The impact of adhesion on cellular invasion processes in cancer and development

The force of cell-cell adhesion in determining the outcome in a nonlocal advection diffusion model of wound healing

A model of wound healing is presented to investigate the connection of the force of cell-cell adhesion to the sensing radius of cells in their spatial environment. The model consists of a partial differential equation with nonlocal advection and diffusion terms, describing the movement of cells in a spatial environment. The model is applied to biological wound healing experiments to understand incomplete wound closure. The analysis demonstrates that for each value of the force of adhesion parameter, there is a critical value of the sensing radius above which complete wound healing does not occur.

Nonlocal multiscale modelling of tumour-oncolytic viruses interactions within a heterogeneous fibrous/non-fibrous extracellular matrix

In this study we investigate computationally tumour-oncolytic virus (OV) interactions that take place within a heterogeneous extracellular matrix (ECM). The ECM is viewed as a mixture of two constitutive phases, namely a fibre phase and a non-fibre phase. The multiscale mathematical model presented here focuses on the nonlocal cell-cell and cell-ECM interactions, and how these interactions might be impacted by the infection of cancer cells with the OV. At macroscale we track the kinetics of cancer cells, virus particles and the ECM. At microscale we track (i) the degradation of ECM by matrix degrading enzymes (MDEs) produced by cancer cells, which further influences the movement of tumour boundary; (ii) the re-arrangement of the microfibres that influences the re-arrangement of macrofibres (i.e., fibres at macroscale). With the help of this new multiscale model, we investigate two questions: (i) whether the infected cancer cell fluxes are the result of local or non-local advection in response to ECM density; and (ii) what is the effect of ECM fibres on the the spatial spread of oncolytic viruses and the outcome of oncolytic virotherapy.

A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis

The formation of new vascular networks is essential for tissue development and regeneration, in addition to playing a key role in pathological settings such as ischemia and tumour development. Experimental findings in the past two decades have led to the identification of a new mechanism of neovascularisation, known as cluster-based vasculogenesis, during which endothelial progenitor cells (EPCs) mobilised from the bone marrow are capable of bridging distant vascular beds in a variety of hypoxic settings in vivo. This process is characterised by the formation of EPC clusters during its early stages and, while much progress has been made in identifying various mechanisms underlying cluster formation, we are still far from a comprehensive description of such spatio-temporal dynamics. In order to achieve this, we propose a novel mathematical model of the early stages of cluster-based vasculogenesis, comprising of a system of nonlocal partial differential equations including key mechanisms such as endogenous chemotaxis, matrix degradation, cell proliferation and cell-to-cell adhesion. We conduct a linear stability analysis on the system and solve the equations numerically. We then conduct a parametric analysis of the numerical solutions of the one-dimensional problem to investigate the role of underlying dynamics on the speed of cluster formation and the size of clusters, measured via appropriate metrics for the cluster width and compactness. We verify the key results of the parametric analysis with simulations of the two-dimensional problem. Our results, which qualitatively compare with data from in vitro experiments, elucidate the complementary role played by endogenous chemotaxis and matrix degradation in the formation of clusters, suggesting chemotaxis is responsible for the cluster topology while matrix degradation is responsible for the speed of cluster formation. Our results also indicate that the nonlocal cell-to-cell adhesion term in our model, even though it initially causes cells to aggregate, is not sufficient to ensure clusters are stable over long time periods. Consequently, new modelling strategies for cell-to-cell adhesion are required to stabilise in silico clusters. We end the paper with a thorough discussion of promising, fruitful future modelling and experimental research perspectives.

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.

Human giant larvae-1 promotes migration and invasion of malignant glioma cells by regulating N-cadherin

