Effect of applied magnetic fields on motility and magnetotaxis in the uncultured magnetotactic multicellular prokaryote ‘Candidatus Magnetoglobus multicellularis’

Summary

Magnetotactic bacteria are found in the chemocline of aquatic environments worldwide. They produce nanoparticles of magnetic minerals arranged in chains in the cytoplasm, which enable these microorganisms to align to magnetic fields while swimming propelled by flagella. Magnetotactic bacteria are diverse phylogenetically and morphologically, including cocci, rods, vibria, spirilla and also multicellular forms, known as magnetotactic multicellular prokaryotes (MMPs). We used video-microscopy to study the motility of the uncultured MMP ‘Candidatus Magnetoglobus multicellularis’ under applied magnetic fields ranging from 0.9 to 32 Oersted (Oe). The bidimensional projections of the tridimensional trajectories where interpreted as plane projections of cylindrical helices and fitted as sinusoidal curves. The results showed that ‘Ca. M. multicellularis’ do not orient efficiently to low magnetic fields, reaching an efficiency of about 0.65 at 0.9–1.5 Oe, which are four to six times the local magnetic field. Good efficiency (0.95) is accomplished for magnetic fields ≥10 Oe. For comparison, unicellular magnetotactic microorganisms reach such efficiency at the local magnetic field. Considering that the magnetic moment of ‘Ca. M. multicellularis’ is sufficient for efficient alignment at the Earth's magnetic field, we suggest that misalignments are due to flagella movements, which could be driven by photo-, chemo- and/or other types of taxis.

Introduction

The main role of motility in bacteria is to increase resource access and/or avoid danger, which in both cases results in increased growth. Chemicals, oxygen, light, mechanical stimuli and even magnetic fields are environmental parameters sensed by bacteria and used to drive motility (Fenchel, 2002). In addition to environmental clues, the metabolic state and history of each individual influence bacterial behaviour. Motility is also energetically expensive. Thus, motility and nutrient uptake must be balanced to enable survival and growth (Mitchell and Kogure, 2006).

The use of the Earth's magnetic field by microorganisms as a guide for swimming is known as magnetotaxis (Frankel, 1984). It has been observed in several microorganisms, collectively known as magnetotactic bacteria. Magnetotaxis occurs due to the presence of chains of membrane-bound magnetic nanoparticles in the cytoplasm, called magnetosomes. These are attached to cytoskeletal fibres allowing the interaction of their magnetic dipole moment with the local field to generate a torque that aligns the whole microorganism along the magnetic field lines while it swims propelled by flagella (Faivre and Schuler, 2008). In addition to passive alignment to magnetic field lines, it was proposed that active sensing of magnetic field direction is present in the spirillum Magnetospirillum magneticum AMB-1 (Zhu et al., 2014). In several cultivated unicellular magnetotactic bacteria, magnetotaxis is coupled to aerotaxis, in a behaviour described as magneto-aerotaxis. Magneto-aerotactic bacteria are phylogenetically and metabolically diverse, but all of them are able to form bands in oxygen gradients (Frankel et al., 1997, 2007; Lefèvre et al., 2014; Felfoul et al., 2016). Magnetotaxis has also been shown to be coupled to chemotaxis (Wenter et al., 2009) and phototaxis (Frankel et al., 1997; Chen et al., 2011; Shapiro et al., 2011; Zhou et al., 2012; Almeida et al., 2013; Azevedo et al., 2013; Zhou et al., 2013; Chen et al., 2015; Zhang et al., 2014; De Melo and Acosta-Avalos, 2017).

