# Size of variable arrays: sizeAlgebraic = 13 sizeStates = 5 sizeConstants = 14 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_voi = "time in component environment (millisecond)" legend_constants[0] = "alpha in component model_constants (dimensionless)" legend_constants[1] = "lamda in component model_constants (dimensionless)" legend_states[0] = "V in component membrane (millivolt)" legend_constants[2] = "Cm in component membrane (microF_per_cm2)" legend_algebraic[8] = "i_Ca_T in component T_type_calcium_current (microA_per_cm2)" legend_algebraic[9] = "i_Ca_L in component L_type_calcium_current (microA_per_cm2)" legend_algebraic[11] = "i_Ca_K in component calcium_activated_potassium_current (microA_per_cm2)" legend_algebraic[10] = "i_K in component potassium_current (microA_per_cm2)" legend_algebraic[12] = "i_Cl in component leak_chloride_current (microA_per_cm2)" legend_algebraic[0] = "V_tilde in component gate_voltage (millivolt)" legend_constants[3] = "E_Ca in component T_type_calcium_current (millivolt)" legend_constants[4] = "g_Ca_T in component T_type_calcium_current (milliS_per_cm2)" legend_algebraic[7] = "m in component T_type_calcium_current_m_gate (dimensionless)" legend_states[1] = "h in component T_type_calcium_current_h_gate (dimensionless)" legend_algebraic[1] = "alpha_m in component T_type_calcium_current_m_gate (per_millisecond)" legend_algebraic[4] = "beta_m in component T_type_calcium_current_m_gate (per_millisecond)" legend_algebraic[2] = "alpha_h in component T_type_calcium_current_h_gate (per_millisecond)" legend_algebraic[5] = "beta_h in component T_type_calcium_current_h_gate (per_millisecond)" legend_constants[5] = "g_Ca_L in component L_type_calcium_current (milliS_per_cm2)" legend_states[2] = "x_Ca in component L_type_calcium_current_x_Ca_gate (dimensionless)" legend_constants[6] = "tau_x_Ca in component L_type_calcium_current_x_Ca_gate (millisecond)" legend_constants[7] = "E_K in component potassium_current (millivolt)" legend_constants[8] = "g_K in component potassium_current (milliS_per_cm2)" legend_states[3] = "n in component potassium_current_n_gate (dimensionless)" legend_algebraic[3] = "alpha_n in component potassium_current_n_gate (per_millisecond)" legend_algebraic[6] = "beta_n in component potassium_current_n_gate (per_millisecond)" legend_states[4] = "Ca in component calcium_activated_potassium_current (millimolar)" legend_constants[9] = "g_Ca_K in component calcium_activated_potassium_current (milliS_per_cm2)" legend_constants[10] = "rho in component calcium_activated_potassium_current (per_millisecond)" legend_constants[11] = "K_c in component calcium_activated_potassium_current (millimolar_per_millivolt)" legend_constants[12] = "g_Cl in component leak_chloride_current (milliS_per_cm2)" legend_constants[13] = "E_Cl in component leak_chloride_current (millivolt)" legend_rates[0] = "d/dt V in component membrane (millivolt)" legend_rates[1] = "d/dt h in component T_type_calcium_current_h_gate (dimensionless)" legend_rates[2] = "d/dt x_Ca in component L_type_calcium_current_x_Ca_gate (dimensionless)" legend_rates[3] = "d/dt n in component potassium_current_n_gate (dimensionless)" legend_rates[4] = "d/dt Ca in component calcium_activated_potassium_current (millimolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0.12 constants[1] = 12.5 states[0] = -55.0 constants[2] = 2.5 constants[3] = 80.0 constants[4] = 0.51 states[1] = 0.01 constants[5] = 0.004 states[2] = 0.01 constants[6] = 500.0 constants[7] = -75.0 constants[8] = 0.3 states[3] = 0.01 states[4] = 1E-4 constants[9] = 0.03 constants[10] = 0.125E3 constants[11] = 425.0E-5 constants[12] = 