Topic 6: Molecular Machines I Linear motors

1
Topic 6 Molecular Machines I Linear motors
Molecular Machines
Example muscles, myosin, actin
MECHANISMS AND MODELS
Single-molecule experiments
Monte-Carlo and Reaction-diffusion equations
2
Reading for Topic 6

• Howard Chapters (5), 14,16
• (Nelson Chapter 10)
• (Alberts Chapter 16)
• Journal Articles

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Force Conjugate flux Chemical Chemical
flux potential Force Displacement
4
Dynein microtubule kinesin
Actin myosin
ATP synthase
Bacterial flagellar motor
5
The mechanism of muscle contraction
6
food eg) glucose
NADH
Actin, Myosin
reproduction
ATP
photons
pmf
growth
transport
movement
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Acto-myosin in vitro motility assay
myosin head
Actin filament
10mm
8
Movie Make dumbell
Movie dumbell experiment
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Single-molecule experiments on Myosin II
Individual myosin heads binding and powerstroke
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Single-molecule experiments on Myosin Revisited
Events detected by eye
Myosin animation (again)
Events detected by reduced Brownian Motion
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The myosin family
12
36 nm
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Actin-myosin crossbridge cycle
ATP binding makes myosin release actin
14
1
4
5
6
2
3
1
4
5
6
1
2
3
15
Phosphate release with powerstroke free energy
landscape
2-D free-energy landscapes
16
Here the whole lever has to move before the
chemical transition (shown as hooks) can
happen. This will be slow (big thing moving, low
D).
Here only small-scale motions are needed, This
will be faster.
17
Crossbridge model for muscle acto-myosin
1
4
5
6
AMDP (4)
2
2
3
AMD (5)
AM (6)
AMT (1)
MT (2)
0
MDP (3)
-10 kT
-20 kT
MT (2)

• Each cycle
• hydrolyses one molecule of ATP,
• releasing 25 kT of free-energy,
• produces one 5 nm powerstroke
• (about half of the free energy could
• be converted to work in the
• powerstroke, the rest is wasted as heat.)

-5 nm 0
binding
un-binding
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Minimal model
AMD (5)
0
MDP (3)
-10 kT
-20 kT
MT (2)
-5 nm 0
binding
un-binding
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If we assume the muscle contracts at a constant
speed, we can use the minimal model to predict
the relationship between force and speed
Dx
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Reaction-Diffusion Equation
Diffusion with an external force (As in topic
1, slide 17, but P(x), the probability of
finding a motor at position x, replaces the
concentration C(x) )
Probability flux

Continuity equation
Fokker-Planck Equation
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Monte-carlo, chemical transitions
At time t, motor is in state i at position
x. State i has chemical transitions to states j (
j )
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Monte-carlo, movement
At time t, motor is in state i at position x,
moving with instantaneous velocity v.