# Size of variable arrays: sizeAlgebraic = 13 sizeStates = 8 sizeConstants = 25 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] = "Pyr in component Pyr (micromolar)" legend_constants[24] = "v1 in component v1 (micromolar_per_second)" legend_algebraic[0] = "v2 in component v2 (micromolar_per_second)" legend_algebraic[5] = "v7 in component v7 (micromolar_per_second)" legend_states[1] = "AcCoA in component AcCoA (micromolar)" legend_algebraic[1] = "v3 in component v3 (micromolar_per_second)" legend_states[2] = "Cit in component Cit (micromolar)" legend_algebraic[2] = "v4 in component v4 (micromolar_per_second)" legend_states[3] = "KG in component KG (micromolar)" legend_algebraic[3] = "v5 in component v5 (micromolar_per_second)" legend_algebraic[4] = "v6 in component v6 (micromolar_per_second)" legend_states[4] = "OAA in component OAA (micromolar)" legend_algebraic[6] = "v8 in component v8 (micromolar_per_second)" legend_states[5] = "NAD in component NAD (micromolar)" legend_algebraic[9] = "vresp in component vresp (micromolar_per_second)" legend_states[6] = "ATP in component ATP (micromolar)" legend_algebraic[12] = "vATP in component vATP (micromolar_per_second)" legend_algebraic[7] = "vANT in component vANT (micromolar_per_second)" legend_states[7] = "delta_psi in component delta_psi (millivolt)" legend_constants[0] = "C in component delta_psi (millimolar_per_millivolt)" legend_algebraic[8] = "vleak in component vleak (micromolar_per_second)" legend_constants[1] = "k1 in component v1 (micromolar_per_second)" legend_constants[2] = "k2 in component v2 (second_order_rate_constant)" legend_constants[3] = "k3 in component v3 (second_order_rate_constant)" legend_constants[4] = "k4 in component v4 (second_order_rate_constant)" legend_constants[5] = "k5 in component v5 (third_order_rate_constant)" legend_constants[6] = "At in component model_parameters (millimolar)" legend_constants[7] = "k6 in component v6 (first_order_rate_constant)" legend_constants[8] = "k7 in component v7 (second_order_rate_constant)" legend_constants[9] = "k8 in component v8 (first_order_rate_constant)" legend_constants[10] = "kANT in component vANT (first_order_rate_constant)" legend_constants[11] = "kleak in component vleak (molar_per_millivolt_per_second)" legend_constants[12] = "kresp in component vresp (millimolar_per_second)" legend_constants[13] = "K in component vresp (millimolar)" legend_constants[14] = "a in component vresp (per_millivolt)" legend_constants[15] = "delta_psi_m in component vresp (millivolt)" legend_constants[16] = "Nt in component model_parameters (millimolar)" legend_constants[17] = "kATP in component vATP (millimolar_per_second)" legend_constants[18] = "b in component vATP (per_micromolar)" legend_algebraic[11] = "ATP_crit_delta_psi in component ATP_crit_delta_psi (micromolar)" legend_constants[19] = "R in component ATP_crit_delta_psi (joule_per_mole_kelvin)" legend_constants[20] = "T in component ATP_crit_delta_psi (kelvin)" legend_constants[21] = "F in component ATP_crit_delta_psi (coulomb_per_mole)" legend_constants[22] = "Kapp in component ATP_crit_delta_psi (per_millimolar)" legend_constants[23] = "Pi in component ATP_crit_delta_psi (millimolar)" legend_algebraic[10] = "delta_G_transport in component ATP_crit_delta_psi (joule_per_mole)" legend_rates[0] = "d/dt Pyr in component Pyr (micromolar)" legend_rates[1] = "d/dt AcCoA in component AcCoA (micromolar)" legend_rates[2] = "d/dt