Physiological insights into electrodiffusive maintenance of gastric mucus through sensitivity analysis and simulations

Abstract

It is generally accepted that the gastric mucosa and adjacent mucus layer are critical in the maintenance of a pH gradient from stomach lumen to stomach wall, protecting the mucosa from the acidic environment of the lumen and preventing auto-digestion of the epithelial layer. No conclusive study has shown precisely which physical, chemical, and regulatory mechanisms are responsible for maintaining this gradient. However, experimental work and modeling efforts have suggested that concentration dependent ion-exchange at the epithelial wall, together with hydrogen ion/mucus network binding, may produce the enormous pH gradients seen in vivo. As of yet, there has been no exhaustive study of how sensitive these modeling results are with respect to variation in model parameters, nor how sensitive such a regulatory mechanism may be to variation in physical/biological parameters. In this work, we perform sensitivity analysis (using Sobol' Indices) on a previously reported model of gastric pH gradient maintenance. We quantify the sensitivity of mucosal wall pH (as a proxy for epithelial health) to variations in biologically relevant parameters and illustrate how variations in these parameters affects the distribution of the measured pH values. In all parameter regimes, we see that the rate of cation/hydrogen exchange at the epithelial wall is the dominant parameter/effect with regards to variation in mucosal pH. By careful sensitivity analysis, we also investigate two different regimes representing high and low hydrogen secretion with different physiological interpretations. By complementing mechanistic modeling and biological hypotheses testing with parametric sensitivity analysis we are able to conclude which biological processes must be tightly regulated in order to robustly maintain the pH values necessary for healthy function of the stomach.

Keywords: Electrodiffusion; Gastric mucus; Physiological gels; Sobol’ sensitivity.

Fig. A.1:

Violin and box plots for log₁₀ (H₀) as a function of (a) bicarbonate offset parameter δ_AB, and (b) hydrogen offset parameter δ_HI during Sobol’ analysis of all 7 parameters.

Fig. A.2:

Violin and box plots for log₁₀ (H₀) as a function of (a) bicarbonate offset parameter (δ_AB), (b) hydrogen offset parameter (δ_HI), (c) lumenal hydrogen concentration H_L, and (d) lumenal cation concentration I_L when hydrogen source is large (S₀ = 10).

Fig. A.3:

Violin and box plots for log₁₀ (H₀) as a function of (a) bicarbonate offset parameter (δ_AB), and (b) hydrogen offset parameter δ_HI, when hydrogen source is small (S₀ = 0.1).

Fig. C.4:

A schematic representation of our computational grid for N = 5. Dashed vertical black lines indicate the boundaries of the computational domain. Circles indicate cell centers, while diamonds indicate cell edges. Interior points are drawn with solid lines while ghost points are drawn with dash-dot lines.

Fig. D.5:

Convergence plots for total SI estimates, when all of the parameters are considered when (a) tol = 0.02 and (b) tol = 0.01, both with batch size k = 2000. At the lower tol value, some of the parameters take a greater number of updates for convergence. Note that the number of updates required for convergence for a parameter will always be a multiple of the batch size k.

Fig. 1:

Illustration of gel volume fraction (θ_g) and Hydrogen/Anion source profiles. Recall that θ_s = 1 – θ_g.

Fig. 2:

Sobol’ indices for boundary pH for each parameter. First order (${\underset{\_}{\mathcal{S}}}_i$) and additional (${\mathcal{A}}_I$) SI are depicted, while their sum indicates total SI (${\overline{\mathcal{S}}}_i$). (a) Source is fixed at 1, and all other parameters are varied in their region of interest, (b) All seven parameters are varied.

Fig. 3:

Violin and box plots for log₁₀ (H₀ as a function of (a) ion source magnitude (S₀), (b) hydrogen exchange rate (k_HI), (c) bicarbonate exchange rate (k_AB), (d) lumenal hydrogen concentration (H_L), and (e) lumenal cation concentration (I_L). White hashes indicate mean of QoI within a subinterval and black hashes indicate the median. Thick black lines indicate the range from first to third quartiles. Black whiskers indicate the extent of the data (sans outliers), and blue x-es indicate individual outliers (median ±1.5 times inter-quartile range). Panel (a) also shows the underlying data (with running mean and mean±std. indicated) for illustrative purposes.

Fig. 4:

Sobol’ indices for the other six parameters when hydrogen source is fixed and large (S₀ = 10). First order (${\underset{\_}{\mathcal{S}}}_i$) and additional (${\mathcal{A}}_I$) SI are depicted, while their sum indicates total SI (${\overline{\mathcal{S}}}_i$).

Fig. 5:

Violin and box plots for log₁₀ (H₀) as a function of (a) hydrogen exchange rate (k_HI) and (b) bicarbonate exchange rate (k_AB), when hydrogen source is large (S₀ = 10). White hashes indicate mean of Qol within a subinterval and black hashes indicate the median. Thick black lines indicate the range from first to third quartiles. Black whiskers indicate the extent of the data (sans outliers), and blue x-es indicate individual outliers (median ±1.5 times inter-quartile range).

Fig. 6:

Sobol’ indices for the other six parameters when hydrogen source is fixed and small (S₀ = 0.1). First order (${\underset{\_}{\mathcal{S}}}_i$) and additional (${\mathcal{A}}_I$) SI are depicted, while their sum indicates total SI (${\overline{\mathcal{S}}}_i$).

Fig. 7:

Violin and box plots for log₁₀ (H₀) as a function of (a) hydrogen exchange rate (k_HI), (b) bicarbonate exchange rate (k_AB, (c) lumenal hydrogen concentration (H_L), and (d) lumenal cation concentration (I_L), when hydrogen source is small (S₀ = 0.1). White hashes indicate mean of QoI within a subinterval and black hashes indicate the median. Thick black lines indicate the range from first to third quartiles. Black whiskers indicate the extent of the data (sans outliers), and blue x-es indicate individual outliers (median ±1.5 times inter-quartile range).

Fig. 8:

First order and additional Sobol’ indices for the other six parameters when hydrogen exchange rate is fixed and small. Panels show (a) k_HI = 10⁻⁶ and (b) k_HI = 10⁻⁸. First order (${\underset{\_}{\mathcal{S}}}_i$) and additional (${\mathcal{A}}_I$) SI are depicted, while their sum indicates total SI (${\overline{\mathcal{S}}}_i$).

Fig. 9:

(a) Total Sobol’ indices of the other six parameters as a function of k_HI. (b) Mean (blue diamonds) and variance (orange squares) of pH at the left boundary as a function of k_HI.