1 | |
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2 | ;; Reference: Theta-Frequency Bursting and Resonance in Cerebellar Granule Cells:Experimental |
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3 | ;; Evidence and Modeling of a Slow K+-Dependent Mechanism |
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4 | ;; Egidio D'Angelo,Thierry Nieus,Arianna Maffei,Simona Armano,Paola Rossi,Vanni Taglietti, |
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5 | ;; Andrea Fontana and Giovanni Naldi |
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6 | |
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7 | (nemo-model CGC |
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8 | |
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9 | ( |
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10 | (input v celsius) |
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11 | |
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12 | (defun sigm (x y) (1 / (exp (x / y) + 1))) |
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13 | |
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14 | (defun linoid (x y) |
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15 | (if ((abs (x / y)) < 1e-6) |
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16 | then (y * (1 - ((x / y) / 2))) |
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17 | else (x / (exp (x / y) - 1)) |
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18 | )) |
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19 | |
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20 | (component (type decaying-pool) (name ca) |
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21 | |
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22 | (input |
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23 | (cai from ion-pools) |
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24 | (ica from ion-currents)) |
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25 | |
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26 | (const F = 96485.0) |
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27 | (const d = .2) |
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28 | (const cao = 2.) |
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29 | (const cai0 = 1e-4) |
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30 | (const beta = 1.5) |
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31 | |
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32 | (d (ca) = ((neg (ica) / (2 * F * d)) * 1e4 - |
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33 | (beta * (cai - cai0))) |
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34 | (initial cai0)) |
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35 | |
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36 | (output ca) |
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37 | ) |
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38 | |
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39 | |
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40 | (component (type ionic-current) (name CaHVA ) |
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41 | |
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42 | (component (type gate) |
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43 | |
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44 | ;; rate constants |
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45 | |
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46 | (Q10 = (pow (3 ((celsius - 20) / 10)))) |
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47 | |
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48 | (const Aalpha_s = 0.04944) |
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49 | (const Kalpha_s = 15.87301587302) |
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50 | (const V0alpha_s = -29.06) |
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51 | |
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52 | (const Abeta_s = 0.08298) |
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53 | (const Kbeta_s = -25.641) |
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54 | (const V0beta_s = -18.66) |
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55 | |
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56 | (const Aalpha_u = 0.0013) |
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57 | (const Kalpha_u = -18.183) |
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58 | (const V0alpha_u = -48) |
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59 | |
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60 | (const Abeta_u = 0.0013) |
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61 | (const Kbeta_u = 83.33) |
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62 | (const V0beta_u = -48) |
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63 | |
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64 | ;; rate functions |
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65 | |
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66 | (defun alpha_s (v Q10) |
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67 | (Q10 * Aalpha_s * exp((v - V0alpha_s) / Kalpha_s))) |
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68 | |
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69 | (defun beta_s (v Q10) |
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70 | (Q10 * Abeta_s * exp((v - V0beta_s) / Kbeta_s))) |
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71 | |
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72 | (defun alpha_u (v Q10) |
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73 | (Q10 * Aalpha_u * exp((v - V0alpha_u) / Kalpha_u))) |
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74 | |
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75 | (defun beta_u (v Q10) |
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76 | (Q10 * Abeta_u * exp((v - V0beta_u) / Kbeta_u))) |
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77 | |
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78 | |
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79 | (hh-ionic-gate |
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80 | (CaHVA ;; ion name: exported variables will be of the form {ion}_{id} |
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81 | (initial-m ((alpha_s (v Q10))/(alpha_s (v Q10) + beta_s (v Q10)) )) |
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82 | (initial-h ((alpha_u (v Q10))/(alpha_u (v Q10) + beta_u (v Q10)) )) |
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83 | (m-power 2) |
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84 | (h-power 1) |
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85 | (m-alpha (alpha_s (v Q10))) |
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86 | (m-beta (beta_s (v Q10))) |
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87 | (h-alpha (alpha_u (v Q10))) |
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88 | (h-beta (beta_u (v Q10))) |
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89 | )) |
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90 | |
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91 | |
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92 | ) |
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93 | |
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94 | (component (type pore) |
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95 | (const gbar = 0.00046) |
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96 | (output gbar )) |
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97 | |
