Transcript Document

Mammalian Muscle Properties
Property
Typical Maximum
Strain (%)
Strain rate (%/s)
Stress (Mpa)
Work Density (kJ/m3)
Specific Power (W/Kg)
Efficiency (%)
Modulus (MPa)
Density (kg/m3)
Cycle Life
20
0.1 (static)
8
50
>40
>50
0.35
40
284
40
40
1037
>109
Madden et al. IEEE J. Oceanic Engr. 29: 706, 2004
Skeletal muscle features
• Muscle surpasses artificial actuators only in
the fuel delivery
• Linear actuation
• Adapted for intermittent duty and stiffness
(compliance) control
• Versatile force control: recruitment +
stiffness modulation (w/o feedback)
Madden et al. IEEE J. Oceanic Engr. 29: 706, 2004
Muscle
Sarcomere
s or Force
Myosin
e
Shortening: “concentric”
contraction causes too much
overlap between ACTIN
and MYOSIN
Actin
or Length
Lengthening: “eccentric”
contraction causes too little
overlap between ACTIN
and MYOSIN
[figures: sources unknown]
Tendons & Ligaments
s
Fibres Start to Experience
Permanent Damage
s
sYield Rupture
Full Fibre
Recruitment
e
s
sRupture
Fast Strain Rate
(D /Dt = large)
e
Hysteresis
Loop
Slow Strain Rate
(D /Dt = small)
e
e
Straightening Fibres Out
(“Toe Region”)
“Toe Region” to “Fibre Recruitment” Process with increasing
e
Hill model : Force dependence on
contraction velocity
Motor
Specific Force
Power (dynes)
Ergs/s-g
Velocity
mm/s
Actin Polymerization 109
mtubule
polymerization
108
10-7
Myosin II
Kinesin
Spasmoneme
108
107
109
10-6
10-7
10-3
4
1
80,000
Car
Striated muscle
Bacterial Flagella
Limulus aroscome
Eukaryote Flagella
Mitotic spindle
106
106
106
104
102
10-6
100 Hz
10
1
.02
10-7
10-5
McKibben muscle
PV   Fl
Wlateral. P  Waxial. P  Wequilibrium. force  0
(2rlP )(r )  r 2 l  Fl  0
r
ro
 sin 
sin  o
;; l
lo
 cos
cos o
 1  cos2  ( l ) 2

o
lo


r  ro 
sin  o 


McK muscles
• Steel braid wrapped
around a rubber tube.
• Crimped at ends
20N/g
Testing
Antagonistic pairs for smooth
torque


M x_ B x Kx  FCE  m g
Friction in the mesh
• Filament on filament friction (no sliding
relative to the tube)
Fstatic.dry . friction.solid  m s S contact P
Fstatic.dry . friction.mesh  m s S contact P

mT  m k  ( m sk  m k )e
 x

xs

F (e , P )  ro P a (1  e )  b
2
2
1
a  3 t an  o ; ; b 
2
sin  o
2
Fmax
e max


Fdyn  F  mT Scontact P(sgn x)
Properties of McK muscles
•
•
•
•
•
1. Fstatic ~ CSA (ro2)
2. Fstatic ~ P
3. Fstatic is independent of initial length
4. Fstatic max ~ 1/o
5. Fstatic ~ 1/e
Molecular Springs & Ratchets
• Spasmoneme of the Vorticella
• Acrosome
• Actin polymerization
Mahdevan, L : Science, 288: 95, 2000.
Spasmoneme of the Vorticella
Actin Spring
• Acrosome needs to
penetrate egg jelly.
• Spring is super-coiledheld twisted by scruin.
• Ca++ Ds scruin
Supramolecular ratchets
• Pawl and ratchet
analogy of actin
polymerization
• How controlled? In
quiescence, profilin is
the shut-off switch.
Stimulus such as pH D
in presence of actin
monomers can start.
• Listeria rides this bus
Overall energy balance
dU  TdS  dW
i
dU  TdS  pdV  fdl   mi dni  .....
U
S
f 
T
l
l
Conducting polymers
• Large molecular deformations (strains)
induced by current
• Reversible Change in oxidation state
ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL
< previous next >
How does muscle fatigue?
• Test of a ‘skinned’ muscle fiber from EDL
of rat.
• Can activate by direct stimulation of any
step in the cascade.
AP in
T system
VS
activation
Pederson, TH: Science 305: 1144, 2004
SR Ca++
release
Force
F1 ATPase: A rotary motor
• Can either make or break ATP, hence is
reversible
• Torque of 40 pN-nM; work in 1/3 rev. is 80
pn-nM (40 * 2/3) equivalent to free energy
from ATP hydrolysis
• Can see rotation by attaching an actin
filament
Rotary Cellular Motors
• The rotary mechanism of ATP synthase , Stock D, Gibbons C,
Arechaga I, Leslie AGW, Walker JE
CURRENT OPINION IN STRUCTURAL BIOLOGY ,10 (6): 672679 DEC 2000
•
• 2. ATP synthase - A marvellous rotary engine of the cell, Yoshida
M, Muneyuki E, Hisabori T
NATURE REVIEWS MOLECULAR CELL BIOLOGY 2 (9):
669-677 SEP 2001
•
• 3. The gamma subunit in chloroplast F-1-ATPase can rotate in a
unidirectional and counter-clockwise manner Hisabori T, Kondoh
A, Yoshida M FEBS LETTERS 463 (1-2): 35-38 DEC 10 1999
•
• 4. Constructing nanomechanical devices powered by biomolecular
motors.C. Montemagno, G Bachand, Nanotechnology 10: 225-2312,
1999.
ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL
< previous next >
Nature Reviews Molecular Cell Biology 2; 669-677 (2001)
ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL
< previous next >
ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL
< previous next >
Comparative motors
For rotary motion:
2
d
I
 M
d t2
 w L
2
M 
4
1  2
I
mL
3
Current is coulombs per second. How many charges in a coulomb?
For this y ou need Faraday 's constant 96,500 Coulombs per mole of
charged m olecules, in this case potassium ions.
0.24  12  18 moles
Q K Kflux
10 2.510
96 500
sec
I f work , W , is done on the partic le during dif f us ion, t hen the t ime is
increased as:
W
t w t d e
kT
So s ay W = 10 KT,
then t w = 20 ms
So how f ast c an t he mot or go? Ass uming a bac k -and-f ort h motion
it would t ake at leas t 40 ms , s o the max f requenc y = 250 H z or
10 nM X 250 per sec ond = 2. 5 mic rons per second. (linear m ot ion).
• When L>> x the chain has many bends and
is always crumpled in solution – the FJC
model applies, with each link approximated
as 2 x and perfectly flexible joints.
• To count all possible curved states in a
smooth-bending rod in solution- it’s a
WLC- supercoiling is possible.
F1 ATPase: A rotary motor
• Can either make or break ATP, hence is
reversible
• Torque of 40 pN-nM; work in 1/3 rev. is 80
pn-nM (40 * 2/3) equivalent to free energy
from ATP hydrolysis
• Can see rotation by attaching an actin
filament
(www.sciencemag.org/feature/data/1049155.shl).