Human giant larvae-1 (Hugl-1) is a human homologue of Drosophila tumor suppressor lethal (2)-giant larvae and has been reported to be involved in the development of human malignancies. Previous studies performed by our group demonstrated that Hugl-1 inhibits glioma cell proliferation in an intracranial model of nude mice. However, the exact molecular mechanisms underlying the participation of Hugl-1 in glioma invasion and migration, and in the depolarizing process remain largely unknown. Utilizing the U251-MG cells with stable expression of Hugl-1, the present study used wound healing, Transwell invasion and western blot assays to explore the role and specific mechanism of Hugl-1 in glioma invasion and migration. The results of the present study demonstrated that overexpression of Hugl-1 decreased cell-cell adhesion and increased cell-cell extracellular matrix adhesion. In addition, overexpression of Hugl-1 promoted pseudopodia formation, glioma cell migration and invasion. The molecular mechanism of action involved the negative regulation of N-cadherin protein levels by Hugl-1. Overexpression or knockdown of N-cadherin partially suppressed or enhanced the effects of Hugl-1 on glioma cell migration and invasion, respectively. Furthermore, Hugl-1 inhibited cell proliferation, while promoting cell migration, which suggests that it may serve a two-sided biological role in cellular processes. Taken together, these results suggest that Hugl-1 promotes the migration and invasion of malignant glioma cells by decreasing N-cadherin expression. Thus, Hugl-1 may be applied in the development of targeted and personalized treatment.

Nonlocal and local models for taxis in cell migration: a rigorous limit procedure

A rigorous limit procedure is presented which links nonlocal models involving adhesion or nonlocal chemotaxis to their local counterparts featuring haptotaxis and classical chemotaxis, respectively. It relies on a novel reformulation of the involved nonlocalities in terms of integral operators applied directly to the gradients of signal-dependent quantities. The proposed approach handles both model types in a unified way and extends the previous mathematical framework to settings that allow for general solution-dependent coefficient functions. The previous forms of nonlocal operators are compared with the new ones introduced in this paper and the advantages of the latter are highlighted by concrete examples. Numerical simulations in 1D provide an illustration of some of the theoretical findings.

Mathematical models for cell migration: a non-local perspective

We provide a review of recent advancements in non-local continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion. Particular emphasis is placed on spatial non-locality occurring in advection terms, used to characterize a cell's motility bias according to its interactions with other cellular and acellular components in its vicinity (e.g. cell-cell and cell-tissue adhesions, non-local chemotaxis), but we also briefly address spatially non-local source terms. Following a short introduction and description of applications, we give a systematic classification of available PDE models with respect to the type of featured non-localities and review some of the mathematical challenges arising from such models, with a focus on analytical aspects. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Cell-Scale Degradation of Peritumoural Extracellular Matrix Fibre Network and Its Role Within Tissue-Scale Cancer Invasion

Local cancer invasion of tissue is a complex, multiscale process which plays an essential role in tumour progression. During the complex interaction between cancer cell population and the extracellular matrix (ECM), of key importance is the role played by both bulk two-scale dynamics of ECM fibres within collective movement of the tumour cells and the multiscale leading edge dynamics driven by proteolytic activity of the matrix-degrading enzymes (MDEs) that are secreted by the cancer cells. As these two multiscale subsystems share and contribute to the same tumour macro-dynamics, in this work we develop further the model introduced in Shuttleworth and Trucu (Bull Math Biol 81:2176–2219, 2019. 10.1007/s11538-019-00598-w) by exploring a new aspect of their interaction that occurs at the cell scale. Specifically, here we will focus on understanding the cell-scale cross talk between the micro-scale parts of these two multiscale subsystems which get to interact directly in the peritumoural region, with immediate consequences both for MDE micro-dynamics occurring at the leading edge of the tumour and for the cell-scale rearrangement of the naturally oriented ECM fibres in the peritumoural region, ultimately influencing the way tumour progresses in the surrounding tissue. To that end, we will propose a new modelling that captures the ECM fibres degradation not only at macro-scale in the bulk of the tumour but also explicitly in the micro-scale neighbourhood of the tumour interface as a consequence of the interactions with molecular fluxes of MDEs that exercise their spatial dynamics at the invasive edge of the tumour.

