Implications of back-and-forth motion and powerful propulsion for spirochetal invasion

The spirochete Leptospira spp. can move in liquid and on a solid surface using two periplasmic flagella (PFs), and its motility is an essential virulence factor for the pathogenic species. Mammals are infected with the spirochete through the wounded dermis, which implies the importance of behaviors on the boundary with such viscoelastic milieu; however, the leptospiral pathogenicity involving motility remains unclear. We used a glass chamber containing a gel area adjoining the leptospiral suspension to resemble host dermis exposed to contaminated water and analyzed the motility of individual cells at the liquid-gel border. Insertion of one end of the cell body to the gel increased switching of the swimming direction. Moreover, the swimming force of Leptospira was also measured by trapping single cells using an optical tweezer. It was found that they can generate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim $$\end{document}∼ 17 pN of force, which is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim $$\end{document}∼ 30 times of the swimming force of Escherichia coli. The force-speed relationship suggested the load-dependent force enhancement and showed that the power (the work per unit time) for the propulsion is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim $$\end{document}∼ 3.1 × 10–16 W, which is two-order of magnitudes larger than the propulsive power of E. coli. The powerful and efficient propulsion of Leptospira using back-and-forth movements could facilitate their invasion.

Scientific RepoRtS | (2020) 10:13937 | https://doi.org/10.1038/s41598-020-70897-z www.nature.com/scientificreports/ of liquid and gel phases to mimic the skin dermis, which is exposed to contaminated environmental water. Furthermore, we expected that there would be a sizable propulsive force for the invasion and, thus, performed force measurements of swimming spirochetes using optical tweezers. Our experiments showed that there is an enhancement of swimming reversal when only one end of the cell body is inserted into the gel, and there is also a much larger swimming force of Leptospira than the known values of exoflagellated bacteria. These results suggest that powerful and efficient swimming with repeated trial-and-error allows Leptospira to obtain a smooth passage for penetration through the host dermis.

Results
Swimming reversal. We observed spirochetes using a flow chamber containing adjoining liquid medium and agar to examine the behaviors of Leptospira during penetration of viscoelastic environments ( Fig. 2A). The saprophytic species Leptospira kobayashii was used in the majority of the experiments. Leptospira cells show relatively smooth swimming in this liquid ( Fig. 2B left and Fig. 2C left). In contrast, when one end of the cell body becomes inserted in the agar, the cells were seen to frequently change direction ( Fig. 2B right and Fig. 2C right). The significant difference in reversal frequencies between cells in liquid and at the liquid-agar border is shown in Fig. 2D. Video 1 shows a Leptospira cell successfully penetrating agar after several back-and-forth movements. The enhancement of swimming reversal at the liquid-agar border was also observed in different species of Leptospira (Video 2 for the pathogenic species L. interrogans and Video 3 for the saprophyte L. biflexa), which suggests that the phenomenon is shared among genera. For pathogenic species, exploring more accessible routes in the dermis, such as structurally disturbed parts (due to injury), and using a "trial-and-error" method could determine the involvement in percutaneous invasion (Fig. 2E).
force measurement for swimming Leptospira. We trapped a microbead attached to swimming cells with optical tweezers in order to measure the swimming force of Leptospira (Fig. 3A, B). The labeling of Leptospira with antibody-coated microbeads was previously performed [17][18][19] and showed that the attached microbeads move on the outer membrane because of the mobility of the targeted antigens and viscous drag exerted on the bead, i.e., the bead is retarded from cell movement by viscous drag. The spontaneous attachment of beads to the Leptospira cell surface without any linkers (nonspecific binding) was utilized in this experiment 19 , but bead movements were also observed (Video 4). To determine the force produced by unidirectional swimming, we measured cells with a bead at the posterior end of the cell body. Bead displacements were converted to swimming force ( F ) by considering the balance with trapping force ( F trap ) and drag force ( F drag ) exerted on the bead; F = F trap + F drag (Fig. 3C, D and Video 5). The swimming force increased with cell displacement and reached saturation when the cell became stalled by the restoring force of the laser trap. The stall force differed widely among measured cells, and the averaged force-time curve showed a stall force of 16.6 ± 2.2 pN (mean ± standard error; n = 24 cells) (Fig. 4A). A model experiment in which a tungsten coil, mimicking the shape of Leptospira, was rotated in a rotational magnetic field, showed that 2.2 pN of force is required for penetrating agar that resembles skin dermis 20 . Actual Leptospira cells could also produce a swimming force approximately eightfold higher than the previous model predicted. Furthermore, the swimming force of Leptospira is found to be ∼ 30 times greater than that of E. coli (~ 0.6 pN) 21 .