Magnetotactic bacteria include cocci, rods, spirilla, vibrios and also multicellular ensembles of cells known as magnetotactic multicellular prokaryote (MMPs) (Faivre and Schuler, 2008). Pure cultures of MMPs are not yet available, and most studies up to now rely on samples obtained from the environment, microcosms or enrichment cultures. Several MMP species have been described at the level of ‘Candidatus’, most of them showing spherical shapes, and a few exhibiting ellipsoidal morphologies. Despite morphological differences, they show coherent phylogeny, structure, life cycle and behaviour (Keim et al., 2004a; Abreu et al., 2007; Zhou et al., 2012, 2013; Chen et al., 2015; Kolinko et al., 2014; Zhang et al., 2014; Chen et al., 2016; Leão et al., 2017). MMPs are motile only when forming the multicellular ensemble, whereas detached cells are immotile and probably dead (Abreu et al., 2007). They proliferate by dividing the whole ensemble into two offspring; no single-cell stage has been detected up to now (Keim et al., 2004b; Zhou et al., 2012, 2013; Chen et al., 2015; Zhang et al., 2014).

Currently, the best studied MMP is ‘Candidatus Magnetoglobus multicellularis’, which is a spherical MMP (Abreu et al., 2007). It contains about 17 cells arranged side by side around a central compartment, such that each cell maintains contact with both the internal compartment and the outer environment. The cell and outer membranes of neighbour cells are juxtaposed, resembling mammalian cell-to-cell junctions (Keim et al., 2004a). Each cell presents about 30 flagella, 0.9–3.8 µm in length, clustered in the part of the cell that faces the environment (Silva et al., 2007). The cytoplasm contains about 80 magnetosomes (Abreu et al., 2008) containing iron sulphide crystals (Keim et al., 2004a) 88 ± 11 nm in length and 65 ± 10 nm in width (Abreu et al., 2008). Magnetosomes are arranged into one to five parallel chains (Abreu et al., 2008), forming planar groups which are close and parallel to the microorganism surface (Silva et al., 2007; Abreu et al., 2013). Cells and magnetosomes are arranged in such a way that the magnetosome chains are roughly parallel to each other in the whole microorganism (Abreu et al., 2013). Indeed, re-magnetization experiments resulted in only approximately 20% increase in the magnetic moment of whole microorganisms, indicating that magnetic dipole orientation are at least 80% aligned in living microorganisms (Winklhöfer et al., 2007).

Under applied magnetic fields, ‘Ca. M. multicellularis’ swims in helical trajectories aligned to the magnetic field lines (Almeida et al., 2013). When they encounter an obstacle, they remain rotating and eventually undergo backward excursions followed by forward movement (Abreu et al., 2007; Keim et al., 2007). At low magnetic fields, such as the Earth's, they swim in complex, looping trajectories nearby the obstacle. When observed from behind, the trajectory and the body rotate clockwise both in forward and looping movements, with about the same frequency (Abreu et al., 2007; Keim et al., 2007). Translational velocities in spherical MMPs, including ‘Ca. M. multicellularis’, range from 50 to 150 µm s⁻¹ (Greenberg et al., 2005; Perantoni et al., 2009; Almeida et al., 2013; Azevedo et al. 2013; Zhou et al., 2013; Zhang et al., 2014). Chemotaxis was observed in a single MMP species (Wenter et al., 2009), whereas photophobic responses have been reported in both spherical and ellipsoidal MMPs (Shapiro et al., 2011; Zhou et al., 2012; Chen et al., 2015; Zhang et al., 2014), including ‘Ca. M. multicellularis’ (Almeida et al., 2013). In addition, ‘Ca. M. multicellularis’ show photokinesis when exposed to different wavelenghts (Azevedo et al., 2013; Azevedo and Acosta-Avalos, 2015).

In a previous work using magnetic fields of 3.9 and 20.0 Oe, we suggested that the trajectory radius, translational and tangential velocities, and angular frequency change with the magnetic field intensity (Almeida et al., 2013). In the present work, we investigate the movements of ‘Ca. M. multicellularis’ under magnetic fields 0.9–32 Oersted (Oe), applied in the direction perpendicular to the optical axis of a light microscope, to observe the effects of the magnetic field intensity on the trajectory parameters. Due to the higher magnetic field intensity range used in the present work, new aspects of motility and magnetotaxis of ‘Ca. M. multicellularis’ emerged.

