# Size of variable arrays: sizeAlgebraic = 20 sizeStates = 4 sizeConstants = 48 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_voi = "t in component BG_Hpump (second)" legend_constants[0] = "R in component params_BG (J_per_K_mol)" legend_constants[1] = "T in component params_BG (kelvin)" legend_constants[2] = "F in component params_BG (C_per_mol)" legend_constants[3] = "K_Hi in component params_BG (per_fmol)" legend_constants[36] = "q_init_Hi in component params_BG (fmol)" legend_constants[4] = "K_Ho in component params_BG (per_fmol)" legend_constants[33] = "q_init_Ho in component params_BG (fmol)" legend_constants[5] = "K_Pi in component params_BG (per_fmol)" legend_constants[39] = "q_init_Pi in component params_BG (fmol)" legend_constants[6] = "K_ATPi in component params_BG (per_fmol)" legend_constants[42] = "q_init_ATPi in component params_BG (fmol)" legend_constants[7] = "K_ADPi in component params_BG (per_fmol)" legend_constants[45] = "q_init_ADPi in component params_BG (fmol)" legend_constants[8] = "K_1 in component params_BG (per_fmol)" legend_constants[9] = "q_init_1 in component params_BG (fmol)" legend_constants[10] = "K_2 in component params_BG (per_fmol)" legend_constants[11] = "q_init_2 in component params_BG (fmol)" legend_constants[12] = "K_3 in component params_BG (per_fmol)" legend_constants[13] = "q_init_3 in component params_BG (fmol)" legend_constants[14] = "K_4 in component params_BG (per_fmol)" legend_constants[15] = "q_init_4 in component params_BG (fmol)" legend_constants[16] = "kappa_r1 in component params_BG (fmol_per_s)" legend_constants[17] = "kappa_r2 in component params_BG (fmol_per_s)" legend_constants[18] = "kappa_r3 in component params_BG (fmol_per_s)" legend_constants[19] = "kappa_r4 in component params_BG (fmol_per_s)" legend_constants[38] = "mu_Hi in component BG_Hpump (J_per_mol)" legend_constants[35] = "mu_Ho in component BG_Hpump (J_per_mol)" legend_constants[41] = "mu_Pi in component BG_Hpump (J_per_mol)" legend_constants[44] = "mu_ATPi in component BG_Hpump (J_per_mol)" legend_constants[47] = "mu_ADPi in component BG_Hpump (J_per_mol)" legend_algebraic[0] = "mu_1 in component BG_Hpump (J_per_mol)" legend_algebraic[18] = "v_1 in component BG_Hpump (fmol_per_s)" legend_algebraic[1] = "mu_2 in component BG_Hpump (J_per_mol)" legend_algebraic[10] = "v_2 in component BG_Hpump (fmol_per_s)" legend_algebraic[2] = "mu_3 in component BG_Hpump (J_per_mol)" legend_algebraic[14] = "v_3 in component BG_Hpump (fmol_per_s)" legend_algebraic[3] = "mu_4 in component BG_Hpump (J_per_mol)" legend_algebraic[19] = "v_4 in component BG_Hpump (fmol_per_s)" legend_algebraic[4] = "A_f_r1 in component BG_Hpump (J_per_mol)" legend_algebraic[6] = "v_r1 in component BG_Hpump (fmol_per_s)" legend_algebraic[5] = "A_r_r1 in component BG_Hpump (J_per_mol)" legend_algebraic[7] = "A_f_r2 in component BG_Hpump (J_per_mol)" legend_algebraic[9] = "v_r2 in component BG_Hpump (fmol_per_s)" legend_algebraic[8] = "A_r_r2 in component BG_Hpump (J_per_mol)" legend_algebraic[11] = "A_f_r3 in component BG_Hpump (J_per_mol)" legend_algebraic[13] = "v_r3 in component BG_Hpump (fmol_per_s)" legend_algebraic[12] = "A_r_r3 in component BG_Hpump (J_per_mol)" legend_algebraic[15] = "A_f_r4 in component BG_Hpump (J_per_mol)" legend_algebraic[17] = "v_r4 in component BG_Hpump (fmol_per_s)" legend_algebraic[16] = "A_r_r4 in component BG_Hpump (J_per_mol)" legend_constants[37] = "q_Hi in component BG_Hpump (fmol)" legend_constants[34] = "q_Ho in component BG_Hpump (fmol)" legend_constants[40] = "q_Pi in component BG_Hpump (fmol)" legend_constants[43] = "q_ATPi in component BG_Hpump (fmol)" legend_constants[46] = "q_ADPi in component BG_Hpump (fmol)" legend_states[0] = "q_1 in component BG_Hpump (fmol)" legend_states[1] = "q_2 in component BG_Hpump (fmol)" legend_states[2] = "q_3 in component BG_Hpump (fmol)" legend_states[3] = "q_4 in component BG_Hpump (fmol)" legend_constants[20] = "z_zr1 in component params_BG (dimensionless)" legend_constants[21] = "z_zr2 in component params_BG (dimensionless)" legend_constants[31] = "mu_zr1 in component BG_Hpump (J_per_mol)" legend_constants[32] = "mu_zr2 in component BG_Hpump (J_per_mol)" legend_constants[30] = "V_Vm in component BG_Hpump (volt)" legend_constants[22] = "V_E in component params_BG (volt)" legend_constants[23] = "V_i in component params_BG (pL)" legend_constants[24] = "H_i in component params_BG (mM)" legend_constants[25] = "H_o in component params_BG (mM)" legend_constants[26] = "Pi_i in component params_BG (mM)" legend_constants[27] = "ATP_i in component params_BG (mM)" legend_constants[28] = "ADP_i in component