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98 | (component (type permeating-ion) (name ca) |
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99 | (const e = 129.33) |
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100 | (output e )) |
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101 | |
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102 | ) ;; end CaHVA current |
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103 | |
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104 | (component (type voltage-clamp) (name CaHVA) |
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105 | |
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106 | (const vchold = -71) |
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107 | (const vcbase = -69) |
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108 | (const vcinc = 10) |
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109 | (const vcsteps = 8) |
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110 | (const vchdur = 30) |
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111 | (const vcbdur = 100) |
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112 | |
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113 | (output vchold vcbase vcinc vcsteps vchdur vcbdur) |
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114 | ) |
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115 | |
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116 | |
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117 | |
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118 | (component (type ionic-current) (name KA ) |
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119 | |
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120 | (component (type gate) |
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121 | |
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122 | ;; rate constants |
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123 | |
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124 | (Q10 = (pow (3 ((celsius - 25.5) / 10)))) |
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125 | |
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126 | (const Aalpha_a = 0.8147) |
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127 | (const Kalpha_a = -23.32708) |
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128 | (const V0alpha_a = -9.17203) |
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129 | (const Abeta_a = 0.1655) |
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130 | (const Kbeta_a = 19.47175) |
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131 | (const V0beta_a = -18.27914) |
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132 | |
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133 | (const Aalpha_b = 0.0368) |
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134 | (const Kalpha_b = 12.8433) |
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135 | (const V0alpha_b = -111.33209) |
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136 | (const Abeta_b = 0.0345) |
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137 | (const Kbeta_b = -8.90123) |
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138 | (const V0beta_b = -49.9537) |
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139 | |
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140 | (const V0_ainf = -38) |
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141 | (const K_ainf = -17) |
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142 | |
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143 | (const V0_binf = -78.8) |
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144 | (const K_binf = 8.4) |
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145 | |
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146 | |
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147 | ;; rate functions |
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148 | |
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149 | (defun alpha_a (v) |
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150 | (Q10 * Aalpha_a * sigm((v - V0alpha_a) Kalpha_a))) |
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151 | |
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152 | (defun beta_a (v) |
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153 | (Q10 * (Abeta_a / exp((v - V0beta_a) / Kbeta_a)))) |
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154 | |
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155 | (defun alpha_b (v) |
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156 | (Q10 * Aalpha_b * sigm((v - V0alpha_b) Kalpha_b))) |
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157 | |
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158 | (defun beta_b (v) |
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159 | (Q10 * Abeta_b * sigm((v - V0beta_b) Kbeta_b))) |
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160 | |
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161 | |
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162 | |
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163 | (a_inf = (1 / (1 + exp ((v - V0_ainf) / K_ainf)))) |
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164 | (tau_a = (1 / (alpha_a (v) + beta_a (v)) )) |
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165 | (b_inf = (1 / (1 + exp ((v - V0_binf) / K_binf)))) |
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166 | (tau_b = (1 / (alpha_b (v) + beta_b (v)) )) |
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167 | |
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168 | (hh-ionic-gate |
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169 | (KA ;; ion name: exported variables will be of the form {ion}_{id} |
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170 | (initial-m (1 / (1 + exp ((v - V0_ainf) / K_ainf))) ) |
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171 | (initial-h (1 / (1 + exp ((v - V0_binf) / K_binf))) ) |
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172 | (m-power 3) |
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173 | (h-power 1) |
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174 | (m-inf a_inf) |
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175 | (m-tau tau_a) |
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176 | (h-inf b_inf) |
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177 | (h-tau tau_b) |
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178 | )) |
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179 | |
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180 | ) |
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181 | |
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182 | |
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183 | (component (type pore) |
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184 | (const gbar = 0.0032) |
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185 | (output gbar )) |
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186 | |
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187 | |
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188 | (component (type permeating-ion) (name k) |
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189 | (const e = -84.69) |
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190 | (output e )) |
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191 | |
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192 | ) ;; end KA current |
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193 | |
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194 | |
