# Size of variable arrays: sizeAlgebraic = 3 sizeStates = 3 sizeConstants = 20 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] = "V_0 in component Vin (micromolar_per_minute)" legend_constants[1] = "V_1 in component Vin (micromolar_per_minute)" legend_constants[2] = "beta in component Vin (dimensionless)" legend_constants[19] = "V_in in component Vin (micromolar_per_minute)" legend_constants[3] = "V_M2 in component V2 (micromolar_per_minute)" legend_states[0] = "Z in component cytosol (micromolar)" legend_constants[4] = "K_2 in component V2 (micromolar)" legend_algebraic[0] = "V_2 in component V2 (micromolar_per_minute)" legend_constants[5] = "V_M3 in component V3 (micromolar_per_minute)" legend_constants[6] = "K_Z in component V3 (micromolar)" legend_constants[7] = "K_A in component V3 (micromolar)" legend_constants[8] = "K_Y in component V3 (micromolar)" legend_constants[9] = "m in component V3 (dimensionless)" legend_states[1] = "Y in component internal_pool (micromolar)" legend_states[2] = "A in component InsP3_conc (micromolar)" legend_algebraic[2] = "V_3 in component V3 (micromolar_per_minute)" legend_constants[10] = "V_M5 in component V5 (micromolar_per_minute)" legend_constants[11] = "K_5 in component V5 (micromolar)" legend_constants[12] = "K_d in component V5 (micromolar)" legend_constants[13] = "p in component V5 (dimensionless)" legend_constants[14] = "n in component V5 (dimensionless)" legend_algebraic[1] = "V_5 in component V5 (micromolar_per_minute)" legend_constants[15] = "k in component cytosol (per_minute)" legend_constants[16] = "k_f in component cytosol (per_minute)" legend_constants[17] = "epsilon in component InsP3_conc (per_minute)" legend_constants[18] = "V_4 in component InsP3_conc (micromolar_per_minute)" legend_rates[0] = "d/dt Z in component cytosol (micromolar)" legend_rates[1] = "d/dt Y in component internal_pool (micromolar)" legend_rates[2] = "d/dt A in component InsP3_conc (micromolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 2 constants[1] = 2 constants[2] = 0.6 constants[3] = 6 states[0] = 0.15 constants[4] = 0.1 constants[5] = 20 constants[6] = 0.5 constants[7] = 0.2 constants[8] = 0.2 constants[9] = 2 states[1] = 1 states[2] = 0.42 constants[10] = 5 constants[11] = 1 constants[12] = 0.4 constants[13] = 2 constants[14] = 4 constants[15] = 10 constants[16] = 1 constants[17] = 0.1 constants[18] = 2 constants[19] = constants[0]+constants[1]*constants[2] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[1] = (((constants[10]*(power(states[2], constants[13])))/(power(constants[11], constants[13])+power(states[2], constants[13])))*(power(states[0], constants[14])))/(power(constants[12], constants[14])+power(states[0], constants[14])) rates[2] = (constants[2]*constants[18]-algebraic[1])-constants[17]*states[2] algebraic[0] = (constants[3]*(power(states[0], 2.00000)))/(power(constants[4], 2.00000)+power(states[0], 2.00000)) algebraic[2] = (((((constants[5]*(power(states[0], constants[9])))/(power(constants[6], constants[9])+power(states[0], constants[9])))*(power(states[1], 2.00000)))/(power(constants[8], 2.00000)+power(states[1], 2.00000)))*(power(states[2], 4.00000)))/(power(constants[7], 4.00000)+power(states[2], 4.00000)) rates[0] = ((constants[19]-algebraic[0])+algebraic[2]+constants[16]*states[1])-constants[15]*states[0] rates[1] = (algebraic[0]-algebraic[2])-constants[16]*states[1] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[1] = (((constants[10]*(power(states[2], constants[13])))/(power(constants[11], constants[13])+power(states[2], constants[13])))*(power(states[0], constants[14])))/(power(constants[12], constants[14])+power(states[0], constants[14])) algebraic[0] = (constants[3]*(power(states[0], 2.00000)))/(power(constants[4], 2.00000)+power(states[0], 2.00000)) algebraic[2] = (((((constants[5]*(power(states[0], constants[9])))/(power(constants[6], constants[9])+power(states[0], constants[9])))*(power(states[1], 2.00000)))/(power(constants[8], 2.00000)+power(states[1], 2.00000)))*(power(states[2], 4.00000)))/(power(constants[7], 4.00000)+power(states[2], 4.00000)) 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)