| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
* Food Engineering Division, National Food Research Institute, Tsukuba, Japan; Department of Mechanical Engineering, Tottori University, Tottori, Japan; and Faculty of Engineering, Toin University of Yokohama, Yokohama, Japan
Correspondence: Address reprint requests to Yukio Magariyama, Food Engineering Division, National Food Research Institute, Tsukuba, 305-8642, Japan. Tel.: 81-29-838-8054; Fax: 81-29-838-7181; E-mail: maga{at}affrc.go.jp.
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
; Blair, 1995). These bacteria have many flagella located all over the cell body, called "peritrichous flagella". They exhibit a swimming pattern in which the "run" mode and the "tumble" mode are alternately repeated (Berg and Brown, 1972). A bacterial cell swims straight in the run mode by rotating the flagellar bundle counterclockwise (CCW). Each flagellum rotates clockwise (CW) in the tumble mode, and the cell cannot move translationally but can randomly change its direction. The cell responds to stimuli by modulating the frequency of the tumble modes (Brown and Berg, 1974).
Bacteria that have single polar flagella (monotrichously flagellated bacteria), such as Vibrio alginolyticus, display a swimming pattern different from peritrichously flagellated bacteria. The cell alternately repeats forward swimming caused by CCW flagellar rotation and backward swimming caused by CW rotation (Homma et al., 1996). It is notable that the cell moves translationally whenever the flagellum rotates. Thus, CW flagellar rotation plays a different role from that of peritrichously flagellated bacteria. The CW rotation of a bundle of peritrichous flagella corresponds to a brief stop of a monotrichous flagellum between CCW and CW rotation. Switching between forward and backward modes is rapid. Chemotaxis is performed by modulating the switching frequency. A cell that goes out, turns, and backs up precisely on track would move only along a straight line and could not scan everywhere. This does not occur in practice, since random forces such as Brownian motion perturb the cell's trajectory (McCarter, 2001).
The CCW and CW rotations of a monotrichous flagellum, i.e., the forward and backward swimming modes, appear to be equivalent from the standpoint of chemotaxis. No difference between the two modes was indicated by the conventional hydrodynamic model for monotrichously flagellated bacteria (Holwill and Burge, 1963; Chwang and Wu, 1971; Magariyama et al., 1995). However, it was reported that the backward swimming speeds of V. alginolyticus are on average 1.5 times greater than the forward swimming speeds (Magariyama et al., 2001).
There are some conceivable causes for the difference in swimming speeds, i.e., the torque characteristics of the flagellar motor, deformation of the flagellar filament, and interaction between the cell and a solid surface. The cause of the difference is not yet known. We consider that flagellar deformation can be eliminated from the three possible causes given above. A very small difference in deformation between forward and backward modes, as well as minimal deformation, was recently confirmed by an experiment and by a numerical analysis (Nishitoba et al., 2003; Takano et al., 2003).
We noted in observations by high-intensity dark-field microscopy and phase-contrast microscopy that the trajectory in the forward mode differs from that in the backward mode (Kudo et al., 2005). The phenomenon was qualitatively analyzed in that article. In this study, to clarify the cause of the difference in the bacterial motion between the forward and backward modes, we carried out a detailed quantitative analysis of the shape of the trajectory and the swimming speed, depending on the distance from a solid surface. These results reveal that the previously reported speed difference is caused by proximity to a surface. We also suggest that a surface affects the chemotactic behavior.
|
MATERIALS AND METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
|
to identify the swimming mode (forward or backward) if necessary. A simple chamber, as depicted in Fig. 1, was assembled from a glass slide (No. 1, 26 x 78 mm2, Matsunami Glass Ind., Kishiwada, Japan) and three coverslips (No. 1, 22 x 22 and 22 x 7 mm2, Matsunami) to examine the wall effect. The cell suspension was put into it and the open edges were completely sealed with nail enamel. Video images of bacterial swimming were recorded by phase-contrast microscopy (BX50, Olympus, Tokyo, Japan; CS220, Olympus; DSR-30, Sony, Tokyo, Japan). The video images were captured on a PC (Endeavor Pro-1000, Epson Direct, Matsumoto, Japan; DVStorm-RT, Canopus, Kobe, Japan). The centers of the cells were determined every frame by NIH Image on an Apple Power Macintosh G3 and the trajectories were then obtained by an original Visual Basic for Applications program in Microsoft Excel 2002/Windows XP.
