Model Mathematics

\frac{d}{d time} (C_m_Na) = - (J_mc_Na + J_ms_Na) \frac{d}{d time} (C_s_Na) = J_ms_Na - J_sc_Na \frac{d}{d time} (C_c_Na) = J_mc_Na + J_sc_Na \frac{d}{d time} (C_m_K) = - (J_mc_K + J_ms_K) \frac{d}{d time} (C_s_K) = J_ms_K - J_sc_K \frac{d}{d time} (C_c_K) = J_mc_K + J_sc_K \frac{d}{d time} (C_m_Cl) = - (J_mc_Cl + J_ms_Cl) \frac{d}{d time} (C_s_Cl) = J_ms_Cl - J_sc_Cl \frac{d}{d time} (C_c_Cl) = J_mc_Cl + J_sc_Cl

J_mc_Na = J_mc_NaCl + G_mc_Na G_mc_Na = P_mc_Na \frac{F (psi_m - psi_c)}{RT} \frac{C_m_Na - (C_c_Na ⅇ^{(- (\frac{F}{RT})) (psi_m - psi_c)})}{1.0 - (ⅇ^{(- (\frac{F}{RT})) (psi_m - psi_c)})} J_mc_NaCl = J_mc_NaCl_max \frac{\frac{C_m_Na}{K_mc_Na_NaCl} \frac{C_m_Cl}{K_mc_Cl_NaCl} - (\frac{C_c_Na}{K_mc_Na_NaCl} \frac{C_c_Cl}{K_mc_Cl_NaCl})}{(1.0 + \frac{C_m_Na}{K_mc_Na_NaCl} \frac{C_m_Cl}{K_mc_Cl_NaCl}) (1.0 + \frac{C_c_Na}{K_mc_Na_NaCl}) (1.0 + \frac{C_c_Cl}{K_mc_Cl_NaCl}) + (1.0 + \frac{C_c_Na}{K_mc_Na_NaCl} \frac{C_c_Cl}{K_mc_Cl_NaCl}) (1.0 + \frac{C_m_Na}{K_mc_Na_NaCl}) (1.0 + \frac{C_m_Cl}{K_mc_Cl_NaCl})}

J_mc_K = J_mc_KCl + G_mc_K G_mc_K = P_mc_K \frac{F (psi_m - psi_c)}{RT} \frac{C_m_K - (C_c_K ⅇ^{(- (\frac{F}{RT})) (psi_m - psi_c)})}{1.0 - (ⅇ^{(- (\frac{F}{RT})) (psi_m - psi_c)})} J_mc_KCl = J_mc_KCl_max \frac{\frac{C_m_K}{K_mc_K_KCl} \frac{C_m_Cl}{K_mc_Cl_KCl} - (\frac{C_c_K}{K_mc_K_KCl} \frac{C_c_Cl}{K_mc_Cl_KCl})}{(1.0 + \frac{C_m_K}{K_mc_K_KCl} \frac{C_m_Cl}{K_mc_Cl_KCl}) (1.0 + \frac{C_c_K}{K_mc_K_KCl}) (1.0 + \frac{C_c_Cl}{K_mc_Cl_KCl}) + (1.0 + \frac{C_c_K}{K_mc_K_KCl} \frac{C_c_Cl}{K_mc_Cl_KCl}) (1.0 + \frac{C_m_K}{K_mc_K_KCl}) (1.0 + \frac{C_m_Cl}{K_mc_Cl_KCl})}

J_mc_Cl = J_mc_NaCl + J_mc_KCl + G_mc_Cl G_mc_Cl = P_mc_Cl \frac{(-1.0) F (psi_m - psi_c)}{RT} \frac{C_m_Cl - (C_c_Cl ⅇ^{(- (\frac{(-1.0) F}{RT})) (psi_m - psi_c)})}{1.0 - (ⅇ^{(- (\frac{(-1.0) F}{RT})) (psi_m - psi_c)})}

J_sc_Na = (-3.0) J_a J_a = J_a_max \frac{1.0}{1.0 + {(\frac{K_Na_ATPase}{C_c_Na})}^{3.0}}

J_sc_K = 2.0 J_a + G_sc_K G_sc_K = P_sc_K \frac{F (psi_s - psi_c)}{RT} \frac{C_s_K - (C_c_K ⅇ^{(- (\frac{F}{RT})) (psi_s - psi_c)})}{1.0 - (ⅇ^{(- (\frac{F}{RT})) (psi_s - psi_c)})}

J_sc_Cl = G_sc_Cl G_sc_Cl = P_sc_Cl \frac{(-1.0) F (psi_s - psi_c)}{RT} \frac{C_s_Cl - (C_c_Cl ⅇ^{(- (\frac{(-1.0) F}{RT})) (psi_s - psi_c)})}{1.0 - (ⅇ^{(- (\frac{(-1.0) F}{RT})) (psi_s - psi_c)})}

J_ms_Na = G_ms_Na G_ms_Na = P_ms_Na \frac{F (psi_m - psi_s)}{RT} \frac{C_m_Na - (C_s_Na ⅇ^{(- (\frac{F}{RT})) (psi_m - psi_s)})}{1.0 - (ⅇ^{(- (\frac{F}{RT})) (psi_m - psi_s)})}

J_ms_K = G_ms_K G_ms_K = P_ms_K \frac{F (psi_m - psi_s)}{RT} \frac{C_m_K - (C_s_K ⅇ^{(- (\frac{F}{RT})) (psi_m - psi_s)})}{1.0 - (ⅇ^{(- (\frac{F}{RT})) (psi_m - psi_s)})}

J_ms_Cl = G_ms_Cl G_ms_Cl = P_ms_Cl \frac{(-1.0) F (psi_m - psi_s)}{RT} \frac{C_m_Cl - (C_s_Cl ⅇ^{(- (\frac{(-1.0) F}{RT})) (psi_m - psi_s)})}{1.0 - (ⅇ^{(- (\frac{(-1.0) F}{RT})) (psi_m - psi_s)})}

J_Na = J_mc_Na + J_ms_Na

J_K = J_mc_K + J_ms_K

J_Cl = J_mc_Cl + J_ms_Cl

Osm_m = C_m_Na + C_m_K + C_m_Cl + C_m_Imp Osm_c = C_c_Na + C_c_K + C_c_Cl + C_c_Imp Osm_s = C_s_Na + C_s_K + C_s_Cl + C_s_Imp

J_mc_v = L_mc_v RT (Osm_m - Osm_c)

J_ms_v = L_ms_v RT (Osm_m - Osm_s)

J_sc_v = L_sc_v RT (Osm_s - Osm_c)

J_v = J_mc_v + J_ms_v