Part 4 · Chapter 4.1

Skeletal Muscle

Skeletal muscle is the archetypal striated muscle: organised into sarcomeres, innervated by motor neurons at the neuromuscular junction (NMJ), recruited in all-or-none motor units. This chapter covers sarcomere structure, the NMJ, motor- unit recruitment (Henneman’s size principle), and the classical length-tension and force-velocity relationships.

1. Sarcomere Architecture

Muscle fibres are syncytial cells (multinucleate) packed with myofibrils; myofibrils are chains of sarcomeres (Z-disc to Z-disc). Each sarcomere contains interdigitating thick (myosin) and thin (actin) filaments. The cross-striated appearance reflects alternating A-band (thick filaments) and I-band (thin only). Huxley & Hanson 1954 resolved the sliding-filament model: contraction is cyclic cross-bridge engagement of myosin heads pulling actin toward sarcomere centre.

2. Length-Tension & Force-Velocity

Gordon, Huxley & Julian 1966 measured tetanic tension vs. sarcomere length in frog muscle. The curve has a plateau at 2.0–2.25 µm (maximum filament overlap), descending limbs on both sides. Hill 1938 characterised force-velocity:

\[ (F + a)(v + b) \;=\; b(F_{max} + a) \]

Peak mechanical power occurs at ~30% of maximum shortening velocity and ~30% of maximum force. Isometric (v=0) and unloaded (F=0) extremes are the corners; physiological contraction operates between them.

Simulation: Length-Tension & Hill Force-Velocity

Python

script.py38 lines

import numpy as np, matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Length-tension: Gordon Huxley Julian 1966 frog sarcomere
L = np.linspace(1.0, 3.8, 400)
# Three plateau segments
T = np.zeros_like(L)
T[(L >= 2.0) & (L <= 2.25)] = 1.0
T[L < 2.0] = np.maximum(0, 1 - 5*(2.0 - L[L<2.0])**2)[L<2.0]
m = (L > 2.25)
T[m] = np.maximum(0, 1 - (L[m] - 2.25)/1.4)
# Force-velocity Hill 1938
v = np.linspace(0, 1, 100)
F_v = (1 - v) / (1 + 3*v)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5), facecolor='#0a0f1e')
for ax in (ax1, ax2):
    ax.set_facecolor('#111e2f'); ax.tick_params(colors='#bae6fd')
    for s in ax.spines.values(): s.set_color('#334155')
    ax.grid(True, color='#334155', alpha=0.3)

ax1.plot(L, T, color='#f87171', lw=2.6)
ax1.axvspan(2.0, 2.25, alpha=0.1, color='#34d399', label='Optimum overlap')
ax1.set_xlabel('Sarcomere length (um)', color='#bae6fd')
ax1.set_ylabel('Relative tension', color='#bae6fd')
ax1.set_title('Length-tension (Gordon 1966)', color='#67e8f9', fontweight='bold')
ax1.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')

ax2.plot(v, F_v, color='#fbbf24', lw=2.6)
ax2.set_xlabel('Shortening velocity (relative)', color='#bae6fd')
ax2.set_ylabel('Force (relative)', color='#bae6fd')
ax2.set_title('Hill force-velocity hyperbola', color='#67e8f9', fontweight='bold')

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0f1e')
print('Length-tension peak 2.0-2.25 um: maximum thick-thin filament overlap')
print('Hill: F * (v + b) = b * (Fmax + a); P_mech = F * v, peaks ~30% vmax')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

3. Motor Units & Size Principle

A motor unit = one alpha-motoneuron + all muscle fibres it innervates (1–1000 fibres). Small-force precise muscles (extraocular) have small units; large-force muscles (gastrocnemius) have 1000+ fibre units. Henneman 1957 size principle: motor units recruit in order of increasing size, producing smooth force gradation. Firing rate (rate coding) and recruitment together span the full force range.

4. Fibre Types

Type I (slow oxidative): high myoglobin, dense mitochondria, fatigue-resistant. Postural muscles.
Type IIa (fast oxidative-glycolytic): intermediate — endurance athletes.
Type IIx (fast glycolytic): low myoglobin, fast fatigue. Sprint muscles.

Key References

• Huxley, A. F. & Niedergerke, R. (1954). “Structural changes in muscle during contraction.” Nature, 173, 971–973.

• Gordon, A. M., Huxley, A. F. & Julian, F. J. (1966). “The variation in isometric tension with sarcomere length.” J. Physiol., 184, 170–192.

• Hill, A. V. (1938). “The heat of shortening and the dynamic constants of muscle.” Proc. R. Soc. B, 126, 136–195.

• Henneman, E. (1957). “Relation between size of neurons and their susceptibility to discharge.” Science, 126, 1345–1347.

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