|
10 µm, since the images slightly out of focus were also processed.
|
. The contact angles were measured to characterize the silanized surfaces. A droplet of 5 µl of HG300 was deposited on a glass slide using a micropipette. The droplet image was recorded (Ai Micro Nikkor, 55 mm, F2.8S, Nikon, Tokyo, Japan; XC-77, Sony; DF-20, Fuji Photo Film, Minami-Ashigara, Japan), the image was analyzed by NIH Image, and the contact angle was determined from the coordinates of the three characteristic points under the assumption that the droplet was spherical (Fig. 3).
|
|
|
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
). In addition to this result, the shape of the swimming subtrajectory differed between the forward and backward modes (Fig. 5), as we reported previously (Kudo et al., 2005). Here, we define the subtrajectory as the trajectory between successive rapid turns. The trajectory depicted in Fig. 5 demonstrates that a YM4 cell swam along an almost straight line in the forward mode, and along a curve in the backward mode. We occasionally observed a cell curving both to the right and the left in the backward mode, although the cell in Fig. 5 curved only to the right.
|
We characterized the bacterial motion by the swimming speed and the turning speed, as defined in Fig. 6. The turning speed is a parameter that represents the shape of the trajectory. It is equal to zero when a cell goes straight; it is positive when a cell curves to the left and negative when it curves to the right. The swimming speed of 558 subtrajectories measured near the upper surface was 73 ± 16 µm/s, that of 475 subtrajectories at the middle position was 66 ± 15 µm/s, and that of 582 subtrajectories near the lower surface was 72 ± 16 µm/s. The turning speeds near the upper surface, at the middle position, and near the lower surface were 0.72 ± 1.32 rps, 0.04 ± 0.72 rps, and -0.73 ± 1.33 rps, respectively. These results may suggest a wall effect on the motion characteristics. Considering the bacterial swimming mode, forward or backward, in analyzing the data would make the wall effect clearer.
|
Typical examples of the motions of YM4 close to and far from any surface are provided in Fig. 7. Almost-straight subtrajectories and subtrajectories curved to the right were repeated alternately near the upper surface (Fig. 7 a). Similar behavior was observed near the lower surface, except that the curving direction was opposite (Fig. 7 e). No marked difference in the characteristics of motion between the subtrajectories before and after a rapid turn was observed at the middle position (Fig. 7 c): the swimming speed did not change very much and the turning speed was almost zero before and after a rapid turn (Fig. 7 d). In contrast, as shown in Fig. 7 f, the swimming speed in the curving subtrajectory seemed to be greater than that in the straight subtrajectory. The same tendency was seen in Fig. 7 b.
|
was introduced in our previous article (Magariyama et al., 2001), where vf and vb are the swimming speeds in the forward and backward modes in a trajectory. According to the previous results, in which a normal slide without spacers was used, the frequency distribution of the indices tended toward the negative side (Fig. 8 a; Table 2), leading us to conclude that the forward swimming speed was lower than the backward speed, and that the cause for the phenomenon was neither individual differences nor changes in physiological condition.
|
|
in this article, since whether the swimming mode was forward or backward could not be distinguished by phase-contrast microscopy. Here, vo and ve are the swimming speeds in the odd- and even-numbered subtrajectories in a trajectory. The values of the index for 150 trajectories measured at the three positions (upper, middle, and lower) in the simple chambers were symmetrically distributed around zero (Fig. 8, c, e, and g; the averages are –0.007, –0.006, and 0.006), as we expected, since the odd- or even-numbered subtrajectories corresponded to either swimming mode, forward or backward.. The distribution at the middle position (Fig. 8 e; standard deviation (SD) 0.075) was slightly narrower than those near the upper (Fig. 8 c; SD 0.094) and lower (Fig. 8 g; SD 0.089) surfaces. Two-sided F-tests with 5% significance level indicate that the variance at the middle position differs from those at the upper and lower positions and cannot reject that the distributions near the upper and lower surfaces have the same variance (Table 2), although those distributions were not as broad as that measured in the normal slide (Fig. 8 a; SD 0.14).
