Problem #3: spindle positioning; chromosomal directional instability; monooriented chromosomal oscillations
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
Pecreaux et al Curr Biol 2006 16 2111
Kozlowski et al Cell 2007 129 499
Interplay between spindle pole movements and microtubule dynamics
Microtubules Contact the Cortex Briefly
before Undergoing Catastrophe
Dynamic Microtubules Associate with Each
Other to Form Persistent Astral Fibers
Microtubule Fibers Contact the Cortex at Fixed
Positions
more MT contacts are made on the side of the
cortex
t that
th t is
i approached
h db
by th
the aster
t th
than on
the receding side.
Kozlowski et al Cell 129 499 2007
N+
y
dN ±
v
⎛
= k1 ⎜1 ±
dt
⎝ V
⎞
⎟ − k2 N ±
⎠
V
d ( N + − N − ) 2k1
v − k2 ( N + − N − )
=
dt
V
v
N−
y
ΔN ±
V ± v ) Δt
(
=
Vδ t
dy
=v
dt
dn 2k1
=
n = N+ − N− ,
v − k2 n
dt
V
f
K
f
K
v = ( N+ − N− ) − y = n − y
ζ
ζ
ζ
ζ
ζ
K
n = v+ y
f
f
ζ dv
⎛ζ
K dy 2k1
K
+
=
v − k2 ⎜ v +
f dt f dt V
f
⎝ f
⎞
y⎟
⎠
2k1 k2ζ ⎞ dy k2 K
+⎜ −
+
y=0
⎟ +
2
f dt
V
f ⎠ dt
f
⎝ f
⎛K
2 fk1 ⎞ dy k2 K
d2y
= − ⎜ + k2 −
y
⎟ −
2
ζ V ⎠ dt ζ
dt
⎝ζ
ζ d2y ⎛ K
ξ
(
1
y ~ e , λ = −ξ ± ξ 2 − 4k
2
λt
k
)
Things
g to think about: dependence
p
of p
period and bifurcation on model p
parameters;
what limits the amplitude of oscillations?
‘Tug of war’ between opposing force generators
The key idea behind the model is that the rate of
detachment of the force generators from MTs
is load dependent
Grill et al Phys Rev Lett 2005 94 108104
Pecreaux et al Curr Biol 2006 16 2111
ζ y = − Ky + ( f + − f − )
y
+
p+ = − koff
p+ + kon (1 − p+ )
−
p− = −koff
p− + kon (1 − p− )
p− , f −
⎛
v⎞
f = f 0 ⎜1 − ⎟
⎝ v0 ⎠
f ± = p± ( f 0 ∓ ϕ y )
±
kon = const ; koff
= k off(0) exp [ f ± / f c ] ≈ k off(0) (1 ∓ α y )
ζ y = − Ky + θ ( p+ − p− ) − σ y ( p+ + p− )
p+ ≈ k − ( a − by ) p+
p = p+ + p−
z = p+ − p−
p− ≈ k − ( a + by ) p−
ζ y = − Ky + θ z − σ yp
p = 2k − ap + byz
z ≈ − az + byp
ζ y = − Ky + θ z − σ yp
p = 2k − ap + byz
z ≈ − az + byp
λ ~ ( s1 − s2 ) ±
s1 , s2 , s3 > 0
y = 0, z = 0, p = 2k / a
⎡ y ⎤ ⎡ y ⎤ ⎡ y0 ⎤
⎢ p ⎥ = ⎢ p ⎥ + ⎢ p ⎥ eλt
⎢ ⎥ ⎢ ⎥ ⎢ 0⎥
⎢⎣ z ⎥⎦ ⎢⎣ z ⎥⎦ ⎢⎣ z0 ⎥⎦
( s1 − s2 )
2
− s32
exp ( γ t ) × sin ( wt )
Things to think about: linearize and do carefully linear perturbation analysis;
dependence of period and bifurcation on model parameters;
what limits the amplitude of oscillations?
Read both papers and think about testing the model
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
plus, rules for MT dynamic instability…
Civelekoglu-Scholey et al., Biophys J. 2006 90:3966-82.
High kinetochore dynein activity is deployed to dampen metaphase oscillations;
Modulation of the MT rescue frequency by the kinetochore-associated kinesin-13
depolymerase promotes metaphase chromosome oscillations
As only a part of the force imbalance is accounted for by the
viscous drag arising from chromosome velocity, a large portion of
this force imbalance is stored as kinetochore resistance, which
depends on both the chromosome position and chromosome velocity
Liu et al. (2007) PNAS 104, 16104-16109
Relative amount of bound motors at
which AP and P forces exactly balance
effect of chromosome friction
sensitivity
of motor unbinding to an external load
Campàs O, Sens P. Phys Rev Lett. 2006 97(12):128102.