Environ. Sci. Technol. 2009, 43, 764–768
Do Microscopic Organisms Feel Turbulent Flows? ¨ EST‡ M I K I H O N D Z O * ,† A N D A L F R E D W U St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, Minnesota 55414-2196, and Eawag, Swiss Federal Institute of Aquatic Science and Technology, Surface Waters Research and Management, CH-6047, Kastanienbaum, Switzerland
Received June 16, 2008. Revised manuscript received November 12, 2008. Accepted November 18, 2008.
Microscopic organisms in aquatic environments are continuously exposed to a variety of physical and chemical conditions. Traditionally, it is accepted that due to their small size the physiology of microscopic organisms is not affected by the moving fluid at their scale. In this study, we demonstrate that the small-scale turbulence significantly modulates algal and bacterial nutrient uptake and growth in comparison to still-water control. The rate of energy dissipation emerges as a physically based scaling parameter integrating turbulence across a range of scales and microscopic organism responses at the cell level. Microbiological laboratory tests and bioassays do not consider fluid motion as an important variable in quantifying the physiological responses of microorganisms. A conceptual model of how to integrate the fluid motion in Monod-type kinetics is proposed. We anticipate our findings will encourage researchers to reconsider the laboratory protocols and modeling procedures in the analysis of microorganism physiological responses to changing physical and chemical environments by integrating the effect of turbulence.
Introduction Aquatic microorganisms control one of the fundamental properties of ecosystems, the so-called photosynthesis to respiration ratio. This ratio is a source of information about metabolic processes that produce and consume organic material in aquatic environments and determine whether a water body, such as lake or ocean, is a source or sink for atmospheric CO2. Autotrophic and heterotrophic biomasses are traditionally related to nutrient concentration, light intensity, predation, and large-scale fluid motions. We demonstrate the effects of small-scale turbulence on Escherichia coli, a single-celled motile heterotroph, and Selenastrum capricornutum, a single-celled nonmotile autotroph. Flows in natural water bodies cover a wide range of spatial scales. They range from large-scale eddies, usually scale as physical boundaries of aquatic environments, down to dissipation scales at which molecular processes erase velocity and concentration fluctuations. Physiological responses of microorganisms to small-scale fluid motion and corresponding nutrient uptake at the cell-scale are contradictory (1, 2). A traditional theoretical argument is that turbulent flows are dissipative and, at the scale of microscopic * Corresponding author phone: 612-625-0053; e-mail:
[email protected]. † University of Minnesota. ‡ Eawag, Swiss Federal Institute of Aquatic Science and Technology. 764
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organisms from 1 to 100 µm, do not significantly influence the uptake of nutrients and specific growth of microorganisms (3). In contrast to the theoretical arguments, several studies have documented changes in the physiological responses of microorganisms when exposed to fluid-stirring (4-11). Highresolution in situ profiling of phytoplankton and bacterial distributions have depicted small-scale vertical heterogeneities and thin layers of biological organisms at a spatial resolution from submillimeters to tens of centimeters in the ocean (12, 13). The traditionally advocated laboratory protocols and procedures quantify the physiological responses of microorganisms and provide the basis for formulating kinetic functions in prediction models. This approach does not explicitly consider the interaction between small-scale fluid motion and microorganism physiology (14, 15). While the responses of microorganisms to turbulence are likely species-specific, the fundamental and challenging questions to the majority of microorganisms are in common: (1) What intrinsic fluid flow parameters mediate the growth and nutrient uptake of microorganisms? (2) How can we introduce fluid motion and turbulence in the laboratory protocols for the examination of physiological responses of microorganisms? and (3) How can we conceptually couple turbulence and microorganism growth in the models of population dynamics?
