# Size of variable arrays: sizeAlgebraic = 9 sizeStates = 4 sizeConstants = 16 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] = "Ca_m in component Ca_m (micromolar)" legend_algebraic[0] = "J_min in component J_min (micromolar)" legend_algebraic[1] = "J_mout in component J_mout (micromolar)" legend_constants[0] = "k_min in component J_min (micromolar)" legend_states[1] = "Ca_cyt in component Ca_cyt (micromolar)" legend_constants[1] = "K_m in component J_min (micromolar)" legend_constants[2] = "n in component J_min (micromolar)" legend_constants[3] = "k_mout in component J_mout (micromolar)" legend_algebraic[2] = "J_ERch in component J_ERch (micromolar)" legend_algebraic[3] = "J_ERpump in component J_ERpump (micromolar)" legend_algebraic[4] = "J_ERleak in component J_ERleak (micromolar)" legend_algebraic[6] = "J_CaPr in component J_CaPr (micromolar)" legend_algebraic[8] = "J_Pr in component J_Pr (micromolar)" legend_constants[4] = "rho_m in component Ca_cyt (dimensionless)" legend_constants[5] = "beta_m in component Ca_cyt (dimensionless)" legend_states[2] = "Ca_tot in component Ca_tot (micromolar)" legend_states[3] = "Ca_ER in component Ca_ER (micromolar)" legend_constants[6] = "rho_ER in component Ca_ER (dimensionless)" legend_constants[7] = "beta_ER in component Ca_ER (dimensionless)" legend_algebraic[5] = "CaPr in component CaPr (micromolar)" legend_constants[8] = "k_ERch in component J_ERch (micromolar)" legend_constants[9] = "K_ch in component J_ERch (micromolar)" legend_constants[10] = "k_ERpump in component J_ERpump (per_second)" legend_constants[11] = "k_ERleak in component J_ERleak (per_second)" legend_constants[12] = "k_min in component J_CaPr (per_second)" legend_constants[13] = "k_plus in component J_Pr (per_micromolar_per_second)" legend_algebraic[7] = "Pr in component Pr (micromolar)" legend_constants[14] = "Ca_tot in component CaPr (micromolar)" legend_constants[15] = "Pr_tot in component Pr (micromolar)" legend_rates[0] = "d/dt Ca_m in component Ca_m (micromolar)" legend_rates[1] = "d/dt Ca_cyt in component Ca_cyt (micromolar)" legend_rates[2] = "d/dt Ca_tot in component Ca_tot (micromolar)" legend_rates[3] = "d/dt Ca_ER in component Ca_ER (micromolar)" 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] = 330 states[1] = 0.01 constants[1] = 1.6 constants[2] = 8 constants[3] = 0.5 constants[4] = 0.01 constants[5] = 0.025 states[2] = 0.01 states[3] = 20 constants[6] = 0.01 constants[7] = 0.0025 constants[8] = 0.001 constants[9] = 5 constants[10] = 20 constants[11] = 0.05 constants[12] = 0.01 constants[13] = 0.1 constants[14] = 90 constants[15] = 120 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = (constants[0]*(power(states[1], constants[2])))/(power(constants[1], constants[2])+power(states[1], constants[2])) algebraic[1] = (constants[3]*states[0])/1.00000 rates[0] = algebraic[0]-algebraic[1] algebraic[2] = ((constants[8]*(power(states[1], 2.00000)))/(power(constants[9], 2.00000)+power(states[1], 2.00000)))*(states[3]-states[1]) algebraic[3] = constants[10]*states[1] algebraic[4] = constants[11]*(states[3]-states[1]) rates[3] = (constants[7]/constants[6])*((algebraic[3]-algebraic[4])-algebraic[2])*1.00000 algebraic[5] = constants[14]-(states[1]+(constants[6]/constants[7])*states[3]) rates[2] = states[1]+(constants[6]/constants[7])*states[3]+(constants[4]/constants[5])*states[0]+algebraic[5] algebraic[6] = constants[12]*algebraic[5] algebraic[7] = constants[15]-algebraic[5] algebraic[8] = constants[13]*states[1]*algebraic[7] rates[1] = ((((algebraic[2]-algebraic[3])+algebraic[4]+algebraic[6])-algebraic[8])+(constants[4]/constants[5])*(algebraic[1]-algebraic[0]))*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]*(power(states[1], constants[2])))/(power(constants[1], constants[2])+power(states[1], constants[2])) algebraic[1] = (constants[3]*states[0])/1.00000 algebraic[2] = ((constants[8]*(power(states[1], 2.00000)))/(power(constants[9], 2.00000)+power(states[1], 2.00000)))*(states[3]-states[1]) algebraic[3] = constants[10]*states[1] algebraic[4] = constants[11]*(states[3]-states[1]) algebraic[5] = constants[14]-(states[1]+(constants[6]/constants[7])*states[3]) algebraic[6] = constants[12]*algebraic[5] algebraic[7] = constants[15]-algebraic[5] algebraic[8] = constants[13]*states[1]*algebraic[7] 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)