Diamagnetic levitation enhances growth of liquid bacterial cultures by increasing oxygen availability

Abstract

Diamagnetic levitation is a technique that uses a strong, spatially varying magnetic field to reproduce aspects of weightlessness, on the Earth. We used a superconducting magnet to levitate growing bacterial cultures for up to 18 h, to determine the effect of diamagnetic levitation on all phases of the bacterial growth cycle. We find that diamagnetic levitation increases the rate of population growth in a liquid culture and reduces the sedimentation rate of the cells. Further experiments and microarray gene analysis show that the increase in growth rate is owing to enhanced oxygen availability. We also demonstrate that the magnetic field that levitates the cells also induces convective stirring in the liquid. We present a simple theoretical model, showing how the paramagnetic force on dissolved oxygen can cause convection during the aerobic phases of bacterial growth. We propose that this convection enhances oxygen availability by transporting oxygen around the liquid culture. Since this process results from the strong magnetic field, it is not present in other weightless environments, e.g. in Earth orbit. Hence, these results are of significance and timely to researchers considering the use of diamagnetic levitation to explore effects of weightlessness on living organisms and on physical phenomena.

1. Introduction

It is important to understand how weightlessness influences bacterial behaviour, not only for the health of astronauts, but also for the long-term future of space exploration [1]. Earth-based techniques can simulate aspects of a microgravity environment, but are either time-limited to a few seconds or minutes (drop towers, parabolic flights and sounding rockets), or use rotation to time-average the gravity vector to zero, which can introduce artefacts owing to the rotating reference frame (clinostats, random positioning machine; [2]).

Here, we use the diamagnetic force induced by a strong, spatially varying magnetic field to balance the force of gravity [3–7]. Just as the centrifugal force balances the gravitational force on an orbiting spacecraft, the diamagnetic force opposes the force of gravity on a levitating object. The potential of diamagnetic levitation as a laboratory-based tool to investigate the effects of weightlessness on living organisms was first demonstrated by Valles et al. [5], who studied levitating frog embryos, and by Berry & Geim [4] who levitated a live frog. Liu et al. [8] recently demonstrated levitation of a live mouse. In common with all ground-based techniques to simulate weightlessness, there are effects introduced by diamagnetic levitation that are not present in a weightless environment. For the first time, we critically assess the effect of diamagnetic levitation on a growing bacterial culture in liquid, over an 18 h period. We use a superconducting magnet to levitate the culture.

Guevorkian & Valles [9] reported that Paramecia change their swimming behaviour in magnetically altered effective gravity, in response to the altered buoyancy of the cells. Coleman et al. [10] investigated the effect of magnetic levitation on growth and cell cycle changes in wild-type yeast cells, concluding that neither the growth nor the cell cycle was affected by the magnetic field when cells were levitated, but that growth was reduced at increased effective gravity. Some selective effects were seen on cells with specific mutation in transcription factors, known to mediate responses to environmental stresses such as gravity and shear stress, indicating that adaptive gene expression was required for the cells to be able to grow normally. Our previous experiments on magnetically levitated Arabidopsis thaliana cell cultures have also shown that adaptive responses occur, again detected by changes in the expression of transcription factors. In this case, the adaptations were similar to those seen when cells experienced simulated weightlessness in a random positioning machine [11]. (Wilson et al. [12] have also shown that space flight alters bacterial gene expression and virulence, in this case owing to a decrease in the levels of the global gene regulator Hfq, again indicating the need for adaptation to the conditions experienced during growth in a weightless environment.)

Here we show that magnetic levitation of bacteria in a liquid culture increases the rate of population growth and the final cell density of the culture. We investigate the mechanism leading to this enhancement.

2. Initial hypothesis

For these experiments, we chose Escherichia coli and Staphylococcus epidermidis as examples of human commensal bacteria, and as representatives of the Gram-negative and Gram-positive groups, respectively. We used a specially designed 17 T superconducting solenoid with a closed-circuit cryogenic system to levitate samples of bacterial culture in liquid nutrient broth. The magnet has a vertical bore. The temperature of the bore was kept at 37°C by forced air flow. Using a superconducting magnet to levitate biological organisms and material [10,11,13–15] rather than a resistive magnet is attractive because we can levitate for periods much longer than can be obtained, economically, using a resistive magnet.

2.1. Effective gravity acting on the liquid culture medium

Water, being diamagnetic, is repelled from the strong magnetic field at the centre of the solenoid. The liquid levitates where the magnetic force balances the gravitational force, approximately 75–80 mm above the geometric centre of the solenoid, depending on the solenoid current [16,17]. Following Valles et al. [5], we define the effective gravity acting on the water as , where B and are the magnitude of the magnetic field and the magnetic field gradient, respectively; χ_w = −9 × 10⁻⁶ (SI units) and ρ_w = 1000 kg m⁻³ are the volume magnetic susceptibility and density of water, respectively; g = 9.8 m s⁻² is the gravitational acceleration at the Earth's surface and μ₀ = 4π × 10⁻⁷NA⁻². At the levitation point Γ_z = 0. Since the culture medium is composed mostly of water, it levitates at the same position, under the same conditions. Note that a positive value of Γ_z indicates a net upward force, and a negative value of Γ_z indicates a net downward force. A more detailed discussion of effective gravity and the variation in Γ near the levitation point can be found in the electronic supplementary material, appendix S1.

