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Skeletal Muscle

•  Muscle is the material that really sets biomechanics apart from other branches of mechanics

•  3 Types: – skeletal (voluntary) }striated – cardiac (involuntary) }striated – smooth (involuntary) }unstriated

•  The main difference between skeletal and cardiac muscle is that skeletal muscle can exhibit a sustained ‘tetanic’ contraction whereas cardiac muscle ‘beats.’

Structure of

Skeletal Muscle

Muscle cell (fiber): •  10-80 µm 𝜙 •  multinucleated •  sarcolemma •  sarcoplasm •  sarcoplasmic

reticulum •  striated

Structure of

Skeletal Muscle Fascicle: Surrounded by collagen sheath

Myofibril (1µm Ø): •  100’s-1000’s per myofiber •  ~ 1500 thick filaments •  ~ 3000 thin filaments

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The Muscle Fiber (cell)

Key Components:

•  Multinucleated •  Longitudinally arranged, circular cross

section •  Sarcolemma (plasma membrane) •  Sarcoplasm (cytosol) •  Sarcoplasmic Reticulum (ER) •  Mitochrondria (ATP powerhouse) •  Transverse (T) Tubule •  Terminal Cisternae •  Network of Triads (T-tubule + 2 Terminal

Cisternae)

Terminal Cisternae

Myofibrils

•  1 µm Ø •  ~1500 thick filaments 12nm Ø •  ~3000 thin filaments 6 nm Ø •  surrounded by sarcoplasmic

reticulum •  A (optically anisotropic) band •  I (optically isotropic) band •  Z-line

The Sarcomere

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The Sarcomere

Anisotropic Isotropic to polarized light ~ 2.0 µm

The Sarcomere

The “Contractile Unit” •  Thick Myosin Filaments •  Thin Actin Filaments •  Z-line to Z-line •  A and I bands •  Sliding Filament Theory

•  Titin a.  Molecular Spring b.  Connects Z-line to M-line,

allows for force transmission.

c.  Limits range of motion of sarcomere in tension, primary

contributor to passive stiffness.

Hexagonal Arrangement of Myofilaments in Cross-Section

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Myofilaments •  Thick myosin filaments (180

myosin molecules polymerized) •  Thin actin filaments •  They interdigitate to form the

SARCOMERE

Actin

•  F-actin molecule formed from G-actin

•  Twisted with a period of 70 nm - double helix

•  Two strands of tropomyosin

•  Globular troponin molecules (with a strong affinity for Ca2+) attached to tropomyosin strands, every 7 G-actin monomers

Myosin •  Subdomains:

Heavy Meromyosin HMM Light Meromyosin LMM S1-Head

•  Myosin leads protrude in pairs at 180º

•  There are about 50 pairs of cross-bridges at each end of the thick filament

•  The filament makes a complete twist 310º every 3 pairs

•  14.3 nm internal between pairs

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The Motor Unit On each muscle fiber, a nerve ending terminates near the center (at the muscle end-plate). Each nerve has from 2-3 to 150 fibers or more depending on the type of muscle. At the end-plate is the neuromuscular junction. Stimulus is transmitted by neurotransmitter Acetylcholine (mopped up by cholinesterase).

Excitation-Contraction Coupling Key Features •  Negative resting membrane potential

-  High Intracellular [K+] -  High Extracellular [Na2+]

•  Action Potential travels along sarcolemma and down the T-tubule activates DHP.

•  What is the DHP receptor?

a.  L-type (long-lasting) calcium voltage gated channel

b.  Mechanically connected to the Ryandine receptors (RyRs).

c.  How is cystosolic [Ca2+] increased? •  What is the primary difference in Ca2+ release between skeletal and cardiac

muscle? - Calcium Induced Calcium Release (CICR)

Calcium Activation Key Features •  Force-development is highly

dependent on [Ca2+]. How is this regulated?

•  Ca2+ binds to troponin-C sites, which are separated by neighboring troponin-C sites every 7 nm (Cooperative Activity).

•  What is cooperative activity?

•  How does [Ca2+] regulate force-relaxation? How is this achieved?

