# Size of variable arrays: sizeAlgebraic = 1 sizeStates = 10 sizeConstants = 38 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 (hour)" legend_states[0] = "MP in component MP (nanomolar)" legend_constants[0] = "vsP in component MP (flux)" legend_constants[1] = "vmP in component MP (flux)" legend_constants[2] = "KmP in component MP (nanomolar)" legend_constants[3] = "KIP in component MP (nanomolar)" legend_constants[4] = "kd in component parameters (first_order_rate_constant)" legend_states[1] = "CN in component CN (nanomolar)" legend_constants[5] = "n in component parameters (dimensionless)" legend_states[2] = "P0 in component P0 (nanomolar)" legend_constants[6] = "ksP in component P0 (first_order_rate_constant)" legend_constants[7] = "V1P in component parameters (flux)" legend_constants[8] = "V2P in component parameters (flux)" legend_constants[9] = "K1P in component parameters (nanomolar)" legend_constants[10] = "K2P in component parameters (nanomolar)" legend_states[3] = "P1 in component P1 (nanomolar)" legend_constants[11] = "V3P in component parameters (flux)" legend_constants[12] = "V4P in component parameters (flux)" legend_constants[13] = "K3P in component parameters (nanomolar)" legend_constants[14] = "K4P in component parameters (nanomolar)" legend_states[4] = "P2 in component P2 (nanomolar)" legend_constants[15] = "vdP in component P2 (flux)" legend_constants[16] = "KdP in component P2 (nanomolar)" legend_algebraic[0] = "Pt in component P2 (nanomolar)" legend_constants[17] = "k3 in component parameters (second_order_rate_constant)" legend_constants[18] = "k4 in component parameters (first_order_rate_constant)" legend_states[5] = "T2 in component T2 (nanomolar)" legend_states[6] = "C in component C (nanomolar)" legend_states[7] = "MT in component MT (nanomolar)" legend_constants[19] = "vsT in component MT (flux)" legend_constants[20] = "vmT in component MT (flux)" legend_constants[21] = "KmT in component MT (nanomolar)" legend_constants[22] = "KIT in component MT (nanomolar)" legend_states[8] = "T0 in component T0 (nanomolar)" legend_constants[23] = "ksT in component T0 (first_order_rate_constant)" legend_constants[24] = "V1T in component parameters (flux)" legend_constants[25] = "V2T in component parameters (flux)" legend_constants[26] = "K1T in component parameters (nanomolar)" legend_constants[27] = "K2T in component parameters (nanomolar)" legend_states[9] = "T1 in component T1 (nanomolar)" legend_constants[28] = "V3T in component parameters (flux)" legend_constants[29] = "V4T in component parameters (flux)" legend_constants[30] = "K3T in component parameters (nanomolar)" legend_constants[31] = "K4T in component parameters (nanomolar)" legend_constants[32] = "vdT in component T2 (flux)" legend_constants[33] = "KdT in component T2 (nanomolar)" legend_constants[34] = "kdC in component C (first_order_rate_constant)" legend_constants[35] = "k1 in component parameters (first_order_rate_constant)" legend_constants[36] = "k2 in component parameters (first_order_rate_constant)" legend_constants[37] = "kdN in component CN (first_order_rate_constant)" legend_rates[0] = "d/dt MP in component MP (nanomolar)" legend_rates[2] = "d/dt P0 in component P0 (nanomolar)" legend_rates[3] = "d/dt P1 in component P1 (nanomolar)" legend_rates[4] = "d/dt P2 in component P2 (nanomolar)" legend_rates[7] = "d/dt MT in component MT (nanomolar)" legend_rates[8] = "d/dt T0 in component T0 (nanomolar)" legend_rates[9] = "d/dt T1 in component T1 (nanomolar)" legend_rates[5] = "d/dt T2 in component T2 (nanomolar)" legend_rates[6] = "d/dt C in component C (nanomolar)" legend_rates[1] = "d/dt CN in component CN (nanomolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.1 constants[0] = 1 constants[1] = 0.7 constants[2] = 0.2 constants[3] = 1.0 constants[4] = 0.01 states[1] = 1.25 constants[5] = 4.0 states[2] = 0.1 constants[6] = 0.9 constants[7] = 8.0 constants[8] = 1.0 constants[9] = 2.0 constants[10] = 2.0 states[3] = 0.1 constants[11] = 8.0 constants[12] = 1.0 constants[13] = 2.0 constants[14] = 1 states[4] = 0.1 constants[15] = 2 constants[16] = 0.2 constants[17] = 1.2 constants[18] = 0.6 states[5] = 0.1 states[6] = 0.1 states[7] = 1.6 constants[19] = 1.0 constants[20] = 0.7 constants[21] = 0.2 constants[22] = 1.0 states[8] = 0.1 constants[23] = 0.9 constants[24] = 8.0 constants[25] = 1.0 constants[26] = 2.0 constants[27] = 2.0 states[9] = 0.1 constants[28] = 8.0 constants[29] = 1.0 constants[30] = 2.0 constants[31] = 1 constants[32] = 2 constants[33] = 0.2 constants[34] = 0.01 constants[35] = 0.6 constants[36] = 0.2 constants[37] = 0.01 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[0]*((power(constants[3], constants[5]))/(power(constants[3], constants[5])+power(states[1], constants[5])))-(constants[1]*(states[0]/(constants[2]+states[0]))+constants[4]*states[0]) rates[2] = (constants[6]*states[0]+constants[8]*(states[3]/(constants[10]+states[3])))-(constants[7]*(states[2]/(constants[9]+states[2]))+constants[4]*states[2]) rates[3] = (constants[7]*(states[2]/(constants[9]+states[2]))+constants[12]*(states[4]/(constants[14]+states[4])))-(constants[8]*(states[3]/(constants[10]+states[3]))+constants[11]*(states[3]/(constants[13]+states[3]))+constants[4]*states[3]) rates[4] = (constants[11]*(states[3]/(constants[13]+states[3]))+constants[18]*states[6])-(constants[12]*(states[4]/(constants[14]+states[4]))+constants[17]*states[4]*states[5]+constants[15]*(states[4]/(constants[16]+states[4]))+constants[4]*states[4]) rates[7] = constants[19]*((power(constants[22], constants[5]))/(power(constants[22], constants[5])+power(states[1], constants[5])))-(constants[20]*(states[7]/(constants[21]+states[7]))+constants[4]*states[7]) rates[8] = (constants[23]*states[7]+constants[25]*(states[9]/(constants[27]+states[9])))-(constants[24]*(states[8]/(constants[26]+states[8]))+constants[4]*states[8]) rates[9] = (constants[24]*(states[8]/(constants[26]+states[8]))+constants[29]*(states[5]/(constants[31]+states[5])))-(constants[25]*(states[9]/(constants[27]+states[9]))+constants[28]*(states[9]/(constants[30]+states[9]))+constants[4]*states[9]) rates[5] = (constants[28]*(states[9]/(constants[30]+states[9]))+constants[18]*states[6])-(constants[29]*(states[5]/(constants[31]+states[5]))+constants[17]*states[4]*states[5]+constants[32]*(states[5]/(constants[33]+states[5]))+constants[4]*states[5]) rates[6] = (constants[17]*states[4]*states[5]+constants[36]*states[1])-(constants[18]*states[6]+constants[35]*states[6]+constants[34]*states[6]) rates[1] = constants[35]*states[6]-(constants[36]*states[1]+constants[37]*states[1]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = states[2]+states[3]+states[4]+states[6]+states[1] 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)