{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"provenance":[{"file_id":"1KarKOpc-_hBHNaNLYPmqkY1HaZ1Gaa3Z","timestamp":1661641717758}],"collapsed_sections":[],"authorship_tag":"ABX9TyPa0V4y0CYmQdYdEuSX6GlO"},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","source":["### Implicit solution of Hodgin Huxley equations for a spherical cell\n","The rate equations are solved using the implicit trapezoid method. Because the HH equations were developed for ms time units and mV voltage, time is kept in ms throughout and voltage is converted to mV within the procedure calculating the HH rates.\n","\n","The backward Euler method is used to solve the voltage equation."],"metadata":{"id":"Fp34L-Tv36YS"}},{"cell_type":"code","execution_count":null,"metadata":{"id":"7T472moO3z7_"},"outputs":[],"source":["import numpy as np\n","import matplotlib.pyplot as plt"]},{"cell_type":"markdown","source":["Define cell parameters\n"],"metadata":{"id":"7zgOLs2asGpy"}},{"cell_type":"code","source":["diameter = 40                 # um   \n","A = 4*np.pi*(diameter/2)**2   # µm^2 membrane area\n","cm_bar = 0.01 *1e-12          # F/µm^2, specific capacitance, 0.01 pF/µm^2\n","\n","gL_bar = 3.0 *1e-12      # S/µm^2, specific leak conductance, 3 pS/µm^2\n","VL = -65 *1e-3           # V, reversal potential for leak conductance \n","\n","ENa = 50 *1e-3           # V, Na reversal potential\n","EK = -77 *1e-3           # V, K reversal potential\n","gNa_bar = 1200 *1e-12    # S/um^2, Na conductance, 1200 pS/um^2\n","gK_bar = 360 *1e-12      # S/um^2, K conductance, 360 pS/um^2 \n","\n","Vrest = -68.57404183502005 *1e-3    # V, initial resting membrane potential\n","\n","# Temperature parameters\n","T_C = 18.5      # temperature C, 18.5*C\n","Q10 = 3**((T_C - 6.3)/10)"],"metadata":{"id":"BZTWb6pu4Vml"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["Calculate cell specific values"],"metadata":{"id":"PJkUaHjsP0D0"}},{"cell_type":"code","source":["Cm = cm_bar*A    # F\n","GL = gL_bar*A    # S\n","GNa = gNa_bar*A  # S\n","GK = gK_bar*A    # S\n","\n","print(\"Area =\", round(A), \"um^2\")\n","print('Cm =', round(Cm*1e12,1), 'pF')\n","print('GL =', round(GL*1e9,1), 'nS')\n","print('GNa =', round(GNa *1e9,1), 'nS')\n","print('GK =', round(GK*1e9,1), 'nS')"],"metadata":{"id":"bdjXuoytPs_7","executionInfo":{"status":"ok","timestamp":1662060183410,"user_tz":240,"elapsed":18,"user":{"displayName":"David McKinnon","userId":"07616626647884468768"}},"colab":{"base_uri":"https://localhost:8080/"},"outputId":"a2184f78-0542-4c2f-d989-70a81f5c54da"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Area = 5027 um^2\n","Cm = 50.3 pF\n","GL = 15.1 nS\n","GNa = 6031.9 nS\n","GK = 1809.6 nS\n"]}]},{"cell_type":"markdown","source":["Simulation parameters"],"metadata":{"id":"W1d4T5cR9X-z"}},{"cell_type":"code","source":["Tend = 6                        # duration of simulation ms\n","dt = 0.01                       # time step ms\n","td = 1/dt                       # inverse time step used to update state variables\n","t = np.arange(0, Tend+dt, dt)   # time vector\n","Nt = len(t)-1                   # number of time steps    "],"metadata":{"id":"sMysk56L9YJg"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["Stimulation protocol"],"metadata":{"id":"jWxfiC4PsNow"}},{"cell_type":"code","source":["# Stimulus parameters for current step\n","t1 = 1          # 5 ms, start of current pulse \n","t2 = 1.3        # 30 ms, end of current pulse \n","amp = 3 *1e-9   # 3 nA, amplitude of current pulse, \n","\n","# Create stimulus vector with current injection starting at time t1 and ending at time t2\n","Nt1 = round(t1/dt)+1\n","Nt2 = round(t2/dt)\n","Istim = np.zeros(Nt+1)  \n","Istim[Nt1:Nt2] = amp  # add current to stimulus vector"],"metadata":{"id":"2lANfJnssN3g"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["Create and initialize voltage, state, conductance and current matrices"],"metadata":{"id":"cHTEa2I6_iKS"}},{"cell_type":"code","source":["V = np.zeros(Nt+1)\n","n = np.zeros(Nt+1)\n","m = np.zeros(Nt+1)\n","h = np.zeros(Nt+1)\n","gNa = np.zeros(Nt+1)\n","gK = np.zeros(Nt+1)\n","INa = np.zeros(Nt+1)\n","IK = np.zeros(Nt+1)"],"metadata":{"id":"JXyfQapz_iVw"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["Calculates HH kinetic rates for a given voltage and temperature. Assumes mV for voltage so have to convert. Output is rate/ms. "],"metadata":{"id":"rRBwvhadAitQ"}},{"cell_type":"code","source":["def Rates(V, Q10):\n","  V = V*1e3 # convert voltage to mV\n","  \n","  an = 0.01 * (V + 55) / (1 - np.exp(-(V + 55)/10)) * Q10\n","  bn = 0.125 * np.exp(-(V + 65)/80) * Q10\n","  am = 0.1 * (V + 40) / (1 - np.exp(-(V + 40)/10)) * Q10\n","  bm = 4 * np.exp(-(V + 65)/18) * Q10\n","  ah = 0.07 * np.exp(-(V + 65)/20) * Q10\n","  bh = 1 / (1 + np.exp(-(V + 35)/10)) * Q10\n","  return an, bn, am, bm, ah, bh"],"metadata":{"id":"Zx9ODn02Ai3R"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["Initialize voltage, state and conductance values."],"metadata":{"id":"XHyhGfu2LSIa"}},{"cell_type":"code","source":["V[0] = Vrest\n","an, bn, am, bm, ah, bh = Rates(V[0], Q10)\n","n[0] = an /(an + bn) \n","m[0] = am /(am + bm) \n","h[0] = ah /(ah + bh) "],"metadata":{"id":"5ISrOs3aLS2h"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["Solve equations."],"metadata":{"id":"vIq3PZrbAD7f"}},{"cell_type":"code","source":["dt = dt *1e-3 # convert ms to s\n","for j in range(0,Nt):\n","  # rates are per ms, and td is 1/ms\n","  # n, m, h are diminensionless\n","  an, bn, am, bm, ah, bh = Rates(V[j], Q10) \n","  c = (an + bn)/2\n","  n[j+1] = ( (td - c)* n[j] + an ) / (td + c)\n","  c = (am + bm)/2\n","  m[j+1] = ( (td - c)* m[j] + am ) / (td + c)\n","  c = (ah + bh)/2\n","  h[j+1] = ( (td - c)* h[j] + ah ) / (td + c)\n","\n","  # update V with half step backward Euler method \n","  GKn4 = GK*n[j+1]**4 \n","  GNam3h = GNa*m[j+1]**3*h[j+1]\n","  numerator = V[j]*2*Cm/dt + Istim[j+1] + GL*VL + GKn4*EK + GNam3h*ENa\n","  denominator = 2*Cm/dt + GL + GKn4 + GNam3h\n","  Vhalf = numerator/denominator\n","  # linearly advance V one half step to t(j+1)\n","  V[j+1]= 2*Vhalf - V[j]"],"metadata":{"id":"wLj6CqY6AEGm"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["Calculate conductance and current values and convert units for plotting"],"metadata":{"id":"31wFZDfW0yGK"}},{"cell_type":"code","source":["# calculate conductance and current in S and A\n","gK = GK*n**4        # S\n","gNa = GNa*m**3*h    # S\n","IK = gK*(V-EK)       # A\n","INa = gNa*(V-ENa)    # A\n","\n","# convert units for plotting\n","V = V *1e3        # V to mV\n","gK = gK *1e6      # S to uS\n","gNa = gNa *1e6    # S to uS\n","IK = IK *1e9      # A to nA\n","INa = INa *1e9    # A to nA"],"metadata":{"id":"jTdoMS0L0yS3"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["Plot results"],"metadata":{"id":"pANFqqaYyHQo"}},{"cell_type":"code","source":["%matplotlib inline\n","plt.rcParams['figure.figsize'] = [8, 10]\n","f, axs = plt.subplots(3, gridspec_kw={'height_ratios': [1, 1, 1]}, sharex='all')\n","\n","axs[0].plot(t,V, '#0066CC')\n","axs[0].set_ylabel('V  (mV)', fontsize=14)\n","\n","axs[1].plot(t,gK, '#0066CC')\n","axs[1].set_ylabel('gK  (uS)', fontsize=14)\n","\n","axs[1].plot(t,gNa, '#AA0000')\n","axs[1].set_ylabel('gNa  (uS)', fontsize=14)\n","\n","axs[2].plot(t,IK, '#0066CC')\n","axs[2].set_ylabel('IK  (nA)', fontsize=14)\n","\n","axs[2].plot(t,INa, '#AA0000')\n","axs[2].set_ylabel('IK  (nA)', fontsize=14)\n","\n","plt.show() # suppresses return values"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":593},"id":"1cclJ6sRAEbb","executionInfo":{"status":"ok","timestamp":1662060184524,"user_tz":240,"elapsed":842,"user":{"displayName":"David McKinnon","userId":"07616626647884468768"}},"outputId":"d3e4109b-ed47-4050-bc79-7c949817d9f4"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 576x720 with 3 Axes>"],"image/png":"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\n"},"metadata":{"needs_background":"light"}}]}]}