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The Crossbridge

Crossbridge Cycle

Crossbridge Cycle Step 1: Cross-bridge (high-energy state) is formed Step 2: Release of stored chemical energy is transferred to mechanical motion, myosin head “power strokes” to it’s rigor position (45 o). Actin slides towards the M-line. Step 3: In rigor conformation, ATP molecule binds to myosin head, releasing myosin (rigor state) from actin filament. Step 4: ATP hydrolysis (ATP à ADP + PI) supplies potential energy to the myosin head. Myosin head is in it’s upright position (90 o) and awaits for next open binding site of actin to form crossbridge.

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Muscle Architecture

Flexor, Extensor, Belly, Tendon, Aponeurosis

Muscle Architecture: Collagen Matrix

Muscle Architectures

Parallel (fusiform) Convergent

Pennate Circular (areolar)

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Muscle Architecture

Figure 9.2:2 from textbook. Diagram illustrating (a) parallel-fibered and (b) pinnate muscles. (c) and (d) illustrate pinnate muscle contraction.

Muscle Mechanics

•  Twitch •  Tetanus •  Isometric contraction •  Isotonic contraction •  Concentric contraction •  Eccentric contraction •  Transient loading

Tests of Contractile Mechanics

Isometric - constant length

Isotonic - constant force

Transient

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Isometric (constant length) Preparations

Forc

e (N

)

Time (s)

0

Frog Semitendinosis Muscle

0.4

Passive

Active

Total

Fast vs. Slow Twitch Muscle Duration of twitch corresponds to functional requirements of muscle

Fast twitch muscle White muscle

lower concentrations of RBCs and myoglobin,

e.g. ocular muscle

Slow twitch muscle Red muscle

e.g. soleus muscle

Soleus (calf) Gastrocnemius (calf)

Ocular (eye)

10 100 time (ms)

TIsometric Twitch Tension T

Stimulation Frequency •  Increasing stimulus frequency will result into wave

summation of multiple twitches. •  As frequency occurs, tetanus can occur (unfused/fused) •  Fused tetanus occurs via recruitment of multiple

muscle fibers at high stimulation frequencies, resulting in a maximum force development (>> twitch) that is sustained over time.

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Passive Properties Non-Stimulated Skel. Muscle: •  Soft mechanical tissue •  Nonlinear stress/strain •  Viscoelastic properties:

(1)  Hysteresis (2)  Stress Relaxation (3)  Creep

Major Contributors: •  ECM proteins

-  Collagen -  Elastin

•  Titin •  Vinculin •  Fiber arrangement

(anisotropy)

Isometric Length-Tension Relationships

Tension-length curves for frog sartorius

muscle at 0ºC

Fixed length Electrical Stimulation Measure Force Generation

Ascending limb is dependent on Ca2+

concentration

Isometric Tension: Sliding Filament Theory

Developed tension versus length for a single fiber of frog semitendinosus muscle

Results in Isometric Length-Tension Relationship of muscle

Lmax

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Isotonic (constant force) Preparations

Time (ms)

F

L

Muscle shortens

Reality: Isometric + Isotonic The majority of skeletal muscles under go both: •  Isometric Contraction (constant length):

Tmuscle < afterload

•  Isotonic Contraction (constant force): Tmuscle

> afterload

Isometric Isotonic

Force

Time

Eccentric and Concentric Contraction L0

L < L0

L > L0

Concentric Contraction: •  Muscle shortens as it

generates tension. •  Tmuscle > afterload

Eccentric Contraction: •  Muscle lengths as it

generates. •  Tmuscle < afterload •  Serves to decelerate

muscle velocity as it lengthens.

•  Ex: placing

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• The shortening part (V>0) of the curve was computed from Hill’s equation with c = 4

• The asymptotes for Hill’s hyperbola (broken lines) are parallel to the T/T0 and V/Vmax axes

• Mechanical power output is the product of T and V

Hill’s Force-Velocity Curve

Hill's Equation

Vmax

T0

Original Form: (T+a)(V+b)=b(T0+a)

Dimensionless forms:

( )

( )

0

max 0

max

0 max

1111

T TVV c T T

V VTT c V V

−=+

−=+

a,b = asymptotes T0=Isometric force Vmax= velocity at T = 0 c = T0/a (ranges from 1.2-4.0)

Hill's Three Element Model Fundamental Assumptions:

•  Resting length-tension relation is governed by an elastic element in parallel with a contractile element. In other words, active and passive tensions add. The parallel elastic element is the passive properties.

•  Active contractile element is determined by active length-tension and velocity-tension relationships only.

