mammalian muscle properties
DESCRIPTION
Mammalian Muscle Properties. 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 - PowerPoint PPT PresentationTRANSCRIPT
Mammalian Muscle PropertiesProperty Typical Maximum
Strain (%) Strain rate (%/s) Stress (Mpa)
20 0.1 (static)
>40 >50 0.35
Work Density (kJ/m3) Specific Power (W/Kg) Efficiency (%)
8 50
40 284 40
Modulus (MPa) Density (kg/m3) Cycle Life
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
or Force
or Length
Shortening: “concentric”contraction causes too much
overlap between ACTINand MYOSIN
Lengthening: “eccentric”contraction causes too littleoverlap between ACTINand MYOSIN
Sarcomere
ActinMyosin
[figures: sources unknown]
Tendons & Ligaments
Fast Strain Rate
Slow Strain Rate
Rupture
(/t = small)
(/t = large)
Rupture
Full FibreRecruitment
Straightening Fibres Out(“Toe Region”)
Fibres Start to ExperiencePermanent Damage
Yield
“Toe Region” to “Fibre Recruitment” Process with increasing
HysteresisLoop
Hill model : Force dependence on contraction velocity
Motor Specific Power
Ergs/s-g
Force
(dynes)
Velocity
m/s
Actin Polymerization
tubule polymerization
109
108
10-7
10-7
1
.02
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
10-5
100 Hz
10
2
McKibben muscle
o
oo
o
oooo
forcemequilibriuPaxialPlateral
ll
rr
ll
rr
lFlrrrlP
WWW
lFVP
sin
)(cos1
coscos;;sin
sin
0))(2(
0
22
2
...
McK muscles
• Steel braid wrapped around a rubber tube.
• Crimped at ends
20N/g
Testing
Antagonistic pairs for smooth torque
mgFKxxBxM CE
_
Friction in the mesh
• Filament on filament friction (no sliding relative to the tube)
sx
x
kskkT
contactsmeshfrictiondrystatic
contactssolidfrictiondrystatic
e
PSF
PSF
)(
...
...
max
max
22
22
sin
1;;tan3
)1(),(
F
ba
baPrPF
oo
o
)(sgn xPSFF contactTdyn
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/
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-coiled- held twisted by scruin.
• Ca++ s scruin
Supramolecular ratchets
• Pawl and ratchet analogy of actin polymerization
• How controlled? In quiescence, profilin is the shut-off switch. Stimulus such as pH n presence of actin monomers can start.
• Listeriaridesthis bus
Overall energy balance
l
ST
l
Uf
dnfdlpdVTdSdU
dWTdSdUi
ii
.....
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.
Pederson, TH: Science 305: 1144, 2004
AP in T system
VS activation
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 JECURRENT OPINION IN STRUCTURAL BIOLOGY ,10 (6): 672-679 DEC 2000
• • 2. ATP synthase - A marvellous rotary engine of the cell, Yoshida M,
Muneyuki E, Hisabori TNATURE 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:
I2t
d
d
2 M M
w L2
4
I1
3m L2
Current is coulombs per second. How many charges in a coulomb?For this you need Faraday's constant 96,500 Coulombs per mole ofcharged molecules, in this case potassium ions.
Q K Kflux0.24
96 50010 12 2.5 10 18 moles
sec
If work, W, is done on the particle during diffusion, then the time is increased as:
So say W = 10 KT, then tw = 20 ms t w t d e
W
kT
So how fast can the motor go? Assuming a back-and-forth motionit would take at least 40 ms, so the max frequency = 250 Hz or10 nM X 250 per second = 2.5 microns per second. (linear motion).
• When L>> the chain has many bends and is always crumpled in solution – the FJC model applies, with each link approximated as 2 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).