Materials and Methods Theory. Under laboratory conditions, microorganisms are either shaken in flasks on tables or fluid motion is introduced by magnetic spinning bars (14, 15). Mechanically generated turbulence characteristics and the rate of dissipation of kinetic energy per unit mass, ε, in these enclosures are unsteady and three-dimensional with high spatial heterogeneities (16). The most widely used functional relationship for the nutrient uptake and growth of microscopic organisms is the hyperbolic function of external growth-limiting nutrient concentration (17). The relationship is empirically described by µ ) µmax
S Ks + S
(1)
where µ is the specific growth rate or rate of nutrient uptake, µmax is the maximum specific growth rate or maximum rate of nutrient uptake, Ks is the half-saturation substrate concentration, and S is the substrate concentration. When applied to growth rates, equation 1 is referred as the Monod equation, but when applied to nutrient uptake the term Michaelis-Menten is used (18). In either case, the functional relationship does not explicitly account for the effects of fluid motion. Peters et al. (19), reported the deficiency of the Michaelis-Menten nutrient uptake functional relationship and qualitatively demonstrated that small scale turbulence has effects on Ks and µmax. Experiments. Two independent sets of laboratory experiments were conducted to quantify the effects of small-scale turbulence on E. coli and S. capricornutum physiology (7, 8). The experiments were performed under constant external conditions, including temperature, light, initial nutrient, and initial biomass concentrations. The only systematically changed independent experimental variable was fluid-stirring in the reactors. The stirring level was controlled so that ε in the reactor was comparable to the reported values, from 10-11 to 10-4 W kg-1, typically reported for aquatic ecosystems (20, 21). Experiments with E.coli were conducted in an oscillating grid setup (8). The velocity spectra demonstrated the existence of turbulent flow in the reactor with the Reynolds number, defined by the 10.1021/es801655p CCC: $40.75
2009 American Chemical Society
Published on Web 12/31/2008
TABLE 1. E. coli and S. capricornutum Specific Growth Rates at Different Energy Dissipation Ratesa S. capricornutum ε(W kg-1)
0
9.6 × 10-9
3.5 × 10-7
1.2 × 10-6
1.5 × 10-4
µet/µes
1
1.5
1.8
1.7
1.4
ε(W kg-1)
0
7.1 × 10-6
2.9 × 10-5
1.0 × 10-4
1.8 × 10-4
µet/µes
1
1.3
1.6
2.5
5.1
E. coli
a
Specific growth rates were estimated during the exponential growth phase. The energy dissipation rates (ε) were averaged over the reactor volume. µet is the specific growth rate in a turbulent flow, µes is the specific growth rate in the still-water control (ε ≈ 0), and µet/µes is the non-dimensional growth rate ratio.
FIGURE 1. Microscopic photos of the E. coli in a stagnant fluid (still-water control), and turbulent fluid. (a) E. coli cells the second day after the initiation of experiment in a still-water control with energy dissipation rate ε ≈ 0 (green designates cells with intact membrane, red designates cells with damaged membrane, an average cell size is Lc ≈ 2 µm); and (b) E. coli cells the second day after the initiation of experiment under identical conditions in a turbulent flow with ε ≈ 10-4 W kg-1. root-mean-square velocity (urms) and the Taylor microscale (λ), in the range of 28 > urms λ/ν > 11. Experiments with S. capricornutum were conducted in a reactor with submersible dual-sound speakers (7). A sine wave voltage pattern with controllable amplitude and frequency was supplied to the speakers, initiating fluid motion in the proximity of the speaker membrane. In front of each speaker, a fixed grid was placed, creating small-scale eddies in the reactor. The velocity spectra depicted turbulent flow in the reactor, and the Reynolds number was 6 > urms λ/ν > 1.