•  Series elastic element becomes evident in quick-release experiments.

Fig 9.8:1 from text. Hill’s functional model

of muscle

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Hill's Three-Element Model (basic equations)

( ) ( )

( ) ( )

stress contributed by the parallel elastic element

stress contributed by the activated actin myosin filaments:

,

P

S

T P L

T S

=

−

= η Δ

( )( )

( )

, is identically zero when the muscle is at rest; so that

, 0 when 0and , 0 when 0

S

S

S

> >< <

η Δ

η Δ η

η Δ = η =

L

h D T T

Limitations of Hill Model Division of forces between parallel and series elements and division of displacements between contractile and elastic elements is arbitrary (i.e. division is not unique). Structural elements cannot be identified for each component.

Hill model is only valid for steady-shortening of tetanized muscle.

1) For a twitch we must include the time-course of activation and hence define "active state"

2) Transient responses observed not reproduced

Series elasticity is not observed. Properties of tendon and crossbridge itself

Small Length Step Response

Tetanized single frog muscle fiber at 0ºC during a 1% shortening step lasting 1 ms

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Instantaneous and Plateau Tension

Solid lines: sarcomere length = 2.2 mm (near maximal myofilament overlap). Broken lines: sarcomere length = 3.1 mm (39% myofilament overlap). Thus instantaneous tension T1 reflects crossbridge stiffness and number of attached crossbridges which varies with myofilament overlap.

Huxley and Simmons Model (1971) Two stable attached states of S-1 head. Thin filament displacement y stretches S-2 spring generating force.

Calculated curves of T1 and T2 versus length step y showing predictions of Huxley and Simmons model

Hill's Two Element Model Fundamental Assumptions:

•  model consists of linear elastance in series with contractile element.

•  Active contractile element (c.e.) depends on both muscle length and shortening velocity.

•  Velocity can be determined from Hill’s equation.

T

T

c.e.

T1

T2

L1

L2

L

L = L1 + L2 T = T1 = T2

L’ = L1’ + L2’ T1 = α*ΔL1

L’ = L1’ + Vc.e.

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Hill’s 2-element model cont.

L’ = L1’ + Vc.e; ; where Vc.e. = L2’ (shortening velocity of contractile element)

From Hill’s Equation: Vc.e. = - b (P-P0)/(P+a)

T = α*ΔL1 à T’ = α L1’ = α (L’ – Vc.e.)

Typical Parameters (Hill 1927, Holmes 2005): a = 380 * 0.098 [mN/mm2] b = 0.325 [mm/s] P0 = a/0.257 [mN/mm2] Vmax

= b/a * P0 [mm/s] Ls.e. 0 = 0.3; assume Ls.e. 0 is 30% of length

T = α (L’ + b(P-P0)/(P+a)

Solving in MATLAB

Ref: Holmes 2005 (AJP)

Input Time and Length Profile

Define Parameters

Initialize Variables (Element Lengths, Tension)

Numerical Solver (generic form)

MATLAB Output (Isometric)

S.E. à linear elastic

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MATLAB Output (Quick Release)

Both Elastic Elements are Inside the Contractile Element

Z-line

Myosin

Actin

Titin

T T

Skeletal Muscle: Summary of Key Points

•  Skeletal muscle is striated and voluntary •  It has a hierarchical organization of myofilaments forming

myofibrils forming myofibers (cells) forming fascicles (bundles) that form the whole muscle

•  Overlapping parallel thick (myosin) and thin (actin) contractile myofilaments are organized into sarcomeres in series

•  Thick filaments bind to thin filaments at crossbridges which cycle on and off during contraction in the presence of ATP

•  Nerve impulses trigger muscle contraction via the neuromuscular junction

•  The parallel and/or pennate architecture of muscle fibers and tendons affects muscle performance

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Muscle Mechanics: Summary of Key Points

•  Skeletal muscle contractions can be twitches or tetani, isometric or isotonic, eccentric or concentric

•  Twitch duration varies 10-fold with muscle fiber type •  Tetanic contraction is achieved by twitch summation •  The isometric length-tension curve is explained by

the sliding filament theory •  Isotonic shortening velocity is inversely related to

force in Hill’s force-velocity equation •  Hill’s three-element model assume passive and

active stresses combine additively •  The series elastance is Hill’s model is probably

experimental artifact, but crossbridges themselves are elastic