Continuous Dynamic Modeling of Regulated Cell Adhesion: Sorting, Intercalation, and Involution

Cell-cell adhesion is essential for tissue growth and multicellular pattern formation and crucial for the cellular dynamics during embryogenesis and cancer progression. Understanding the dynamical gene regulation of cell adhesion molecules (CAMs) responsible for the emerging spatial tissue behaviors is a current challenge because of the complexity of these nonlinear interactions and feedback loops at different levels of abstraction-from genetic regulation to whole-organism shape formation. To extend our understanding of cell and tissue behaviors due to the regulation of adhesion molecules, here we present a novel, to our knowledge, model for the spatial dynamics of cellular patterning, growth, and shape formation due to the differential expression of CAMs and their regulation. Capturing the dynamic interplay between genetic regulation, CAM expression, and differential cell adhesion, the proposed continuous model can explain the complex and emergent spatial behaviors of cell populations that change their adhesion properties dynamically because of inter- and intracellular genetic regulation. This approach can demonstrate the mechanisms responsible for classical cell-sorting behaviors, cell intercalation in proliferating populations, and the involution of germ layer cells induced by a diffusing morphogen during gastrulation. The model makes predictions on the physical parameters controlling the amplitude and wavelength of a cellular intercalation interface, as well as the crucial role of N-cadherin regulation for the involution and migration of cells beyond the gradient of the morphogen Nodal during zebrafish gastrulation. Integrating the emergent spatial tissue behaviors with the regulation of genes responsible for essential cellular properties such as adhesion will pave the way toward understanding the genetic regulation of large-scale complex patterns and shapes formation in developmental, regenerative, and cancer biology.

A chemotaxis-based explanation of spheroid formation in 3D cultures of breast cancer cells

Three-dimensional cultures of cells are gaining popularity as an in vitro improvement over 2D Petri dishes. In many such experiments, cells have been found to organize in aggregates. We present new results of three-dimensional in vitro cultures of breast cancer cells exhibiting patterns. Understanding their formation is of particular interest in the context of cancer since metastases have been shown to be created by cells moving in clusters. In this paper, we propose that the main mechanism which leads to the emergence of patterns is chemotaxis, i.e., oriented movement of cells towards high concentration zones of a signal emitted by the cells themselves. Studying a Keller-Segel PDE system to model chemotactical auto-organization of cells, we prove that it admits Turing unstable solutions under a time-dependent condition. This result is illustrated by two-dimensional simulations of the model showing spheroidal patterns. They are qualitatively compared to the biological results and their variability is discussed both theoretically and numerically.

Multiscale dynamics of a heterotypic cancer cell population within a fibrous extracellular matrix

Local cancer cell invasion is a complex process involving many cellular and tissue interactions and is an important prerequisite for metastatic spread, the main cause of cancer related deaths. As a tumour increases in malignancy, the cancer cells adopt the ability to mutate into secondary cell subpopulations giving rise to a heterogeneous tumour. This new cell subpopulation often carries higher invasive abilities and permits a quicker spread of the tumour. Building upon the recent multiscale modelling framework for cancer invasion within a fibrous ECM introduced in Shuttleworth and Trucu, (2019), in this paper we consider the process of local invasion by a heterotypic tumour consisting of two cancer cell populations mixed with a two-phase ECM. To that end, we address the double feedback link between the tissue-scale cancer dynamics and the cell-scale molecular processes through the development of a two-part modelling framework that crucially incorporates the multiscale dynamic redistribution of oriented fibres occurring within a two-phase extra-cellular matrix and combines this with the multiscale leading edge dynamics exploring key matrix-degrading enzymes molecular processes along the tumour interface that drive the movement of the cancer boundary. The modelling framework will be accompanied by computational results that explore the effects of the underlying fibre network on the overall pattern of cancer invasion.

Continuum descriptions of spatial spreading for heterogeneous cell populations: Theory and experiment

Variability in cell populations is frequently observed in both in vitro and in vivo settings. Intrinsic differences within populations of cells, such as differences in cell sizes or differences in rates of cell motility, can be present even within a population of cells from the same cell line. We refer to this variability as cell heterogeneity. Mathematical models of cell migration, for example, in the context of tumour growth and metastatic invasion, often account for both undirected (random) migration and directed migration that is mediated by cell-to-cell contacts and cell-to-cell adhesion. A key feature of standard models is that they often assume that the population is composed of identical cells with constant properties. This leads to relatively simple single-species homogeneous models that neglect the role of heterogeneity. In this work, we use a continuum modelling approach to explore the role of heterogeneity in spatial spreading of cell populations. We employ a three-species heterogeneous model of cell motility that explicitly incorporates different types of experimentally-motivated heterogeneity in cell sizes: (i) monotonically decreasing; (ii) uniform; (iii) non-monotonic; and (iv) monotonically increasing distributions of cell size. Comparing the density profiles generated by the three-species heterogeneous model with density profiles predicted by a more standard single-species homogeneous model reveals that when we are dealing with monotonically decreasing and uniform distributions a simple and computationally efficient single-species homogeneous model can be remarkably accurate in describing the evolution of a heterogeneous cell population. In contrast, we find that the simpler single-species homogeneous model performs relatively poorly when applied to non-monotonic and monotonically increasing distributions of cell sizes. Additional results for heterogeneity in parameters describing both undirected and directed cell migration are also considered, and we find that similar results apply.

