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Trade-Offs of Chemotactic Foraging in Turbulent Water

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Science  02 Nov 2012:
Vol. 338, Issue 6107, pp. 675-679
DOI: 10.1126/science.1219417

Abstract

Bacteria play an indispensable role in marine biogeochemistry by recycling dissolved organic matter. Motile species can exploit small, ephemeral solute patches through chemotaxis and thereby gain a fitness advantage over nonmotile competitors. This competition occurs in a turbulent environment, yet turbulence is generally considered inconsequential for bacterial uptake. In contrast, we show that turbulence affects uptake by stirring nutrient patches into networks of thin filaments that motile bacteria can readily exploit. We find that chemotactic motility is subject to a trade-off between the uptake benefit due to chemotaxis and the cost of locomotion, resulting in an optimal swimming speed. A second trade-off results from the competing effects of stirring and mixing and leads to the prediction that chemotaxis is optimally favored at intermediate turbulence intensities.

The average milliliter of seawater contains a million heterotrophic bacteria that play an essential role in remineralizing dissolved organic matter (DOM) by decomposing 35 to 80% of net primary production (1) and converting it into particulate form, available for consumption by larger organisms. Most marine environments are turbulent, ranging from the energetic mixed-layer and surf zone to calmer thermoclines, yet the effect of turbulence on bacterial uptake of DOM has remained elusive. This is due in part to the difficulty of quantifying the microscale biogeochemical variability generated by turbulence. At the same time, the physics of transport at micrometer scales dictates that DOM uptake occurs primarily by diffusion of nutrient molecules to cells (2). In a homogeneous nutrient environment, marine turbulence is insufficient to increase bacterial uptake (2, 3), at least for low–molecular weight substrates. For example, relatively strong turbulence (ϵ = 10−6 W kg−1, where ϵ is the turbulent dissipation rate) increases the uptake of amino acids by <1%, and as a result turbulence has been considered inconsequential for bacterial uptake (2).

Many DOM sources occur as small, discrete patches, including cell lysis, phytoplankton exudation, marine snow particles, oil droplets, and excretions by larger organisms (4, 5). Numerous bacterial taxa have evolved the ability to sense chemical gradients associated with patches and swim toward more favorable conditions (58), a process called chemotaxis. Chemotaxis can affect marine biogeochemical cycles by increasing remineralization rates (5, 9), and community composition by affording motile bacteria a benefit over nonmotile competitors (7). Yet, most knowledge of chemotactic foraging is based on studies in still fluid, simple flows, or synthetic advection (7, 10, 11).

Here, we show that turbulence can affect the relative uptake of DOM by motile and nonmotile bacteria by reshaping the nutrient landscape to which chemotactic bacteria respond. To study the trade-offs of chemotaxis in the turbulent ocean, we used direct numerical simulations (DNS) (12). This method has been applied extensively to model passive scalars in turbulence (13). We use it to resolve the smallest turbulent scales and quantify their impact on the nutrient competition between motile and nonmotile bacteria.

A range of spatial scales affect bacterial foraging in the ocean (Fig. 1). Bacteria experience turbulence as smooth, slowly varying velocity gradients, because their size (≈1 μm) is considerably smaller than the Kolmogorov scale, lK (≈1 to 10 mm in the ocean) (3), the smallest scale at which turbulent velocity fluctuations occur. Gradients in nutrient concentration persist down to a smaller scale, the Batchelor scale lB (≈10 to 300 μm in the ocean) (14). Motile bacteria can exploit nutrient gradients if their “motility range”—the distance they can cover over the lifetime of the patch—is larger than the Batchelor scale (Fig. 1). This is generally the case, because bacteria swim up gradients at 5 to 40 μm s−1 (8, 15) and can thus travel a distance of lB in a few seconds.

Fig. 1

Physical and biological length scales in the ocean. Turbulent stirring generates variance in the distribution of dissolved nutrients on scales as small as the Batchelor scale, lB, but does not directly affect the diffusive flux of nutrients on the scales of bacterial cells. However, motile bacteria sample spatial scales considerably larger than their size: Their “motility range” is the distance that they can travel during the lifetime of a typical nutrient patch, while moving up nutrient gradients at the chemotactic velocity VC. Here, ϵ is the turbulent dissipation rate, ν is the kinematic viscosity of seawater, and κC is the nutrient diffusivity.