0.003 constants[13] = -40.0 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[4] = (constants[10]/constants[0])*(constants[11]*states[2]*(constants[3]-states[0])-states[4]) algebraic[0] = (127.000*states[0]+8265.00)/105.000 rates[2] = (1.00000/(1.00000+exp(0.150000*(-algebraic[0]-50.0000)))-states[2])/(constants[0]*constants[6]) algebraic[2] = 0.0700000*exp((25.0000-algebraic[0])/20.0000) algebraic[5] = 1.00000/(1.00000+exp(5.50000-algebraic[0]*0.100000)) rates[1] = (algebraic[2]*(1.00000-states[1])-algebraic[5]*states[1])/(constants[0]*constants[1]) algebraic[3] = (0.0100000*(55.0000-algebraic[0]))/(exp((55.0000-algebraic[0])/10.0000)-1.00000) algebraic[6] = 0.125000*exp((45.0000-algebraic[0])/80.0000) rates[3] = (algebraic[3]*(1.00000-states[3])-algebraic[6]*states[3])/(constants[0]*constants[1]) algebraic[1] = (0.100000*(50.0000-algebraic[0]))/(exp(5.00000-algebraic[0]*0.100000)-1.00000) algebraic[4] = 4.00000*exp((25.0000-algebraic[0])/18.0000) algebraic[7] = algebraic[1]/(algebraic[1]+algebraic[4]) algebraic[8] = constants[4]*(power(algebraic[7], 3.00000))*states[1]*(states[0]-constants[3]) algebraic[9] = constants[5]*states[2]*(states[0]-constants[3]) algebraic[11] = (constants[9]*states[4]*(states[0]-constants[7]))/(0.500000+states[4]) algebraic[10] = constants[8]*(power(states[3], 4.00000))*(states[0]-constants[7]) algebraic[12] = constants[12]*(states[0]-constants[13]) rates[0] = -(1.00000/(constants[2]*constants[0]))*(algebraic[8]+algebraic[9]+algebraic[11]+algebraic[10]+algebraic[12]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = (127.000*states[0]+8265.00)/105.000 algebraic[2] = 0.0700000*exp((25.0000-algebraic[0])/20.0000) algebraic[5] = 1.00000/(1.00000+exp(5.50000-algebraic[0]*0.100000)) algebraic[3] = (0.0100000*(55.0000-algebraic[0]))/(exp((55.0000-algebraic[0])/10.0000)-1.00000) algebraic[6] = 0.125000*exp((45.0000-algebraic[0])/80.0000) algebraic[1] = (0.100000*(50.0000-algebraic[0]))/(exp(5.00000-algebraic[0]*0.100000)-1.00000) algebraic[4] = 4.00000*exp((25.0000-algebraic[0])/18.0000) algebraic[7] = algebraic[1]/(algebraic[1]+algebraic[4]) algebraic[8] = constants[4]*(power(algebraic[7], 3.00000))*states[1]*(states[0]-constants[3]) algebraic[9] = constants[5]*states[2]*(states[0]-constants[3]) algebraic[11] = (constants[9]*states[4]*(states[0]-constants[7]))/(0.500000+states[4]) algebraic[10] = constants[8]*(power(states[3], 4.00000))*(states[0]-constants[7]) algebraic[12] = constants[12]*(states[0]-constants[13]) return algebraic def solve_model(): """Solve model with ODE solver""" from scipy.integrate import ode # Initialise constants and state variables (init_states, constants) = initConsts() # Set timespan to solve over voi = linspace(0, 10, 500) # Construct ODE object to solve r = ode(computeRates) r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1) r.set_initial_value(init_states, voi[0]) r.set_f_params(constants) # Solve model states = array([[0.0] * len(voi)] * sizeStates) states[:,0] = init_states for (i,t) in enumerate(voi[1:]): if r.successful(): r.integrate(t) states[:,i+1] = r.y else: break # Compute algebraic variables algebraic = computeAlgebraic(constants, states, voi) return (voi, states, algebraic) def plot_model(voi, states, algebraic): """Plot variables against variable of integration""" import pylab (legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends() pylab.figure(1) pylab.plot(voi,vstack((states,algebraic)).T) pylab.xlabel(legend_voi) pylab.legend(legend_states + legend_algebraic, loc='best') pylab.show() if __name__ == "__main__": (voi, states, algebraic) = solve_model() plot_model(voi, states, algebraic)