# Size of variable arrays: sizeAlgebraic = 2 sizeStates = 13 sizeConstants = 65 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 (ms)" legend_constants[0] = "V in component membrane (V)" legend_algebraic[1] = "i_Na in component sodium_current (dimensionless)" legend_constants[1] = "E_Na in component sodium_current (V)" legend_constants[2] = "g_Na in component sodium_current (per_V)" legend_algebraic[0] = "P_open in component Markov_model (dimensionless)" legend_states[0] = "O1 in component Markov_model (dimensionless)" legend_states[1] = "O2 in component Markov_model (dimensionless)" legend_states[2] = "C0 in component Markov_model (dimensionless)" legend_states[3] = "C1 in component Markov_model (dimensionless)" legend_states[4] = "C2 in component Markov_model (dimensionless)" legend_states[5] = "C3 in component Markov_model (dimensionless)" legend_states[6] = "C4 in component Markov_model (dimensionless)" legend_states[7] = "C0I in component Markov_model (dimensionless)" legend_states[8] = "C1I in component Markov_model (dimensionless)" legend_states[9] = "C2I in component Markov_model (dimensionless)" legend_states[10] = "C3I in component Markov_model (dimensionless)" legend_states[11] = "C4I in component Markov_model (dimensionless)" legend_states[12] = "I in component Markov_model (dimensionless)" legend_constants[3] = "a in component Markov_model (dimensionless)" legend_constants[51] = "alpha in component rate_constants (first_order_rate_constant)" legend_constants[52] = "beta in component rate_constants (first_order_rate_constant)" legend_constants[53] = "cf in component rate_constants (first_order_rate_constant)" legend_constants[54] = "cn in component rate_constants (first_order_rate_constant)" legend_constants[55] = "of in component rate_constants (first_order_rate_constant)" legend_constants[56] = "on in component rate_constants (first_order_rate_constant)" legend_constants[57] = "eta in component rate_constants (first_order_rate_constant)" legend_constants[58] = "gamma in component rate_constants (first_order_rate_constant)" legend_constants[59] = "delta in component rate_constants (first_order_rate_constant)" legend_constants[60] = "epsilon in component rate_constants (first_order_rate_constant)" legend_constants[61] = "omega in component rate_constants (first_order_rate_constant)" legend_constants[62] = "v in component rate_constants (first_order_rate_constant)" legend_constants[63] = "gamma_gamma in component rate_constants (first_order_rate_constant)" legend_constants[64] = "delta_delta in component rate_constants (first_order_rate_constant)" legend_constants[4] = "R in component rate_constants (J_mol_K)" legend_constants[5] = "T in component rate_constants (K)" legend_constants[6] = "F in component rate_constants (C_mol)" legend_constants[7] = "k in component rate_constants (J_K)" legend_constants[8] = "h in component rate_constants (J_ms)" legend_constants[9] = "z_alpha in component rate_constants (dimensionless)" legend_constants[10] = "z_beta in component rate_constants (dimensionless)" legend_constants[11] = "z_gamma in component rate_constants (dimensionless)" legend_constants[12] = "z_delta in component rate_constants (dimensionless)" legend_constants[13] = "z_on in component rate_constants (dimensionless)" legend_constants[14] = "z_of in component rate_constants (dimensionless)" legend_constants[15] = "z_gamma_gamma in component rate_constants (dimensionless)" legend_constants[16] = "z_delta_delta in component rate_constants (dimensionless)" legend_constants[17] = "z_epsilon in component rate_constants (dimensionless)" legend_constants[18] = "z_omega in component rate_constants (dimensionless)" legend_constants[19] = "z_eta in component rate_constants (dimensionless)" legend_constants[20] = "z_v in component rate_constants (dimensionless)" legend_constants[21] = "z_cn in component rate_constants (dimensionless)" legend_constants[22] = "z_cf in component rate_constants (dimensionless)" legend_constants[23] = "delta_H_alpha in component rate_constants (J_mol)" legend_constants[24] = "delta_H_beta in component rate_constants (J_mol)" legend_constants[25] = "delta_H_cf in component rate_constants (J_mol)" legend_constants[26] = "delta_H_cn in component rate_constants (J_mol)" legend_constants[27] = "delta_H_of in component rate_constants (J_mol)" legend_constants[28] = "delta_H_on in component rate_constants (J_mol)" legend_constants[29] = "delta_H_eta in component rate_constants (J_mol)" legend_constants[30] = "delta_H_gamma in component rate_constants (J_mol)" legend_constants[31] = "delta_H_delta in component rate_constants (J_mol)" legend_constants[32] = "delta_H_epsilon in