Thermal Stress Disrupts Symbiotic Fluid Dynamics in Bobtail Squid

TL;DR

This work addresses how thermal stress alters the establishment of symbiosis between Euprymna scolopes and Vibrio fischeri by linking climate-driven breathing changes to internal fluid dynamics. It introduces a two-dimensional fluid-structure model solved with the Method of Regularised Stokeslets to simulate ventilation- and cilia-driven flows and the advection of bacteria near the light organ, coupled with a Sobol-based sensitivity analysis over breathing parameters. The study identifies key drivers of colonisation potential—ventilation strength, breathing frequency, and initial bacterial position—showing that shallower or faster breathing can substantially reduce the time bacteria spend in the critical zone needed for successful colonisation. These findings highlight a potential climate-related vulnerability of this mutualism and provide a mechanistic framework for predicting how physiological responses to warming may affect host-microbe interactions.

Abstract

The impact of thermal stress on beneficial symbiosis, in the face of rapid climate change, remains poorly understood. We investigate this using the model system, Euprymna scolopes, the Hawaiian Bobtail Squid, and its bioluminescent symbiont, Vibrio fischeri, which enables the squid to camouflage itself through counter-illumination. Successful colonisation of the squid by V. fischeri must occur hours after hatching and is mediated by fluid flow due to respiration within the squid mantle cavity. To study this process, we develop a mathematical model using the Method of Regularised Stokeslets to simulate the flow and resulting bacterial trajectories within the squid. We explore how thermal stress, mediated by physiological changes in respiration, ciliary dynamics, and internal geometry, affects this early colonisation by analysing the time bacteria spend in regions crucial to the establishment of symbiosis in these simulations. A variance-based sensitivity analysis of physiologically relevant parameters on these metrics demonstrates that changes in the breath cycle significantly impact and reduce the time bacteria spend in the critical zone within the squid, hindering colonisation.

Figures (10)

• Figure 1: Squid internal cavity. A) A grey-scale experimental image of Euprymna scolopes is shown. Overlaid on the image, the external walls of the internal cavity, a funnel-like structure, are highlighted in red. The body of the bi-lobed light organ is highlighted in light blue. The individual appendages are highlighted in dark blue. B) A schematic of the internal flows and ventilation boundary conditions resulting from the expansion of the mantle within the squid during a breath cycle. The expansion directions of the mantle during an inhale are shown in blue, and green arrows indicate where fluid enters the squid at the base of the mantle (left). A schematic of the Poiseuille flow boundary conditions at the inlet on the internal cavity, which models the breath cycle of the squid (right). C) The two major flow regimes experienced by bacteria within the cavity. The Poiseuille or ventilation flow dominates the far-field. Close to the appendages, the beating of the cilia on their surface drives the flow. The bi-lobed light organ is highlighted in light blue, and the cross sections (red) are those used in the two-dimensional simulations. Long cilia-covered regions are shown (dark blue), as well as short cilia regions (yellow), and the pair of three pores, through which the bacteria can pass into the internal ducts of the light organ, are marked (black, P).
• Figure 2: Model schematic. A) Schematic of the model of the internal cavity, a two-dimensional channel geometry intersecting through the squid, see Figure \ref{['fig:figure1']}. Slice through the light organ is shown in grey, and cross sections of the appendages are shown in black. The initial distance of Vf from the appendages is shown as a red dashed line. Relevant measurements required to characterise this internal channel of the squid are labelled. B) A close-up of the appendage pairs is shown. Top left: The flow directions (black arrows), driven by the beating of the cilia, on the appendage surface are shown, as well as the angle $\psi_0$ which defines the orientation of each appendage in the $\hat{\psi}$ direction. Bottom left: Key flow speeds of average beating cilia are shown. Top right: Appendage spacing, $d$, and the relative angle, $\phi$, between the appendage pairs are defined. Bottom right: The radius, $R$, at which steric (contact) interactions occur is defined, and the effective radius, $R_\text{eff}$, at which the Stokeslets are placed. C) Magnitude of the tangential flow along the surface of one of the appendages. Blue and red dots along this curve correspond to those in Figure 2B.
• Figure 3: Flow fields during a breath cycle in the internal cavity. A) The maximum magnitude of the temporally-varying Poiseuille flow boundary condition, \ref{['timeDependenceVent']}. Five points are indicated along half of the breath cycle, from an exhale (where the ventilation flow at the inlet is maximal) to an inhale (where the ventilation flow at the inlet is zero). The dynamics are symmetric in time about the midpoint of the breath cycle. B-F) The panels present the flow field at the highlighted time points in (A). The squid internal cavity boundaries are shown in red. The local colour of the background presents the magnitude of the normalised local flow, scaled to the colour bar given in (A).
• Figure 4: Bacterial Trajectories. A) The trajectories for a set of bacteria in a time-independent flow field. Schematics of bacteria are shown at the initial position (not to scale). One hundred bacteria are initially seeded uniformly on this line. The flow is time-independent, with the ventilation boundary condition set using \ref{['timeDependenceVent']} with $2\pi\omega t = 0$ and a maximum strength of $U_B = 125\mu\text{m s}^{-1}$ (shown at the bottom in black) remaining constant. Several regions of interest are highlighted: Stagnant zones (SZ), where the fluid velocity is low, vortical zones close to the appendage pairs (VZ1), and vortical zones downstream of the appendages (VZ2). B) The trajectories for a set of bacteria in a time-dependent ventilation flow. The same number of bacteria are initialised in the same location as in (A). The time-dependent ventilation boundary condition at the inlet is set using \ref{['timeDependenceVent']}, with a maximum strength of $U_B = 125~\mu\text{m s}^{-1}$, and the resulting fluid flow is presented in \ref{['fig:figure3']}. The trajectories span 14 breath cycles. In (A) and (B), the background colour indicates the local flow velocity (yellow for the fastest flows and blue for the slowest).
• Figure 5: Critical zone metrics. A) Collection of bacterial trajectories, as in \ref{['fig:figure4']}B, overlaid by the critical zone used for the metrics, $\tau_{tot}$ and $\tau_{max}$. One hundred bacteria are initially seeded at the bottom of the channel. The system boundaries are shown in red, and the trajectories are shown in blue for 14 breath cycles. The four yellow annuli show the critical distance and corresponding zone used for metric calculation. B) Heatmap of bacteria proximity to the appendages as a function of time for given initial positions of bacteria, $X_0$, on the dotted red line. When a coordinate is yellow, it indicates that the bacteria are in the critical zone (yellow regions in (A)). C) The total time each bacterium, initialised at $X_0$, is in the critical zone (yellow regions in (A)). The mean of these values, $\tau_{tot}$, is given in the inset. D) The maximum continuous time each bacterium, initialised at $X_0$, spends in the critical zone (yellow regions in (A)). The maximum across all the bacteria is marked with dark red arrows, and the corresponding value, $\tau_{max}$, is given in the inset.