# Size of variable arrays: sizeAlgebraic = 3 sizeStates = 9 sizeConstants = 18 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] = "NGF in component NGF (dimensionless)" legend_constants[1] = "pro_TrkA in component pro_TrkA (dimensionless)" legend_states[0] = "TrkA in component TrkA (dimensionless)" legend_states[1] = "NGF_TrkA in component NGF_TrkA (dimensionless)" legend_constants[2] = "k2_NGF_TrkA in component model_parameters (first_order_rate_constant)" legend_constants[3] = "k1_NGF_TrkA in component model_parameters (first_order_rate_constant)" legend_constants[4] = "TrkA_turnover in component model_parameters (first_order_rate_constant)" legend_constants[5] = "k1_TrkA_phosphorylation in component model_parameters (first_order_rate_constant)" legend_states[2] = "pTrkA in component pTrkA (dimensionless)" legend_states[3] = "pTrkA_Akt in component pTrkA_Akt (dimensionless)" legend_states[4] = "Akt in component Akt (dimensionless)" legend_constants[6] = "k1_pTrkA_degradation in component model_parameters (first_order_rate_constant)" legend_constants[7] = "k1_Akt_phosphorylation in component model_parameters (first_order_rate_constant)" legend_constants[8] = "k1_pTrkA_Akt in component model_parameters (first_order_rate_constant)" legend_constants[9] = "k2_pTrkA_Akt in component model_parameters (first_order_rate_constant)" legend_states[5] = "pAkt in component pAkt (dimensionless)" legend_constants[10] = "k1_pAkt_dephosphorylation in component model_parameters (first_order_rate_constant)" legend_states[6] = "S6 in component S6 (dimensionless)" legend_states[7] = "pAkt_S6 in component pAkt_S6 (dimensionless)" legend_constants[11] = "k1_pAkt_S6 in component model_parameters (first_order_rate_constant)" legend_constants[12] = "k2_pAkt_S6 in component model_parameters (first_order_rate_constant)" legend_constants[13] = "k1_S6_phosphorylation in component model_parameters (first_order_rate_constant)" legend_states[8] = "pS6 in component pS6 (dimensionless)" legend_constants[14] = "k1_pS6_dephosphorylation in component model_parameters (first_order_rate_constant)" legend_algebraic[0] = "pTrkA_total in component pTrkA_total (dimensionless)" legend_constants[15] = "pTrkA_scalefactor in component pTrkA_total (dimensionless)" legend_algebraic[1] = "pAkt_total in component pAkt_total (dimensionless)" legend_constants[16] = "pAkt_scalefactor in component pAkt_total (dimensionless)" legend_algebraic[2] = "pS6_total in component pS6_total (dimensionless)" legend_constants[17] = "pS6_scalefactor in component pS6_total (dimensionless)" legend_rates[0] = "d/dt TrkA in component TrkA (dimensionless)" legend_rates[1] = "d/dt NGF_TrkA in component NGF_TrkA (dimensionless)" legend_rates[2] = "d/dt pTrkA in component pTrkA (dimensionless)" legend_rates[3] = "d/dt pTrkA_Akt in component pTrkA_Akt (dimensionless)" legend_rates[4] = "d/dt Akt in component Akt (dimensionless)" legend_rates[5] = "d/dt pAkt in component pAkt (dimensionless)" legend_rates[7] = "d/dt pAkt_S6 in component pAkt_S6 (dimensionless)" legend_rates[6] = "d/dt S6 in component S6 (dimensionless)" legend_rates[8] = "d/dt pS6 in component pS6 (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 30.0 constants[1] = 8.52065e0 states[0] = 8.52065e0 states[1] = 0.0 constants[2] = 1.33747e-2 constants[3] = 2.69408e-3 constants[4] = 0.0011032440769796 constants[5] = 8.33178e-3 states[2] = 0.0 states[3] = 0.0 states[4] = 1.15595e0 constants[6] = 6.8084e-2 constants[7] = 2.02517e-2 constants[8] = 8.82701e-2 constants[9] = 1.47518e-10 states[5] = 0.0 constants[10] = 1.28135e0 states[6] = 3.55234e0 states[7] = 0.0 constants[11] = 6.83666e1 constants[12] = 5.23519e-00 constants[13] = 5.65150e-3 states[8] = 0.0 constants[14] = 2.93167e-4 constants[15] = 8.48783e-1 constants[16] = 2.42381e0 constants[17] = 5.25843e-1 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = (constants[2]*states[1]+constants[4]*(constants[1]-states[0]))-constants[3]*constants[0]*states[0] rates[1] = constants[3]*constants[0]*states[0]-(constants[2]*states[1]+constants[5]*states[1]) rates[2] = (constants[5]*states[1]+constants[7]*states[3]+constants[9]*states[3])-(constants[6]*states[2]+constants[8]*states[2]*states[4]) rates[3] = constants[8]*states[2]*states[4]-(constants[9]*states[3]+constants[7]*states[3]) rates[4] = (constants[9]*states[3]+constants[10]*states[5])-constants[8]*states[2]*states[4] rates[5] = (constants[7]*states[3]+constants[12]*states[7]+constants[13]*states[7])-(constants[10]*states[5]+constants[11]*states[5]*states[6]) rates[7] = constants[11]*states[5]*states[6]-(constants[12]*states[7]+constants[13]*states[7]) rates[6] = (constants[12]*states[7]+constants[14]*states[8])-constants[11]*states[5]*states[6] rates[8] = constants[13]*states[7]-constants[14]*states[8] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = (states[2]+states[3])*constants[15] algebraic[1] = (states[5]+states[7])*constants[16] algebraic[2] = states[8]*constants[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)