Research ArticleAPPLIED ECOLOGY

Chain formation can enhance the vertical migration of phytoplankton through turbulence

See allHide authors and affiliations

Science Advances  16 Oct 2019:
Vol. 5, no. 10, eaaw7879
DOI: 10.1126/sciadv.aaw7879
  • Fig. 1 Both single phytoplankton cells and multicellular phytoplankton chains have elongated shapes, which can markedly affect their ability to migrate through turbulence.

    (A) The unicellular Chlorogonium elongatum displays a highly elongated morphology, a characteristic of many species of motile phytoplankton (2). (B) The center of mass of unicellular phytoplankton (blue circle) can be separated from their center of buoyancy (gray circle), for example, because dense organelles are asymmetrically distributed within their bodies (21). This gives rise to a stabilizing torque that acts to keep the direction of motility p pointed in the vertical direction and facilitates migration over the depth of the water column. (C) Chain-forming species, such as the eight-cell chain of the dinoflagellate Gymnodinium catenatum shown here, also exhibit a highly elongated morphology. (D) By analyzing the balance of torques on the idealized chain shown here, we predict that when longer chains are perturbed away from their equilibrium orientations, they require a much larger characteristic time scale, B, to return than that of a single cell (Materials and Methods). (E) The gyrotactic reorientation time scale, B, increases with chain length. While single cells have reorientation time scales of order B = 5 s, a hydrodynamic model predicts that the B of a chain eight cells long is an order of magnitude greater. (F) The nondimensional parameter Ψ = BωK measures the stability of a cell relative to the Kolmogorov scale shear, ωK, that they experience in turbulent environments. When Ψ ≳ 1, vertical motility is expected to be suppressed (20). Thus, based purely on stability considerations, chains larger than eight cells are expected to lack the ability to migrate through even relatively weak turbulence (i.e., with a dissipation rate of ε = 10−9 W/kg). The cell shown in (A) is approximately 100 μm long and is reproduced with permission of Y. Tsukii (Hosei University, Japan). The chain shown in (C) is approximately 300 μm long and is reproduced with permission of H. Chang (National Institute of Water and Atmospheric Research, New Zealand).

  • Fig. 2 Elongation stabilizes the orientation of cells in turbulent flow, allowing them to keep a larger fraction of their motility oriented in the vertical direction.

    (A and B) Here, we plot the trajectories of 200 single spherical cells [α = 0 (A)] and highly elongated chains [α = 1 (B)] that are swimming in a DNS of turbulence. While chain formation can affect both the intrinsic stability (Fig. 1) and the swimming speed (Fig. 4A), here, we use [Ψ = 10, Φ = 10] in both simulations to isolate the effect of swimmer shape. As advection by flow adds considerable noise, the trajectories shown here have been postprocessed to show movement only due to motility (dx/dt = Φp). Trajectories show movement over 20 Kolmogorov time scales (20ωK1) and have been color-coded to reflect the instantaneous vertical fluid velocity, uz/VK, at the cell location. While these trajectories occur at different positions within our three-dimensional computational domain, for the purposes of presentation, we have taken the [x, z] projection of each trajectory and moved its initial position to the origin. (C) To more directly quantify how elongation affects swimming direction in turbulence, we measured the mean vertical projection of the swimming direction, 〈pz〉, for 100,000 swimmers with either spherical (filled symbols) or highly elongated (open symbols) morphologies. A population of cells that swims strictly upward against gravity yields 〈pz〉 = 1, while 〈pz〉 = 0 for a population of cells that move in random directions. This analysis shows that elongation can substantially enhance the stability of cells, and this effect becomes more pronounced as cell speed, Φ, increases.

  • Fig. 3 Single spherical cells accumulate where they have to swim against the flow, while elongated chains accumulate where flow propels them in the same direction as their motility.

    (A to C) Two simulations were performed with identical motility parameters [Ψ = 1, Φ = 10], except that in one simulation, cells were spherical α = 0, whereas in the other, they were highly elongated, α = 1. (A) and (C) show a horizontal slice through the three-dimensional simulations, in which the white circles show cell positions and the color map shows the vertical fluid velocity, uz, normalized by the Kolmogorov velocity, VK. (B) We measured uz at the location of 100,000 cells to quantify how shape affects the vertical transport of cells by flow. Upward-migrating spherical cells (blue) tend to accumulate in regions of downwelling (uz < 0), whereas upward-migrating elongated cells (red) tend to accumulate in regions of upwelling (uz > 0). (D) To understand how these dynamics vary with chain length, we calculated the mean vertical fluid velocity at the location of swimmers with different chain lengths. We find that as chains get longer, they progressively move from downwelling to upwelling regions of the flow, suggesting that longer chains benefit from this mechanism more than shorter ones. Similar trends were observed for different values of the nondimensional stability number, Ψ, although the transition to upwelling occurs at larger chain lengths for more stable cells (i.e., for smaller Ψ). All simulations used a nondimensional swimming speed Φ = 10.

