# Size of variable arrays: sizeAlgebraic = 10 sizeStates = 5 sizeConstants = 11 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_voi = "t in component environment (second)" legend_constants[0] = "C_m in component environment (fF)" legend_states[0] = "q_mem in component environment (fC)" legend_constants[1] = "R in component environment (J_per_K_per_mol)" legend_constants[2] = "T in component environment (kelvin)" legend_constants[3] = "F in component environment (C_per_mol)" legend_algebraic[7] = "v_pCa_R1 in component pCa (fmol_per_sec)" legend_algebraic[8] = "v_pCa_R2 in component pCa (fmol_per_sec)" legend_states[1] = "q_Ca_o in component environment (fmol)" legend_states[2] = "q_Ca_i in component environment (fmol)" legend_states[3] = "q_pCa in component environment (fmol)" legend_states[4] = "q_pCa_Ca in component environment (fmol)" legend_algebraic[1] = "V_mem in component environment (J_per_C)" legend_algebraic[9] = "I_mem_pCa in component pCa (fA)" legend_algebraic[2] = "Ca_T in component environment (fmol)" legend_algebraic[3] = "channel_T in component environment (fmol)" legend_constants[4] = "kappa_pCa_R1 in component pCa_parameters (fmol_per_sec)" legend_constants[5] = "kappa_pCa_R2 in component pCa_parameters (fmol_per_sec)" legend_constants[6] = "K_Ca_i in component pCa_parameters (per_fmol)" legend_constants[7] = "K_Ca_o in component pCa_parameters (per_fmol)" legend_constants[8] = "K_pCa in component pCa_parameters (per_fmol)" legend_constants[9] = "K_pCa_Ca in component pCa_parameters (per_fmol)" legend_constants[10] = "zCa in component pCa_parameters (dimensionless)" legend_algebraic[0] = "mu_Ca_i in component pCa (J_per_mol)" legend_algebraic[4] = "mu_Ca_o in component pCa (J_per_mol)" legend_algebraic[5] = "mu_pCa in component pCa (J_per_mol)" legend_algebraic[6] = "mu_pCa_Ca in component pCa (J_per_mol)" legend_rates[2] = "d/dt q_Ca_i in component environment (fmol)" legend_rates[1] = "d/dt q_Ca_o in component environment (fmol)" legend_rates[3] = "d/dt q_pCa in component environment (fmol)" legend_rates[4] = "d/dt q_pCa_Ca in component environment (fmol)" legend_rates[0] = "d/dt q_mem in component environment (fC)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 153400 states[0] = -13039 constants[1] = 8.31 constants[2] = 310 constants[3] = 96500 states[1] = 9.3276 states[2] = 0.00456 states[3] = 0.0032 states[4] = 1e-9 constants[4] = 2647.75 constants[5] = 2.95771e-05 constants[6] = 26.4744 constants[7] = 8.78733e-05 constants[8] = 0.0120554 constants[9] = 0.00548953 constants[10] = 2 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[1]*constants[2]*log(constants[6]*states[2]) algebraic[5] = constants[1]*constants[2]*log(constants[8]*states[3]) algebraic[6] = constants[1]*constants[2]*log(constants[9]*states[4]) algebraic[7] = constants[4]*(exp((algebraic[0]+algebraic[5])/(constants[1]*constants[2]))-exp(algebraic[6]/(constants[1]*constants[2]))) rates[2] = -algebraic[7] algebraic[4] = constants[1]*constants[2]*log(constants[7]*states[1]) algebraic[8] = constants[5]*(exp(algebraic[6]/(constants[1]*constants[2]))-exp((algebraic[4]+algebraic[5])/(constants[1]*constants[2]))) rates[1] = algebraic[8] rates[3] = -algebraic[7]+algebraic[8] rates[4] = algebraic[7]-algebraic[8] algebraic[9] = -constants[10]*constants[3]*algebraic[8] rates[0] = algebraic[9] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[1]*constants[2]*log(constants[6]*states[2]) algebraic[5] = constants[1]*constants[2]*log(constants[8]*states[3]) algebraic[6] = constants[1]*constants[2]*log(constants[9]*states[4]) algebraic[7] = constants[4]*(exp((algebraic[0]+algebraic[5])/(constants[1]*constants[2]))-exp(algebraic[6]/(constants[1]*constants[2]))) algebraic[4] = constants[1]*constants[2]*log(constants[7]*states[1]) algebraic[8] = constants[5]*(exp(algebraic[6]/(constants[1]*constants[2]))-exp((algebraic[4]+algebraic[5])/(constants[1]*constants[2]))) algebraic[9] = -constants[10]*constants[3]*algebraic[8] algebraic[1] = states[0]/constants[0] algebraic[2] = states[2]+states[1]+states[4] algebraic[3] = states[3]+states[4] 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)