# Size of variable arrays: sizeAlgebraic = 21 sizeStates = 11 sizeConstants = 33 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] = "k1_ in component rate_constants (first_order_rate_constant)" legend_constants[2] = "k1__ in component rate_constants (first_order_rate_constant)" legend_constants[3] = "kn1 in component rate_constants (first_order_rate_constant)" legend_constants[4] = "k2 in component rate_constants (first_order_rate_constant)" legend_constants[5] = "kn2 in component rate_constants (first_order_rate_constant)" legend_constants[6] = "k3 in component rate_constants (first_order_rate_constant)" legend_constants[7] = "k3_ in component rate_constants (first_order_rate_constant)" legend_constants[8] = "kn4 in component rate_constants (first_order_rate_constant)" legend_constants[9] = "k5 in component rate_constants (first_order_rate_constant)" legend_constants[10] = "kn6 in component rate_constants (first_order_rate_constant)" legend_constants[11] = "k8 in component rate_constants (first_order_rate_constant)" legend_constants[12] = "k9 in component rate_constants (first_order_rate_constant)" legend_constants[13] = "k10 in component rate_constants (first_order_rate_constant)" legend_constants[14] = "k17 in component rate_constants (first_order_rate_constant)" legend_constants[15] = "k18 in component rate_constants (first_order_rate_constant)" legend_constants[16] = "k19 in component rate_constants (first_order_rate_constant)" legend_constants[17] = "k20 in component rate_constants (first_order_rate_constant)" legend_constants[18] = "k21 in component rate_constants (first_order_rate_constant)" legend_constants[19] = "k22 in component rate_constants (first_order_rate_constant)" legend_constants[20] = "k24 in component rate_constants (first_order_rate_constant)" legend_constants[21] = "k25 in component rate_constants (first_order_rate_constant)" legend_constants[22] = "k25_ in component rate_constants (first_order_rate_constant)" legend_constants[23] = "k26 in component rate_constants (first_order_rate_constant)" legend_constants[24] = "k26_ in component rate_constants (first_order_rate_constant)" legend_constants[25] = "k28 in component rate_constants (first_order_rate_constant)" legend_constants[26] = "k29 in component rate_constants (first_order_rate_constant)" legend_states[0] = "a_CyclinE_Cdk2 in component a_CyclinE_Cdk2 (dimensionless)" legend_algebraic[0] = "V_2 in component V_2 (first_order_rate_constant)" legend_algebraic[13] = "V_10 in component V_10 (first_order_rate_constant)" legend_algebraic[2] = "V_n2 in component V_n2 (first_order_rate_constant)" legend_algebraic[12] = "V_9 in component V_9 (first_order_rate_constant)" legend_algebraic[14] = "V_21 in component V_21 (first_order_rate_constant)" legend_states[1] = "i_CyclinE_Cdk2 in component i_CyclinE_Cdk2 (dimensionless)" legend_algebraic[5] = "V_3 in component V_3 (first_order_rate_constant)" legend_algebraic[9] = "V_5 in component V_5 (first_order_rate_constant)" legend_states[2] = "pRB_E2F in component pRB_E2F (dimensionless)" legend_constants[32] = "V_n1 in component V_n1 (first_order_rate_constant)" legend_algebraic[1] = "V_1 in component V_1 (first_order_rate_constant)" legend_states[3] = "E2F in component E2F (dimensionless)" legend_constants[27] = "V_4 in component E2F (first_order_rate_constant)" legend_algebraic[6] = "V_18 in component V_18 (first_order_rate_constant)" legend_algebraic[3] = "V_n4 in component V_n4 (first_order_rate_constant)" legend_states[4] = "pRB in component pRB (dimensionless)" legend_constants[28] = "V_27 in component pRB (first_order_rate_constant)" legend_algebraic[4] = "V_26 in component V_26 (first_order_rate_constant)" legend_algebraic[10] = "V_29 in component V_29 (first_order_rate_constant)" legend_algebraic[7] = "V_28 in component V_28 (first_order_rate_constant)" legend_states[5] = "CycD_Cdk4 in component CycD_Cdk4 (dimensionless)" legend_constants[29] = "V_6 in component CycD_Cdk4 (first_order_rate_constant)" legend_algebraic[18] = "V_20 in component V_20 (first_order_rate_constant)" legend_algebraic[8] = "V_n6 in component V_n6 (first_order_rate_constant)" legend_algebraic[16] = "V_19 in component V_19 (first_order_rate_constant)" legend_algebraic[15] = "V_17 in component V_17 (first_order_rate_constant)" legend_states[6] = "p27 in component p27 (dimensionless)" legend_constants[30] = "V_7 in component p27 (first_order_rate_constant)" legend_algebraic[11] = "V_8 in component V_8 (first_order_rate_constant)" legend_algebraic[20] = "V_22 in component V_22 (first_order_rate_constant)" legend_states[7] = "CycE_Cdk2_p27 in component CycE_Cdk2_p27 (dimensionless)" legend_states[8] = "CycD_Cdk4_p27 in component CycD_Cdk4_p27 (dimensionless)" legend_states[9] = "p16 in component p16 (dimensionless)" legend_constants[31] = "V_23 in component p16 (first_order_rate_constant)" legend_algebraic[19] = "V_25 in component V_25 (first_order_rate_constant)" legend_algebraic[17] = "V_24 in component V_24 (first_order_rate_constant)" legend_states[10] = "pRB_P in component pRB_P (dimensionless)" legend_rates[0] = "d/dt a_CyclinE_Cdk2 in component a_CyclinE_Cdk2 (dimensionless)" legend_rates[1] = "d/dt i_CyclinE_Cdk2 in component i_CyclinE_Cdk2 (dimensionless)" legend_rates[2] = "d/dt pRB_E2F in component pRB_E2F (dimensionless)" legend_rates[3] = "d/dt E2F in component E2F (dimensionless)" legend_rates[4] = "d/dt pRB in component pRB (dimensionless)" legend_rates[5] = "d/dt CycD_Cdk4 in component CycD_Cdk4 (dimensionless)" legend_rates[6] = "d/dt p27 in component p27 (dimensionless)" legend_rates[7] = "d/dt CycE_Cdk2_p27 in component CycE_Cdk2_p27 (dimensionless)" legend_rates[8] = "d/dt CycD_Cdk4_p27 in component CycD_Cdk4_p27 (dimensionless)" legend_rates[9] = "d/dt p16 in component p16 (dimensionless)" legend_rates[10] = "d/dt pRB_P in component pRB_P (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0.1 constants[1] = 0.5 constants[2] = 0.5 constants[3] = 0.001 constants[4] = 0.1 constants[5] = 1 constants[6] = 1.42 constants[7] = 0 constants[8] = 0.016 constants[9] = 0.02 constants[10] = 5 constants[11] = 2 constants[12] = 2 constants[13] = 0.035 constants[14] = 3.5 constants[15] = 0.0001 constants[16] = 0.05 constants[17] = 0.01 constants[18] = 0.1 constants[19] = 0.001 constants[20] = 0.1 constants[21] = 0.01 constants[22] = 0.02 constants[23] = 0.01 constants[24] = 0.1 constants[25] = 0.01 constants[26] = 0.001 states[0] = 0 states[1] = 0.01 states[2] = 1.95 states[3] = 0 constants[27] = 0.000001 states[4] = 0.05 constants[28] = 0.01 states[5] = 0 constants[29] = 0.018 states[6] = 5 constants[30] = 0.0001 states[7] = 1 states[8] = 0 states[9] = 5 constants[31] = 0.2 states[10] = 0.01 constants[32] = constants[3] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[1] = constants[1]*states[5]*states[2]+constants[2]*states[8]*states[2]+constants[0]*states[0]*states[2] rates[2] = constants[32]-algebraic[1] algebraic[6] = constants[15]*states[3] algebraic[3] = constants[8]*states[3] rates[3] = (algebraic[1]+constants[27]+algebraic[6])-(constants[32]+algebraic[3]) algebraic[0] = constants[4]*states[0]*states[1] algebraic[2] = constants[5]*states[0] algebraic[5] = constants[6]*states[3]+constants[7] algebraic[9] = constants[9]*states[1] rates[1] = (algebraic[5]+algebraic[2])-(algebraic[0]+algebraic[9]) algebraic[4] = constants[23]/((1.00000+constants[24]*states[9])*1.00000) algebraic[10] = constants[26]*states[10] algebraic[7] = constants[25]*states[4] rates[4] = (constants[28]+algebraic[4]+algebraic[10])-(constants[32]+algebraic[7]) rates[10] = algebraic[1]-algebraic[10] algebraic[13] = constants[13]*states[7] algebraic[12] = constants[12]*states[6]*states[0] rates[7] = algebraic[12]-algebraic[13] algebraic[14] = constants[18]*(power(states[0], 2.00000)) rates[0] = (algebraic[0]+algebraic[13])-(algebraic[2]+algebraic[12]+algebraic[14]) algebraic[18] = constants[17]*states[8] algebraic[8] = constants[10]*states[5] algebraic[16] = constants[16]*states[6]*states[5] algebraic[15] = constants[14]*states[9]*states[5] rates[5] = (constants[29]+algebraic[18])-(algebraic[8]+algebraic[16]+algebraic[15]) rates[8] = algebraic[16]-algebraic[18] algebraic[19] = constants[21]/((1.00000+constants[22]*states[4])*1.00000) algebraic[17] = constants[20]*states[9] rates[9] = (constants[31]+algebraic[19])-(algebraic[15]+algebraic[17]) algebraic[11] = constants[11]*states[6]*states[0] algebraic[20] = constants[19]*states[6] rates[6] = (constants[30]+algebraic[13]+algebraic[18])-(algebraic[11]+algebraic[12]+algebraic[16]+algebraic[20]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[1] = constants[1]*states[5]*states[2]+constants[2]*states[8]*states[2]+constants[0]*states[0]*states[2] algebraic[6] = constants[15]*states[3] algebraic[3] = constants[8]*states[3] algebraic[0] = constants[4]*states[0]*states[1] algebraic[2] = constants[5]*states[0] algebraic[5] = constants[6]*states[3]+constants[7] algebraic[9] = constants[9]*states[1] algebraic[4] = constants[23]/((1.00000+constants[24]*states[9])*1.00000) algebraic[10] = constants[26]*states[10] algebraic[7] = constants[25]*states[4] algebraic[13] = constants[13]*states[7] algebraic[12] = constants[12]*states[6]*states[0] algebraic[14] = constants[18]*(power(states[0], 2.00000)) algebraic[18] = constants[17]*states[8] algebraic[8] = constants[10]*states[5] algebraic[16] = constants[16]*states[6]*states[5] algebraic[15] = constants[14]*states[9]*states[5] algebraic[19] = constants[21]/((1.00000+constants[22]*states[4])*1.00000) algebraic[17] = constants[20]*states[9] algebraic[11] = constants[11]*states[6]*states[0] algebraic[20] = constants[19]*states[6] 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)