Table 1.

Parameters used in the simulations of Equations (6)–(10). The carrying capacities of normal and tumour cells (K_1,2 respectively), growth rates (r_1,2), tumour diffusion (D₂), acid diffusion (D₃, and vascular evacuation (d₃) parameters were taken from a previous acid-invasion modelling and experimental study by Gatenby and Gawlinski (1996). The diffusion of protons occurs in association with mobile buffer species to ensure charge balance, and the effective diffusion coefficient value used was estimated in Gatenby and Gawlinski (1996). From these values, Gatenby and Gawlinski (1996) calculate the tumour acid production rate (r₃), and a range of values for the normal cell death rate from acid (d₁) from which we select. Due to the large size of the MMP molecule, we assume that the diffusion of the active MMPs (D₅) is 1/10th that of acid. We assume the rate of loss of the MMPs (d₅) is the same order of magnitude as the excess acid (due to vascular evacuation), but reduced by about 1/3 as the MMPs are not locally buffered as is the case with the protons.

Parameter	Definition	Value	Reference
γ1	$\frac{d_1{r}_3{K}_2}{d_3{r}_1}$	1–100	(Gatenby and Gawlinski, 1996)
δ2	r2/r1	1	(Gatenby and Gawlinski, 1996)
α2	D2/D3	4 × 10−5	(Gatenby and Gawlinski, 1996)
δ3	d3/r1	70	(Gatenby and Gawlinski, 1996)
δ5	$\frac{r_5{K}_1{K}_2{d}_4}{r_1^2}$	100	estimated
γ5	d5/r1	50	estimated
α5	D5/D3	0.1	estimated