You are here: Home / Exposures / Yanagihara, Noma, Irisawa, 1980 / Reconstruction of sino-atrial node pacemaker potential based on the voltage clamp experiments

Model Mathematics

Component based math viewer is available

Component: environment

Component: membrane

\frac{d}{d time} (V) = \frac{- (i_Na + i_K + i_Leak + i_s + i_h)}{Cm}

Component: sodium_channel

i_Na = 0.5 m^{3} h (V - 30)

Component: sodium_channel_m_gate

alpha_m = \frac{1 (V + 37)}{(- (ⅇ^{\frac{V + 37}{- 10}})) + 1} beta_m = 40 ⅇ^{\frac{V + 62}{- 17.8}} \frac{d}{d time} (m) = alpha_m (1 - m) - (beta_m m)

Component: sodium_channel_h_gate

alpha_h = 1.209 e -3 ⅇ^{\frac{V + 20}{- 6.534}} beta_h = \frac{1}{1 + ⅇ^{\frac{V + 30}{- 10}}} \frac{d}{d time} (h) = alpha_h (1 - h) - (beta_h h)

Component: potassium_channel

i_K = \frac{0.7 n (ⅇ^{0.0277 (V + 90)} - 1)}{ⅇ^{0.0277 (V + 40)}}

Component: potassium_channel_n_gate

alpha_n = \frac{0.009 1}{1 + ⅇ^{\frac{- (V + 3.8)}{9.71}}} + 0.0006 beta_n = \frac{(- 2.25 e -4) (V + 40)}{1 - (ⅇ^{\frac{V + 40}{13.3}})} \frac{d}{d time} (n) = alpha_n (1 - n) - (beta_n n)

Component: leakage_current

i_Leak = 0.8 (1 - (ⅇ^{\frac{- (V + 60)}{20}}))

Component: calcium_channel

i_s = 12.5 (0.95 d + 0.05) (0.95 f + 0.05) (ⅇ^{\frac{V - 10}{15}} - 1)

Component: calcium_channel_d_gate

alpha_d = \frac{0.0145 (V + 35)}{1 - (ⅇ^{\frac{- (V + 35)}{2.5}})} + \frac{0.03125 V}{1 - (ⅇ^{\frac{- V}{4.8}})} beta_d = \frac{(- 4.21 e -3) (V - 5)}{(- (ⅇ^{\frac{V - 5}{2.5}})) + 1} \frac{d}{d time} (d) = alpha_d (1 - d) - (beta_d d)

Component: calcium_channel_f_gate

alpha_f = \frac{(- 3.55 e -4) (V + 20)}{(- (ⅇ^{\frac{V + 20}{5.633}})) + 1} beta_f = \frac{0.000944 (V + 60)}{1 + ⅇ^{\frac{- (V + 29.5)}{4.16}}} \frac{d}{d time} (f) = alpha_f (1 - f) - (beta_f f)

Component: hyperpolarization_activated_channel

i_h = 0.4 q (V + 45)

Component: hyperpolarization_activated_channel_q_gate

alpha_q = \frac{0.00034 (V + 100)}{ⅇ^{\frac{V + 100}{4.4}} - 1} + 0.0000495 beta_q = \frac{0.0005 (V + 40)}{1 - (ⅇ^{\frac{- (V + 40)}{6}})} + 0.0000845 \frac{d}{d time} (q) = alpha_q (1 - q) - (beta_q q)

Source: Derived from workspace Yanagihara 1980 at changeset 17c2f541f211.

Collaboration: To begin collaborating on this work, please use your git client and issue this command:

Downloads

Views Available

Tools

License: This work is licensed under a Creative Commons Attribution 3.0 Unported License.

Reconstruction of sino-atrial node pacemaker potential based on the voltage clamp experiments