To determine the impact of turbulence on chemotactic foraging, we used DNS to simulate the competition between motile and nonmotile bacteria for a DOM patch occurring in a turbulent flow (16). The two bacterial species were initially distributed uniformly, each with concentration B0 = 2.5 × 1011 cells m−3. Bacteria consume nutrients at a rate 1/τU, where τU ≈ 200 s is a typical uptake time scale (16). Nonmotile bacteria remain uniformly distributed and rely on diffusion to obtain nutrients. Motile bacteria swim up nutrient gradients with a chemotactic velocity that increases with the gradient’s magnitude, up to a maximum velocity VC (16). Using dissolved organic carbon as a representative nutrient, we assumed an initial peak concentration of C0 = 10 μMC to reflect the approximately three orders of magnitude concentration enhancement within patches compared to background levels (typically, 0.1 to 50 nMC) (17). In this large difference lies the potential benefit of chemotaxis.

Turbulence affects uptake by reshaping the patch into a complex nutrient landscape (movie S1), dramatically changing the gradients experienced by chemotactic bacteria. Consider motile bacteria (VC = 20 μm s−1) in relatively strong turbulence (ϵ = 10−6 W kg−1) (Fig. 2 and movie S1). Within seconds, turbulence stirs the patch into filaments and sheets as thin as lB (Fig. 2, top row), which the chemotactic bacteria quickly locate (Fig. 2, bottom row). Fifteen seconds after release of the patch, nutrient filaments are pervasive and harbor concentrations of motile bacteria 50% above background. At 30 s, the patch has morphed into a web of tangled filaments, whose topology is mirrored in the distribution of motile bacteria. After 60 s, the remaining nutrients are well-mixed (the standard deviation of the nutrient concentration is 3.5% of its initial value) and the clustering of motile bacteria begins to fade.

Fig. 2

Stirring of a nutrient patch and response of chemotactic bacteria. As a nutrient patch is stirred by a turbulent flow (top row, showing nutrient concentration C), chemotactic bacteria respond by accumulating within nutrient filaments (bottom row, showing concentration of motile bacteria BM), thereby enhancing their uptake. For this simulation, the chemotactic velocity was VC = 20 μm s−1, the turbulent dissipation rate ϵ = 10−6 W kg−1, and the domain size L = 5.65 cm. Values of C and BM are normalized by the initial maximum nutrient concentration, C0, and the concentration of nonmotile bacteria, BNM, respectively. The lowest value on each color scale is made transparent, and opacity increases linearly with concentration. Images generated using Vapor (www.vapor.ucar.edu).

Accumulation of motile bacteria within nutrient-rich filaments increases their uptake rate compared with nonmotile bacteria (Fig. 3A). The difference in the population-averaged, per-cell uptake rate between motile and nonmotile bacteria (16) is a measure of the motility benefit. After rescaling by the number of patches occurring in the computational volume in a day, based on a carbon injection rate of C˙inj=0.12gCm3day1 (16), and by the carbon content in one cell (16), the motility benefit can be expressed in units of new cell equivalents produced by each bacterium per day. For the scenario shown in Fig. 2, the motility benefit peaks 13.2 s after injection of the patch. At this time, motile cells consume 23% more than nonmotile cells, an equivalent benefit of more than one new cell per day (per individual) if the uptake difference was sustained at this level (relative to 4.5 new cells per day produced by each cell of either species in the absence of chemotaxis). Instead, the motility benefit nearly vanishes after 50 s, even though 59% of the nutrient is still available, because what remains has been mixed, erasing any advantage of motility. The instantaneous motility benefit, like the nutrient filaments, is therefore highly transient.

Fig. 3

Trade-offs of chemotactic foraging. (A) The instantaneous motility benefit as a function of time since release of the nutrient patch, for different turbulence intensities ϵ and chemotactic velocities VC. (B) The motility benefit, shown for three carbon injection rates Embedded Image (solid lines), increases with the chemotactic velocity VC, but the cost of swimming (dashed red line) increases more rapidly (quadratically) with VC. The trade-off between motility benefit and swimming cost results in an optimal chemotactic velocity (dotted lines) of VC ≈ 15 to 25 μm s−1. (C) The trade-off between stirring and mixing results in an optimal value of turbulence (dotted lines) that depends on the initial patch size, σ. For large patches, the motility benefit is optimal in moderate turbulence (orange line), whereas smaller patches lead to an optimum in weak turbulence (blue line). Values of the motility benefit in the absence of flow (ϵ = 0) are connected with dashed lines (values of ϵ < 7.7 × 10−10 W kg−1 were not considered owing to computational restrictions).

