# Size of variable arrays: sizeAlgebraic = 16 sizeStates = 6 sizeConstants = 19 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] = "q_PKACI_init in component environment (fmol)" legend_constants[1] = "q_Ip_init in component environment (fmol)" legend_constants[2] = "q_Ip_PKACI_init in component environment (fmol)" legend_constants[3] = "q_PP2a_init in component environment (fmol)" legend_constants[4] = "q_Ip_PP2a_init in component environment (fmol)" legend_constants[5] = "q_I_init in component environment (fmol)" legend_algebraic[0] = "q_PKACI in component environment (fmol)" legend_algebraic[1] = "q_Ip in component environment (fmol)" legend_algebraic[2] = "q_Ip_PKACI in component environment (fmol)" legend_algebraic[3] = "q_PP2a in component environment (fmol)" legend_algebraic[4] = "q_Ip_PP2a in component environment (fmol)" legend_algebraic[5] = "q_I in component environment (fmol)" legend_states[0] = "q_PKACI in component Inhib1 (fmol)" legend_states[1] = "q_Ip in component Inhib1 (fmol)" legend_states[2] = "q_Ip_PKACI in component Inhib1 (fmol)" legend_states[3] = "q_PP2a in component Inhib1 (fmol)" legend_states[4] = "q_Ip_PP2a in component Inhib1 (fmol)" legend_states[5] = "q_I in component Inhib1 (fmol)" legend_constants[6] = "kappa_PKAi1 in component Inhib1_parameters (fmol_per_sec)" legend_constants[7] = "kappa_PKAi2 in component Inhib1_parameters (fmol_per_sec)" legend_constants[8] = "kappa_PP2ai1 in component Inhib1_parameters (fmol_per_sec)" legend_constants[9] = "kappa_PP2ai2 in component Inhib1_parameters (fmol_per_sec)" legend_constants[10] = "K_PKACI in component Inhib1_parameters (per_fmol)" legend_constants[11] = "K_Ip in component Inhib1_parameters (per_fmol)" legend_constants[12] = "K_Ip_PKACI in component Inhib1_parameters (per_fmol)" legend_constants[13] = "K_PP2a in component Inhib1_parameters (per_fmol)" legend_constants[14] = "K_Ip_PP2a in component Inhib1_parameters (per_fmol)" legend_constants[15] = "K_I in component Inhib1_parameters (per_fmol)" legend_constants[16] = "R in component constants (J_per_K_per_mol)" legend_constants[17] = "T in component constants (kelvin)" legend_algebraic[12] = "vPKAi1 in component Inhib1 (fmol_per_sec)" legend_algebraic[13] = "vPKAi2 in component Inhib1 (fmol_per_sec)" legend_algebraic[14] = "vPP2ai1 in component Inhib1 (fmol_per_sec)" legend_algebraic[15] = "vPP2ai2 in component Inhib1 (fmol_per_sec)" legend_algebraic[6] = "mu_PKACI in component Inhib1 (J_per_mol)" legend_algebraic[7] = "mu_Ip in component Inhib1 (J_per_mol)" legend_algebraic[8] = "mu_Ip_PKACI in component Inhib1 (J_per_mol)" legend_algebraic[9] = "mu_PP2a in component Inhib1 (J_per_mol)" legend_algebraic[10] = "mu_Ip_PP2a in component Inhib1 (J_per_mol)" legend_algebraic[11] = "mu_I in component Inhib1 (J_per_mol)" legend_constants[18] = "F in component constants (C_per_mol)" legend_rates[0] = "d/dt q_PKACI in component Inhib1 (fmol)" legend_rates[1] = "d/dt q_Ip in component Inhib1 (fmol)" legend_rates[2] = "d/dt q_Ip_PKACI in component Inhib1 (fmol)" legend_rates[3] = "d/dt q_PP2a in component Inhib1 (fmol)" legend_rates[4] = "d/dt q_Ip_PP2a in component Inhib1 (fmol)" legend_rates[5] = "d/dt q_I in component Inhib1 (fmol)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 1.117E-03 constants[1] = 9.994E-04 constants[2] = 1e-13 