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.

Evolutionary dynamics of glucose-deprived cancer cells: insights from experimentally informed mathematical modelling.

Glucose is a primary energy source for cancer cells. Several lines of evidence support the idea that monocarboxylate transporters, such as MCT1, elicit metabolic reprogramming of cancer cells in glucose-poor environments, allowing them to re-use lactate, a by-product of glucose metabolism, as an alternative energy source with serious consequences for disease progression. We employ a synergistic experimental and mathematical modelling approach to explore the evolutionary processes at the root of cancer cell adaptation to glucose deprivation, with particular focus on the mechanisms underlying the increase in MCT1 expression observed in glucose-deprived aggressive cancer cells. Data from in vitro experiments on breast cancer cells are used to inform and calibrate a mathematical model that comprises a partial integro-differential equation for the dynamics of a population of cancer cells structured by the level of MCT1 expression. Analytical and numerical results of this model suggest that environment-induced changes in MCT1 expression mediated by lactate-associated signalling pathways enable a prompt adaptive response of glucose-deprived cancer cells, while fluctuations in MCT1 expression due to epigenetic changes create the substrate for environmental selection to act upon, speeding up the selective sweep underlying cancer cell adaptation to glucose deprivation, and may constitute a long-term bet-hedging mechanism.

An individual-based model to explore the impact of psychological stress on immune infiltration into tumour spheroids.

In recentin vitroexperiments on co-culture between breast tumour spheroids and activated immune cells, it was observed that the introduction of the stress hormone cortisol resulted in a decreased immune cell infiltration into the spheroids. Moreover, the presence of cortisol deregulated the normal levels of the pro- and anti-inflammatory cytokines IFN-γand IL-10. We present an individual-based model to explore the interaction dynamics between tumour and immune cells under psychological stress conditions. With our model, we explore the processes underlying the emergence of different levels of immune infiltration, with particular focus on the biological mechanisms regulated by IFN-γand IL-10. The set-up of numerical simulations is defined to mimic the scenarios considered in the experimental study. Similarly to the experimental quantitative analysis, we compute a score that quantifies the level of immune cell infiltration into the tumour. The results of numerical simulations indicate that the motility of immune cells, their capability to infiltrate through tumour cells, their growth rate and the interplay between these cell parameters can affect the level of immune cell infiltration in different ways. Ultimately, numerical simulations of this model support a deeper understanding of the impact of biological stress-induced mechanisms on immune infiltration.

Discrete and continuum models for the coevolutionary dynamics between CD8+ cytotoxic T lymphocytes and tumour cells.

We present an individual-based model for the coevolutionary dynamics between CD8+ cytotoxic T lymphocytes (CTLs) and tumour cells. In this model, every cell is viewed as an individual agent whose phenotypic state is modelled by a discrete variable. For tumour cells, this variable represents a parameterization of the antigen expression profiles, while for CTLs it represents a parameterization of the target antigens of T-cell receptors (TCRs). We formally derive the deterministic continuum limit of this individual-based model, which comprises a non-local partial differential equation for the phenotype distribution of tumour cells coupled with an integro-differential equation for the phenotype distribution of CTLs. The biologically relevant homogeneous steady-state solutions of the continuum model equations are found. The linear-stability analysis of these steady-state solutions is then carried out in order to identify possible conditions on the model parameters that may lead to different outcomes of immune competition and to the emergence of patterns of phenotypic coevolution between tumour cells and CTLs. We report on computational results of the individual-based model, and show that there is a good agreement between them and analytical and numerical results of the continuum model. These results shed light on the way in which different parameters affect the coevolutionary dynamics between tumour cells and CTLs. Moreover, they support the idea that TCR-tumour antigen binding affinity may be a good intervention target for immunotherapy and offer a theoretical basis for the development of anti-cancer therapy aiming at engineering TCRs so as to shape their affinity for cancer targets.

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.

A Hybrid Discrete-Continuum Modelling Approach to Explore the Impact of T-Cell Infiltration on Anti-tumour Immune Response.

We present a spatial hybrid discrete-continuum modelling framework for the interaction dynamics between tumour cells and cytotoxic T cells, which play a pivotal role in the immune response against tumours. In this framework, tumour cells and T cells are modelled as individual agents while chemokines that drive the chemotactic movement of T cells towards the tumour are modelled as a continuum. We formally derive the continuum counterpart of this model, which is given by a coupled system that comprises an integro-differential equation for the density of tumour cells, a partial differential equation for the density of T cells and a partial differential equation for the concentration of chemokines. We report on computational results of the hybrid model and show that there is an excellent quantitative agreement between them and numerical solutions of the corresponding continuum model. These results shed light on the mechanisms that underlie the emergence of different levels of infiltration of T cells into the tumour and elucidate how T-cell infiltration shapes anti-tumour immune response. Moreover, to present a proof of concept for the idea that, exploiting the computational efficiency of the continuum model, extensive numerical simulations could be carried out, we investigate the impact of T-cell infiltration on the response of tumour cells to different types of anti-cancer immunotherapy.