The turning speed in the forward mode (–0.08 ± 0.55 rps) was generally lower than that in the backward mode (0.14 ± 1.27 rps) in the normal slide, as described in the first section of Results (Fig. 8 b). Different phenomena were observed in the simple chamber, depending on the distance from a surface. A set of 
o and e near the upper surface had a set of large negative and small values, or the converse (Fig. 8 d). Thus, a bacterial cell generally alternated between an almost-straight run and curving to the right in every turn. The same result was obtained near the lower surface, except that the turning speed had positive values, i.e., a cell curved not to the right but to the left (Fig. 8 h). The values of both o and e were nearly zero at the middle position (Fig. 8 f). There was no difference between the characteristics of the bacterial motion far from the wall before and after a rapid turn.
Relationship between the swimming-speed difference and turning-speed difference
We have shown a wall effect on the swimming speed and the turning speed. However, that effect on the swimming speed was not as apparent as the effect on the turning speed. We analyzed the correlation between the swimming speed and the turning speed near the upper surface, at the middle position, and near the lower surface to examine the wall effect on the swimming speed. Instead of the swimming speed and the turning speed, 
and 
were used to eliminate the effect of individual differences. Fig. 9 indicates a negative correlation near the upper surface, no correlation at the middle position, and a positive correlation near the lower surface between the two parameters and 
Therefore, we concluded that the swimming speed and the turning speed were affected by a wall.
|
|
|
|
|
). The values of the parameters used in the calculation are summarized in Table 4. The adopted values of swimming speed and turn speed were close to the values measured in this study. We let the backward swimming speed be greater than the forward swimming speed based on a previous report (Magariyama et al., 2001). Fig. 12 a indicates that the turn angle at a mode switch conformed to a normal distribution with a mean of 0° and a standard deviation of 20°. Therefore, those values were adopted in the calculation. The probabilities of mode switching in a uniform environment, 2.5 times/s for switching from forward mode to backward and 4.0 times/s for the opposite switching, were based on the mean periods of the forward and the backward mode, 0.40 s and 0.23 s (Magariyama et al., 2001). The probabilities under the taxis condition were determined relative to those in a uniform environment for simplification. Thus, we let the probability be half as great as the standard when the cell went to a better environment, and twice the standard when going to a worse environment. Fig. 12 b contains examples of the swimming trajectory under the uniform environment. The thick line is a calculated trajectory near a surface and the thin line is a trajectory far from any surface. Both lines are similar to the experimental result (see Fig. 7). Fig. 12, c and d, depicts 10 calculated trajectories of a cell that has (c) different or (d) the same motility characteristics between forward and backward modes. The trajectories in Fig. 12 d tended to spread wider than those in Fig. 12 c. We simulated a condition in which the point source of an attractant was located 1 mm from the starting point to investigate the macroscopic taxis behavior. Fig. 12, e and f, depicts the cell positions 60 s later. The cells had (e) different or (f) the same motility characteristics between swimming modes. The positions in Fig. 12 e tended to be closer to the target than those in Fig. 12 f. The former cells tended to approach the target straighter and faster than the latter (data not shown). The slow approach to the target rather than the low accuracy is the reason for the wide spread of the points in Fig. 12 f.
These results demonstrate that the macroscopic motion characteristics such as spreading and chemotactic behavior are affected by the microscopic swimming pattern of the difference in the swimming speed and the turning speed between forward and backward modes.
|
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
A swimming bacterial cell must be affected by some force from a solid surface. That force is neither hydrophobic interaction nor electrostatic interaction since the motion characteristics were not affected by chemical surface modifications with silane-coupling agents. Hydrodynamic interaction is a possibility since it is a long-range force. The difference in the motion characteristics between the forward and backward modes has not been explained yet, although hydrodynamic analyses have succeeded in explaining most other bacterial motion phenomena (Holwill and Burge, 1963; Chwang and Wu, 1971; Magariyama et al., 1995; Azuma, 1992; Ramia et al., 1993, Goto et al., 2001). Streams are symmetrical between the forward and backward directions in low Reynolds number hydrodynamics, leading us to expect the same motion characteristics between the forward and backward modes. We believe that important factors have been overlooked. The problem to be solved now is to identify those factors and to explain the phenomenon described in this article.