Kinetic models with non-local sensing determining cell polarization and speed according to independent cues

Cells move by run and tumble, a kind of dynamics in which the cell alternates runs over straight lines and re-orientations. This erratic motion may be influenced by external factors, like chemicals, nutrients, the extra-cellular matrix, in the sense that the cell measures the external field and elaborates the signal eventually adapting its dynamics. We propose a kinetic transport equation implementing a velocity-jump process in which the transition probability takes into account a double bias, which acts, respectively, on the choice of the direction of motion and of the speed. The double bias depends on two different non-local sensing cues coming from the external environment. We analyze how the size of the cell and the way of sensing the environment with respect to the variation of the external fields affect the cell population dynamics by recovering an appropriate macroscopic limit and directly integrating the kinetic transport equation. A comparison between the solutions of the transport equation and of the proper macroscopic limit is also performed.

Non-muscle myosin II as a predictive factor in head and neck squamous cell carcinoma

Background

The present study attempted to provide information regarding non-muscle myosin II (MII) isoforms immunoreactivity in patients with head and neck squamous cell carcinoma (HNSCC) and analysis of the patients’ clinical status after 5 years of monitoring.

Material and Methods

A semiquantitative analysis of the immunoreactivity of the MII isoforms was performed in 54 surgical specimens and its correlation with clinical and pathological variables and prognosis was verified. Data were analyzed using chi-square, Mann-Whitney and Kruskal-Wallis tests. To evaluate the survival over the total monitoring time and any connection with the proteins studied, the Kaplan-Meier analysis was used. P values ≤0.05 were considered statistically significant.

Results

In the advanced stages of pathological tumor-node-metastasis, the expression of MIIB in adjacent non-neoplastic epithelial tissues tended to increase (p = 0.057). In tumoral zones there was an association of high expression among the three isoforms (MIIA/MIIB p=0,001, MIIB/MIIC p=0,006 and MIIA/MIIC p=0,012). Negative clinical evolution in patients was directly correlated to increased MIIC expression in the tumoral zone of invasion in HNSCC (p = 0.017). Based on clinical evolution after the monitoring period, patients with tumors expressing MIIC had poorer prognoses (p = 0.048).

Conclusions

The present study suggests that MIIB expression in non-neoplastic adjacent epithelial tissues may indicate a potential for regional metastasis and that MIIC expression in the tumoral zone of invasion is predictive of negative evolution of the disease.

Key words:Head and neck squamous cell carcinoma, oral cancer, myosin type II, non-muscle myosin, immunohistochemistry.

A particle system approach to aggregation phenomena

Inspired by a PDE–ODE system of aggregation developed in the biomathematical literature, we investigate an interacting particle system representing aggregation at the level of individuals. We prove that the empirical density of the individual converges to the solution of the PDE–ODE system.

A space-jump derivation for non-local models of cell-cell adhesion and non-local chemotaxis

Cellular adhesion provides one of the fundamental forms of biological interaction between cells and their surroundings, yet the continuum modelling of cellular adhesion has remained mathematically challenging. In 2006, Armstrong et al. proposed a mathematical model in the form of an integro-partial differential equation. Although successful in applications, a derivation from an underlying stochastic random walk has remained elusive. In this work we develop a framework by which non-local models can be derived from a space-jump process. We show how the notions of motility and a cell polarization vector can be naturally included. With this derivation we are able to include microscopic biological properties into the model. We show that particular choices yield the original Armstrong model, while others lead to more general models, including a doubly non-local adhesion model and non-local chemotaxis models. Finally, we use random walk simulations to confirm that the corresponding continuum model represents the mean field behaviour of the stochastic random walk.

