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Myosin physics
• Globular head– Actin binding– ATP binding
• Filamentous neck– Flexible– Light chain binding
• Filamentous tail– Dimerization– Oligomerization
Actin Binding
ATP cleftHinge
Neck
S-1 Fragment
Native Myosin
Measuring myosin steps• Compliant traps• Low ATP• Record position
Position data:
Many steps:
BrownianMotion
“Step”
Actin-myosin chemical scheme
• State/compartment model• Actin-myosin bound/unbound• ATP bound/unbound• ATP/ADP+Pi
• Hidden states
Crossbridge Cycle• Actin catalyzes Pi release• ATP catalyzes A release
AM AMT AMDP AMD AM
MT MDPMT MD M
T
T P
P D
D
AMDP AMD AM
MT MDPM
T
PP DD
A ActinM MyosinT ATPD ADPP Pi
Shape ChangesLymn & Taylor 1971
First cycle:
Repeatable:
Quenched-flow chemistry
• Reactions in moving medium– Steady-state relation btw time
and distance– Measure very fast reactions
Reagent 1 Reagent 2
Mix
ATPPi byo Actin-myosin• Myosin alone
o AM + ATPAMADP + Pi• M+ATP MADP + Pi
Quench
After an initial burst, actin accelerates reaction
Initial ATP hydrolysis independent of actin, sustained Rx catalyzed by actin
Actin-myosin dissociated by ATP
• Stopped-flow measurements• Light scattering by A-M filaments
– ie, turbidity
AM + ATP A + M●ATP
Turbidity
Reagent 1 Reagent 2
Mix
Quench
Detector
Lymn & Taylor (1971)
AM AMT
MTMT
T
Phosphate release catalyzed by actin
• Pi release by fluorescence• More actinfaster release
Heeley & al (2002)
AM AMT AMDP AMD
MT MDP MD
T P
P
Add actin
75 s-1
1-2 s-1
Chemical summary
• Myosin is an ATPase with large shape differences– M-MATP– MATP-MADP– MADP-M
• Filamentous actin facilitates Pi release
• ATP facilitates f-actin release
Relate chemistry to force
• AF Huxley 1957 Crossbridge model• Two states: myosin attached or myosin not
attached• Force results from elasticity of individual
crossbridges• Myosin interacts with actin at discrete sites• Attachment and detachment rates are
position dependent
Cartoon: capture the minimal process• Modeling crossbridge attachment
– Imagine Pi release & power stroke instantaneous– A + M AM + Force with rate constant f– AM A + M●ATP with rate constant g
• Think about behavior of single crossbridge• Imagine many crossbridges spanning all configs
Thick filament
Thin filament
Rigor State
x=0
Max Attachment length
x=h
Mathematics
• Two states: myosin attached (n) or myosin not attached (1-n)
• Force results from elasticity of individual crossbridges– Individual: Fb=kx
– All:
)()()1( xngxfndt
dn
)()()( xgxfnxfdt
dn
dxnxkF
Mathematical features
• First order: exponential• Steady state
– dn/dt 0– – n(x) = f/(f+g)
)()()( xgxfnxfdt
dn
Crossbridge attachment rate
• Relate crossbridge physics to x• Energy released by binding• Energy required for deformation
-2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Position (X)
Binding
Deformation
“Energy”
An unbound myosin is positioned just at “x=1” and can drop onto actin without any bending
0 h0.0
f1
Position (X)
f
Prohibit attachment x>h
Crossbridge detachment rate
• Release deformation energy• Release conformation energy
– Discrete change x<0
-2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Position (X)
BindingDeformation“Energy”
0 h0.0
g1
g3
Position (X)
g
A bound myosin is positioned just at “x=0” and any displacement requires bending
Steady state crossbridge attachment
• n(x) = f/(f+g)• x<0 ; x>h n=0
– 0<x<h n=f1/(f1+g1)
• Force=∫k n xdx∙ ∙– k(f1/(f1+g1))(h2/2)
– Crossbridge stiffness– Ratio of f:g 0 h
0.0
g1
g3
Position (X)0 h
0.0
f1
Position (X)
f1/(f1+g1)
Crossbridge behavior during shortening
• Since n=n(x), dn/dt depends on dx/dt
• Crossbridge moving in from x>>h– No chance to attach until x=h– High probability to attach, but limited time– Probability to attach decreases to x=0, but time rises– Rapid detachment x<0
nxgxfxfx
nv )()()(
x
nv
t
x
x
n
dt
dn
Crossbridge distribution
• V=0– Uniform attachment– Mean x = h/2
• V= Vmax/3– No saturation– Mean x
-0.01 0 0.010
0.2
0.4
0.6
0.8
1
x
n
-0.01 0 0.010
0.2
0.4
0.6
0.8
1
xn
x>0force > 0
x>0force < 0These crossbridges resist shortening
Transition to lengthening
• Fully attached crossbridges get over-stretched• Unattached crossbridges dragged in from left
• Fully attached crossbridged get compressed• Unbound crossbridges dragged in from right
Transition to shortening
Damping without viscosity
• Qualitative (and quantitative) results of crossbridge and Hill models similar– Even the math: dL/dt = F/b - k/b L– dn/dt = f - (f+g)n
• Mechanisms behind the models are very different– Crossbridge predicts/validated by biochemistry
Energy prediction
• Energy liberation– Power from P*v– Heat from dn/dt: increased by shortening
-0.01 0 0.010
0.2
0.4
0.6
0.8
1
x
n
Shortening Vopt
Accelerated binding
Accelerated release
Total energy rate
– Hill’s datao Huxley’s model
Issues
• Fast length changes– < 2 ms (500 s-1)– Violates “one process”
assumption
• Lengthening– Too many very long x-bridges
• Residual force enhancement• Double-hyperbolic F-V
100 ms
T0
T1
T2
ModelData