# Model Mathematics

### Component: environment

$dd time cp = alpha ⁢ I_rel - I_d + i_Ca$

### Component: Ca_concentration_in_the_local_JSR

$dd time cf_jsr = I_tr - I_rel$

### Component: release_current

$I_rel = gs ⁢ a ⁢ cf_jsr - cp dd time a = a_infinity - a tau_a a_infinity = cp 2.0 cp 2.0 + cp_ 2.0 tau_a = 1.0 kd ⁢ cp 2.0 + cp_ 2.0$

### Component: diffusion_current

$I_d = cp - cs tau_p$

### Component: transfer_current

$I_tr = cf_nsr - cf_jsr tau_tr$

### Component: L_type_Ca_channel

$I_Ca = M ⁢ Po ⁢ i_Ca Po = d_infinity ⁢ f ⁢ q q_infinity = 1.0 1.0 + cs cs_ gamma tau_q = q_infinity ko alpha_q = q_infinity tau_q beta_q = 1.0 - q_infinity tau_q dd time q = alpha_q ⁢ 1.0 - q - beta_q ⁢ q i_Ca = i_Ca_ ⁢ P_Ca ⁢ 4.0 ⁢ V ⁢ F 2.0 R ⁢ T ⁢ cs ⁢ⅇ 2.0 ⁢ V ⁢ F 2.0 R ⁢ T - 0.341 ⁢ Cao ⅇ 2.0 ⁢ V ⁢ F 2.0 R ⁢ T - 1.0 M$

### Component: L_type_Ca_channel_d_gate

$alpha_d = d_infinity tau_d d_infinity = 1.0 1.0 +ⅇ- V - 5.0 6.24 beta_d = 1.0 - d_infinity tau_d dd time d = alpha_d ⁢ 1.0 - d - beta_d ⁢ d$

### Component: L_type_Ca_channel_f_gate

$alpha_f = f_infinity tau_f f_infinity = 1.0 1.0 +ⅇ V + 35.0 8.6 beta_f = 1.0 - f_infinity tau_f dd time f = alpha_f ⁢ 1.0 - f - beta_f ⁢ f$

### Component: Na_Ca_exchanger

$I_NaCa = K_NaCa ⁢ 1.0 K_mNa 3.0 + Nao 3.0 ⁢ 1.0 K_mCa + Cao ⁢ 1.0 1.0 + K_sat ⁢ⅇ eta - 1.0 ⁢ V ⁢ F R ⁢ T ⁢ⅇ eta ⁢ V ⁢ F R ⁢ T ⁢ Nai 3.0 ⁢ Cao -ⅇ eta - 1.0 ⁢ V ⁢ F R ⁢ T ⁢ Nao 3.0 ⁢ cs$

### Component: uptake_current

$I_up = vup ⁢ ci 2.0 ci 2.0 + cup 2.0$

### Component: calcium_buffering

$dd time CaTi = I_trpn_i I_trpn_i = kT_on ⁢ ci ⁢ BT - CaTi - kT_off ⁢ CaTi beta_ci = 1.0 + BSR ⁢ KSR ci + KSR 2.0 + BCd ⁢ KCd ci + KCd 2.0 -1.0 dd time CaTs = I_trpn_s I_trpn_s = kT_on ⁢ cs ⁢ BT - CaTs - kT_off ⁢ CaTs beta_cs = 1.0 + BSR ⁢ KSR cs + KSR 2.0 + BCd ⁢ KCd cs + KCd 2.0 -1.0$

### Component: Ca_concentration_in_the_submembrane_space

$dd time cs = beta_cs ⁢ vi vs ⁢ I_r - cs - ci taus + I_Ca + I_NaCa - I_trpn_s$

### Component: Ca_concentration_in_the_cytosol

$dd time ci = beta_ci ⁢ cs - ci taus - I_up + I_trpn_i$

### Component: total_Ca_concentration_in_the_SR

$dd time cj = I_up - I_r$

### Component: average_Ca_concentration_in_unrecruited_JSR_compartments

$dd time cj_ = cj - cj_ taua$

### Component: Ca_flux_out_of_the_SR

$I_r =- g ⁢ I_Ca ⁢ Q ⁢ I_r taur N =- g ⁢ I_Ca ⁢ A Q = 0.0 if cj_ < 50.0 ∧ cj_ > 0.0 cj_ - 50.0 if cj_ < 115.0 ∧ cj_ ≥ 50.0 u ⁢ cj_ + s if cj_ ≥ 115.0$

### Component: membrane

$V = Vmin + Vmax - Vmin ⁢ 1.0 - time - m ⁢ T m ⁢ T 2.0 0.5 if time ≦ m ⁢ T + x ⁢ T ∧ time ≥ m ⁢ T Vmin if time < m + 1.0 ⁢ T ∧ time > m ⁢ T + x ⁢ T x = a a + T$

### Component: intracellular_Na_concentration

$Nai = a 1.0 + b ⁢ T 0.5$

### Component: physical_constants_and_ionic_concentrations

Source
Derived from workspace Shiferaw, Watanabe, Garfinkel, Weiss, Karma, 2003 at changeset b21a103f3f16.
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