Materials and methods

Sample collection and preparation, light microscopy, video microscopy and video processing

Water and sediment containing the MMP ‘Candidatus Magnetoglobus multicellularis’ were collected in Araruama Lagoon, Rio de Janeiro State, Brazil (22°55′24″S, 42°18′12″W). Previous work shows that ‘Ca. M. multicellularis’ is the only MMP found in this environment (Martins et al., 2012). Samples were maintained in a 10 L plastic box for a few weeks in the lab in Rio de Janeiro city, Brazil, where the geomagnetic parameters are: horizontal component = 0.18 Oe, vertical component = −0.15 Oe; total intensity = 0.23 Oe.

When needed, a sub-sample was transferred to a specially designed flask containing a lateral capillary aperture, which was placed inside a homemade coil to generate a magnetic field about 5 Oe aligned to the capillary aperture (Lins et al., 2003). ‘Ca. M. multicellularis’ swam toward the capillary and, after 20 min, enriched samples were collected.

To obtain light micrographs, enriched samples were placed between slide and coverslip and observed with a Zeiss Axioplan 2 microscope using the Nomarski interference contrast mode.

Several attempts to provide an oxygen gradient suitable for band formation were unsuccessful. Under a black FeS/oxygen gradient made with lagoon water and black FeS produced according to Kucera and Wolfe (1957), ‘Ca. M. multicellularis’ swam until they reached the FeS at the end of the tube; using 2 mmol L⁻¹ titanium citrate as a reducing agent (Zehnder and Wuhrmann, 1976) in lagoon water resulted in immotile microorganisms. In the video-microscopy experiments reported here, samples containing ‘Ca. M. multicellularis’ were placed between slide and coverslip separated by an O-ring.

High resolution video microscopy was done on an inverted Nikon Eclipse TE300 light microscope using a 100×, 1.45 NA objective lens, a Hamamatsu C2400 CCD camera, and a FG-7 frame grabber (Scion Corporation, Torrance, CA). An electronic chariot enabled following individual microorganisms for several micrometres. These videos were used mainly for qualitative analysis, since the chariot movements precluded accurate velocity measurements.

To record the movements of ‘Ca. M. multicellularis’ for trajectory analysis, samples were observed with a Bioval L2000 light microscope equipped with a pair of hand-made coils producing magnetic fields perpendicular to the optical axis of the microscope (horizontal plane). We used a 25× objective lens and the intensities of the applied magnetic fields were 0.9, 1.5, 2.8, 5.0, 10.0, 20.0 and 32.0 Oe, as measured by a gaussmeter (Global Mag TLMP-HALL-050). Each sample was examined at all magnetic field intensities, in both ascending and descending order.

Digital video records were obtained with a Hamamatsu C2400 CCD camera and a PixelView XCapture USB device using the Cyberlink PowerDirector V7 software. Video records were processed and analyzed with ImageJ software (NIH). The Mtrack2 plugin was used to track individual microorganisms frame by frame, producing worksheets, as previously described (Almeida et al., 2013). We limited analysis to trajectories larger than 30 frames (1 second). Trajectory coordinates were analyzed with the MicroCal Origin software. It was assumed that the observed trajectories are plane projections of cylindrical helixes (see Eqs. 1a and 2a below). For each trajectory, the translational velocity V_T, helix frequency f_H, helix radius R, pitch P (calculated as V_T/f_H) and helix angle θ_H [calculated as tanθ_H = (2πR/P)] were estimated. Also for each magnetic field, the distribution of orientation angles θ around the magnetic field direction was estimated. The trajectory worksheets were analyzed with the MicroCal Origin software. Statistical tests were done with the software GraphPad InStat, except for the angular statistics, which were done with the software Oriana 4.02.

Interpretation of the 2D projections of the trajectories

The movement of these microorganisms occurs under the low Reynolds’ number regime (Purcell, 1977). One implication is that their trajectory must be a cylindrical helix (Nogueira and Lins de Barros, 1995), whose equations parametrized in time are:

(1a)

(1b)

(1c)

where the X axis coincides with the helix axis, R is the helix radius, f_H is the helix frequency (f_H = 1/τ, where τ is the period and ω = 2πf_H is the angular frequency) and V_T is the axial or translational velocity.

