Density-dependent quiescence in glioma invasion: instability in a simple reaction-diffusion model for the migration/proliferation dichotomy

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.

Evolution of phenotypic plasticity leads to tumor heterogeneity with implications for therapy

Cancer is a significant global health issue, with treatment challenges arising from intratumor heterogeneity. This heterogeneity stems mainly from somatic evolution, causing genetic diversity within the tumor, and phenotypic plasticity of tumor cells leading to reversible phenotypic changes. However, the interplay of both factors has not been rigorously investigated. Here, we examine the complex relationship between somatic evolution and phenotypic plasticity, explicitly focusing on the interplay between cell migration and proliferation. This type of phenotypic plasticity is essential in glioblastoma, the most aggressive form of brain tumor. We propose that somatic evolution alters the regulation of phenotypic plasticity in tumor cells, specifically the reaction to changes in the microenvironment. We study this hypothesis using a novel, spatially explicit model that tracks individual cells' phenotypic and genetic states. We assume cells change between migratory and proliferative states controlled by inherited and mutation-driven genotypes and the cells' microenvironment. We observe that cells at the tumor edge evolve to favor migration over proliferation and vice versa in the tumor bulk. Notably, different genetic configurations can result in this pattern of phenotypic heterogeneity. We analytically predict the outcome of the evolutionary process, showing that it depends on the tumor microenvironment. Synthetic tumors display varying levels of genetic and phenotypic heterogeneity, which we show are predictors of tumor recurrence time after treatment. Interestingly, higher phenotypic heterogeneity predicts poor treatment outcomes, unlike genetic heterogeneity. Our research offers a novel explanation for heterogeneous patterns of tumor recurrence in glioblastoma patients.

Deep learning identifies heterogeneous subpopulations in breast cancer cell lines

Motivation

Cells exhibit a wide array of morphological features, enabling computer vision methods to identify and track relevant parameters. Morphological analysis has long been implemented to identify specific cell types and cell responses. Here we asked whether morphological features might also be used to classify transcriptomic subpopulations within in vitro cancer cell lines. Identifying cell subpopulations furthers our understanding of morphology as a reflection of underlying cell phenotype and could enable a better understanding of how subsets of cells compete and cooperate in disease progression and treatment.

Results

We demonstrate that cell morphology can reflect underlying transcriptomic differences in vitro using convolutional neural networks. First, we find that changes induced by chemotherapy treatment are highly identifiable in a breast cancer cell line. We then show that the intra cell line subpopulations that comprise breast cancer cell lines under standard growth conditions are also identifiable using cell morphology. We find that cell morphology is influenced by neighborhood effects beyond the cell boundary, and that including image information surrounding the cell can improve model discrimination ability.

A simple agent-based hybrid model to simulate the biophysics of glioblastoma multiforme cells and the concomitant evolution of the oxygen field

BACKGROUND AND OBJECTIVES

Glioblastoma multiforme (GBM) is one of the most aggressive cancers of the central nervous system. It is characterized by a high mitotic activity and an infiltrative ability of the glioma cells, neovascularization and necrosis. GBM evolution entails the continuous interplay between heterogeneous cell populations, chemotaxis, and physical cues through different scales. In this work, an agent-based hybrid model is proposed to simulate the coupling of the multiscale biological events involved in the GBM invasion, specifically the individual and collective migration of GBM cells and the concurrent evolution of the oxygen field and phenotypic plasticity. An asset of the formulation is that it is conceptually and computationally simple but allows to reproduce the complexity and the progression of the GBM micro-environment at cell and tissue scales simultaneously.

METHODS

The migration is reproduced as the result of the interaction between every single cell and its micro-environment. The behavior of each individual cell is formulated through genotypic variables whereas the cell micro-environment is modeled in terms of the oxygen concentration and the cell density surrounding each cell. The collective behavior is formulated at a cellular scale through a flocking model. The phenotypic plasticity of the cells is induced by the micro-environment conditions, considering five phenotypes.