constants[3] = 8.512E-03 constants[4] = 1e-13 constants[5] = 1.140E-02 states[0] = 1e-16 states[1] = 1e-16 states[2] = 1e-16 states[3] = 1e-16 states[4] = 1e-16 states[5] = 1e-16 constants[6] = 20.9606 constants[7] = 22.2706 constants[8] = 5.39341 constants[9] = 5.30013 constants[10] = 0.284433 constants[11] = 0.133405 constants[12] = 1.38688 constants[13] = 0.0704691 constants[14] = 0.342795 constants[15] = 0.150247 constants[16] = 8.31 constants[17] = 310 constants[18] = 96485 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = states[0]+constants[0] algebraic[6] = constants[16]*constants[17]*log(constants[10]*algebraic[0]) algebraic[2] = states[2]+constants[2] algebraic[8] = constants[16]*constants[17]*log(constants[12]*algebraic[2]) algebraic[5] = states[5]+constants[5] algebraic[11] = constants[16]*constants[17]*log(constants[15]*algebraic[5]) algebraic[12] = constants[6]*(exp((algebraic[6]+algebraic[11])/(constants[16]*constants[17]))-exp(algebraic[8]/(constants[16]*constants[17]))) algebraic[1] = states[1]+constants[1] algebraic[7] = constants[16]*constants[17]*log(constants[11]*algebraic[1]) algebraic[13] = constants[7]*(exp(algebraic[8]/(constants[16]*constants[17]))-exp((algebraic[6]+algebraic[7])/(constants[16]*constants[17]))) rates[0] = algebraic[13]-algebraic[12] rates[2] = algebraic[12]-algebraic[13] algebraic[3] = states[3]+constants[3] algebraic[9] = constants[16]*constants[17]*log(constants[13]*algebraic[3]) algebraic[4] = states[4]+constants[4] algebraic[10] = constants[16]*constants[17]*log(constants[14]*algebraic[4]) algebraic[14] = constants[8]*(exp((algebraic[9]+algebraic[7])/(constants[16]*constants[17]))-exp(algebraic[10]/(constants[16]*constants[17]))) rates[1] = algebraic[13]-algebraic[14] algebraic[15] = constants[9]*(exp(algebraic[10]/(constants[16]*constants[17]))-exp((algebraic[9]+algebraic[11])/(constants[16]*constants[17]))) rates[3] = algebraic[15]-algebraic[14] rates[4] = algebraic[14]-algebraic[15] rates[5] = algebraic[15]-algebraic[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]+constants[0] algebraic[6] = constants[16]*constants[17]*log(constants[10]*algebraic[0]) algebraic[2] = states[2]+constants[2] algebraic[8] = constants[16]*constants[17]*log(constants[12]*algebraic[2]) algebraic[5] = states[5]+constants[5] algebraic[11] = constants[16]*constants[17]*log(constants[15]*algebraic[5]) algebraic[12] = constants[6]*(exp((algebraic[6]+algebraic[11])/(constants[16]*constants[17]))-exp(algebraic[8]/(constants[16]*constants[17]))) algebraic[1] = states[1]+constants[1] algebraic[7] = constants[16]*constants[17]*log(constants[11]*algebraic[1]) algebraic[13] = constants[7]*(exp(algebraic[8]/(constants[16]*constants[17]))-exp((algebraic[6]+algebraic[7])/(constants[16]*constants[17]))) algebraic[3] = states[3]+constants[3] algebraic[9] = constants[16]*constants[17]*log(constants[13]*algebraic[3]) algebraic[4] = states[4]+constants[4] algebraic[10] = constants[16]*constants[17]*log(constants[14]*algebraic[4]) algebraic[14] = constants[8]*(exp((algebraic[9]+algebraic[7])/(constants[16]*constants[17]))-exp(algebraic[10]/(constants[16]*constants[17]))) algebraic[15] = constants[9]*(exp(algebraic[10]/(constants[16]*constants[17]))-exp((algebraic[9]+algebraic[11])/(constants[16]*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)