# Size of variable arrays: sizeAlgebraic = 8 sizeStates = 4 sizeConstants = 17 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_states[0] = "Ca_cyt in component Ca_cyt (micromolar)" legend_algebraic[0] = "J_ERch in component J_ERch (micromolar)" legend_algebraic[3] = "J_ERpump in component J_ERpump (micromolar)" legend_algebraic[6] = "J_in in component J_in (micromolar)" legend_algebraic[7] = "J_out in component J_out (micromolar)" legend_states[1] = "Ca_ER in component Ca_ER (micromolar)" legend_states[2] = "PLC in component PLC (micromolar)" legend_algebraic[1] = "J_PLCact in component J_PLCact (micromolar)" legend_algebraic[4] = "J_PLCinact in component J_PLCinact (micromolar)" legend_states[3] = "G_alpha in component G_alpha (micromolar)" legend_algebraic[2] = "J_actG_alpha in component J_actG_alpha (micromolar)" legend_algebraic[5] = "J_inactG_alpha in component J_inactG_alpha (micromolar)" legend_constants[0] = "k_10 in component J_ERch (dimensionless)" legend_constants[1] = "K_11 in component J_ERch (dimensionless)" legend_constants[2] = "K_17 in component J_ERpump (dimensionless)" legend_constants[3] = "k_16 in component J_ERpump (dimensionless)" legend_constants[4] = "K_12 in component J_in (dimensionless)" legend_constants[5] = "k_13 in component J_in (dimensionless)" legend_constants[6] = "k_14 in component J_out (dimensionless)" legend_constants[7] = "K_15 in component J_out (dimensionless)" legend_constants[8] = "k_7 in component J_PLCact (dimensionless)" legend_constants[9] = "k_8 in component J_PLCinact (dimensionless)" legend_constants[10] = "K_9 in component J_PLCinact (dimensionless)" legend_constants[11] = "k_1 in component J_actG_alpha (dimensionless)" legend_constants[12] = "k_2 in component J_actG_alpha (dimensionless)" legend_constants[13] = "k_3 in component J_inactG_alpha (dimensionless)" legend_constants[14] = "K_4 in component J_inactG_alpha (dimensionless)" legend_constants[15] = "k_5 in component J_inactG_alpha (dimensionless)" legend_constants[16] = "K_6 in component J_inactG_alpha (dimensionless)" legend_rates[0] = "d/dt Ca_cyt in component Ca_cyt (micromolar)" legend_rates[1] = "d/dt Ca_ER in component Ca_ER (micromolar)" legend_rates[2] = "d/dt PLC in component PLC (micromolar)" legend_rates[3] = "d/dt G_alpha in component G_alpha (micromolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.01 states[1] = 20 states[2] = 0.01 states[3] = 0.01 constants[0] = 5 constants[1] = 3 constants[2] = 0.05 constants[3] = 5.37 constants[4] = 2.8 constants[5] = 13.4 constants[6] = 153 constants[7] = 0.16 constants[8] = 2.08 constants[9] = 32.24 constants[10] = 29.09 constants[11] = 0.01 constants[12] = 0.1 constants[13] = 0.64 constants[14] = 0.09 constants[15] = 4.88 constants[16] = 1.18 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[0]*states[0]*states[2]*(states[1]/(constants[1]+states[1])) algebraic[3] = constants[3]*(states[0]/(constants[2]+states[1])) rates[1] = (algebraic[3]-algebraic[0])*1.00000 algebraic[1] = constants[8]*states[3] algebraic[4] = constants[9]*(states[2]/(constants[10]+states[2])) rates[2] = (algebraic[1]-algebraic[4])*1.00000 algebraic[2] = constants[11]+constants[12]*states[3] algebraic[5] = constants[13]*states[2]*(states[3]/(constants[14]+states[3]))+constants[15]*states[0]*(states[3]/(constants[16]+states[3])) rates[3] = (algebraic[2]-algebraic[5])*1.00000 algebraic[6] = constants[4]*states[2]+constants[5]*states[3] algebraic[7] = constants[6]*(states[0]/(constants[7]+states[0])) rates[0] = (((algebraic[0]-algebraic[3])+algebraic[6])-algebraic[7])*1.00000 return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[0]*states[0]*states[2]*(states[1]/(constants[1]+states[1])) algebraic[3] = constants[3]*(states[0]/(constants[2]+states[1])) algebraic[1] = constants[8]*states[3] algebraic[4] = constants[9]*(states[2]/(constants[10]+states[2])) algebraic[2] = constants[11]+constants[12]*states[3] algebraic[5] = constants[13]*states[2]*(states[3]/(constants[14]+states[3]))+constants[15]*states[0]*(states[3]/(constants[16]+states[3])) algebraic[6] = constants[4]*states[2]+constants[5]*states[3] algebraic[7] = constants[6]*(states[0]/(constants[7]+states[0])) 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)