Bacterial swimming speed and rotation rate of bundled agella

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1 FEMS Microbiology Letters 199 (2001) 125^129 Bacterial swimming speed and rotation rate of bundled agella Yukio Magariyama a; *, Shigeru Sugiyama a, Seishi Kudo b Abstract b a National Food Research Institute, Kan-nondai, Tsukuba , Japan Faculty of Engineering, Toin University of Yokohama, 1614 Kurogane-cho, Aoba-ku, Yokohama , Japan Received 22 October 2000; received in revised form 5 February 2001; accepted 30 March 2001 First published online 20 April 2001 Swimming speed (v) and flagellar-bundle rotation rate (f)ofsalmonella typhimurium, which has peritrichous flagella, were simultaneously measured by laser dark-field microscopy (LDM). Clear periodic changes in the LDM signals from a rotating bundle indicated in-phase rotation of the flagella in the bundle. A roughly linear relation between v and f was observed, though the data points were widely distributed. The ratio of v to f (v^f ratio), which indicates the propulsive distance during one flagellar rotation, was 0.27 Wm (11% of the flagellar pitch) on average. The experimental v^f ratio was twice as large as the calculated one on the assumption that a cell had a single flagellum. A flagellar bundle was considered to propel a cell more efficiently than a single flagellum. ß 2001 Federation of European Microbiological Societies. Published by Elsevier Science B.V. All rights reserved. Keywords: Laser dark- eld microscopy; Swimming speed; Flagellar rotation rate; Salmonella typhimurium 1. Introduction Bacteria swim by means of agella, each of which consists of a thin helical lament, a rotary motor ( agellar motor), and other smaller parts [1]. Rotation of the helical lament driven by the agellar motor generates propulsive force by interaction with surrounding uid. The detailed analyses of bacterial agellar motion are signi cantly important for understanding the mechanism of microbial locomotion. In the previous paper, we succeeded in measuring a wide range of swimming speeds (v) and agellar rotation rates (f) of individual cells of Vibrio alginolyticus, which have single polar agella in a liquid medium [2]. This was carried out by laser dark- eld microscopy (LDM, [3]), which has a high temporal resolution, and therefore we could obtain the data under natural conditions. The observed relation between v and f was roughly linear, and the average of the ratio of v to f (v^f ratio) was 0.11 Wm (7% of the agellar pitch). These results were essentially consistent with the expectation based on a simple hydrodynamic model [2]. It should be noted that the v^f ratio refers to * Corresponding author. Tel.: +81 (298) ; Fax: +81 (298) ; maga@a rc.go.jp how long a cell progresses during one agellar rotation, i.e., it corresponds to the e ciency of agellar propulsion. For peritrichously agellated bacteria, Shimada et al. measured v and f of Salmonella typhimurium by cinemicrography, and reported almost linear relations between v and f for four individual cells [4]. The measured v^f ratios were, however, much larger than the expectation. One of the reasons for the distinction might be that the experiment was performed not under natural conditions but under viscous conditions using a viscous agent to slow down the agellar rotation. In this study, we have applied LDM to the investigation of the dynamics of bundled agella of S. typhimurium at a wide range of v and f under natural conditions. On the basis of the results, we discuss the feature of agellar bundle as screw propellers. 2. Materials and methods 2.1. Preparation of bacterial cells An S. typhimurium mutant, SJW3076 (smooth swimming, v(chea-chez); [5]) was used in this study. Cells were grown with shaking at 37³C in LB (1% peptone, 0.5% yeast extract, and 0.5% NaCl). The cells were har / 01 / $20.00 ß 2001 Federation of European Microbiological Societies. Published by Elsevier Science B.V. All rights reserved. PII: S (01)

