Satellite cells are adult muscle stem cells that sit quiescent between the sarcolemma and basal lamina of a myofiber, marked by the transcription factor Pax7. Injury releases HGF, which binds the c-Met receptor and, together with Notch/Wnt signaling, breaks quiescence. This 2D view unrolls the cylindrical fiber surface into a flat strip: horizontal position is distance along the fiber, vertical position is angle around its circumference — the same two coordinates the 3D model tracks, just laid flat instead of wrapped.
dQ/dt = -a·S(t)·Q + 2·p·r·A
dA/dt = a·S(t)·Q - p·A
dD/dt = 2·p·(1-r)·A - f·D
S(t) = exp(-t / τ) (decaying injury signal)
Q = quiescent pool, A = activated/proliferating myoblasts (MyoD+), D = differentiation-committed cells fusing into the fiber. Each proliferating cell divides at rate p; on division, a fraction r of daughters returns to the quiescent state (self-renewal, keeping Pax7 high) while the rest commit to differentiation (Pax7 off, Myogenin on) and fuse, restoring the fiber. This stochastic, asymmetric-fate model (Kuang et al., 2007) is how the finite satellite-cell reserve survives repeated rounds of muscle damage instead of being exhausted by a single injury.
- Injury severity — how much of the fiber is damaged, setting the activation radius and the fusion target for full repair.
- Activation signal — strength of the HGF/c-Met chemical gradient driving Q → A transitions near the wound.
- Self-renewal probability r — the fate-decision knob: low r drains the stem pool fast but repairs quickly; high r preserves the reserve for future injuries at the cost of slower repair.
- Proliferation / fusion rate — how fast activated cells divide, and how fast committed cells fuse into the fiber.
- Drag / scroll — pan and zoom the unrolled fiber strip.