Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 24
sizeStates = 5
sizeConstants = 37
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_states[0] = "V in component membrane (millivolt)"
legend_constants[0] = "Cm in component membrane (femtoF)"
legend_algebraic[1] = "i_K in component K_current (picoA)"
legend_algebraic[11] = "i_K_Ca in component K_Ca_current (picoA)"
legend_algebraic[4] = "i_K_ATP in component K_ATP_current (picoA)"
legend_algebraic[15] = "i_CRAC in component CRAC_current (picoA)"
legend_algebraic[10] = "i_Ca in component Ca_current_total (picoA)"
legend_algebraic[17] = "i_leak in component leak_current (picoA)"
legend_constants[1] = "V_K in component K_current (millivolt)"
legend_constants[2] = "g_K in component K_current (picoS)"
legend_states[1] = "n in component K_channel_n_gate (dimensionless)"
legend_algebraic[0] = "n_infinity in component K_channel_n_gate (dimensionless)"
legend_algebraic[3] = "tau_n in component K_channel_n_gate (millisecond)"
legend_constants[3] = "Vn in component K_channel_n_gate (millivolt)"
legend_constants[4] = "Sn in component K_channel_n_gate (millivolt)"
legend_constants[5] = "lambda_n in component K_channel_n_gate (dimensionless)"
legend_constants[6] = "g_K_ATP in component K_ATP_current (picoS)"
legend_algebraic[7] = "i_Ca_f in component fast_Ca_current (picoA)"
legend_constants[7] = "V_Ca in component fast_Ca_current (millivolt)"
legend_constants[8] = "g_Ca_f in component fast_Ca_current (picoS)"
legend_algebraic[6] = "m_f_infinity in component fast_Ca_channel_m_gate (dimensionless)"
legend_constants[9] = "Vm_f in component fast_Ca_channel_m_gate (millivolt)"
legend_constants[10] = "Sm_f in component fast_Ca_channel_m_gate (millivolt)"
legend_algebraic[9] = "i_Ca_s in component slow_Ca_current (picoA)"
legend_constants[11] = "g_Ca_s in component slow_Ca_current (picoS)"
legend_algebraic[8] = "m_s_infinity in component slow_Ca_channel_m_gate (dimensionless)"
legend_states[2] = "jm in component slow_Ca_channel_j_gate (dimensionless)"
legend_constants[12] = "Vm_s in component slow_Ca_channel_m_gate (millivolt)"
legend_constants[13] = "Sm_s in component slow_Ca_channel_m_gate (millivolt)"
legend_algebraic[2] = "jm_infinity in component slow_Ca_channel_j_gate (dimensionless)"
legend_constants[14] = "Vj in component slow_Ca_channel_j_gate (millivolt)"
legend_algebraic[5] = "tau_j in component slow_Ca_channel_j_gate (millisecond)"
legend_constants[15] = "Sj in component slow_Ca_channel_j_gate (millivolt)"
legend_constants[16] = "g_K_Ca in component K_Ca_current (picoS)"
legend_states[3] = "Ca_i in component Ca_equations (micromolar)"
legend_constants[17] = "kdkca in component K_Ca_current (micromolar)"
legend_constants[18] = "g_CRAC in component CRAC_current (picoS)"
legend_constants[19] = "V_CRAC in component CRAC_current (millivolt)"
legend_states[4] = "Ca_er in component Ca_equations (micromolar)"
legend_algebraic[13] = "r_infinity in component CRAC_r_gate (dimensionless)"
legend_constants[20] = "Ca_er_bar in component CRAC_r_gate (micromolar)"
legend_constants[21] = "sloper in component CRAC_r_gate (micromolar)"
legend_constants[22] = "g_leak in component leak_current (picoS)"
legend_algebraic[12] = "J_er_p in component ER_parameters (micromolar_per_millisecond)"
legend_constants[23] = "IP3 in component ER_parameters (micromolar)"
legend_constants[24] = "kerp in component ER_parameters (micromolar)"
legend_constants[25] = "verp in component ER_parameters (micromolar_per_millisecond)"
