# Size of variable arrays: sizeAlgebraic = 11 sizeStates = 7 sizeConstants = 14 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_GTP in component environment (fmol)" legend_states[1] = "q_E5c in component environment (fmol)" legend_states[2] = "q_cGMP in component environment (fmol)" legend_states[3] = "q_PDE in component environment (fmol)" legend_states[4] = "q_GTP_E5c in component environment (fmol)" legend_states[5] = "q_cGMP_PDE in component environment (fmol)" legend_states[6] = "q_GMP in component environment (fmol)" legend_algebraic[7] = "v_R_1a_cGMP in component cGMP (fmol_per_sec)" legend_algebraic[8] = "v_R_1b_cGMP in component cGMP (fmol_per_sec)" legend_algebraic[9] = "v_R_2a_cGMP in component cGMP (fmol_per_sec)" legend_algebraic[10] = "v_R_2b_cGMP in component cGMP (fmol_per_sec)" legend_constants[0] = "kappa_R_1a_cGMP in component cGMP_parameters (fmol_per_sec)" legend_constants[1] = "kappa_R_1b_cGMP in component cGMP_parameters (fmol_per_sec)" legend_constants[2] = "kappa_R_2a_cGMP in component cGMP_parameters (fmol_per_sec)" legend_constants[3] = "kappa_R_2b_cGMP in component cGMP_parameters (fmol_per_sec)" legend_constants[4] = "K_GTP in component cGMP_parameters (per_fmol)" legend_constants[5] = "K_E5c in component cGMP_parameters (per_fmol)" legend_constants[6] = "K_cGMP in component cGMP_parameters (per_fmol)" legend_constants[7] = "K_PDE in component cGMP_parameters (per_fmol)" legend_constants[8] = "K_GTP_E5c in component cGMP_parameters (per_fmol)" legend_constants[9] = "K_cGMP_PDE in component cGMP_parameters (per_fmol)" legend_constants[10] = "K_GMP in component cGMP_parameters (per_fmol)" legend_constants[11] = "R in component constants (J_per_K_per_mol)" legend_constants[12] = "T in component constants (kelvin)" legend_algebraic[0] = "mu_GTP in component cGMP (J_per_mol)" legend_algebraic[1] = "mu_E5c in component cGMP (J_per_mol)" legend_algebraic[2] = "mu_cGMP in component cGMP (J_per_mol)" legend_algebraic[3] = "mu_PDE in component cGMP (J_per_mol)" legend_algebraic[4] = "mu_GTP_E5c in component cGMP (J_per_mol)" legend_algebraic[5] = "mu_cGMP_PDE in component cGMP (J_per_mol)" legend_algebraic[6] = "mu_GMP in component cGMP (J_per_mol)" legend_constants[13] = "F in component constants (C_per_mol)" legend_rates[0] = "d/dt q_GTP in component environment (fmol)" legend_rates[1] = "d/dt q_E5c in component environment (fmol)" legend_rates[2] = "d/dt q_cGMP in component environment (fmol)" legend_rates[3] = "d/dt q_PDE in component environment (fmol)" legend_rates[4] = "d/dt q_GTP_E5c in component environment (fmol)" legend_rates[5] = "d/dt q_cGMP_PDE in component environment (fmol)" legend_rates[6] = "d/dt q_GMP 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] = 1e-18 states[1] = 1e-18 states[2] = 1e-18 states[3] = 1e-18 states[4] = 1e-18 states[5] = 1e-18 states[6] = 1e-18 constants[0] = 1772.99 constants[1] = 0.0302117 constants[2] = 73652.7 constants[3] = 0.0143623 constants[4] = 1600.8 constants[5] = 0.0255983 constants[6] = 0.0939434 constants[7] = 10.5002 constants[8] = 152.027 constants[9] = 7.31926 constants[10] = 0.000481761 constants[11] = 8.31 constants[12] = 310 constants[13] = 96485 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[11]*constants[12]*log(constants[4]*states[0]) algebraic[1] = constants[11]*constants[12]*log(constants[5]*states[1]) algebraic[4] = constants[11]*constants[12]*log(constants[8]*states[4]) algebraic[7] = constants[0]*(exp((algebraic[0]+algebraic[1])/(constants[11]*constants[12]))-exp(algebraic[4]/(constants[11]*constants[12]))) rates[0] = -algebraic[7] algebraic[2] = constants[11]*constants[12]*log(constants[6]*states[2]) algebraic[8] = constants[1]*(exp(algebraic[4]/(constants[11]*constants[12]))-exp((algebraic[2]+algebraic[1])/(constants[11]*constants[12]))) rates[1] = -algebraic[7]+algebraic[8] rates[4] = algebraic[7]-algebraic[8] algebraic[3] = constants[11]*constants[12]*log(constants[7]*states[3]) algebraic[5] = constants[11]*constants[12]*log(constants[9]*states[5]) algebraic[9] = constants[2]*(exp((algebraic[2]+algebraic[3])/(constants[11]*constants[12]))-exp(algebraic[5]/(constants[11]*constants[12]))) algebraic[6] = constants[11]*constants[12]*log(constants[10]*states[6]) algebraic[10] = constants[3]*(exp((algebraic[5]+algebraic[2])/(constants[11]*constants[12]))-exp((algebraic[6]+algebraic[3])/(constants[11]*constants[12]))) rates[2] = (algebraic[8]-algebraic[9])-algebraic[10] rates[3] = -algebraic[9]+algebraic[10] rates[5] = algebraic[9]-algebraic[10] rates[6] = algebraic[10] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[11]*constants[12]*log(constants[4]*states[0]) algebraic[1] = constants[11]*constants[12]*log(constants[5]*states[1]) algebraic[4] = constants[11]*constants[12]*log(constants[8]*states[4]) algebraic[7] = constants[0]*(exp((algebraic[0]+algebraic[1])/(constants[11]*constants[12]))-exp(algebraic[4]/(constants[11]*constants[12]))) algebraic[2] = constants[11]*constants[12]*log(constants[6]*states[2]) algebraic[8] = constants[1]*(exp(algebraic[4]/(constants[11]*constants[12]))-exp((algebraic[2]+algebraic[1])/(constants[11]*constants[12]))) algebraic[3] = constants[11]*constants[12]*log(constants[7]*states[3]) algebraic[5] = constants[11]*constants[12]*log(constants[9]*states[5]) algebraic[9] = constants[2]*(exp((algebraic[2]+algebraic[3])/(constants[11]*constants[12]))-exp(algebraic[5]/(constants[11]*constants[12]))) algebraic[6] = constants[11]*constants[12]*log(constants[10]*states[6]) algebraic[10] = constants[3]*(exp((algebraic[5]+algebraic[2])/(constants[11]*constants[12]))-exp((algebraic[6]+algebraic[3])/(constants[11]*constants[12]))) 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)