# Size of variable arrays: sizeAlgebraic = 29 sizeStates = 15 sizeConstants = 46 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] = "k1 in component rate_constants (first_order_rate_constant)" legend_constants[1] = "kn1 in component rate_constants (first_order_rate_constant)" legend_constants[2] = "k2 in component rate_constants (first_order_rate_constant)" legend_constants[3] = "kn2 in component rate_constants (first_order_rate_constant)" legend_constants[4] = "k2_ in component rate_constants (first_order_rate_constant)" legend_constants[5] = "k3_ in component rate_constants (first_order_rate_constant)" legend_constants[6] = "kn3_ in component rate_constants (first_order_rate_constant)" legend_constants[7] = "k4 in component rate_constants (first_order_rate_constant)" legend_constants[8] = "k5 in component rate_constants (first_order_rate_constant)" legend_constants[9] = "k6 in component rate_constants (first_order_rate_constant)" legend_constants[10] = "k7 in component rate_constants (first_order_rate_constant)" legend_constants[11] = "kn7 in component rate_constants (first_order_rate_constant)" legend_constants[12] = "k8 in component rate_constants (first_order_rate_constant)" legend_constants[13] = "kn8 in component rate_constants (first_order_rate_constant)" legend_constants[14] = "k8_ in component rate_constants (first_order_rate_constant)" legend_constants[15] = "k9 in component rate_constants (first_order_rate_constant)" legend_constants[16] = "kn9 in component rate_constants (first_order_rate_constant)" legend_constants[17] = "k9_ in component rate_constants (first_order_rate_constant)" legend_constants[18] = "k10 in component rate_constants (first_order_rate_constant)" legend_constants[19] = "k11 in component rate_constants (first_order_rate_constant)" legend_constants[20] = "k12 in component rate_constants (first_order_rate_constant)" legend_constants[21] = "k13 in component rate_constants (first_order_rate_constant)" legend_constants[22] = "k14 in component rate_constants (first_order_rate_constant)" legend_constants[23] = "k14_ in component rate_constants (first_order_rate_constant)" legend_constants[24] = "k15 in component rate_constants (first_order_rate_constant)" legend_constants[25] = "k16 in component rate_constants (first_order_rate_constant)" legend_constants[26] = "k17 in component rate_constants (first_order_rate_constant)" legend_constants[27] = "k18 in component rate_constants (first_order_rate_constant)" legend_constants[28] = "kn18 in component rate_constants (first_order_rate_constant)" legend_constants[29] = "k20 in component rate_constants (first_order_rate_constant)" legend_constants[30] = "k21 in component rate_constants (first_order_rate_constant)" legend_constants[31] = "k22 in component rate_constants (first_order_rate_constant)" legend_constants[32] = "k23 in component rate_constants (first_order_rate_constant)" legend_constants[33] = "kn23 in component rate_constants (first_order_rate_constant)" legend_constants[34] = "kPlk1 in component rate_constants (first_order_rate_constant)" legend_constants[35] = "kPlk1_ in component rate_constants (first_order_rate_constant)" legend_constants[36] = "kctak1 in component rate_constants (first_order_rate_constant)" legend_constants[37] = "kctak1_ in component rate_constants (first_order_rate_constant)" legend_constants[38] = "kex in component rate_constants (first_order_rate_constant)" legend_states[0] = "Chk1P in component Chk1P (dimensionless)" legend_algebraic[11] = "V_n1 in component V_n1 (first_order_rate_constant)" legend_algebraic[7] = "V_1 in component V_1 (first_order_rate_constant)" legend_states[1] = "Rad3 in component Rad3 (dimensionless)" legend_constants[41] = "V_4 in component V_4 (first_order_rate_constant)" legend_algebraic[1] = "V_5 in component V_5 (first_order_rate_constant)" legend_states[2] = "p53 in component p53 (dimensionless)" legend_constants[42] = "V_10 in component V_10 (first_order_rate_constant)" legend_algebraic[2] = "V_11 in component V_11 (first_order_rate_constant)" legend_states[3] = "preMPF in component preMPF (dimensionless)" legend_algebraic[12] = "V_14 in component V_14 (first_order_rate_constant)" legend_algebraic[8] = "V_n9 in component V_n9 (first_order_rate_constant)" legend_algebraic[3] = "V_9 in component V_9 (first_order_rate_constant)" legend_states[4] = "MPF in component MPF (dimensionless)" legend_algebraic[26] = "V_n23 in component V_n23 (first_order_rate_constant)" legend_algebraic[21] = "V_23 in component V_23 (first_order_rate_constant)" legend_algebraic[13] = "V_15 in component V_15 (first_order_rate_constant)" legend_states[5] = "p21 in component p21 (dimensionless)" legend_constants[43] = "V_21 in component V_21 (first_order_rate_constant)" legend_algebraic[16] = "V_20 in component V_20 (first_order_rate_constant)" legend_algebraic[18] = "V_22 in component V_22 (first_order_rate_constant)" legend_states[6] = "p21_MPF in component p21_MPF (dimensionless)" legend_states[7] = "iCdc25 in component iCdc25 (dimensionless)" legend_algebraic[27] = "V_n7 in component V_n7 (first_order_rate_constant)" legend_algebraic[19] = "V_n3_ in component V_n3_ (first_order_rate_constant)" legend_algebraic[22] = "V_7 in component V_7 (first_order_rate_constant)" legend_algebraic[14] = "V_2_ in component V_2_ (first_order_rate_constant)" legend_constants[39] = "V_in in component V_in (first_order_rate_constant)" legend_states[8] = "iCdc25Ps216 in component iCdc25Ps216 (dimensionless)" legend_algebraic[23] = "V_n18 in component V_n18 (first_order_rate_constant)" legend_algebraic[20] = "V_18 in component V_18 (first_order_rate_constant)" legend_algebraic[17] = "V_3_ in component V_3_ (first_order_rate_constant)" legend_states[9] = "iCdc25Ps216_protein1433 in component iCdc25Ps216_protein1433 (dimensionless)" legend_algebraic[24] = "V_ex in component V_ex (first_order_rate_constant)" legend_states[10] = "aCdc25 in component aCdc25 (dimensionless)" legend_algebraic[9] = "V_n2 in component V_n2 (first_order_rate_constant)" legend_algebraic[4] = "V_2 in component V_2 (first_order_rate_constant)" legend_states[11] = "aCdc25Ps216 in component aCdc25Ps216 (dimensionless)" legend_states[12] = "protein1433 in component protein1433 (dimensionless)" legend_algebraic[25] = "V_6 in component V_6 (first_order_rate_constant)" legend_constants[44] = "V_13 in component V_13 (first_order_rate_constant)" legend_algebraic[28] = "V_12 in component V_12 (first_order_rate_constant)" legend_states[13] = "Wee1 in component Wee1 (dimensionless)" legend_constants[45] = "V_16 in component V_16 (first_order_rate_constant)" legend_algebraic[10] = "V_n8 in component V_n8 (first_order_rate_constant)" legend_algebraic[5] = "V_8 in component V_8 (first_order_rate_constant)" legend_states[14] = "Wee1P in component Wee1P (dimensionless)" legend_algebraic[15] = "V_17 in component V_17 (first_order_rate_constant)" legend_algebraic[6] = "aCdc25_T in component aCdc25_T (dimensionless)" legend_algebraic[0] = "Chk1 in component V_1 (dimensionless)" legend_constants[40] = "Chk1_T in component V_1 (dimensionless)" legend_rates[0] = "d/dt Chk1P in component Chk1P (dimensionless)" legend_rates[1] = "d/dt Rad3 in component Rad3 (dimensionless)" legend_rates[2] = "d/dt p53 in component p53 (dimensionless)" legend_rates[3] = "d/dt preMPF in component preMPF (dimensionless)" legend_rates[4] = "d/dt MPF in component MPF (dimensionless)" legend_rates[5] = "d/dt p21 in component p21 (dimensionless)" legend_rates[6] = "d/dt p21_MPF in component p21_MPF (dimensionless)" legend_rates[7] = "d/dt iCdc25 in component iCdc25 (dimensionless)" legend_rates[8] = "d/dt iCdc25Ps216 in component iCdc25Ps216 (dimensionless)" legend_rates[9] = "d/dt iCdc25Ps216_protein1433 in component iCdc25Ps216_protein1433 (dimensionless)" legend_rates[10] = "d/dt aCdc25 in component aCdc25 (dimensionless)" legend_rates[11] = "d/dt aCdc25Ps216 in component aCdc25Ps216 (dimensionless)" legend_rates[12] = "d/dt protein1433 in component protein1433 (dimensionless)" legend_rates[13] = "d/dt Wee1 in component Wee1 (dimensionless)" legend_rates[14] = "d/dt Wee1P in component Wee1P (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 1 constants[1] = 10 constants[2] = 0.1 constants[3] = 0.01 constants[4] = 0.1 constants[5] = 100 constants[6] = 0 constants[7] = 0 constants[8] = 1 constants[9] = 0.01 constants[10] = 1 constants[11] = 0.01 constants[12] = 0.1 constants[13] = 0.01 constants[14] = 0 constants[15] = 1 constants[16] = 1 constants[17] = 0 constants[18] = 0 constants[19] = 1 constants[20] = 0.1 constants[21] = 1 constants[22] = 0.0005 constants[23] = 1 constants[24] = 0.01 constants[25] = 0.0002 constants[26] = 0.1 constants[27] = 1 constants[28] = 0.01 constants[29] = 0.1 constants[30] = 0.01 constants[31] = 0.1 constants[32] = 0.1 constants[33] = 1 constants[34] = 0 constants[35] = 0 constants[36] = 