  • Fig. 4 Chain formation allows motile phytoplankton to migrate faster through relatively weak turbulence.

    (A) Empirical measurements show that swimming speed increases with chain length, a finding that is consistent with models that assume that thrust increases at a faster rate than hydrodynamic drag as a chain gets longer (green symbols; Materials and Methods). While there is variability across different species, these results suggest that the swimming speed of a chain of length n can be approximated using VC(n)/VC(1)nβ, where VC(1) is the swimming speed of a single cell and β is an exponent with a value on the interval [0.2 0.6]. We note that we omitted (16) from this analysis because they only reported swimming speeds projected along a single axis. (B and C) We combine a model that estimates how the gyrotactic orientation time scale B(n) changes with chain length (Fig. 1E) with our expression for VC(n) to understand the [Ψ, Φ] parameter space sampled by a chain as it increases in length and experiences different turbulent dissipation rates, ε. Here, we assume that single cells have B(1) = 5 s and VC(1)=500 μm/s, which are representative values from the literature (2, 2123, 28). Solid lines show results for β = 0.4, while dashed lines show β = 0.2 and 0.6 to illustrate potential variability in Φ (lower and upper dashed lines, respectively). The color map in (B) shows 〈uz〉/vK, the mean vertical fluid velocity at the centroid of swimmers (α = 1), which indicates that chain formation in relatively weak turbulence (ε = 10−9 to 10−8 W/kg) induces a shift from accumulating in downwelling parts of the flow 〈uz〉 < 0 to accumulating in upwelling parts of the flow 〈uz〉 > 0. However, in stronger turbulence (ε > 10−7 W/kg), both single cells and chains accumulate in downwelling regions. The color map in (C) shows the change in the average swimming direction 〈pz〉 caused by elongation, calculated here as the difference in 〈pz〉 between highly elongated chains (α = 1) and spherical single cells (α = 0). This indicates that chain formation enhances the ability of cells to keep their motility pointed in the vertical direction in all but the most intense turbulence (i.e., as long as ε < 10−6 W/kg). (D) Using both our model for Ψ (Fig. 1F) and our fit of empirical data for Φ [(A), β = 0.4], we estimate how chain formation affects the overall migration rate of cells at different turbulent dissipation rates. We normalized T(n), the time required for a chain to traverse a fixed distance through a turbulent water column, by T(1), the time needed by a single cell to swim the same distance. Thus, if T(n)/T(1) is smaller than unity, chains can migrate through turbulence more quickly than single cells. This analysis indicates that chain formation markedly enhances vertical migration in relatively weak turbulence. However, in stronger turbulence, chain formation can either increase or decrease migration time, depending on the length of the chain.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/10/eaaw7879/DC1

    Fig. S1. Elongation drives patchiness in the distribution of motile cells swimming in turbulence, and this peaks at intermediate swimming speeds.

    Fig. S2. Elongation causes the distribution of gyrotactic swimmers to become less patchy at small values of ψ and more patchy at large values of ψ.

    Fig. S3. Spherical gyrotactic swimmers (α = 0) preferentially sample flows that move in the direction opposite to that of their motility.

    Fig. S4. Stronger turbulence impedes vertical migration, increasing the amount of time that chains require to traverse a water column.

    Fig. S5. A simple model of bottom heaviness reveals that the distance between the center of mass and center of buoyancy of a chain is independent of chain length.

    Table S1. The drag force shape correction factors, K, for the two models used to estimate chain swimming speed.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Elongation drives patchiness in the distribution of motile cells swimming in turbulence, and this peaks at intermediate swimming speeds.
    • Fig. S2. Elongation causes the distribution of gyrotactic swimmers to become less patchy at small values of ψ and more patchy at large values of ψ.
    • Fig. S3. Spherical gyrotactic swimmers (α = 0) preferentially sample flows that move in the direction opposite to that of their motility.
    • Fig. S4. Stronger turbulence impedes vertical migration, increasing the amount of time that chains require to traverse a water column.
    • Fig. S5. A simple model of bottom heaviness reveals that the distance between the center of mass and center of buoyancy of a chain is independent of chain length.
    • Table S1. The drag force shape correction factors, K, for the two models used to estimate chain swimming speed.

    Download PDF

    Files in this Data Supplement:

Stay Connected to Science Advances

Navigate This Article