# Size of variable arrays: sizeAlgebraic = 13 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 (second)" legend_algebraic[4] = "phi3_c1 in component phi (per_second)" legend_states[0] = "h1 in component h1 (dimensionless)" legend_algebraic[0] = "phi1_c1 in component phi (second_order_rate)" legend_algebraic[2] = "phi2_c1 in component phi (per_second)" legend_constants[0] = "p in component model_parameters (micro_molar)" legend_algebraic[1] = "phi_1_c1 in component phi (per_second)" legend_algebraic[8] = "phi3_c2 in component phi (per_second)" legend_states[1] = "h2 in component h2 (dimensionless)" legend_algebraic[3] = "phi1_c2 in component phi (second_order_rate)" legend_algebraic[6] = "phi2_c2 in component phi (per_second)" legend_algebraic[5] = "phi_1_c2 in component phi (per_second)" legend_constants[1] = "r2 in component model_parameters (second_order_rate)" legend_constants[2] = "R1 in component model_parameters (micro_molar)" legend_constants[3] = "k1 in component model_parameters (micro_molar_per_second)" legend_constants[4] = "R3 in component model_parameters (micro_molar)" legend_constants[5] = "k2 in component model_parameters (micro_molar_per_second)" legend_constants[6] = "r4 in component model_parameters (per_second)" legend_constants[7] = "k3 in component model_parameters (micro_molar_per_second)" legend_constants[8] = "R5 in component model_parameters (micro_molar)" legend_states[2] = "c1 in component c1 (micro_molar)" legend_states[3] = "c2 in component c2 (micro_molar)" legend_constants[9] = "Vp in component model_parameters (micro_molar_per_second)" legend_constants[10] = "Kp in component model_parameters (micro_molar)" legend_algebraic[7] = "j_pump_c1 in component j_pump (micro_molar_per_second)" legend_algebraic[9] = "j_pump_c2 in component j_pump (micro_molar_per_second)" legend_constants[11] = "kf in component model_parameters (micro_molar_per_second)" legend_algebraic[10] = "j_receptor_c1 in component j_receptor (micro_molar_per_second)" legend_algebraic[11] = "j_receptor_c2 in component j_receptor (micro_molar_per_second)" legend_algebraic[12] = "j_diffusion in component j_diffusion (micro_molar_per_second)" legend_constants[12] = "D in component model_parameters (per_second)" legend_constants[13] = "j_leak in component model_parameters (micro_molar_per_second)" legend_rates[0] = "d/dt h1 in component h1 (dimensionless)" legend_rates[1] = "d/dt h2 in component h2 (dimensionless)" legend_rates[2] = "d/dt c1 in component c1 (micro_molar)" legend_rates[3] = "d/dt c2 in component c2 (micro_molar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.8 constants[0] = 0.2778 states[1] = 0.1 constants[1] = 100 constants[2] = 6 constants[3] = 44 constants[4] = 50 constants[5] = 26.5 constants[6] = 20 constants[7] = 1.6 constants[8] = 1.6 states[2] = 0.3 states[3] = 0.1 constants[9] = 1.2 constants[10] = 0.18 constants[11] = 28 constants[12] = 0.01 constants[13] = 0.2 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[4] = constants[7]/(constants[8]+states[2]) algebraic[0] = (constants[1]*states[2])/(constants[2]+states[2]) algebraic[2] = (constants[5]+constants[6]*states[2])/(constants[4]+states[2]) algebraic[1] = constants[3]/(constants[4]+states[2]) rates[0] = algebraic[4]*(1.00000-states[0])-(algebraic[0]*algebraic[2]*states[0]*constants[0])/(algebraic[0]*constants[0]+algebraic[1]) algebraic[8] = constants[7]/(constants[8]+states[3]) algebraic[3] = (constants[1]*states[3])/(constants[2]+states[3]) algebraic[6] = (constants[5]+constants[6]*states[3])/(constants[4]+states[3]) algebraic[5] = constants[3]/(constants[4]+states[3]) rates[1] = algebraic[8]*(1.00000-states[1])-(algebraic[3]*algebraic[6]*states[1]*constants[0])/(algebraic[3]*constants[0]+algebraic[5]) algebraic[7] = (constants[9]*(power(states[2], 2.00000)))/(power(constants[10], 2.00000)+power(states[2], 2.00000)) algebraic[10] = constants[11]*(power((constants[0]*states[0]*algebraic[0])/(algebraic[0]*constants[0]+algebraic[1]), 4.00000)) algebraic[12] = constants[12]*(states[3]-states[2]) rates[2] = (algebraic[10]-algebraic[7])+constants[13]+algebraic[12] algebraic[9] = (constants[9]*(power(states[3], 2.00000)))/(power(constants[10], 2.00000)+power(states[3], 2.00000)) algebraic[11] = constants[11]*(power((constants[0]*states[1]*algebraic[3])/(algebraic[3]*constants[0]+algebraic[5]), 4.00000)) rates[3] = (algebraic[11]-algebraic[9])+constants[13]+algebraic[12] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[4] = constants[7]/(constants[8]+states[2]) algebraic[0] = (constants[1]*states[2])/(constants[2]+states[2]) algebraic[2] = (constants[5]+constants[6]*states[2])/(constants[4]+states[2]) algebraic[1] = constants[3]/(constants[4]+states[2]) algebraic[8] = constants[7]/(constants[8]+states[3]) algebraic[3] = (constants[1]*states[3])/(constants[2]+states[3]) algebraic[6] = (constants[5]+constants[6]*states[3])/(constants[4]+states[3]) algebraic[5] = constants[3]/(constants[4]+states[3]) algebraic[7] = (constants[9]*(power(states[2], 2.00000)))/(power(constants[10], 2.00000)+power(states[2], 2.00000)) algebraic[10] = constants[11]*(power((constants[0]*states[0]*algebraic[0])/(algebraic[0]*constants[0]+algebraic[1]), 4.00000)) algebraic[12] = constants[12]*(states[3]-states[2]) algebraic[9] = (constants[9]*(power(states[3], 2.00000)))/(power(constants[10], 2.00000)+power(states[3], 2.00000)) algebraic[11] = constants[11]*(power((constants[0]*states[1]*algebraic[3])/(algebraic[3]*constants[0]+algebraic[5]), 4.00000)) 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)