# Size of variable arrays: sizeAlgebraic = 13 sizeStates = 8 sizeConstants = 16 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_states[0] = "q_PLB in component environment (fmol)" legend_states[1] = "q_PKACI in component environment (fmol)" legend_states[2] = "q_PLB_PKACI in component environment (fmol)" legend_states[3] = "q_PP1 in component environment (fmol)" legend_states[4] = "q_PLBp_PP1 in component environment (fmol)" legend_states[5] = "q_PLBp in component environment (fmol)" legend_states[6] = "q_Ip in component environment (fmol)" legend_states[7] = "q_Ip_PP1 in component environment (fmol)" legend_algebraic[8] = "v_PLBph1 in component PLB (fmol_per_sec)" legend_algebraic[9] = "v_PLBph2 in component PLB (fmol_per_sec)" legend_algebraic[10] = "v_PLBd1 in component PLB (fmol_per_sec)" legend_algebraic[11] = "v_PLBd2 in component PLB (fmol_per_sec)" legend_algebraic[12] = "v_Inh in component PLB (fmol_per_sec)" legend_constants[0] = "kappa_PLBph1 in component PLB_parameters (fmol_per_sec)" legend_constants[1] = "kappa_PLBph2 in component PLB_parameters (fmol_per_sec)" legend_constants[2] = "kappa_PLBd1 in component PLB_parameters (fmol_per_sec)" legend_constants[3] = "kappa_PLBd2 in component PLB_parameters (fmol_per_sec)" legend_constants[4] = "kappa_Inh in component PLB_parameters (fmol_per_sec)" legend_constants[5] = "K_PLB in component PLB_parameters (per_fmol)" legend_constants[6] = "K_PKACI in component PLB_parameters (per_fmol)" legend_constants[7] = "K_PLB_PKACI in component PLB_parameters (per_fmol)" legend_constants[8] = "K_PP1 in component PLB_parameters (per_fmol)" legend_constants[9] = "K_PLBp_PP1 in component PLB_parameters (per_fmol)" legend_constants[10] = "K_PLBp in component PLB_parameters (per_fmol)" legend_constants[11] = "K_Ip in component PLB_parameters (per_fmol)" legend_constants[12] = "K_Ip_PP1 in component PLB_parameters (per_fmol)" legend_constants[13] = "R in component constants (J_per_K_per_mol)" legend_constants[14] = "T in component constants (kelvin)" legend_algebraic[0] = "mu_PLB in component PLB (J_per_mol)" legend_algebraic[1] = "mu_PKACI in component PLB (J_per_mol)" legend_algebraic[2] = "mu_PLB_PKACI in component PLB (J_per_mol)" legend_algebraic[3] = "mu_PP1 in component PLB (J_per_mol)" legend_algebraic[4] = "mu_PLBp_PP1 in component PLB (J_per_mol)" legend_algebraic[5] = "mu_PLBp in component PLB (J_per_mol)" legend_algebraic[6] = "mu_Ip in component PLB (J_per_mol)" legend_algebraic[7] = "mu_Ip_PP1 in component PLB (J_per_mol)" legend_constants[15] = "F in component constants (C_per_mol)" legend_rates[0] = "d/dt q_PLB in component environment (fmol)" legend_rates[1] = "d/dt q_PKACI in component environment (fmol)" legend_rates[2] = "d/dt q_PLB_PKACI in component environment (fmol)" legend_rates[3] = "d/dt q_PP1 in component environment (fmol)" legend_rates[4] = "d/dt q_PLBp_PP1 in component environment (fmol)" legend_rates[5] = "d/dt q_PLBp in component environment (fmol)" legend_rates[6] = "d/dt q_Ip in component environment (fmol)" legend_rates[7] = "d/dt q_Ip_PP1 in component environment (fmol)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 4.028E+00 states[1] = 1.117E-03 states[2] = 1e-13 states[3] = 3.382E-02 states[4] = 1e-13 states[5] = 1.560E-01 states[6] = 9.994E-04 states[7] = 1e-13 constants[0] = 