component rate_constants (J_mol)" legend_constants[33] = "delta_H_omega in component rate_constants (J_mol)" legend_constants[34] = "delta_H_v in component rate_constants (J_mol)" legend_constants[35] = "delta_H_gamma_gamma in component rate_constants (J_mol)" legend_constants[36] = "delta_H_delta_delta in component rate_constants (J_mol)" legend_constants[37] = "delta_S_alpha in component rate_constants (J_mol_K)" legend_constants[38] = "delta_S_beta in component rate_constants (J_mol_K)" legend_constants[39] = "delta_S_cf in component rate_constants (J_mol_K)" legend_constants[40] = "delta_S_cn in component rate_constants (J_mol_K)" legend_constants[41] = "delta_S_of in component rate_constants (J_mol_K)" legend_constants[42] = "delta_S_on in component rate_constants (J_mol_K)" legend_constants[43] = "delta_S_eta in component rate_constants (J_mol_K)" legend_constants[44] = "delta_S_gamma in component rate_constants (J_mol_K)" legend_constants[45] = "delta_S_delta in component rate_constants (J_mol_K)" legend_constants[46] = "delta_S_epsilon in component rate_constants (J_mol_K)" legend_constants[47] = "delta_S_omega in component rate_constants (J_mol_K)" legend_constants[48] = "delta_S_v in component rate_constants (J_mol_K)" legend_constants[49] = "delta_S_gamma_gamma in component rate_constants (J_mol_K)" legend_constants[50] = "delta_S_delta_delta in component rate_constants (J_mol_K)" legend_rates[2] = "d/dt C0 in component Markov_model (dimensionless)" legend_rates[3] = "d/dt C1 in component Markov_model (dimensionless)" legend_rates[4] = "d/dt C2 in component Markov_model (dimensionless)" legend_rates[5] = "d/dt C3 in component Markov_model (dimensionless)" legend_rates[6] = "d/dt C4 in component Markov_model (dimensionless)" legend_rates[0] = "d/dt O1 in component Markov_model (dimensionless)" legend_rates[1] = "d/dt O2 in component Markov_model (dimensionless)" legend_rates[7] = "d/dt C0I in component Markov_model (dimensionless)" legend_rates[8] = "d/dt C1I in component Markov_model (dimensionless)" legend_rates[9] = "d/dt C2I in component Markov_model (dimensionless)" legend_rates[10] = "d/dt C3I in component Markov_model (dimensionless)" legend_rates[11] = "d/dt C4I in component Markov_model (dimensionless)" legend_rates[12] = "d/dt I in component Markov_model (dimensionless)" 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] = 0.044675 constants[2] = 0.0131 states[0] = 0.0 states[1] = 0.0 states[2] = 1.0 states[3] = 0.0 states[4] = 0.0 states[5] = 0.0 states[6] = 0.0 states[7] = 0.0 states[8] = 0.0 states[9] = 0.0 states[10] = 0.0 states[11] = 0.0 states[12] = 0.0 constants[3] = 2.5218 constants[4] = 8.314472 constants[5] = 286.0 constants[6] = 96500.0 constants[7] = 1.3806504E-23 constants[8] = 6.62607095E-31 constants[9] = 0 constants[10] = -0.9701 constants[11] = 1.5703 constants[12] = -1.3266 constants[13] = 0.6625 constants[14] = 0 constants[15] = 0 constants[16] = -3.5596 constants[17] = 0 constants[18] = 0 constants[19] = 1.5717 constants[20] = -1.3281 constants[21] = 0 constants[22] = 0 constants[23] = 116900 constants[24] = 263870 constants[25] = 57533 constants[26] = 293270 constants[27] = 79035 constants[28] = 62385 constants[29] = 150333 constants[30] = 200240 constants[31] = 127970 constants[32] = 79183 constants[33] = 123020 constants[34] = 121900 constants[35] = -99967 constants[36] = 62555 constants[37] = 224.114 constants[38] = 708.146 constants[39] = 0.00711 constants[40] = 786.217 constants[41] = 1.510 constants[42] = 39.295 constants[43] = 338.915 constants[44] = 529.952 constants[45] = 229.205 constants[46] = 70.078 constants[47] = 225.175 constants[48] = 193.265 constants[49] = -578.317 constants[50] = -130.639 constants[51] = ((constants[7]*constants[5])/constants[8])*exp(-constants[23]/(constants[4]*constants[5])+constants[37]/constants[4]+(constants[9]*constants[6]*constants[0])/(constants[4]*constants[5])) constants[52] = ((constants[7]*constants[5])/constants[8])*exp(-constants[24]/(constants[4]*constants[5])+constants[38]/constants[4]+(constants[10]*constants[6]*constants[0])/(constants[4]*constants[5])) constants[53] = ((constants[7]*constants[5])/constants[8])*exp(-constants[25]/(constants[4]*constants[5])+constants[39]/constants[4]+(constants[22]*constants[6]*constants[0])/(constants[4]*constants[5])) constants[54] = ((constants[7]*constants[5])/constants[8])*exp(-constants[26]/(constants[4]*constants[5])+constants[40]/constants[4]+(constants[21]*constants[6]*constants[0])/(constants[4]*constants[5])) constants[55] = ((constants[7]*constants[5])/constants[8])*exp(-constants[27]/(constants[4]*constants[5])+constants[41]/constants[4]+(constants[14]*constants[6]*constants[0])/(constants[4]*constants[5])) constants[56] = ((constants[7]*constants[5])/constants[8])*exp(-constants[28]/(constants[4]*constants[5])+constants[42]/constants[4]+(constants[13]*constants[6]*constants[0])/(constants[4]*constants[5])) constants[57] = ((constants[7]*constants[5])/constants[8])*exp(-constants[29]/(constants[4]*constants[5])+constants[43]/constants[4]+(constants[19]*constants[6]*constants[0])/(constants[4]*constants[5])) constants[58] = ((constants[7]*constants[5])/constants[8])*exp(-constants[30]/(constants[4]*constants[5])+constants[44]/constants[4]+(constants[11]*constants[6]*constants[0])/(constants[4]*constants[5])) constants[59] = ((constants[7]*constants[5])/constants[8])*exp(-constants[31]/(constants[4]*constants[5])+constants[45]/constants[4]+(constants[12]*constants[6]*constants[0])/(constants[4]*constants[5])) constants[60] = ((constants[7]*constants[5])/constants[8])*exp(-constants[32]/(constants[4]*constants[5])+constants[46]/constants[4]+(constants[17]*constants[6]*constants[0])/(constants[4]*constants[5])) constants[61] = ((constants[7]*constants[5])/constants[8])*exp(-constants[33]/(constants[4]*constants[5])+constants[47]/constants[4]+(constants[18]*constants[6]*constants[0])/(constants[4]*constants[5])) constants[62] = ((constants[7]*constants[5])/constants[8])*exp(-constants[34]/(constants[4]*constants[5])+constants[48]/constants[4]+(constants[20]*constants[6]*constants[0])/(constants[4]*constants[5])) constants[63] = ((constants[7]*constants[5])/constants[8])*exp(-constants[35]/(constants[4]*constants[5])+constants[49]/constants[4]+(constants[15]*constants[6]*constants[0])/(constants[4]*constants[5])) constants[64] = ((constants[7]*constants[5])/constants[8])*exp(-constants[36]/(constants[4]*constants[5])+constants[50]/constants[4]+(constants[16]*constants[6]*constants[0])/(constants[4]*constants[5])) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[2] = (constants[52]*states[3]+constants[53]*states[7])-(constants[54]+4.00000*constants[51])*states[2] rates[3] = (2.00000*constants[52]*states[4]+4.00000*constants[51]*states[2]+(constants[53]/constants[3])*states[8])-(constants[52]+3.00000*constants[51]+constants[54]*constants[3])*states[3] rates[4] = (3.00000*constants[52]*states[5]+3.00000*constants[51]*states[3]+(constants[53]/(power(constants[3], 2.00000)))*states[9])-(2.00000*constants[52]+2.00000*constants[51]+constants[54]*(power(constants[3], 2.00000)))*states[4] rates[5] = (4.00000*constants[52]*states[6]+2.00000*constants[51]*states[4]+(constants[53]/(power(constants[3], 3.00000)))*states[10])-(3.00000*constants[52]+constants[51]+constants[54]*(power(constants[3], 3.00000)))*states[5] rates[6] = (constants[59]*states[0]+constants[62]*states[1]+constants[51]*states[5]+(constants[53]/(power(constants[3], 4.00000)))*states[11])-(4.00000*constants[52]+constants[58]+constants[57]+constants[54]*(power(constants[3], 4.00000)))*states[6] rates[0] = (constants[58]*states[6]+constants[61]*states[1]+constants[55]*states[12])-(constants[59]+constants[60]+constants[56])*states[0] rates[1] = (constants[60]*states[0]+constants[57]*states[6])-(constants[62]+constants[61])*states[1] rates[7] = ((constants[52]/constants[3])*states[8]+constants[54]*states[2])-(constants[53]+4.00000*constants[51]*constants[3])*states[7] rates[8] = (((2.00000*constants[52])/constants[3])*states[9]+4.00000*constants[51]*constants[3]*states[7]+constants[54]*constants[3]*states[3])-(constants[52]/constants[3]+3.00000*constants[51]*constants[3]+constants[53]/constants[3])*states[8] rates[9] = (((3.00000*constants[52])/constants[3])*states[10]+3.00000*constants[51]*constants[3]*states[8]+constants[54]*(power(constants[3], 2.00000))*states[4])-((2.00000*constants[52])/constants[3]+2.00000*constants[51]*constants[3]+constants[53]/(power(constants[3], 2.00000)))*states[9] rates[10] = (((4.00000*constants[52])/constants[3])*states[11]+2.00000*constants[51]*constants[3]*states[9]+constants[54]*(power(constants[3], 3.00000))*states[5])-((3.00000*constants[52])/constants[3]+constants[51]*constants[3]+constants[53]/(power(constants[3], 3.00000)))*states[10] rates[11] = (constants[64]*states[12]+constants[51]*constants[3]*states[10]+constants[54]*(power(constants[3], 4.00000))*states[6])-((4.00000*constants[52])/constants[3]+constants[63]+constants[53]/(power(constants[3], 4.00000)))*states[11] rates[12] = (constants[63]*states[11]+constants[56]*states[0])-(constants[64]+constants[55])*states[12] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = states[0]+states[1] algebraic[1] = constants[2]*algebraic[0]*(constants[0]-constants[1]) 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)