A continuum approximation to an off-lattice individual-cell based model of cell migration and adhesion

Cell-cell adhesion plays a key role in the collective migration of cells and in determining correlations in the relative cell positions and velocities. Recently, it was demonstrated that off-lattice individual cell based models (IBMs) can accurately capture the correlations observed experimentally in a migrating cell population. However, IBMs are often computationally expensive and difficult to analyse mathematically. Traditional continuum-based models, in contrast, are amenable to mathematical analysis and are computationally less demanding, but typically correspond to a mean-field approximation of cell migration and so ignore cell-cell correlations. In this work, we address this problem by using an off-lattice IBM to derive a continuum approximation which does take into account correlations. We furthermore show that a mean-field approximation of the off-lattice IBM leads to a single partial integro-differential equation of the same form as proposed by Sherratt and co-workers to model cell adhesion. The latter is found to be only effective at approximating the ensemble averaged cell number density when mechanical interactions between cells are weak. In contrast, the predictions of our novel continuum model for the time-evolution of the ensemble cell number density distribution and of the density-density correlation function are in close agreement with those obtained from the IBM for a wide range of mechanical interaction strengths. In particular, we observe 'front-like' propagation of cells in simulations using both our IBM and our continuum model, but not in the continuum model simulations obtained using the mean-field approximation.

Matrigel induces L-plastin expression and promotes L-plastin-dependent invasion in human cholangiocarcinoma cells

The function of the extracellular matrix (ECM) in the tumor microenvironment is not limited to forming a barrier against tumor invasion. As demonstrated in pathological specimens, cholangiocarcinoma samples exhibit an enrichment of the ECM surrounding the tumor cells. In this study, we examined involvement of the ECM in the regulation of the invasiveness of cholangiocarcinoma cells. The RMCCA1 cholangiocarcinoma cell line was cultured in culture plates either with or without a coating of reconstituted ECM basement membrane preparation (BD Matrigel matrix). In vitro invasion assays were then performed. In addition, the protein expression profile of the cell line was examined using two-dimensional gel electrophoresis and liquid chromatography-tandem mass spectrometry. The proteins expressed and their functional associations with cancer progression were determined. Culturing the RMCCA1 cell line in the BD Matrigel matrix induced cell invasion. Numerous proteins were induced by culturing the RMCCA1 cells in the matrix gel. The expression of L-plastin, an actin-binding protein, was significantly upregulated. The knockdown of L-plastin expression by siRNA silencing significantly suppressed the cellular response to matrix gel-stimulated cancer cell invasion. The ECM promotes the invasiveness of cholangiocarcinoma cells by upregulating L-plastin. These findings suggest the potential exploitation of this mechanism as a means of inhibiting the invasiveness of cholangiocarcinoma cells.

A non-local evolution equation model of cell-cell adhesion in higher dimensional space

A model for cell-cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell-cell adhesion, J. Theor. Biol. 243 (2006), pp. 98-113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dimensional infinite domain. It has a non-local flux term which models the component of cell motion attributable to cells having formed bonds with other nearby cells. Using the theory of fractional powers of analytic semigroup generators and working in spaces with bounded uniformly continuous derivatives, the local existence of classical solutions is proved. Positivity and boundedness of solutions is then established, leading to global existence of solutions. Finally, the asymptotic behaviour of solutions about the spatially uniform state is considered. The model is illustrated by simulations that can be applied to in vitro wound closure experiments.

Interleukin 11 regulates endometrial cancer cell adhesion and migration via STAT3

