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A mathematical model of tumour and blood pHe regulation: The HCO3-/CO2 buffering system.

ABSTRACT: Malignant tumours are characterised by a low, acidic extracellular pH (pHe) which facilitates invasion and metastasis. Previous research has proposed the potential benefits of manipulating systemic pHe, and recent experiments have highlighted the potential for buffer therapy to raise tumour pHe, prevent metastases, and prolong survival in laboratory mice. To examine the physiological regulation of tumour buffering and investigate how perturbations of the buffering system (via metabolic/respiratory disorders or changes in parameters) can alter tumour and blood pHe, we develop a simple compartmentalised ordinary differential equation model of pHe regulation by the HCO3-/CO2 buffering system. An approximate analytical solution is constructed and used to carry out a sensitivity analysis, where we identify key parameters that regulate tumour pHe in both humans and mice. From this analysis, we suggest promising alternative and combination therapies, and identify specific patient groups which may show an enhanced response to buffer therapy. In addition, numerical simulations are performed, validating the model against well-known metabolic/respiratory disorders and predicting how these disorders could change tumour pHe.

SUBMITTER: Martin NK

PROVIDER: S-EPMC3045481 | biostudies-other | 2011 Mar

REPOSITORIES: biostudies-other

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A mathematical model of tumour and blood pHe regulation: The HCO3-/CO2 buffering system.

Martin Natasha K NK Gaffney Eamonn A EA Gatenby Robert A RA Gillies Robert J RJ Robey Ian F IF Maini Philip K PK

Mathematical biosciences 20101215 1

Malignant tumours are characterised by a low, acidic extracellular pH (pHe) which facilitates invasion and metastasis. Previous research has proposed the potential benefits of manipulating systemic pHe, and recent experiments have highlighted the potential for buffer therapy to raise tumour pHe, prevent metastases, and prolong survival in laboratory mice. To examine the physiological regulation of tumour buffering and investigate how perturbations of the buffering system (via metabolic/respirato ...[more]

PMID: 21167185

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Project description:Xenografts--as simplified animal models of cancer-differ substantially in vasculature and stromal architecture when compared to clinical tumours. This makes mathematical model-based predictions of clinical outcome challenging. Our objective is to further understand differences in tumour progression and physiology between animal models and the clinic. To achieve that, we propose a mathematical model based upon tumour pathophysiology, where oxygen--as a surrogate for endocrine delivery--is our main focus. The Oxygen-Driven Model (ODM), using oxygen diffusion equations, describes tumour growth, hypoxia and necrosis. The ODM describes two key physiological parameters. Apparent oxygen uptake rate (k'R) represents the amount of oxygen cells seem to need to proliferate. The more oxygen they appear to need, the more the oxygen transport. k'R gathers variability from the vasculature, stroma and tumour morphology. Proliferating rate (kp) deals with cell line specific factors to promote growth. The KH,KN describe the switch of hypoxia and necrosis. Retrospectively, using archived data, we looked at longitudinal tumour volume datasets for 38 xenografted cell lines and 5 patient-derived xenograft-like models. Exploration of the parameter space allows us to distinguish 2 groups of parameters. Group 1 of cell lines shows a spread in values of k'R and lower kp, indicating that tumours are poorly perfused and slow growing. Group 2 share the value of the oxygen uptake rate (k'R) and vary greatly in kp, which we interpret as having similar oxygen transport, but more tumour intrinsic variability in growth. However, the ODM has some limitations when tested in explant-like animal models, whose complex tumour-stromal morphology may not be captured in the current version of the model. Incorporation of stroma in the ODM will help explain these discrepancies. We have provided an example. The ODM is a very simple -and versatile- model suitable for the design of preclinical experiments, which can be modified and enhanced whilst maintaining confidence in its predictions.

Project description:BackgroundCancer cell invasion, dissemination, and metastasis have been linked to an epithelial-mesenchymal transition (EMT) of individual tumour cells. During EMT, adhesion molecules like E-cadherin are downregulated and the decrease of cell-cell adhesion allows tumour cells to dissociate from the primary tumour mass. This complex process depends on intracellular cues that are subject to genetic and epigenetic variability, as well as extrinsic cues from the local environment resulting in a spatial heterogeneity in the adhesive phenotype of individual tumour cells. Here, we use a novel mathematical model to study how adhesion heterogeneity, influenced by intrinsic and extrinsic factors, affects the dissemination of tumour cells from an epithelial cell population. The model is a multiscale cellular automaton that couples intracellular adhesion receptor regulation with cell-cell adhesion.ResultsSimulations of our mathematical model indicate profound effects of adhesion heterogeneity on tumour cell dissemination. In particular, we show that a large variation of intracellular adhesion receptor concentrations in a cell population reinforces cell dissemination, regardless of extrinsic cues mediated through the local cell density. However, additional control of adhesion receptor concentration through the local cell density, which can be assumed in healthy cells, weakens the effect. Furthermore, we provide evidence that adhesion heterogeneity can explain the remarkable differences in adhesion receptor concentrations of epithelial and mesenchymal phenotypes observed during EMT and might drive early dissemination of tumour cells.ConclusionsOur results suggest that adhesion heterogeneity may be a universal trigger to reinforce cell dissemination in epithelial cell populations. This effect can be at least partially compensated by a control of adhesion receptor regulation through neighbouring cells. Accordingly, our findings explain how both an increase in intra-tumour adhesion heterogeneity and the loss of control through the local environment can promote tumour cell dissemination.ReviewersThis article was reviewed by Hanspeter Herzel, Thomas Dandekar and Marek Kimmel.

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A mathematical model of tumour and blood pHe regulation: The HCO3-/CO2 buffering system.

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A mathematical model of tumour and blood pHe regulation: The HCO3-/CO2 buffering system.

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