# Size of variable arrays: sizeAlgebraic = 15 sizeStates = 7 sizeConstants = 29 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 (millisecond)" legend_constants[0] = "A_iso in component parameters (mN_per_mm2_per_mM)" legend_constants[1] = "k_off in component parameters (per_msec)" legend_constants[2] = "k_on in component parameters (per_mM_per_msec)" legend_constants[3] = "k_onI in component parameters (per_msec)" legend_constants[4] = "k_offi in component parameters (per_msec)" legend_constants[5] = "k_OFF in component parameters (dimensionless)" legend_constants[6] = "k_xboff in component parameters (dimensionless)" legend_constants[7] = "k_tmoff in component parameters (per_msec)" legend_constants[8] = "k_tmonc in component parameters (per_msec)" legend_constants[9] = "k_tmRU in component parameters (dimensionless)" legend_constants[10] = "k_tmxb in component parameters (dimensionless)" legend_constants[11] = "k_12 in component parameters (per_mM_per_msec)" legend_constants[12] = "k_minus12 in component parameters (per_msec)" legend_constants[13] = "k_Titin in component parameters (dimensionless)" legend_constants[14] = "k_3c in component parameters (per_msec)" legend_constants[15] = "k_3f in component parameters (dimensionless)" legend_constants[16] = "k_3xb in component parameters (dimensionless)" legend_constants[17] = "k_minus3 in component parameters (per_msec)" legend_constants[18] = "k_4 in component parameters (per_msec)" legend_constants[19] = "k_minus4 in component parameters (per_msec)" legend_constants[20] = "k_5 in component parameters (per_msec)" legend_algebraic[0] = "F_b in component active_force (mN_per_mm2)" legend_states[0] = "RUA_MADPPi in component RU_species (mM)" legend_states[1] = "RUA_MADP in component RU_species (mM)" legend_algebraic[5] = "Q_CaB in component Ca_binding_rate (mM_per_msec)" legend_algebraic[3] = "RUNA in component RU_species (mM)" legend_states[2] = "Ca in component RU_species (mM)" legend_states[3] = "RUTCa_off in component RU_species (mM)" legend_algebraic[11] = "Q_TCaA in component TnI_conf_change_rate (mM_per_msec)" legend_algebraic[9] = "k_offI in component TnI_conf_change_rate (per_msec)" legend_states[4] = "RUTCa_on in component RU_species (mM)" legend_algebraic[7] = "RUA in component RU_species (mM)" legend_constants[21] = "RU_total in component RU_species (mM)" legend_algebraic[2] = "Q_TMA in component Tm_conf_change_rate (mM_per_msec)" legend_algebraic[1] = "k_tmon in component Tm_conf_change_rate (per_msec)" legend_states[5] = "RUTM_on in component RU_species (mM)" legend_algebraic[10] = "Q_MB in component myosin_binding_rate (mM_per_msec)" legend_constants[28] = "KTitin in component KTitin (dimensionless)" legend_constants[24] = "L in component length (mmeter)" legend_constants[22] = "L_0 in component length (mmeter)" legend_constants[23] = "MADPPi in component RU_species (mM)" legend_algebraic[8] = "RUTM_on_eff in component RU_species (mM)" legend_states[6] = "RUAMADPPi in component RU_species (mM)" legend_constants[25] = "f_titinNormal in component KTitin (dimensionless)" legend_constants[27] = "f_titinDamaged in component KTitin (dimensionless)" legend_algebraic[14] = "Q_Fgen in component Force_Generating_rate (mM_per_msec)" legend_algebraic[13] = "k_3 in component Force_Generating_rate (per_msec)" legend_algebraic[12] = "RUTCa_on_eff in component RU_species (mM)" legend_algebraic[4] = "Q_PiR in component Pi_release_rate (mM_per_msec)" legend_algebraic[6] = "Q_ADPR in component ADP_release_rate (mM_per_msec)" legend_constants[26] = "alpha in component alpha (dimensionless)" legend_rates[3] = "d/dt RUTCa_off in component RU_species (mM)" legend_rates[4] = "d/dt RUTCa_on in component RU_species (mM)" legend_rates[5] = "d/dt RUTM_on in component RU_species (mM)" legend_rates[6] = "d/dt RUAMADPPi in component RU_species (mM)" legend_rates[0] = "d/dt RUA_MADPPi in component RU_species (mM)" legend_rates[1] = "d/dt RUA_MADP in component RU_species (mM)" legend_rates[2] = "d/dt Ca in component RU_species (mM)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 9000 constants[1] = 0.2 constants[2] = 17.3 constants[3] = 0.2 constants[4] = 0.075 