RESULTS

The model has been contrasted by benchmark problems and experimental tests showing the ability to reproduce different scenarios of glioma cell migration. In all cases, the individual and collective cell migration and the coupled evolution of both the oxygen field and phenotypic plasticity have been properly simulated. This simple formulation allows to mimic the formation of relevant hallmarks of glioblastoma multiforme, such as the necrotic cores, and to reproduce experimental evidences related to the mitotic activity in pseudopalisades.

CONCLUSIONS

In the collective migration, the survival of the clusters prevails at the expense of cell mitosis, regardless of the size of the groups, which delays the formation of necrotic foci and reduces the rate of oxygen consumption.

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.

Traveling wave speed and profile of a "go or grow" glioblastoma multiforme model

Glioblastoma multiforme (GBM) is a fast-growing and deadly brain tumor due to its ability to aggressively invade the nearby brain tissue. A host of mathematical models in the form of reaction-diffusion equations have been formulated and studied in order to assist clinical assessment of GBM growth and its treatment prediction. To better understand the speed of GBM growth and form, we propose a two population reaction-diffusion GBM model based on the 'go or grow' hypothesis. Our model is validated by in vitro data and assumes that tumor cells are more likely to leave and search for better locations when resources are more limited at their current positions. Our findings indicate that the tumor progresses slower than the simpler Fisher model, which is known to overestimate GBM progression. Moreover, we obtain accurate estimations of the traveling wave solution profiles under several plausible GBM cell switching scenarios by applying the approximation method introduced by Canosa.

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.

Modelling glioma progression, mass effect and intracranial pressure in patient anatomy

Increased intracranial pressure is the source of most critical symptoms in patients with glioma, and often the main cause of death. Clinical interventions could benefit from non-invasive estimates of the pressure distribution in the patient's parenchyma provided by computational models. However, existing glioma models do not simulate the pressure distribution and they rely on a large number of model parameters, which complicates their calibration from available patient data. Here we present a novel model for glioma growth, pressure distribution and corresponding brain deformation. The distinct feature of our approach is that the pressure is directly derived from tumour dynamics and patient-specific anatomy, providing non-invasive insights into the patient's state. The model predictions allow estimation of critical conditions such as intracranial hypertension, brain midline shift or neurological and cognitive impairments. A diffuse-domain formalism is employed to allow for efficient numerical implementation of the model in the patient-specific brain anatomy. The model is tested on synthetic and clinical cases. To facilitate clinical deployment, a high-performance computing implementation of the model has been publicly released.

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.

Image-based personalization of computational models for predicting response of high-grade glioma to chemoradiation

High-grade gliomas are an aggressive and invasive malignancy which are susceptible to treatment resistance due to heterogeneity in intratumoral properties such as cell proliferation and density and perfusion. Non-invasive imaging approaches can measure these properties, which can then be used to calibrate patient-specific mathematical models of tumor growth and response. We employed multiparametric magnetic resonance imaging (MRI) to identify tumor extent (via contrast-enhanced T1-weighted, and T2-FLAIR) and capture intratumoral heterogeneity in cell density (via diffusion-weighted imaging) to calibrate a family of mathematical models of chemoradiation response in nine patients with unresected or partially resected disease. The calibrated model parameters were used to forecast spatially-mapped individual tumor response at future imaging visits. We then employed the Akaike information criteria to select the most parsimonious member from the family, a novel two-species model describing the enhancing and non-enhancing components of the tumor. Using this model, we achieved low error in predictions of the enhancing volume (median: - 2.5%, interquartile range: 10.0%) and a strong correlation in total cell count (Kendall correlation coefficient 0.79) at 3-months post-treatment. These preliminary results demonstrate the plausibility of using multiparametric MRI data to inform spatially-informative, biologically-based predictive models of tumor response in the setting of clinical high-grade gliomas.

