Spatiotemporal Dynamics of Coral Polyps on a Fluidic Platform

Reef-building corals are inherently sessile organisms. However, motion is an important behavioral trait of coral polyps, which plays an essential role in feeding, competition, defense, reproduction, and thus, survival and fitness. Notwithstanding the importance of inherent temporal and spatial multiscale features of polyps, their quantitative properties and modeling still remain challenging and unexplored. Here, we observe Pocillopora acuta in vivo under different light and temperature conditions using a fluidic platform that allows the direct microscopic study of small live coral fragments, where the stochastic dynamics of the in-plane waving motion of polyps is uncovered. The relationship between polyps on nubbins is described by motion-correlation analysis. Additionally, the fractional Brownian motions of polyps under certain light conditions and temperatures are revealed by the Hurst index via power spectral analysis. Finally, the motion of polyps is modeled by Langevin dynamics, numerically obtained by data-driven parameterization. This combination of experimental observations, numerical analysis, and theoretical modeling opens an avenue to boost our understanding of the biological and physical behaviors of corals in relation to changing environmental conditions.

Figure 1

Experimental observation of coral in the fluidic platform. (a) Schematic of our octagonal fluidic platform with a coral nubbin in the chamber. Inset shows our octagonal fluidic platform for experiment made by 3D printing with VeroClear resin. Valves control the flow of fluid. (b) Coral nubbin observed under the microscope under normal light conditions and 25 °C. Polyps being analyzed in this case are labeled by numbers and color codes used in subsequent figures. (c) Trajectory of polyps. (d) Azimuthal angles, $\theta$, of different polyps as a function of duration. (e) Probability density function of the azimuthal angles, $\theta$, of different polyps after being centered on zero. Colors in (c)–(e) correspond to the colors of labels in (b).

Figure 2

Analysis of correlation and phase synchronization. (a) Correlation coefficients between polyps on the same coral nubbin under different light conditions (wavelength). Correlations and anticorrelations are shown in orange and green, respectively. (b) Correlation coefficients between polyps on the same coral nubbin under different temperatures. Correlations and anticorrelations are shown in orange and green, respectively. (c) Phase-locking value characterizing phase synchronization between polyps on the same coral nubbin under different light conditions. (d) Phase-locking value characterizing phase synchronization between polyps on the same coral nubbin under different temperatures. Cross and triangle symbols in (a)–(d) represent the outliers and mean, respectively.

Figure 3

Power spectrum analysis of experimental data sets under different light conditions. (a) PSD of representative in-plane waving motions represented by the azimuthal angle, $\theta$, under different light conditions. Dashed gray lines show the $1/f^{1.08}$ and $1/f^{1.42}$ trends for normal light, $1/f^{1.19}$ and $1/f^{1.28}$ trends for blue light, $1/f^{1.41}$ and $1/f^2$ trends for green light, and $1/f^{1.77}$ and $1/f^2$ trends for red light. (b) PSDs evaluated at zero frequency shown in dots for normal light, blue light, green light, and red light from left to right. Solid lines show the fitted results. Both x and y axes are on the logarithmic scale. (c) Hurst indices for cases under normal light, blue light, green light, and red light. Subdiffusion and superdiffusion areas are shaded in green and orange, respectively.

Figure 4

Power spectrum analysis of experimental data sets under different temperatures. (a) PSD of representative in-plane waving motions represented by the azimuthal angle, $\theta$, under different temperatures. Dashed gray lines show the $1/f^{1.20}$ and $1/f^2$ trends for 15 °C, $1/f^{1.08}$ and $1/f^{1.42}$ trends for 25 °C, and $1/f^{1.25}$ and $1/f^2$ trends for 30 °C. (b) PSDs evaluated at zero frequency are shown as dots for 15, 25, and 30 °C from left to right. Solid lines show the fitted results. Both x and y axes are on the logarithmic scale. (c) Hurst indices for cases at 15, 25, and 30 °C. Subdiffusion and superdiffusion areas are shaded in green and orange, respectively.

Figure 5

Model of the in-plane waving motion of coral polyps under different light conditions. (a) Value of the memory-kernel function at the Markovian limit, $\hat{K}(\mathrm{\infty })$, of polyps under normal, blue, green, and red light. (b) Parameter $\lambda$ for the exponential distribution to model the white-noise term under normal, blue, green, and red light. (c) Fitted PDF of the white-noise terms under different light conditions by using the average parameter $\lambda$. (d) Simulated in-plane waving motions of five polyps under normal light and 25 °C based on the generalized Langevin equation. Hurst indices are shown below the simulated results. Corresponding PDFs of simulated results are exhibited on the right panel. Cross and triangle symbols in (a),(b) represent the outliers and mean, respectively.

Figure 6

Computational fluid-dynamics simulation with different flow rates of our fluidic platform. Velocity distribution of the fluid is shown in the tubes and chamber. Three slices are shown in the chamber, one of which shows the velocity distribution near the coral nubbin. Results of using flow rates of 5, 25, and 50 µl/s are shown in (a)–(c), respectively.

Figure 7

Laplace transform of the memory kernel for modeling the in-plane motion of coral polyps. First-order, second-order, third-order, and fourth-order estimations of the Laplace transform of the memory kernel are shown in different colors. Third-order and fourth-order estimations overlap. These curves converge to a certain value with the increase of $\zeta$.

Figure 8

Probability density function of the white-noise term. Probability density function of the white-noise term, W, is shaded in gray. Red, blue, and green dashed lines show the fitted exponential function, power-law function, and Gaussian function, respectively.

Figure 9

Model of in-plane waving motion of coral polyps under different temperatures. (a) Value of the memory-kernel function at the Markovian limit, $\hat{K}(\mathrm{\infty })$, of coral polyps at 15, 25, and 30 °C. (b) Parameter $\lambda$ for the exponential distribution to model the white-noise term at 15, 25, and 30 °C. (c) Fitted PDF of the white-noise terms at different temperatures by using the average parameter $\lambda$. Cross and triangle symbols in (a),(b) represent the outliers and mean, respectively.