The recording of the microorganism swimming in a microscope produces bidimensional data. Considering that the X axis is parallel to the helix axis and located on the focal plane together with the Y axis, the observed trajectory must be an undulation with parametric Eqs. 1b and 1c. However, if the helix axis does not coincide with the X axis but is inclined by an angle θ, the parametric equations for the X and Y coordinates must be as follows:

(2a)

(2b)

Equations 2a and 2b represent straight lines with sinusoidal perturbations.

Magnetotactic microorganisms swim along the magnetic field lines, and thus the helical trajectory of a magnetotactic microorganism must have its axis parallel to the magnetic field vector. However, there is some dispersion in orientation around the magnetic field, with the average value of cosθ associated with the Langevin function (Kalmijn, 1981):

(3)

Experimentally, the angle θ and the helix parameters can be calculated through Eqs. 2a and 2b using data obtained from video-microscopy, considering that for video-microscopy we adjusted the camera position such that the horizontal axes of the frames were aligned about the applied magnetic field lines.

Results

Under light microscopy, ‘Ca. M. multicellularis’ showed the spherical morphology described previously (Keim et al., 2004a, 2004b; Abreu et al., 2007, 2013) (Fig. 1). They swam actively after magnetic separation. High resolution light microscopy showed that ‘Ca. M. multicellularis’ presents a consistent axis of motility (Supporting Information Video S1), as shown previously for ellipsoidal MMPs (Zhou et al., 2012). The rotational component of the trajectory is not straightforward in the video because of slight changes in the plane of focus during swimming, but careful observation shows that the body rotates around a motility axis almost parallel to the trajectory axis, and the motility axis also shows precession (Supporting Information Video S1). By observing Supporting Information Video S1 frame by frame, it was possible to estimate the rotation and precession periods of a single microorganism, which are 0.68 s (f = 1.47 Hz) and 0.86 s (f = 1.16 Hz) respectively.

Figure 1

Light micrograph of ‘Ca. Magnetoglobus multicellularis’. The radial arrangement of cells and the internal compartment are evident in some individuals. Bar = 5 µm.

By applying the magnetic field perpendicular to the optical axis of the microscope, we observed trajectories that are similar to the 2D projections of cylindrical helixes, that is, plane sinusoidal curves (Fig. 2, Supporting Information Videos S2 and S3). The use of magnetic fields of varying intensities showed the dependence of the trajectories on the magnetic field. For instance, the alignment of the trajectory axes to the magnetic field lines increased substantially with magnetic field intensity (Fig. 2). In addition, Fig. 2 shows some trajectories with bent or sinuous axes at low intensity magnetic fields (0.9–5.0 Oe), and progressively straighter axes at higher magnetic field intensities (>10 Oe). Furthermore, careful observation shows that the sinusoidal projections of most trajectories were rather irregular, especially at low magnetic field intensities (Fig. 2). Such irregularities in the 2D projections of the trajectories must be due to irregularities in the 3D helical trajectory.

Figure 2

Examples of trajectories of ‘Ca. M. multicellularis’ under magnetic fields 1.5 to 32 Oe. The sinusoidal shape results from helical trajectories seen in projection. Time between sequential points within a trajectory is 0.1 s. Note that both the alignment along magnetic field lines and the regularity of the sinusoidal projections increases with the magnetic field intensity.

As the interplay between helical motility and magnetotaxis is of major interest here, for the mathematical analysis we considered the trajectories as bidimensional sinusoidal curves, which correspond to tridimensional cylindrical helixes, as parametrized by Eqs. 1 and 2. Table 1 shows the results obtained from fitting of the trajectories to Eqs. 2 for each applied magnetic field. The values found for translational velocity (V_T), frequency (f_H), pitch (P) and helix radius (R) agree with the previous work of Almeida et al. (2013). It is observed that V_T and f_H do not change significantly with increase in magnetic field intensity (ANOVA test, p > 0.05). The pitch P was calculated as P = V_T/f_H (Almeida et al., 2013). P does not change significantly with the applied magnetic field, which was expected since V_T and f_H were stable in the magnetic field range used in this work. In fact, the relatively large values of standard deviation (SD) indicate a large variability in V_T, f_H and P at all magnetic field intensities used in this work. Note that the body axis precession frequency obtained from Supporting Information Video S1 (see above) lies within the range of values observed for f_H.

