CoCalc Shared FilesHodgkinsHuxleyManipulation.sagewsOpen in CoCalc with one click!
Author: Aarushi Solanki
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from scipy.integrate import solve_ivp #Constants C_m = 0.01 E_Na = 55.17 E_K = -72.14 E_l = -49.42 g_Na = 1.2 g_K = 0.36 g_l = 0.003 #Rate Functions for Potassium Ion Channel alpha_n(v) = (0.01 * (v+50)) / (1 - e^(-(v+50)/10)) beta_n(v) = 0.125 * e^(-(v+60) / 80 ) #Rate Functions for Sodium Ion Channel alpha_m(v) = (0.1 * (v+35)) / (1 - e^( -(v+35) / 10)) beta_m(v) = 4.0 * e^(-0.0556 * (v+60)) alpha_h(v) = 0.07 * e^(-0.05 * (v+60)) beta_h(v) = 1 / (1 + e^(-0.1 * (v+30))) #Initial values for n, m, and h nnaught = alpha_n(-60) / (alpha_n(-60) + beta_n(-60)) mnaught = alpha_m(-60) / (alpha_m(-60) + beta_m(-60)) hnaught = alpha_h(-60) / (alpha_h(-60) + beta_h(-60)) @interact def neuron(vnaught=(-60,60), Inaught=(0,1,0.01)): def diffeqs(t, state): n,m,h,v = state nprime = (alpha_n(v) * (1 - n)) - (beta_n(v) * n) mprime = (alpha_m(v) * (1 - m)) - (beta_m(v) * m) hprime = (alpha_h(v) * (1 - h)) - (beta_h(v) * h) vprime = (1/C_m) * (Inaught - (g_Na * m^3 * h * (v - E_Na)) - (g_K * n^4 * (v - E_K)) - (g_l * (v - E_l))) return (nprime, mprime, hprime, vprime) t_span = (0,100) solution = solve_ivp(diffeqs, t_span, (nnaught, mnaught, hnaught, vnaught), method="LSODA") Vsol = solution.y[3] p = list_plot(zip(solution.t,Vsol), axes_labels=["t", "Voltage (mV)"], plotjoined=True, ymax=100) show(p)
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#when I = 0, action potential fires when V>=-53.4 #When I = 1, v=60 actually most, periodic # btwn 0.05 and 0.06 theres the hopf bifurcation #spiral inward to spiral outward --> hopf bifurcation