# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 8 sizeConstants = 13 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] = "Rs in component Rs (number_per_cell)" legend_states[1] = "L in component L (picomolar)" legend_states[2] = "Cs in component Cs (number_per_cell)" legend_constants[0] = "Vs in component model_parameters (number_per_cell_minute)" legend_constants[10] = "kf in component model_parameters (second_order_rate_constant)" legend_constants[1] = "kr in component model_parameters (first_order_rate_constant)" legend_constants[2] = "kt in component model_parameters (first_order_rate_constant)" legend_constants[3] = "ksyn in component model_parameters (first_order_rate_constant)" legend_constants[4] = "ke in component model_parameters (first_order_rate_constant)" legend_states[3] = "Ri in component Ri (number_per_cell)" legend_states[4] = "Li in component Li (picomolar)" legend_states[5] = "Ci in component Ci (number_per_cell)" legend_constants[12] = "kfe in component model_parameters (second_order_rate_constant)" legend_constants[11] = "kre in component model_parameters (first_order_rate_constant)" legend_constants[5] = "kh in component model_parameters (first_order_rate_constant)" legend_constants[6] = "kx in component model_parameters (first_order_rate_constant)" legend_constants[7] = "Ve in component model_parameters (L_per_cell)" legend_constants[8] = "NA in component model_parameters (number_per_picomole)" legend_states[6] = "Ld in component Ld (number_per_cell)" legend_states[7] = "Y in component Y (cell_per_L)" legend_constants[9] = "IL2 in component model_parameters (dimensionless)" legend_rates[0] = "d/dt Rs in component Rs (number_per_cell)" legend_rates[2] = "d/dt Cs in component Cs (number_per_cell)" legend_rates[3] = "d/dt Ri in component Ri (number_per_cell)" legend_rates[5] = "d/dt Ci in component Ci (number_per_cell)" legend_rates[4] = "d/dt Li in component Li (picomolar)" legend_rates[6] = "d/dt Ld in component Ld (number_per_cell)" legend_rates[1] = "d/dt L in component L (picomolar)" legend_rates[7] = "d/dt Y in component Y (cell_per_L)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 1500 states[1] = 10 states[2] = 1 constants[0] = 11 constants[1] = 0.0138 constants[2] = 0.007 constants[3] = 0.0011 constants[4] = 0.04 states[3] = 300 states[4] = 0.01 states[5] = 1 constants[5] = 0.035 constants[6] = 0.15 constants[7] = 1e-14 constants[8] = 6.022e11 states[6] = 1 states[7] = 2.5e8 constants[9] = 1 constants[10] = custom_piecewise([equal(constants[9] , 1.00000), constants[1]/11.1000 , True, constants[1]/8.20000]) constants[11] = custom_piecewise([equal(constants[9] , 1.00000), constants[1]*8.00000 , True, constants[1]*5.00000]) constants[12] = custom_piecewise([equal(constants[9] , 1.00000), constants[11]/1000.00 , True, constants[11]/3000.00]) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = ((constants[1]+constants[3])*states[2]+constants[0])-(constants[10]*states[1]*states[0]+constants[2]*states[0]) rates[2] = constants[10]*states[1]*states[0]-(constants[1]+constants[4])*states[2] rates[3] = (constants[11]*states[5]+constants[2]*states[0])-(constants[12]*states[4]*states[3]+constants[5]*states[3]) rates[5] = (constants[12]*states[4]*states[3]+constants[4]*states[2])-(constants[11]+constants[5])*states[5] rates[4] = (constants[11]*states[5]-constants[12]*states[4]*states[3])/(constants[7]*constants[8])-constants[6]*states[4] rates[6] = constants[5]*states[5] rates[1] = (((constants[1]*states[2]+constants[6]*states[4]*constants[7]*constants[8])-constants[10]*states[1]*states[0])*states[7])/constants[8] rates[7] = custom_piecewise([greater((600.000*states[2])/(250.000+states[2])-200.000 , 0.00000), ((600.000*states[2])/(250.000+states[2])-200.000)*1000.00 , True, 0.00000]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) 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)