# Size of variable arrays: sizeAlgebraic = 7 sizeStates = 3 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 (second)" legend_algebraic[0] = "Ca_Pr in component total_calcium (micromolar)" legend_constants[0] = "Ca_tot in component total_calcium (micromolar)" legend_constants[1] = "rho_ER in component ER_calcium (dimensionless)" legend_constants[2] = "beta_ER in component ER_calcium (dimensionless)" legend_constants[3] = "rho_m in component mitochondrial_calcium (dimensionless)" legend_constants[4] = "beta_m in component mitochondrial_calcium (dimensionless)" legend_states[0] = "Ca_cyt in component cytosolic_calcium (micromolar)" legend_states[1] = "Ca_ER in component ER_calcium (micromolar)" legend_states[2] = "Ca_m in component mitochondrial_calcium (micromolar)" legend_algebraic[1] = "Pr in component total_protein (micromolar)" legend_constants[5] = "Pr_tot in component total_protein (micromolar)" legend_constants[6] = "k_plus in component cytosolic_calcium (second_order_rate_constant)" legend_constants[7] = "k_minus in component cytosolic_calcium (first_order_rate_constant)" legend_algebraic[3] = "J_ch in component Ca_efflux_from_the_ER (flux)" legend_algebraic[4] = "J_leak in component Ca_leak_flux_from_the_ER (flux)" legend_algebraic[2] = "J_pump in component ATP_dependent_Ca_uptake_into_the_ER (flux)" legend_algebraic[6] = "J_out in component mitochondrial_Ca_release (flux)" legend_algebraic[5] = "J_in in component mitochondrial_Ca_uptake (flux)" legend_constants[8] = "k_pump in component ATP_dependent_Ca_uptake_into_the_ER (first_order_rate_constant)" legend_constants[9] = "k_ch in component Ca_efflux_from_the_ER (first_order_rate_constant)" legend_constants[10] = "K1 in component Ca_efflux_from_the_ER (micromolar)" legend_constants[11] = "k_leak in component Ca_leak_flux_from_the_ER (first_order_rate_constant)" legend_constants[12] = "k_in in component mitochondrial_Ca_uptake (flux)" legend_constants[13] = "K2 in component mitochondrial_Ca_uptake (micromolar)" legend_constants[14] = "k_out in component mitochondrial_Ca_release (first_order_rate_constant)" legend_constants[15] = "k_m in component mitochondrial_Ca_release (first_order_rate_constant)" legend_constants[16] = "K3 in component mitochondrial_Ca_release (micromolar)" legend_rates[0] = "d/dt Ca_cyt in component cytosolic_calcium (micromolar)" legend_rates[1] = "d/dt Ca_ER in component ER_calcium (micromolar)" legend_rates[2] = "d/dt Ca_m in component mitochondrial_calcium (micromolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 90.0 constants[1] = 0.01 constants[2] = 0.0025 constants[3] = 0.01 constants[4] = 0.0025 states[0] = 0.05 states[1] = 1.0 states[2] = 0.4 constants[5] = 120.0 constants[6] = 0.1 constants[7] = 0.01 constants[8] = 20.0 constants[9] = 4100.0 constants[10] = 5.0 constants[11] = 0.05 constants[12] = 300.0 constants[13] = 0.8 constants[14] = 125.0 constants[15] = 0.00625 constants[16] = 5.0 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[3] = constants[9]*((power(states[0], 2.00000))/(power(constants[10], 2.00000)+power(states[0], 2.00000)))*(states[1]-states[0]) algebraic[4] = constants[11]*(states[1]-states[0]) algebraic[2] = constants[8]*states[0] rates[1] = (constants[2]/constants[1])*(algebraic[2]-(algebraic[3]+algebraic[4])) algebraic[0] = constants[0]-(states[0]+(constants[1]/constants[2])*states[1]+(constants[3]/constants[4])*states[2]) algebraic[1] = constants[5]-algebraic[0] algebraic[6] = (constants[14]*((power(states[0], 2.00000))/(power(constants[16], 2.00000)+power(states[0], 2.00000)))+constants[15])*states[2] algebraic[5] = constants[12]*((power(states[0], 8.00000))/(power(constants[13], 8.00000)+power(states[0], 8.00000))) rates[0] = (algebraic[3]+algebraic[4]+algebraic[6]+constants[7]*algebraic[0])-(algebraic[2]+algebraic[5]+constants[6]*states[0]*algebraic[1]) rates[2] = (constants[4]/constants[3])*(algebraic[5]-algebraic[6]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[3] = constants[9]*((power(states[0], 2.00000))/(power(constants[10], 2.00000)+power(states[0], 2.00000)))*(states[1]-states[0]) algebraic[4] = constants[11]*(states[1]-states[0]) algebraic[2] = constants[8]*states[0] algebraic[0] = constants[0]-(states[0]+(constants[1]/constants[2])*states[1]+(constants[3]/constants[4])*states[2]) algebraic[1] = constants[5]-algebraic[0] algebraic[6] = (constants[14]*((power(states[0], 2.00000))/(power(constants[16], 2.00000)+power(states[0], 2.00000)))+constants[15])*states[2] algebraic[5] = constants[12]*((power(states[0], 8.00000))/(power(constants[13], 8.00000)+power(states[0], 8.00000))) 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)