# Size of variable arrays: sizeAlgebraic = 20 sizeStates = 14 sizeConstants = 24 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_states[0] = "NatP in component NatP (molecules)" legend_constants[22] = "v1 in component v1 (flux)" legend_algebraic[0] = "v2 in component v2 (flux)" legend_algebraic[4] = "v5 in component v5 (flux)" legend_states[1] = "MisP in component MisP (molecules)" legend_algebraic[1] = "v3 in component v3 (flux)" legend_algebraic[3] = "v4 in component v4 (flux)" legend_algebraic[5] = "v6 in component v6 (flux)" legend_algebraic[6] = "v7 in component v7 (flux)" legend_states[2] = "MCom in component MCom (molecules)" legend_states[3] = "Hsp90 in component Hsp90 (molecules)" legend_algebraic[8] = "v9 in component v9 (flux)" legend_algebraic[16] = "v16 in component v16 (flux)" legend_algebraic[7] = "v8 in component v8 (flux)" legend_algebraic[17] = "v17 in component v17 (flux)" legend_states[4] = "HCom in component HCom (molecules)" legend_states[5] = "HSF1 in component HSF1 (molecules)" legend_algebraic[14] = "v13 in component v13 (flux)" legend_algebraic[12] = "v12 in component v12 (flux)" legend_algebraic[10] = "v10 in component v10 (flux)" legend_algebraic[11] = "v11 in component v11 (flux)" legend_states[6] = "DiH in component DiH (molecules)" legend_states[7] = "TriH in component TriH (molecules)" legend_algebraic[13] = "v14 in component v14 (flux)" legend_algebraic[15] = "v15 in component v15 (flux)" legend_states[8] = "HSE_TriH in component HSE_TriH (molecules)" legend_states[9] = "HSE in component HSE (molecules)" legend_states[10] = "AggP in component AggP (molecules)" legend_algebraic[9] = "v7b in component v7b (flux)" legend_states[11] = "ROS in component ROS (molecules)" legend_constants[23] = "v20 in component v20 (flux)" legend_algebraic[2] = "v21 in component v21 (flux)" legend_states[12] = "ATP in component ATP (molecules)" legend_algebraic[18] = "v18 in component v18 (flux)" legend_algebraic[19] = "v19 in component v19 (flux)" legend_states[13] = "ADP in component ADP (molecules)" legend_constants[0] = "k1 in component v1 (flux)" legend_constants[1] = "k2 in component v2 (second_order_rate_constant)" legend_constants[2] = "k3 in component v3 (second_order_rate_constant)" legend_constants[3] = "k4 in component v4 (first_order_rate_constant)" legend_constants[4] = "k5 in component v5 (second_order_rate_constant)" legend_constants[5] = "k6 in component v6 (second_order_rate_constant)" legend_constants[6] = "k7 in component v7 (second_order_rate_constant)" legend_constants[7] = "k7 in component v7b (second_order_rate_constant)" legend_constants[8] = "k8 in component v8 (second_order_rate_constant)" legend_constants[9] = "k9 in component v9 (first_order_rate_constant)" legend_constants[10] = "k10 in component v10 (second_order_rate_constant)" legend_constants[11] = "k11 in component v11 (second_order_rate_constant)" legend_constants[12] = "k12 in component v12 (first_order_rate_constant)" legend_constants[13] = "k13 in component v13 (first_order_rate_constant)" legend_constants[14] = "k14 in component v14 (second_order_rate_constant)" legend_constants[15] = "k15 in component v15 (first_order_rate_constant)" legend_constants[16] = "k16 in component v16 (first_order_rate_constant)" legend_constants[17] = "k17 in component v17 (second_order_rate_constant)" legend_constants[18] = "k18 in component v18 (first_order_rate_constant)" legend_constants[19] = "k19 in component v19 (first_order_rate_constant)" legend_constants[20] = "k20 in component v20 (flux)" legend_constants[21] = "k21 in component v21 (first_order_rate_constant)" legend_rates[0] = "d/dt NatP in component NatP (molecules)" legend_rates[1] = "d/dt MisP in component MisP (molecules)" legend_rates[2] = "d/dt MCom in component MCom (molecules)" legend_rates[3] = "d/dt Hsp90 in component Hsp90 (molecules)" legend_rates[4] = "d/dt HCom in component HCom (molecules)" legend_rates[5] = "d/dt HSF1 in component HSF1 (molecules)" legend_rates[6] = "d/dt DiH in component DiH (molecules)" legend_rates[7] = "d/dt TriH