2.2. Effective gravity acting on the cells

Whether an individual cell floats or sinks in the liquid culture medium depends on Archimedes' principle, i.e. on the difference between the cell's weight and the weight of fluid displaced by the cell. In a weightless environment, e.g. in an orbiting spacecraft, both weights are zero, so the cells are neutrally buoyant. We express the net force acting on the cell, including buoyancy forces, as an effective gravity: , where Δχ = χ_c − χ_w and Δρ = ρ_c − ρ_w. Here, χ_c is the spatially averaged volume magnetic susceptibility of the cell and ρ_c is the spatially averaged (‘buoyant’) density of the cell (i.e. its mass divided by its volume). See the electronic supplementary material, appendix S2.1, for the derivation and additional discussion.

For neutral buoyancy, we require the net force acting on the cell to be zero; that is, we require . Outside the magnet, , since the buoyant density of the bacterial cells is ρ_c ≈ 1090 kg m⁻³ [18]; hence, we expect the cells to sediment in the culture medium, outside the magnet. We now consider whether the diamagnetic force on the cells and on the fluid can prevent the cells from sinking. We estimate Δχ = −(8 ± 3) × 10⁻⁷ experimentally by measuring the levitation position of a bacterial pellet in the bore [19]; most of the experimental error in this measurement is owing to uncertainty in the water content of the bacterial pellet. From this result, we estimate that at the levitation point of the culture medium. This analysis suggests that it is possible to achieve a pseudo-weightless condition in the magnetically levitated bacterial culture, in the sense that the fluid medium is weightless and the cells are simultaneously neutrally buoyant in the fluid ().

2.3. Estimate of the effect of levitation on the sedimentation rate of the cells

Based on our experimental measure of Δχ, we estimate that the sedimentation rate should be reduced to (10 ± 30) per cent of the rate exhibited outside the magnet. The negative percentage encompassed by the uncertainty in this value indicates that our estimate includes the possibility that the cells will float to the surface, rather than sink. We have expressed the sedimentation rate as a percentage of the 1g control rate, rather than an absolute value, since the rate is dependent on the cell size. The calculation is outlined in the electronic supplementary material, appendix S2.2.

3. Controls

We use culture volumes of more than 1 ml to allow for sampling during the experiment and to ensure that the culture volume is not significantly affected by evaporation. Strong magnetic fields of the order of 10 T are required to magnetically levitate culture volumes of this size; in our experiments, B = 12.3 T at the levitation point. There is evidence that B fields of this strength affect biological organisms at the cellular level. For example, striking changes were observed in the orientation of cell-division cleavage planes in developing frog embryos in a static field B ∼ 1 T [20,21]. Stresses can arise from a magnetic torque resulting from anisotropy in the magnetic susceptibility of structures [21,22]. The significance of these forces depends on whether the energy associated with such forces is larger than the thermal energy scale. Another possibility is that the magnetic field can affect biochemical kinetics [23]. Internal stresses in a biological cell can also be altered in a gradient magnetic field, owing to variations in the magnetic susceptibility of the cell's constituents. Valles et al. [5] performed experiments on magnetically levitated frog embryos, concluding that levitation reduced the gravity-induced internal stresses within the cell.

We shall not analyse these possibilities in further detail here. However, by using a control sample placed at the centre of the solenoid coil, enclosing the Γ = 1g point, we can distinguish experimentally between the effects of magnetic forces that are proportional to the field–field gradient product , and magnetic effects that depend only on B [5,24]. As an additional control, a sample container was also placed below the centre of the solenoid, enclosing the Γ = 2g point, where gravity and the magnetic force are additive, and B = 12.3 T. For convenience, we label the sample containers ‘0g*’, ‘1g*’ and ‘2g*’ corresponding to the effective gravity enclosed by each container; the asterisk on the label indicates the sample is in a strong magnetic field, either 16.3 T at 1g* or 12.3 T at 0g* and 2g*. The variation of Γ in the 0g* container is discussed in the electronic supplementary material, appendix S1, and shown in the electronic supplementary material, figure S1. We use the label ‘1g’ to indicate the control sample, grown outside the magnet.