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195 | (component (type voltage-clamp) (name KA) |
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196 | |
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197 | (const vchold = -71) |
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198 | (const vcbase = -69) |
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199 | (const vcinc = 10) |
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200 | (const vcsteps = 8) |
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201 | (const vchdur = 30) |
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202 | (const vcbdur = 100) |
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203 | |
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204 | (output vchold vcbase vcinc vcsteps vchdur vcbdur) |
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205 | ) |
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206 | |
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207 | |
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208 | (component (type ionic-current) (name KCa ) |
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209 | |
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210 | |
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211 | (input |
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212 | (cai from ion-pools)) |
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213 | |
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214 | |
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215 | (component (type gate) |
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216 | |
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217 | ;; rate constants |
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218 | (Q10 = (pow (3 ((celsius - 30) / 10)))) |
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219 | |
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220 | (const Aalpha_c = 2.5) |
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221 | (const Balpha_c = 1.5e-3) |
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222 | |
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223 | (const Kalpha_c = -11.765) |
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224 | |
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225 | (const Abeta_c = 1.5) |
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226 | (const Bbeta_c = 0.15e-3) |
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227 | |
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228 | (const Kbeta_c = -11.765) |
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229 | |
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230 | ;; rate functions |
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231 | (defun alpha_c (v cai Q10) |
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232 | (Q10 * Aalpha_c / (1 + (Balpha_c * exp(v / Kalpha_c) / cai)))) |
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233 | |
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234 | (defun beta_c (v cai Q10) |
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235 | (Q10 * Abeta_c / (1 + (cai / (Bbeta_c * exp (v / Kbeta_c))) ))) |
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236 | |
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237 | |
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238 | (hh-ionic-gate |
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239 | (KCa ;; ion name: exported variables will be of the form {ion}_{id} |
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240 | (initial-m ((alpha_c (v cai Q10)) / (alpha_c (v cai Q10) + beta_c (v cai Q10)) )) |
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241 | (m-power 1) |
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242 | (h-power 0) |
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243 | (m-alpha (alpha_c (v cai Q10))) |
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244 | (m-beta (beta_c (v cai Q10))) |
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245 | )) |
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246 | |
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247 | ) |
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248 | |
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249 | (component (type pore) |
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250 | (const gbar = 0.003) |
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251 | (output gbar )) |
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252 | |
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253 | |
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254 | (component (type permeating-ion) (name k) |
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255 | (const e = -84.69) |
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256 | (output e )) |
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257 | |
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258 | (component (type modulating-ion) (name ca) |
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259 | ) |
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260 | |
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261 | ) ;; end KCa current |
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262 | |
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263 | (component (type voltage-clamp) (name KCa) |
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264 | |
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265 | (const vchold = -71) |
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266 | (const vcbase = -69) |
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267 | (const vcinc = 10) |
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268 | (const vcsteps = 8) |
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269 | (const vchdur = 30) |
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270 | (const vcbdur = 100) |
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271 | |
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272 | (output vchold vcbase vcinc vcsteps vchdur vcbdur) |
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273 | ) |
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274 | |
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275 | |
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276 | |
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277 | (component (type ionic-current) (name Kir ) |
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278 | |
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279 | (component (type gate) |
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280 | |
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281 | ;; rate constants |
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282 | (Q10 = (pow (3 ((celsius - 30) / 10)))) |
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283 | |
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284 | (const Aalpha_d = 0.13289) |
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285 | (const Kalpha_d = -24.3902) |
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286 | |
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287 | (const V0alpha_d = -83.94) |
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288 | (const Abeta_d = 0.16994) |
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289 | |
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290 | (const Kbeta_d = 35.714) |
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291 | (const V0beta_d = -83.94) |
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292 | |
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293 | ;; rate functions |
