A model of flagellar movement based on cooperative dynamics of dyneintubulin

Transcription

1 Murase, M. and Shimuzu, H. A model of flagellar movement based on cooperative dynamics of dyneintubulin crossbridges. J. Theor. Biol. 119, (1986).

2 Experimental Observation 1 C. J. Brokaw J. Cell Biol. 114, 6 (1991)

3 What mechanism causes bending? (a) (b) (c) (d) Diagrams showing how a local sliding between two filaments can cause bending. When sliding occurs without resistance, it does not cause bending. When sliding occurs locally because of the presence of resistance, it can cause bending. From C. Shingyoji, A. Murakami and K. Takahashi Nature 265, (1977)

4 Experimental Observation 1 The regular basetotip bend propagation of sea urchin sperm flagellum. From R. Rikmenspoel J. Cell Biol. 76, (1978) 50 μm

5 Conflicts within the subsystems

6 Descriptions of the flagellar configuration y s = 0 s = L θ x If the filaments are tied together at the base, θ(s) = σ(s) holds. The flagellar shape is plotted against an (x, y) coordinate. σ s The shear, σ, is defined as a function of length, s, measured along the flagellum.

7 The model equation The momentbalance equation for a flagellum is written by: M S + M E + M V = 0 where M S, M E and M V are the viscous, shear and elastic moments, respectively. See Appendix where S is the shear force, σ is the shear, E B is the bending resistance, C N is the external viscous drag coefficient and γ is the internal viscous drag coefficient.

8 Appendix 1 (S γσ t ) ds σ (S γσ t ) κ

9 Appendix 2 The viscous moment, M V, is given by the external viscous force: The external viscous force, F N, in turn obeys the forcebalance equation: where C N and V N are normal components of the external viscous drag coefficient and the velocity, respectively. The normal component of the velocity, V N, is then specified under the condition of continuation:

10 Bistability and hysteresis switch σ σ Intrasubsystems conflicts

11 The flagellar bend propagation M s σ

12 Brokaw, C. J. J. Exp. Biol. 54, (1970)

13 Total flagellar length :bending points :unbending points Brokaw, C. J. J. Exp. Biol. 54, (1970)

14 Masatoshi Murase The Dynamics of Cellular Motility Wiley p32, 38, 1992 H. Lodish et al. Molecular Cell Biology 1995 Fig.214 on page 928 Muscle Nerve C. F. Stevens (1979) Sci. Am. 241, 48

15 Conflicts between the subsystems generate rich dynamics. Intersubsystems conflicts S(σ) ss + E B σ ssss + C N σ t = 0 0 Spatiotemporal chaos t Flagellar equation can be an interesting extension of the KuramotoSivashinsky equation s 100

16 Experimental Observation 2 S. F. Goldstein et al. J. Exp. Biol. 53, (1970)

17 Experimental Observation 3 15 μm 20 μm 28 μm The motion of a 800 μmlong cricket sperm flagellum. Different sections have different wavelengths and different frequencies. From R. Rikmenspoel Biophys. J. 23, (1978)

18 Experimental Observation 4 The motion of Strigomonas Oncopelti. Two waves propagating in the opposite directions do not annihilate upon collision. 10 μm From M. E. J. Holwill J. Exp. Biol. 42, (1965)

19 Conflicts between the subsystems generate rich dynamics. (S(σ) γσ t ) ss + E B σ ssss + C N σ t = 0 γ << C N S(σ) ss + E B σ ssss + C N σ t = 0 0 t Flagellar equation can be an interesting extension of the KuramotoSivashinsky equation s 100

20 (S(σ) γσ t ) ss + E B σ ssss + C N σ t = 0 γ >> C N Simplified case γ << C N Real case γσ t = E B σ ss + S(σ) S(σ) ss + E B σ ssss + C N σ t = 0 Intersubsystems conflicts

21 Hierarchical structures are responsible for complex biological phenomena. Masatoshi Murase The Dynamics of Cellular Motility Wiley 1992

22 Conflicts between the subsystems Intersubsystems conflicts Further conflicts regulate intrinsic instability. Transsubsystems conflicts S(σ) ss + E B σ ssss + C N σ t = 0 Two waves propagating in the opposite directions do not annihilate on collision.

23 非線形物理学 L Lo Goldstein et al. (1970) Dynamics as emergent phenomena Brokaw (1986) M. Murase John Wiley & Sons (1992) Suprastructural polarity can control spatiotemporal chaos.

24 Herman Haken Synergetics in Psychology in SelfOrganization and Clinikal Psychology Springer Series in Synergetics, Vol. 58 Editors: W. Tschacher, G. Schiepek, and E. J. Brunner p3254 (1992) Fig. 14 on page 45

25 Life as complex chemomechanical systems Complex dynamics resulting from antagonistic interactions of opposed elements can be under the control of suprastructural asymmetry, irrespective of boundary conditions. 非線形生命物理学 M. Murase Wiley (1992) Suprastructural polarity can control spatiotemporal chaos.

26 (a) Nerve impulse Na K (b) Na Na K Na +

27 Magnet Magnet (a) (b) (c) Masatoshi Murase

28 Ionic Alternating Current (AC) Na K Na + + Cell body Semiconducting Direct Current (DC)

29 Tacoma Narrows Bridge Collapse, Wind velocity: ~ 20 m/sec

30 Moth (43.5 Hz) Nerve Muscle Fly (155 Hz) Nerve Muscle Masatoshi Murase The Dynamics of Cellular Motility Wiley 1992

31 Maatoshi Murase The Dynamics of Cellular Motility Wiley (1992), p5

32 The emergence of complex dynamics as a result of intra, interand transsubsystems conflicts. Intersubsystems conflicts Intrasubsystems conflicts Transsubsystems conflicts

33 Hierarchical structures are responsible for complex biological phenomena. Masatoshi Murase The Dynamics of Cellular Motility Wiley p 国立民族博物館編集 2003 年 マンダラ チベット ネパールの仏たち