# Size of variable arrays: sizeAlgebraic = 4 sizeStates = 6 sizeConstants = 28 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 (minute)" legend_constants[0] = "H_1 in component parameters (dimensionless)" legend_constants[1] = "H_2 in component parameters (dimensionless)" legend_constants[2] = "H_3 in component parameters (dimensionless)" legend_constants[3] = "H_4 in component parameters (dimensionless)" legend_constants[4] = "K_1 in component parameters (dimensionless)" legend_constants[5] = "K_2 in component parameters (dimensionless)" legend_constants[6] = "K_3 in component parameters (dimensionless)" legend_constants[7] = "K_4 in component parameters (dimensionless)" legend_constants[8] = "V_M1 in component parameters (first_order_rate_constant)" legend_constants[9] = "V_M3 in component parameters (first_order_rate_constant)" legend_constants[10] = "U_M1 in component parameters (first_order_rate_constant)" legend_constants[11] = "U_M3 in component parameters (first_order_rate_constant)" legend_constants[12] = "V_2 in component parameters (first_order_rate_constant)" legend_constants[13] = "V_4 in component parameters (first_order_rate_constant)" legend_constants[14] = "U_2 in component parameters (first_order_rate_constant)" legend_constants[15] = "U_4 in component parameters (first_order_rate_constant)" legend_constants[16] = "K_c1 in component parameters (micromolar)" legend_constants[17] = "K_c2 in component parameters (micromolar)" legend_constants[18] = "K_d1 in component parameters (micromolar)" legend_constants[19] = "K_d2 in component parameters (micromolar)" legend_constants[20] = "v_d1 in component parameters (flux)" legend_constants[21] = "v_d2 in component parameters (flux)" legend_constants[22] = "v_i1 in component parameters (flux)" legend_constants[23] = "v_i2 in component parameters (flux)" legend_constants[24] = "k_d1 in component parameters (first_order_rate_constant)" legend_constants[25] = "k_d2 in component parameters (first_order_rate_constant)" legend_constants[26] = "K_im1 in component parameters (dimensionless)" legend_constants[27] = "K_im2 in component parameters (dimensionless)" legend_states[0] = "C_1 in component C_1 (micromolar)" legend_states[1] = "M_2 in component M_2 (dimensionless)" legend_states[2] = "X_1 in component X_1 (dimensionless)" legend_states[3] = "M_1 in component M_1 (dimensionless)" legend_algebraic[0] = "V_1 in component V_1 (first_order_rate_constant)" legend_algebraic[1] = "V_3 in component V_3 (first_order_rate_constant)" legend_states[4] = "C_2 in component C_2 (micromolar)" legend_states[5] = "X_2 in component X_2 (dimensionless)" legend_algebraic[2] = "U_1 in component U_1 (first_order_rate_constant)" legend_algebraic[3] = "U_3 in component U_3 (first_order_rate_constant)" legend_rates[0] = "d/dt C_1 in component C_1 (micromolar)" legend_rates[3] = "d/dt M_1 in component M_1 (dimensionless)" legend_rates[2] = "d/dt X_1 in component X_1 (dimensionless)" legend_rates[4] = "d/dt C_2 in component C_2 (micromolar)" legend_rates[1] = "d/dt M_2 in component M_2 (dimensionless)" legend_rates[5] = "d/dt X_2 in component X_2 (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0.01 constants[1] = 0.01 constants[2] = 0.01 constants[3] = 0.01 constants[4] = 0.01 constants[5] = 0.01 constants[6] = 0.01 constants[7] = 0.01 constants[8] = 0.3 constants[9] = 0.1 constants[10] = 0.3 constants[11] = 0.1 constants[12] = 0.15 constants[13] = 0.05 constants[14] = 0.15 constants[15] = 0.05 constants[16] = 0.5 constants[17] = 0.5 constants[18] = 0.02 constants[19] = 0.02 constants[20] = 0.025 constants[21] = 0.025 constants[22] = 0.05 constants[23] = 0.05 constants[24] = 0.001 constants[25] = 0.001 constants[26] = 0.03 constants[27] = 0.03 states[0] = 2 states[1] = 0 states[2] = 0 states[3] = 1 states[4] = 0 states[5] = 0 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = ((constants[22]*constants[26])/(constants[26]+states[1])-(constants[20]*states[2]*states[0])/(constants[18]+states[0]))-constants[24]*states[0] rates[4] = ((constants[23]*constants[27])/(constants[27]+states[3])-(constants[21]*states[5]*states[4])/(constants[19]+states[4]))-constants[25]*states[4] algebraic[0] = (states[0]/(constants[16]+states[0]))*constants[8] rates[3] = (algebraic[0]*(1.00000-states[3]))/(constants[4]+(1.00000-states[3]))-(constants[12]*states[3])/(constants[5]+states[3]) algebraic[1] = states[3]*constants[9] rates[2] = (algebraic[1]*(1.00000-states[2]))/(constants[6]+(1.00000-states[2]))-(constants[13]*states[2])/(constants[7]+states[2]) algebraic[2] = (states[4]/(constants[17]+states[4]))*constants[10] rates[1] = (algebraic[2]*(1.00000-states[1]))/(constants[0]+(1.00000-states[1]))-(constants[14]*states[1])/(constants[1]+states[1]) algebraic[3] = states[1]*constants[11] rates[5] = (algebraic[3]*(1.00000-states[5]))/(constants[2]+(1.00000-states[5]))-(constants[15]*states[5])/(constants[3]+states[5]) 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[16]+states[0]))*constants[8] algebraic[1] = states[3]*constants[9] algebraic[2] = (states[4]/(constants[17]+states[4]))*constants[10] algebraic[3] = states[1]*constants[11] 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)