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Reference model by Chang and coworkers for fitting CaMKII-CaMCa binding.

ca=[Ca]avg2+v1=k1⋅ca2⋅CaMApok1=CaM1ConCaM2ConCaM1Coff+CaM2Con⋅cav2=k2⋅Ca2CaMCk2=CaM1CoffCaM2CoffCaM1Coff+CaM2Con⋅cav3=k3⋅ca2⋅CaMApok3=CaM1NonCaM2NonCaM1Noff+CaM2Non⋅cav4=k4⋅Ca2CaMNk4=CaM1NoffCaM2NoffCaM1Noff+CaM2Non⋅cav5=k5⋅ca2⋅Ca2CaMCk5=k3v6=k6⋅Ca4CaMk6=k4v7=k7⋅ca2⋅Ca2CaMNk7=k1v8=k8⋅Ca4CaMk8=k2v9=k9⋅ca2⋅KCaMApok9=KCaM1ConKCaM2ConKCaM1Coff+KCaM2Con⋅cav10=k10⋅KCa2CaMCk10=KCaM1CoffKCaM2CoffKCaM1Coff+KCaM2Con⋅cav11=k11⋅ca2⋅KCaMApok11=KCaM1NonKCaM2NonKCaM1Noff+KCaM2Non⋅cav12=k12⋅KCa2CaMNk12=KCaM1NoffKCaM2NoffKCaM1Noff+KCaM2Non⋅cav13=k13⋅ca2⋅KCa2CaMCk13=k11v14=k14⋅KCa4CaMk14=k12v15=k15⋅ca2⋅KCa2CaMNk15=k9v16=k16⋅KCa4CaMk16=k10v17=k17⋅CaMK⋅CaMApov18=k18KCaMApov19=k19⋅CaMK⋅Ca2CaMCv20=k20KCa2CaMCv21=k21⋅CaMK⋅Ca2CaMNv22=k22KCa2CaMNv23=k23⋅CaMK⋅Ca4CaMv24=k24KCa4CaM\begin{align} ca &= \mathrm{[Ca]^{2+}_{avg}} \\ v_1 &= k_1 \cdot ca^2 \cdot CaM_{Apo} \\ k_1 &= \frac{CaM1C_{on} CaM2C_{on}}{CaM1C_{off} + CaM2C_{on} \cdot ca} \\ v_2 &= k_2 \cdot Ca2CaM_C \\ k_2 &= \frac{CaM1C_{off} CaM2C_{off}}{CaM1C_{off} + CaM2C_{on} \cdot ca} \\ v_3 &= k_3 \cdot ca^2 \cdot CaM_{Apo} \\ k_3 &= \frac{CaM1N_{on} CaM2N_{on}}{CaM1N_{off} + CaM2N_{on} \cdot ca} \\ v_4 &= k_4 \cdot Ca2CaM_N \\ k_4 &= \frac{CaM1N_{off} CaM2N_{off}}{CaM1N_{off} + CaM2N_{on} \cdot ca} \\ v_5 &= k_5 \cdot ca^2 \cdot Ca2CaM_C \\ k_5 &= k_3 \\ v_6 &= k_6 \cdot Ca4CaM \\ k_6 &= k_4 \\ v_7 &= k_7 \cdot ca^2 \cdot Ca2CaM_N \\ k_7 &= k_1 \\ v_8 &= k_8 \cdot Ca4CaM \\ k_8 &= k_2 \\ v_9 &= k_9 \cdot ca^2 \cdot KCaM_{Apo} \\ k_9 &= \frac{KCaM1C_{on} KCaM2C_{on}}{KCaM1C_{off} + KCaM2C_{on} \cdot ca} \\ v_{10} &= k_{10} \cdot KCa2CaM_C \\ k_{10} &= \frac{KCaM1C_{off} KCaM2C_{off}}{KCaM1C_{off} + KCaM2C_{on} \cdot ca} \\ v_{11} &= k_{11} \cdot ca^2 \cdot KCaM_{Apo} \\ k_{11} &= \frac{KCaM1N_{on} KCaM2N_{on}}{KCaM1N_{off} + KCaM2N_{on} \cdot ca} \\ v_{12} &= k_{12} \cdot KCa2CaM_N \\ k_{12} &= \frac{KCaM1N_{off} KCaM2N_{off}}{KCaM1N_{off} + KCaM2N_{on} \cdot ca} \\ v_{13} &= k_{13} \cdot ca^2 \cdot KCa2CaM_C \\ k_{13} &= k_{11} \\ v_{14} &= k_{14} \cdot