A review of dynamical systems approaches for the detection of chaotic attractors in cancer networks

Cancers are complex dynamical systems. They remain the leading cause of disease-related pediatric mortality in North America. To overcome this burden, we must decipher the state-space attractor dynamics of gene expression patterns and protein oscillations orchestrated by cancer stemness networks. The review provides an overview of dynamical systems theory to steer cancer research in pattern science. While most of our current tools in network medicine rely on statistical correlation methods, causality inference remains primitively developed. As such, a survey of attractor reconstruction methods and machine algorithms for the detection of causal structures applicable in experimentally derived time series cancer datasets is presented. A toolbox of complex systems approaches are discussed for reconstructing the signaling state space of cancer networks, interpreting causal relationships in their time series gene expression patterns, and assisting clinical decision making in computational oncology. As a proof of concept, the applicability of some algorithms are demonstrated on pediatric brain cancer datasets and the requirement of their time series analysis is highlighted.

Fractional Mathematical Oncology: On the potential of non-integer order calculus applied to interdisciplinary models

Mathematical Oncology investigates cancer-related phenomena through mathematical models as comprehensive as possible. Accordingly, an interdisciplinary approach involving concepts from biology to materials science can provide a deeper understanding of biological systems pertaining the disease. In this context, fractional calculus (also referred to as non-integer order) is a branch in mathematical analysis whose tools can describe complex phenomena comprising different time and space scales. Fractional-order models may allow a better description and understanding of oncological particularities, potentially contributing to decision-making in areas of interest such as tumor evolution, early diagnosis techniques and personalized treatment therapies. By following a phenomenological (i.e. mechanistic) approach, the present study surveys and explores different aspects of Fractional Mathematical Oncology, reviewing and discussing recent developments in view of their prospective applications.

Cell – extracellular matrix interaction in glioma growth. In silico model

The study aims to investigate the role of viscoelastic interactions between cells and extracellular matrix (ECM) in avascular tumor growth. Computer simulations of glioma multicellular tumor spheroid (MTS) growth are being carried out for various conditions. The calculations are based on a continuous model, which simulates oxygen transport into MTS; transitions between three cell phenotypes, cell transport, conditioned by hydrostatic forces in cell–ECM composite system, cell motility and cell adhesion. Visco-elastic cell aggregation and elastic ECM scaffold represent two compressible constituents of the composite. Cell–ECM interactions form a Transition Layer on the spheroid surface, where mechanical characteristics of tumor undergo rapid transition. This layer facilitates tumor progression to a great extent. The study demonstrates strong effects of ECM stiffness, mechanical deformations of the matrix and cell–cell adhesion on tumor progression. The simulations show in particular that at certain, rather high degrees of matrix stiffness a formation of distant multicellular clusters takes place, while at further increase of ECM stiffness subtumors do not form. The model also illustrates to what extent mere mechanical properties of cell–ECM system may contribute into variations of glioma invasion scenarios.

WHERE DID THE TUMOR START? AN INVERSE SOLVER WITH SPARSE LOCALIZATION FOR TUMOR GROWTH MODELS

We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction-diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of Magnetic Resonance Imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver.

Simulation of glioblastoma growth using a 3D multispecies tumor model with mass effect

In this article, we present a multispecies reaction-advection-diffusion partial differential equation coupled with linear elasticity for modeling tumor growth. The model aims to capture the phenomenological features of glioblastoma multiforme observed in magnetic resonance imaging (MRI) scans. These include enhancing and necrotic tumor structures, brain edema and the so-called "mass effect", a term-of-art that refers to the deformation of brain tissue due to the presence of the tumor. The multispecies model accounts for proliferating, invasive and necrotic tumor cells as well as a simple model for nutrition consumption and tumor-induced brain edema. The coupling of the model with linear elasticity equations with variable coefficients allows us to capture the mechanical deformations due to the tumor growth on surrounding tissues. We present the overall formulation along with a novel operator-splitting scheme with components that include linearly-implicit preconditioned elliptic solvers, and a semi-Lagrangian method for advection. We also present results showing simulated MRI images which highlight the capability of our method to capture the overall structure of glioblastomas in MRIs.