Endometrial carcinoma is the most common gynaecological malignancy. There is however a lack of curative therapies, especially for patients diagnosed with late stage, recurrent or aggressive disease, who have a poor prognosis. Interleukin (IL) 11 is a pleiotropic cytokine that has a role in a number of cancers including colon and breast cancer. IL11 was recently found to be upregulated in endometrial cancers, however the function of IL11 in endometrial cancer is not known. This study aimed to determine the effects of IL11 on endometrial cancer cell proliferation, adhesion and migration. Three endometrial cancer cell lines, Ishikawa, HEC-1A and AN3CA (derived from endometrial cancers grade I, II and III, respectively), were used to determine the effect of IL11 on endometrial cancer cell function. Cell proliferation and viability were assessed by BrdU and Wst-1 assays. Cell adhesion to the extracellular matrix proteins fibronectin, collagen I and IV, vitronectin and laminin was assessed. Modified boyden chambers were utilized to access IL11 action on migration and invasion, respectively. The specific effect of IL11 action on these processes was determined using a unique IL11 inhibitor. IL11 phosphorylated (p)-STAT3 protein abundance in all 3 cell lines but had no effect on pERK and pAKT abundance. Similarly, IL11 had no effect on cell proliferation and viability but increased adhesion of ANC3A cells to fibronectin while having no effect on the other extracellular matrix proteins. IL11 did not alter the adhesive properties of the Ishikawa and HEC-1A cells. In the AN3CA cells, IL11 treatment resulted in a 50% increase in migration and co-treatment with the specific IL11 inhibitor or a STAT3 inhibitor abolished the effect. This study shows a role for IL11 in endometrial cancer and suggests IL11 may be involved in endometrial cancer development and thus may be useful as a therapeutic target.

Establishment and validation of computational model for MT1-MMP dependent ECM degradation and intervention strategies

MT1-MMP is a potent invasion-promoting membrane protease employed by aggressive cancer cells. MT1-MMP localizes preferentially at membrane protrusions called invadopodia where it plays a central role in degradation of the surrounding extracellular matrix (ECM). Previous reports suggested a role for a continuous supply of MT1-MMP in ECM degradation. However, the turnover rate of MT1-MMP and the extent to which the turnover contributes to the ECM degradation at invadopodia have not been clarified. To approach this problem, we first performed FRAP (Fluorescence Recovery after Photobleaching) experiments with fluorescence-tagged MT1-MMP focusing on a single invadopodium and found very rapid recovery in FRAP signals, approximated by double-exponential plots with time constants of 26 s and 259 s. The recovery depended primarily on vesicle transport, but negligibly on lateral diffusion. Next we constructed a computational model employing the observed kinetics of the FRAP experiments. The simulations successfully reproduced our FRAP experiments. Next we inhibited the vesicle transport both experimentally, and in simulation. Addition of drugs inhibiting vesicle transport blocked ECM degradation experimentally, and the simulation showed no appreciable ECM degradation under conditions inhibiting vesicle transport. In addition, the degree of the reduction in ECM degradation depended on the degree of the reduction in the MT1-MMP turnover. Thus, our experiments and simulations have established the role of the rapid turnover of MT1-MMP in ECM degradation at invadopodia. Furthermore, our simulations suggested synergetic contributions of proteolytic activity and the MT1-MMP turnover to ECM degradation because there was a nonlinear and marked reduction in ECM degradation if both factors were reduced simultaneously. Thus our computational model provides a new in silico tool to design and evaluate intervention strategies in cancer cell invasion.

Prevention of invasion is important in cancer therapy. MT1-MMP is a membrane protein involved in degradation of ECM (extracellular matrix) that is highly expressed at invadopodia, which are small protrusions of cancer cells. ECM degradation by MT1-MMP at invadopodia is hypothesized as the initial step of cancer cell invasion. However, MT1-MMP is inhibited by the endogenous inhibitor TIMP-2, so continuous turnover of MT1-MMP at the surface of invadopodia would be required. In agreement, it has been reported that the blockade of vesicle transport, which is one mechanism involved in the turnover, blocked the ECM degradation. However, the turnover rate of MT1-MMP at invadopodia and the extent to which the turnover is critical for the degradation of ECM have not been clarified. In this report we measured the turnover rate of MT1-MMP at a single invadopodium and found rapid turnover rates with time constants of 26 s and 259 s, which primarily depended on the vesicle transport. A computational model was constructed based on the observed kinetics. If we blocked the rapid turnover, the ECM degradation was blocked both experimentally and in simulations. These results established the role of the rapid turnover of MT1-MMP in the ECM degradation at invadopodia.