To determine the chemotactic velocity that optimizes foraging, we performed competition simulations where we varied the maximum chemotactic velocity, VC, while keeping the turbulence intensity constant at an intermediate level (ϵ = 1.2×10−8 W kg−1). The advantage afforded by chemotaxis depends strongly on VC (Fig. 3, A and B). The motility benefit is weak throughout the patch lifetime for slow chemotaxers. For example, motility enhances the instantaneous uptake by at most 15%, affording a time-averaged benefit of 0.3 new cells per day, for VC = 5 μm s−1. A chemotactic velocity of this order is typical of the enteric bacterium Escherichia coli (VC = 0.6 to 13.8 μm s−1) (15), the traditional model organism for the study of chemotaxis. In contrast, marine bacteria are capable of much higher swimming speeds (up to a few hundred μm s−1) and high-performance chemotaxis (6, 7, 18). For chemotactic velocities of VC = 20 to 60 μm s−1, associated with swimming speeds of VS = 60 to 170 μm s−1 (16), the motility benefit can be much larger, with motile cells instantaneously consuming up to 58 to 133% more than nonmotile cells and experiencing a time-averaged benefit of 1.1 to 2.3 additional new cells per day (Fig. 3, A and B).

Motility can be costly for marine bacteria. The motility benefit grows approximately linearly with chemotactic velocity (Fig. 3B), whereas propulsive power increases quadratically with the swimming speed (16). This suggests a trade-off between enhanced uptake and swimming cost, and the existence of an optimal chemotactic velocity. To test this prediction, we computed the net motility benefit as the difference between the motility benefit and the power required for swimming (16). In intermediate turbulence (ϵ = 1.2 × 10−8 W kg−1), the net motility benefit is maximal for VC ≈ 15 to 25 μm s−1 (Fig. 3B), corresponding to swimming speeds VS of 45 to 70 μm s−1 (16). These values are in good agreement with speeds recorded for several species of marine bacteria (68, 18, 19), suggesting that motility in marine bacteria might be under selection for chemotactic fitness.

The effectiveness of chemotaxis as a foraging strategy further depends on the intensity of turbulence through the stirring and mixing of nutrient patches. We quantified this dependence by varying the turbulence intensity, while keeping the chemotactic velocity constant (VC = 20 μm s−1). For an initial patch size of σ = 2.5 mm, chemotaxis is optimally favored at weak turbulence intensities (ϵ ≈ 10−9 W kg−1), characteristic of the ocean thermocline (20), where the motility benefit is slightly larger than in the absence of turbulence (Fig. 3C). In contrast, the motility benefit is fivefold smaller at ϵ = 10−6 W kg−1 (Fig. 3C), indicating that chemotaxis is less effective in highly turbulent regions, such as the upper ocean. For larger patches the optimum turbulence intensity shifts to intermediate values (ϵ ≈ 10−8 to 10−7 W kg−1 for σ = 7.5 mm; Fig. 3C), characteristic of the upper thermocline (20). Although observations of motility in the ocean are insufficient to test these predictions, it will be interesting to determine whether changes in the prevalence of motility and chemotaxis with depth revealed by metagenomic studies (21) are in part determined by turbulence levels.

The existence of an optimal turbulence intensity points to a second, more subtle trade-off: that between stirring and mixing. Stirring increases the surface area between the nutrient patch and the surrounding water (Fig. 2). Mixing refers to homogenization of the nutrients, which is aided by stirring but ultimately occurs by molecular diffusion. Stronger turbulence produces thinner filaments and steeper nutrient gradients that elicit faster chemotaxis, but also accelerates mixing, which erases the motility benefit. This trade-off results in an optimal turbulence intensity, whereby the maximum motility benefit depends jointly on the size and lifetime of DOM filaments.

Constraints on chemotaxis can be understood in terms of three fundamental time scales (16). The chemotaxis time scale, τC = lB/VC, is the time it takes a bacterium to swim to the core of a nutrient filament, whose characteristic width is the Batchelor scale, lB. Stronger turbulence creates finer filaments (smaller lB and τC), but also decreases the filaments’ lifetime, which is characterized by the mixing time scale, τM= lB2C, where κC is the nutrient diffusivity. One thus expects that the motility benefit depends on the relative magnitude of τC and τM. A further condition for motility to be beneficial is that the consumption of the patch through uptake is slower than chemotactic migration, i.e., τC < τU. We quantify the relative magnitude of the three time scales by means of two Frost numbers, FrM = τCM and FrU = τCU (16, 22). When FrM >> 1 or FrU >> 1, chemotaxis is too slow relative to mixing (the “mixing-limited regime”) or consumption (the “uptake-limited regime”), respectively, for motile bacteria to gain appreciable benefit. This argument is verified by a formal scaling analysis (16), whose prediction (Eq. S40) is in good agreement with the DNS results.