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294 | (defun alpha_d (v Q10) |
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295 | (Q10 * Aalpha_d * exp((v - V0alpha_d) / Kalpha_d))) |
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296 | |
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297 | (defun beta_d (v Q10) |
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298 | (Q10 * Abeta_d * exp((v - V0beta_d) / Kbeta_d) )) |
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299 | |
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300 | (hh-ionic-gate |
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301 | (Kir ;; ion name: exported variables will be of the form {ion}_{id} |
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302 | (initial-m ((alpha_d (v Q10)) / (alpha_d (v Q10) + beta_d (v Q10)) )) |
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303 | (m-power 1) |
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304 | (h-power 0) |
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305 | (m-alpha (alpha_d (v Q10))) |
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306 | (m-beta (beta_d (v Q10))) |
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307 | )) |
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308 | |
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309 | ) |
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310 | |
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311 | |
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312 | (component (type pore) |
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313 | (const gbar = 0.0009) |
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314 | (output gbar )) |
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315 | |
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316 | |
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317 | (component (type permeating-ion) (name k) |
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318 | (const e = -84.69) |
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319 | (output e )) |
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320 | |
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321 | ) ;; end Kir current |
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322 | |
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323 | |
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324 | |
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325 | (component (type voltage-clamp) (name Kir) |
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326 | |
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327 | (const vchold = -71) |
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328 | (const vcbase = -69) |
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329 | (const vcinc = 10) |
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330 | (const vcsteps = 8) |
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331 | (const vchdur = 30) |
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332 | (const vcbdur = 100) |
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333 | |
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334 | (output vchold vcbase vcinc vcsteps vchdur vcbdur) |
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335 | ) |
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336 | |
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337 | |
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338 | (component (type ionic-current) (name KM ) |
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339 | |
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340 | (component (type gate) |
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341 | |
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342 | ;; rate constants |
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343 | (const Aalpha_n = 0.0033) |
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344 | |
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345 | (const Kalpha_n = 40) |
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346 | (const V0alpha_n = -30) |
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347 | (const Abeta_n = 0.0033) |
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348 | |
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349 | (const Kbeta_n = -20) |
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350 | (const V0beta_n = -30) |
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351 | (const V0_ninf = -30) |
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352 | (const B_ninf = 6) |
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353 | |
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354 | (Q10 = (pow (3 ((celsius - 22) / 10)))) |
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355 | |
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356 | ;; rate equations |
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357 | (defun alpha_n (v Q10) |
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358 | (Q10 * Aalpha_n * exp((v - V0alpha_n) / Kalpha_n) )) |
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359 | |
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360 | (defun beta_n (v Q10) |
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361 | (Q10 * Abeta_n * exp((v - V0beta_n) / Kbeta_n) )) |
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362 | |
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363 | (hh-ionic-gate |
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364 | (KM ;; ion name: exported variables will be of the form {ion}_{id} |
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365 | (initial-m (alpha_n (v Q10)) / (alpha_n (v Q10) + beta_n (v Q10)) ) |
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366 | (m-power 1) |
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367 | (h-power 0) |
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368 | (m-tau (1 / (alpha_n(v Q10) + beta_n (v Q10)) )) |
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369 | (m-inf (1 / (1 + exp((neg (v - V0_ninf)) / B_ninf)))) |
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370 | )) |
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371 | ) |
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372 | |
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373 | (component (type pore) |
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374 | (const gbar = 0.00025) |
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375 | (output gbar )) |
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376 | |
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377 | (component (type permeating-ion) (name k) |
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378 | (const e = -84.69) |
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379 | (output e )) |
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380 | |
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381 | ) ;; end KM current |
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382 | |
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383 | |
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384 | (component (type voltage-clamp) (name KM) |
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385 | |
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386 | (const vchold = -71) |
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387 | (const vcbase = -69) |
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388 | (const vcinc = 10) |
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389 | (const vcsteps = 8) |
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390 | (const vchdur = 30) |