Invasion from a cell aggregate--the roles of active cell motion and mechanical equilibrium

Cell invasion from an aggregate into a surrounding extracellular matrix (ECM) is an important process during development disease, e.g., vascular network assembly or tumor progression. To describe the behavior emerging from autonomous cell motility, cell-cell adhesion and contact guidance by ECM filaments, we propose a suitably modified cellular Potts model. We consider an active cell motility process in which internal polarity is governed by a positive feedback from cell displacements, a mechanism that can result in highly persistent motion when constrained by an oriented ECM structure. The model allows us to explore the interplay between haptotaxis, matrix degradation and active cell movement. We show that for certain conditions the cells are able to both invade the ECM and follow the ECM tracks. Furthermore, we argue that enforcing mechanical equilibrium within a bulk cell mass is of key importance in multicellular simulations.

Cellular modeling of cancer invasion: integration of in silico and in vitro approaches

Cancer invasion is one of the hallmarks of cancer and a prerequisite for cancer metastasis. However, the invasive process is very complex, depending on multiple correlated intrinsic and environmental factors, and thus is difficult to study experimentally in a fully controlled way. Therefore, there is an increased demand for interdisciplinary integrated approaches combining laboratory experiments with multiscale in silico modeling. In this review, we will summarize current computational techniques applicable to model cancer invasion in silico, with a special focus on a class of individual-cell-based models developed in our laboratories. We also discuss their integration with traditional and novel in vitro experimentation, including new invasion assays whose design was inspired by computational modeling.

SPARC mediates Src-induced disruption of actin cytoskeleton via inactivation of small GTPases Rho-Rac-Cdc42

The matricellular glycoprotein Secreted Protein Acidic and Rich in Cysteine (SPARC) plays an important role in the regulation of cell adhesion and proliferation as well as in tumorigenesis and metastasis. Earlier, we reported that, in addition to its potent anti-angiogenic functions, SPARC also induces apoptosis in medulloblastoma cells, mediated by autophagy. We therefore sought to investigate the underlying molecular mechanism through which SPARC inhibits migration and invasion of Daoy medulloblastoma cells, both in vitro and in vivo. For this study, we used SPARC-overexpressing stable Daoy medulloblastoma cells. SPARC overexpression in Daoy medulloblastoma cells inhibited migration and invasion in vitro. Additionally, SPARC overexpression significantly suppressed the activity of Rho, Rac and Cdc42, which all regulate the actin cytoskeleton. This suppression was accompanied by an increase in the phosphorylation of Src at Tyr-416, which led to a loss of actin stress fibers and focal contacts and a decrease in the phosphorylation level of cofilin. The reduced phosphorylation level of cofilin, which is indicative of receding Rho function, in turn led to inhibition of active Rho A. To confirm the role of SPARC in inhibition of migration and invasion of Daoy medulloblastoma cells, we transfected parental and SPARC-overexpressing Daoy cells with a plasmid vector carrying siRNA against SPARC. Transfection with SPARC siRNA reversed Src-mediated disruption of the cytoskeleton organization as well as dephosphorylation of cofilin and activation of Rho A. Taken together, these results establish SPARC as an effector of Src-induced cytoskeleton disruption in Daoy medulloblastoma cells, which subsequently led to decreased migration and invasion.

Cellular automata and integrodifferential equation models for cell renewal in mosaic tissues

Mosaic tissues are composed of two or more genetically distinct cell types. They occur naturally, and are also a useful experimental method for exploring tissue growth and maintenance. By marking the different cell types, one can study the patterns formed by proliferation, renewal and migration. Here, we present mathematical modelling suggesting that small changes in the type of interaction that cells have with their local cellular environment can lead to very different outcomes for the composition of mosaics. In cell renewal, proliferation of each cell type may depend linearly or nonlinearly on the local proportion of cells of that type, and these two possibilities produce very different patterns. We study two variations of a cellular automaton model based on simple rules for renewal. We then propose an integrodifferential equation model, and again consider two different forms of cellular interaction. The results of the continuous and cellular automata models are qualitatively the same, and we observe that changes in local environment interaction affect the dynamics for both. Furthermore, we demonstrate that the models reproduce some of the patterns seen in actual mosaic tissues. In particular, our results suggest that the differing patterns seen in organ parenchymas may be driven purely by the process of cell replacement under different interaction scenarios.

Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation

The ability of cancer cells to break out of tissue compartments and invade locally gives solid tumours a defining deadly characteristic. One of the first steps of invasion is the remodelling of the surrounding tissue or extracellular matrix (ECM) and a major part of this process is the over-expression of proteolytic enzymes, such as the urokinase-type plasminogen activator (uPA) and matrix metalloproteinases (MMPs), by the cancer cells to break down ECM proteins. Degradation of the matrix enables the cancer cells to migrate through the tissue and subsequently to spread to secondary sites in the body, a process known as metastasis. In this paper we undertake an analysis of a mathematical model of cancer cell invasion of tissue, or ECM, which focuses on the role of the urokinase plasminogen activation system. The model consists of a system of five reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, uPA, uPA inhibitors, plasmin and the host tissue. Cancer cells react chemotactically and haptotactically to the spatio-temporal effects of the uPA system. The results obtained from computational simulations carried out on the model equations produce dynamic heterogeneous spatio-temporal solutions and using linear stability analysis we show that this is caused by a taxis-driven instability of a spatially homogeneous steady-state. Finally we consider the biological implications of the model results, draw parallels with clinical samples and laboratory based models of cancer cell invasion using three-dimensional invasion assay, and go on to discuss future development of the model.

Suppression of uPAR retards radiation-induced invasion and migration mediated by integrin β1/FAK signaling in medulloblastoma

BACKGROUND

Despite effective radiotherapy for the initial stages of cancer, several studies have reported the recurrence of various cancers, including medulloblastoma. Here, we attempt to capitalize on the radiation-induced aggressive behavior of medulloblastoma cells by comparing the extracellular protease activity and the expression pattern of molecules, known to be involved in cell adhesion, migration and invasion, between non-irradiated and irradiated cells.

METHODOLOGY/PRINCIPAL FINDINGS

We identified an increase in invasion and migration of irradiated compared to non-irradiated medulloblastoma cells. RT-PCR analysis confirmed increased expression of uPA, uPAR, focal adhesion kinase (FAK), N-Cadherin and integrin subunits (e.g., α3, α5 and β1) in irradiated cells. Furthermore, we noticed a ∼2-fold increase in tyrosine phosphorylation of FAK in irradiated cells. Immunoprecipitation studies confirmed increased interaction of integrin β1 and FAK in irradiated cells. In addition, our results show that overexpression of uPAR in cancer cells can mimic radiation-induced activation of FAK signaling. Moreover, by inhibiting FAK phosphorylation, we were able to reduce the radiation-induced invasiveness of the cancer cells. In this vein, we studied the effect of siRNA-mediated knockdown of uPAR on cell migration and adhesion in irradiated and non-irradiated medulloblastoma cells. Downregulation of uPAR reduced the radiation-induced adhesion, migration and invasion of the irradiated cells, primarily by inhibiting phosphorylation of FAK, Paxillin and Rac-1/Cdc42. As observed from the immunoprecipitation studies, uPAR knockdown reduced interaction among the focal adhesion molecules, such as FAK, Paxillin and p130Cas, which are known to play key roles in cancer metastasis. Pretreatment with uPAR shRNA expressing construct reduced uPAR and phospho FAK expression levels in pre-established medulloblastoma in nude mice.

CONCLUSION/SIGNIFICANCE

Taken together, our results show that radiation enhances uPAR-mediated FAK signaling and by targeting uPAR we can inhibit radiation-activated cell adhesion and migration both in vitro and in vivo.

How does cellular contact affect differentiation mediated pattern formation?

In this paper, we present a two-population continuous integro-differential model of cell differentiation, using a non-local term to describe the influence of the local environment on differentiation. We investigate three different versions of the model, with differentiation being cell autonomous, regulated via a community effect, or weakly dependent on the local cellular environment. We consider the spatial patterns that such different modes of differentiation produce, and investigate the formation of both stripes and spots by the model. We show that pattern formation only occurs when differentiation is regulated by a strong community effect. In this case, permanent spatial patterns only occur under a precise relationship between the parameters characterising cell dynamics, although transient patterns can persist for biologically relevant timescales when this condition is relaxed. In all cases, the long-lived patterns consist only of stripes, not spots.