Wall effect on the swimming speed and turning speed
According to the two-sided F-tests, the distribution of the swimming speed index near a surface differed from that far from any surfaces. In addition, a correlation between the index and the turning speed was seen only when the cells swam close to surfaces. Therefore, we concluded that the swimming speed difference between forward and backward modes was caused by a surface. However, the frequency distribution of measured near a surface in the simple chamber with spacers (Fig. 8, c and g) was narrower than that measured in a normal slide without spacers (Fig. 8 a); we had expected their distributions to be similar. The difference between the forward and backward swimming speeds was comparatively small in our results. The distance from a cell to a nearby surface was <5 µm in the normal slide since the sample medium thickness was 10 µm. Thus, a cell always swims near either surface in a normal slide. In contrast, the distance from a cell to the surface in a simple chamber is not always <5 µm since the side other than the surface is open and the motion of a cell >5 µm away from the surface may also be recorded and analyzed. The difference in swimming speed near the surface was comparatively small and was similar to the difference at the middle position, probably because cells >5 µm away from the surface were included in the data.
In contrast to the swimming speed, the difference in the turning speed, representing the shape of the trajectory, between the forward and backward swimming modes near a surface clearly differed from the difference at the middle position. This result indicates that the force in the progress direction that acted on the cell rapidly decreased with distance from the surface, whereas the force in the lateral direction did not decrease as rapidly. This problem will also be solved if the law governing the wall effect on bacterial motion is clarified.
Significance of the surface for bacteria
V. alginolyticus is a marine bacterium. Although the bacterium is known to swim considerably fast (up to 150 µm/s; Magariyama et al., 1994), its motility and chemotaxis do not seem to indicate a sufficient effect in the vast ocean since the bacterial swimming speed is much lower than the flow speed of water caused by oceanic currents and the motions of other large organisms such as fish. In addition, the concentration of each chemical substance is much lower than the limit of bacterial chemosensing (1 µM; Macnab, 1987), although the concentration of the total dissolved organic carbon in surface sea waters is 60–80 µM (Ogawa and Tanoue, 2003). Effective bacterial chemotaxis in the vast ocean would require remarkably advanced performance.
Large living or dead organisms are suitable nutrient sources for bacteria in the ocean since the nutrient molecules around and diffusing from the organism are much more concentrated than in the bulk of sea water. Therefore, a bacterial cell must exhibit effective chemotaxis near a solid surface. The motion characteristics of V. alginolyticus near a surface reported in this article fulfill that requirement. The curved trajectory in the backward mode allows the bacterial cell to approach a target position faster than a straight trajectory. The attractive force between the surface and the cell in the backward mode allows the cell to stay near the surface for a long time.
Kogure et al. (1998) reported the positive correlation between the probability of attachment to a glass surface and the swimming speed of V. alginolyticus. The results of our study may explain this phenomenon. The attractive force probably strengthens as the swimming speed increases. Therefore, a faster-swimming cell may stay longer near the surface. It is possible that remaining near the surface may result in an attachment of the cell to the surface. Therefore, we expect that the probability of attachment to the surface increases with the swimming speed. A few problems with this reasoning must be solved, such as the relationship between the attractive force to the surface (or the resident time near the surface) and the swimming speed, and the attachment mechanism of the swimming cell.
We stated in the Introduction that the CW flagellar rotation of V. alginolyticus plays a different role from that of peritrichously flagellated bacteria. This is always correct from a microscopic standpoint. It is also accurate when a cell swims far from any surface. However, it does not hold true near a surface from a macroscopic viewpoint. The backward swimming mode caused by CW flagellar rotation is functionally the same as the tumble mode of peritrichously flagellated bacteria since the cell turns only in a limited area. The "run-tumble" pattern seems to have an advantage in taxis response (see Fig. 12, e and f). However, the "run-back" pattern may have an advantage in spreading in a uniform environment (see Fig. 12, c and d). Monotrichously flagellated bacteria switch the run-back and run-tumble patterns depending on the distance from a solid surface at the moment. They appear to select their swimming pattern according to the function currently necessary. Some bacteria, including the Aeromonas, Azospirillum, Rhodospirillum, and Vibrio species, exhibit two flagellation patterns, single polar flagellation and peritrichous flagellation (Allen and Baumann, 1971; McCarter, 2004). Peritrichous flagella appear only when grown on solid media or in viscous environments (McCarter, 2001; Atsumi et al., 1996; Kawagishi et al., 1996). This bacterial strategy is reasonable, since the above-mentioned advantage would be lost if the planktonic cell had peritrichous flagella.