KCa4CaM \\ k_{14} &= k_{12} \\ v_{15} &= k_{15} \cdot ca^2 \cdot KCa2CaM_N \\ k_{15} &= k_{9} \\ v_{16} &= k_{16} \cdot KCa4CaM \\ k_{16} &= k_{10} \\ v_{17} &= k_{17} \cdot CaMK \cdot CaM_{Apo} \\ v_{18} &= k_{18} KCaM_{Apo} \\ v_{19} &= k_{19} \cdot CaMK \cdot Ca2CaM_C \\ v_{20} &= k_{20} KCa2CaM_C \\ v_{21} &= k_{21} \cdot CaMK \cdot Ca2CaM_N \\ v_{22} &= k_{22} KCa2CaM_N \\ v_{23} &= k_{23} \cdot CaMK \cdot Ca4CaM \\ v_{24} &= k_{24} KCa4CaM \\ \end{align}
(1)
ddtCa2CaMC=v1−v2−v5+v6−v19+v20ddtCa2CaMN=v3−v4−v7+v8−v21+v22ddtCa4CaM=v5−v6+v7−v8−v23+v24ddtKCaMApo=−v9+v10−v11+v12+v17−v18ddtKCa2CaMC=v9−v10−v13+v14+v19−v20ddtKCa2CaMN=v11−v12−v15+v16+v21−v22ddtKCa4CaM=v13−v14+v15−v16+v23−v24\begin{align} \frac{d}{dt} Ca2CaM_C &= v_1 - v_2 - v_5 + v_6 - v_{19} + v_{20} \\ \frac{d}{dt} Ca2CaM_N &= v_3 - v_4 - v_7 + v_8 - v_{21} + v_{22} \\ \frac{d}{dt} Ca4CaM &= v_5 - v_6 + v_7 - v_8 - v_{23} + v_{24} \\ \frac{d}{dt} KCaM_{Apo} &= -v_9 + v_{10} - v_{11} + v_{12} + v_{17} - v_{18} \\ \frac{d}{dt} KCa2CaM_C &= v_9 - v_{10} - v_{13} + v_{14} + v_{19} - v_{20} \\ \frac{d}{dt} KCa2CaM_N &= v_{11} - v_{12} - v_{15} + v_{16} + v_{21} - v_{22} \\ \frac{d}{dt} KCa4CaM &= v_{13} - v_{14} + v_{15} - v_{16} + v_{23} - v_{24}\\ \end{align}
(2)
CaMT=CaMApo+Ca2CaMC+Ca2CaMN+Ca4CaM+KCaMApo+KCa2CaMC+KCa2CaMN+KCa4CaMCaMKT=CaMK+KCaMApo+KCa2CaMC+KCa2CaMN+KCa4CaM\begin{align} CaM_T &= CaM_{Apo} + Ca2CaM_C + Ca2CaM_N + Ca4CaM + KCaM_{Apo} + KCa2CaM_C + KCa2CaM_N + KCa4CaM \\ CaMK_T &= CaMK + KCaM_{Apo} + KCa2CaM_C + KCa2CaM_N + KCa4CaM \end{align}
(3)

Parameters

k17: Chang’s parameter (3.8) is different from Pepke’s (0.0038), probably a unit error.

ParameterValueUnitsDescription
CaM_T30μM
CaMK_T70μM
CaM1C_on51/μM/s
CaM1C_off501/s
CaM2C_on101/μM/s
CaM2C_off101/s
CaM1N_on1001/μM/s
CaM1N_off20001/s
CaM2N_on2001/μM/s
CaM2N_off5001/s
KCaM1C_on441/μM/s
KCaM1C_off331/s
KCaM2C_on441/μM/s
KCaM2C_off0.81/s
KCaM1N_on761/μM/s
KCaM1N_off3001/s
KCaM2N_on761/μM/s
KCaM2N_off201/s
k_170.00381/μM/s
k_185.51/s
k_190.921/μM/s
k_206.81/s
k_210.121/μM/s
k_221.71/s
k_23301/μM/s
k_241.51/s
NRVM CaMKII model
CaMKII system
NRVM CaMKII model
Parameters