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391 | (const vcbdur = 100) |
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392 | |
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393 | (output vchold vcbase vcinc vcsteps vchdur vcbdur) |
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394 | ) |
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395 | |
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396 | (component (type ionic-current) (name KV ) |
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397 | |
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398 | (component (type gate) |
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399 | |
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400 | ;; rate constants |
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401 | (Q10 = (pow (3 ((celsius - 6.3) / 10)))) |
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402 | |
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403 | (const Aalpha_n = -0.01) |
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404 | (const Kalpha_n = -10) |
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405 | (const V0alpha_n = -25) |
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406 | (const Abeta_n = 0.125) |
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407 | |
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408 | (const Kbeta_n = -80) |
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409 | (const V0beta_n = -35) |
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410 | |
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411 | ;; rate functions |
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412 | (defun alpha_n (v Q10) |
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413 | (Q10 * Aalpha_n * linoid ((v - V0alpha_n) Kalpha_n))) |
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414 | |
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415 | (defun beta_n (v Q10) |
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416 | (Q10 * Abeta_n * exp((v - V0beta_n) / Kbeta_n) )) |
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417 | |
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418 | (hh-ionic-gate |
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419 | (KV ;; ion name: exported variables will be of the form {ion}_{id} |
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420 | (initial-m ((alpha_n (v Q10)) / (alpha_n (v Q10) + beta_n (v Q10)) )) |
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421 | (m-power 4) |
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422 | (h-power 0) |
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423 | (m-alpha (alpha_n(v Q10))) |
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424 | (m-beta (beta_n(v Q10))) |
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425 | )) |
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426 | ) |
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427 | |
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428 | (component (type pore) |
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429 | (const gbar = 0.003) |
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430 | (output gbar )) |
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431 | |
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432 | (component (type permeating-ion) (name k) |
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433 | (const e = -84.69) |
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434 | (output e )) |
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435 | |
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436 | ) ;; end KV current |
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437 | |
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438 | |
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439 | (component (type voltage-clamp) (name KV) |
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440 | |
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441 | (const vchold = -71) |
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442 | (const vcbase = -69) |
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443 | (const vcinc = 10) |
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444 | (const vcsteps = 8) |
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445 | (const vchdur = 30) |
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446 | (const vcbdur = 100) |
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447 | |
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448 | (output vchold vcbase vcinc vcsteps vchdur vcbdur) |
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449 | ) |
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450 | |
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451 | |
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452 | (component (type ionic-current) (name Lkg1) |
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453 | |
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454 | (component (type pore) |
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455 | (const gbar = (5.68e-5)) |
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456 | (output gbar)) |
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457 | |
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458 | (component (type permeating-ion) (name non-specific) |
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459 | (const e = -16.5) |
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460 | (output e )) |
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461 | |
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462 | ) ;; end leak current |
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463 | |
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464 | |
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465 | (component (type ionic-current) (name Lkg2) |
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466 | |
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467 | (component (type pore) |
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468 | (const ggaba = (3e-5)) |
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469 | (output ggaba)) |
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470 | |
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471 | (component (type permeating-ion) (name non-specific) |
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472 | (const egaba = -65) |
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473 | (output egaba )) |
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474 | |
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475 | ) ;; end leak current |
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476 | |
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477 | |
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478 | (component (type ionic-current) (name Na ) |
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479 | |
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480 | (component (type gate) |
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481 | |
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482 | ;; rate constants |
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483 | (Q10 = (pow (3 ((celsius - 20) / 10)))) |
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484 | |
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485 | (const Aalfa = 353.91) |
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486 | (const Valfa = 13.99) |
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487 | (const Abeta = 1.272) |
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488 | (const Vbeta = 13.99) |
