# Size of variable arrays: sizeAlgebraic = 0 sizeStates = 5 sizeConstants = 21 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] = "G_a in component G_a (micromolar)" legend_constants[0] = "k1 in component model_parameters (dimensionless)" legend_constants[1] = "k2 in component model_parameters (dimensionless)" legend_constants[2] = "k3 in component model_parameters (dimensionless)" legend_states[1] = "PLC in component PLC (micromolar)" legend_states[2] = "Ca_cyt in component Ca_cyt (micromolar)" legend_constants[3] = "K4 in component model_parameters (dimensionless)" legend_constants[4] = "k5 in component model_parameters (dimensionless)" legend_constants[5] = "K6 in component model_parameters (dimensionless)" legend_constants[6] = "k7 in component model_parameters (dimensionless)" legend_constants[7] = "k8 in component model_parameters (dimensionless)" legend_constants[8] = "K9 in component model_parameters (dimensionless)" legend_states[3] = "Ca_ER in component Ca_ER (micromolar)" legend_constants[9] = "k10 in component model_parameters (dimensionless)" legend_constants[10] = "K11 in component model_parameters (dimensionless)" legend_constants[11] = "k16 in component model_parameters (dimensionless)" legend_constants[12] = "K17 in component model_parameters (dimensionless)" legend_states[4] = "Ca_mit in component Ca_mit (micromolar)" legend_constants[13] = "k18 in component model_parameters (dimensionless)" legend_constants[14] = "K19 in component model_parameters (dimensionless)" legend_constants[15] = "k20 in component model_parameters (dimensionless)" legend_constants[16] = "K21 in component model_parameters (dimensionless)" legend_constants[17] = "k12 in component model_parameters (dimensionless)" legend_constants[18] = "k13 in component model_parameters (dimensionless)" legend_constants[19] = "k14 in component model_parameters (dimensionless)" legend_constants[20] = "K15 in component model_parameters (dimensionless)" legend_rates[0] = "d/dt G_a in component G_a (micromolar)" legend_rates[1] = "d/dt PLC in component PLC (micromolar)" legend_rates[3] = "d/dt Ca_ER in component Ca_ER (micromolar)" legend_rates[4] = "d/dt Ca_mit in component Ca_mit (micromolar)" legend_rates[2] = "d/dt Ca_cyt in component Ca_cyt (micromolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.01 constants[0] = 0.01 constants[1] = 1.42 constants[2] = 0.64 states[1] = 0.01 states[2] = 0.01 constants[3] = 0.19 constants[4] = 4.88 constants[5] = 1.18 constants[6] = 2.08 constants[7] = 32.24 constants[8] = 29.09 states[3] = 10 constants[9] = 0.7 constants[10] = 3 constants[11] = 7 constants[12] = 0.05 states[4] = 0.001 constants[13] = 79 constants[14] = 3.5 constants[15] = 0.81 constants[16] = 4.5 constants[17] = 2.8 constants[18] = 13.4 constants[19] = 153 constants[20] = 0.16 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = ((constants[0]+constants[1]*states[0])-(constants[2]*states[0]*states[1])/(states[0]+constants[3]))-(constants[4]*states[2]*states[0])/(states[0]+constants[5]) rates[1] = constants[6]*states[0]-(constants[7]*states[1])/(states[1]+constants[8]) rates[3] = -(states[3]-states[2])*((constants[9]*states[2]*(power(states[1], 4.00000)))/(power(states[1], 4.00000)+power(constants[10], 4.00000)))+(constants[11]*states[2])/(states[2]+constants[12]) rates[4] = (constants[13]*(power(states[2], 8.00000)))/(power(constants[14], 8.00000)+power(states[2], 8.00000))-(states[4]-states[2])*((constants[15]*states[2])/(states[2]+constants[16])) rates[2] = (((((states[3]-states[2])*((constants[9]*states[2]*(power(states[1], 4.00000)))/(power(states[1], 4.00000)+power(constants[10], 4.00000)))+constants[17]*states[1]+constants[18]*states[0])-(constants[19]*states[2])/(constants[20]+states[2]))-(constants[11]*states[2])/(constants[12]+states[2]))-(constants[13]*(power(states[2], 8.00000)))/(power(constants[14], 8.00000)+power(states[2], 8.00000)))+(states[4]-states[2])*((constants[15]*states[2])/(states[2]+constants[16])) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) 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)