# Size of variable arrays: sizeAlgebraic = 4 sizeStates = 4 sizeConstants = 14 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_states[0] = "r in component r (nanomolar)" legend_algebraic[0] = "Ir in component r (flux)" legend_constants[0] = "k6 in component r (first_order_rate_constant)" legend_states[1] = "s in component s (nanomolar)" legend_algebraic[1] = "Is in component model_parameters (flux)" legend_constants[1] = "k7 in component model_parameters (first_order_rate_constant)" legend_states[2] = "f in component f (dimensionless)" legend_constants[2] = "k1 in component f (second_order_rate_constant)" legend_constants[3] = "k2 in component f (first_order_rate_constant)" legend_constants[4] = "k3 in component f (first_order_rate_constant)" legend_algebraic[2] = "phi_b_s in component f (dimensionless)" legend_constants[5] = "sb in component f (dimensionless)" legend_constants[6] = "delta_b in component f (dimensionless)" legend_constants[7] = "c in component model_parameters (nanomolar)" legend_states[3] = "h in component h (nanomolar)" legend_constants[8] = "k4 in component h (first_order_rate_constant)" legend_constants[9] = "k5 in component h (first_order_rate_constant)" legend_algebraic[3] = "phi_r_s in component h (dimensionless)" legend_constants[10] = "sr in component h (dimensionless)" legend_constants[11] = "delta_r in component h (dimensionless)" legend_constants[12] = "k8 in component model_parameters (first_order_rate_constant)" legend_constants[13] = "j1 in component model_parameters (dimensionless)" legend_rates[0] = "d/dt r in component r (nanomolar)" legend_rates[1] = "d/dt s in component s (nanomolar)" legend_rates[2] = "d/dt f in component f (dimensionless)" legend_rates[3] = "d/dt h in component h (nanomolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.0 constants[0] = 5.0 states[1] = 0.0 constants[1] = 5.0 states[2] = 0.3 constants[2] = 0.1 constants[3] = 0.002 constants[4] = 0.018 constants[5] = 0.029 constants[6] = 0.3 constants[7] = 0.01 states[3] = 0.0 constants[8] = 9.0 constants[9] = 71.0 constants[10] = -0.56 constants[11] = 0.3 constants[12] = 0.07 constants[13] = 10 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = custom_piecewise([greater_equal(voi , 0.00000) & less_equal(voi , 90.0000), 0.00000 , greater_equal(voi , 91.0000) & less_equal(voi , 92.0000), 10.0000 , greater_equal(voi , 93.0000) & less_equal(voi , 113.000), 0.00000 , greater_equal(voi , 114.000) & less_equal(voi , 115.000), 10.0000 , greater_equal(voi , 116.000) & less_equal(voi , 136.000), 0.00000 , greater_equal(voi , 137.000) & less_equal(voi , 138.000), 10.0000 , greater_equal(voi , 139.000) & less_equal(voi , 159.000), 0.00000 , greater_equal(voi , 160.000) & less_equal(voi , 161.000), 10.0000 , greater_equal(voi , 162.000) & less_equal(voi , 252.000), 0.00000 , greater_equal(voi , 253.000) & less_equal(voi , 254.000), 10.0000 , greater_equal(voi , 255.000) & less_equal(voi , 275.000), 0.00000 , greater_equal(voi , 276.000) & less_equal(voi , 277.000), 10.0000 , greater_equal(voi , 278.000) & less_equal(voi , 298.000), 0.00000 , greater_equal(voi , 299.000) & less_equal(voi , 300.000), 10.0000 , greater_equal(voi , 301.000) & less_equal(voi , 321.000), 0.00000 , greater_equal(voi , 322.000) & less_equal(voi , 323.000), 10.0000 , True, 0.00000]) rates[0] = algebraic[0]-constants[0]*states[0] algebraic[1] = custom_piecewise([greater(voi , 0.00000) & less_equal(voi , 90.0000), 10.0000 , greater(voi , 90.0000) & less_equal(voi , 180.000), 0.00000 , greater(voi , 180.000) & less_equal(voi , 270.000), 10.0000 , greater(voi , 270.000) & less_equal(voi , 360.000), 0.00000 , True, 0.00000]) rates[1] = algebraic[1]-constants[1]*states[1] algebraic[2] = 1.00000/(1.00000+exp(-(log(1.00000*states[1], 10)-constants[5])/constants[6])) rates[2] = -(constants[2]*(states[0]+constants[7])*states[2])+(constants[3]+constants[4]*algebraic[2])*(1.00000-states[2]) algebraic[3] = 1.00000/(1.00000+exp(-(log(1.00000*states[1], 10)-constants[10])/constants[11])) rates[3] = constants[13]*((constants[8]+constants[9]*(1.00000-algebraic[3]))*((states[0]+constants[7])*states[2])-constants[12]*states[3]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = custom_piecewise([greater_equal(voi , 0.00000) & less_equal(voi , 90.0000), 0.00000 , greater_equal(voi , 91.0000) & less_equal(voi , 92.0000), 10.0000 , greater_equal(voi , 93.0000) & less_equal(voi , 113.000), 0.00000 , greater_equal(voi , 114.000) & less_equal(voi , 115.000), 10.0000 , greater_equal(voi , 116.000) & less_equal(voi , 136.000), 0.00000 , greater_equal(voi , 137.000) & less_equal(voi , 138.000), 10.0000 , greater_equal(voi , 139.000) & less_equal(voi , 159.000), 0.00000 , greater_equal(voi , 160.000) & less_equal(voi , 161.000), 10.0000 , greater_equal(voi , 162.000) & less_equal(voi , 252.000), 0.00000 , greater_equal(voi , 253.000) & less_equal(voi , 254.000), 10.0000 , greater_equal(voi , 255.000) & less_equal(voi , 275.000), 0.00000 , greater_equal(voi , 276.000) & less_equal(voi , 277.000), 10.0000 , greater_equal(voi , 278.000) & less_equal(voi , 298.000), 0.00000 , greater_equal(voi , 299.000) & less_equal(voi , 300.000), 10.0000 , greater_equal(voi , 301.000) & less_equal(voi , 321.000), 0.00000 , greater_equal(voi , 322.000) & less_equal(voi , 323.000), 10.0000 , True, 0.00000]) algebraic[1] = custom_piecewise([greater(voi , 0.00000) & less_equal(voi , 90.0000), 10.0000 , greater(voi , 90.0000) & less_equal(voi , 180.000), 0.00000 , greater(voi , 180.000) & less_equal(voi , 270.000), 10.0000 , greater(voi , 270.000) & less_equal(voi , 360.000), 0.00000 , True, 0.00000]) algebraic[2] = 1.00000/(1.00000+exp(-(log(1.00000*states[1], 10)-constants[5])/constants[6])) algebraic[3] = 1.00000/(1.00000+exp(-(log(1.00000*states[1], 10)-constants[10])/constants[11])) return algebraic def custom_piecewise(cases): """Compute result of a piecewise function""" return select(cases[0::2],cases[1::2]) 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)