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489 | (const Agamma = 150) |
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490 | (const Adelta = 40) |
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491 | (const Aepsilon = 1.75) |
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492 | (const Ateta = 0.0201) |
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493 | (const Vteta = 25) |
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494 | (const ACon = 0.005) |
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495 | (const ACoff = 0.5) |
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496 | (const AOon = 0.75) |
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497 | (const AOoff = 0.005) |
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498 | (const n1 = 5.422) |
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499 | (const n2 = 3.279) |
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500 | (const n3 = 1.83) |
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501 | (const n4 = 0.738) |
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502 | |
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503 | (gamma = (Q10 * Agamma)) |
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504 | (delta = (Q10 * Adelta)) |
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505 | (epsilon = (Q10 * Aepsilon)) |
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506 | (Con = (Q10 * ACon)) |
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507 | (Coff = (Q10 * ACoff)) |
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508 | (Oon = (Q10 * AOon)) |
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509 | (Ooff = (Q10 * AOoff)) |
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510 | (a = (pow ((Oon / Con) (1.0 / 4.0)))) |
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511 | (b = (pow ((Ooff/Coff) (1.0 / 4.0)))) |
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512 | |
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513 | ;; rate functions |
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514 | (defun alfa (v Q10) |
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515 | (Q10 * Aalfa * exp (v / Valfa))) |
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516 | |
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517 | (defun beta (v Q10) |
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518 | (Q10 * Abeta * exp(((neg v) / Vbeta)))) |
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519 | |
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520 | (defun teta (v Q10) |
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521 | (Q10 * Ateta * exp(((neg v) / Vteta)))) |
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522 | |
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523 | |
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524 | (reaction |
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525 | (Na_z |
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526 | (transitions |
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527 | (<-> C1 C2 (n1 * alfa (v Q10)) (n4 * beta (v Q10))) |
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528 | (<-> C2 C3 (n2 * alfa (v Q10)) (n3 * beta (v Q10))) |
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529 | (<-> C3 C4 (n3 * alfa (v Q10)) (n2 * beta (v Q10))) |
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530 | (<-> C4 C5 (n4 * alfa (v Q10)) (n1 * beta (v Q10))) |
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531 | (<-> C5 O gamma delta) |
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532 | (<-> O B epsilon (teta (v Q10))) |
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533 | |
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534 | (<-> I1 I2 (n1 * alfa (v Q10) * a) (n4 * beta (v Q10) * b)) |
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535 | (<-> I2 I3 (n2 * alfa (v Q10) * a) (n3 * beta (v Q10) * b)) |
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536 | (<-> I3 I4 (n3 * alfa (v Q10) * a) (n2 * beta (v Q10) * b)) |
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537 | (<-> I4 I5 (n4 * alfa (v Q10) * a) (n1 * beta (v Q10) * b)) |
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538 | (<-> I5 I6 gamma delta) |
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539 | |
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540 | (<-> C1 I1 Con Coff) |
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541 | (<-> C2 I2 (Con * a) (Coff * b)) |
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542 | (<-> C3 I3 (Con * pow (a, 2)) (Coff * pow (b,2))) |
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543 | (<-> C4 I4 (Con * pow (a, 3)) (Coff * pow (b, 3))) |
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544 | (<-> C5 I5 (Con * pow (a, 4)) (Coff * pow (b, 4))) |
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545 | |
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546 | (O <-> I6 Oon Ooff) |
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547 | |
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548 | (conserve (1 = (C1 + C2 + C3 + C4 + C5 + O + B + I1 + I2 + I3 + I4 + I5 + I6))) |
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549 | |
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550 | (open O) (power 1))) |
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551 | |
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552 | (output Na_z ) |
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553 | |
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554 | ) |
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555 | |
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556 | (component (type pore) |
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557 | (const gbar = 0.013) |
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558 | (output gbar )) |
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559 | |
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560 | |
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561 | (component (type permeating-ion) (name na) |
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562 | (const e = 87.39) |
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563 | (output e )) |
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564 | |
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565 | ) ;; end Na current |
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566 | |
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567 | |
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568 | (component (type voltage-clamp) (name Na) |
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569 | |
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570 | (const vchold = -71) |
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571 | (const vcbase = -60) |
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572 | (const vcinc = 10) |
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573 | (const vcsteps = 9) |
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574 | (const vchdur = 30) |
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575 | (const vcbdur = 100) |
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576 | |
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577 | (output vchold vcbase vcinc vcsteps vchdur vcbdur)) |
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578 | |
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579 | |
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580 | |
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581 | )) |
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