constants[5] = -0.32 constants[6] = -1.37 constants[7] = 0.067 constants[8] = 0.014 constants[9] = 10 constants[10] = -1.86 constants[11] = 2 constants[12] = 0.6 constants[13] = 0.2 constants[14] = 0.025 constants[15] = 50 constants[16] = -1.23 constants[17] = 0.008 constants[18] = 0.077 constants[19] = 0.001 constants[20] = 0.03723 states[0] = 0 states[1] = 0 states[2] = 0.01 states[3] = 0 states[4] = 0 constants[21] = 0.0726 states[5] = 0 constants[22] = 0.001 constants[23] = 0.1375 states[6] = 0 constants[24] = constants[22] constants[25] = constants[13]*(9.96630/(1.00000+exp((constants[24]/constants[22]+1.06390)/0.0696000))) constants[26] = custom_piecewise([less(constants[24] , 1.00000), 1.50000*(constants[24]/constants[22])-0.500000 , less_equal(1.00000 , constants[24]) & less(constants[24] , 1.10000), 1.00000 , True, -1.60000*(constants[24]/constants[22])+2.76000]) constants[27] = constants[13]*(-31.0000*(constants[24]/constants[22])+40.0000) constants[28] = custom_piecewise([less_equal(constants[24] , 1.10000), constants[25] , True, constants[27]]) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[4] = constants[18]*states[0]-constants[19]*states[1] algebraic[6] = constants[20]*states[1] rates[1] = algebraic[4]-algebraic[6] algebraic[3] = constants[21]-(states[3]+states[4]+states[5]+states[6]+states[0]+states[1]) algebraic[5] = constants[2]*algebraic[3]*states[2]-constants[1]*states[3] rates[2] = -algebraic[5] algebraic[1] = constants[8]*(states[4]/constants[21])*(power(1.00000+constants[9]*(states[5]/constants[21]), 2.00000))*(power(1.00000+constants[10]*((states[0]+states[1])/constants[21]), 2.00000)) algebraic[2] = algebraic[1]*states[4]-constants[7]*states[5] algebraic[8] = constants[26]*states[5] algebraic[10] = constants[11]*constants[28]*constants[23]*algebraic[8]-constants[12]*states[6] rates[5] = (algebraic[2]-algebraic[10])+algebraic[6] algebraic[7] = states[4]+states[5]+states[6]+states[0]+states[1] algebraic[9] = constants[4]*(power(1.00000+constants[5]*(algebraic[7]/constants[21]), 2.00000))*(power(1.00000+constants[6]*((states[0]+states[1])/constants[21]), 4.40000)) algebraic[11] = constants[3]*states[3]-algebraic[9]*states[4] rates[3] = algebraic[5]-algebraic[11] rates[4] = algebraic[11]-algebraic[2] algebraic[12] = constants[26]*states[4] algebraic[13] = constants[14]*(power(1.00000+(constants[15]*(algebraic[12]+algebraic[8]+states[6]))/constants[21], 2.00000))*(power(1.00000+(constants[16]*(states[0]+states[1]))/constants[21], 2.00000)) algebraic[14] = algebraic[13]*states[6]-constants[17]*states[0] rates[6] = algebraic[10]-algebraic[14] rates[0] = algebraic[14]-algebraic[4] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[4] = constants[18]*states[0]-constants[19]*states[1] algebraic[6] = constants[20]*states[1] algebraic[3] = constants[21]-(states[3]+states[4]+states[5]+states[6]+states[0]+states[1]) algebraic[5] = constants[2]*algebraic[3]*states[2]-constants[1]*states[3] algebraic[1] = constants[8]*(states[4]/constants[21])*(power(1.00000+constants[9]*(states[5]/constants[21]), 2.00000))*(power(1.00000+constants[10]*((states[0]+states[1])/constants[21]), 2.00000)) algebraic[2] = algebraic[1]*states[4]-constants[7]*states[5] algebraic[8] = constants[26]*states[5] algebraic[10] = constants[11]*constants[28]*constants[23]*algebraic[8]-constants[12]*states[6] algebraic[7] = states[4]+states[5]+states[6]+states[0]+states[1] algebraic[9] = constants[4]*(power(1.00000+constants[5]*(algebraic[7]/constants[21]), 2.00000))*(power(1.00000+constants[6]*((states[0]+states[1])/constants[21]), 4.40000)) algebraic[11] = constants[3]*states[3]-algebraic[9]*states[4] algebraic[12] = constants[26]*states[4] algebraic[13] = constants[14]*(power(1.00000+(constants[15]*(algebraic[12]+algebraic[8]+states[6]))/constants[21], 2.00000))*(power(1.00000+(constants[16]*(states[0]+states[1]))/constants[21], 2.00000)) algebraic[14] = algebraic[13]*states[6]-constants[17]*states[0] algebraic[0] = constants[0]*(states[0]+states[1]) return algebraic def custom_piecewise(cases): """Compute result of a piecewise function""" return select(cases[0::2],cases[1::2]) 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)