# Size of variable arrays: sizeAlgebraic = 3 sizeStates = 1 sizeConstants = 43 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 GLUT2_BG (second)" legend_constants[0] = "K_Ai in component params_BG (per_fmol)" legend_constants[1] = "K_Ao in component params_BG (per_fmol)" legend_constants[2] = "K_1 in component params_BG (per_fmol)" legend_constants[3] = "K_2 in component params_BG (per_fmol)" legend_constants[4] = "K_3 in component params_BG (per_fmol)" legend_constants[5] = "K_4 in component params_BG (per_fmol)" legend_constants[6] = "kappa_r1 in component params_BG (fmol_per_s)" legend_constants[7] = "kappa_r2 in component params_BG (fmol_per_s)" legend_constants[8] = "kappa_r3 in component params_BG (fmol_per_s)" legend_constants[9] = "kappa_r4 in component params_BG (fmol_per_s)" legend_constants[30] = "q_Ai in component GLUT2_BG (fmol)" legend_algebraic[0] = "q_Ao in component GLUT2_BG (fmol)" legend_constants[37] = "lambda in component GLUT2_BG (dimensionless)" legend_constants[33] = "q_tot in component GLUT2_BG (fmol)" legend_constants[38] = "v_max in component GLUT2_BG (fmol_per_s)" legend_constants[39] = "k_m_1 in component GLUT2_BG (dimensionless)" legend_constants[40] = "k_m_2 in component GLUT2_BG (dimensionless)" legend_constants[41] = "k_m_3 in component GLUT2_BG (dimensionless)" legend_algebraic[1] = "v in component GLUT2_BG (fmol_per_s)" legend_constants[35] = "v_max_free in component GLUT2_BG (fmol_per_s)" legend_algebraic[2] = "v_free in component GLUT2_BG (fmol_per_s)" legend_constants[34] = "k_m_1_free in component GLUT2_BG (dimensionless)" legend_constants[36] = "k_m_2_free in component GLUT2_BG (dimensionless)" legend_constants[10] = "k_m_3_free in component GLUT2_BG (dimensionless)" legend_constants[11] = "k_oi_math in component GLUT2_BG (mM)" legend_constants[12] = "k_io_math in component GLUT2_BG (mM)" legend_constants[13] = "v_oi_max in component GLUT2_BG (mM_per_s)" legend_constants[14] = "v_io_max in component GLUT2_BG (mM_per_s)" legend_constants[15] = "V_E in component GLUT2_BG (pL)" legend_constants[16] = "GC in component GLUT2_BG (uM)" legend_constants[17] = "g_i in component GLUT2_BG (mM)" legend_states[0] = "g_o in component GLUT2_BG (mM)" legend_constants[18] = "V_i in component GLUT2_BG (pL)" legend_constants[19] = "V_o in component GLUT2_BG (pL)" legend_constants[20] = "R in component params_BG (J_per_K_mol)" legend_constants[21] = "T in component params_BG (kelvin)" legend_constants[31] = "q_init_Ai in component params_BG (fmol)" legend_constants[32] = "q_init_Ao in component params_BG (fmol)" legend_constants[22] = "q_init_1 in component params_BG (fmol)" legend_constants[23] = "q_init_2 in component params_BG (fmol)" legend_constants[24] = "q_init_3 in component params_BG (fmol)" legend_constants[25] = "q_init_4 in component params_BG (fmol)" legend_constants[26] = "V_i in component params_BG (pL)" legend_constants[27] = "g_i in component params_BG (mM)" legend_constants[28] = "g_o in component params_BG (mM)" legend_constants[29] = "V_o in component params_BG (pL)" legend_rates[0] = "d/dt g_o in component GLUT2_BG (mM)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 149.65 constants[1] = 149.65 constants[2] = 33.20 constants[3] = 4.25e+03 constants[4] = 344.59 constants[5] = 1.99 constants[6] = 0.36 constants[7] = 0.26 constants[8] = 1.01e+05 constants[9] = 1.01e+04 constants[10] = 218.96 constants[11] = 0.1094 constants[12] = 1.609 constants[13] = 0.004839 constants[14] = 0.07117 constants[15] = 1 constants[16] = 6.67 constants[17] = 1e-8 states[0] = 1e-8 constants[18] = 0.09 constants[19] = 0.09 constants[20] = 8.31 constants[21] = 273.15 constants[22] = 0.0017 constants[23] = 0.0017 constants[24] = 0.0017 constants[25] = 0.0017 constants[26] = 0.09 constants[27] = 10 constants[28] = 1e-5 constants[29] = 0.09 constants[30] = constants[17]*constants[18] constants[31] = constants[27]*constants[26] constants[32] = constants[28]*constants[29] constants[42] = 1.00000 constants[33] = (constants[16]*constants[15]*1.00000)/1000.00 constants[34] = constants[11]*constants[18]*constants[0] constants[35] = (constants[13]*constants[15])/constants[34] constants[36] = (constants[14]*constants[15])/constants[35] constants[37] = constants[7]/constants[6] constants[38] = (constants[33]*constants[7]*constants[4])/(constants[4]/constants[2]+constants[4]/constants[5]) constants[39] = (constants[4]/constants[2]+constants[4]/constants[5])/(constants[4]/constants[3]+(constants[37]*constants[4])/constants[5]) constants[40] = (constants[4]/constants[2]+constants[4]/constants[5])/(1.00000+(constants[37]*constants[4])/constants[2]) constants[41] = (constants[4]/constants[2]+constants[4]/constants[5])/(constants[37]*(1.00000+constants[4]/constants[3])) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[42] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = states[0]*constants[19] algebraic[1] = (constants[38]*(constants[1]*algebraic[0]-constants[0]*constants[30]))/(1.00000+(constants[1]*algebraic[0])/constants[39]+(constants[0]*constants[30])/constants[40]+(constants[1]*algebraic[0]*constants[0]*constants[30])/constants[41]) algebraic[2] = (constants[35]*(constants[1]*algebraic[0]-constants[0]*constants[30]))/(1.00000+(constants[1]*algebraic[0])/constants[34]+(constants[0]*constants[30])/constants[36]+(constants[1]*algebraic[0]*constants[0]*constants[30])/constants[10]) 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)