# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 11 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] = "k11 in component kinetic_constants (second_order_rate_constant)" legend_constants[1] = "k11_ in component kinetic_constants (first_order_rate_constant)" legend_constants[2] = "k71 in component kinetic_constants (first_order_rate_constant)" legend_constants[3] = "k72 in component kinetic_constants (first_order_rate_constant)" legend_constants[4] = "k12 in component kinetic_constants (second_order_rate_constant)" legend_constants[5] = "k12_ in component kinetic_constants (first_order_rate_constant)" legend_constants[6] = "k51 in component kinetic_constants (first_order_rate_constant)" legend_constants[7] = "k52 in component kinetic_constants (first_order_rate_constant)" legend_constants[8] = "k41 in component kinetic_constants (first_order_rate_constant)" legend_constants[9] = "k31 in component kinetic_constants (first_order_rate_constant)" legend_constants[10] = "k32 in component kinetic_constants (first_order_rate_constant)" legend_constants[11] = "k42 in component kinetic_constants (first_order_rate_constant)" legend_constants[12] = "k22 in component kinetic_constants (first_order_rate_constant)" legend_constants[13] = "k22_ in component kinetic_constants (first_order_rate_constant)" legend_constants[14] = "k21 in component kinetic_constants (first_order_rate_constant)" legend_constants[15] = "k21_ in component kinetic_constants (first_order_rate_constant)" legend_states[0] = "PB in component PB (micromolar)" legend_constants[16] = "kreset1 in component kreset1 (first_order_rate_constant)" legend_states[1] = "A1 in component A1 (micromolar)" legend_states[2] = "A2 in component A2 (micromolar)" legend_states[3] = "PC1 in component PC1 (micromolar)" legend_states[4] = "PF1 in component PF1 (micromolar)" legend_states[5] = "PG1 in component PG1 (micromolar)" legend_states[6] = "PC2 in component PC2 (micromolar)" legend_states[7] = "PF2 in component PF2 (micromolar)" legend_states[8] = "PD1 in component PD1 (micromolar)" legend_states[9] = "PE1 in component PE1 (micromolar)" legend_states[10] = "PD2 in component PD2 (micromolar)" legend_constants[17] = "PE2 in component PE2 (micromolar)" legend_rates[0] = "d/dt PB in component PB (micromolar)" legend_rates[1] = "d/dt A1 in component A1 (micromolar)" legend_rates[2] = "d/dt A2 in component A2 (micromolar)" legend_rates[3] = "d/dt PC1 in component PC1 (micromolar)" legend_rates[8] = "d/dt PD1 in component PD1 (micromolar)" legend_rates[9] = "d/dt PE1 in component PE1 (micromolar)" legend_rates[4] = "d/dt PF1 in component PF1 (micromolar)" legend_rates[5] = "d/dt PG1 in component PG1 (micromolar)" legend_rates[6] = "d/dt PC2 in component PC2 (micromolar)" legend_rates[10] = "d/dt PD2 in component PD2 (micromolar)" legend_rates[7] = "d/dt PF2 in component PF2 (micromolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 110.0 constants[1] = 25.0 constants[2] = 0.1 constants[3] = 60.0 constants[4] = 110.0 constants[5] = 0.2 constants[6] = 7.0 constants[7] = 0.0 constants[8] = 60.0 constants[9] = 500.0 constants[10] = 50.0 constants[11] = 70.0 constants[12] = 100.0 constants[13] = 17.0 constants[14] = 100.0 constants[15] = 0.2 states[0] = 0.1 constants[16] = 35.0 states[1] = 0.1 states[2] = 0.1 states[3] = 0.1 states[4] = 0.1 states[5] = 0.1 states[6] = 0.1 states[7] = 0.1 states[8] = 0.1 states[9] = 0.1 states[10] = 0.1 constants[17] = 0.1 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = (constants[1]*states[3]+constants[2]*states[4]+constants[16]*states[5]+constants[5]*states[6]+constants[3]*states[7])-(constants[0]*states[1]*states[0]+constants[4]*states[2]*states[0]) rates[1] = constants[1]*states[3]-constants[0]*states[1]*states[0] rates[2] = constants[5]*states[6]-constants[4]*states[2]*states[0] rates[3] = (constants[0]*states[1]*states[0]-(constants[1]+constants[14])*states[3])+constants[15]*states[8] rates[8] = constants[14]*states[3]-(constants[15]+constants[9])*states[8] rates[9] = constants[9]*states[8]-constants[8]*states[9] rates[4] = constants[8]*states[9]-(constants[6]+constants[2])*states[4] rates[5] = constants[6]*states[4]-constants[16]*states[5] rates[6] = (constants[4]*states[2]*states[0]-(constants[5]+constants[12])*states[6])+constants[13]*states[10] rates[10] = constants[12]*states[6]-(constants[13]+constants[10])*states[10] rates[7] = constants[11]*constants[17]-(constants[7]+constants[3])*states[7] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) 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)