# Model Mathematics

### Component: subspace

$J_xfer = 1.0 tau_xfer ⁢ Ca_SS - Ca_myo$$J_DHPR = I_DHPR ⁢ DHPR_open 2.0 ⁢ F ⁢ V_SS$$I_DHPR = P_Ca ⁢ 4.0 ⁢ V ⁢ F 2.0 R ⁢ T ⁢ 0.001 ⁢ⅇ 2.0 ⁢ V ⁢ F R ⁢ T - 0.341 ⁢ Ca_o ⅇ 2.0 ⁢ V ⁢ F R ⁢ T - 1.0$$DHPR_open = 1.0 if i = O ∨ i = O_Ca 0.0 otherwise$$J_RyR =∑ i = 1.0 8.0 J_RyR_perm ⁢ RyR_open ⁢ Ca_JSR - Ca_SS$$RyR_open = 1.0 if i = P_O3 ∨ i = P_O4 0.0 otherwise$$dd time Ca_SS = beta_SS ⁢ J_DHPR + J_RyR + V_myo V_SS ⁢ J_xfer$$beta_SS = 1.0 + B_SR ⁢ K_BSR K_BSR + Ca_SS 2.0 + B_SL ⁢ K_BSL K_BSL + Ca_SS 2.0 -1.0$

### Component: sarcoplasmic_reticulum

$dd time Ca_JSR = beta_JSR ⁢ J_tr - V_SS V_JSR ⁢ J_RyR$$beta_JSR = 1.0 + CSQN_tot ⁢ K_CSQN K_CSQN + Ca_JSR 2.0 -1.0$$J_tr = 1.0 tau_tr ⁢ Ca_NSR - Ca_JSR$

### Component: C0

$C0 = C1 ⁢ beta + C_Ca0 ⁢ omega - C0 ⁢ 4.0 ⁢ alpha + C0 ⁢ gamma$

### Component: C1

$C1 = C0 ⁢ 4.0 ⁢ alpha + C2 ⁢ 2.0 ⁢ beta + C_Ca1 ⁢ omega b - C1 ⁢ beta + C1 ⁢ 3.0 ⁢ alpha + C1 ⁢ gamma ⁢ a$

### Component: C2

$C2 = C1 ⁢ 3.0 ⁢ alpha + C3 ⁢ 3.0 ⁢ beta + C_Ca2 ⁢ omega b 2.0 - C2 ⁢ 2.0 ⁢ beta + C2 ⁢ 2.0 ⁢ alpha + C2 ⁢ gamma ⁢ a 2.0$

### Component: C3

$C3 = C2 ⁢ 2.0 ⁢ alpha + C4 ⁢ 4.0 ⁢ beta + C_Ca3 ⁢ omega b 3.0 - C3 ⁢ 3.0 ⁢ beta + C3 ⁢ alpha + C3 ⁢ gamma ⁢ a 3.0$

### Component: C4

$C4 = C3 ⁢ alpha + O ⁢ g + C_Ca4 ⁢ omega b 4.0 - C4 ⁢ 4.0 ⁢ beta + C4 ⁢ f + C4 ⁢ gamma ⁢ a 4.0$

### Component: O

$O = C4 ⁢ f - O ⁢ g$

### Component: C_Ca0

$C_Ca0 = C0 ⁢ gamma + C_Ca1 ⁢ beta_ - C_Ca0 ⁢ 4.0 ⁢ alpha_ + C_Ca0 ⁢ omega$

### Component: C_Ca1

$C_Ca1 = C_Ca0 ⁢ 4.0 ⁢ alpha_ + C_Ca2 ⁢ 2.0 ⁢ beta_ + C1 ⁢ gamma ⁢ a - C_Ca1 ⁢ beta_ + C_Ca1 ⁢ 3.0 ⁢ alpha_ + C_Ca1 ⁢ omega b$

### Component: C_Ca2

$C_Ca2 = C_Ca1 ⁢ 3.0 ⁢ alpha_ + C_Ca3 ⁢ 3.0 ⁢ beta_ + C2 ⁢ gamma ⁢ a 2.0 - C_Ca2 ⁢ 2.0 ⁢ beta_ + C_Ca2 ⁢ 2.0 ⁢ alpha_ + C_Ca2 ⁢ omega b 2.0$

### Component: C_Ca3

$C_Ca3 = C_Ca2 ⁢ 2.0 ⁢ alpha_ + C_Ca4 ⁢ 4.0 ⁢ beta_ + C3 ⁢ gamma ⁢ a 3.0 - C_Ca3 ⁢ 3.0 ⁢ beta_ + C_Ca3 ⁢ alpha_ + C_Ca3 ⁢ omega b 3.0$

### Component: C_Ca4

$C_Ca4 = C_Ca3 ⁢ alpha_ + O_Ca ⁢ g_ + C4 ⁢ gamma ⁢ a 4.0 - C_Ca4 ⁢ 4.0 ⁢ beta_ + C_Ca4 ⁢ f_ + C_Ca4 ⁢ omega b 4.0$

### Component: O_Ca

$O_Ca = C_Ca4 ⁢ f_ - O_Ca ⁢ g_$

### Component: P_C1

$P_C1 = P_C2 ⁢ k21 - P_C1 ⁢ k12$

### Component: P_C2

$P_C2 = P_C1 ⁢ k12 + P_O3 ⁢ k32 + P_C5 ⁢ k52 - P_C2 ⁢ k21 + P_C2 ⁢ k23 + P_C2 ⁢ k25$

### Component: P_O3

$P_O3 = P_C2 ⁢ k23 + P_O4 ⁢ k43 - P_O3 ⁢ k32 + P_O3 ⁢ k34$

### Component: P_O4

$P_O4 = P_O3 ⁢ k34 + P_C5 ⁢ k54 - P_O4 ⁢ k43 + P_O4 ⁢ k45$

### Component: P_C5

$P_C5 = P_C2 ⁢ k25 + P_O4 ⁢ k45 + P_C6 ⁢ k65 - P_C5 ⁢ k52 + P_C5 ⁢ k54 + P_C5 ⁢ k56$

### Component: P_C6

$P_C6 = P_C6 ⁢ k65 - P_C5 ⁢ k56$

### Component: DHPR_transition_probabilities

$gamma = Ca_SS ⁢ 0.1875$$alpha = 0.4 ⁢ⅇ V + 6.0 25.0$$beta = 0.05 ⁢ⅇ- V + 6.0 29.0$$alpha_ = alpha ⁢ a$$beta_ = beta b$

### Component: RyR_transition_probabilities

$k12 = 3.0E6 ⁢ Ca_SS 4.0 2.68 4.0 + Ca_SS 4.0$$k23 = 3.0E7 ⁢ Ca_SS 4.0 2.68 4.0 + Ca_SS 4.0$$k34 = 3.0E6 ⁢ Ca_SS 4.0 2.68 4.0 + Ca_SS 4.0$$k54 = 198.0 ⁢ Ca_SS 4.0 2.68 4.0 + Ca_SS 4.0$$k25 = 3.0E5 ⁢ Ca_SS 4.0 2.68 4.0 + Ca_SS 4.0$$k56 = 3.0E6 ⁢ Ca_SS 4.0 2.68 4.0 + Ca_SS 4.0$
Source
Derived from workspace Rice, Winslow, Jafri, 1999 at changeset 8868a51f5a60.
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