Table 1. Parameters obtained for the non-linear fits of Eqs. 2 to the trajectories of ‘Ca. M. multicellularis’.

B (Oe)	VT (μm s^−1)	fH (Hz)	P (μm)	R (μm)	θH (rad)	<cosθ>	N
0.9	91 ± 29^a	1.17 ± 0.37^a	85 ± 36^a	8.4 ± 5.2^a	0.55 ± 0.25^a,b	0.64 ± 0.29^a	32
1.5	93 ± 28^a	1.27 ± 0.59^a	102 ± 84^a	8.7 ± 6.7^a	0.59 ± 0.33^a	0.65 ± 0.29^a	56
2.8	77 ± 35^a	1.11 ± 0.60^a	119 ± 128^a	12.6 ± 8.9^a	0.68 ± 0.40^a	0.84 ± 0.26^a	24
5.0	52 ± 37^b	0.93 ± 0.55^a	65 ± 46^a	5.7 ± 4.5^a,b	0.55 ± 0.36^a,b	0.94 ± 0.12^b	37
10	79 ± 27^a	1.25 ± 0.69^a	97 ± 88^a	4.4 ± 1.9^b	0.38 ± 0.22^b	0.99 ± 0.01^c	34
20	88 ± 24^a	1.17 ± 0.52^a	97 ± 83^a	4.6 ± 1.8^b	0.35 ± 0.14^b	0.99 ± 0.01^c	30
32	91 ± 27^a	1.33 ± 0.55^a	85 ± 53^a	4.4 ± 2.3^b	0.37 ± 0.22^b	0.99 ± 0.003^c	33

• Values correspond to mean ± standard deviation (SD). V_T is the translation velocity. R, f_H, P and θ_H correspond, respectively, to the radius, frequency, pitch and helix angle for the helical trajectory. <cosθ> corresponds to the mean orientation relative to the magnetic field orientation, <cosθ> = 1 meaning full orientation. θ is the angle of the trajectory relative to the magnetic field direction. N is the number of analyzed trajectories. In each column, different letters mean statistical difference (ANOVA test, different letters: p < 0.05, equal letters: p > 0.05).

In contrast to V_T, P and f_H, the helix radius R decreases when the magnetic field increases. Table 1 shows that, for magnetic fields of 2.8 Oe or lower, the mean trajectory radius ranges from 8.4 to 12.6 μm, whereas for fields 10 Oe or higher, it decreases to 4.4–4.6 μm. Thus, the helical trajectory narrows and stabilizes at B ≥ 10 Oe. In addition, greater variability in R was recorded between 0.9 and 2.8 Oe compared with values at magnetic fields ≥10 Oe. Similar to the radius R, θ_H decreased from 0.55 to 0.68 rad at magnetic fields ≤5 Oe to 0.35–0.38 rad for magnetic fields ≥10 Oe. The similarity in the behaviour of R and θ_H was expected, since the helix angle was calculated as tanθ_H = (2πR/P) (Almeida et al., 2013) and mean P was relatively stable. Variability in cosθ decreased steadily with increasing magnetic field intensity (Table 1) which may be explained by progressive neutralization of misalignment produced by flagella due to the increase in magnetic torque. Taken together, results in Table 1 shows a stabilization in the helical trajectories of ‘Ca. M. multicellularis’ at magnetic fields ≥10 Oe, evidenced by stabilization of the mean values of R and θ_H.

