Generated Code
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The raw code is available.
# 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)