4. Reduced sedimentation rate

To test our hypothesis that levitation inhibits sedimentation of the bacteria in the liquid culture, we used E. coli transformed to a green fluorescence protein (GFP) to visualize the distribution of cells within the culture vessel. Cultures were exposed to the magnetic field, one at each of the positions 0g*, 1g* and 2g*, simultaneously at a temperature of 37°C for 18 h. Figure 1 shows that the sedimentation rate of cells was reduced in the 0g* position, compared with the 1g* sample, indicated by the higher optical density of the 0g* culture throughout the tube. Sedimentation at the 2g* position was enhanced compared with the 1g* sample: the supernatant was almost clear, with the cells forming a layer on the bottom of the vessel. In separate experiments, the optical density (OD_{600 nm}) OD₁ of the supernatant was measured to determine the cell density remaining in suspension. A second optical density measurement OD₂ was taken immediately after vortexing each sample to determine the OD value of an evenly suspended culture. The fraction of sedimented cells after the 18 h period is S = 1 − OD₁/OD₂, which is proportional to the sedimentation speed and the time of incubation. The OD₁ of the 0g* culture was higher than that of the 1g* sample in the magnet, and the 1g control outside the magnet. The fraction of sedimented cells at the 0g* position was S(0g*) = 0.38 ± 0.06, whereas in the 1g* control, S(1g*) = 0.54 ± 0.01. In the 1g control outside the magnet, S(1g) = 0.50 ± 0.01. The uncertainties are one standard deviation. These results indicate that significantly more bacteria remain in suspension in 0g* than in the 1g and 1g* samples. There is a small difference between S(1g) and S(1g*) which may be owing to some mixing as the 1g* sample is withdrawn from the magnetic field. The ratios S(0g*)/S(1g) and S(0g*)/S(1g*) lie just outside the range we estimate from the Stokes drag analysis. This suggests that another mechanism may be influencing the apparent sedimentation rate. In §7, we discuss experiments in which we image the samples in situ. These experiments show that the gradient magnetic field can cause convective stirring where there is a gradient in the dissolved oxygen concentration.

Figure 1.

Sedimentation and growth of cultures in the magnet. Samples of E. coli (pSB2999) culture in 25 mm diameter containers, expressing the green fluorescence protein, were grown in the magnet at 0g*, 1g* and 2g* statically for 18 h at 37°C and then visualized under UV illumination. The liquid depth is 15 mm.

5. Effect on growth phases

To investigate the effect of levitation on the growth of these cultures, cell density was measured as a function of time by taking optical density (OD_{600 nm}) measurements at approximately 1 h intervals to determine growth rate and lag time. Cultures of untransformed E. coli and S. epidermidis were grown within the magnet at the three different positions (0g*, 1g* and 2g*). In addition, control samples were incubated outside the magnet (1g). Cultures within the magnet bore and the 1g control sample were incubated statically at 37°C. Each sample was mixed prior to measurement. Figure 2 shows that for both E. coli and S. epidermidis cultures grown at 0g*, an overall enhancement of growth was apparent compared with the static (1g) control cultures. No difference in the lag phase or initial growth rate was observed when cultures had low cell density. However, the cultures at 1g* and 2g* and the 1g control all showed a lower initial growth rate than the 0g* cultures (figure 2). The final cell density in the 0g* samples was approximately 1.5 times that of the other cultures. These results are reproducible and statistically significant. The growth in the 1g control is comparable with that in the 1g* sample, demonstrating that, in the absence of a magnetic field gradient, the magnetic field has no observable effect on the growth. For comparison, we performed an experiment on a shaken culture outside the magnet, in which we expect the liquid to be fully aerated. We found that, although growth was enhanced at 0g* compared with all the static cultures, it was not as high as that achieved by the aerated culture outside the magnet (table 1). Liquid loss via evaporation was insignificant because the culture vessels were airtight.

Figure 2.

Growth of E. coli and S. epidermidis. Cultures of (a) E. coli and (b) S. epidermidis were grown at 37°C in nutrient broth. They were either exposed to altered effective gravity in the magnet bore (filled diamond, 0g*; filled square, 1g*; filled triangle, 2g*) or were grown outside the magnet (1g) (open circle, statically; open diamond, aerated). Samples were collected at hourly intervals in order to determine the cell density, using OD_{600 nm}. Error bars show 1 s.d.

Table 1.

Effects of culture conditions on cell growth. Cultures were grown under different test conditions for 18 h at 37°C in the 0g*, 1g* and 2g* positions. The 1g control samples were grown outside the magnet either statically (1g) or with shaking (1g aerated). Optical density (OD_{600 nm}) of samples was determined after 18 h. (a) Final optical densities of cultures of E. coli grown without and with O₂-gassed perfluorodecalin (PFC) layer at the bottom of the culture. (b) Ratios of final cell density values of E. coli and S. epidermidis cultures. Only E. coli static cultures were oxygenated from the bottom of the culture by adding O₂-gassed PFC. n.d. not determined.

	final cell density (OD600 nm)
condition	without PFC	with PFC
(a)
0g*	1.9 ± 0.3	2.3 ± 0.1
1g*	1.4 ± 0.1	1.9 ± 0.1
2g*	1.3 ± 0.2	1.8 ± 0.1
1g	1.3 ± 0.1	1.8 ± 0.1
1g aerated	2.4 ± 0.2	n.d.
(b)
test comparison	E. coli	E. coli with PFC	S. epidermidis
0g*/1g	1.73 ± 0.35	1.24 ± 0.05	1.94 ± 0.16
1g*/1g	1.09 ± 0.03	1.06 ± 0.07	1.17 ± 0.25
2g*/1g	1.04 ± 0.08	1.01 ± 0.02	0.73 ± 0.11
0g*/1g*	1.59 ± 0.29	1.16 ± 0.03	1.53 ± 0.16
0g*/1g aerated	0.9 ± 0.05	n.d.	0.81 ± 0.02

