Computed Simulations of Ciliary and Flagellar Motility Using the Geometric Clutch Model can Replicate a Wide Variety of Experimental Conditions

  • Charles B. Lindemann
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 124)


The Geometric Clutch hypothesis proposes that the strain that develops between the outer doublets of the flagellar/ciliary axoneme acts as the principal control to regulate the function of the dynein motor proteins. In this hypothetical scheme, the forces that develop transverse to the axis of the doublets (t-forces) act as a clutch to engage or disengage the dynein arms from their binding sites on adjacent doublets. These forces can be easily computed from the longitudinal tension, or compression, on a doublet and the local curvature. A computer model has been developed based on the Geometric Clutch principle. When the model is scaled as closely as possible to the physical dimensions and mechanical properties that have been measured in real cilia and flagella, the computed simulations successfully replicate the basic patterns of motility of the biological systems. Observed phenomena, such as the effective and recovery stroke of cilia, can be readily reproduced; and mechanical-sensitivity, a known property of cilia and flagella, is intrinsic to the computer simulation. Recently, the model has been further tested by comparing computed behavior and real behavior of bull sperm under identical conditions of mechanical restraint and dissection. The results of the real and computed experiments are in good agreement. The simulation accurately predicts the observed changes in the beating pattern, and the conditions that cause the beat to arrest.


