Modelling multiscale architecture of biofilm extracellular matrix and its role in oxygen transport

TL;DR

This paper addresses how the microarchitecture of the biofilm extracellular matrix, specifically a bacterial capsule surrounding cells, governs oxygen transport. It introduces a multiscale cell-capsule framework that treats the capsule as a low-diffusivity phase and analyzes diffusion-reaction across capsule, biofilm, and bulk phases in a one-dimensional setting. Key contributions include the formulation of a resistance-in-series mechanism due to the capsule, quantification of how capsule thickness $oldsymbol{L_p}$ and compaction $oldsymbol{\e_c}$ modulate oxygen transfer (up to about $oldsymbol{70 ext{ extpercent}}$ reduction), and image-informed parameterization of capsule patterns with a four-parameter distribution. The findings offer mechanistic insight into early-stage oxygen limitation in biofilms and have practical implications for reactor design and antimicrobial strategies targeting capsule structure, with publicly available code and data for reproducibility.

Abstract

The extracellular matrix of biofilms presents a dense and intricate architecture. Numerous biophysical properties of the matrix surrounding microbial cells contribute to the heterogeneity of biofilms and their functions at the microscale. Previous mathematical models assume the matrix to be homogeneous, often overlooking the need for a detailed mechanistic understanding of the extracellular space. In this theoretical study, we introduce a novel cell-capsule approach to investigate geometric patterns in biofilm morphology and predict their role in oxygen transport. The thickness of the capsule and the arrangement of cell-capsule patterns can influence matrix heterogeneity, providing a clear picture of biofilm structure. By incorporating the bacterial capsule as a distinct, low-diffusivity phase, our novel cell-capsule model reveals that this architecture acts as a significant 'resistance-in-series' barrier. We found that a thick capsule/dense matrix arrangement can reduce local oxygen transfer by approximately 70%, a substantial drop that may give drive further research into oxygen limitations during early stage biofilm development.

Figures (5)

• Figure 1: Role of capsule geometry of extracellular matrix as a 'resistance-in-series' model: Representative spatial profiles of oxygen concentration subjected to with or without mass transfer resistance (model parameters are listed in Table \ref{['tab:2D-model-without-flow-coupled-transport-parameters-list']}) in the radial direction. A fixed capsule thickness ($L_\mathrm{p}$ = 0.70 $\mu$m) is assumed to simulate the mass transfer characteristics of the biofilm extracellular matrix.
• Figure 2: Benchmark analysis: Comparison between standard reaction-diffusion model Stewart2016 and the present study for a known set of model kinetic parameters (refer to Table \ref{['tab:2D-model-without-flow-coupled-transport-parameters-list-benchmark-analysis']}) are shown using three different physiologically relevant thickness values ($L_\mathrm{p}$), and at two different initial oxygen concentrations (${C_{\mathrm{bulk,0}}}$): (A) thin capsule ($L_\mathrm{p}$ = 0.14 $\mu$m), ${C_{\mathrm{bulk,0}}}$ = 5 mg L$^{-1}$ (B) thin capsule ($L_\mathrm{p}$ = 0.14 $\mu$m), ${C_{\mathrm{bulk,0}}}$ = 5 mg L$^{-1}$ (C) intermediate ($L_\mathrm{p}$ = 0.42 $\mu$m), ${C_{\mathrm{bulk,0}}}$ = 9.5 mg L$^{-1}$ (D) intermediate ($L_\mathrm{p}$ = 0.42 $\mu$m), ${C_{\mathrm{bulk,0}}}$ = 9.5 mg L$^{-1}$ (E) thick capsule ($L_\mathrm{p}$ = 0.70 $\mu$m), ${C_{\mathrm{bulk,0}}}$ = 5 mg L$^{-1}$ (F) thick capsule ($L_\mathrm{p}$ = 0.70 $\mu$m), ${C_{\mathrm{bulk,0}}}$ = 5 mg L$^{-1}$. The black-colored dotted lines (long-dashed, single-dotted or dot-dashed) represent the numerical solutions obtained from the standard model, and solid-colored lines (orange, blue or green) represent the numerical solutions obtained from our model for three different values of biofilm thickness ($L_\mathrm{f}$ = 10, 25 or 50 $\mu$m) respectively. The model-based oxygen concentration profiles for the thin capsule thickness are observed to closely follow the standard model (see panels A and B). Note: Normalized distance is calculated as the ratio of distance from the substratum, $z$ to the biofilm thickness, $L_\mathrm{f}$. Corresponding biofilm thickness is shown (see panel A) for the purpose of better visualization.
• Figure 3: Effect of geometrical spacing on the density of extracellular matrix: Typical cell-capsule patterns in the radial direction, x, generated as input datasets in our present study for a given, dimensionless unit surface area. For a fixed capsule thickness, $L_\mathrm{p}$ of 0.70 µm, different patterns are generated by varying the compactness factor (${\epsilon_{\mathrm{c}}}$) as: (A) 0.057 $\pm$ 0.001 (B) 0.213 $\pm$ 0.008 (C) 6.677 $\pm$ 0.686 (D) 17.615 $\pm$ 1.104. Note: Random distribution of perfect spheres are subjected to image analysis using ImageJ software (ImageJ, NIH, USA), with blue-colored capsule around the pink-colored cells. (E) Graphical representation of different biofilm morphologies with varying compactness factor for cell-capsule patterns (${\epsilon_{\mathrm{c}}}$) is plotted. The blue-colored dotted guide lines correspond to an estimate of normalized density at ${\epsilon_{\mathrm{c}}}$ = 1.002. A fixed capsule thickness, $L_\mathrm{p}$ = 0.70 $\mu$m is assumed for generation of the above spatial patterns, where ${\epsilon_{\mathrm{c}}}$ varies between 0.057 and 17.615. Note: Normalized density ($\hat{{\rho}}$) is estimated as the ratio of density of the capsule relative to the density of the EPS matrix. Trendline along the data points is shown for the purpose of better visualization.
• Figure 4: Effect of capsule thickness on the measure of mass transfer resistance due to extracellular matrix: Graphical representation of different scenarios with varying capsule thickness ($L_\mathrm{p}$). For a given $L_\mathrm{p}$, Sherwood number (${Sh}_\mathrm{p}$) is defined as the ratio of resistance due to oxygen diffusion and the resistance due to reaction kinetics for oxygen utilization in the capsule. Two representative cell-capsule patterns using thin capsule ($L_\mathrm{p}$ = 0.14 $\mu$m) and thick capsule ($L_\mathrm{p}$ = 0.98 $\mu$m) are shown. Note: Random distribution of perfect spheres are subjected to image analysis using ImageJ software (ImageJ, NIH, USA), with blue-colored capsule around the pink-colored cells. Trendline along the data points is shown for tracing the estimated variations in case of a given random distribution of spheres’ arrangement, and for the purpose of better visualization.
• Figure 5: Predicted oxygen mass transfer performance in the capsule for various structured arrangements: The curve shows effectiveness factors ($\eta$) obtained from oxygen profiles in the capsule region for varying compactness factor (${\epsilon_{\mathrm{c}}}$). For densely arranged matrix (say, ${\epsilon_{\mathrm{c}}}$ of nearly 0.2 or lower), where diffusion resistance just begins to intrude, the effectiveness factor can slightly increase. The conceptual representation of the spatial patterns at corresponding effectiveness factors are provided. Note: Simulation results with different values of ${\epsilon_{\mathrm{c}}}$ are shown assuming a fixed capsule thickness, $L_\mathrm{p}$ = 0.70 $\mu$m.