6. Oxygen availability limiting growth

6.1. Experiments with perfluorodecalin

The lower growth rate in the static cultures, compared with the shaken cultures, suggests that availability of O₂ is limiting growth in the static cultures. To test this experimentally, we performed experiments in tubes containing different volumes of liquid medium V. We also performed experiments in tubes of different diameters, to see the effect of varying the area of the air–liquid interface A. We found a clear positive relationship between final cell number density and A/V (figure 3). This result lends weight to the hypothesis that the availability of O₂ is limiting growth in these experiments, since the O₂ flux across the air–water interface is proportional to A and the O₂ concentration of the liquid resulting from this flux is inversely proportional to V. To confirm that availability of O₂ is limiting growth, cultures were oxygenated from the bottom of the vessel by using a perfluorocarbon (PFC) artificial gas carrier: perfluorodecalin. PFC has a high saturation capacity for O₂, and is both more dense than, and immiscible with, water; it forms a discrete layer at the bottom of the culture and has been shown previously to enhance growth of bacterial cultures [25]. All the samples with PFC showed enhanced growth compared with samples without PFC. Under these conditions, the final cell number density of the 0g* sample was as high as in the aerated cultures and the 1g*, 2g* and 1g cultures all grew as well as the 0g* sample without PFC (table 1). This confirms that lack of O₂ is limiting growth in the lower region of the static cultures. Further, these results suggest a reason for the 0g* growth enhancement: magnetic levitation increases the availability of O₂. We test this hypothesis by a gene expression study in the following section. The fact that the growth rate of the 1g* culture is increased by inclusion of the PFC layer indicates that the magnetic field does not limit growth in these experiments.

Figure 3.

Relationship between final cell density and liquid–air interface area/sample volume. Samples were incubated for 18 h in tubes with different dimensions (see the electronic supplementary material, table S1). The optical density (OD_{600 nm}) after 18 h shows a clear increase with A/V; A is the area of the liquid–air interface and V is the sample volume. (a) OD of the 0g* sample, OD(0g*), relative to the OD of the 1g* control sample in the magnet, OD(1g*). (b) OD of the 0g* sample, OD(0g*), relative to the OD of the 1g control outside the magnet, OD(1g). (c) OD of the 1g control. The scatter in the data points gives a good indication of the experimental uncertainty. Lines show the least-squares linear fit to the data. The gradients of the lines are, including standard errors, 8 ± 2, 11 ± 2 and 6.5 ± 1.0 µl mm⁻² for the data in (a), (b) and (c), respectively.

6.2. Changes in gene expression

In adapting to different growth conditions, E. coli alters the composition of its respiratory pathways, changing the amount of different terminal oxidases to optimize its respiratory chain according to the substrates present and the physiological needs of the cell. Cytochrome b_o, encoded by the cyoABCDE operon, operates at high oxygen concentration and has low affinity for oxygen. Expression of the cyo operon is decreased under anaerobic conditions by the global anaerobic regulators ArcA and Fnr [26]. The appB cytochrome bd-type oxidase has a high oxygen affinity and is encoded in an operon with appA (pH 2.5 acid phosphatase). Their expression is regulated by appY and stress-response sigma factor RpoS under microaerobic conditions, when appB may be required for efficient electron transport [25]. We used microarray-based gene expression profiling to investigate the response to O₂ depletion. RNA was extracted from each of the E. coli cultures grown under the different test conditions when the cells reached mid-exponential growth phase (OD_{600 nm} = 0.5) and samples analysed on an E. coli oligonucleotide array (table 2). Expression of genes in the cyo operon were consistently approximately twofold upregulated in the 0g* samples compared with all other static samples. No significant difference in expression of these genes was detected between the 0g* static culture and the 1g aerated culture. The opposite pattern was seen for genes in the app operon; the expression of these genes was enhanced at 2g*. Additionally, the anaerobic growth regulator fnr was downregulated in the 0g* compared with 2g* sample. In general, genes known to be associated with anaerobic adaptation were more highly expressed in samples with the lowest growth. Changes in expression of cyoA and appB were also confirmed by measuring mRNA levels using quantitative real-time reverse transcriptase polymerase chain reaction (qRT-PCR) analysis and showed that the expression of the cyoA gene was enhanced at 0g* compared with the control (table 3), with the 1.5-fold change observed being similar to results obtained from the microarray analysis. The expression of the appB gene was downregulated at 0g* but was enhanced at the 2g* position compared with the control by approximately twofold. Importantly, no differences in level of expression of these cytochromes were found between the 1g* and 1g static samples, indicating that their expression was not influenced by the magnetic field or by differences in distribution of other nutrients influenced by the magnetic field, but rather by differences in oxygen availability under the different test conditions.