The biology and mathematical modelling of glioma invasion: a review

Adult gliomas are aggressive brain tumours associated with low patient survival rates and limited life expectancy. The most important hallmark of this type of tumour is its invasive behaviour, characterized by a markedly phenotypic plasticity, infiltrative tumour morphologies and the ability of malignant progression from low- to high-grade tumour types. Indeed, the widespread infiltration of healthy brain tissue by glioma cells is largely responsible for poor prognosis and the difficulty of finding curative therapies. Meanwhile, mathematical models have been established to analyse potential mechanisms of glioma invasion. In this review, we start with a brief introduction to current biological knowledge about glioma invasion, and then critically review and highlight future challenges for mathematical models of glioma invasion.

A Brownian dynamics tumor progression simulator with application to glioblastoma

Tumor progression modeling offers the potential to predict tumor-spreading behavior to improve prognostic accuracy and guide therapy development. Common simulation methods include continuous reaction-diffusion (RD) approaches that capture mean spatio-temporal tumor spreading behavior and discrete agent-based (AB) approaches which capture individual cell events such as proliferation or migration. The brain cancer glioblastoma (GBM) is especially appropriate for such proliferation-migration modeling approaches because tumor cells seldom metastasize outside of the central nervous system and cells are both highly proliferative and migratory. In glioblastoma research, current RD estimates of proliferation and migration parameters are derived from computed tomography or magnetic resonance images. However, these estimates of glioblastoma cell migration rates, modeled as a diffusion coefficient, are approximately 1-2 orders of magnitude larger than single-cell measurements in animal models of this disease. To identify possible sources for this discrepancy, we evaluated the fundamental RD simulation assumptions that cells are point-like structures that can overlap. To give cells physical size (~10 μm), we used a Brownian dynamics approach that simulates individual single-cell diffusive migration, growth, and proliferation activity via a gridless, off-lattice, AB method where cells can be prohibited from overlapping each other. We found that for realistic single-cell parameter growth and migration rates, a non-overlapping model gives rise to a jammed configuration in the center of the tumor and a biased outward diffusion of cells in the tumor periphery, creating a quasi-ballistic advancing tumor front. The simulations demonstrate that a fast-progressing tumor can result from minimally diffusive cells, but at a rate that is still dependent on single-cell diffusive migration rates. Thus, modeling with the assumption of physically-grounded volume conservation can account for the apparent discrepancy between estimated and measured diffusion of GBM cells and provide a new theoretical framework that naturally links single-cell growth and migration dynamics to tumor-level progression.

Density-Dependent Regulation of Glioma Cell Proliferation and Invasion Mediated by miR-9

The phenotypic axis of invasion and proliferation in malignant glioma cells is a well-documented phenomenon. Invasive glioma cells exhibit a decreased proliferation rate and a resistance to apoptosis, and invasive tumor cells dispersed in brain subsequently revert to proliferation and contribute to secondary tumor formation. One miRNA can affect dozens of mRNAs, and some miRNAs are potent oncogenes. Multiple miRNAs are implicated in glioma malignancy, and several of which have been identified to regulate tumor cell motility and division. Using rat 9 L gliosarcoma and human U87 glioblastoma cell lines, we investigated miRNAs associated with the switch between glioma cell invasion and proliferation. Using micro-dissection of 9 L glioma tumor xenografts in rat brain, we identified disparate expression of miR-9 between cells within the periphery of the primary tumor, and those comprising tumor islets within the invasive zone. Modifying miR-9 expression in in vitro assays, we report that miR-9 controls the axis of glioma cell invasion/proliferation, and that its contribution to invasion or proliferation is biphasic and dependent upon local tumor cell density. In addition, immunohistochemistry revealed elevated hypoxia inducible factor 1 alpha (HIF-1α) in the invasive zone as compared to the primary tumor periphery. We also found that hypoxia promotes miR-9 expression in glioma cells. Based upon these findings, we propose a hypothesis for the contribution of miR-9 to the dynamics glioma invasion and satellite tumor formation in brain adjacent to tumor.