0 constants[37] = 0 constants[38] = 1 states[0] = 0.000001 states[1] = 0 states[2] = 0 states[3] = 0.000001 states[4] = 0.00000001 states[5] = 0 states[6] = 0 states[7] = 0.000001 constants[39] = 0.00001 states[8] = 0.00002 states[9] = 0.03 states[10] = 0.000001 states[11] = 0 states[12] = 2 states[13] = 0.001 states[14] = 0 constants[40] = 1 constants[41] = constants[7] constants[42] = constants[18] constants[43] = constants[30] constants[44] = constants[21] constants[45] = constants[25] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[1] = constants[8]*states[1] rates[1] = constants[41]-algebraic[1] algebraic[2] = constants[19]*states[2] rates[2] = constants[42]-algebraic[2] algebraic[10] = constants[13]*states[14] algebraic[5] = constants[12]*states[4]*states[13]+constants[14]*states[13] rates[13] = (constants[45]+algebraic[10])-algebraic[5] algebraic[11] = constants[1]*states[0] algebraic[0] = constants[40]-states[0] algebraic[7] = constants[0]*algebraic[0]*states[1] rates[0] = algebraic[7]-algebraic[11] algebraic[12] = (constants[22]/(1.00000+constants[23]*states[2]))*1.00000 algebraic[8] = constants[16]*states[4]*states[13] algebraic[3] = constants[15]*(states[10]+states[11])*states[3]+constants[17]*states[3] rates[3] = (algebraic[12]+algebraic[8])-algebraic[3] algebraic[15] = constants[26]*states[14] rates[14] = algebraic[5]-(algebraic[10]+algebraic[15]) algebraic[14] = constants[4]*states[0]*states[7]+constants[37]*states[7] algebraic[23] = constants[28]*states[11] algebraic[20] = constants[27]*states[4]*states[8]+constants[35]*states[8] algebraic[17] = constants[5]*states[8]*states[12] rates[8] = (algebraic[14]+algebraic[23])-(algebraic[20]+algebraic[17]) algebraic[19] = constants[6]*states[9] algebraic[24] = constants[38]*states[9] rates[9] = algebraic[17]-(algebraic[19]+algebraic[24]) algebraic[9] = constants[3]*states[11] algebraic[4] = constants[2]*states[0]*states[10]+constants[36]*states[10] rates[11] = (algebraic[4]+algebraic[20])-(algebraic[9]+algebraic[23]) algebraic[26] = constants[33]*states[6] algebraic[21] = constants[32]*states[4]*states[5] algebraic[13] = constants[24]*(power(states[4], 2.00000)) rates[4] = (algebraic[3]+algebraic[26])-(algebraic[8]+algebraic[21]+algebraic[13]) algebraic[16] = constants[29]*states[2] algebraic[18] = constants[31]*states[5] rates[5] = (algebraic[16]+constants[43]+algebraic[26])-(algebraic[18]+algebraic[21]) rates[6] = algebraic[21]-algebraic[26] algebraic[27] = constants[11]*states[10] algebraic[22] = constants[10]*states[4]*states[7]+constants[34]*states[7] rates[7] = (algebraic[27]+algebraic[19]+constants[39])-(algebraic[22]+algebraic[14]) rates[10] = (algebraic[22]+algebraic[9])-(algebraic[27]+algebraic[4]) algebraic[25] = constants[9]*states[2] algebraic[28] = constants[20]*states[12] rates[12] = (algebraic[25]+constants[44]+algebraic[19])-(algebraic[17]+algebraic[28]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[1] = constants[8]*states[1] algebraic[2] = constants[19]*states[2] algebraic[10] = constants[13]*states[14] algebraic[5] = constants[12]*states[4]*states[13]+constants[14]*states[13] algebraic[11] = constants[1]*states[0] algebraic[0] = constants[40]-states[0] algebraic[7] = constants[0]*algebraic[0]*states[1] algebraic[12] = (constants[22]/(1.00000+constants[23]*states[2]))*1.00000 algebraic[8] = constants[16]*states[4]*states[13] algebraic[3] = constants[15]*(states[10]+states[11])*states[3]+constants[17]*states[3] algebraic[15] = constants[26]*states[14] algebraic[14] = constants[4]*states[0]*states[7]+constants[37]*states[7] algebraic[23] = constants[28]*states[11] algebraic[20] = constants[27]*states[4]*states[8]+constants[35]*states[8] algebraic[17] = constants[5]*states[8]*states[12] algebraic[19] = constants[6]*states[9] algebraic[24] = constants[38]*states[9] algebraic[9] = constants[3]*states[11] algebraic[4] = constants[2]*states[0]*states[10]+constants[36]*states[10] algebraic[26] = constants[33]*states[6] algebraic[21] = constants[32]*states[4]*states[5] algebraic[13] = constants[24]*(power(states[4], 2.00000)) algebraic[16] = constants[29]*states[2] algebraic[18] = constants[31]*states[5] algebraic[27] = constants[11]*states[10] algebraic[22] = constants[10]*states[4]*states[7]+constants[34]*states[7] algebraic[25] = constants[9]*states[2] algebraic[28] = constants[20]*states[12] algebraic[6] = states[10]+states[11] 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)