Table 2.

Microarray analysis of changes in expression of cytochromes and fnr. Comparison of significant fold changes in expression for genes involved in cytochrome regulation in E. coli K12 MG1655. Samples were exposed to altered effective gravity at 37°C in the magnet bore (0g*, 1g* or 2g*) or grown outside the magnet (1g) either statically or aerated. All samples were harvested at OD_{600 nm} = 0.5 for RNA extraction to minimize effects caused by changes in cell population and associated depletion of gases and nutrients. Total RNA was extracted from four independent replicates and used for microarray analysis. Data were analysed using GeneSpring GX 7.3, and normalized against 50% of signal for each independent array and filtered using p-value = 0.05.

test conditions	gene	gene product	fold change
0g* versus 1g*	cyoA	cytochrome o ubiquinol oxidase subunit II	2.11
	cyoB	cytochrome o ubiquinol oxidase subunit I	2.34
	appA	phosphoanhydride phosphorylase	0.47
	appC	cytochrome bd-II oxidase, subunit I	0.45
0g* versus 2g*	cyoB	cytochrome o ubiquinol oxidase subunit I	2.98
	appB	cytochrome bd-II oxidase, subunit II	0.33
	appC	cytochrome bd-II oxidase, subunit I	0.2
	Fnr	DNA-binding transcriptional dual regulator, global regulator of anaerobic growth	0.43
0g* versus 1g	cyoD	cytochrome o ubiquinol oxidase subunit IV	2.12
	cyoE	protoheme IX farnesyltransferase	2.12
	Fnr	DNA-binding transcriptional dual regulator, global regulator of anaerobic growth	0.37
1g* versus 1g aerated	cyoB	cytochrome o ubiquinol oxidase subunit I	0.42
1g* versus 2g*	appB	cytochrome bd-II oxidase, subunit II	0.47
	appC	cytochrome bd-II oxidase, subunit I	0.4

Table 3.

Comparison of qRT-PCR and microarray data for cyoA and appB. Samples of RNA extracted for the array experiments from four independent replicates of cells grown in altered effective gravity at 37°C in the magnet bore (0g*, 1g* or 2g*) or statically outside the magnet (1g) were used for qRT-PCR analysis. Cells were recovered from each culture for RNA extraction when OD_{600 nm} = 0.5. Levels of cyoA and appB were compared in each case with the 1g control sample. Details of TaqMan probes and dyes used are provided in the electronic supplementary material, table S3. Values that were statistically different at the 5% level from a 1 : 1 ratio are indicated by an asterisk. *p-values <0.05.

test conditions	fold change
	cyoA		appB
	arrays	qRT-PCR	arrays	qRT-PCR
0g*/1g	1.49*	1.57*	0.69	0.80
1g*/1g	0.71	0.90	0.88	0.92
2g*/1g	0.95	0.80	1.82*	2.20*

7. Magnetically induced convection

One might speculate that the increase in oxygen availability in the levitated (0g*) sample may be owing to the observed reduction in the rate of sedimentation. This allows bacteria to remain closer to the surface where the liquid is enriched by oxygen diffusing across the air–liquid interface. While this is a plausible hypothesis, we also investigated whether previous studies of magnetically induced convection in water could be relevant [13,27–32]. Molecular oxygen is paramagnetic and is attracted to a magnetic field: molecular oxygen above the solenoid is pulled towards the centre of the solenoid, where the field is largest. This force enhances the buoyancy of objects immersed in a paramagnetic fluid [33–36]. Although the paramagnetism of O₂ at room temperature is weaker than that of liquid oxygen, the paramagnetic force on the O₂ molecules in air in the bore of our superconducting magnet is nevertheless significant owing to the large gradient magnetic field. This is easily demonstrated by levitating a droplet of water in the magnet: in air, the droplet levitates 6 mm higher than its position in nitrogen gas (at the same temperature and pressure) owing to the additional buoyancy force provided by the paramagnetic force on the O₂ molecules in the air [17]. Ueno [37] showed that the paramagnetic force on O₂ in the air is strong enough to extinguish a burning candle with a 1.5 T electromagnet. O₂ dissolved in the liquid culture medium is similarly attracted by the magnetic field [38]. Since O₂ in the liquid is consumed by the bacteria and replaced at the liquid–air interface (from the O₂ in the air above the liquid), an O₂ concentration gradient results, producing a corresponding gradient in the magnetic force density. Analogous magnetic effects on convection have been observed in crystal growth experiments in high gradient magnetic fields, resulting from a concentration gradient of solute [39,40].

