Biology subjects

Chaplain, M. A.

Publications and source records attributed to Chaplain, M. A..

10 recordsLinked to original sources

bioRxiv2026

Modelling phenotypic plasticity in cancer invasion and metastasis: from microscopic interactions to macroscopic dynamics

Cancer progression is driven by the interplay between cancer cell phenotypic variability regulated by EMT/MET, and cell-cell and cell-matrix interactions. Starting with an individual-based model, in which every cell is characterised by its position, velocity and a continuously varying epithelial-mesenchymal phenotype, we derive, via a kinetic description and a mean-field limit, two alternative macroscopic formulations: an Euler-like system that couples mass and momentum to the phenotypic variable, and a single advection-aggregation-diffusion equation (AADE) for the cancer cell density. Both macroscopic models retain the non-local adhesion-repulsion forces, haptotactic response to an evolving ECM, and phenotype-dependent transition dynamics driven by TGF-{beta}. Numerical experiments in two spatial dimensions indicate that the macroscopic equations reproduce key scenarios obtained at the individual scale. In particular, a microscopic-macroscopic comparison shows that the AADE density reproduces acurately both the spatial localisation and the phenotypic decomposition of the individual cell population. We also demonstrate that varying only the steepness of the TGF-{beta} switch function, changes the EMT response from an almost binary epithelial-mesenchymal (EM) separation to a partial EM phenotypes. This study provides a systematic bridge from stochastic, heterogeneous cell dynamics to continuum descriptions, for investigating phenotype driven tumour invasion and supporting the choice of macroscopic models in large-scale simulations and analytical studies.

cancer biology↗

bioRxiv2025

Mathematical Modeling of Cancer Cell Invasion of Tissue: Development of an in silico Organotypic Assay

BackgroundOrganotypic assays are three-dimensional in vitro models widely used in cancer research to mimic the in vivo extracellular matrix (ECM) and to study cancer cell invasion by allowing investigation of critical interactions between tumor cells and their microenvironment. During invasion, cancer cells undergo genetic and epigenetic changes that disrupt cell-cell adhesion, enabling detachment from the primary tumor. Subsequently, invasive cells must (i) breach the basement membrane, a dense protein meshwork that restricts cell movement, and (ii) migrate through the surrounding ECM. This process relies on proteolytic enzyme secretion to degrade structural barriers, followed by cell-matrix adhesion-mediated migration. MethodsWe present an in silico model of cancer cell invasion in organotypic assays. The model is formulated as a system of partial differential equations capturing spatiotemporal dynamics, with nonlocal terms representing preferential adhesion-driven movement. Key variables in the model are cancer cells, proteolytic enzymes, and the ECM. ResultsComputational simulations demonstrate that modulation of cell-cell and cell-matrix adhesion parameters significantly influences tumor invasiveness. This result is consistent with experimental observations, demonstrating the models ability to accurately reflect in vitro behavior.

biophysics↗

bioRxiv2025

Modelling cancer cell dormancy in mice: statistical distributions predict reactivation times and survival dynamics

In predicting metastatic potential and improving treatment outcomes in cancer research, it is crucial that we understand the dynamics of cancer cell dormancy and reactivation. In this paper we propose, study, and evaluate a cancer growth model that incorporates cell death, dormancy, reactivation, and proliferation in the secondary sites. Using experimental data on mice, we test various statistical distributions and identify models that represent the asymmetry and variability observed in dormancy durations. Notably, the estimated cancer cell death rate remained consistent across all tested distributions, supporting its biological relevance as a robust parameter for modelling dormancy survival dynamics. The most suitable among the distributions we studied, the most suitable ones exhibit heavy-tails and asymmetric skewness; this aligns with the prolonged and rare dormancy periods expected of cancer cells. Our findings stress the importance of selecting appropriate statistical models for dormancy, both in predicting cancer cell reactivation events, and in informing therapeutic strategies that focus dormancy-driven metastasis.

cancer biology↗

bioRxiv2024

A genuinely hybrid, multiscale 3D cancer invasion and metastasis modelling framework