Results and Discussion Growth and Diffusive Sublayer. Concurrent experiments were conducted under turbulent and stagnant or still-water conditions. The still-water experiments provided controls to the experiments with stirred fluid (7, 8). Small-scale turbulence facilitated the growth of E. coli and S. capricornutum (Figure 1, Table 1). The specific growth of E. coli increased with ε and was up to five times larger in the turbulent flow than in the still-water control. S. capricornutum experienced up to two times the increase in the specific growth in the turbulent flow. At ε >10-6 W kg-1, the specific growth rate of S. capricornutum was gradually hindered by other factors, including mechanical cell membrane damage caused by a
fluid-flow strain rate. Even so, at the higest ε the specific growth rate of S. capricornutum was superior to still-water control. Microscopic organisms, whether they live in a turbulent or nonturbulent fluid, take up nutrients from the ambient fluid across the diffusive sublayer (δD) surrounding the cell (22). In the diffusive sublayer, molecular diffusive transport of molecules to the cell dominates over the corresponding advective transport. The ratio between diffusive sublayer thickness surrounding the cells in a turbulent fluid, δDt, and the corresponding diffusive sublayer in the still-water control, δDs, is depicted in Figure 2. The ratio, δDt/δDs, decreased up to 90% in comparison to the still-water control. The turbulent flow controlled δDt and facilitated the uptake of nutrients up to five times more in comparison to the still-water control for E. coli and up to three times more for S. capricornutum. The solid lines, intended to display overall trend rather than regression functions, are defined by Kolmogorov velocity, determined by the intrinsic fluid flow parameter ε. Figure 2 depicts a scaling relationship δDt/δDs ∼uKLc/D∼(εν)1/4 Lc/ D∼PeK where uK is the Kolmogorov velocity, ν is the kinematic viscosity of the fluid, Lc is the characteristic linear dimension of the cell, D is the molecular diffusion coefficient, and PeK is the Pe´clet number. The relative importance of advective nutrient transport to the cells in comparison to transport by molecular diffusion is depicted by the Pe´clet number in the range 10 > PeK > 0 (Figure 2). Furthermore, the result implies a different definition of advective velocity in the proximity of cell ucK ) uK ) (εν)1/4 which determines the change in δDt/δDs over the physically meaningful range of PeK. Mechanistic models of plankton population dynamics (23-25) customarily define the advective velocity scale by ucp ≈ β (ε/ ν)1/2 Lc where β ≈ 0.1. For specified values of ε, ν, and Lc, the advective velocities ucK and ucp are significantly different (ucp,ucK). This implies that the traditional definition of advective velocity (ucp) defines Pecp ) β (εν)1/2 L2c/D that is much smaller than the proposed PeK ) (εν)1/4 Lc/D defined by the velocity scale ucK. Since Pecp , PeK, the ucp cannot explain the enhanced growth and nutrient uptake of E. coli and S. capricornutum in the PeK > 1 (Figure 2). Physically Based Scaling. A variety of turbulence descriptors with associated velocity and length scales can be used to quantify turbulence levels. However, it is unclear what turbulence variables under laboratory measurements should be matched to the field measurements to study physiological responses of microorganisms. In a turbulent flow, energy is transported progressively from larger to smaller scales through an energy cascade. The cascade can be effectively visualized through the universal spectra of temperature fluctuations (Figure 3). The spectral density of temperature fluctuations versus wavenumber on a log-log VOL. 43, NO. 3, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Diffusive boundary layer (δDt) surrounding E. coli and S. capricornutum in turbulent fluid normalized by the corresponding still-water control (δDs). Solid lines have a functional form δDt/δD s ) exp(- PeK/a) where a ) 1.5 for oxygen, a ) 4.2 for glucose, and a ) 7.8 for SRP. The following values of molecular diffusion coefficient were used: D ) 2.1 × 10-9 m2 s-1 (oxygen), D ) 6.7 × 10-10 m2 s-1 (glucose), D ) 7.8 × 10-10 m2 s-1 (SRP), and ν ) 1.0 × 10-6 m2 s-1.