legend_constants[26] = "dact in component ER_parameters (micromolar)"
legend_constants[27] = "dinh in component ER_parameters (micromolar)"
legend_constants[28] = "dip3 in component ER_parameters (micromolar)"
legend_algebraic[14] = "a_infinity in component ER_parameters (dimensionless)"
legend_constants[36] = "b_infinity in component ER_parameters (dimensionless)"
legend_algebraic[16] = "h_infinity in component ER_parameters (dimensionless)"
legend_algebraic[18] = "O in component ER_parameters (per_millisecond)"
legend_algebraic[21] = "J_er_tot in component Ca_equations (micromolar_per_millisecond)"
legend_algebraic[20] = "J_er_IP3 in component Ca_equations (micromolar_per_millisecond)"
legend_algebraic[19] = "J_er_leak in component Ca_equations (micromolar_per_millisecond)"
legend_algebraic[23] = "J_mem_tot in component Ca_membrane_flux (micromolar_per_millisecond)"
legend_constants[29] = "perl in component Ca_equations (per_millisecond)"
legend_constants[30] = "lambda_er in component Ca_equations (dimensionless)"
legend_constants[31] = "sigma_er in component Ca_equations (dimensionless)"
legend_constants[32] = "kmp in component Ca_membrane_flux (micromolar)"
legend_constants[33] = "vmp in component Ca_membrane_flux (micromolar)"
legend_constants[34] = "gamma in component Ca_membrane_flux (micromolar_per_picoA)"
legend_algebraic[22] = "Jmp in component Ca_membrane_flux (micromolar)"
legend_constants[35] = "f in component Ca_membrane_flux (per_millisecond)"
legend_rates[0] = "d/dt V in component membrane (millivolt)"
legend_rates[1] = "d/dt n in component K_channel_n_gate (dimensionless)"
legend_rates[2] = "d/dt jm in component slow_Ca_channel_j_gate (dimensionless)"
legend_rates[4] = "d/dt Ca_er in component Ca_equations (micromolar)"
legend_rates[3] = "d/dt Ca_i in component Ca_equations (micromolar)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = -61
constants[0] = 6158
constants[1] = -70
constants[2] = 3900
states[1] = 0.0005
constants[3] = -15
constants[4] = 6
constants[5] = 1.85
constants[6] = 150
constants[7] = 100
constants[8] = 810
constants[9] = -20
constants[10] = 7.5
constants[11] = 510
states[2] = 0.12
constants[12] = -16
constants[13] = 10
constants[14] = -53
constants[15] = 2
constants[16] = 1200
states[3] = 0.11
constants[17] = 0.55
constants[18] = 75
constants[19] = 0
states[4] = 60
constants[20] = 40
constants[21] = 3
constants[22] = 0
constants[23] = 0
constants[24] = 0.09
constants[25] = 0.24
constants[26] = 0.35
constants[27] = 0.4
constants[28] = 0.2
constants[29] = 0.003
constants[30] = 250
constants[31] = 1
constants[32] = 0.35
constants[33] = 0.08
constants[34] = 0.000003607
constants[35] = 0.01
constants[36] = constants[23]/(constants[23]+constants[28])
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[0] = 1.00000/(1.00000+exp((constants[3]-states[0])/constants[4]))
algebraic[3] = 9.09000/(1.00000+exp((states[0]-constants[3])/constants[4]))
rates[1] = (constants[5]*(algebraic[0]-states[1]))/algebraic[3]
algebraic[2] = 1.00000-1.00000/(1.00000+exp((states[0]-constants[14])/constants[15]))
algebraic[5] = 50000.0/(exp((states[0]-constants[14])/4.00000)+exp((constants[14]-states[0])/4.00000))+1500.00
rates[2] = (algebraic[2]-states[2])/algebraic[5]
algebraic[1] = constants[2]*states[1]*(states[0]-constants[1])
algebraic[11] = ((constants[16]*(power(states[3], 5.00000)))/(power(states[3], 5.00000)+power(constants[17], 5.00000)))*(states[0]-constants[1])