In addition to swimming speed and turbulence intensity, the net benefit of chemotaxis depends on multiple features of the nutrient landscape, as additional simulations reveal (16). The total nutrient injection rate must be sufficient to justify the investment in motility. We used a baseline value of 0.12 gC m−3 day−1, representative of relatively nutrient-rich conditions (1, 16). Fast chemotaxis is optimal at higher injection rates (Fig. 3B), whereas lower input rates shift the competition in favor of nonmotile bacteria, in line with evidence that abundant species in the oligotrophic open ocean are nonmotile (23). The benefit of chemotaxis further depends on patch size. In the absence of flow, the motility benefit is optimal for a patch size of σ ≈ 650 μm; larger patches are too vast for bacteria to reach their nutrient-rich core, whereas smaller patches quickly diffuse away. The motility benefit is less dependent on the initial patch size in a turbulent flow, because the patch is stirred into Batchelor-scale filaments. Therefore, turbulence can significantly favor the utilization of larger patches by motile bacteria (Fig. 3C). Finally, an important role is played by the nutrient diffusivity, because higher–molecular weight solutes, abundant in the ocean, diffuse more slowly, prolonging the filaments’ lifetime and favoring chemotaxis (16). Taken together, these findings indicate that, although our fundamental conclusions apply to a broad range of nutrient conditions, the net motility benefit is environment-dependent: It will be lower than predicted here, or vanish entirely, for oligotrophic conditions or very small patches, and it might be higher for intermediate patch sizes or high–molecular weight solutes.

Our results indicate that, in contrast to E. coli (24), motile marine bacteria spend a sizable fraction of their metabolic budget on locomotion. Whereas many coastal ocean bacteria are motile (9, 25), dominant clades in the open ocean, like SAR11 (23), are nonmotile, providing evidence that motility is not without cost. We propose that a fundamental determinant of the prevalence of motility in a given environment is the trade-off between motility benefit and swimming cost. Chemotaxis in the heterogeneous, time-varying nutrient landscape prevalent in the ocean should be seen as an optimal foraging problem, where the most successful strategy depends on the nutrient distribution and turbulence intensity. In addition to the trade-offs presented here, other factors can affect the optimal foraging behavior. Additional costs, associated with biosynthesis of flagella, operation of chemotaxis pathways, increased encounter rates with predators, and less effective uptake kinetics, might reduce the optimal chemotactic velocity and the net motility benefit. In contrast, the benefits of motility could be augmented by the ability of fast cells to escape capture (26) or to modulate swimming so as to combine intermediate exploration speeds with fast exploitation speeds (27). Indeed, most bacteria remain outside of nutrient filaments (e.g., less than 1.7% of the cells experience C > 0.01C0 at any given time) and can be considered in “exploration mode,” using undirected motility to search for a chemical signal that they can exploit through chemotaxis.

DNS provides a quantitative framework to investigate this optimal foraging problem, and we have applied it to show that turbulence can affect the competition between motile and nonmotile bacteria. The outcome of this competition will be an important determinant of species succession when environmental conditions change—for example, during algal blooms or oil spills, when the abundance of DOM sources varies greatly. More broadly, DNS promises to be a valuable tool to address the elusive effects of turbulence on microscale biophysical processes, such as gamete encounter rates (28), phytoplankton patchiness (29), microbial productivity in bioreactors (30), and the fate of microbial nutrient sources, including particle plumes and oil droplets.

The results presented here upend the prevailing view on the effect of turbulence on aquatic microorganisms. Contrary to current understanding, based on homogeneous nutrient environments where turbulence is inconsequential for bacterial uptake (2), motile bacteria are directly affected by fluid motion in a heterogeneous environment, where they can exploit thin nutrient filaments generated by turbulence. This process generalizes to a broad spectrum of nutrient sources, because turbulence will stir even large DOM patches into a tangled web of filaments. Accordingly, the nutrient landscape experienced by aquatic microorganisms might be even more heterogeneous and intermittent than previously thought (4), renewing the challenge of capturing the effect of this variability on microbial adaptations and marine biochemistry.

Supplementary Materials

www.sciencemag.org/cgi/content/full/338/6107/675/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S9

Table S1

References

Movie S1

References and Notes

  1. Supplementary materials are available on Science Online.
  2. Acknowledgments: We thank W. M. Durham, R. Ferrari, M. Follows, M. Garren, F. Menolascina, S. Merrifield, T. Pedley, S. Smriga, and R. Watteaux for helpful comments and suggestions. The calculation of the resistive force coefficient for a bacterium was performed by Marcos. J.R.T. was supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship. R.S. acknowledges NSF grants OCE-0744641-CAREER and CBET-1066566.
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