Shear Stress Transmission Model for the Flagellar Rotary Motor
Abstract
:1. Introduction
2. Objects to be discussed
2.1. Structure of the flagellar rotary motor
2.2. Major experimental results to be explained by the model
- (1)
- One revolution of the flagellar rotation consists of a constant number of steps at low speed [1].
- (2)
- The flagellar rotation velocity ω is proportional to the transmembrane potential difference at low speed [1].
- (3a)
- (3b)
- (3c)
- (3d)
- (4)
- There are experimental observations that the flagellar rotate in the same direction when the direction of the proton passage is reversed (for references, cf. Section 5.2).
- (5)
- The cell produces constant torque to rotate a flagellum even when the cell is rotated relative to the flagellum by external forces (for references, cf. Section 5.3).
- (6)
- The cell has a switch that reverses the sense of the flagelllar rotation with the same absolute value of torque for chemotaxis (for references, cf. Section 5.4).
3. Basic ideas of the new model
3.1. Mot* is assumed to be a shear force generator
3.2. The RS layer is viscoelastic
3.3. Expression for the shear force transmitted into the RS layer
4. Theoretical predictions on flagellar rotation
4.1. Flagellar rotation velocity and torque
4.1.a. Step size of Rotor rotation
4.1.b. Rotation velocity as a function of the transmembrane potential difference
4.1.c. Energy balance and critical rotation velocity
4.1.d. Torque as a function of rotation velocity
4.1.e. On the effect of temperature
- (3b) ωη does not depend upon cRS according to (32), (34).
- (3c) ωcr is inversely proportional to cRS according to (34).
- (3d) ω* and ω*η are proportional to 1/cRS1/2 and hence decreases with increasing cRS according to (32), (44).
4.1.f. On the energy efficiency
4.2. Effect of reversal of proton passage direction
4.3. Effect of externally applied torque on rotor
4.4. Switch mechanism for changing rotation direction
5. Comparison of the theoretical predictions with experimental observations
5.1. The flagellar rotation velocity and torque
5.1.a. Number of rotation steps per one revolution
5.1.b. Rotation velocity as a function of the transmembrane potential difference
5.1.c. Torque as a function of rotation velocity
5.1.d. On the effect of temperature
- (3b) When ω <ωcr, the torque varies little with temperature because ωη does not depend upon cRS, in agreement with the observation (3b) cited in Section 2.2.
- (3c) The critical velocity ωcr decreases at lower temperatures because ωcr is inversely proportional to cRS, in agreement with the experimental results cited in Figure 8 (a) and (b).
- (3d) When ω <ωcr, the torque declines more steeply at lower temperature because ω*η is proportional to 1/cRS1/2, in agreement with the experimental results cited in Figures 8 (a) and (b).
5.2. Effect of reversal of proton passage direction
5.3. Effect of externally applied torque on rotor
5.4. Switch mechanism for changing rotation direction
6. Discussion
6.1. Summary and discussion
- (1)
- When the flagellar rotation velocity ω is smaller than the critical velocity ωcr , one revolution of the flagellar rotation consists of a constant number of rotation steps as proved at the end of Section 5.1a.
- (2)
- (3a)
- As indicated by the lines and curves in Figure 8, the torque exerted on the flagella by the cell is independent of the flagellar rotation velocity ω and remains constant when ω < ωcr, and then sharply decreases above ωcr, in agreement with the experimental data.
- (3b)
- When ω< ωcr, the torque is expected to vary little with temperature, as discussed in Section 5.1c, in agreement with experimental observations.
- (3c)
- The critical velocity ωcr shifts to lower speeds at lower temperatures as discussed in Section 5.1c (cf. Figure 8(a) and (b)).
- (3d)
- When ω>ωcr, the torque declines more steeply at lower temperatures as discussed in Section 5.1c (cf. Figure 8(a) and (b)).
- (4)
- The model predicts that the flagella rotate in the same direction when direction of the proton passage is reversed, as discussed in Section 4.2 and 5.2 (cf. Figure 9).
- (5)
- The cell produces constant torque for the flagellum even when the cell is rotated relative to the flagellum by external forces, as discussed in Sects. 4.3 and 5.3 (cf. Figure 10).
- (6)
- It is possible that the cell reverses the sense of the flagelllar rotation with the same absolute value of velocity if the direction of P0y is changeable by chemical modification of Mot*, as discussed in Sects. 4. 4 and 5. 4.
6.2. Comparison of the flagellar motor with the FOF1-ATPase motor
Appendix
Calculation of the electric field produced by the proton pair in dielectric membrane
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Mitsui, T.; Ohshima, H. Shear Stress Transmission Model for the Flagellar Rotary Motor. Int. J. Mol. Sci. 2008, 9, 1595-1620. https://doi.org/10.3390/ijms9091595
Mitsui T, Ohshima H. Shear Stress Transmission Model for the Flagellar Rotary Motor. International Journal of Molecular Sciences. 2008; 9(9):1595-1620. https://doi.org/10.3390/ijms9091595
Chicago/Turabian StyleMitsui, Toshio, and Hiroyuki Ohshima. 2008. "Shear Stress Transmission Model for the Flagellar Rotary Motor" International Journal of Molecular Sciences 9, no. 9: 1595-1620. https://doi.org/10.3390/ijms9091595