2 126 Y. Magariyama et al. / FEMS Microbiology Letters 199 (2001) 125^129 Fig. 1. Principle of agellar-bundle rotation rate measurement. Laser dark- eld illumination creates the image of agellar bundle as a series of bright spots because parts of agellar laments illuminated normally (indicated by dashed circles) are much brighter than other parts. As the agella rotate, the bright spots move backward. Light intensity change caused by the motion of bright spots was detected and recorded through an optical slit. Bundle rotation rate can be determined from the intensity change. vested by centrifugation at late exponential phase and suspended in a bu er solution (10 mm KH 2 PO 4,20mM KCl, and 10 mm glucose; adjust ph to 7.0 by KOH). The cell density was adjusted to 10 8 ml 31. The cells were incubated at 25³C for 1 h before use Measurements of motility and morphology Flagellar-bundle rotation rates and swimming speeds of individual cells were measured using LDM [2]. As shown in Fig. 1, parts of agellar laments illuminated approximately normally become bright. The bright parts move backward with agellar rotation. Such images were focused on an optical slit and changes in the light intensity passing through it were detected and recorded. The rotation rate was determined from the light intensity changes and swimming speed of the cell was determined from the video image recordings. Morphological parameters of cell and agellum were measured by transmission electron microscopy (TEM) according to [2]. Flagellar-bundle rotation rates (f) and swimming speeds (v) of individual cells of S. typhimurium SJW3076 were simultaneously measured by LDM. Fig. 2 shows an example of LDM data. In Fig. 2a, a large increase in the signal corresponding to the passage of a cell body (`CELL' period) is followed by a smaller increase corresponding to the passage of a agellar bundle (`FLA' period). Fig. 2b shows the `FLA' period with expanded time and intensity scales in which periodic changes are observed. Because the LDM signal in the `FLA' period is the sum of the light intensities scattered from individual agella, the peaks are enhanced only when the individual intensities change in phase. Consequently, Fig. 2b indicates that the agella in a bundle rotated in phase (see Fig. 1). Thus, one cycle of intensity change corresponds to one bundle rotation. This enabled us to determine f from peak intervals of LDM data. Swimming speed v of the corresponding cell was determined from the video recording. The values of f and v obtained at 25, 30, and 35³C for individual cells are shown in Fig. 3. Both f and v increased 3. Results and discussion 3.1. Relation between agellar-bundle rotation rate and swimming speed Fig. 2. An example of LDM data for an S. typhimurium SJW3076 cell. (a) The `CELL' and `FLA' periods correspond to the passages of the cell body and agellar bundle, respectively. (b) The `FLA' period with expanded scales. A period from one peak to the next corresponds to the period for one revolution of the agellar bundle. The gate time of photon counting was set to 0.2 ms.

3 Y. Magariyama et al. / FEMS Microbiology Letters 199 (2001) 125^ Analysis of v^f ratio Fig. 3. Relation between swimming speed and agellar-bundle rotation rate. Each symbol represents a set of swimming speed (v) and agellarbundle rotation rate (f) of a cell. A solid line and two dashed lines indicate the average (0.27 Wm), maximum (0.36 Wm), and minimum (0.15 Wm) of the ratios of v to f, respectively. with temperature and the relation between them was roughly linear, but the data points were widely distributed. The averages of f and v at 25, 30, and 35³C were 112, 162, and 198 rps, and 29, 43, and 55 Wm s 31, respectively. The values were much smaller than those of V. alginolyticus (690, 910, and 1050 rps, and 77, 100, and 116 Wm s 31, respectively; [2]), while they were comparable to those reported for peritrichously agellated bacteria (170 rps and 28 Wm s 31 at 37³C for Streptococcus; 270 rps and 36 Wm s 31 at 32³C for Escherichia coli; [6]). The ratios of v to f (v^f ratios) of individual cells were much di erent from cell to cell. The values were widely distributed from 0.15 to 0.36 Wm and the average was 0.27 Wm, indicated by two dashed lines and a solid line, respectively, in Fig. 3. The average value corresponded to 11% of the agellar pitch. It should be noted that both the distribution and average of v^f ratios were almost independent of temperature as in the case of V. alginolyticus [2]. Table 1 Morphological parameters of S. typhimurium SJW3076 The value of the v^f ratio refers to how e ciently agella propel a cell because it means how long a cell progresses during one agellar rotation. First, the v^f ratios of bundled agella (S. typhimurium) and a single agellum (V. alginolyticus) are compared. The average of v^f ratios (0.27 Wm) obtained in this study for S. typhimurium is about twice as large as that (0.11 Wm) obtained for V. alginolyticus [2]. The value, however, is changed depending on the morphological parameters of agella that are known to be di erent among species. So we calculated the v^f ratio for S. typhimurium with a single agellum by a model (see Appendix), and compared it with the experimental one to clarify whether the di erence between the v^f ratios for the two species is caused by their agellar morphologies. The morphological parameters used in the calculation were determined by TEM for the same cell suspensions as the LDM measurement and are summarized in Table 1. The calculated value of v^f ratio was 0.13 Wm, which is about half of the experimental average value, indicating that the large v^f ratio observed for S. typhimurium is not due to the morphological parameters. Thus, the bundled agella are suggested to propel a cell more e ciently than a single agellum. Bundled agella are considered to propel a cell more e ciently by generating larger thrust than a single agellum. It is known that a viscous drag acting on two thin parallel cylinders placed closely in a uniform stream at low Reynolds number equals a drag acting on a single cylinder with slightly larger radius, rather than the sum of drags acting on independent cylinders [7]. One possible explanation for the larger thrust is that a bundle acts as a virtual thick single agellum. To match the theoretical value of v^f ratio to the experimental one (0.27 Wm), the e ective diameter of virtual agellum was calculated to be 1.06 Wm. The value is about 40 times larger than that of a single agellum (0.024 Wm), while the average number of agella per cell was about 5. It is also almost equal to the width of a cell body. However, the dark- eld microscopic Parameter Average S.D. Symbol Cell width 0.73 (Wm) 0.02 (Wm) 2a Cell length 1.4 (Wm) 0.3 (Wm) 2b Number of agella n Length of agellar lament 5.7 (Wm) L Radius of agellar lament a (Wm) 1.2 (Wm) d Pitch of agellar helix b 2.5 (Wm) 0.2 (Wm) p Radius of agellar helix c 0.18 (Wm) 0.03 (Wm) r Parameters were measured for 28 cells and 137 agella by TEM. a The radius of agellar lament was taken from [10]. b The pitch measured using an optical dark- eld microscope was 2.4 Wm (S.D. = 0.2 Wm). c The radius of agellar helix (r) was obtained from the pitch (p) and the lament length per pitch (l) of agellar helix according to: p l r ˆ 2 3p 2 : 2Z

