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# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 6 sizeConstants = 16 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] = "n in component parameters (dimensionless)" legend_constants[12] = "alpha_0 in component parameters (dimensionless)" legend_constants[13] = "alpha in component parameters (dimensionless)" legend_constants[14] = "beta in component parameters (dimensionless)" legend_constants[1] = "K_m in component parameters (dimensionless)" legend_constants[2] = "efficiency in component parameters (dimensionless)" legend_constants[3] = "mRNA_halflife in component parameters (minute)" legend_constants[7] = "t_ave in component parameters (minute)" legend_constants[8] = "kd_prot in component parameters (first_order_rate_constant)" legend_constants[9] = "kd_mRNA in component parameters (first_order_rate_constant)" legend_constants[4] = "prot_halflife in component parameters (minute)" legend_constants[5] = "tps_repr in component parameters (per_sec)" legend_constants[6] = "tps_active in component parameters (per_sec)" legend_constants[15] = "k_tl in component parameters (first_order_rate_constant)" legend_constants[10] = "a_tr in component parameters (first_order_rate_constant)" legend_constants[11] = "a0_tr in component parameters (first_order_rate_constant)" legend_states[0] = "M_lacl in component M_lacl (dimensionless)" legend_states[1] = "P_cl in component P_cl (dimensionless)" legend_states[2] = "M_tetR in component M_tetR (dimensionless)" legend_states[3] = "P_lacl in component P_lacl (dimensionless)" legend_states[4] = "M_cl in component M_cl (dimensionless)" legend_states[5] = "P_tetR in component P_tetR (dimensionless)" legend_rates[0] = "d/dt M_lacl in component M_lacl (dimensionless)" legend_rates[2] = "d/dt M_tetR in component M_tetR (dimensionless)" legend_rates[4] = "d/dt M_cl in component M_cl (dimensionless)" legend_rates[3] = "d/dt P_lacl in component P_lacl (dimensionless)" legend_rates[5] = "d/dt P_tetR in component P_tetR (dimensionless)" legend_rates[1] = "d/dt P_cl in component P_cl (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 2 constants[1] = 40 constants[2] = 20 constants[3] = 2 constants[4] = 10 constants[5] = 5e-4 constants[6] = 0.5 states[0] = 0 states[1] = 0 states[2] = 20 states[3] = 0 states[4] = 0 states[5] = 0 constants[7] = constants[3]/log(2.00000) constants[8] = log(2.00000)/constants[4] constants[9] = log(2.00000)/constants[3] constants[10] = (constants[6]-constants[5])*60.0000 constants[11] = constants[5]*60.0000 constants[12] = (constants[11]*constants[2])/(constants[8]*constants[1]) constants[13] = (constants[10]*constants[2])/(constants[8]*constants[1]) constants[14] = constants[8]/constants[9] constants[15] = constants[2]*constants[9] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = (constants[11]+(constants[10]*(power(constants[1], constants[0])))/(power(constants[1], constants[0])+power(states[1], constants[0])))-constants[9]*states[0] rates[2] = ((constants[10]*(power(constants[1], constants[0])))/(power(constants[1], constants[0])+power(states[3], constants[0]))+constants[11])-constants[9]*states[2] rates[4] = ((constants[10]*(power(constants[1], constants[0])))/(power(constants[1], constants[0])+power(states[5], constants[0]))+constants[11])-constants[9]*states[4] rates[3] = constants[15]*states[0]-constants[8]*states[3] rates[5] = constants[15]*states[2]-constants[8]*states[5] rates[1] = constants[15]*states[4]-constants[8]*states[1] 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)