Cit in component Cit (micromolar)" legend_rates[3] = "d/dt KG in component KG (micromolar)" legend_rates[4] = "d/dt OAA in component OAA (micromolar)" legend_rates[5] = "d/dt NAD in component NAD (micromolar)" legend_rates[6] = "d/dt ATP in component ATP (micromolar)" legend_rates[7] = "d/dt delta_psi in component delta_psi (millivolt)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.154 states[1] = 0.063 states[2] = 0.44 states[3] = 0.225 states[4] = 0.005 states[5] = 0.856 states[6] = 3.536 states[7] = 150.0 constants[0] = 6.75e-06 constants[1] = 38.0 constants[2] = 152.0 constants[3] = 57142.0 constants[4] = 53.0 constants[5] = 82361.0 constants[6] = 4.160 constants[7] = 3.2e-3 constants[8] = 40.0 constants[9] = 3.6 constants[10] = 0.1 constants[11] = 0.426 constants[12] = 2.5 constants[13] = 2 constants[14] = 0.1 constants[15] = 150.0 constants[16] = 1.070 constants[17] = 131.9 constants[18] = 4 constants[19] = 8.314 constants[20] = 298 constants[21] = 96485 constants[22] = 4.4e-6 constants[23] = 2.440 constants[24] = constants[1] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[2]*states[0]*states[5] algebraic[1] = constants[3]*states[4]*states[1] rates[1] = algebraic[0]-algebraic[1] algebraic[2] = constants[4]*states[2]*states[5] rates[2] = algebraic[1]-algebraic[2] algebraic[3] = constants[5]*states[3]*states[5]*(constants[6]-states[6]) algebraic[4] = constants[7]*(states[4]-states[3]) rates[3] = (algebraic[2]+algebraic[4])-algebraic[3] algebraic[5] = constants[8]*states[0]*states[6] rates[0] = constants[24]-(algebraic[0]+algebraic[5]) algebraic[6] = constants[9]*states[4] rates[4] = (algebraic[3]+algebraic[5])-(algebraic[1]+algebraic[6]+algebraic[4]) algebraic[9] = constants[12]*((constants[16]-states[5])/((constants[13]+constants[16])-states[5]))*(1.00000/(1.00000+exp(constants[14]*(states[7]-constants[15])))) rates[5] = algebraic[9]-(algebraic[0]+algebraic[2]+2.00000*algebraic[3]) algebraic[10] = 0.00120000*constants[21]*states[7] algebraic[11] = constants[6]/(1.00000+exp((-3.00000*algebraic[10])/(constants[19]*constants[20]))/(constants[22]*constants[23])) algebraic[12] = constants[17]*(2.00000/(1.00000+exp(constants[18]*(states[6]-algebraic[11])))-1.00000) algebraic[7] = constants[10]*states[6] rates[6] = (algebraic[12]+algebraic[3])-(algebraic[7]+algebraic[5]) algebraic[8] = constants[11]*states[7] rates[7] = (1.00000/constants[0])*(10.0000*algebraic[9]-(3.00000*algebraic[12]+algebraic[8]+algebraic[7])) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[2]*states[0]*states[5] algebraic[1] = constants[3]*states[4]*states[1] algebraic[2] = constants[4]*states[2]*states[5] algebraic[3] = constants[5]*states[3]*states[5]*(constants[6]-states[6]) algebraic[4] = constants[7]*(states[4]-states[3]) algebraic[5] = constants[8]*states[0]*states[6] algebraic[6] = constants[9]*states[4] algebraic[9] = constants[12]*((constants[16]-states[5])/((constants[13]+constants[16])-states[5]))*(1.00000/(1.00000+exp(constants[14]*(states[7]-constants[15])))) algebraic[10] = 0.00120000*constants[21]*states[7] algebraic[11] = constants[6]/(1.00000+exp((-3.00000*algebraic[10])/(constants[19]*constants[20]))/(constants[22]*constants[23])) algebraic[12] = constants[17]*(2.00000/(1.00000+exp(constants[18]*(states[6]-algebraic[11])))-1.00000) algebraic[7] = constants[10]*states[6] algebraic[8] = constants[11]*states[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)