4 128 Y. Magariyama et al. / FEMS Microbiology Letters 199 (2001) 125^129 image of a bundle usually looks thinner than that of a cell body. In addition to the large average value of the experimental v^f ratios, the wide distribution could not be fully explained. The cell-to-cell variation of the calculated v^f ratio is caused by the di erences in the lament and cell lengths among the cells. However, even if the variations were taken into consideration, the range of the v^f ratios calculated on the assumption of an e ectively thick single lament with a diameter of 1.06 Wm was only from 0.21 to 0.30 Wm, which is narrower than the experimental one (0.15^0.36 Wm). The assumption of an e ectively thick lament seems to be insu cient to explain the larger thrust. A dynamic scheme, in which laments in a bundle continuously slip to one another and change their relative positions, might be necessary to be taken into consideration. Actually, the wave shape of light intensity change for the `FLA' period (Fig. 2b) was more disordered than that observed for V. alginolyticus [2], suggesting that a agellar bundle has a dynamically changing structure rather than a rigid helix. Turner et al. recently reported that not every lament on a cell needs to change its direction of rotation in `tumble' (mode of moving erratically in place) [8]. Some tumbles to be hardly distinguished from `run' (mode of moving steadily forward) might result in the wide distribution of v^f ratio observed in this experiment. Although the strain used here, SJW3076 (v(chea-chez)), is not generally considered to show any tumbles, we cannot completely eliminate the possibility that a single lament within the agellar bundle of swimming SJW3076 transiently changes its rotational direction and/or departs from the bundle. In fact, an abrupt slowdown of agellar rotation of SJW3076 was observed [3]. The value of the v^f ratio might be in uenced by such phenomena. It was also reported that some mutants defective in switch complex (FliG, FliM, and FliN) with v(chea-chez) background showed tumbly swimming [5]. It might be noteworthy that the calculated values of v^f ratio were in good agreement with the experimental results when each agellum in the bundle was considered to propel the cell individually, though the assumption seems contrary to our knowledge of hydrodynamics. Shimada et al. also investigated the relation between v and f of the S. typhimurium strain, SJ25 [4]. They used a viscous agent, methylcellulose, to slow down the agellar rotation (below 17 rps). The v^f ratios reported by them were 0.50^0.75 Wm (24^36% of the agellar pitch), which were two to three times larger than the values obtained in the present study. The discrepancy is likely to be caused by the addition of methylcellulose, since it was reported that a solution of methylcellulose is highly structured even when quite diluted [9]. In our experiment, the cell of SJW3076 progressed by 11% of the agellar pitch per one revolution in the medium without any viscous agents, meaning that the agella slipped by 89%. It is possible that the addition of methylcellulose reduces the slip and increases the v^f ratio. The e ect of the viscous agents on the bacterial motility, however, has been examined only with respect to the swimming speed in most cases. More detailed investigations of the dependence of the v^f relations on the viscous agents are now in progress. Acknowledgements We thank F. Oosawa, K. Namba, S. Asakura, S. Tsuge, K. Kawachi, and I. Yamashita for their discussions. This work was partly supported by Special Coordination Funds of the Science and Technology Agency of the Japanese Government. Appendix To analyze the experimental data, we used a hydrodynamic model. In the model, we adopted the Stokes' approximation and considered a steady state. Drag forces on a cell and agellum are summarized as follows [2]: Drag force on a cell: F c ˆ K c v A1 Drag force on a agellum: F f ˆ K f v Q f g f Drag coe cients: K c ˆ 36ZW a b a K f ˆ 3 8Z 2 r 2 p 2 C 0 Q f ˆ 2Zr 2 pc 0 32ZW L C 0 ˆ log d 2p 1 4Z 2 2 r 2 p 2 A2 A3 A4 A5 A6 where v and g f are swimming speed and angular velocity of agellar bundle (rad s 31 ), W is viscosity, a and b are shorter and longer radii of cell body, r and p are radius and pitch of agellar helix, L and d are length and radius of agellar lament. The equation of motion is: F c F f ˆ 0 A7 From Eqs. A1, A2, and A7, the v^f ratio is obtained as: v f ˆ 2Zv ˆ 32ZQ f A8 g f K c K f where f is rotation rate of a agellar bundle (g f =2Zf).

