Ls 2.20 umCa 0.10 uMForce 0.00 F0v 0.0 L0/sATP 5.0 mMPCr 25 mMpH 7.10FPS 0

actin troponin myosin Ca2+ ATP / sliding. Drag to orbit, wheel or pinch to zoom, keys 1-5 change scale, Space stimulates. Educational model, not medical advice.

Muscle Fibre Cutaway: Calcium, ATP and Force

Zoom from a runner's knee into one sarcomere. Control the nerve signal, calcium, ATP, length and load, and watch the cross-bridges make force.

Educational model, not medical advice. No training, health or supplement guidance.

Nerve signal and calcium

Length, load, fibre

Time

Missions

Live graphs

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom. Buttons 1-5 or the view strip fly the camera from the whole leg down to single molecules.
Space: start or stop the nerve stimulus train (rate slider; 0 Hz gives one twitch). C: one Ca2+ pulse. A: ATP supply on or off. Left / Right: sarcomere length. R: reset.
Isometric mode clamps the length so you can map force against length. Load mode lets the fibre shorten against a weight (Hill force-velocity).
Ca2+ clamp holds calcium at a fixed value; set it back to 0 for normal pulses.
The molecular cycle is drawn in slow motion (slider); the physics runs at the real rates. Time scale speeds up the physics only.

The science

Sliding filaments. Thick (myosin) and thin (actin) filaments keep their length; the sarcomere shortens because they slide past each other. Filament lengths used: thick 1.6 um, thin 1.0 um, bare zone 0.2 um.

Excitation and calcium switch. A nerve impulse releases Ca2+ from the sarcoplasmic reticulum (each pulse adds 1.5 uM here, a model value) and a saturable pump removes it. Activation follows a Hill curve Act = Caⁿ/(Caⁿ+Ca50ⁿ) with Ca50 = 0.8 uM, n = 3.5, low-pass filtered with tau = 30 ms (this produces twitch versus tetanus summation).

Cross-bridges. Two-state kinetics: dA/dt = kon(1-A) - koff A, kon = 50 Act s^-1, koff = 20 s^-1 x ATP/(ATP+0.1 mM). Without ATP the head cannot detach and the fibre goes into rigor (rigor mortis is the same effect).

Force-length. Force follows the filament overlap, a piece-wise linear Gordon-Huxley-Julian curve: zero at 1.27 and 3.65 um, plateau 2.0-2.25 um. F = F0 ov(Ls) A.

Force-velocity (Hill). (F+a)(v+b) = (F0+a) b, a/F0 = 0.25, vmax 8 (fast) or 4 (slow) L0/s. The power-optimal speed has the closed form b(sqrt((F0+a)/a) - 1); the page checks it.

Energy and fatigue. Hydrolysis rate = tension cost (Jiso A) + work term so that mechanical efficiency never exceeds 25 %. Phosphocreatine (PCr + ADP to ATP + Cr), glycolysis and oxidative supply refill ATP; Pi and H+ accumulate and make the fibre less sensitive to Ca2+: Ca50' = Ca50 (1 + 0.05 (Pi-2) + 0.5 (7.1-pH)). The page checks that d(ATP+PCr) equals supply minus hydrolysis exactly.

Honest simplifications. Mean-field two-state model instead of the full Huxley-1957 equations; no titin, no series elasticity, no temperature dependence, one fibre, constant parameters (all numbers are illustrative model values, typical orders of magnitude only). The molecular drawing is stylised and not to scale (the lattice is widened so the filaments can be seen). Sources to read: Alberts, Molecular Biology of the Cell; Guyton and Hall, Textbook of Medical Physiology; OpenStax Anatomy and Physiology; Huxley (1957), Hill (1938), Gordon-Huxley-Julian (1966).

Educational model, not medical advice. Built with Blender (leg, fibre bundle, molecule models) and rendered with Three.js.