problem #3: spindle positioning
TRANSCRIPT
Problem #3: spindle positioning
Oegema and Hyman Cell division 2006 WormBook
How many motors pull spindle to the cortex?
Grill et al 2003 Science 301 518 Grill and Hyman Dev Cell 8 461 2005
Spindle oscillates as it moves in the posterior direction
Kozlowski et al Cell 2007 129 499Pecreaux et al Curr Biol 2006 16 2111
‘Tug of war’ between opposing force generatorsThe key idea behind the model is that the rate ofdetachment of the force generators from MTs is load dependent
Grill et al Phys Rev Lett 2005 94 108104Pecreaux et al Curr Biol 2006 16 2111
y ( )y Ky f fζ = − + −& ( )( )( )1
1off on
y Ky f f
p k p k p
p k p k p
ζ + −
+ + +
= +
= − + −
+
&
&
,p f− −
( )1off onp k p k p− − −= − + −
0 1 vf fv
⎛ ⎞= −⎜ ⎟
⎝ ⎠0f f yϕ± = &m [ ] ( )(0) (0); exp / 1
off offon off ck const k k f f k yα= = ≈ − &0v⎝ ⎠
( ) ( )y Ky p p y p pζ α αβ+ − + −= − + − − +& & 0, /y p p k a+ −= = =
( )( )
p k a by p
p k a by p+ +
− −
≈ − −
≈ − −
& &
& &
0
1t
y y yp p p eλ+ +
⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥= +⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥
( )p y p2p p p− −⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦
( ) ( )2 21 2 1 2 3~ s s s s sλ α α− ± − −( ) ( )1 2 1 2 3
1 2 3, , 0
s s s s s
s s s
λ α α±
> ( ) ( )exp sint wtγ ×
Interplay between spindle pole movements and microtubule dynamics
Microtubules Contact the Cortex Brieflybefore Undergoing Catastrophe
Dynamic Microtubules Associate with EachOther to Form Persistent Astral Fibers
Microtubule Fibers Contact the Cortex at FixedPositionsPositions
more MT contacts are made on the side of the cortex that is approached by the aster than on the receding side.
Kozlowski et al Cell 129 499 2007
vf vf
y1
1.5
2
( )f y&0.4
0.6y
( )y Ky f y= − +& & -0.5
0
0.5
1
-0.2
0
0.2
y&
( )y Ky f y+
-20 -15 -10 -5 0 5 10 15 20-2
-1.5
-1
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-0.8
-0.6
-0.4
( )1 f y yK
−⎡ ⎤⎣ ⎦& &
Another example of oscillations: Directional instability phenomenon
Joglekar and Hunt Biophys J 2002 83 42
Gardner and Odde Cur Opin Cell Biol 2006 18:639
Problem #4: spindle length
vf vf
Two Opposing Motorsv v
f
Two Opposing Motors
Can two opposing motors compete?+-
KF NFv
k Klp n Ncd
1n kn
vnf k vV
ζ⎛ ⎞− =⎜ ⎟
⎝ ⎠
( ),
1
n
n
n
V x nv xx x n k
Vε
ζ
⎝ ⎠
= =+ − +
4.5k nn
n
Vf
ζε = ≈
1kvkf n vζ
⎛ ⎞− =⎜ ⎟
( )( )
1
1,
1
k nk
k
kf n vV
V x nv xx x n k
ζ
ε
⎜ ⎟⎝ ⎠
−= =
+ +( )1
0.25
k
n kk
k
x x n kVf
εζε
− + +
= ≈
~ ~ ~ 0.05 pN×sec/nmk n ktζ ζ t ~ 0.01/sec, k ~ 1 pN/nm
23 4 2
dS k k Sdt
ς = −2S
3S 35 6 3
dS k k Sdt
ς = −dt
( )4dS k L S k Sς = ( )7 4 8 4k L S k Sdt
ς = − −
Nédélec J Cell Biol 2002 158 1005
S1SL
( )11 1 2 1
dS k L S k Sdt
ς = − −⎡ ⎤⎣ ⎦
Important here is that due to transport properties of the motors there is a selectionof the motors of the same polarity at parallel overlapping MT pairs.p y p pp g p
Nédélec J Cell Biol 2002 158 1005
Nédélec J Cell Biol 2002 158 1005
Ambrose et al Mol Biol Cell 2005 16 1584
Motors4 5
What determinesstable length ofbi-polar spindle?
Force balance models4,5
MT dynamics1,6
Concentration gradient of morphogens models
p p
,“spindle matrix”
3
Extrinsic mechanisms
cortex forces2
depletion of molecules
Intrinsic mechanisms
depletion of molecules1
Balance of dynein (outward) and ncd (inward) forces explains pole Balance of dynein (outward) and ncd (inward) forces explains pole separation and transient steady state in interphase separation and transient steady state in interphase -- prophaseprophase
S
Geometry questions:
dynF
Geometry questions: where are dynein, ncd, actin? Are MT asters asymmetric
ncdF
yand how are they madeasymmetric?Mechanical questions:
Sharp et al., Mol. Biol. Cell. 2000 11:241
qhow strong are the forces?
( )2dyn ncd
dS F k Sdt ς
= −pCytrynbaum et al., Biophys. J. 2003 84:757
( )ydt ς( )/
0 1 t TS S e−≈ −
?