This is a 2D mechanistic-diagram counterpart of the CaMKII bistable-switch 3D sim: instead of a rotating holoenzyme, it draws the actual dynamical-systems picture biophysicists use to reason about this switch — a 1-D potential energy landscape U(P) that reshapes itself in real time as Ca²⁺ pulses arrive, plus live Ca²⁺(t)/P(t) traces and a Ca–P phase portrait.
dCa/dt = -Ca/τ_Ca + Σ pulses(t)
G(Ca,P) = Ca⁴/(Ca⁴+K_act⁴) + κ·P (Ca/CaM activation + CaM-trapping)
dP/dt = G(Ca,P)·(k0 + k1·P)·(1-P) - kpp·P/(Kpp+P)
U(P) = -∫ dP/dt dP at fixed (Ca,PP1) → ball rolls downhill on U(P)
Any 1-D ODE dP/dt = f(P) is exactly the gradient flow of the potential U(P) = -∫f(P)dP, so the phospho-CaMKII fraction can be drawn as a literal ball rolling down a landscape whose shape depends on the instantaneous Ca²⁺ and phosphatase levels — a double well when the switch is bistable, a single well when it isn't. Watch the well on the left (OFF) get shallower and the well on the right (ON) deepen as Ca²⁺ rises during a train; once the ball rolls over the central barrier it drops into the ON well and stays there.
Correction versus the 3D model: the original 3D sim's rate law gates the entire autocatalytic (neighbor-phosphorylates-neighbor) term by Ca⁴/(Ca⁴+K_act⁴) alone. Numerically stepping that exact equation shows the "ON" well disappears once Ca²⁺ decays back to the ~0.02 µM resting level — the switch always relaxes fully to OFF, contradicting the persistent-memory claim in its own description. Real CaMKII autophosphorylation increases the kinase domain's affinity for Ca²⁺/calmodulin roughly 1000-fold ("CaM trapping"), so a subunit that is already phosphorylated stays active at resting Ca²⁺ even without a fresh Ca²⁺ transient. This 2D model adds that mechanism explicitly as the κ·P term in G(Ca,P) (verified numerically: with κ=0.85 a second stable root re-appears at basal Ca, and a tetanus-switched ball genuinely stays parked in the ON well after Ca²⁺ fully decays — see the verification script). The landscape view makes the fixed missing physics visible directly: without κ·P the right-hand well collapses the instant Ca²⁺ drops.
- Stimulation frequency — less time between pulses for Ca²⁺ to decay (τ_Ca≈80 ms) means Ca²⁺ summates to a higher plateau, tilting the landscape toward the ON well faster — the real biophysical reason tetanic stimulation favors LTP and slow trains favor LTD.
- Ca²⁺ influx per pulse — models NMDA-receptor conductance; bigger pulses reach the switching barrier in fewer stimuli.
- Phosphatase (PP1) activity — raising it deepens the OFF well and can even erase the ON well outright, pulling an already-switched synapse back down — exactly how LTD reverses prior potentiation.
- Synaptic weight readout — W = 50% + 100%·P, a linear proxy for AMPA-receptor-mediated conductance.