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights

Gliomas are highly invasive brain tumours characterised by poor prognosis and limited response to therapy. There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve tumour blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation induced by blood vessel occlusion/collapse. In contrast, the therapeutic intention of normalising the abnormal tumour vasculature is to improve the efficacy of conventional treatment modalities. Although these strategies have shown therapeutic potential, it remains unclear why they both often fail to control glioma growth. To shed some light on this issue, we propose a mathematical model based on the migration/proliferation dichotomy of glioma cells in order to investigate why vaso-modulatory interventions have shown limited success in terms of tumour clearance. We found the existence of a critical cell proliferation/diffusion ratio that separates glioma responses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the front speed and increase the infiltration width, for those in the other regime, the invasion speed increases and infiltration width decreases. We discuss how these in silico findings can be used to guide individualised vaso-modulatory approaches to improve treatment success rates.

Instability of turing patterns in reaction-diffusion-ODE systems

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.

An Emerging Allee Effect Is Critical for Tumor Initiation and Persistence

Tumor cells develop different strategies to cope with changing microenvironmental conditions. A prominent example is the adaptive phenotypic switching between cell migration and proliferation. While it has been shown that the migration-proliferation plasticity influences tumor spread, it remains unclear how this particular phenotypic plasticity affects overall tumor growth, in particular initiation and persistence. To address this problem, we formulate and study a mathematical model of spatio-temporal tumor dynamics which incorporates the microenvironmental influence through a local cell density dependence. Our analysis reveals that two dynamic regimes can be distinguished. If cell motility is allowed to increase with local cell density, any tumor cell population will persist in time, irrespective of its initial size. On the contrary, if cell motility is assumed to decrease with respect to local cell density, any tumor population below a certain size threshold will eventually extinguish, a fact usually termed as Allee effect in ecology. These results suggest that strategies aimed at modulating migration are worth to be explored as alternatives to those mainly focused at keeping tumor proliferation under control.

Controlling tumor growth remains a major medical challenge. Current clinical therapies focus on strategies to reduce tumor cell proliferation. However, during tumor progression, tumor cells may switch between proliferative and migratory behaviors, thereby allowing adaptation to microenvironmental changes that result in variations in local tumor cell density. We herein explore by means of a mathematical model the impact of migration-proliferation plasticity on tumor initiation and persistence. Our work suggests that small tumors can become extinct solely by their intrinsic cell population dynamics if cell motility decreases along with local cell density. In contrast, if cell motility increases with cell density, the tumor inevitably grows. Our model suggests that the regulation of cell migration plays a key role in tumor growth as a whole, making this feature a potential target for clinical studies.

Spontaneous formation of large clusters in a lattice gas above the critical point

We consider clustering of particles in the lattice gas model above the critical point. We find the probability for large density fluctuations over scales much larger than the correlation length. This fundamental problem is of interest in various biological contexts such as quorum sensing and clustering of motile, adhesive, cancer cells. In the latter case, it may give a clue to the problem of growth of recurrent tumors. We develop a formalism for the analysis of this rare event employing a phenomenological master equation and measuring the transition rates in numerical simulations. The spontaneous clustering is treated in the framework of the eikonal approximation to the master equation.