The influence of magnetic field intensity on the distribution of orientation angles of the trajectories relative to the magnetic field direction is shown in Table 2 and Fig. 3. In Fig. 3, the average orientation angle approaches the magnetic field direction but the dispersion is higher for the lower magnetic field (B = 1.5 Oe) as compared with the higher magnetic field (B = 20 Oe) intensity. Accordingly, Table 2 shows that the average orientation angle θ (mean vector direction) approaches the magnetic field direction for all intensities. In addition, as the magnetic field increases, circular standard deviation decreases while concentration (deviation of angle distribution from a uniform distribution to a circular Gaussian, which is the von Misses distribution) increases. This reflects the decrease in the orientation angle dispersion when the magnetic field increases. The distributions of orientation angles for 0.9 and 1.5 Oe are wide and challenges the traditional understanding on the efficiency of magnetotaxis because those magnetic fields are about 4 and 6 times the local geomagnetic field. The classical interpretation of magnetotaxis considers that magnetotactic bacteria align passively to the Earth's magnetic field, which results in swimming along magnetic field lines. Because the magnetic interaction energy (mB) exceeds the thermal energy (kT) by 5–10 times, most magnetotactic microorganisms show high efficiency in alignment and swimming along the Earth's magnetic field lines (Kalmijn, 1981; Blakemore, 1982), but this is clearly not the case for ‘Ca. M. multicellularis’ (see Figs. 2-4 and Table 2).

Table 2. Circular statistics for ‘Ca. M. multicellularis’ trajectory orientation relative to the magnetic field direction.

B (Oe)	Mean vector direction (°)	Circular SD (°)	Concentration	N
0.9	359	54	1.67	32
1.5	3.4	53	1.74	56
2.8	351	37	3.03	24
5.0	3.8	19	9.77	37
10	359	6	94.5	34
20	359	7	71.4	30
32	0.5	4	160.7	33

• ‘Mean vector direction’ represents the average orientation angle. All the mean vector directions are statistically significant (Rayleigh test: p < 0.05). That means that for each magnetic field, the observed population of ‘Ca. M. multicellularis’ swim around the mean angle and not in random directions. The magnetic field direction corresponds to 0°. The concentration measures the departure of the angle distribution from a uniform distribution to a circular Gaussian (the von Misses distribution): the higher its value the more similar to a von Misses distribution. N is the number of angles analyzed. To calculate the circular SD, the following formula was used: circular SD = (1 − r)^1/2, where r = (<cosθ>² +<sinθ>²)^1/2; r is known as the length of the mean vector, and shows values between 0 and 1

Figure 3

Distribution of orientation angles θ for the magnetic fields 1.5 and 20 Oe. In this representation, the applied magnetic field is aligned to the vertical line at 0°. Each point represents the orientation angle of each curve relative to the magnetic field direction. Observe that for the lower magnetic field (1.5 Oe), the scattering is higher than for the higher magnetic field (20 Oe).

Figure 4

Average value of cosθ (<cosθ>) as function of the magnetic field. The points represent the average experimental values, and the bars correspond to the standard deviation. The continuous line is the fit to the Langevin function (Eq. 3) that depends on the magnetic energy to thermal energy ratio mB/kT. A non-linear fit permits to adjust <cosθ> as function of B using the Langevin function, and as a result a value of 2.45 ± 0.33 was obtained for (mB/kT), which corresponds to a magnetic moment value of 9.4 × 10⁻¹⁷ Am².

Figure 2 indicates that the alignment of the trajectories to the magnetic field lines increases with the magnetic field. The alignment to the magnetic field lines was estimated using cosθ as calculated by Eqs. 2 using the expressions for V_x and V_y. The variation of <cosθ> as a function of the magnetic field (Fig. 4) confirms the increase in alignment with the increase in magnetic field intensity. Furthermore, it shows that good alignment (>0.95 according to Mao et al., 2014) occurs for magnetic fields higher than 5 Oe. The curve obtained for <cosθ> resembles a Langevin curve, as showed by Kalmijn (1981) for magnetotactic bacteria and by Mao et al. (2014) for ‘Candidatus Magnetobacterium bavaricum’ and magnetotactic cocci. The fit of this curve to a Langevin curve produces an estimate for the magnetic moment of ‘Candidatus Magnetoglobus multicellularis’ of 9.4 × 10⁻¹⁷ Am². This value is 100 times lower than the value measured before in the same species using the U-turn method, which was about 9 × 10⁻¹⁵ Am² (Perantoni et al., 2009). If we interpret our results in terms of an effective temperature as done by Rosenblatt et al. (1982), Nadkarni et al. (2013) and Zhu et al. (2014), our result means that ‘Ca. M. multicellularis’ would be exposed to an effective temperature of about 3 × 10⁴ K. In agreement with Rosenblatt et al. (1982), Nadkarni et al. (2013) and Zhu et al. (2014), Brownian motion alone is not enough to explain the high values obtained for effective temperature, and we must search for additional causes.

