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Chromosome Oscillations in Mitosis

Chromosome Oscillations in Mitosis. Otger Camp à s 1,2 and Pierre Sens 1,3. 1 I nstitut Curie, UMR 168, Laboratoire Physico-Chimie «Curie». 2 Dept. Estructura i Constituents de la Matèria, Universitat de Barcelona. 3 ESPCI , UMR 7083, Laboratoire Physico-Chimie Théorique. Anaphase A.

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Chromosome Oscillations in Mitosis

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  1. Chromosome Oscillations in Mitosis Otger Campàs 1,2 and Pierre Sens 1,3 1 Institut Curie, UMR 168, Laboratoire Physico-Chimie «Curie» 2Dept. Estructura i Constituents de la Matèria, Universitat de Barcelona 3 ESPCI, UMR 7083, Laboratoire Physico-Chimie Théorique

  2. Anaphase A Prophase Anaphase B Prometaphase Metaphase Telophase Scholey et al., Nature 422, 746 (2003) Phases of cell division

  3. Chromosome mouvement in mitosis Rieder et al., Science 300, 91 (2003) Schematic representation of "typical" chromosome motions. M - monooriented, characterized by oscillatory motion; C - congression, characterized by movement away from the attached spindle pole by the trailing kinetochore and movement toward the attached spindle pole by the leading kinetochore; B - bioriented and congressed, characterized by oscillatory motion; A - anaphase, characterized by poleward movement of all kinetochores. G refers to a short rapid poleward glide that often occurs during initial monooriented attachment. R. V. Skibbens, Victoria P. Skeen, and E. D. Salmon J. Cell Biol., 122 (1993) 859-875

  4. Away from pole force chromokinesin on microtubule Poleward force Away from pole force (Chromokinesines) Poleward force (kinetochore) DNA DNA centrosome Kid kinetochore kinetochore Kid No Kid Levesque & Compton, J. Cell Biol. 154, 1135 (2001) Balance of forces on the chromosome

  5. chromokinesin on microtubule Force - Velocity Force - Unbinding Maximal velocity (at zero force) unbinding Stall force Force Microscopic length Unbinding rate Svoboda & block Balance of forces on the chromosome Equation for chromosome motion Phenomenological friction Chromokinesins Force (Away-from-the-Pole) Kinetochore Force (poleward)

  6. Chromokinesin Kinetics Equation for the number of bound motors (that can exert a force on the chromosome) Available motors Binding rate (depends on MT concentration) Unbinding rate (depends on motor load) Velocity (depends on load) Spatial information Collective effects r The total force is equally shared by all motors for an isotropic aster

  7. Main control parameters Stall number (number of motors needed to balance the kinetochore force) Friction number (kinetochore friction compared to Effective chromokinesin friction ) Detachment force (influence of applied force on detachment rate) Dynamical equations chromosome motion & motor binding Motor speed = chromosome velocity

  8. fixed point & gives Stability of the fixed point Linear stability analysis Eigenvalues Linear Dynamics Stability of the fixed point Dynamical system

  9. Independent of Dynamical behavior unstable stable

  10. Stable fixed point Unbinding rate Unstable fixed point Chromosome friction High friction each motor feels its stall force (small velocity) and is independent from the other ones Unstable Low friction, the motors share the kinetochore force (no friction force) Very cooperative:the unbinding rate depends strongly on ‘n’ Unstable at low friction Kinetochore force Linear Dynamics Stability of the fixed point

  11. Non-Linear Dynamics Nullclines and Phase flows NullCline number of bound motors number of bound motors Stable fixed point distance to centrosome distance to centrosome The motor kinetics is much faster than the motion of the chromosome

  12. Non-Linear Dynamics Nullclines and Phase flows NullCline number of bound motors number of bound motors Unstable fixed point distance to centrosome distance to centrosome The system reaches a LIMIT CYCLE The n-Nullcline is non-monotonous

  13. (slow) linear motion at constant speed No of bound CK motion at natural Kinetochore speed (slow) linear motion at constant speed Lot of bound CK motion at maximum CK speed Sharp change of direction Collective CK binding or unbinding parameters Experimental oscillations Skibbens et al., J. Cell Biol. 122, 859 (1993) Asymmetry of the oscillations: Numerical Integration and comparizon with experiments Number of bound motors Chromosome position

  14. Experimental predictions Easiest parameter to modify: Total number of motors: N There is a critical number of motors below which oscillations stop

  15. Chromosome oscillations occur because the astral MTs provide a ‘position-dependent’ substrate for CK binding Chromosome instability occurs because of collective motor dynamics - Refinement: Force-sensitive kinetochore ‘Concept: ‘smart kinetochore’ Can sense both position and force Our model so far: ‘very dumb kinetochore’ Constant force and constant firction The kinetochore is treated like one big (infinitely processive) motor Maximum velocity Stall force Main outcome of the model

  16. Conclusions • Oscillations arise from the interplay between the cooperative dynamics of chromokinesins and the morphological properties of the MT aster. • Highly non-linear oscillations, similar to those observed in-vivo, appear in a considerable region of the parameter space. • Sawtooth shaped oscillations come from different kinetics of chromosome motion and motor binding dynamics • Testable prediction - critical number of CK for oscillations

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