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Model Mathematics

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Component: output

Component: clamp_para

KCl = X Clo = 147 + KCl

Component: free_para

Component: noise_G

Component: SMC

Component: Cai

\frac{d}{d t} (c_i) = ((J_IP3i + J_VOCCi - J_NCXi - J_SERCAi) + J_CICRi - J_PMCAi) + J_leaki

Component: Casr

\frac{d}{d t} (s_i) = J_SERCAi - J_CICRi - J_leaki

Component: IP3

\frac{d}{d t} (I_i) = J_PLCagonisti + J_PLC_delta_i - J_degradi

Component: JCICRi

J_CICRi = C \frac{{s_i}^{2}}{{s_i}^{2} + {s_c}^{2}} \frac{{c_i}^{4}}{{c_i}^{4} + {c_c}^{4}}

Component: JCli

J_Cli = G_Cl (v_i - v_Cl)

Component: E_Na

Component: E_Ca

Component: E_K

Component: E_Cl

Component: Nernst_potential

E = \frac{R T}{z F} \ln (\frac{X_o}{X_i})

Component: Nernst_potential

E = \frac{R T}{z F} \ln (\frac{X_o}{X_i})

Component: Nernst_potential

E = \frac{R T}{z F} \ln (\frac{X_o}{X_i})

Component: Nernst_potential

E = \frac{R T}{z F} \ln (\frac{X_o}{X_i})

Component: JIP3i

J_IP3i = F_IP3 \frac{{I_i}^{2}}{{K_r}^{2} + {I_i}^{2}}

Component: JKi

J_Ki = G_Ki w_i (v_i - v_K) \frac{d}{d t} (w_i) = lambda (K_activationi - w_i) K_activationi = \frac{{(c_i + c_w)}^{2}}{{(c_i + c_w)}^{2} + beta ⅇ^{\frac{- (v_i - v_Ca3)}{R_K}}}

Component: E_Na

Component: E_Ca

Component: E_K

Component: E_Cl

Component: E_NaComp

E = \frac{R T}{z F} \ln (\frac{X_o}{X_i})

Component: E_CaComp

E = \frac{R T}{z F} \ln (\frac{X_o}{X_i})

Component: E_KComp

E = \frac{R T}{z F} \ln (\frac{X_o}{X_i})

Component: E_ClComp

E = \frac{R T}{z F} \ln (\frac{X_o}{X_i})

Component: JNCXi

J_NCXi = G_NCX \frac{c_i}{c_i + c_NCX} (v_NCX - v_i)

Component: JNKAi

J_NKAi = F_NKA

Component: JPLCdeltai

J_PLC_delta_i = E \frac{{c_i}^{2}}{{K_Ca}^{2} + {c_i}^{2}}

Component: JPMCAi

J_PMCAi = D c_i (1 + \frac{v_i - v_d}{R_d})

Component: JSERCAi

J_SERCAi = B \frac{{c_i}^{2}}{{c_i}^{2} + {c_b}^{2}}

Component: JVOCCi

J_VOCCi = G_Ca \frac{v_Ca1 - v_i}{1 + ⅇ^{\frac{v_Ca2 - v_i}{R_Ca}}}

Component: Jdegradi

J_degradi = k I_i

Component: Jleaki

J_leaki = L s_i

Component: Vm

\frac{d}{d t} (v_i) = gamma ((- J_NKAi - J_Cli) + 2 J_VOCCi + J_NCXi - J_Ki)

Component: Para

Component: X_clamp_protocol

X = \{\begin{matrix} X_Holding if time < t_ss \\ X_Test if time \geq t_ss \land time < t_act + t_ss \\ X_Holding otherwise \end{matrix}

Component: time_ms

Component: time_s

Source: Derived from workspace Modeling the Recruitment and Synchronization of SMCs (Koenigsberger et al. 2004) at changeset eb9b6ae06871.

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SMC_KCl_noise.cellml