1. 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.’
23-Feb-1999
Good framework for a lecture but contains some redundancy. Improve by:
1. remove repetition
2. use state of the art illustrations especially for activation and crossbridge cycle. See Opie and refs therein
3. add some state of the art such as single myosin molecule studies by Yanagida or Spudich
4. scan Netter slides for images of neuromuscular junction
5. Add material on muscle fiber architecture from JAP 1998;85(4): or simlar refs.

2. Structure of Skeletal Muscle

3. Structure of Skeletal Muscle
Fascicle:
Surrounded by collagen sheath
Myofibril (1μm Ø):
100’s-1000’s per myofiber
~ 1500 thick filaments
~ 3000 thin filaments
Muscle cell (fiber):
10-80 μm 𝜙
multinucleated
sarcolemma
sarcoplasm
sarcoplasmic reticulum
striated

4. 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

5. 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

6. The Sarcomere

7. Anisotropic Isotropic to polarized light ~ 2.0 μm
The Sarcomere
Anisotropic Isotropic to polarized light ~ 2.0 μm

8. The Sarcomere The “Contractile Unit” Thick Myosin Filaments
Thin Actin Filaments
Z-line to Z-line
A and I bands
Sliding Filament Theory
Titin
Molecular Spring
Connects Z-line to M-line, allows for force transmission.
Titin is important in the contraction of striated muscle tissues. It connects the Z line to the M line in the sarcomere. The protein contributes to force transmission at the Z line and resting tension in the I band region.[7] It limits the range of motion of the sarcomere in tension, thus contributing to the passive stiffness of muscle.
Limits range of motion of sarcomere in tension, primary contributor to passive stiffness.

9. Hexagonal Arrangement of Myofilaments in Cross-Section

10. Myofilaments Thick myosin filaments (180 myosin molecules polymerized)
Thin actin filaments
They interdigitate to form the SARCOMERE

11. 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

12. 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

13. 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).
The Motor Unit

14. 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?
L-type (long-lasting) calcium voltage gated channel
Mechanically connected to the Ryandine receptors (RyRs).
How is cystosolic [Ca2+] increased?
What is the primary difference in Ca2+ release between skeletal and cardiac muscle?
- Calcium Induced Calcium Release (CICR)

15. 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?
Strong cross-bridges are red. Ca2+ binding induces increased Ca2+ affinity in that and n-n TnC (A). Strong cross-bridge binding increases Ca2+ binding to TnC in that unit and the n-n unit (B). Strong cross-bridge binding increases strong cross-bridge binding in that and the n-n unit (C). Strong cross-bridge binding influences actin structure in that and n-n unit to increase cross-bridge binding (D).

16. The Crossbridge

17. Crossbridge Cycle

18. 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  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.

19. Muscle Architecture
Flexor, Extensor, Belly, Tendon, Aponeurosis

20. Muscle Architecture: Collagen Matrix

21. Muscle Architectures Parallel (fusiform) Convergent Pennate
Circular (areolar)

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

23. Muscle Mechanics Twitch Tetanus Isometric contraction
Isotonic contraction
Concentric contraction
Eccentric contraction
Transient loading
25-feb-1999
Deidre says:
The lecture went great. It was the perfect length ... I finished
the last slide at 10:50. There were lots of questions
afterwards, but not because things weren't clear but because
they actually understood enough to ask questions.
I'd be happy to do that one again.

24. Tests of Contractile Mechanics
Isometric - constant length
Isotonic - constant force
Transient

25. Isometric (constant length) Preparations
Frog Semitendinosis Muscle
0.4
Active
Force (N)
Total
Passive
Time (s)

26. 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 10
100
time (ms) T
Isometric Twitch Tension T
Ocular (eye)
Gastrocnemius (calf)
Soleus (calf)

27. 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.

28. Passive Properties Non-Stimulated Skel. Muscle: Soft mechanical tissue
Nonlinear stress/strain
Viscoelastic properties:
Hysteresis
Stress Relaxation
Creep
Major Contributors:
ECM proteins
Collagen
Elastin
Titin
Vinculin
Fiber arrangement (anisotropy)

29. Isometric Length-Tension Relationships
Tension-length curves for frog sartorius muscle at 0ºC
Fixed length Electrical Stimulation Measure Force Generation

30. Isometric Tension: Sliding Filament Theory
Lmax
Developed tension versus length for a single fiber of frog semitendinosus muscle
Ascending limb is dependent on Ca2+ concentration
Results in Isometric Length-Tension Relationship of muscle

31. Isotonic (constant force) PreparationsL
Muscle shortens
Time (ms)

32. Reality: Isometric + Isotonic
The majority of skeletal muscles under go both:
Isometric Contraction (constant length):
Tmuscle < afterload
Isotonic Contraction (constant force):
Tmuscle > afterload
Force
Time
Isometric
Isotonic

33. Eccentric and Concentric ContractionL0
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
L < L0
L > L0

34. Hill’s Force-Velocity Curve
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

35. Hill's Equation Original Form: (T+a)(V+b)=b(T0+a) a,b = asymptotes
Dimensionless forms:
a,b = asymptotes
T0=Isometric force
Vmax= velocity at T = 0
c = T0/a (ranges from )
Vmax T0

36. 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

37. Hill's Three-Element Model (basic equations)

38. 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

39. Small Length Step Response
Tetanized single frog muscle fiber at 0ºC during a 1% shortening step lasting 1 ms

40. 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.

41. 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

42. 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. T1 L1 L
c.e. T2
L = L1 + L2 T = T1 = T2 L2
L’ = L1’ + L2’ T1 = α*ΔL1
L’ = L1’ + Vc.e. T

43. 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  T’ = α L1’ = α (L’ – Vc.e.)
T = α (L’ + b(P-P0)/(P+a)
Typical Parameters (Hill 1927, Holmes 2005):
a = 380 * [mN/mm2]
b = [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

44. Solving in MATLAB Input Time and Length Profile Define Parameters
Initialize Variables (Element Lengths, Tension)
Numerical Solver (generic form)
Ref: Holmes 2005 (AJP)

45. MATLAB Output (Isometric)
S.E.  linear elastic

46. MATLAB Output (Quick Release)

47. Both Elastic Elements are Inside the Contractile Element
Actin
Myosin
Titin
Z-line T

48. 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

49. 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