A multilayer grow-or-go model for GBM: effects of invasive cells and anti-angiogenesis on growth

The recent use of anti-angiogenesis (AA) drugs for the treatment of glioblastoma multiforme (GBM) has uncovered unusual tumor responses. Here, we derive a new mathematical model that takes into account the ability of proliferative cells to become invasive under hypoxic conditions; model simulations generate the multilayer structure of GBM, namely proliferation, brain invasion, and necrosis. The model is able to replicate and justify the clinical observation of rebound growth when AA therapy is discontinued in some patients. The model is interrogated to derive fundamental insights int cancer biology and on the clinical and biological effects of AA drugs. Invasive cells promote tumor growth, which in the long run exceeds the effects of angiogenesis alone. Furthermore, AA drugs increase the fraction of invasive cells in the tumor, which explain progression by fluid-attenuated inversion recovery (FLAIR) signal and the rebound tumor growth when AA is discontinued.

Exploring the competition between proliferative and invasive cancer phenotypes in a continuous spatial model

Tumor is characterized by extensive heterogeneity with respect to its microenvironment and its genetic composition. We extend a previously developed monoclonal continuous spatial model of tumor growth to account for polyclonal cell populations and investigate the interplay between a more proliferative and a more invasive phenotype under different conditions. The model simulations demonstrate a transition from the dominance of the proliferative to the dominance of the invasive phenotype resembling malignant tumor progression and show a time period where both subpopulations are abundant. As the dominant phenotype switches from proliferative to invasive, the geometry of tumor changes from a compact and almost spherical shape to a more diffusive and fingered morphology with the proliferative phenotype to be restricted in the tumor bulk and the invasive to dominate at tumor edges. Different micro-environmental conditions and different phenotypic properties can promote or inhibit invasion demonstrating their mutual importance. The model provides a computational framework to investigate tumor heterogeneity and the constant interplay between the environment and the specific characteristics of phenotypes that should be taken into account for the prediction of tumor evolution, morphology and effective treatment.

Choindroitinase ABC I-mediated enhancement of oncolytic virus spread and anti tumor efficacy: a mathematical model

Oncolytic viruses are genetically engineered viruses that are designed to kill cancer cells while doing minimal damage to normal healthy tissue. After being injected into a tumor, they infect cancer cells, multiply inside them, and when a cancer cell is killed they move on to spread and infect other cancer cells. Chondroitinase ABC (Chase-ABC) is a bacterial enzyme that can remove a major glioma ECM component, chondroitin sulfate glycosoamino glycans from proteoglycans without any deleterious effects in vivo. It has been shown that Chase-ABC treatment is able to promote the spread of the viruses, increasing the efficacy of the viral treatment. In this paper we develop a mathematical model to investigate the effect of the Chase-ABC on the treatment of glioma by oncolytic viruses (OV). We show that the model's predictions agree with experimental results for a spherical glioma. We then use the model to test various treatment options in the heterogeneous microenvironment of the brain. The model predicts that separate injections of OV, one into the center of the tumor and another outside the tumor will result in better outcome than if the total injection is outside the tumor. In particular, the injection of the ECM-degrading enzyme (Chase-ABC) on the periphery of the main tumor core need to be administered in an optimal strategy in order to infect and eradicate the infiltrating glioma cells outside the tumor core in addition to proliferative cells in the bulk of tumor core. The model also predicts that the size of tumor satellites and distance between the primary tumor and multifocal/satellite lesions may be an important factor for the efficacy of the viral therapy with Chase treatment.

c-Src and neural Wiskott-Aldrich syndrome protein (N-WASP) promote low oxygen-induced accelerated brain invasion by gliomas

