# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 6 sizeConstants = 25 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] = "j_1 in component parameters (flux)" legend_constants[1] = "j_2 in component parameters (flux)" legend_constants[2] = "j_3 in component parameters (flux)" legend_constants[3] = "v_d1 in component parameters (flux)" legend_constants[4] = "v_d2 in component parameters (flux)" legend_constants[5] = "v_d3 in component parameters (flux)" legend_constants[6] = "k_d1 in component parameters (first_order_rate_constant)" legend_constants[7] = "k_d2 in component parameters (first_order_rate_constant)" legend_constants[8] = "k_d3 in component parameters (first_order_rate_constant)" legend_constants[9] = "k_c1 in component parameters (first_order_rate_constant)" legend_constants[10] = "k_c2 in component parameters (first_order_rate_constant)" legend_constants[11] = "k_c3 in component parameters (first_order_rate_constant)" legend_constants[12] = "k_m1 in component parameters (nanomolar)" legend_constants[13] = "k_m2 in component parameters (nanomolar)" legend_constants[14] = "k_m3 in component parameters (nanomolar)" legend_constants[15] = "v_12 in component parameters (flux)" legend_constants[16] = "v_11 in component parameters (flux)" legend_constants[17] = "v_10 in component parameters (flux)" legend_constants[18] = "k_120 in component parameters (nanomolar)" legend_constants[19] = "k_110 in component parameters (nanomolar)" legend_constants[20] = "k_100 in component parameters (nanomolar)" legend_constants[21] = "k_d4 in component parameters (first_order_rate_constant)" legend_constants[22] = "k_d5 in component parameters (first_order_rate_constant)" legend_constants[23] = "k_d6 in component parameters (first_order_rate_constant)" legend_constants[24] = "n in component parameters (dimensionless)" legend_states[0] = "C_1 in component C_1 (nanomolar)" legend_states[1] = "C_2 in component C_2 (nanomolar)" legend_states[2] = "T_1 in component T_1 (nanomolar)" legend_states[3] = "C_3 in component C_3 (nanomolar)" legend_states[4] = "T_2 in component T_2 (nanomolar)" legend_states[5] = "T_3 in component T_3 (nanomolar)" legend_rates[0] = "d/dt C_1 in component C_1 (nanomolar)" legend_rates[1] = "d/dt C_2 in component C_2 (nanomolar)" legend_rates[3] = "d/dt C_3 in component C_3 (nanomolar)" legend_rates[2] = "d/dt T_1 in component T_1 (nanomolar)" legend_rates[4] = "d/dt T_2 in component T_2 (nanomolar)" legend_rates[5] = "d/dt T_3 in component T_3 (nanomolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0.9 constants[1] = 0.5 constants[2] = 0.6 constants[3] = 6 constants[4] = 1.052 constants[5] = 3 constants[6] = 0.8 constants[7] = 0.9 constants[8] = 0.8 constants[9] = 0.2 constants[10] = 0.22 constants[11] = 0.6 constants[12] = 5 constants[13] = 5 constants[14] = 5 constants[15] = 15 constants[16] = 15 constants[17] = 15 constants[18] = 10 constants[19] = 10 constants[20] = 10 constants[21] = 0.16 constants[22] = 0.16 constants[23] = 0.16 constants[24] = 2 states[0] = 0 states[1] = 0 states[2] = 6 states[3] = 0 states[4] = 5 states[5] = 1 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = (constants[15]*(power(states[2], constants[24])))/(power(constants[18], constants[24])+power(states[2], constants[24])+power(states[1], constants[24]))-constants[21]*states[0] rates[1] = (constants[16]*(power(states[4], constants[24])))/(power(constants[19], constants[24])+power(states[4], constants[24])+power(states[3], constants[24]))-constants[22]*states[1] rates[3] = (constants[17]*(power(states[5], constants[24])))/(power(constants[20], constants[24])+power(states[5], constants[24])+power(states[0], constants[24]))-constants[23]*states[3] rates[2] = (constants[0]+(constants[3]*(power(states[5], constants[24])))/(power(constants[12], constants[24])+power(states[5], constants[24]))+constants[9]*states[0])-constants[6]*states[2] rates[4] = (constants[1]+(constants[4]*(power(states[2], constants[24])))/(power(constants[13], constants[24])+power(states[2], constants[24]))+constants[10]*states[1])-constants[7]*states[4] rates[5] = (constants[2]+(constants[5]*(power(states[4], constants[24])))/(power(constants[14], constants[24])+power(states[4], constants[24]))+constants[11]*states[3])-constants[8]*states[5] 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)