7.1. Theory

We now consider whether this force gradient can cause convection of the liquid medium by comparison with convection driven by a temperature-dependent density gradient, which is well understood. We define an effective liquid density P such that the net vertical force on a volume V of liquid in the magnetic field can be written F_z = PVΓ, where P = ρ_w + (χ − χ_w)BB′_z/(Γμ₀); ρ_w and χ are the liquid density (approximately the same as water) and the volume magnetic susceptibility, respectively. For simplicity, we consider the forces on-axis only, where Γ = Γ_z. Importantly, note that χ depends on the concentration C (here, measured in molecules per m³) of dissolved oxygen in the liquid: χ(C) = χ_w + γC, where γ = 43 × 10⁻⁹ m³ mol⁻¹/N_A is the molecular magnetic susceptibility of O₂ at room temperature [41]; N_A is Avagadro's number. Therefore, the effective density of the liquid P depends on the concentration of dissolved oxygen C. A gradient in the oxygen-dependent effective density can give rise to convection in an entirely analogous way to a temperature-dependent density gradient. In the text-book problem of Rayleigh–Bénard (RB) convection (e.g. [42]), a temperature gradient is established between a hot plate at the base of the liquid and a cold plate at the top. The difference in density between the warm liquid near the base and the cooler liquid at the top causes the system to become unstable to convection when the temperature gradient exceeds a critical value, determined by the Rayleigh number. For example, for 20°C water between plates separated by 1 cm, we expect to observe convection when the temperature gradient exceeds approximately 0.15 K cm⁻¹. We now consider an analogous configuration, which will allow us to use the existing theory on RB convection to provide an insight into the present problem: we assume for the moment that the bacteria lie in a layer at the bottom of the vessel, consuming O₂, so that, in equilibrium, C decreases linearly from C_i at the liquid–air interface to C_b at the container bottom. We can define a Rayleigh number for this configuration, in an exact analogy with the thermal convection problem,

Here, ΔC = C_b − C_i, h ∼ 1 cm is the depth of the liquid, D ∼ 3 × 10⁻⁹ m² s⁻¹ is the diffusivity of O₂ molecules in the medium at 37°C (approximately the same as that in water; [43]), v ∼ 1 × 10⁻⁶ m² s⁻¹ is the kinematic viscosity of the medium and α is the fractional change of P with C,

Note that the molecular diffusivity D and the concentration difference ΔC are the analogues of the thermal diffusivity and temperature difference, respectively, in the thermal convection problem. Poodt et al. [44] used a Rayleigh number for analysing the results of the similar problem of mass-transport in magnetically levitated crystal growth, although they do not introduce the concept of effective density explicitly. We emphasize that Ra* is not the same as the ‘magnetic Rayleigh number’ that characterizes convection driven by temperature-induced changes in fluid magnetization (e.g. [45]). In the present problem, the O₂ concentration gradient is responsible for convection, not the temperature, which is uniform throughout the liquid. Since the diffusivity of O₂ in air is ∼1 × 10⁴ times larger than in water [46], we can assume that there is a negligible O₂ concentration gradient in the air above the liquid. Hence, we assume that the concentration of O₂ in the surface liquid is approximately the same as that in water in equilibrium with the air, which is C₀ ∼ 1 × 10²³ molecules per m³ at 37°C [47]. At the container bottom, the bacteria consume O₂ until its concentration reaches C_b ≈ 0.01C₀, at which point the low O₂ concentration limits the activity of the bacteria ([48]; at these cell densities, 5 × 10⁷–5 × 10⁹ m⁻³, the rate of O₂ diffusion through the liquid limits the bacterial O₂ consumption). For simplicity, we use the approximation C_b = 0. In the 0g* position, the effective density P of the O₂-rich liquid at the surface is greater than that of the O₂-poor region below. From existing theory on RB convection, we know that this configuration is unstable above Ra* ∼ 2000. (Note that the culture at 2g* is stable against this type of convection since the paramagnetic force on the O₂ pulls upward in this location.) Calculating the Ra* number for the model system, we find that, within the 0g* sample, Ra* >1 × 10⁶ on-axis, assuming a constant ‘mean’ Γ in the range 0.01 g to 0.1 g, in this simple model. Hence, we expect our model 0g* system to be unstable to convection. Although, in the experiments, a fraction of the bacteria is suspended in the liquid, as we demonstrated in §4, and the E. coli are also motile, the large Ra* number for the model 0g* system suggests that convection driven by an O₂ concentration gradient could be possible under experimental conditions, too.