A mathematical model to study the impact of intra-tumour heterogeneity on anti-tumour CD8+ T cell immune response.

Intra-tumour heterogeneity (ITH) has a strong impact on the efficacy of the immune response against solid tumours. The number of sub-populations of cancer cells expressing different antigens and the percentage of immunogenic cells (i.e. tumour cells that are effectively targeted by immune cells) in a tumour are both expressions of ITH. Here, we present a spatially explicit stochastic individual-based model of the interaction dynamics between tumour cells and CD8+ T cells, which makes it possible to dissect out the specific impact of these two expressions of ITH on anti-tumour immune response. The set-up of numerical simulations of the model is defined so as to mimic scenarios considered in previous experimental studies. Moreover, the ability of the model to qualitatively reproduce experimental observations of successful and unsuccessful immune surveillance is demonstrated. First, the results of numerical simulations of this model indicate that the presence of a larger number of sub-populations of tumour cells that express different antigens is associated with a reduced ability of CD8+ T cells to mount an effective anti-tumour immune response. Secondly, the presence of a larger percentage of tumour cells that are not effectively targeted by CD8+ T cells may reduce the effectiveness of anti-tumour immunity. Ultimately, the mathematical model presented in this paper may provide a framework to help biologists and clinicians to better understand the mechanisms that are responsible for the emergence of different outcomes of immunotherapy.

Evolutionary dynamics in an SI epidemic model with phenotype-structured susceptible compartment.

We present an SI epidemic model whereby a continuous structuring variable captures variability in proliferative potential and resistance to infection among susceptible individuals. The occurrence of heritable, spontaneous changes in these phenotypic characteristics and the presence of a fitness trade-off between resistance to infection and proliferative potential are explicitly incorporated into the model. The model comprises an ordinary differential equation for the number of infected individuals that is coupled with a partial integrodifferential equation for the population density function of susceptible individuals through an integral term. The expression for the basic reproduction number [Formula: see text] is derived, the disease-free equilibrium and endemic equilibrium of the model are characterised and a threshold theorem involving [Formula: see text] is proved. Analytical results are integrated with the results of numerical simulations of a calibrated version of the model based on the results of artificial selection experiments in a host-parasite system. The results of our mathematical study disentangle the impact of different evolutionary parameters on the spread of infectious diseases and the consequent phenotypic adaption of susceptible individuals. In particular, these results provide a theoretical basis for the observation that infectious diseases exerting stronger selective pressures on susceptible individuals and being characterised by higher infection rates are more likely to spread. Moreover, our results indicate that heritable, spontaneous phenotypic changes in proliferative potential and resistance to infection can either promote or prevent the spread of infectious diseases depending on the strength of selection acting on susceptible individuals prior to infection. Finally, we demonstrate that, when an endemic equilibrium is established, higher levels of resistance to infection and lower degrees of phenotypic heterogeneity among susceptible individuals are to be expected in the presence of infections which are characterised by lower rates of death and exert stronger selective pressures.

A Mathematical Study of the Influence of Hypoxia and Acidity on the Evolutionary Dynamics of Cancer.

Hypoxia and acidity act as environmental stressors promoting selection for cancer cells with a more aggressive phenotype. As a result, a deeper theoretical understanding of the spatio-temporal processes that drive the adaptation of tumour cells to hypoxic and acidic microenvironments may open up new avenues of research in oncology and cancer treatment. We present a mathematical model to study the influence of hypoxia and acidity on the evolutionary dynamics of cancer cells in vascularised tumours. The model is formulated as a system of partial integro-differential equations that describe the phenotypic evolution of cancer cells in response to dynamic variations in the spatial distribution of three abiotic factors that are key players in tumour metabolism: oxygen, glucose and lactate. The results of numerical simulations of a calibrated version of the model based on real data recapitulate the eco-evolutionary spatial dynamics of tumour cells and their adaptation to hypoxic and acidic microenvironments. Moreover, such results demonstrate how nonlinear interactions between tumour cells and abiotic factors can lead to the formation of environmental gradients which select for cells with phenotypic characteristics that vary with distance from intra-tumour blood vessels, thus promoting the emergence of intra-tumour phenotypic heterogeneity. Finally, our theoretical findings reconcile the conclusions of earlier studies by showing that the order in which resistance to hypoxia and resistance to acidity arise in tumours depend on the ways in which oxygen and lactate act as environmental stressors in the evolutionary dynamics of cancer cells.

