A mathematical analysis of obstructed diffusion within skeletal muscle

Area of Science:

• Biophysics
• Skeletal Muscle Physiology
• Computational Biology

Background:

• Skeletal muscle activation involves complex molecular transport within the myofilament lattice.
• Intracellular structures like myofilaments, myosin heads, sarcoplasmic reticulum, t-tubules, and mitochondria impede molecular diffusion.
• Understanding diffusion dynamics is crucial for muscle function and disease research.

Purpose of the Study:

• To investigate the effects of obstructed diffusion within the skeletal muscle myofilament lattice.
• To quantify the impact of intracellular obstacles on molecular transport and diffusion anisotropy.
• To model the influence of protein size and calcium dynamics on diffusion processes.

Main Methods:

• Monte Carlo simulation
• Level-set methods
• Homogenization theory applied to myofilament lattice diffusion

Main Results:

• Intracellular obstacles significantly reduce diffusion rates in skeletal muscle.
• Diffusion anisotropy was observed, with slower radial than longitudinal diffusion, matching experimental findings.
• Protein size critically affects diffusion; anomalous diffusion occurs for proteins near myofilament spacing.
• Obstructed transport of calcium ions (Ca2+) and ATP-bound Ca2+ leads to smaller Ca2+ transients.
• Nonuniform distribution of troponin binding sites and sarcoplasmic reticulum Ca2+-ATPase pumps cause minor asymmetries in Ca2+ dynamics.

Conclusions:

• Obstructed diffusion is a key factor in regulating molecular transport within skeletal muscle fibers.
• The physical constraints of the myofilament lattice significantly influence diffusion behavior and anisotropy.
• Protein size and calcium handling are modulated by the obstructed diffusion environment, impacting muscle activation and signaling.