# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 18 sizeConstants = 37 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 (second)" legend_constants[0] = "mostot in component total_concs (micromolar)" legend_constants[1] = "e1tot in component total_concs (micromolar)" legend_constants[2] = "e2tot in component total_concs (micromolar)" legend_constants[3] = "mektot in component total_concs (micromolar)" legend_constants[4] = "mekpasetot in component total_concs (micromolar)" legend_constants[5] = "mapktot in component total_concs (micromolar)" legend_constants[6] = "mapkpasetot in component total_concs (micromolar)" legend_constants[7] = "a1 in component rate_constants (second_order_rate_constant_units)" legend_constants[8] = "a2 in component rate_constants (second_order_rate_constant_units)" legend_constants[9] = "a3 in component rate_constants (second_order_rate_constant_units)" legend_constants[10] = "a4 in component rate_constants (second_order_rate_constant_units)" legend_constants[11] = "a5 in component rate_constants (second_order_rate_constant_units)" legend_constants[12] = "a6 in component rate_constants (second_order_rate_constant_units)" legend_constants[13] = "a7 in component rate_constants (second_order_rate_constant_units)" legend_constants[14] = "a8 in component rate_constants (second_order_rate_constant_units)" legend_constants[15] = "a9 in component rate_constants (second_order_rate_constant_units)" legend_constants[16] = "a10 in component rate_constants (second_order_rate_constant_units)" legend_constants[17] = "d1 in component rate_constants (first_order_rate_constant_units)" legend_constants[18] = "d2 in component rate_constants (first_order_rate_constant_units)" legend_constants[19] = "d3 in component rate_constants (first_order_rate_constant_units)" legend_constants[20] = "d4 in component rate_constants (first_order_rate_constant_units)" legend_constants[21] = "d5 in component rate_constants (first_order_rate_constant_units)" legend_constants[22] = "d6 in component rate_constants (first_order_rate_constant_units)" legend_constants[23] = "d7 in component rate_constants (first_order_rate_constant_units)" legend_constants[24] = "d8 in component rate_constants (first_order_rate_constant_units)" legend_constants[25] = "d9 in component rate_constants (first_order_rate_constant_units)" legend_constants[26] = "d10 in component rate_constants (first_order_rate_constant_units)" legend_constants[27] = "k1 in component rate_constants (first_order_rate_constant_units)" legend_constants[28] = "k2 in component rate_constants (first_order_rate_constant_units)" legend_constants[29] = "k3 in component rate_constants (first_order_rate_constant_units)" legend_constants[30] = "k4 in component rate_constants (first_order_rate_constant_units)" legend_constants[31] = "k5 in component rate_constants (first_order_rate_constant_units)" legend_constants[32] = "k6 in component rate_constants (first_order_rate_constant_units)" legend_constants[33] = "k7 in component rate_constants (first_order_rate_constant_units)" legend_constants[34] = "k8 in component rate_constants (first_order_rate_constant_units)" legend_constants[35] = "k9 in component rate_constants (first_order_rate_constant_units)" legend_constants[36] = "k10 in component rate_constants (first_order_rate_constant_units)" legend_states[0] = "mos in component mos (micromolar)" legend_states[1] = "mosstar in component mosstar (micromolar)" legend_states[2] = "mose1 in component mose1 (micromolar)" legend_states[3] = "mosstare2 in component mosstare2 (micromolar)" legend_states[4] = "mekstarmosstar in component mekstarmosstar (micromolar)" legend_states[5] = "mekmosstar in component mekmosstar (micromolar)" legend_states[6] = "mekstar in component mekstar (micromolar)" legend_states[7] = "mekstarstar in component mekstarstar (micromolar)" legend_states[8] = "mekstarmekpase in component mekstarmekpase (micromolar)" legend_states[9] = "mekstarstarmekpase in component mekstarstarmekpase (micromolar)" legend_states[10] = "mapkmekstarstar in component mapkmekstarstar (micromolar)" legend_states[11] = "mapkstarmekstarstar in component mapkstarmekstarstar (micromolar)" legend_states[12] = "mek in component mek (micromolar)" legend_states[13] = "mapkstar in component mapkstar (micromolar)" legend_states[14] = "mapkstarstar in component mapkstarstar (micromolar)" legend_states[15] = "mapkstarmapkpase in component mapkstarmapkpase (micromolar)" legend_states[16] = "mapkstarstarmapkpase in component mapkstarstarmapkpase (micromolar)" legend_states[17] = "mapk in component mapk (micromolar)" legend_rates[0] = "d/dt mos in component mos (micromolar)" legend_rates[2] = "d/dt mose1 in component mose1 (micromolar)" legend_rates[1] = "d/dt mosstar in component mosstar (micromolar)" legend_rates[3] = "d/dt mosstare2 in component mosstare2 (micromolar)" legend_rates[12] = "d/dt mek in component mek (micromolar)" legend_rates[5] = "d/dt mekmosstar in component mekmosstar (micromolar)" legend_rates[6] = "d/dt mekstar in component mekstar (micromolar)" legend_rates[8] = "d/dt mekstarmekpase