# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 16 sizeConstants = 21 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_voi = "t in component environment (s)" legend_constants[0] = "kM2T2_on in component Model (second_order_rate_constant)" legend_constants[1] = "kM2T2_off in component Model (first_order_rate_constant)" legend_constants[2] = "kM2T2_iso in component Model (first_order_rate_constant)" legend_constants[3] = "kM2T2_negativeiso in component Model (first_order_rate_constant)" legend_constants[4] = "kM2C1_on in component Model (second_order_rate_constant)" legend_constants[5] = "kM2C1_off in component Model (first_order_rate_constant)" legend_constants[6] = "kM2C1_cat in component Model (first_order_rate_constant)" legend_constants[7] = "kMT1T2_on in component Model (second_order_rate_constant)" legend_constants[8] = "kMT1T2_off in component Model (first_order_rate_constant)" legend_constants[9] = "kMT1T2M2pro_on in component Model (second_order_rate_constant)" legend_constants[10] = "kMT1T2M2pro_off in component Model (first_order_rate_constant)" legend_constants[11] = "kM2_act in component Model (first_order_rate_constant)" legend_constants[12] = "kMT1_shedeff in component Model (second_order_rate_constant)" legend_constants[13] = "kMT1C1_cat in component Model (first_order_rate_constant)" legend_constants[14] = "kMT1C1_on in component Model (second_order_rate_constant)" legend_constants[15] = "kMT1C1_off in component Model (first_order_rate_constant)" legend_constants[16] = "kMT1T2M2proMT1_on in component Model (second_order_rate_constant)" legend_constants[17] = "kMT1T2M2proMT1_off in component Model (first_order_rate_constant)" legend_states[0] = "M2T2 in component Model (M)" legend_states[1] = "M2C1 in component Model (M)" legend_states[2] = "MT1T2 in component Model (M)" legend_states[3] = "MT1T2M2proMT1 in component Model (M)" legend_states[4] = "MT1C1 in component Model (M)" legend_states[5] = "M2 in component Model (M)" legend_states[6] = "MT1 in component Model (M)" legend_states[7] = "M2_p in component Model (M)" legend_states[8] = "T2 in component Model (M)" legend_states[9] = "C1_D in component Model (M)" legend_states[10] = "C1 in component Model (M)" legend_states[11] = "MT1_cat in component Model (M)" legend_states[12] = "MT1_t in component Model (M)" legend_states[13] = "MT1T2M2pro in component Model (M)" legend_constants[18] = "qMT1 in component Model (flux)" legend_constants[19] = "qT2 in component Model (flux)" legend_constants[20] = "qpro in component Model (flux)" legend_states[14] = "MT1T2_star in component Model (um)" legend_states[15] = "M2T2_star in component Model (um)" legend_rates[5] = "d/dt M2 in component Model (M)" legend_rates[6] = "d/dt MT1 in component Model (M)" legend_rates[12] = "d/dt MT1_t in component Model (M)" legend_rates[4] = "d/dt MT1C1 in component Model (M)" legend_rates[2] = "d/dt MT1T2 in component Model (M)" legend_rates[13] = "d/dt MT1T2M2pro in component Model (M)" legend_rates[3] = "d/dt MT1T2M2proMT1 in component Model (M)" legend_rates[10] = "d/dt C1 in component Model (M)" legend_rates[9] = "d/dt C1_D in component Model (M)" legend_rates[11] = "d/dt MT1_cat in component Model (M)" legend_rates[8] = "d/dt T2 in component Model (M)" legend_rates[7] = "d/dt M2_p in component Model (M)" legend_rates[0] = "d/dt M2T2 in component Model (M)" legend_rates[15] = "d/dt M2T2_star in component Model (um)" legend_rates[1] = "d/dt M2C1 in component Model (M)" legend_rates[14] = "d/dt MT1T2_star in component Model (um)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 5900000 constants[1] = 6.3 constants[2] = 33 constants[3] = 0.00000002 constants[4] = 2600 constants[5] = 0.0021 constants[6] = 0.0045 constants[7] = 2980000 constants[8] = 0.202 constants[9] = 140000 constants[10] = 0.0047 constants[11] = 0.02 constants[12] = 2800 constants[13] = 0.00197 constants[14] = 1000 constants[15] = 1 constants[16] = 3000 constants[17] = 0.0009 states[0] = 0.0000000072 states[1] = 0.0000085 states[2] = 0.00000000139 states[3] = 0.00000000056 states[4] = 0.0000029 states[5] = 0 states[6] = 0 states[7] = 0 states[8] = 0 states[9] = 0 states[10] = 0 states[11] = 0 states[12] = 0 states[13] = 0 constants[18] = 0 constants[19] = 0 constants[20] = 0 states[14] = 0 states[15] = 0 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[5] = ((-constants[0]*states[5]*states[8]+constants[1]*states[0])-constants[4]*states[5]*states[10])+(constants[5]+constants[6])*states[1]+constants[11]*states[3] rates[6] = ((((((constants[18]-constants[12]*states[6]*states[6])-constants[7]*states[6]*states[8])+constants[8]*states[2])-constants[14]*states[6]*states[10])+(constants[15]+constants[13])*states[4])-constants[16]*states[6]*states[13])+constants[17]*states[3]+constants[11]*states[3] rates[12] = constants[12]*states[6]*states[6] rates[4] = constants[14]*states[6]*states[10]-(constants[15]+constants[13])*states[4] rates[2] = ((constants[7]*states[6]*states[8]-constants[8]*states[2])-constants[9]*states[2]*states[7])+constants[10]*states[13] rates[13] = ((constants[9]*states[2]*states[7]-constants[10]*states[13])-constants[16]*states[6]*states[13])+constants[17]*states[3] rates[3] = (constants[16]*states[6]*states[13]-constants[17]*states[3])-constants[11]*states[3] rates[10] = ((-constants[14]*states[6]*states[10]+constants[15]*states[4])-constants[4]*states[5]*states[10])+constants[5]*states[1] rates[9] = constants[6]*states[1]+constants[13]*states[4] rates[11] = constants[12]*states[6]*states[6] rates[8] = ((-constants[0]*states[5]*states[8]+constants[1]*states[0]+constants[19])-constants[7]*states[6]*states[8])+constants[8]*states[2] rates[7] = (constants[20]-constants[9]*states[2]*states[7])+constants[10]*states[13] rates[0] = ((constants[0]*states[5]*states[8]-constants[1]*states[0])-constants[2]*states[0])+constants[3]*states[15] rates[15] = constants[2]*states[0]-constants[3]*states[15] rates[1] = constants[4]*states[5]*states[10]-(constants[5]+constants[6])*states[1] rates[14] = constants[11]*states[3] 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)