cytoskeleton-based positioning during development, cell ...€¦ · cytoskeleton-based positioning...

Cytoskeleton-based positioning during

development, cell division

C elegans fertilization - pronuclei

migration and reorientation

Ed Munro and Chris Schoff (Center for

Cell Dynamics)

C elegans fertilization - chromosome alignment

and segregation

George von Dassow (Center for Cell Dynamics)

Wednesday, December 2, 2009

What forces are involved?



• Cortical dynein pulls on aster.




• MTs push against cortex by polymerizing.




• MTs push against cortex by polymerizing.

• Motors push/pull against organelles.


Forces, steady states and their stability



• Cortical pulling - destabilizing.




• Cortical pushing - stabilizing.





• Cytoplasmic pulling - stabilizing.





• Cytoplasmic pulling - stabilizing.

• Cytoplasmic pushing - destabilizing.


Two-D simulation - cytoplasmic pulling


One-D model of motor-based centering

∂g

∂t= −vg

∂g

∂l− cg + rs

∂s

∂t= vs

∂s

∂l+ cg − rs

Microtubule (MT) dynamics - stochastic transitions between

growing and shrinking states

(density of growing MTs)

(density of shrinking MTs)


One-D model of motor-based centering

∂g

∂t= −vg

∂g

∂l− cg + rs

∂s

∂t= vs

∂s

∂l+ cg − rs

Microtubule (MT) dynamics - stochastic transitions between

growing and shrinking states

(density of growing MTs)

(density of shrinking MTs)

g(l) + s(l) = Ae−λl

�where λ =

vsc− vgr

vgvs

�

(density of MT of length )l


One-D model - calculating forces from MT densities

Tips(x) = Ae−λ|x−xc|

0 L




Fpull(xc) = B(−e−λxc + e−λ(L−xc))

If motors pull only at the cell periphery,

0 L






0 L

xc = L/2and the steady state position is at . 0 LL/2






0 L


For stability, check derivative of :Fpull

0 LL/2






0 L



0 LL/2

F �pull (L/2) = Bλ(e−λL/2 + e−λL/2) > 0






0 L



0 LL/2

F �pull (L/2) = Bλ(e−λL/2 + e−λL/2) > 0

Center is unstable!


Fpull(xc) = −C

� xc

0Tips(x) dx + C

� L

xc

Tips(x) dx


0 LIf motors pull all MT tips,


Fpull(xc) = −C

� xc

0Tips(x) dx + C

� L

xc

Tips(x) dx


=C

λ(e−λxc − e−λ(L−xc))



Fpull(xc) = −C

� xc

0Tips(x) dx + C

� L

xc

Tips(x) dx

F �pull (L/2) = C(−e−λL/2 − e−λL/2) < 0


=C




Fpull(xc) = −C

� xc

0Tips(x) dx + C

� L

xc

Tips(x) dx

F �pull (L/2) = C(−e−λL/2 − e−λL/2) < 0


=C



Center is stable!


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