Length tension relationship

• Sliding filament theory– Tension is produced by interaction of thick & thin

filaments– Interference at short lengths (ascending limb)– Reduced interaction at long lengths (descending)

• Supporting evidence– Single fibers– Special conditions for descending limb

SteepAscending

ShallowAscending

Plateau

Descending

Force length relationship

• Crossbridge availability– Overlap

• Structural interference

1.6 um1.25 um

4.1 um

1.25 um

1.25 um 1.25 um

2.5 um

Plateau

LongestLength

Historical context

• Blix 1893– Total force follows an “S-shaped” relation to

length– Heat production continuously increases

• Evans & Hill 1914– Active vs total tension– Heat production parallels

active tension

Passive tension

Total tensionActive tension

Heat rate

Historical context

• Ramsey & Street, 1940– Single frog fibers– Passive tension (myofibrils vs sarcolemma)– Distinct force maximum, both total and active– Loss of sarcomere alignment with long stretch

Length (% rest)

Ten

sion

(%

max

)

Passive tension

Active tension

Possible mechanisms

• Coiling of ‘kinked’ fibers– Mechanical spring– Striation & changes during stretch

• Shortening of one structure– eg, dehydration– Only I-band changes length

• Bi-molecular interaction– X-ray (1935)– Structural derangements

“delta” state (R&S 1940)

The Big Key

• Hugh Huxley 1957– Visibly interdigitating filament arrays– Visible molecular interactions (crossbridges)

AF Huxley & Peachey 1961

• Single frog fibers• Monitor striation• “Isometric” fiber does

not have isometric striations

Gordon, Huxley & Julian (1966)

• Single fiber segments– “Spot follower”– Control sub-segment of

larger fiber– Assume intervening

material is functionally static

• Still not measuring actual striations

GHJ raw measurements

Near Lopt

Above Lopt Below Lopt

GHJ Long lengths

• Continuous tension rise– Striation irregularities (instability)– Internal rearrangement w/o membrane motion

• Extrapolation– Undesirable but consistent

GHJ Synthesis

Mammalian fibers

• Actin filament 1.1 um• Myosin filament 1.63 um

Edman 2005

Fiber segment summary

• Peak force corresponds with max overlap of thin filaments and crossbridges (± bare zone)

• Force decreases linearly with decreasing overlap (descending limb)

• Force decreases slowly as thin filaments overlap (shallow ascending limb)

• Force decreases rapidly as thick filament overlaps Z-disk (steep ascending limb)

Single myofibrils

• Rassier, Herzog & Pollack (2003)– Isolate myofibril segments ~ 20 sarcomeres– Activate by direct calcium bath

Fibril image

Intensity profile

Sarcomeres are not all equal

• Heterogeneity increases with movement– Just like R&S– GHJ

• ~200 sarcomeres• ~2000 myofibrils

Single Sarcomere

• Rassier & Pavlov 2008– Even this is not constant– A-band wobbles between Z-disks

Other length trajectories

• GHJ: start long passive, unloaded shortening to test length

• Abbot & Aubert (1952)– Allow force development before length change– Residual force

enhancement– Persistent loss

of force

Residual force enhancement

• Joumaa, Leonard & Herzog (2008)– Single myofibrils– Generate greater than ‘maximum’ tension on

descending limb

Residual force enhancement

• Nonuniformity– Fiber, fibril, sarcomere– “Weak” sarcomere/half-sarcomere stretches,

gaining from force-velocity property

• Other sources of force– Titin– Myofilament shortening

Nagornyak & al., 2004

Submaximal activation

• Rack & Westbury, 1969– “Normal” activation frequency low, subfused– Distributed stim allows lower f but steady force

At lower activation, length-tension shifts to longer lengths

Passive tension

• Banus & Zetlin (1938)– Muscles with fibers “scooped out” have same passive tension

epi-/peri-mysium gives passive tension

• Ramsey & Street (1940)– Pinched sections of fiber w/o sarcomeres carry same tension as

intact sections sarcolemma gives passive tension

• DK Hill (1950)– Passive tension is viscoelasticresidual crossbridges

• Magid & Law (1985)– Skinned fiber passive elasticity is the same as whole muscle and not

visco-elastic myofibrils give passive tension

Titin hypothesis

• Horowits & al 1986– Skinned, irradiated fibers– ln(A/A0)=2.3e11 Mr D (Mr, mass; D dose)

• Titin– 2-4 MD– ~ 5x larger than next

largest protein

Normal fiber

Irradiated fiber

Horowits & al

• Tension declines with dose– ~3.4 MD passive– ~3.2 MD active

• Experimental measures match theory quantitatively

Titin Model

• Modular spring– Discrete, independent

elastic domains– Segmental association

with thick filament

• Spring + yield– Linear elastic– Perfectly plastic

• ECM dominates at long lengths

Summary

• Sliding filament theory– Steep ascending limb– Shallow ascending limb– Plateau– Descending limb

• Passive tension– ECM: chinese finger trap– Titin: modular spring