# Size of variable arrays: sizeAlgebraic = 9 sizeStates = 13 sizeConstants = 15 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_algebraic[0] = "v1 in component main (flux)" legend_algebraic[1] = "v2 in component main (flux)" legend_algebraic[2] = "v3 in component main (flux)" legend_algebraic[3] = "v4 in component main (flux)" legend_algebraic[4] = "v5 in component main (flux)" legend_algebraic[5] = "v6 in component main (flux)" legend_algebraic[6] = "v7 in component main (flux)" legend_algebraic[7] = "v8 in component main (flux)" legend_algebraic[8] = "v9 in component main (flux)" legend_states[0] = "MT1 in component main (molar)" legend_states[1] = "MT1cat in component main (molar)" legend_states[2] = "MT1T2 in component main (molar)" legend_states[3] = "MT1T2M2P in component main (molar)" legend_states[4] = "M2P in component main (molar)" legend_states[5] = "M2 in component main (molar)" legend_states[6] = "M2T2 in component main (molar)" legend_states[7] = "M2T2star in component main (molar)" legend_states[8] = "M2C1 in component main (molar)" legend_states[9] = "C1 in component main (molar)" legend_states[10] = "C1dmt1 in component main (molar)" legend_states[11] = "C1dm2 in component main (molar)" legend_states[12] = "T2 in component main (molar)" legend_constants[0] = "kshed_eff in component model_parameters (second_order_rate_constant)" legend_constants[1] = "kon_MT1T2 in component model_parameters (second_order_rate_constant)" legend_constants[2] = "ki_MT1T2 in component model_parameters (molar)" legend_constants[3] = "kon_MT1T2M2P in component model_parameters (second_order_rate_constant)" legend_constants[4] = "koff_MT1T2M2P in component model_parameters (first_order_rate_constant)" legend_constants[5] = "kact_eff_m2 in component model_parameters (second_order_rate_constant)" legend_constants[6] = "kon_M2T2 in component model_parameters (second_order_rate_constant)" legend_constants[7] = "ki_M2T2 in component model_parameters (molar)" legend_constants[8] = "kiso_M2T2 in component model_parameters (first_order_rate_constant)" legend_constants[9] = "k_iso_M2T2 in component model_parameters (first_order_rate_constant)" legend_constants[10] = "kon_M2C1 in component model_parameters (second_order_rate_constant)" legend_constants[11] = "koff_M2C1 in component model_parameters (first_order_rate_constant)" legend_constants[12] = "kcat_M2C1 in component model_parameters (first_order_rate_constant)" legend_constants[13] = "kcat_MT1C1 in component model_parameters (first_order_rate_constant)" legend_constants[14] = "km_MT1C1 in component model_parameters (molar)" legend_rates[0] = "d/dt MT1 in component main (molar)" legend_rates[1] = "d/dt MT1cat in component main (molar)" legend_rates[2] = "d/dt MT1T2 in component main (molar)" legend_rates[3] = "d/dt MT1T2M2P in component main (molar)" legend_rates[4] = "d/dt M2P in component main (molar)" legend_rates[5] = "d/dt M2 in component main (molar)" legend_rates[6] = "d/dt M2T2 in component main (molar)" legend_rates[7] = "d/dt M2T2star in component main (molar)" legend_rates[8] = "d/dt M2C1 in component main (molar)" legend_rates[9] = "d/dt C1 in component main (molar)" legend_rates[10] = "d/dt C1dmt1 in component main (molar)" legend_rates[11] = "d/dt C1dm2 in component main (molar)" legend_rates[12] = "d/dt T2 in component main (molar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 100e-9 states[1] = 0 states[2] = 0 states[3] = 0 states[4] = 50e-9 states[5] = 0 states[6] = 0 states[7] = 0 states[8] = 0 states[9] = 1e-6 states[10] = 0 states[11] = 0 states[12] = 50e-9 constants[0] = 2.8e3 constants[1] = 3.54e6 constants[2] = 4.9e-9 constants[3] = 0.14e6 constants[4] = 4.7e-3 constants[5] = 2.8e3 constants[6] = 5.9e6 constants[7] = 1.07e-6 constants[8] = 33 constants[9] = 2e-8 constants[10] = 2.6e3 constants[11] = 2.1e-3 constants[12] = 4.5e-3 constants[13] = 1.97e-3 constants[14] = 2.9e-6 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[0]*states[0]*states[0] rates[1] = algebraic[0] algebraic[1] = constants[1]*states[0]*states[12]-constants[2]*constants[1]*states[2] rates[0] = -algebraic[0]-algebraic[1] algebraic[2] = constants[3]*states[2]*states[4]-constants[4]*states[3] rates[2] = algebraic[1]-algebraic[2] rates[4] = -algebraic[2] algebraic[3] = constants[5]*states[0]*states[3] rates[3] = algebraic[2]-algebraic[3] algebraic[4] = constants[6]*states[5]*states[12]-constants[6]*constants[7]*states[6] rates[12] = -algebraic[1]-algebraic[4] algebraic[6] = constants[10]*states[5]*states[9]-constants[11]*states[8] rates[5] = (algebraic[3]-algebraic[4])-algebraic[6] algebraic[5] = constants[8]*states[6]-constants[9]*states[7] rates[6] = algebraic[4]-algebraic[5] rates[7] = algebraic[5] algebraic[7] = constants[12]*states[8] rates[8] = algebraic[6]-algebraic[7] algebraic[8] = (constants[13]/constants[14])*states[0]*states[9] rates[9] = -algebraic[6]-algebraic[8] rates[10] = algebraic[8] rates[11] = algebraic[7] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[0]*states[0]*states[0] algebraic[1] = constants[1]*states[0]*states[12]-constants[2]*constants[1]*states[2] algebraic[2] = constants[3]*states[2]*states[4]-constants[4]*states[3] algebraic[3] = constants[5]*states[0]*states[3] algebraic[4] = constants[6]*states[5]*states[12]-constants[6]*constants[7]*states[6] algebraic[6] = constants[10]*states[5]*states[9]-constants[11]*states[8] algebraic[5] = constants[8]*states[6]-constants[9]*states[7] algebraic[7] = constants[12]*states[8] algebraic[8] = (constants[13]/constants[14])*states[0]*states[9] 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)