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Cytoplasmic streaming in drosophila oocytes

During development of drosophila oocytes (fruit fly eggs), there is a phase in which the egg undergoes fast cytoplasmic streaming. This has been extensively studied, see the article by Serbus et al. Links to an external site. and movies Links to an external site. of this streaming have been made. You can see the motion of yolk particles inside the egg and the undulating motion of a lot of microtubules. Since there is no microscopic osterizer or even any flagella in this egg, it is not clear what causes this fast streaming and the wave-like motion of the microtubules. The above movie has been sped up and the period of these microtubule waves is about 5 minutes.

Through a clever set of experiments Serbus et al were able to determine that that kinesin is necessary to get this fast cytoplasmic streaming. Clearly microtubules are involved as well.Using the experimental data, recently a simple of model of this phenomenon was proposed Links to an external site., analyzed Links to an external site. and tested (Copyright 2016 Elsevier B.V. or its licensors or contributors).

The points of the model are as follows

  • 1. Kinesin attaches cargo that act as impellers) and these walks along microtubules from the outside wall (cortex). The microtubules are in contact with the cortex at their minus ends.
  • 2. Because hydrodynamic forces are long range, the impellers affect the velocity of the fluid far from the microtubules. A relatively small fraction of impellers causes a large streaming velocity.
  • 3. Because of Newton's third law, the upward motion of kinesin causes a downward force on a microtubule. Assuming quite a high density of microtubules, this can be modeled by saying there is a downwards force tangent to the local direction of the microtubule.
  • 4. A downwards force along the microtubule will cause a buckling-like instability to form causing the microtubule to wave.

The code hw8/egg/egg.py models this instability and simulates a single microtubule with kinesin walking up it. There are some parameters that you can vary to see how this changes the motion:

  • The number of beads, n. It's interesting but slower making it longer.
  • Kinesin constant fk. This is a measure of how much force the kinesin is applying tangent to the direction of the microtubule. (The value in this code, is equal to the same quantity in the [paper Links to an external site. but is smaller by a factor of 2.) What does negative fk represent physically? What happens if you run the simulation in that situation? Can you understand your results?
  • The elastic constant of the microtubule, StiffnessConst.
  • The force due to an external velocity field, f_const.

The last quantity is a "mean field" way of modeling the effects of all the other microtubules with kinesin driven impellers. These are all producing a streaming velocity field that act on each other. If you turn it off, that would be equivalent to a single microtubule with kinesin in isolation.
  • Dimensionally, the elastic constant C has dimensions [Force][Length2] where as the constant fk associated with the force due to kinesin has dimensions [Force]/[Length]. By using a combination of C and fk, come up with something with the dimensions of length. This should tell you the way the radius of curvature scales with elastic constant. Change graphics = True to graphics = False. The code will now output the radius of curvature in the middle of the chain as it progresses. Set the external force field f_const[1] to zero and run the code for StiffnessConst = 10. Change the value of the StiffnessConst from 10 to 20 and see if the result you get agrees with your dimensional analysis.
  • Try adding in a wall force (see comment in function dx_dt), and set f_const[1] 0, 0.3 and 0.9. Turn the graphics back on, and see what happens. The wall force prevents the microtubule from penetrating a wall located at the plane x = -1. Can you qualitatively explain these results?

Biology

  • One experiment that Serbus et al did was to inhibit the motor protein dynein before the fast streaming stage. What did this do to cytoplasmic streaming?
  • What happened when they loosened the strength of the actin cytoskeleton before the fast streaming stage?
  • How did Serbus et al determine that Kinesin was necessary for fast streaming?
  • Why happens to development of the oocyte when cytoplasmic streaming is suppressed?

 

Code update: When the graphics is turned off, there is a bug in the python 3 version of the code that is corrected  here Links to an external site..