7.2. Experiment to test for magnetically induced convection

We tested this hypothesis experimentally by performing growth experiments on E. coli including the redox dye resazurin. This blue, water-soluble, dye is reduced, irreversibly, to the pink dye resorufin by reactions associated with bacterial respiration [49]. Resorufin can itself be further reduced to the colourless hydroresorufin by the same processes. However, the second reaction is reversible by O₂ [49]. Since the dye molecules are diamagnetic, the magnetic force on each is small compared with the force on an O₂ molecule; we measured the susceptibility of the powdered dyes using the Gouy method. Therefore, we do not expect the introduction of the dye to have any effect on the convection. Figure 4 shows cultures containing the dye in the 0g* and 2g* positions, and in a control sample (1g) outside the magnet. The photographs were obtained in situ, 6 h after introduction of the dye. Unlike the experiment performed to measure growth, where samples were mixed prior to sampling, these static cultures were left undisturbed. Just after the dye was introduced, all samples had a uniform blue colour, but turned pink after approximately 2 h owing to bacterial aerobic respiration. The pink colour of the 1g control sample faded to colourless after a further 1–2 h, as the dissolved O₂ was depleted and the resorufin was further reduced. However, close to the air–liquid interface, the liquid remained pink owing to O₂ diffusion across the interface, which prevented the reduction of resorufin to hydroresorufin. In contrast, the colour of the sample in the 0g* position did not fade to colourless, remaining bright pink (including in the region at the bottom of the container), except for the appearance of two paler oval-shaped areas. Comparison with the control sample suggests that within these pale ovals, the O₂ concentration must be lower than in the rest of the fluid. We also note that the oval shapes of these regions are reminiscent of the shape of stagnant regions in thermal convection cells [42]. These two observations suggest that the concentration of dissolved O₂ outside the oval regions is increased by convective transport of O₂ from the relatively O₂-rich surface liquid to the rest of the sample. The fluid within the ovals stagnates, as is typical in a convection cell, and therefore O₂ levels in these regions are depleted by bacterial respiration, allowing resorufin to be reduced to its colourless form. Since the paramagnetic force on the O₂ in the 2g* sample acts upwards, we expect these samples to be stable against paramagnetic O₂ convection. This is evident from the well-defined pink layer at the top of this container.

Figure 4.

Magnetic convection in a bacterial culture. Static bacterial cultures (E. coli) in 10 mm × 10 mm × 45 mm cuvettes, containing resazurin dye. The liquid depth is 12 mm. Cuvettes in the 0g* and 2g* positions in the magnet, and 1g control outside the magnet, photographed in situ after 6 h. The dye turns pink in regions where bacteria are undergoing aerobic metabolism but have not become anaerobic, highlighting areas with a relatively high O₂ concentration. The image top right, labelled ‘F’, is a false-colour version of the 0g* image shown top left. In this image, the O₂-depleted regions are coloured blue. The shapes of these regions are reminiscent of the shape of thermal convection cells.

Since the nutrient broth contains paramagnetic metal ions, Fe²⁺, Cu²⁺ and Mn²⁺, in concentrations comparable with C₀, one might ask whether these ions could also give rise to convection, since the bacteria require these ions for their metabolic processes. However, Bovallius & Zacharias [50] showed that, in nutrient broth, these ions are present at sufficient concentration to avoid rate-limiting the bacterial growth. Hence, we do not expect a significant concentration gradient of these ions to arise; we emphasize that a concentration gradient is required to generate convection by this mechanism. Conversely, since we have shown that O₂ depletion limits growth in our experiments, we expect a significant O₂ concentration gradient. We have shown, theoretically and experimentally, how such an O₂ concentration gradient in the magnetic field can generate convection.

A natural question to ask at this point is whether the sedimentation itself is inhibited by the paramagnetic convective stirring, rather than by diamagnetic levitation. Since we observe an increase in the rate of sedimentation in the 2g* position, this demonstrates that the diamagnetic force on the liquid and the cells does indeed have a direct effect on sedimentation (increasing the sedimentation rate in the 2g* sample), since the liquid in this position is stable against the paramagnetically induced convection discussed above. However, we must conclude that the convective stirring has a significant effect on the availability of O₂ to the bacteria in the 0g* sample, since the convective flow transports O₂ from the O₂-rich surface through the bulk of the liquid.

8. Conclusion

From our experimental data, we attribute the increase in bacterial growth rate and higher final cell density in the 0g* samples to greater oxygen availability. The effect becomes enhanced at high cell density when the respiration of the bacteria rapidly depletes oxygen levels. This explanation is supported by the observations that (i) the 0g* sample supplemented with PFC behaves as a uniformly aerated culture and (ii) the anaerobic adaptation genes were more strongly induced in the 1g* and 2g* cultures, confirming that they were experiencing oxygen depletion. We have shown that the diamagnetic force can directly affect the sedimentation rate of a bacterial culture. We have also demonstrated that the gradient magnetic field in the 0g* position has a significant effect on the transport of O₂ in the liquid culture: the consumption of O₂ by the living cells and its replenishment by O₂ diffusing across the liquid–air interface can generate convection in the magnetic field, analogous to the thermal, RB convection process. It is probable that the enhanced availability of O₂ in 0g* is owing to this latter effect. Diamagnetic levitation has the potential to be a powerful technique to study the effects of weightlessness on biological cells, to complement existing Earth-based techniques such as clinorotation and random positioning. However, for diamagnetic levitation to be a useful model of the weightless space environment, where density-driven convective transport is absent, paramagnetically driven convection of O₂ should be prevented. One possibility is to perform experiments on anerobically metabolizing organisms, or in non-liquid cultures [51].