in component TriH (molecules)" legend_rates[8] = "d/dt HSE_TriH in component HSE_TriH (molecules)" legend_rates[9] = "d/dt HSE in component HSE (molecules)" legend_rates[10] = "d/dt AggP in component AggP (molecules)" legend_rates[11] = "d/dt ROS in component ROS (molecules)" legend_rates[12] = "d/dt ATP in component ATP (molecules)" legend_rates[13] = "d/dt ADP in component ADP (molecules)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 6000000 states[1] = 0 states[2] = 0 states[3] = 300000 states[4] = 5900 states[5] = 100 states[6] = 0 states[7] = 0 states[8] = 0 states[9] = 1 states[10] = 0 states[11] = 100 states[12] = 10000 states[13] = 1000 constants[0] = 10 constants[1] = 0.00002 constants[2] = 50 constants[3] = 0.00001 constants[4] = 4e-6 constants[5] = 6e-7 constants[6] = 1e-7 constants[7] = 1e-7 constants[8] = 500 constants[9] = 1 constants[10] = 0.01 constants[11] = 100 constants[12] = 0.5 constants[13] = 0.5 constants[14] = 0.05 constants[15] = 0.08 constants[16] = 1000 constants[17] = 8.02e-9 constants[18] = 12 constants[19] = 0.02 constants[20] = 0.1 constants[21] = 0.00001 constants[22] = constants[0] constants[23] = constants[20] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[1]*states[0]*states[11] algebraic[2] = constants[21]*states[11] rates[11] = (algebraic[0]+constants[23])-(algebraic[0]+algebraic[2]) algebraic[4] = constants[4]*states[2]*states[12] rates[0] = (constants[22]+algebraic[4])-algebraic[0] algebraic[1] = constants[2]*states[1]*states[3] algebraic[3] = constants[3]*states[2] rates[2] = algebraic[1]-(algebraic[3]+algebraic[4]) algebraic[5] = constants[5]*states[1]*states[12] algebraic[6] = constants[6]*states[1]*states[1] rates[1] = (algebraic[0]+algebraic[3])-(algebraic[1]+algebraic[5]+2.00000*algebraic[6]) algebraic[8] = constants[9]*states[4] algebraic[7] = constants[8]*states[5]*states[3] rates[4] = algebraic[7]-algebraic[8] algebraic[9] = constants[7]*states[1]*states[10] rates[10] = (algebraic[6]+2.00000*algebraic[9])-algebraic[9] algebraic[14] = constants[13]*states[6] algebraic[12] = constants[12]*states[7] algebraic[10] = constants[10]*states[5]*states[5] algebraic[11] = constants[11]*states[6]*states[5] rates[5] = (algebraic[8]+2.00000*algebraic[14]+algebraic[12])-(algebraic[7]+2.00000*algebraic[10]+algebraic[11]) rates[6] = (algebraic[10]+algebraic[12])-(algebraic[11]+algebraic[14]) algebraic[13] = constants[14]*states[9]*states[7] algebraic[15] = constants[15]*states[8] rates[7] = (algebraic[11]+algebraic[15])-(algebraic[12]+algebraic[13]) rates[9] = algebraic[15]-algebraic[13] algebraic[16] = constants[16]*states[8] rates[8] = (algebraic[13]+algebraic[16])-(algebraic[15]+algebraic[16]) algebraic[17] = constants[17]*states[3]*states[12] rates[3] = (algebraic[4]+algebraic[3]+algebraic[8]+algebraic[16])-(algebraic[1]+algebraic[7]+algebraic[17]) algebraic[18] = constants[18]*states[13] algebraic[19] = constants[19]*states[12] rates[12] = algebraic[18]-(algebraic[4]+algebraic[5]+algebraic[17]+algebraic[19]) rates[13] = (algebraic[4]+algebraic[5]+algebraic[17]+algebraic[19])-algebraic[18] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[1]*states[0]*states[11] algebraic[2] = constants[21]*states[11] algebraic[4] = constants[4]*states[2]*states[12] algebraic[1] = constants[2]*states[1]*states[3] algebraic[3] = constants[3]*states[2] algebraic[5] = constants[5]*states[1]*states[12] algebraic[6] = constants[6]*states[1]*states[1] algebraic[8] = constants[9]*states[4] algebraic[7] = constants[8]*states[5]*states[3] algebraic[9] = constants[7]*states[1]*states[10] algebraic[14] = constants[13]*states[6] algebraic[12] = constants[12]*states[7] algebraic[10] = constants[10]*states[5]*states[5] algebraic[11] = constants[11]*states[6]*states[5] algebraic[13] = constants[14]*states[9]*states[7] algebraic[15] = constants[15]*states[8] algebraic[16] = constants[16]*states[8] algebraic[17] = constants[17]*states[3]*states[12] algebraic[18] = constants[18]*states[13] algebraic[19] = constants[19]*states[12] 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)