Does bacterial chemotaxis have no power in the bulk space of the ocean? Luchsinger et al. (1999) suggested that the swimming pattern of monotrichously flagellated bacteria was more suitable than that of peritrichously flagellated bacteria under turbulent conditions such as those in the ocean. The calculated result in this study also suggests that monotrichously flagellated bacteria have an advantage over peritrichously flagellated bacteria in the aspect of diffusion. Some marine bacteria swim faster than V. alginolyticus (up to 400 µm/s; Mitchell et al., 1995). It has been reported that the marine bacteria Pseudoalteromonas haloplanktis and Shewanella putrefaciens change their swimming speeds depending on the presence of the motile algae Pavlova lutheri, up to 445 µm/s in its presence and up to 126 µm/s in its absence (Barbara and Mitchell, 2003). Those bacteria may perform effective chemotaxis by combining an unknown strategy with a forward-backward swimming pattern.
|
ACKNOWLEDGEMENTS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
This work was partly supported by the Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (No. 15560143).
|
FOOTNOTES |
|---|
Kousou Nakata's present address is Shin Nippon Air Technologies, Tokyo, 103-0021, Japan.
Submitted on October 7, 2004; accepted for publication January 18, 2005.
|
REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
Atsumi, T., Y. Maekawa, T. Yamada, I. Kawagishi, Y. Imae, and M. Homma. 1996. Effect of viscosity on swimming by the lateral and polar flagella of Vibrio alginolyticus. J. Bacteriol. 178:5024–5026.
Azuma, A. 1992. The Biokinetics of Flying and Swimming. Springer-Verlag, Tokyo.
Barbara, G. M., and J. G. Mitchell. 2003. Bacterial tracking of motile algae. FEMS Microbiol. Ecol. 44:79–87.[CrossRef]
Berg, H. C., and D. A. Brown. 1972. Chemotaxis in Escherichia coli analysed by three-dimensional tracking. Nature. 239:500–504.[CrossRef][Medline]
Blair, D. F. 1995. How bacteria sense and swim. Annu. Rev. Microbiol. 49:489–532.[CrossRef][Medline]
Brown, D. A., and H. C. Berg. 1974. Temporal stimulation of chemotaxis in Escherichia coli. Proc. Natl. Acad. Sci. USA. 71:1388–1392.
Chwang, A. T., and T. Y. Wu. 1971. A note on the helical movement of micro-organisms. Proc. Roy. Soc. Lond. B. 178:327–346.[Medline]
Goto, T., S. Masuda, K. Terada, and Y. Takano. 2001. Comparison between observation and boundary element analysis of bacterium swimming motion. JSME Int. J. Ser. C. 44:958–963.[CrossRef]
Holwill, M. E. J., and R. E. Burge. 1963. A hydrodynamic study of the motility of flagellated bacteria. Arch. Biochem. Biophys. 101:249–260.[CrossRef][Medline]
Homma, M., H. Oota, S. Kojima, I. Kawagishi, and Y. Imae. 1996. Chemotactic responses to an attractant and a repellent by the polar and lateral flagellar systems of Vibrio alginolyticus. Microbiol. 142:2777–2783.[Abstract]
Kawagishi, I., M. Imagawa, Y. Imae, L. McCarter, and M. Homma. 1996. The sodium-driven polar flagellar motor of marine Vibrio as the mechanosensor that regulates lateral flagellar expression. Mol. Microbiol. 20:693–699.[CrossRef][Medline]
Kogure, K., E. Ikemoto, and H. Morisaki. 1998. Attachment of Vibrio alginolyticus to glass surface is dependent on swimming speed. J. Bacteriol. 180:932–937.
Kudo, S., N. Imai, M. Nishitoba, S. Sugiyama, and Y. Magariyama. 2005. Asymmetric swimming pattern of Vibrio alginolyticus cells with single polar flagella. FEMS Microbiol. Lett. 242:221–225.[CrossRef][Medline]
Luchsinger, R. H., B. Bergersen, and J. G. Mitchell. 1999. Bacterial swimming and turbulence. Biophys. J. 77:2377–2386.
