Final Report Summary - M5CGS (From Mutations to Metastases: Multiscale Mathematical Modelling of Cancer Growth and Spread)
This project developed novel multi-scale mathematical models for the growth and spread of cancer and has focused on three main scales of interest: the sub-cellular, cellular and tissue scale.
At the sub-cellular scale, we developed novel spatio-temporal and stochastic spatio-temproal mathematical models of transcription factors and gene regulatory networks that have an important role in cancer development – Hes1, p53-Mdm2 and NF-kB. These systems are so-called “negative feedback systems” and have trademark oscillatory dynamics in terms of the concentrations of the mRNA and protein molecules. We derived systems of partial differential equations to capture the evolution in space and time of the variables in the Hes1 and p53-Mdm2 systems. Through computational simulations we showed that our reaction-diffusion models are able to produce sustained oscillations both spatially and temporally, accurately reflecting experimental evidence and advancing previous models. We have shown rigorously that it is the spatial movement of the molecules (proteins and mRNA) that causes the oscillations.
At the cellular scale our modelling developed a force-based, individual-based model which links single cell migration with matrix fibres and cell-matrix interactions through contact guidance and matrix remodelling. With this approach we highlighted the significance of the cell’s environment on its migration. We investigated the influence of matrix stiffness, matrix architecture and cell speed on migration, using quantitative measures that allow us to compare the results to experiments. We found that matrix remodelling due to cell traction forces might be an important part in two dimensional cell migration. We further developed this into a multi-scale multi-compartment model that accounts for the principal biophysical interactions and adhesion pathways not only at a cell–cell level but also at the level of cell colonies. Our simulation results demonstrated that adhesion/separation forces between cells may be lower in cell colonies than traditional isolated single-cell experiments infer. We also developed a hybrid, individual-based approach that analyses spatio-temporal dynamics of solid tumour growth at the level of cells, linking individual cell behaviour with the macroscopic behaviour of cell organisation and the microenvironment. We also used this multi-scale hybrid model to investigate the optimum sequencing and scheduling of these chemotherapy and radiotherapy treatments, and the impact of internal and external heterogeneity on the spatio-temporal patterning of the distribution of cancer cells and their response to different treatment schedules. This computational model is currently being explored as a tool to assist in clinical decision making with Clinical Oncologists and Radiation Oncologists at Ninewells Hospital, Dundee.
At the tissue scale we developed a mathematical model of cancer cell invasion of the extracellular matrix by incorporating cell-cell adhesion as well as cell-matrix adhesion into the model. In general the results from the computational simulations show that an increased value of the cell-cell adhesion parameter results in a more heterogeneous pattern of invasion whereas an increased value of the cell-matrix adhesion parameter results in a faster invasion. Using this approach, coupled with accurate parameter estimation, it will be possible to develop a mathematical model of cancer invasion that assesses invasion objectively and provides a numerical “Invasion Index”. Our computational simulation results demonstrated a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as tumour infiltrative growth patterns (INF). Finally we introduced a novel multiscale model describing cancer invasion of tissue. The two-scale model focused on the macroscopic dynamics of the distributions of cancer cells and of the surrounding extracellular matrix (ECM), and on the microscale dynamics of the matrix degrading enzymes (MDEs), produced at the level of the individual cancer cells. The microscale dynamics took place at the interface of the cancer cells and the ECM and give rise to a moving boundary at the macroscale.
This computational model is currently being explored as a tool to assist in clinical decision making with Surgical Oncologists at the University of Texas MD Anderson Cancer Center, Houston, Texas, USA.
At the sub-cellular scale, we developed novel spatio-temporal and stochastic spatio-temproal mathematical models of transcription factors and gene regulatory networks that have an important role in cancer development – Hes1, p53-Mdm2 and NF-kB. These systems are so-called “negative feedback systems” and have trademark oscillatory dynamics in terms of the concentrations of the mRNA and protein molecules. We derived systems of partial differential equations to capture the evolution in space and time of the variables in the Hes1 and p53-Mdm2 systems. Through computational simulations we showed that our reaction-diffusion models are able to produce sustained oscillations both spatially and temporally, accurately reflecting experimental evidence and advancing previous models. We have shown rigorously that it is the spatial movement of the molecules (proteins and mRNA) that causes the oscillations.
At the cellular scale our modelling developed a force-based, individual-based model which links single cell migration with matrix fibres and cell-matrix interactions through contact guidance and matrix remodelling. With this approach we highlighted the significance of the cell’s environment on its migration. We investigated the influence of matrix stiffness, matrix architecture and cell speed on migration, using quantitative measures that allow us to compare the results to experiments. We found that matrix remodelling due to cell traction forces might be an important part in two dimensional cell migration. We further developed this into a multi-scale multi-compartment model that accounts for the principal biophysical interactions and adhesion pathways not only at a cell–cell level but also at the level of cell colonies. Our simulation results demonstrated that adhesion/separation forces between cells may be lower in cell colonies than traditional isolated single-cell experiments infer. We also developed a hybrid, individual-based approach that analyses spatio-temporal dynamics of solid tumour growth at the level of cells, linking individual cell behaviour with the macroscopic behaviour of cell organisation and the microenvironment. We also used this multi-scale hybrid model to investigate the optimum sequencing and scheduling of these chemotherapy and radiotherapy treatments, and the impact of internal and external heterogeneity on the spatio-temporal patterning of the distribution of cancer cells and their response to different treatment schedules. This computational model is currently being explored as a tool to assist in clinical decision making with Clinical Oncologists and Radiation Oncologists at Ninewells Hospital, Dundee.
At the tissue scale we developed a mathematical model of cancer cell invasion of the extracellular matrix by incorporating cell-cell adhesion as well as cell-matrix adhesion into the model. In general the results from the computational simulations show that an increased value of the cell-cell adhesion parameter results in a more heterogeneous pattern of invasion whereas an increased value of the cell-matrix adhesion parameter results in a faster invasion. Using this approach, coupled with accurate parameter estimation, it will be possible to develop a mathematical model of cancer invasion that assesses invasion objectively and provides a numerical “Invasion Index”. Our computational simulation results demonstrated a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as tumour infiltrative growth patterns (INF). Finally we introduced a novel multiscale model describing cancer invasion of tissue. The two-scale model focused on the macroscopic dynamics of the distributions of cancer cells and of the surrounding extracellular matrix (ECM), and on the microscale dynamics of the matrix degrading enzymes (MDEs), produced at the level of the individual cancer cells. The microscale dynamics took place at the interface of the cancer cells and the ECM and give rise to a moving boundary at the macroscale.
This computational model is currently being explored as a tool to assist in clinical decision making with Surgical Oncologists at the University of Texas MD Anderson Cancer Center, Houston, Texas, USA.