We introduce in this paper substantial enhancements to a previously proposed hybrid multiscale cancer invasion modelling framework to better reflect the biological reality and dynamics of cancer. These model updates contribute to a more accurate representation of cancer dynamics, they provide deeper insights and enhance our predictive capabilities. Key updates include the integration of porous medium-like diffusion for the evolution of Epithelial-like Cancer Cells and other essential cellular constituents of the system, more realistic modelling of Epithelial-Mesenchymal Transition and Mesenchymal-Epithelial Transition models with the inclusion of Transforming Growth Factor beta within the tumour microenvironment, and the introduction of Compound Poisson Process in the Stochastic Differential Equations that describe the migration behaviour of the Mesenchymal-like Cancer Cells. Another innovative feature of the model is its extension into a multi-organ metastatic framework. This framework connects various organs through a circulatory network, enabling the study of how cancer cells spread to secondary sites.

cancer biology↗

bioRxiv2022

Stochastic differential equation modelling of cancer cell migration and tissue invasion

Invasion of the surrounding tissue is a key aspect of cancer growth and spread involving a coordinated effort between cell migration and matrix degradation, and has been the subject of mathematical modelling for almost 30 years. In this current paper we address a long-standing question in the field of cancer cell migration modelling. Namely, identify the migratory pattern and spread of individual cancer cells, or small clusters of cancer cells, when the macroscopic evolution of the cancer cell colony is dictated by a specific partial differential equation (PDE). We show that the usual heuristic understanding of the diffusion and advection terms of the PDE being one-to-one responsible for the random and biased motion of the solitary cancer cells, respectively, is not precise. On the contrary, we show that the drift term of the correct stochastic differential equation (SDE) scheme that dictates the individual cancer cell migration, should account also for the divergence of the diffusion of the PDE. We support our claims with a number of numerical experiments and computational simulations.

biophysics↗

bioRxiv2021

Modelling rheumatoid arthritis: A hybrid modelling framework to describe pannus formation in a small joint

Rheumatoid arthritis (RA) is a chronic inflammatory disorder that causes pain, swelling and stiffness in the joints, and negatively impacts the life of affected patients. The disease does not have a cure yet, as there are still many aspects of this complex disorder that are not fully understood. While mathematical models can shed light on some of these aspects, to date there are few such models that can be used to better understand the disease. As a first step in the mechanistic understanding of RA, in this study we introduce a new hybrid mathematical modelling framework that describes pannus formation in a small proximal interphalangeal (PIP) joint. We perform numerical simulations with this new model, to investigate the impact of different levels of immune cells (macrophages and fibroblasts) on the degradation of bone and cartilage. Since many model parameters are unknown and cannot be estimated due to a lack of experiments, we also perform a sensitivity analysis of model outputs to various model parameters (single parameters or combinations of parameters). Finally, we discuss how our model could be applied to investigate current treatments for RA, for example, methotrexate, TNF-inhibitors or tocilizumab, which can impact different model parameters.

immunology↗

bioRxiv2020

Development of a Coupled Simulation Toolkit for Computational Radiation Biology Based on Geant4 and CompuCell3D

Understanding and designing clinical radiation therapy is one of the most important areas of state-of-the-art oncological treatment regimens. Decades of research have gone into developing sophisticated treatment devices and optimization protocols for schedules and dosages. In this paper, we presented a comprehensive computational platform that facilitates building of the sophisticated multi-cell-based model of how radiation affects the biology of living tissue. We designed and implemented a coupled simulation method, including a radiation transport model, and a cell biology model, to simulate the tumor response after irradiation. The radiation transport simulation was implemented through Geant4 which is an open-source Monte Carlo simulation platform that provides many flexibilities for users, as well as low energy DNA damage simulation physics, Geant4-DNA. The cell biology simulation was implemented using CompuCell3D (CC3D) which is a cell biology simulation platform. In order to couple Geant4 solver with CC3D, we developed a "bridging" module that extracts tumor cellular geometry of the CC3D simulation (including specification of the individual cells) and ported it to the Geant4 for radiation transport simulation. The cell dose and cell DNA damage distribution in multicellular system were obtained using Geant4. The tumor response was simulated using cell-based tissue models based on CC3D. By merging two powerful and widely used modeling platforms, CC3D and Geant4, we delivered a novel tool that can give us the ability to simulate the dynamics of biological tissue in the presence of ionizing radiation, which provides a powerful framework for quantifying the biological consequences of radiation therapy. The developed tool has an advantage on that it has strong extensibility due to the exploitability of two modeling platforms. In this introductory methods paper, we described our modeling platform in detail and showed how it can be applied to study the application of radiotherapy to a vascularized tumor.