in component mekstarmekpase (micromolar)" legend_rates[4] = "d/dt mekstarmosstar in component mekstarmosstar (micromolar)" legend_rates[7] = "d/dt mekstarstar in component mekstarstar (micromolar)" legend_rates[9] = "d/dt mekstarstarmekpase in component mekstarstarmekpase (micromolar)" legend_rates[17] = "d/dt mapk in component mapk (micromolar)" legend_rates[10] = "d/dt mapkmekstarstar in component mapkmekstarstar (micromolar)" legend_rates[13] = "d/dt mapkstar in component mapkstar (micromolar)" legend_rates[11] = "d/dt mapkstarmekstarstar in component mapkstarmekstarstar (micromolar)" legend_rates[14] = "d/dt mapkstarstar in component mapkstarstar (micromolar)" legend_rates[15] = "d/dt mapkstarmapkpase in component mapkstarmapkpase (micromolar)" legend_rates[16] = "d/dt mapkstarstarmapkpase in component mapkstarstarmapkpase (micromolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0.003 constants[1] = 0.0003 constants[2] = 0.0003 constants[3] = 1.2 constants[4] = 0.0003 constants[5] = 1.2 constants[6] = 0.12 constants[7] = 1000 constants[8] = 1000 constants[9] = 1000 constants[10] = 1000 constants[11] = 1000 constants[12] = 1000 constants[13] = 1000 constants[14] = 1000 constants[15] = 1000 constants[16] = 1000 constants[17] = 150 constants[18] = 150 constants[19] = 150 constants[20] = 150 constants[21] = 150 constants[22] = 150 constants[23] = 150 constants[24] = 150 constants[25] = 150 constants[26] = 150 constants[27] = 150 constants[28] = 150 constants[29] = 150 constants[30] = 150 constants[31] = 150 constants[32] = 150 constants[33] = 150 constants[34] = 150 constants[35] = 150 constants[36] = 150 states[0] = 0.003 states[1] = 0 states[2] = 0 states[3] = 0 states[4] = 0 states[5] = 0 states[6] = 0 states[7] = 0 states[8] = 0 states[9] = 0 states[10] = 0 states[11] = 0 states[12] = 1.2 states[13] = 0 states[14] = 0 states[15] = 0 states[16] = 0 states[17] = 1.2 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = -constants[7]*(((((constants[0]-states[1])-states[2])-states[3])-states[5])-states[4])*(constants[1]-states[2])+constants[17]*states[2]+constants[28]*states[3] rates[2] = constants[7]*(((((constants[0]-states[1])-states[2])-states[3])-states[5])-states[4])*(constants[1]-states[2])-(constants[17]+constants[27])*states[2] rates[1] = (((-constants[8]*states[1]*(constants[2]-states[3])+constants[18]*states[3]+constants[27]*states[2]+(constants[29]+constants[19])*states[5])-constants[9]*states[1]*((((((((constants[3]-states[6])-states[7])-states[8])-states[9])-states[5])-states[4])-states[10])-states[11]))+(constants[31]+constants[21])*states[4])-constants[11]*states[6]*states[1] rates[3] = constants[8]*states[1]*(constants[2]-states[3])-(constants[18]+constants[28])*states[3] rates[12] = -constants[9]*((((((((constants[3]-states[6])-states[7])-states[8])-states[9])-states[5])-states[4])-states[10])-states[11])*states[1]+constants[19]*states[5]+constants[30]*states[8] rates[5] = constants[9]*((((((((constants[3]-states[6])-states[7])-states[8])-states[9])-states[5])-states[4])-states[10])-states[11])*states[1]-(constants[19]+constants[29])*states[5] rates[6] = (-constants[10]*states[6]*((constants[4]-states[8])-states[9])+constants[20]*states[8]+constants[29]*states[5]+constants[32]*states[9]+constants[21]*states[4])-constants[11]*states[6]*states[1] rates[8] = constants[10]*states[6]*((constants[4]-states[8])-states[9])-(constants[20]+constants[30])*states[8] rates[4] = constants[11]*states[6]*states[1]-(constants[21]+constants[31])*states[4] rates[7] = ((((constants[31]*states[4]-constants[12]*states[7]*((constants[4]-states[8])-states[9]))+constants[22]*states[9])-constants[13]*states[7]*((((((constants[5]-states[13])-states[14])-states[15])-states[16])-states[10])-states[11]))+(constants[23]+constants[33])*states[10]+(constants[25]+constants[35])*states[11])-constants[15]*states[13]*states[7] rates[9] = constants[12]*states[7]*((constants[4]-states[8])-states[9])-(constants[22]+constants[32])*states[9] rates[17] = -constants[13]*((((((constants[5]-states[13])-states[14])-states[15])-states[16])-states[10])-states[11])*states[7]+constants[23]*states[10]+constants[34]*states[15] rates[10] = constants[13]*((((((constants[5]-states[13])-states[14])-states[15])-states[16])-states[10])-states[11])*states[7]-(constants[23]+constants[33])*states[10] rates[13] = (((constants[33]*states[10]-constants[14]*states[13]*((constants[6]-states[15])-states[16]))+constants[24]*states[15])-constants[15]*states[13]*states[7])+constants[25]*states[11]+constants[36]*states[16] rates[11] = constants[15]*states[13]*states[7]-(constants[25]+constants[35])*states[11] rates[14] = -constants[16]*states[14]*((constants[6]-states[15])-states[16])+constants[26]*states[16]+constants[35]*states[11] rates[15] = constants[14]*states[13]*((constants[6]-states[15])-states[16])-(constants[24]+constants[34])*states[15] rates[16] = constants[16]*states[14]*((constants[6]-states[15])-states[16])-(constants[26]+constants[36])*states[16] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) 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)