Compute Simulation Global Component Bull Sperm Beat Cycle Principal Piece 
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  1. [1]
    Afzelius, B (1959). Electron Microscopy of the Sperm Tail. Results Obtained with a New Fixative. J. Biophys. Biochem. Cytol. 5: 269–278.CrossRefGoogle Scholar
  2. [2]
    Afzelius, B (1961). The Fine Structure of the Cilia from Ctenophore Swimming Plates. J. Biophys. Biochem. Cytol. 9: 383–394.CrossRefGoogle Scholar
  3. [3]
    Brokaw, C.J. (1961). Movement and Nucleoside Polyphosphatase Activity of Isolated Flagella from Polytoma uvella. Exp.Cell Res., 22: 151–162.CrossRefGoogle Scholar
  4. [4]
    Gibbons, I.R. (1961). The Relationship Between the Fine Structure and Direction of Beat in Gill Cilia of a Lamellibranch Mollusc. J. Biophys. Biochem. Cytol. 11: 179–205.CrossRefGoogle Scholar
  5. [5]
    Gibbons, I.R. and Grimstone, A.V. (1960). On Flagellar Structure in Certain Flagellates. J. Biophys. Biochem. Cytol. 7: 697–716.CrossRefGoogle Scholar
  6. [6]
    Gibbons, I.R. and Rowe, A.J. (1965). Dynein: A Protein with Adenosine Triphosphatase Activity from Cilia. Science, 149: 424–426.CrossRefGoogle Scholar
  7. [7]
    Gibbons, I.R. and Gibbons, B.H. (1972). Flagellar Movement and Adenosine Triphosphatase Activity in Sea Urchin Sperm Extracted with Triton X-100. J. Cell Biol., 54: 75–97.CrossRefGoogle Scholar
  8. [8]
    Gibbons, I.R. and Gibbons, B.H. (1973). The Effect of Partial Extraction of Dynein Arms on the Movement of Reactivated Sea-urchin Sperm. J. Cell Sci., 13: 337–357.Google Scholar
  9. [9]
    Holcomb-Wygle, D.L., Schmitz, K.A., and Lindemann, C.B. (1999). Flagellar Arrest Behavior Predicted by the Geometric Clutch Model is Confirmed Experimentally by Micromanipulation Experiments on Reactivated Bull Sperm. Cell Motil. Cytoskeleton, 44: 177–189.CrossRefGoogle Scholar
  10. [10]
    Kamiya, R. and Okagaki, T. (1986). Cyclical Bending of Two Outer-doublet Microtubules in Frayed Axonemes of Chlamydomonas. Cell Motil. Cytoskeleton, 6: 580–585.CrossRefGoogle Scholar
  11. [11]
    Kanous, K.S., Casey, C., and Lindemann, C.B. (1993). Inhibition of Microtubule Sliding by Ni+2 and Cd+2 Evidence for a Differential Response of Certain Microtubule Pairs Within the Bovine Sperm Axoneme. Cell Motil. Cytoskeleton, 26: 66–76.CrossRefGoogle Scholar
  12. [12]
    Lindemann, C.B. (1994a). A Geometric Clutch Hypothesis to Explain Oscillations of the Axoneme of Cilia and Flagella. J. Theor. Biol., 168: 175–189.CrossRefGoogle Scholar
  13. [13]
    Lindemann, C. B. (1994b). A Model of Flagellar and Ciliary Functioning Which Uses the Forces Transverse to the Axoneme as the Regulator of Dynein Activation. Cell Motil. Cytoskeleton, 29: 141–154.CrossRefGoogle Scholar
  14. [14]
    Lindemann, C.B. (1996). The Functional Significance of the Outer Dense Fibers of Mammalian Sperm Examined by Computer Simulations with the Geometric Clutch model. Cell Motil. Cytoskeleton, 34: 258–270.CrossRefGoogle Scholar
  15. [15]
    Lindemann, C.B. and Kanous, K.S. (1995). “Geometric Clutch” hypothesis of Axonemal Function: Key Issues and Testable Predictions. Cell Motil. Cytoskeleton, 31: 1–8.CrossRefGoogle Scholar
  16. [16]
    Lindemann, C.B. and Kanous, K.S. (1997). A Model for Flagellar Motility. Int. Rev. of Cytol., 173: 1–72.CrossRefGoogle Scholar
  17. [17]
    Lindemann, C.B., Orlando, A. and Kanous, K.S. (1992). The Flagellar Beat of Rat Sperm is Organized by the Interaction of Two Functionally Distinct Populations of Dynein Bridges with a Stable Central Axonemal Partition. J. Cell Sci., 102: 249–260.Google Scholar
  18. [18]
    Lindemann, C.B. and Rikmenspoel, R. (1972a). Sperm Flagella: Autonomous Oscillations of the Contractile System. Science, 175: 337–338.CrossRefGoogle Scholar
  19. [19]
    Lindemann, C.B. and Rikmenspoel, R. (1972b). Sperm Flagellar Motion Maintained by ADP. Exp. Cell Res., 73: 255–259.CrossRefGoogle Scholar
  20. [20]
    Sale, W.S. and Satir, P. (1977). Direction of Active Sliding of Microtubules in Tetrahymena Cilia. Proc. Natl. Acad. Sci. USA, 74: 2045–2049.CrossRefGoogle Scholar
  21. [21]
    Satir, P. (1965). Studies in Cilia. II. Examination of the Distal Region of the Ciliary Shaft and the Role of the Filaments in Motility. J. Cell Biol., 26: 805–834.CrossRefGoogle Scholar
  22. [22]
    Satir, P. (1968). Studies on Cilia. III. Further Studies on the Cilium Tip and a “Sliding Filament” Model of Ciliary Motility. J. Cell Biol., 39: 77–94.CrossRefGoogle Scholar
  23. [23]
    Summers, K.E. and Gibbons, I.R. (1971). Adenosine Triphosphate-induced Sliding of tubules in Trypsin-treated Flagella of Sea Urchin Sperm. Proc. Natl. Acad. Sci. USA, 68: 3092–3096.CrossRefGoogle Scholar
  24. [24]
    Tamm, S.L. and Tamm, S. (1984). Alternate Patterns of Doublet Microtubule Sliding in ATP-disintegrated Macrocilia of the Ctenophore Beroe. J. Cell Biol., 99: 1364–1371.CrossRefGoogle Scholar
  25. [25]
    Warner, F.D. and Satir, P. (1974). The Structural Basis of Ciliary Bend Formation. Radial Spoke Position Changes Accompanying Microtubule Sliding. J. Cell Biol., 63: 35–63.CrossRefGoogle Scholar
  26. [26]
    Yagi, T. and Kamiya, R. (1995). Novel Mode of Hyper-oscillation in the Paralyzed Axoneme of a Chlamydomonas Mutant Lacking the Central-pair Microtubules. Cell Motil. Cytoskeleton, 31: 207–214.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Charles B. Lindemann
    • 1
  1. 1.Department of Biological SciencesOakland UniversityRochester

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