Obstructed metabolite diffusion within skeletal muscle cells in silico

Abstract

Using a Monte Carlo simulation technique, we have modeled 3D diffusion of low molecular weight metabolites inside a skeletal muscle cell. The following structural elements are considered: (i) a regular lattice of actin and myosin filaments inside a myofibril, (ii) the membranes of sarcoplasmic reticulum and mitochondria surrounding the myofibrils, (iii) a set of myofibrils inside a skeletal muscle cell encircled by the outer cell membrane, and (iv) an additional set of regular intracellular structures (“macrocompartments”) embedded into the cell interior. The macrocompartments are considered to simulate diffusion restrictions because of hypothetical cylindrical structures (16–22 μm in diameter) suggested earlier (de Graaf et al. Biophys J 78: 1657–1664, 2000). This model allowed us to calculate the apparent coefficients of particle diffusion in the radial and axial directions, $D_{ \bot }^{\text{app}}$ and $D_{II}^{\text{app}}$, respectively. Particle movements in the axial direction are considered, at first approximation, as unrestricted diffusion ($D_{II}^{\text{app}}$ = const). The apparent coefficient of radial diffusion, $D_{ \bot }^{\text{app}}$, decreases with time because of particle collisions with myofilaments and other rigid obstacles. Results of our random walk simulations are in fairly good agreement with experimental data on NMR measurements of restricted radial diffusion of phosphocreatine in white and red skeletal muscles of goldfish (Kinsey et al. NMR Biomed 12:1–7, 1999). Particle reflections from the low-permeable borders of macrocompartments (efficient diameter, $d_{\text{MC}}^{\text{eff}}$ ≈ 9.2–10.4 μm) are the prerequisite for agreeing theoretical and experimental data. The low-permeable coverage of hypothetical macrocompartments (99.8% of coverage) provides the main contribution to time-dependent decrease in $D_{ \bot }^{\text{app}}$.