FIGURE 3. Temperature fluctuation spectra in Lake Baikal at 250 m depth (20) with ε ≈ 10-11 W kg-1 and in an open channel (26) (4 m wide and 2.4 m deep) with ε ≈ 4 × 10-8 W kg-1. Fluid flow-related nutrient transfer to the microorganisms is triggered in the “biotic establishment” region (1) and is transferred to the cells in the “biomass increase” region (2). scale depicts the characteristic domains of the energy cascade, including the production, inertial with a “-5/3” slope, and the dissipation subranges. Since energy is generated at largescales and almost entirely dissipated at small-scales, ε represents a physically based turbulence quantity that through the energy cascade integrates large-scale fluid motion with metabolic responses of microorganisms. Kolmogorov velocity is determined by ε and defines a velocity scale that can be used to quantify the uptake of nutrients by 766
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microorganisms in a turbulent flow (Figure 2). In the production and inertial regions, the corresponding largescale eddies can transport microorganisms through a variety of nutrient concentrations and, therefore, set up a potential background for biotic establishment in the moving fluid. The fluid flow-related nutrient transfer and corresponding biomass increase at the cell-scale is determined in and far beyond the dissipation range in the biomass increase region (Figure 3). The classical theory of turbulence assumes the
velocity and concentration fluctuations are dissipated at the Kolmogorov and Batchelor microscales, respectively. Recent studies have revealed the existence of sub-Kolmogorov-scale velocity fluctuations and regions of very strong and intermittent gradients concentrated in three-dimensional sheets (27-29). The enhanced growth and nutrient uptake of E. coli (Lc ≈ 2 µm) and S. capricornutum (Lc ≈ 5 µm) demonstrate the mediating effects of turbulence on microorganisms at the sub-Kolmogorov microscales. Integrating Turbulence and Physiological Responses of Microorganisms. Following the approach of Edelstein-Keshet (30) and extending the analysis by introducing a diffusive sublayer at the water side of microorganisms, we derived the following expression µ ) µmax
S Ks +S (1 + R)
(2)
where R is the dimensionless constant that designates the ratio of nutrient mass transfer rate through δD surrounding microorganism versus nutrient uptake rate through the receptors in the cell. If fluid surrounding the cells is stagnant, δD is not determined by moving fluid, i.e., R ) 0 and eq 2 is reduced to the familiar format of eq 1. Several estimation procedures of constants in eq 1 are available in the literature (31). Equation 2 can be rearranged as Ks 1 1 1 + ) µ µmax(1 + R) S µmax
()
(3)
On a two-dimensional plot, 1/µ versus 1/S, eq 3 depicts a straight line. The best-fit line through the experimental data provides an estimate of µmax at the intercept. A mediating effect of fluid motion, R, can be estimated from the following equality µmaxt ) µmaxs(1+R) where µmaxt is the maximum specific growth rate or nutrient uptake in a turbulent fluid, and µmaxs is the corresponding coefficient in the still-water control. The equality implies R ) (µmaxt/µmaxs) -1. The magnitude and sign of R provide an experimental quantification of the role of turbulence on microorganism growth and nutrient uptake, i.e., R > 0 implies a facilitated role of turbulence and R < 0 designates inhibitory effects on microorganisms. For the given estimates of µmax and R; Ks can be calculated from a slope of the line depicted by eq 3. At the scale of micrometers, E. coli and S. capricornutum were significantly affected by small-scale turbulence. The rate of dissipation of energy mediated the thickness of δD and corresponding nutrient uptake. Through the energy spectral density in a turbulent flow, ε is a physically based fluid flow parameter integrating turbulence across the range of scales from large-scale eddies to microorganism scales. Laboratory studies examining the effects of turbulence on microorganisms should be conducted at the magnitude and range of ε observed in nature (20, 21). A Monod-type kinetics of functional dependence is proposed that explicitly accounts for the effect of turbulence on microorganism growth and nutrient uptake. Equation 3 can be used in conjunction with laboratory measurements and the prediction models of autotrophic and heterotrophic biomasses in aquatic ecosystems. We have demonstrated a functional dependence for δDt/δDs and ε and envision similar relationships between R and ε for a variety of physiological characteristics of microorganisms. Our measurements imply that physical processes including turbulence at the cell-scale interact with the balance of organic material production and decomposition in aquatic ecosystems.
Acknowledgments This study was funded by the National Center for Earthsurface Dynamics (NCED), a Science and Technology Center funded by the Office of Integrative Activities of the
National Science Foundation (under agreement EAR0120914). Experiments with S. capricornutum were conducted by Dr. Tanya Warnaars (University of Minnesota) and those with E. coli were conducted by Dr. Amer AlHomoud (University of Minnesota). We are also grateful to the Swiss Federal Institute of Aquatic Science and Technology, Eawag, for providing a partial support during the preparation of manuscript at the Department of Surface Waters - Research and Management, Kastanienbaum, Switzerland. We thank Dr. Christopher Ellis (St. Anthony Falls Laboratory, University of Minnesota) for his valuable assistance with data acquisition.
Note Added after ASAP Publication There was an error in Table 1 in the version of this paper that published ASAP December 31, 2008; the corrected version published ASAP January 29, 2009.
Supporting Information Available Detailed explanations of experimental procedure, and diffusive sublayer thickness estimation. This material is available free of charge via the Internet at http://pubs.acs.org.
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