force-speed relationship. The relationship between force and speed was obtained from force-time plots, which showed that swimming forces linearly decreased as the swimming speed increased (Fig. 4B). The forcespeed curves suggest that Leptospira can vary their propulsive force depending on the load exerted on the cell such as viscous drag and trapping forces. We calculated the work per unit time, Fv , for Leptospira propulsion using measured values (Fig. 4C). The propulsive power of Leptospira ranges from 1 × 10 −16 to 7 × 10 −16 W, which is two orders of magnitude greater than that of E. coli (5.8 × 10 −18 W) 21 . These results suggest that Leptospira can produce a large force and maintain high efficiency when penetrating gel-like viscous materials.

Discussion
We focused on the association of motility with the invasion of the Leptospira spirochete. Our biophysical experiments reveal that the back-and-forth movement of Leptospira is enhanced when only one of the cellular ends is exposed to a high viscosity medium and spirochetes can produce a much larger swimming force than exoflagellated bacteria. The trial-and-error behavior that permits the cell to find preferable entrances will be significant for infection through the dermis because heterogeneous fibrous structures may obstruct spirochetal invasion even though they can elicit high propulsion forces. The viscosity-dependent swimming reversal was observed in both pathogenic and nonpathogenic species, which implies that Leptospires can penetrate the dermis regardless of kinematic pathogenicity. However, since the motility of nonpathogenic L. biflexa is lost immediately after exposure to physiological osmotic conditions 22 , dissemination within the host is not deemed possible. Previously, the enhancement of swimming reversal was observed in polymer solutions where the entire spirochetal body was exposed to changes in environmental viscosity or viscoelasticity 12 . However, we found that swimming reversal is increased by a minimal part of the cell body that is placed in the viscoelastic milieu. Because the torque for rotating the spiral body of Leptospira is produced by PFs residing at both cellular ends, it is expected that the two PFs should cooperatively rotate. In this context, our results suggest that some signal transduction between the two cell ends. Thus, one issue that remains unclear is the mechanism by which Leptospires sense a viscoelastic change at one end and rapidly transmit the mechanical signal to the other end (within < 1 s; see Video 6 for this rapid reversal). Coordinated rotations observed between E. coli flagellar motors depend on the diffusion of the phosphorylated chemotactic signaling protein CheY-P 23 . Leptospira spp. also possess several CheY homologs 24 . However, the formula t = x 2 /D indicates that for CheY with a diffusion coefficient D = 10 μm 2 /s 23 , there is an estimated 40 s (t) to diffuse x = 20 μm (the approximate distance between the leptospiral motors). Therefore, rather than cytoplasmic signaling, the relatively stiff protoplasmic cylinder may be a medium for mechanical signal transduction 11,25 . Thus, elucidating the PF coordinated control mechanism warrants further investigation.