5 Y. Magariyama et al. / FEMS Microbiology Letters 199 (2001) 125^ References [1] Macnab, R.M. (1996) Flagella and motility. In: Escherichia coli and Salmonella: Cellular and Molecular Biology, Vol. 1, 2nd edn. (Neidhart, F.C., Curtiss III, R., Ingraham, J.L., Lin, E.C.C., Low, K.B., Magasanik, B., Rezniko, W.S., Riley, M., Schaechter, M. and Umbarger, H.E., Eds.), pp. 123^145. American Society for Microbiology, Washington, DC. [2] Magariyama, Y., Sugiyama, S., Muramoto, K., Kawagishi, I., Imae, Y. and Kudo, S. (1995) Simultaneous measurement of bacterial agellar rotation rate and swimming speed. Biophys. J. 69, 2154^ [3] Kudo, S., Magariyama, Y. and Aizawa, S.-I. (1990) Abrupt changes in agellar rotation observed by laser dark- eld microscopy. Nature 346, 677^680. [4] Shimada, K., Ikkai, T., Yoshida, T. and Asakura, S. (1976) Cinemicrographic analysis of the movement of agellated bacteria. II. The ratio of the propulsive velocity to the frequency of the wave propagation along agellar tail. J. Mech.chem. Cell Motil. 3, 185^193. [5] Magariyama, Y., Yamaguchi, S. and Aizawa, S.-I. (1990) Genetic and behavioral analysis of agellar switch mutants of Salmonella typhimurium. J. Bacteriol. 172, 4359^4369. [6] Lowe, G., Meister, M. and Berg, H.C. (1987) Rapid rotation of agellar bundles in swimming bacteria. Nature 325, 637^640. [7] Fujikawa, H. (1956) The forces acting on two equal circular cylinders placed in a uniform stream at low values of Reynolds number. J. Phys. Soc. Japan 11, 558^569. [8] Turner, L., Ryu, W.S. and Berg, H.C. (2000) Real-time imaging of uorescent agellar laments. J. Bacteriol. 182, 2793^2801. [9] Berg, H.C. and Turner, L. (1979) Movement of microorganisms in viscous environments. Nature 278, 349^351. [10] Namba, K., Yamashita, I. and Vonderviszt, F. (1989) Structure of the core and central channel of bacterial agella. Nature 342, 648^ 654.

A Mathematical Explanation of an Increase in Bacterial Swimming Speed with Viscosity in Linear-Polymer Solutions

Biophysical Journal Volume 83 August 2002 733 739 733 A Mathematical Explanation of an Increase in Bacterial Swimming Speed with Viscosity in Linear-Polymer Solutions Yukio Magariyama* and Seishi Kudo