Diffusion Dynamics in Biofilms with Time-Varying Channels

TL;DR

The paper addresses how diffusion of quorum-sensing autoinducers in biofilms evolves during maturation when water channels form. It extends a static anisotropic diffusion model to a time-varying channel (TVC) with a coherence time, validated by Green's-function CIR derivations and particle-based simulations. The TVC behaves as a hybrid of isotropic and anisotropic diffusion, and mutual information between transmitter and receiver increases with higher AI counts, shorter transmitter-receiver distance, greater anisotropy, and shorter inter-symbol interference, with results scalable via dimensional analysis. These insights illuminate quorum sensing coordination in maturing biofilms and may inform strategies for antimicrobial resistance management and bioprocessing applications, while highlighting avenues for experimental validation of diffusion dynamics during maturation.

Abstract

A biofilm is a self-contained community of bacteria that uses signaling molecules called autoinducers (AIs) to coordinate responses through the process of quorum sensing. Biofilms exhibit a dual role that drives interest in both combating antimicrobial resistance (AMR) and leveraging their potential in bioprocessing, since their products can have commercial potential. Previous work has demonstrated how the distinct anisotropic channel geometry in some biofilms affects AIs propagation therein. In this paper, a 2D anisotropic biofilm channel model is extended to be a time-varying channel (TVC), in order to represent the diffusion dynamics during the maturation phase when water channels develop. Since maturation is associated with the development of anisotropy, the time-varying model captures the shift from isotropic to anisotropic diffusion. Particle-based simulation results illustrate how the TVC is a hybrid scenario incorporating propagation features of both isotropic and anisotropic diffusion. This hybrid behavior aligns with biofilm maturation. Further study of the TVC includes characterization of the mutual information (MI), which reveals that an increased AI count, reduced transmitter -- receiver distance, greater degree of anisotropy, and shorter inter-symbol interference lengths increase the MI. Finally, a brief dimensional analysis demonstrates the scalability of the anisotropic channel results for larger biofilms and timescales.

Figures (8)

• Figure 1: Schematic representation of AI molecule propagation in a 2D biofilm with a time-varying channel (TVC). There is anisotropic propagation from a point TX to a passive and transparent RX. AIs diffuse according to $D_{\rho}(t)$ and $D_{\theta}(t)$, which are both constant in the static channel case. The outer circular boundary is reflective and the AIs can degrade according a first-order degradation process.
• Figure 2: 2D spatiotemporal profile of anisotropic diffusion organized into two rows corresponding to different biofilm radii and pixel size, $\rho_{c} = \{100, 200\}\,\mu\mathrm{m}$ and pixel dimension $\ell= \{2.5, 5\}\mu$m across, respectively. The top row shows temporal snapshots at $t = \{20, 40, 60, 80\}\,\mathrm{s}$, while the bottom row shows snapshots at $t = \{80, 160, 240, 320\}\,\mathrm{s}$.
• Figure 3: 2D spatiotemporal profile of isotropic ($D_{\theta}=5\times 10^{-10}\,\text{m}^2 \cdot \text{s}^{-1}$), anisotropic ($D_{\theta}=5\times 10^{-11}\,\text{m}^2 \cdot \text{s}^{-1}$), and time-varying ($D_{\theta}=D_{\theta}(t)$ as in (\ref{['eqn_timevarying']})) diffusion. In all cases, $D_{\rho}=5\times 10^{-10}\,\text{m}^2 \cdot \text{s}^{-1}$ and the TX is placed at the rightmost edge. Each column corresponds to temporal snapshots at $\mathrm{t}$ = {20, 40, 60, 80} s.
• Figure 4: 2D diffusion profiles under isotropic {(a), (b)}, anisotropic {(c), (d)}, and time-varying {(e), (f)} conditions simulated for 600 s. The top row shows peak times measured at least 0.3 s and within 300 s after molecule release. The bottom row shows the peak values.
• Figure 5: The relationship of the MI and $p_0$ for different number of AIs ($N$).