The measured swimming force of Leptospira is found to be ∼ 30 times greater than E. coli 21 . This ability to generate a higher force by the spirochete could be attributed to drag coefficients and high torque from the motor. Hydrodynamic studies of a low Reynolds number using resistive force theory showed that the drag force exerted on a spherical cell body with a spiral thin body, which rotates at ω Lep and translates at v Lep in liquid, is calculated using F Lep = α Lep v Lep + β Lep ω Lep , where α Lep and β Lep are the drag coefficients for the spiral cell body 6,11,26 . Similarly, the drag force on externally flagellated bacteria with a spherical body and flagellum is given by F Efb = α Efb v Efb + β Ef ω Ef , where α Efb is the sum of the drag coefficients for the translating spherical cell body, α Cell , and filament α Ef ( α Efb = α Cell + α Ef ) and β Ef is the drag coefficient for the flagellar rotation. Furthermore, v Efb and ω Ef are the swimming speed and the flagellar rotation rate, respectively 27 . These drag coefficients depend on geometrical parameters such as the length and width of the cell body, the wavelength and the amplitude of a helix, and fluid viscosity (see "Methods"). Calculations using morphological parameters of L. biflexa 11 and E. coli show that α Lep = − 0.056 pN·s/μm, β Lep = 0.002 pN·s, α Ef = − 0.02 pN·s/μm, and β Ef = 0.0003 pN·s. Thus, the drag coefficients for the leptospiral body are larger than those for E. coli. Despite these large drag coefficients, the swimming speed (~ 20 μm/s) and cell body rotation rates (> 100 Hz) of Leptospira spp. are comparable to those of E. coli 21 . Cryo-electron microscopy has showed that compared with conventional flagellar motors, such as E. coli and Salmonella spp., the rotor ring of the spirochetal flagellar motor is determined to be larger 28 , and a greater number of torque generators (stator units) are assembled 29 . Thus, the large swimming force of Leptospira www.nature.com/scientificreports/ could be provided by the high torque from a motor that rotates the heavy cell body. Since the cell morphology, motor structure, and swimming velocity are similar among different species of Leptospira 22,29 , the spirochetal genus is characterized as powerful swimmers. The stall force was found to be uneven among measured cells (Fig. 4A). In the high load, the motor torque of the external flagellum depends on the number of stators and input energy ion motive force (IMF) 30 . Due to the stable incorporation of the full number of stator units to the motor, which is shown in Leptospira spp. by electron cryo-tomography 29 , the difference in IMF could be a cause of varied stall force. Furthermore, since intimate contact between PFs and cell membranes is necessary for spirochetal swimming 31 , PF-membrane interaction or morphological differences of PFs, such as length, could affect propulsion.
The force-speed relationship (Fig. 4B) showed that swimming force decreases with increased speed. Leptospira might have a mechanism to control propulsive output in response to changes in load. However, although the load-dependent assembly of stator units is observed in flagellar motors of E. coli and Salmonella 32-35 , these stator dynamics seem to be implausible for Leptospira motor as mentioned above. A motility study of B. burgdorferi by Harman et al. has discussed the balance between power input by the flagellar motor and power dissipation by swimming through a viscous liquid. According to Harman et al., the power input is defined by the motor torque ( M ) times the cell rotation rate ω and the power dissipation given by the sum of the term proportional to ω 2 and proportional to Fv : Mω = Aω 2 + BFv , where A and B are proportional coefficients comprising the parameters for cell morphology and drag coefficients 36 . Based on v ∝ ω 11,19 and the assumption that M is not dependent on load, the equation can be simplified into F = C − Dv , where C and D are proportional coefficients. Thus, the power dissipation model explains the observed force-speed relationship plausibly. Although the current experiments could not determine whether the speed-dependent reduction of swimming force is due to active force control by Leptospira or power dissipation by moving through viscous media, the spirochete is expected to invade highly viscous environments while maintaining a large output of power.
Measurement of swimming reversal. The Leptospira culture was centrifuged at 1,000g for 10 min at 23 °C, and the precipitated cells were resuspended in the motility medium without dilution. The bacterial suspension was infused to a flow chamber that was made by sticking a coverslip and a glass slide with double-sided tape (90 μm in thickness) that contained 1% agar so that the agar and liquid area were contiguous in the chamber ( Fig. 2A). The liquid-agar border was observed with a dark-field microscope (BX53, 40× objective, 5× relay lens, Olympus, Tokyo, Japan), and behaviors of cells inserting one end of the cell body into agar were recorded with the CMOS camera at 250 Hz.
The swimming reversal was measured by tracing the cellular centroid in general 39,40 . However, the morphology of the Leptospira cell changes frequently, thus affecting the consistency between the centroid displacement and the actual cell movement (Supplementary Fig. S3). The positions of both ends of the cell body were determined together with the centroid, and simultaneous displacements of the three points were recognized as cell movements to avoid the false recognition of the reversal (Fig. S3A). Swimming speeds were measured by line fitting to the time courses of the cell displacements at an interval of 0.1 s, < 1 μm/s was judged as "pausing". The reversal frequency was determined by normalizing the number of the reversals ( N rev ) by the observation time ( t ), such that N rev /t . The data were analyzed with ImageJ software (National Institutes of Health, Rockville, MD) and programs originally developed using LabVIEW 2014 (National Instruments). Data of each condition were obtained by more than five independent experiments.

