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
Force length relationship
• Crossbridge availability
– Overlap
• Structural interference
4.1 um
Longest
Length
Plateau
1.25 um
1.6 um
1.25 um
Shallow
Ascending
2.5 um
Descending
Steep
Ascending
Plateau
1.25 um
1.25 um
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
Total tension
Active tension
Heat rate
Passive tension
Historical context
• Ramsey & Street, 1940
Tension (% max)
– Single frog fibers
– Passive tension (myofibrils vs sarcolemma)
– Distinct force maximum, both total and active
– Loss of sarcomere alignment with long stretch
Active tension
Passive tension
Length (% rest)
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 viscoelasticresidual 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