the context of real world examples of chemotactic aggregation, as well as theoretical aspects of the model such as global existence and blow-up of solutions.

Non-local multiscale approach for the impact of go or grow hypothesis on tumour-viruses interactions

We propose and study computationally a novel non-local multiscale moving boundary mathematical model for tumour and oncolytic virus (OV) interactions when we consider the go or grow hypothesis for cancer dynamics. This spatio-temporal model focuses on two cancer cell phenotypes that can be infected with the OV or remain uninfected, and which can either move in response to the extracellular-matrix (ECM) density or proliferate. The interactions between cancer cells, those among cancer cells and ECM, and those among cells and OV occur at the macroscale. At the micro-scale, we focus on the interactions between cells and matrix degrading enzymes (MDEs) that impact the movement of tumour boundary. With the help of this multiscale model we explore the impact on tumour invasion patterns of two different assumptions that we consider in regard to cell-cell and cell-matrix interactions. In particular we investigate model dynamics when we assume that cancer cell fluxes are the result of local advection in response to the density of extracellular matrix (ECM), or of non-local advection in response to cell-ECM adhesion. We also investigate the role of the transition rates between mainly-moving and mainly-growing cancer cell sub-populations, as well as the role of virus infection rate and virus replication rate on the overall tumour dynamics.

Cancer metastasis as a non-healing wound

Most cancer deaths are caused by metastasis: recurrence of disease by disseminated tumour cells at sites distant from the primary tumour. Large numbers of disseminated tumour cells are released from the primary tumour, even during the early stages of tumour growth. However, only a minority survive as potential seeds for future metastatic outgrowths. These cells must adapt to a relatively inhospitable microenvironment, evade immune surveillance and progress from the micro- to macro-metastatic stage to generate a secondary tumour. A pervasive driver of this transition is chronic inflammatory signalling emanating from tumour cells themselves. These signals can promote migration and engagement of stem and progenitor cell function, events that are also central to a wound healing response. In this review, we revisit the concept of cancer as a non-healing wound, first introduced by Virchow in the 19th century, with a new tumour cell-intrinsic perspective on inflammation and focus on metastasis. Cellular responses to inflammation in both wound healing and metastasis are tightly regulated by crosstalk with the surrounding microenvironment. Targeting or restoring canonical responses to inflammation could represent a novel strategy to prevent the lethal spread of cancer.

Mathematical Model of Tumour Spheroid Experiments with Real-Time Cell Cycle Imaging

Three-dimensional (3D) in vitro tumour spheroid experiments are an important tool for studying cancer progression and potential cancer drug therapies. Standard experiments involve growing and imaging spheroids to explore how different conditions lead to different rates of spheroid growth. These kinds of experiments, however, do not reveal any information about the spatial distribution of the cell cycle within the expanding spheroid. Since 2008, a new experimental technology called fluorescent ubiquitination-based cell cycle indicator (FUCCI) has enabled real-time in situ visualisation of the cell cycle progression. Observations of 3D tumour spheroids with FUCCI labelling reveal significant intratumoural structure, as the cell cycle status can vary with location. Although many mathematical models of tumour spheroid growth have been developed, none of the existing mathematical models are designed to interpret experimental observations with FUCCI labelling. In this work, we adapt the mathematical framework originally proposed by Ward and King (Math Med Biol 14:39-69, 1997. https://doi.org/10.1093/imammb/14.1.39 ) to produce a new mathematical model of FUCCI-labelled tumour spheroid growth. The mathematical model treats the spheroid as being composed of three subpopulations: (i) living cells in G1 phase that fluoresce red; (ii) living cells in S/G2/M phase that fluoresce green; and (iii) dead cells that are not fluorescent. We assume that the rates at which cells pass through different phases of the cell cycle, and the rate of cell death, depend upon the local oxygen concentration. Parameterising the new mathematical model using experimental measurements of cell cycle transition times, we show that the model can qualitatively capture important experimental observations that cannot be addressed using previous mathematical models. Further, we show that the mathematical model can be used to qualitatively mimic the action of anti-mitotic drugs applied to the spheroid. All software programs required to solve the nonlinear moving boundary problem associated with the new mathematical model are available on GitHub. at https://github.com/wang-jin-mathbio/Jin2021.

A novel mathematical model of heterogeneous cell proliferation

We present a novel mathematical model of heterogeneous cell proliferation where the total population consists of a subpopulation of slow-proliferating cells and a subpopulation of fast-proliferating cells. The model incorporates two cellular processes, asymmetric cell division and induced switching between proliferative states, which are important determinants for the heterogeneity of a cell population. As motivation for our model we provide experimental data that illustrate the induced-switching process. Our model consists of a system of two coupled delay differential equations with distributed time delays and the cell densities as functions of time. The distributed delays are bounded and allow for the choice of delay kernel. We analyse the model and prove the nonnegativity and boundedness of solutions, the existence and uniqueness of solutions, and the local stability characteristics of the equilibrium points. We find that the parameters for induced switching are bifurcation parameters and therefore determine the long-term behaviour of the model. Numerical simulations illustrate and support the theoretical findings, and demonstrate the primary importance of transient dynamics for understanding the evolution of many experimental cell populations.