9. Material and methods

9.1. Bacterial cultures

Escherichia coli K12 MG1655 and S. epidermidis NCTC11 047 were grown in nutrient broth (NB; Oxoid, UK). Gfp⁺ bacteria were E. coli TOPO(pSB2999) (P_{rpsJB.subitilis}::gfp in pDEST R4-R3; P.J. Hill, University of Nottingham) which were grown in NB supplemented with ampicillin (50 µgml⁻¹). All cultures were grown at 37°C. Aerated cultures were shaken at 150 r.p.m.

9.2. Experimental levitation magnet system

The superconducting solenoid has a 50 mm diameter vertical bore, open to the laboratory at both ends (see the electronic supplementary material, figure S2). A closed-cycle coolant system allows the magnet to run at high magnetic field on time scales of the order of several months. A constant mean temperature of 37°C in the bore was maintained, with variation over time less than 0.2°C, by temperature-regulated forced air flow with feedback control. The temperature-controlled chamber consists of an acrylic tube (length 60 cm, internal diameter 44 mm), inserted into the magnet bore, containing three specimen tubes (25 mm internal diameter, 25 ml capacity), one at each of the 0g*, 1g* and 2g* positions (see the electronic supplementary material, figure S3). The 1g* sample is located at the centre of the coil; the 0g* and 2g* samples are located 75 mm above and below the 1g* position, respectively. The temperature of each sample was monitored by a thermocouple in contact with each specimen tube. The effect of magnetic field up to 17 T on the thermocouples was negligible.

9.3. Growth experiments

Cultures were inoculated into fresh NB at an OD_{600 nm} = 0.05. The growth experiments and sedimentation experiments presented in §§4 and 5 were performed in 25 ml containers (25 mm internal diameter, 50 mm tall). The containers were filled with the liquid culture to a depth of 15 mm. The experiments to determine the effect of the liquid surface area to volume ratio (§6) were performed in containers of varying sizes and culture volumes; their dimensions are summarized in the electronic supplementary material, table S1. Samples were exposed to 0g*, 1g* or 2g* for varying periods of time, in the dark at 37 ± 0.1°C. Each sample was removed from the magnet, mixed, and its cell numbers determined at approximately 1 h intervals to determine growth rate and lag time. Cell number was determined by viable count or by optical density (OD_{600 nm}). In the experiments to visualize convection (§7), spectrophotometer cuvettes (10 mm × 10 mm × 45 mm) were filled with the liquid culture to a depth of 12 mm and incubated at 0g*, 1g*, 2g* and 1g at 24°C; the lower temperature slowed bacterial growth to allow changes within the fluid to be visualized more easily. Resazurin was used at a final concentration of 67 mg ml⁻¹.

9.4. Perfluorocarbon

Perfluorodecalin (Flutec PP6) liquid was oxygenated for 20 min with 100 per cent oxygen gas and dispensed as 4 ml aliquots in sample tubes. For growth experiments, 4 ml of bacterial suspension was overlaid on the PFC and samples exposed to altered gravity in the magnet for 16 h. The position of the sample in the magnet bore was altered to compensate for the raised height of the growth medium owing to the presence of the PFC layer in the bottom of the tube. Data were analysed using the one-way ANOVA and Tukey's pair-wise comparisons post hoc analysis with a 95% CI, using SPSS software.

9.5. Microarray analysis

Samples were exposed to each test condition and cells harvested in the mid-exponential phase of growth and four independent replicates of each experiment were performed. Total RNA were extracted and labelled using the protocol outlined in MessageAmp II-Bacteria. RNA (700 ng) was labelled with 5-(3-aminoallyl)-UTP. Samples (5 µg) of RNA were labelled with Cy5 using NHS-ester reactive dye packs and purified using RNeasy MinElute columns. The DNA reference samples (1 µg) were labelled using the Invitrogen ‘BioPrime DNA labelling system’, with Cy3-dCTP. Agilent MG1655 microarray slides were hybridized at 65°C for 17 h and scanned at 5 µm resolution using the extended dynamic range (high 100%, low 10%). Data were analysed using Agilent Feature Extraction software and imported into the GeneSpring GX package, normalized per chip to 50 per cent of signal and genes whose normalized expression levels changed twofold or more were identified by applying a t-test (p = 0.05). Differentially transcribed genes were divided into functional groups using COG and KEGG. A complete analysis of genes involved in oxidative phosphorylation pathway with a significantly different level of expression is presented in the electronic supplementary material, table S2.

9.6. Quantitative real-time polymerase chain reaction (qRT-PCR)

All qRT-PCR experiments were performed in triplicate on RNA used for microarray analysis and cDNA was synthesized from 2 µg RNA. Custom TaqMan assays for cyoA, appB and envZ genes were used (see the electronic supplementary material, table S3). The thermal profile employed was 50°C for 2 min, 95°C for 10 min, and 40 cycles of 95°C for 15 s, 60°C for 1 min. Average C_T values and standard deviation were calculated for the three replicates. ΔΔC_T was calculated by the difference between ΔC_T of test samples (0g*, 1g*, 2g* and 1g aerated) and control sample (1g static).