Measurement of swimming force.
A dark-field microscope (BX50, Olympus, Tokyo, Japan) that is essential for observing a thin leptospiral cell body (~ 140 nm in diameter) was equipped with an optical tweezer ( Fig. 2A). The cell suspension prepared by the same procedure as the reversal measurement was mixed with 1.0 μm carboxyl latex beads (ThermoFisher Scientific, Waltham, MA) and was incubated at 23 °C for 10 min. The mixture was infused to the glass-made chamber, and spontaneous bead attachments to swimming cells were observed. The attached beads did not interfere with the Leptospira swimming (Video 7). The attached bead was trapped by a 1064 nm semiconductor laser (TLD001, Laser Diode Driver, Thorlabs Inc. Newton, NJ) through an ×100 oil immersion objective lens (UPlanFLN, Olympus, Tokyo, Japan), and the bead movement was recorded with a CMOS video camera (acA800-510um, Basler, Ahrensburg, Germany) at a frame rate of 500 Hz. The numerical aperture of the objective was adjusted with the objective-lens aperture to perform dark-field observation and laser trapping simultaneously. The recorded movie was analyzed to determine the bead displacement with a custom-made program developed using LabVIEW 2014 (National Instruments, Austin, TX).
Displacement of a trapped bead ( x ) can be calibrated to a restoring force of optical tweezer ( F trap ) using the equation F trap = k x , where k is a spring constant. The values of k were determined in each flow chamber by trapping a bead free from cells and analyzing its positional fluctuation. The positional distribution of the trapped bead showed a Gaussian distribution f (x) ∝ exp −x 2 /2σ 2 , where σ is the standard deviation (Fig. 2B, black line), obeying Boltzmann's law P(x) ∝ exp(−�U/k B T) , where U is the potential energy, k B is the Boltzmann constant (1.38 ×10 -23 J/K), and T is the absolute temperature (296 K), namely, �U = k B T/2σ 2 x 2 (Fig. 2B, red  line). Since the thermal fluctuation of the bead captured by a spring with k can be described by the harmonic Scientific RepoRtS | (2020) 10:13937 | https://doi.org/10.1038/s41598-020-70897-z www.nature.com/scientificreports/ function U(x) = 1/2kx 2 , k = k B T/σ 2 . The swimming force was determined using F trap and F drag (Fig. 2C). When the bead with a diameter of r is moved at a speed of v (swimming speed of the cell) in a solution with a viscosity of µ , F drag = 6πµrv , where 6πµr is a drag coefficient given by Stokes' low. The viscosity of the motility medium was measured with a tuning-fork-type viscometer (SV-1A, A&D, Tokyo, Japan), giving 0.8 mPa s at 23 °C. Data were obtained by five independent experiments. Drag coefficients. Drag coefficients for the spirochete and externally flagellated bacterium are calculated as described previsouly 11,27 . For the Leptospira cell, the protoplasmic cylinder lacking bending at the cell ends was assumed: Here, r Lep , p Lep , L Lep , and 2d Lep are the helix radius (0.09 μm), helix pitch (0.7 μm), length (20 μm), and diameter (0.14 μm) of the leptospiral cell body 11,41 . Drag coefficients for the externally flagellated bacterium that was assumed to consist of a spherical body and a helical filament, referring to the morphology of Vibrio alginolyticus 27 , were calculated as follows: Here, 2a and 2b are the diameter (0.8 μm) and length (1.92 μm) of the cell body, and r Ef , p Ef , L Ef , and 2d Ef are the helix radius (0.14 μm), helix pitch (1.58 μm), length (5.02 μm), and diameter (0.032 μm) of the flagellum. The medium viscosity µ was assumed to be 1 mPa s. α Ef = C Ef 8π 2 r Ef 2 + p Ef 2 ; β Ef = −2C Ef πr 2 p Ef ;