algebraic[4] = constants[6]*(states[0]-constants[1])
algebraic[13] = 1.00000/(1.00000+exp((states[4]-constants[20])/constants[21]))
algebraic[15] = constants[18]*algebraic[13]*(states[0]-constants[19])
algebraic[6] = 1.00000/(1.00000+exp((constants[9]-states[0])/constants[10]))
algebraic[7] = constants[8]*algebraic[6]*(states[0]-constants[7])
algebraic[8] = 1.00000/(1.00000+exp((constants[12]-states[0])/constants[13]))
algebraic[9] = constants[11]*algebraic[8]*(1.00000-states[2])*(states[0]-constants[7])
algebraic[10] = algebraic[7]+algebraic[9]
algebraic[17] = constants[22]*(states[0]-constants[19])
rates[0] = -(algebraic[10]+algebraic[1]+algebraic[4]+algebraic[11]+algebraic[15]+algebraic[17])/constants[0]
algebraic[12] = (constants[25]*(power(states[3], 2.00000)))/(power(states[3], 2.00000)+power(constants[24], 2.00000))
algebraic[14] = 1.00000/(1.00000+constants[26]/states[3])
algebraic[16] = 1.00000/(1.00000+states[3]/constants[27])
algebraic[18] = (power(algebraic[14], 3.00000))*(power(constants[36], 3.00000))*(power(algebraic[16], 3.00000))*1.00000
algebraic[20] = algebraic[18]*(states[4]-states[3])
algebraic[19] = constants[29]*(states[4]-states[3])
algebraic[21] = (algebraic[19]+algebraic[20])-algebraic[12]
rates[4] = -algebraic[21]/(constants[30]*constants[31])
algebraic[22] = (constants[33]*(power(states[3], 2.00000)))/(power(states[3], 2.00000)+power(constants[32], 2.00000))
algebraic[23] = -constants[35]*(constants[34]*algebraic[10]+algebraic[22])
rates[3] = algebraic[21]/constants[30]+algebraic[23]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = 1.00000/(1.00000+exp((constants[3]-states[0])/constants[4]))
algebraic[3] = 9.09000/(1.00000+exp((states[0]-constants[3])/constants[4]))
algebraic[2] = 1.00000-1.00000/(1.00000+exp((states[0]-constants[14])/constants[15]))
algebraic[5] = 50000.0/(exp((states[0]-constants[14])/4.00000)+exp((constants[14]-states[0])/4.00000))+1500.00
algebraic[1] = constants[2]*states[1]*(states[0]-constants[1])
algebraic[11] = ((constants[16]*(power(states[3], 5.00000)))/(power(states[3], 5.00000)+power(constants[17], 5.00000)))*(states[0]-constants[1])
algebraic[4] = constants[6]*(states[0]-constants[1])
algebraic[13] = 1.00000/(1.00000+exp((states[4]-constants[20])/constants[21]))
algebraic[15] = constants[18]*algebraic[13]*(states[0]-constants[19])
algebraic[6] = 1.00000/(1.00000+exp((constants[9]-states[0])/constants[10]))
algebraic[7] = constants[8]*algebraic[6]*(states[0]-constants[7])
algebraic[8] = 1.00000/(1.00000+exp((constants[12]-states[0])/constants[13]))
algebraic[9] = constants[11]*algebraic[8]*(1.00000-states[2])*(states[0]-constants[7])
algebraic[10] = algebraic[7]+algebraic[9]
algebraic[17] = constants[22]*(states[0]-constants[19])
algebraic[12] = (constants[25]*(power(states[3], 2.00000)))/(power(states[3], 2.00000)+power(constants[24], 2.00000))
algebraic[14] = 1.00000/(1.00000+constants[26]/states[3])
algebraic[16] = 1.00000/(1.00000+states[3]/constants[27])
algebraic[18] = (power(algebraic[14], 3.00000))*(power(constants[36], 3.00000))*(power(algebraic[16], 3.00000))*1.00000
algebraic[20] = algebraic[18]*(states[4]-states[3])
algebraic[19] = constants[29]*(states[4]-states[3])
algebraic[21] = (algebraic[19]+algebraic[20])-algebraic[12]
algebraic[22] = (constants[33]*(power(states[3], 2.00000)))/(power(states[3], 2.00000)+power(constants[32], 2.00000))
algebraic[23] = -constants[35]*(constants[34]*algebraic[10]+algebraic[22])
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)