Mechanical Models of Pattern and Form in Biological Tissues: The Role of Stress-Strain Constitutive Equations.

Mechanical and mechanochemical models of pattern formation in biological tissues have been used to study a variety of biomedical systems, particularly in developmental biology, and describe the physical interactions between cells and their local surroundings. These models in their original form consist of a balance equation for the cell density, a balance equation for the density of the extracellular matrix (ECM), and a force-balance equation describing the mechanical equilibrium of the cell-ECM system. Under the assumption that the cell-ECM system can be regarded as an isotropic linear viscoelastic material, the force-balance equation is often defined using the Kelvin-Voigt model of linear viscoelasticity to represent the stress-strain relation of the ECM. However, due to the multifaceted bio-physical nature of the ECM constituents, there are rheological aspects that cannot be effectively captured by this model and, therefore, depending on the pattern formation process and the type of biological tissue considered, other constitutive models of linear viscoelasticity may be better suited. In this paper, we systematically assess the pattern formation potential of different stress-strain constitutive equations for the ECM within a mechanical model of pattern formation in biological tissues. The results obtained through linear stability analysis and the dispersion relations derived therefrom support the idea that fluid-like constitutive models, such as the Maxwell model and the Jeffrey model, have a pattern formation potential much higher than solid-like models, such as the Kelvin-Voigt model and the standard linear solid model. This is confirmed by the results of numerical simulations, which demonstrate that, all else being equal, spatial patterns emerge in the case where the Maxwell model is used to represent the stress-strain relation of the ECM, while no patterns are observed when the Kelvin-Voigt model is employed. Our findings suggest that further empirical work is required to acquire detailed quantitative information on the mechanical properties of components of the ECM in different biological tissues in order to furnish mechanical and mechanochemical models of pattern formation with stress-strain constitutive equations for the ECM that provide a more faithful representation of the underlying tissue rheology.

Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion.

In this paper, we carry out a travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion. We consider two types of invasive fronts of tumour tissue into extracellular matrix (ECM), which represents healthy tissue. These types differ according to whether the density of ECM far ahead of the wave front is maximal or not. In the former case, we use a shooting argument to prove that there exists a unique travelling-wave solution for any positive propagation speed. In the latter case, we further develop this argument to prove that there exists a unique travelling-wave solution for any propagation speed greater than or equal to a strictly positive minimal wave speed. Using a combination of analytical and numerical results, we conjecture that the minimal wave speed depends monotonically on the degradation rate of ECM by tumour cells and the ECM density far ahead of the front.

A hybrid discrete-continuum approach to model Turing pattern formation.

Since its introduction in 1952, with a further refinement in 1972 by Gierer and Meinhardt, Turing's (pre-)pattern theory (the chemical basis of morphogenesis) has been widely applied to a number of areas in developmental biology, where evolving cell and tissue structures are naturally observed. The related pattern formation models normally comprise a system of reaction-diffusion equations for interacting chemical species (morphogens), whose heterogeneous distribution in some spatial domain acts as a template for cells to form some kind of pattern or structure through, for example, differentiation or proliferation induced by the chemical pre-pattern. Here we develop a hybrid discrete-continuum modelling framework for the formation of cellular patterns via the Turing mechanism. In this framework, a stochastic individual-based model of cell movement and proliferation is combined with a reaction-diffusion system for the concentrations of some morphogens. As an illustrative example, we focus on a model in which the dynamics of the morphogens are governed by an activator-inhibitor system that gives rise to Turing pre-patterns. The cells then interact with the morphogens in their local area through either of two forms of chemically-dependent cell action: Chemotaxis and chemically-controlled proliferation. We begin by considering such a hybrid model posed on static spatial domains, and then turn to the case of growing domains. In both cases, we formally derive the corresponding deterministic continuum limit and show that that there is an excellent quantitative match between the spatial patterns produced by the stochastic individual-based model and its deterministic continuum counterpart, when sufficiently large numbers of cells are considered. This paper is intended to present a proof of concept for the ideas underlying the modelling framework, with the aim to then apply the related methods to the study of specific patterning and morphogenetic processes in the future.

Comparative study between discrete and continuum models for the evolution of competing phenotype-structured cell populations in dynamical environments.

Deterministic continuum models formulated as nonlocal partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the adaptation of asexual species to periodically fluctuating environmental conditions. These models are usually defined on the basis of population-scale phenomenological assumptions and cannot capture adaptive phenomena that are driven by stochastic variability in the evolutionary paths of single individuals. In light of these considerations, in this paper we develop a stochastic individual-based model for the coevolution of two competing phenotype-structured cell populations that are exposed to time-varying nutrient levels and undergo spontaneous, heritable phenotypic changes with different probabilities. Here, the evolution of every cell is described by a set of rules that result in a discrete-time branching random walk on the space of phenotypic states, and nutrient levels are governed by a difference equation in which a sink term models nutrient consumption by the cells. We formally show that the deterministic continuum counterpart of this model comprises a system of nonlocal partial differential equations for the cell population density functions coupled with an ordinary differential equation for the nutrient concentration. We compare the individual-based model and its continuum analog, focusing on scenarios whereby the predictions of the two models differ. The results obtained clarify the conditions under which significant differences between the two models can emerge due to bottleneck effects that bring about both lower regularity of the density functions of the two populations and more pronounced demographic stochasticity. In particular, bottleneck effects emerge in the presence of lower probabilities of phenotypic variation and are more apparent when the two populations are characterized by lower fitness initial mean phenotypes and smaller initial levels of phenotypic heterogeneity. The emergence of these effects, and thus the agreement between the two modeling approaches, is also dependent on the initial proportions of the two populations. As an illustrative example, we demonstrate the implications of these results in the context of the mathematical modeling of the early stage of metastatic colonization of distant organs.

A Mathematical Dissection of the Adaptation of Cell Populations to Fluctuating Oxygen Levels.

The disordered network of blood vessels that arises from tumour angiogenesis results in variations in the delivery of oxygen into the tumour tissue. This brings about regions of chronic hypoxia (i.e. sustained low oxygen levels) and regions with alternating periods of low and relatively higher oxygen levels, and makes it necessary for cancer cells to adapt to fluctuating environmental conditions. We use a phenotype-structured model to dissect the evolutionary dynamics of cell populations exposed to fluctuating oxygen levels. In this model, the phenotypic state of every cell is described by a continuous variable that provides a simple representation of its metabolic phenotype, ranging from fully oxidative to fully glycolytic, and cells are grouped into two competing populations that undergo heritable, spontaneous phenotypic variations at different rates. Model simulations indicate that, depending on the rate at which oxygen is consumed by the cells, dynamic nonlinear interactions between cells and oxygen can stimulate chronic hypoxia and cycling hypoxia. Moreover, the model supports the idea that under chronic-hypoxic conditions lower rates of phenotypic variation lead to a competitive advantage, whereas higher rates of phenotypic variation can confer a competitive advantage under cycling-hypoxic conditions. In the latter case, the numerical results obtained show that bet-hedging evolutionary strategies, whereby cells switch between oxidative and glycolytic phenotypes, can spontaneously emerge. We explain how these results can shed light on the evolutionary process that may underpin the emergence of phenotypic heterogeneity in vascularised tumours.

From a discrete model of chemotaxis with volume-filling to a generalized Patlak-Keller-Segel model.

We present a discrete model of chemotaxis whereby cells responding to a chemoattractant are seen as individual agents whose movement is described through a set of rules that result in a biased random walk. In order to take into account possible alterations in cellular motility observed at high cell densities (i.e. volume-filling), we let the probabilities of cell movement be modulated by a decaying function of the cell density. We formally show that a general form of the celebrated Patlak-Keller-Segel (PKS) model of chemotaxis can be formally derived as the appropriate continuum limit of this discrete model. The family of steady-state solutions of such a generalized PKS model are characterized and the conditions for the emergence of spatial patterns are studied via linear stability analysis. Moreover, we carry out a systematic quantitative comparison between numerical simulations of the discrete model and numerical solutions of the corresponding PKS model, both in one and in two spatial dimensions. The results obtained indicate that there is excellent quantitative agreement between the spatial patterns produced by the two models. Finally, we numerically show that the outcomes of the two models faithfully replicate those of the classical PKS model in a suitable asymptotic regime.

Evolutionary dynamics of competing phenotype-structured populations in periodically fluctuating environments.

Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in ecology, which is used to explain how species may survive when faced with the evolutionary risks associated with temporally varying environments. In order to support a deeper understanding of the adaptive role of spontaneous phenotypic variations in fluctuating environments, we consider a system of non-local partial differential equations modelling the evolutionary dynamics of two competing phenotype-structured populations in the presence of periodically oscillating nutrient levels. The two populations undergo heritable, spontaneous phenotypic variations at different rates. The phenotypic state of each individual is represented by a continuous variable, and the phenotypic landscape of the populations evolves in time due to variations in the nutrient level. Exploiting the analytical tractability of our model, we study the long-time behaviour of the solutions to obtain a detailed mathematical depiction of the evolutionary dynamics. The results suggest that when nutrient levels undergo small and slow oscillations, it is evolutionarily more convenient to rarely undergo spontaneous phenotypic variations. Conversely, under relatively large and fast periodic oscillations in the nutrient levels, which bring about alternating cycles of starvation and nutrient abundance, higher rates of spontaneous phenotypic variations confer a competitive advantage. We discuss the implications of our results in the context of cancer metabolism.

Bridging the gap between individual-based and continuum models of growing cell populations.

Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations that describe the evolution of cellular densities in response to pressure gradients generated by population growth. Little prior work has explored the relation between such continuum models and related single-cell-based models. We present here a simple stochastic individual-based model for the spatial dynamics of multicellular systems whereby cells undergo pressure-driven movement and pressure-dependent proliferation. We show that nonlinear partial differential equations commonly used to model the spatial dynamics of growing cell populations can be formally derived from the branching random walk that underlies our discrete model. Moreover, we carry out a systematic comparison between the individual-based model and its continuum counterparts, both in the case of one single cell population and in the case of multiple cell populations with different biophysical properties. The outcomes of our comparative study demonstrate that the results of computational simulations of the individual-based model faithfully mirror the qualitative and quantitative properties of the solutions to the corresponding nonlinear partial differential equations. Ultimately, these results illustrate how the simple rules governing the dynamics of single cells in our individual-based model can lead to the emergence of complex spatial patterns of population growth observed in continuum models.

A structured population model of clonal selection in acute leukemias with multiple maturation stages.

Recent progress in genetic techniques has shed light on the complex co-evolution of malignant cell clones in leukemias. However, several aspects of clonal selection still remain unclear. In this paper, we present a multi-compartmental continuously structured population model of selection dynamics in acute leukemias, which consists of a system of coupled integro-differential equations. Our model can be analysed in a more efficient way than classical models formulated in terms of ordinary differential equations. Exploiting the analytical tractability of this model, we investigate how clonal selection is shaped by the self-renewal fraction and the proliferation rate of leukemic cells at different maturation stages. We integrate analytical results with numerical solutions of a calibrated version of the model based on real patient data. In summary, our mathematical results formalise the biological notion that clonal selection is driven by the self-renewal fraction of leukemic stem cells and the clones that possess the highest value of this parameter are ultimately selected. Moreover, we demonstrate that the self-renewal fraction and the proliferation rate of non-stem cells do not have a substantial impact on clonal selection. Taken together, our results indicate that interclonal variability in the self-renewal fraction of leukemic stem cells provides the necessary substrate for clonal selection to act upon.

A Mathematical Framework for Modelling the Metastatic Spread of Cancer.

Cancer is a complex disease that starts with mutations of key genes in one cell or a small group of cells at a primary site in the body. If these cancer cells continue to grow successfully and, at some later stage, invade the surrounding tissue and acquire a vascular network, they can spread to distant secondary sites in the body. This process, known as metastatic spread, is responsible for around 90% of deaths from cancer and is one of the so-called hallmarks of cancer. To shed light on the metastatic process, we present a mathematical modelling framework that captures for the first time the interconnected processes of invasion and metastatic spread of individual cancer cells in a spatially explicit manner-a multigrid, hybrid, individual-based approach. This framework accounts for the spatiotemporal evolution of mesenchymal- and epithelial-like cancer cells, membrane-type-1 matrix metalloproteinase (MT1-MMP) and the diffusible matrix metalloproteinase-2 (MMP-2), and for their interactions with the extracellular matrix. Using computational simulations, we demonstrate that our model captures all the key steps of the invasion-metastasis cascade, i.e. invasion by both heterogeneous cancer cell clusters and by single mesenchymal-like cancer cells; intravasation of these clusters and single cells both via active mechanisms mediated by matrix-degrading enzymes (MDEs) and via passive shedding; circulation of cancer cell clusters and single cancer cells in the vasculature with the associated risk of cell death and disaggregation of clusters; extravasation of clusters and single cells; and metastatic growth at distant secondary sites in the body. By faithfully reproducing experimental results, our simulations support the evidence-based hypothesis that the membrane-bound MT1-MMP is the main driver of invasive spread rather than diffusible MDEs such as MMP-2.