mammalian muscle properties

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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 Presentation

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Page 1: Mammalian Muscle Properties
Page 2: Mammalian Muscle Properties

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

Page 3: Mammalian Muscle Properties

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

Page 4: Mammalian Muscle Properties

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]

Page 5: Mammalian Muscle Properties

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

Page 6: Mammalian Muscle Properties

Hill model : Force dependence on contraction velocity

Page 7: Mammalian Muscle Properties

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

Page 8: Mammalian Muscle Properties

McKibben muscle

o

oo

o

oooo

forcemequilibriuPaxialPlateral

ll

rr

ll

rr

lFlrrrlP

WWW

lFVP

sin

)(cos1

coscos;;sin

sin

0))(2(

0

22

2

...

Page 9: Mammalian Muscle Properties

McK muscles

• Steel braid wrapped around a rubber tube.

• Crimped at ends

Page 10: Mammalian Muscle Properties

20N/g

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Testing

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Antagonistic pairs for smooth torque

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mgFKxxBxM CE

_

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Friction in the mesh

• Filament on filament friction (no sliding relative to the tube)

sx

x

kskkT

contactsmeshfrictiondrystatic

contactssolidfrictiondrystatic

e

PSF

PSF

)(

...

...

Page 15: Mammalian Muscle Properties

max

max

22

22

sin

1;;tan3

)1(),(

F

ba

baPrPF

oo

o

Page 16: Mammalian Muscle Properties

)(sgn xPSFF contactTdyn

Page 17: Mammalian Muscle Properties

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/

Page 18: Mammalian Muscle Properties

Molecular Springs & Ratchets

• Spasmoneme of the Vorticella

• Acrosome

• Actin polymerization

Mahdevan, L : Science, 288: 95, 2000.

Page 19: Mammalian Muscle Properties

Spasmoneme of the Vorticella

Page 20: Mammalian Muscle Properties

Actin Spring

• Acrosome needs to penetrate egg jelly.

• Spring is super-coiled- held twisted by scruin.

• Ca++ s scruin

Page 21: Mammalian Muscle Properties

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

Page 22: Mammalian Muscle Properties
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Overall energy balance

l

ST

l

Uf

dnfdlpdVTdSdU

dWTdSdUi

ii

.....

Page 24: Mammalian Muscle Properties

Conducting polymers

• Large molecular deformations (strains) induced by current

• Reversible Change in oxidation state

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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

Page 33: Mammalian Muscle Properties

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

Page 34: Mammalian Muscle Properties

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.

Page 36: Mammalian Muscle Properties

Nature Reviews Molecular Cell Biology 2; 669-677 (2001)ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL

< previous  next >

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Comparative motors

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For rotary motion:

I2t

d

d

2 M M

w L2

4

I1

3m L2

Page 45: Mammalian Muscle Properties

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

Page 46: Mammalian Muscle Properties

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).

Page 47: Mammalian Muscle Properties

• 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.

Page 48: Mammalian Muscle Properties
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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

Page 51: Mammalian Muscle Properties