45.5263 constants[1] = 6.55904 constants[2] = 0.386674 constants[3] = 1.21269 constants[4] = 431.435 constants[5] = 0.00235741 constants[6] = 0.395191 constants[7] = 0.638527 constants[8] = 0.361989 constants[9] = 0.203757 constants[10] = 0.326014 constants[11] = 5.41093 constants[12] = 0.0673793 constants[13] = 8.31 constants[14] = 310 constants[15] = 96485 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[13]*constants[14]*log(constants[5]*states[0]) algebraic[1] = constants[13]*constants[14]*log(constants[6]*states[1]) algebraic[2] = constants[13]*constants[14]*log(constants[7]*states[2]) algebraic[8] = constants[0]*(exp((algebraic[0]+algebraic[1])/(constants[13]*constants[14]))-exp(algebraic[2]/(constants[13]*constants[14]))) algebraic[5] = constants[13]*constants[14]*log(constants[10]*states[5]) algebraic[9] = constants[1]*(exp(algebraic[2]/(constants[13]*constants[14]))-exp((algebraic[5]+algebraic[1])/(constants[13]*constants[14]))) rates[1] = algebraic[9]-algebraic[8] rates[2] = algebraic[8]-algebraic[9] algebraic[3] = constants[13]*constants[14]*log(constants[8]*states[3]) algebraic[4] = constants[13]*constants[14]*log(constants[9]*states[4]) algebraic[10] = constants[2]*(exp((algebraic[5]+algebraic[3])/(constants[13]*constants[14]))-exp(algebraic[4]/(constants[13]*constants[14]))) rates[5] = algebraic[9]-algebraic[10] algebraic[11] = constants[3]*(exp(algebraic[4]/(constants[13]*constants[14]))-exp((algebraic[0]+algebraic[3])/(constants[13]*constants[14]))) rates[0] = algebraic[11]-algebraic[8] rates[4] = algebraic[10]-algebraic[11] algebraic[6] = constants[13]*constants[14]*log(constants[11]*states[6]) algebraic[7] = constants[13]*constants[14]*log(constants[12]*states[7]) algebraic[12] = constants[4]*(exp((algebraic[3]+algebraic[6])/(constants[13]*constants[14]))-exp(algebraic[7]/(constants[13]*constants[14]))) rates[3] = (algebraic[11]-algebraic[10])-algebraic[12] rates[6] = -algebraic[12] rates[7] = algebraic[12] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[13]*constants[14]*log(constants[5]*states[0]) algebraic[1] = constants[13]*constants[14]*log(constants[6]*states[1]) algebraic[2] = constants[13]*constants[14]*log(constants[7]*states[2]) algebraic[8] = constants[0]*(exp((algebraic[0]+algebraic[1])/(constants[13]*constants[14]))-exp(algebraic[2]/(constants[13]*constants[14]))) algebraic[5] = constants[13]*constants[14]*log(constants[10]*states[5]) algebraic[9] = constants[1]*(exp(algebraic[2]/(constants[13]*constants[14]))-exp((algebraic[5]+algebraic[1])/(constants[13]*constants[14]))) algebraic[3] = constants[13]*constants[14]*log(constants[8]*states[3]) algebraic[4] = constants[13]*constants[14]*log(constants[9]*states[4]) algebraic[10] = constants[2]*(exp((algebraic[5]+algebraic[3])/(constants[13]*constants[14]))-exp(algebraic[4]/(constants[13]*constants[14]))) algebraic[11] = constants[3]*(exp(algebraic[4]/(constants[13]*constants[14]))-exp((algebraic[0]+algebraic[3])/(constants[13]*constants[14]))) algebraic[6] = constants[13]*constants[14]*log(constants[11]*states[6]) algebraic[7] = constants[13]*constants[14]*log(constants[12]*states[7]) algebraic[12] = constants[4]*(exp((algebraic[3]+algebraic[6])/(constants[13]*constants[14]))-exp(algebraic[7]/(constants[13]*constants[14]))) 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)