Discussion

Magnetotactic bacteria swim in the direction of the lines of applied magnetic fields. This is the hallmark of magnetotactic bacteria and has been used to concentrate them for microscopy, culturing and molecular phylogeny studies (Faivre and Schuler, 2008). It was proposed that increasing the magnetic field intensity improves the alignment of magnetotactic bacteria to the magnetic field lines because it would decrease the relative influence of thermal energy (Frankel, 1984; Lins de Barros et al., 1990). Here we show that effective alignment of ‘Ca. M. multicellularis’ occurs only for magnetic fields ≥10 Oe, which is about 40 times the local magnetic field intensity. At the lower magnetic field intensities used in this work (0.9–1.5 Oe), which are four to six times the local magnetic field, the alignment efficiency of ‘Ca. M. multicellularis’ is around 65% (see Fig. 4). In terms of the magnetic-to-thermal energy ratio (mB/kT) for those magnetic fields, consider the magnetic moment of ‘Ca. M. multicellularis’ as 9 × 10⁻¹⁵ Am² (Perantoni et al., 2009) and kT = 4.14 × 10⁻²¹ J for ambient temperature. The energy ratios (mB/kT) obtained are 195 and 326 for 0.9 and 1.5 Oe respectively. Those ratios are very high, meaning that the orientation by magnetotaxis measured through <cosθ> must be near 1. For comparison, at the local magnetic field intensity, some unicellular magnetotactic bacteria reach an alignment efficiency of about 85% (Kalmijn, 1981), some cocci 90% and the rod ‘Candidatus Magnetobacterium bavaricum’ approaches 100% (Mao et al., 2014). Despite the fact that ‘Ca. M. multicellularis’ presents a magnetic moment sufficient for efficient alignment to the geomagnetic field (Perantoni et al., 2009), this microorganism does not orient efficiently in the geomagnetic field. Thus, the behaviour of ‘Ca. M. multicellularis’ challenges the currently accepted hypothesis explaining the eco-physiological function of magnetotaxis, which assumes that passive magnetic orientation reduce the search for the best layer in the chemocline of aquatic environments from three dimensions (as in chemotaxis) to one dimension, through swimming back and forth along the Earth's magnetic field lines (Frankel et al., 2007).

Here, <cosθ> was calculated as the average ratio between translational velocity (along any direction) and speed of migration along magnetic field lines. At 0.9–1.5 Oe, <cosθ> is about 0.65 for ‘Ca. M. multicellularis’. Similarly, the efficiency of chemotaxis has been calculated as the ratio between run velocity and migration in the direction of the chemical gradient. In E. coli, it is about 0.2 (Berg and Turner, 1990). Because both represent velocity ratios, they are directly comparable. Thus, magnetotaxis in ‘Ca. M. multicellularis’ at 0.9–1.5 Oe is more than three times more efficient than chemotaxis in E. coli. If chemotaxis efficiency in ‘Ca. M. multicellularis’ was similar to that observed in E. coli, than at magnetic fields ≥0.9 Oe magnetotaxis would overcome chemotaxis.

One could consider that, for the low magnetic fields used in this work, an efficient magnetic orientation would be reached in larger time periods. However, the time needed for magnetic orientation is related to the orientation of the magnetic dipole to the magnetic field, which is equivalent to the time needed for re-orientation after reversion of the magnetic field direction, which is known as the U turn time. For ‘Ca. M. multicellularis’, the U-turn time is around 1 s at 1.4 Oe (Azevedo et al., 2013). As we limited our analysis to trajectories ≥1 s, we can consider that time is not an issue here. In addition, the magnetic field direction was maintained for a couple of seconds before starting the video recordings.