biophysics↗

bioRxiv2019

Targeting Cellular DNA Damage Responses: Predicting in vivo treatment responses using an in vitro-calibrated agent-based mathematical model.

We combine a systems pharmacology approach with an agent-based modelling approach to simulate LoVo cells subjected to AZD6738, an ATR (ataxia telangiectasia mutated and rad3-related kinase) inhibiting anti-cancer drug that can hinder tumour proliferation by targeting cellular DNA damage responses. The agent-based model used in this study is governed by a set of empirically observable rules. By adjusting only the rules when moving between monolayer and multi-cellular tumour spheroid simulations, whilst keeping the fundamental mathematical model and parameters intact, the agent-based model is first parameterised by monolayer in vitro data and is thereafter used to simulate treatment responses in in vitro tumour spheroids subjected to dynamic drug delivery. Spheroid simulations are subsequently compared to in vivo data from xenografts in mice. The spheroid simulations are able to capture the dynamics of in vivo tumour growth and regression for approximately eight days post tumour injection. Translating quantitative information between in vitro and in vivo research remains a scientifically and financially challenging step in preclinical drug development processes. However, well-developed in silico tools can be used to facilitate this in vitro to in vivo translation, and in this article we exemplify how data-driven, agent-based models can be used to bridge the gap between in vitro and in vivo research. We further highlight how agent-based models, that are currently underutilised in pharmaceutical contexts, can be used in preclinical drug development.

cancer biology↗

bioRxiv2019

A mathematical multi-organ model for bidirectional epithelial-mesenchymal transitions in the metastatic spread of cancer

Cancer invasion and metastatic spread to secondary sites in the body are facilitated by a complex interplay between cancer cells of different phenotypes and their microenvironment. A trade-off between the cancer cells ability to invade the tissue and to metastasise, and their ability to proliferate has been observed. This gives rise to the classification of cancer cells into those of mesenchymal and epithelial phenotype, respectively. Additionally, mixed phenotypic states between these two extremes exist. Cancer cells can transit between these states via epithelial-mesenchymal transition (EMT) and the reverse process, mesenchymal-epithelial transition (MET). These processes are crucial both for the local tissue invasion and the metastatic spread of cancer cells. To shed light on the role of these phenotypic states and the transitions between them in the invasive and metastatic process, we extend our recently published multi-grid, hybrid, individual-based mathematical metastasis framework (Franssen et al., 2019a). In addition to cancer cells of epithelial and of mesenchymal phenotype, we now also include those of an intermediate partial-EMT phenotype. Furthermore, we allow for the switching between these phenotypic states via EMT and MET at the biologically appropriate steps of the invasion-metastasis cascade. We also account for the likelihood of spread of cancer cells to the various secondary sites and differentiate between the tissues of the organs involved in our simulations. Finally, we consider the maladaptation of metastasised cancer cells to the new tumour microenvironment at secondary sites as well as the immune response at these sites by accounting for cancer cell dormancy and death. This way, we create a first mathematical multi-organ model that explicitly accounts for EMT-processes in individual cancer cells in the context of the invasion-metastasis cascade.

cancer biology↗

bioRxiv2018

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 (tumour-induced angiogenesis), 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.\n\nTo 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 multi-grid, hybrid, individual-based approach. This framework accounts for the spatio-temporal evolution of mesenchymal- and epithelial-like cancer cells, as well as MT1-MMP and MMP-2 dynamics, and interactions with the extracellular matrix.\n\nUsing 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 like MMP-2.

cancer biology↗