Macnab, R. M. 1987. Motility and chemotaxis. In Escherichia coli and Salmonella typhimurium. J. Ingraham, K. B. Low, B. Magasanik, M. Schaechter, H. E. Umbarger, and F. C. Neidhardt, editors. American Society for Microbiology, Washington, DC. 732–759.
Magariyama, Y., S. Masuda, Y. Takano, T. Ohtani, and S. Kudo. 2001. Difference between forward and backward swimming speeds of the single polar-flagellated bacterium, Vibrio alginolyticus. FEMS Microbiol. Lett. 205:343–347.[CrossRef][Medline]
Magariyama, Y., S. Sugiyama, K. Muramoto, I. Kawagishi, Y. Imae, and S. Kudo. 1995. Simultaneous measurement of bacterial flagellar rotation rate and swimming speed. Biophys. J. 69:2154–2162.
Magariyama, Y., S. Sugiyama, K. Muramoto, Y. Maekawa, I. Kawagishi, Y. Imae, and S. Kudo. 1994. Very fast flagellar rotation. Nature. 371:752.[Medline]
McCarter, L. 2001. Polar flagellar motility of the Vibrionaceae. Microbiol. Mol. Biol. Rev. 65:445–462.
McCarter, L. L. 2004. Dual flagellar systems enable motility under different circumstances. J. Mol. Microbiol. Biotechnol. 7:18–29.[CrossRef][Medline]
Mitchell, J. G., L. Pearson, A. Bonazinga, S. Dillon, H. Khouri, and R. Paxinos. 1995. Long lag times and high velocities in the motility of natural assemblages of marine bacteria. Appl. Environ. Microbiol. 61:877–882.[Abstract]
Nishitoba, M., Y. Magariyama, and S. Kudo. 2003. Bacterial flagellar deformation observed by laser dark-field microscopy. Proc. 2nd Int. Symp. Aqua Biomech, Honolulu. 1–5.
Ogawa, H., and E. Tanoue. 2003. Dissolved organic matter in oceanic waters. J. Oceanogr. 59:129–147.[CrossRef]
Ramia, M. D., L. Tullock, and N. Phan-Thien. 1993. The role of hydrodynamic interaction in the locomotion of microorganisms. Biophys. J. 65:755–778.
Sasou, M., S. Sugiyama, T. Yoshino, and T. Ohtani. 2003. Molecular flat mica surface silanized with methyltrimethoxysilane for fixing and straightening DNA. Langmuir. 19:9845–9849.[CrossRef]
Takano, Y., K. Yoshida, S. Kudo, M. Nishitoba, and Y. Magariyama. 2003. Analysis of small deformation of helical flagellum of swimming Vibrio alginolyticus. JSME Int. J. Ser. C. 46:1241–1247.[CrossRef]
This article has been cited by other articles:
 |
|
 |
|
  E. Lauga, W. R. DiLuzio, G. M. Whitesides, and H. A. Stone Swimming in Circles: Motion of Bacteria near Solid Boundaries Biophys. J., January 15, 2006; 90(2): 400 - 412. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
T. Goto, K. Nakata, K. Baba, M. Nishimura, and Y. Magariyama A Fluid-Dynamic Interpretation of the Asymmetric Motion of Singly Flagellated Bacteria Swimming Close to a Boundary Biophys. J., December 1, 2005; 89(6): 3771 - 3779. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
can be calculated from the coordinates of points A, B, and C under the assumption that the droplet is spherical. Here, A and B are the contacts with the surface, C is the vertex, D is the foot dropped perpendicularly from point C to line AB, O is the center of the circular arc ACB, r is the radius of arc ACB, a is the length of line AD, and b is the length of line CD. Contact angle 
t (1 ms). A random number (0–1) generated by the computer is compared with the switching possibility (Pf or Pb) in the sixth step, and the mode is changed in the seventh step if the random number is smaller than the switching possibility. Here, the value of the switching possibility is equal to one-thousandth of the value of the corresponding switching frequency shown in 
The relationship of the turning speed between the forward and backward subtrajectories is provided in b, and those between the odd and even subtrajectories are given in d, f, and h. The set of swimming speeds of the odd and even subtrajectories was obtained from a trajectory, such as in 
to which the measured data was fitted. Here, t is the residence time, 
is the average residence time, and 
is the constant. The value of 