The possible causes of the high effective temperatures obtained from Langevin curve adjustment (Fig. 4) can be observed in the trajectories shown in Fig. 2. At low intensity magnetic fields (1.5–5.0 Oe) many trajectories had bent or sinuous axes, but increasing the magnetic field intensity led the microorganisms to produce straighter and well-aligned trajectories. We should remember that these bents and misalignments are the very cause of the dispersion in the values of the θ angle, and thus have strong influence on <cosθ>. Since Brownian motion is not the only factor responsible for misalignment, the model based on Langevin theory should not be applied to calculate <cosθ> or magnetic moment of ‘Ca. M. multicellularis’ and probably other magnetotactic microorganisms. Stimuli other than the magnetic field (e.g., chemo- and photo-taxis) would be involved in determining swimming direction.

Comparison of data presented in Table 1 with those presented by Almeida et al. (2013) brings interesting conclusions. They compared R, P, f_H, V_T and θ_H of ‘Ca. M. multicellularis’ trajectories at 3.9 and 20 Oe, and found statistically significant differences for all parameters except P (Almeida et al., 2013), whereas we found significant differences only for R and θ_H. In addition, they obtained lower values of SD compared with our present results. A key difference in the experimental settings is that we used several distinct samples, but all of them in all magnetic field intensities, whereas Almeida et al. (2013) used a single, distinct sample for each magnetic field intensity. Thus, the statistically significant differences in the mean V_t and f_H values found by Almeida et al. (2013) are probably due to the use of distinct samples of ‘Ca. M. multicellularis’. On the other hand, our results suggest that the statistical differences in mean values of R and θ_H are due to the magnetic field intensity. In addition, comparison with data from Almeida et al. (2013) suggests that the main factor responsible for our larger SD could be the use of several samples for trajectory measurements in each magnetic field.

Unlike some unicellular magnetotactic bacteria, in which the trajectory pitch decreases and the trajectory radius increases with increasing magnetic field intensity (Pan et al., 2009; Yang et al., 2012), we found that helical trajectories in ‘Ca. M. multicellularis’ decrease the radius and maintain the pitch (Almeida et al., 2013; this work). Using the rationale proposed by Pan et al. (2009) and reinforced by Yang et al. (2012), we propose that the magnetosomes in ‘Ca. M. multicellularis’ produce a resultant magnetic moment which is aligned to the trajectory axis during swimming. This is not the case in other magnetotactic bacteria (Pan et al., 2009; Yang et al, 2012). Indeed, previous works using different approaches support this interpretation for both ‘Ca. M. multicellularis’ (Winklhöfer et al., 2007) and the ellipsoidal MMP ‘Candidatus Magnetananas tsingtaoensis’ (Zhou et al., 2012).

Conclusions

Our results show that ‘Ca. M. multicellularis’ do not orient efficiently to the local geomagnetic field lines, due to flagella movements that causes bends and curves in the trajectories. These flagella movements reduce the apparent magnetic moment of ‘Ca. M. multicellularis’ by about a hundred times (as obtained by the Langevin curve adjustment) and may be driven by chemo-, photo- and even other modes of taxis. Our results raise the possibility that this microorganism is able to control how much of its motility will be driven by photo-, chemo- and other modes of taxis, according to environmental signals and/or its physiological state, leaving the efficiency of magnetotaxis dependent on both environmental and physiological factors. Furthermore, the statistical character of magnetotaxis (Kalmijn, 1981) becomes evident in ‘Ca. M. multicellularis’ at low magnetic fields, since the mean direction of several trajectories is well aligned to the local magnetic field, but the instantaneous direction diverges widely. In this regard, magnetotaxis in ‘Ca. M. multicellularis’ shows some similarities with the run-and-tumble model of chemotaxis in enteric bacteria, since in both cases the microorganisms swim in many directions, but net migration occurs in the expected direction (Berg, 1985).

Acknowledgements

We thank to FAPERJ (Carlos Chagas Filho Research Support Foundation) and CNPq (National Council for Scientific and Technological Development) Brazilian agencies for financial support.