params_BG (mM)" legend_constants[29] = "V_o in component params_BG (pL)" legend_rates[0] = "d/dt q_1 in component BG_Hpump (fmol)" legend_rates[1] = "d/dt q_2 in component BG_Hpump (fmol)" legend_rates[2] = "d/dt q_3 in component BG_Hpump (fmol)" legend_rates[3] = "d/dt q_4 in component BG_Hpump (fmol)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 8.31 constants[1] = 273.15 constants[2] = 96485 constants[3] = 1 constants[4] = 1 constants[5] = 1 constants[6] = 1 constants[7] = 1 constants[8] = 1 constants[9] = 1 constants[10] = 1 constants[11] = 1 constants[12] = 1 constants[13] = 1 constants[14] = 1 constants[15] = 1 constants[16] = 1 constants[17] = 1 constants[18] = 1 constants[19] = 1 constants[20] = 1 constants[21] = 1 constants[22] = -0.05 constants[23] = 0.09 constants[24] = 1 constants[25] = 1e-5 constants[26] = 1e-5 constants[27] = 1e-5 constants[28] = 1e-5 constants[29] = 0.09 constants[30] = constants[22] constants[31] = constants[20]*constants[2]*constants[30] constants[32] = constants[21]*constants[2]*constants[30] constants[33] = constants[25]*constants[29] constants[34] = constants[33] constants[35] = constants[0]*constants[1]*log(constants[4]*constants[34]) constants[36] = constants[24]*constants[23] constants[37] = constants[36] constants[38] = constants[0]*constants[1]*log(constants[3]*constants[37]) constants[39] = constants[26]*constants[23] constants[40] = constants[39] constants[41] = constants[0]*constants[1]*log(constants[5]*constants[40]) constants[42] = constants[27]*constants[23] constants[43] = constants[42] constants[44] = constants[0]*constants[1]*log(constants[6]*constants[43]) constants[45] = constants[28]*constants[23] constants[46] = constants[45] constants[47] = constants[0]*constants[1]*log(constants[7]*constants[46]) states[0] = constants[9] states[1] = constants[11] states[2] = constants[13] states[3] = constants[15] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[0]*constants[1]*log(constants[8]*states[0]) algebraic[4] = algebraic[0] algebraic[1] = constants[0]*constants[1]*log(constants[10]*states[1]) algebraic[5] = algebraic[1]+constants[41] algebraic[6] = constants[16]*(exp(algebraic[4]/(constants[0]*constants[1]))-exp(algebraic[5]/(constants[0]*constants[1]))) algebraic[7] = algebraic[1]+constants[44] algebraic[2] = constants[0]*constants[1]*log(constants[12]*states[2]) algebraic[8] = algebraic[2] algebraic[9] = constants[17]*(exp(algebraic[7]/(constants[0]*constants[1]))-exp(algebraic[8]/(constants[0]*constants[1]))) algebraic[10] = algebraic[6]-algebraic[9] rates[1] = algebraic[10] algebraic[11] = algebraic[2]+constants[38] algebraic[3] = constants[0]*constants[1]*log(constants[14]*states[3]) algebraic[12] = algebraic[3]+constants[47]+constants[31] algebraic[13] = constants[18]*(exp(algebraic[11]/(constants[0]*constants[1]))-exp(algebraic[12]/(constants[0]*constants[1]))) algebraic[14] = algebraic[9]-algebraic[13] rates[2] = algebraic[14] algebraic[15] = algebraic[3] algebraic[16] = algebraic[0]+constants[35]+constants[32] algebraic[17] = constants[19]*(exp(algebraic[15]/(constants[0]*constants[1]))-exp(algebraic[16]/(constants[0]*constants[1]))) algebraic[18] = algebraic[17]-algebraic[6] rates[0] = algebraic[18] algebraic[19] = algebraic[13]-algebraic[17] rates[3] = algebraic[19] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[0]*constants[1]*log(constants[8]*states[0]) algebraic[4] = algebraic[0] algebraic[1] = constants[0]*constants[1]*log(constants[10]*states[1]) algebraic[5] = algebraic[1]+constants[41] algebraic[6] = constants[16]*(exp(algebraic[4]/(constants[0]*constants[1]))-exp(algebraic[5]/(constants[0]*constants[1]))) algebraic[7] = algebraic[1]+constants[44] algebraic[2] = constants[0]*constants[1]*log(constants[12]*states[2]) algebraic[8] = algebraic[2] algebraic[9] = constants[17]*(exp(algebraic[7]/(constants[0]*constants[1]))-exp(algebraic[8]/(constants[0]*constants[1]))) algebraic[10] = algebraic[6]-algebraic[9] algebraic[11] = algebraic[2]+constants[38] algebraic[3] = constants[0]*constants[1]*log(constants[14]*states[3]) algebraic[12] = algebraic[3]+constants[47]+constants[31] algebraic[13] = constants[18]*(exp(algebraic[11]/(constants[0]*constants[1]))-exp(algebraic[12]/(constants[0]*constants[1]))) algebraic[14] = algebraic[9]-algebraic[13] algebraic[15] = algebraic[3] algebraic[16] = algebraic[0]+constants[35]+constants[32] algebraic[17] = constants[19]*(exp(algebraic[15]/(constants[0]*constants[1]))-exp(algebraic[16]/(constants[0]*constants[1]))) algebraic[18] = algebraic[17]-algebraic[6] algebraic[19] = algebraic[13]-algebraic[17] 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)