Malignant gliomas remain associated with poor prognosis and high morbidity because of their ability to invade the brain; furthermore, human gliomas exhibit a phenotype of accelerated brain invasion in response to anti-angiogenic drugs. Here, we study 8 human glioblastoma cell lines; U251, U87, D54 and LN229 show accelerated motility in low ambient oxygen. Src inhibition by Dasatinib abrogates this phenotype. Molecular discovery and validation studies evaluate 46 molecules related to motility or the src pathway in U251 cells. Demanding that the molecular changes induced by low ambient oxygen are reversed by Dasatinib in U251 cells, identifies neural Wiskott-Aldrich syndrome protein (NWASP), Focal adhesion Kinase (FAK), -Catenin, and Cofilin. However, only Src-mediated NWASP phosphorylation distinguishes the four cell lines that exhibit enhanced motility in low ambient oxygen. Downregulating c-Src or NWASP by RNA interference abrogates the low-oxygen-induced enhancement in motility by in vitro assays and in organotypic brain slice cultures. The findings support the idea that c-Src and NWASP play key roles in mediating the molecular pathogenesis of low oxygen-induced accelerated brain invasion by gliomas.

MiR-29c inhibits glioma cell proliferation, migration, invasion and angiogenesis

Previous studies reported that miR-29c is significantly downregulated in several tumors. However, little is known about the effect and molecular mechanisms of action of miR-29c in human glioma. Using quantitative RT-PCR, we demonstrated that miR-29c was significantly downregulated in glioma cell lines and human primary glioma tissues, compared to normal human astrocytes and matched non-tumor associated tissues (P < 0.05, χ(2) test). Overexpression of miR-29c dramatically reduced the proliferation and caused cessation of cell cycle. The reduced cell proliferation is due to G1 phase arrest as cyclin D1 and cyclin E are diminished whereas p27 and p21 are upregulated. We further demonstrated that miR-29c overexpression suppressed the glioma cell migration and invasion abilities by targeting MMP-2. In addition, we also found that overexpression of miR-29c sharply inhibited angiogenesis, which correlated with down-regulation of VEGF. The data indicate that miR-29c may be a tumor suppressor involved in the progression of glioma.

Regulation of cell proliferation and migration in glioblastoma: new therapeutic approach

Glioblastoma is the most aggressive brain cancer with the poor survival rate. A microRNA, miR-451, and its downstream molecules, CAB39/LKB1/STRAD/AMPK, are known to play a critical role in regulating a biochemical balance between rapid proliferation and invasion in the presence of metabolic stress in microenvironment. We develop a novel multi-scale mathematical model where cell migration and proliferation are controlled through a core intracellular control system (miR-451-AMPK complex) in response to glucose availability and physical constraints in the microenvironment. Tumor cells are modeled individually and proliferation and migration of those cells are regulated by the intracellular dynamics and reaction-diffusion equations of concentrations of glucose, chemoattractant, extracellular matrix, and MMPs. The model predicts that invasion patterns and rapid growth of tumor cells after conventional surgery depend on biophysical properties of cells, dynamics of the core control system, and microenvironment as well as glucose injection methods. We developed a new type of therapeutic approach: effective injection of chemoattractant to bring invasive cells back to the surgical site after initial surgery, followed by glucose injection at the same location. The model suggests that a good combination of chemoattractant and glucose injection at appropriate time frames may lead to an effective therapeutic strategy of eradicating tumor cells.

Identification of intrinsic in vitro cellular mechanisms for glioma invasion

Invasion of malignant glioma is a highly complex phenomenon involving molecular and cellular processes at various spatio-temporal scales, whose precise interplay is still not fully understood. In order to identify the intrinsic cellular mechanisms of glioma invasion, we study an in vitro culture of glioma cells. By means of a computational approach, based on a cellular automaton model, we compare simulation results to the experimental data and deduce cellular mechanisms from microscopic and macroscopic observables (experimental data). For the first time, it is shown that the migration/proliferation dichotomy plays a central role in the invasion of glioma cells. Interestingly, we conclude that a diverging invasive zone is a consequence of this dichotomy. Additionally, we observe that radial persistence of glioma cells in the vicinity of dense areas accelerates the invasion process. We argue that this persistence results from a cell-cell repulsion mechanism. If glioma cell behavior is regulated through a migration/proliferation dichotomy and a self-repellent mechanism, our simulations faithfully reproduce all the experimental observations.