SOX9: An emerging driving factor from cancer progression to drug resistance

Dysregulation of transcription factors is one of the common problems in the pathogenesis of human cancer. Among them, SOX9 is one of the critical transcription factors involved in various diseases, including cancer. The expression of SOX9 is regulated by microRNAs (miRNAs), methylation, phosphorylation, and acetylation. Interestingly, SOX9 acts as a proto-oncogene or tumor suppressor gene, relying upon kinds of cancer. Recent studies have reported the critical role of SOX9 in the regulation of the tumor microenvironment (TME). Additionally, activation of SOX9 signaling or SOX9 regulated signaling pathways play a crucial role in cancer development and progression. Accumulating evidence also suggests that SOX9 acquires stem cell features to induce epithelial-mesenchymal transition (EMT). Moreover, SOX9 has been broadly studied in the field of cancer stem cell (CSC) and EMT in the last decades. However, the link between SOX9 and cancer drug resistance has only recently been discovered. Furthermore, its differential expression could be a potential biomarker for tumor prognosis and progression. This review outlined the various biological implications of SOX9 in cancer progression and cancer drug resistance and elucidated its signaling network, which could be a potential target for designing novel anticancer drugs.

Integrating Mathematical Modeling with High-Throughput Imaging Explains How Polyploid Populations Behave in Nutrient-Sparse Environments

Breast cancer progresses in a multistep process from primary tumor growth and stroma invasion to metastasis. Nutrient-limiting environments promote chemotaxis with aggressive morphologies characteristic of invasion. It is unknown how coexisting cells differ in their response to nutrient limitations and how this impacts invasion of the metapopulation as a whole. In this study, we integrate mathematical modeling with microenvironmental perturbation data to investigate invasion in nutrient-limiting environments inhabited by one or two cancer cell subpopulations. Subpopulations were defined by their energy efficiency and chemotactic ability. Invasion distance traveled by a homogeneous population was estimated. For heterogeneous populations, results suggest that an imbalance between nutrient efficacy and chemotactic superiority accelerates invasion. Such imbalance will spatially segregate the two populations and only one type will dominate at the invasion front. Only if these two phenotypes are balanced, the two subpopulations compete for the same space, which decelerates invasion. We investigate ploidy as a candidate biomarker of this phenotypic heterogeneity and discuss its potential to inform the dose of mTOR inhibitors (mTOR-I) that can inhibit chemotaxis just enough to facilitate such competition. SIGNIFICANCE: This study identifies the double-edged sword of high ploidy as a prerequisite to personalize combination therapies with cytotoxic drugs and inhibitors of signal transduction pathways such as mTOR-Is. GRAPHICAL ABSTRACT: http://cancerres.aacrjournals.org/content/canres/80/22/5109/F1.large.jpg.

Epigenetic feedback and stochastic partitioning during cell division can drive resistance to EMT

Epithelial-mesenchymal transition (EMT) and its reverse process mesenchymal-epithelial transition (MET) are central to metastatic aggressiveness and therapy resistance in solid tumors. While molecular determinants of both processes have been extensively characterized, the heterogeneity in the response of tumor cells to EMT and MET inducers has come into focus recently, and has been implicated in the failure of anti-cancer therapies. Recent experimental studies have shown that some cells can undergo an irreversible EMT depending on the duration of exposure to EMT-inducing signals. While the irreversibility of MET, or equivalently, resistance to EMT, has not been studied in as much detail, evidence supporting such behavior is slowly emerging. Here, we identify two possible mechanisms that can underlie resistance of cells to undergo EMT: epigenetic feedback in ZEB1/GRHL2 feedback loop and stochastic partitioning of biomolecules during cell division. Identifying the ZEB1/GRHL2 axis as a key determinant of epithelial-mesenchymal plasticity across many cancer types, we use mechanistic mathematical models to show how GRHL2 can be involved in both the abovementioned processes, thus driving an irreversible MET. Our study highlights how an isogenic population may contain subpopulation with varying degrees of susceptibility or resistance to EMT, and proposes a next set of questions for detailed experimental studies characterizing the irreversibility of MET/resistance to EMT.

Population Dynamics with Threshold Effects Give Rise to a Diverse Family of Allee Effects

The Allee effect describes populations that deviate from logistic growth models and arises in applications including ecology and cell biology. A common justification for incorporating Allee effects into population models is that the population in question has altered growth mechanisms at some critical density, often referred to as a threshold effect. Despite the ubiquitous nature of threshold effects arising in various biological applications, the explicit link between local threshold effects and global Allee effects has not been considered. In this work, we examine a continuum population model that incorporates threshold effects in the local growth mechanisms. We show that this model gives rise to a diverse family of Allee effects, and we provide a comprehensive analysis of which choices of local growth mechanisms give rise to specific Allee effects. Calibrating this model to a recent set of experimental data describing the growth of a population of cancer cells provides an interpretation of the threshold population density and growth mechanisms associated with the population.