# Size of variable arrays: sizeAlgebraic = 6 sizeStates = 12 sizeConstants = 34 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] = "k2 in component rate_constants (first_order_rate_constant)" legend_constants[2] = "k3 in component rate_constants (first_order_rate_constant)" legend_constants[3] = "k4 in component rate_constants (first_order_rate_constant)" legend_constants[4] = "k5 in component rate_constants (first_order_rate_constant)" legend_constants[5] = "k6 in component rate_constants (first_order_rate_constant)" legend_constants[6] = "k7 in component rate_constants (first_order_rate_constant)" legend_constants[7] = "k8 in component rate_constants (first_order_rate_constant)" legend_constants[8] = "k9 in component rate_constants (first_order_rate_constant)" legend_constants[9] = "k10 in component rate_constants (first_order_rate_constant)" legend_constants[10] = "k11 in component rate_constants (first_order_rate_constant)" legend_constants[11] = "k12 in component rate_constants (first_order_rate_constant)" legend_constants[12] = "k13 in component rate_constants (first_order_rate_constant)" legend_constants[13] = "k14 in component rate_constants (first_order_rate_constant)" legend_constants[14] = "k15 in component rate_constants (first_order_rate_constant)" legend_constants[15] = "k16 in component rate_constants (first_order_rate_constant)" legend_constants[16] = "k2u in component rate_constants (first_order_rate_constant)" legend_constants[17] = "k7u in component rate_constants (first_order_rate_constant)" legend_constants[18] = "k16u in component rate_constants (first_order_rate_constant)" legend_constants[19] = "az in component rate_constants (first_order_rate_constant)" legend_constants[20] = "bz in component rate_constants (first_order_rate_constant)" legend_constants[21] = "cz in component rate_constants (first_order_rate_constant)" legend_constants[22] = "aw in component rate_constants (first_order_rate_constant)" legend_constants[23] = "bw in component rate_constants (first_order_rate_constant)" legend_constants[24] = "cw in component rate_constants (first_order_rate_constant)" legend_constants[25] = "ai in component rate_constants (first_order_rate_constant)" legend_constants[26] = "bi in component rate_constants (first_order_rate_constant)" legend_constants[27] = "ci in component rate_constants (first_order_rate_constant)" legend_states[0] = "cyclin_CDK_active in component cyclin_CDK_active (dimensionless)" legend_algebraic[0] = "kplus_z in component rate_constants (first_order_rate_constant)" legend_algebraic[1] = "kplus_w in component rate_constants (first_order_rate_constant)" legend_algebraic[2] = "kplus_i in component rate_constants (first_order_rate_constant)" legend_constants[31] = "kminus_z in component rate_constants (first_order_rate_constant)" legend_constants[32] = "kminus_w in component rate_constants (first_order_rate_constant)" legend_constants[33] = "kminus_i in component rate_constants (first_order_rate_constant)" legend_states[1] = "cyclin in component cyclin (dimensionless)" legend_states[2] = "cyclin_CDK_inactive in component cyclin_CDK_inactive (dimensionless)" legend_algebraic[3] = "CDK in component CDK (dimensionless)" legend_states[3] = "APC in component APC (dimensionless)" legend_states[4] = "wee1 in component wee1 (dimensionless)" legend_states[5] = "Cdc25_2P in component Cdc25_2P (dimensionless)" legend_states[6] = "CKI in component CKI (dimensionless)" legend_states[7] = "cyclin_CDK_CKI in component cyclin_CDK_CKI (dimensionless)" legend_states[8] = "cyclin_CDK_CKI_P in component cyclin_CDK_CKI_P (dimensionless)" legend_states[9] = "Cdc25 in component Cdc25 (dimensionless)" legend_states[10] = "Cdc25_P in component Cdc25_P (dimensionless)" legend_states[11] = "wee1_P in component wee1_P (dimensionless)" legend_constants[28] = "tau in component APC (minute)" legend_algebraic[4] = "h_x in component APC (dimensionless)" legend_constants[29] = "a in component APC (dimensionless)" legend_constants[30] = "CDK_T in component CDK (dimensionless)" legend_algebraic[5] = "cyclin_T in component cyclin_T (dimensionless)" legend_rates[1] = "d/dt cyclin in component cyclin (dimensionless)" legend_rates[2] = "d/dt cyclin_CDK_inactive in component cyclin_CDK_inactive (dimensionless)" legend_rates[0] = "d/dt cyclin_CDK_active in component cyclin_CDK_active (dimensionless)" legend_rates[9] = "d/dt Cdc25 in component Cdc25 (dimensionless)" legend_rates[10] = "d/dt Cdc25_P in component Cdc25_P (dimensionless)" legend_rates[5] = "d/dt Cdc25_2P in component Cdc25_2P (dimensionless)" legend_rates[4] = "d/dt wee1 in component wee1 (dimensionless)" legend_rates[11] = "d/dt wee1_P in component wee1_P (dimensionless)" legend_rates[3] = "d/dt APC in component APC (dimensionless)" legend_rates[6] = "d/dt CKI in component CKI (dimensionless)" legend_rates[7] = "d/dt cyclin_CDK_CKI in component cyclin_CDK_CKI (dimensionless)" legend_rates[8] = "d/dt cyclin_CDK_CKI_P in component cyclin_CDK_CKI_P (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 300 constants[1] = 5 constants[2] = 30 constants[3] = 30 constants[4] = 0.1 constants[5] = 1 constants[6] = 10 constants[7] = 100 constants[8] = 1 constants[9] = 10 constants[10] = 1 constants[11] = 0 constants[12] = 1 constants[13] = 1 constants[14] = 1 constants[15] = 2 constants[16] = 50 constants[17] = 0 constants[18] = 25 constants[19] = 10 constants[20] = 0.1 constants[21] = 1 constants[22] = 10 constants[23] = 0.1 constants[24] = 1 constants[25] = 10 constants[26] = 0.1 constants[27] = 1 states[0] = 0.1 states[1] = 0 states[2] = 0.1 states[3] = 0 states[4] = 0 states[5] = 0 states[6] = 0 states[7] = 0 states[8] = 0 states[9] = 0 states[10] = 0 states[11] = 0 constants[28] = 25 constants[29] = 4 constants[30] = 200 constants[31] = constants[19] constants[32] = constants[22] constants[33] = constants[25] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = (((((constants[4]*states[2]+states[5]*states[2]*1.00000)-constants[5]*states[0])-states[4]*states[0]*1.00000)-(constants[6]+constants[17]*states[3])*states[0])-constants[13]*states[0]*states[6])+constants[14]*states[7]+(constants[15]+constants[18]*states[3])*states[8] rates[6] = ((constants[11]-constants[12]*states[6])-constants[11]*states[0]*states[6])+constants[14]*states[7] algebraic[3] = ((((constants[30]-states[0])-states[2])-states[7])-states[8])/constants[30] rates[1] = ((constants[0]+constants[3]*states[2])-constants[2]*states[1]*algebraic[3])-(constants[1]+constants[16]*states[3])*states[1] rates[2] = (((constants[2]*states[1]*algebraic[3]+constants[5]*states[0]+states[4]*states[0]*1.00000)-constants[3]*states[2])-constants[4]*states[2])-states[5]*states[2]*1.00000 algebraic[0] = constants[20]+constants[21]*states[0] rates[9] = ((constants[7]+constants[31]*states[10])-algebraic[0]*states[9])-constants[8]*states[9] rates[10] = (algebraic[0]*(states[9]-states[10])+constants[31]*(states[5]-states[10]))-constants[8]*states[10] rates[5] = (algebraic[0]*states[10]-constants[31]*states[5])-constants[8]*states[5] algebraic[1] = constants[23]+constants[24]*states[0] rates[4] = ((constants[9]+constants[32]*states[11])-algebraic[1]*states[4])-constants[10]*states[4] rates[11] = (algebraic[1]*states[4]-constants[32]*states[11])-constants[10]*states[11] algebraic[4] = (power(states[0], 2.00000))/(power(constants[29], 2.00000)+power(states[0], 2.00000)) rates[3] = (algebraic[4]-states[3])/constants[28] algebraic[2] = constants[26]+constants[27]*states[0] rates[7] = ((constants[13]*states[0]*states[6]-constants[14]*states[7])+constants[33]*states[8])-algebraic[2]*states[7] rates[8] = (algebraic[2]*states[7]-constants[33]*states[8])-(constants[15]+constants[18]*states[3])*states[8] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[3] = ((((constants[30]-states[0])-states[2])-states[7])-states[8])/constants[30] algebraic[0] = constants[20]+constants[21]*states[0] algebraic[1] = constants[23]+constants[24]*states[0] algebraic[4] = (power(states[0], 2.00000))/(power(constants[29], 2.00000)+power(states[0], 2.00000)) algebraic[2] = constants[26]+constants[27]*states[0] algebraic[5] = states[1]+states[0]+states[2] 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)