# Model Mathematics

### Component: membrane

$dd time V =- 1.0 Cm ⁢ i_Na + i_Ca + i_K + i_K_A + i_K_Ca + i_L$

### Component: sodium_channel

$i_Na = g_Na ⁢ m 3.0 ⁢ h ⁢ V - E_Na$

### Component: sodium_channel_m_gate

$alpha_m = -0.6 ⁢ V + 30.0 ⅇ -0.1 ⁢ V + 30.0 - 1.0 beta_m = 20.0 ⁢ⅇ- V + 55.0 18.0 dd time m = alpha_m ⁢ 1.0 - m - beta_m ⁢ m$

### Component: sodium_channel_h_gate

$alpha_h = 0.4 ⁢ⅇ- V + 50.0 20.0 beta_h = 6.0 ⅇ -0.1 ⁢ V + 20.0 + 1.0 dd time h = alpha_h ⁢ 1.0 - h - beta_h ⁢ h$

### Component: calcium_channel

$i_Ca = g_Ca ⁢ c 3.0 ⁢ V - E_Ca E_Ca = R ⁢ T 2.0 ⁢ F ⁢ln⁡ Ca_e Ca_i$

### Component: calcium_channel_c_gate

$alpha_c = -0.3 ⁢ V + 13.0 ⅇ -0.1 ⁢ V + 13.0 - 1.0 beta_c = 10.0 ⁢ⅇ- V + 38.0 18.0 dd time c = alpha_c ⁢ 1.0 - c - beta_c ⁢ c$

### Component: delayed_rectifier_potassium_channel

$i_K = g_K ⁢ n 4.0 ⁢ V - E_K$

### Component: delayed_rectifier_potassium_channel_n_gate

$alpha_n = -0.02 ⁢ V + 40.0 ⅇ -0.1 ⁢ V + 40.0 - 1.0 beta_n = 0.4 ⁢ⅇ- V + 50.0 80.0 dd time n = alpha_n ⁢ 1.0 - n - beta_n ⁢ n$

### Component: A_type_potassium_channel

$i_K_A = g_K_A ⁢ a 3.0 ⁢ h ⁢ V - E_K$

### Component: A_type_potassium_channel_a_gate

$alpha_a = -0.006 ⁢ V + 90.0 ⅇ -0.1 ⁢ V + 90.0 - 1.0 beta_a = 0.1 ⁢ⅇ- V + 30.0 10.0 dd time a = alpha_a ⁢ 1.0 - a - beta_a ⁢ a$

### Component: A_type_potassium_channel_h_gate

$alpha_h = 0.04 ⁢ⅇ- V + 70.0 20.0 beta_h = 0.6 ⅇ -0.1 ⁢ V + 40.0 + 1.0 dd time h = alpha_h ⁢ 1.0 - h - beta_h ⁢ h$

### Component: calcium_activated_potassium_channel

$i_K_Ca = g_K_Ca ⁢ V - E_K g_K_Ca_gate = g_K_Ca ⁢ Ca_i Ca_diss 2.0 1.0 + Ca_i Ca_diss 2.0$

### Component: leakage_channel

$i_L = g_L ⁢ V - E_L$

### Component: parameters

$dd time Ca_i = -3.0 ⁢ i_Ca 2.0 ⁢ F ⁢ r - Ca_i - Ca_res tau_Ca$
Source
Derived from workspace Fohlmeister, Miller, 1997 at changeset 5ae153e5c645.
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