# Size of variable arrays:
sizeAlgebraic = 9
sizeStates = 5
sizeConstants = 20
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] = "tau_c in component nucleotides (second)"
legend_constants[1] = "eta in component nucleotides (dimensionless)"
legend_constants[2] = "v in component nucleotides (dimensionless)"
legend_constants[3] = "k in component nucleotides (dimensionless)"
legend_algebraic[0] = "phi in component nucleotides (dimensionless)"
legend_states[0] = "ADP in component nucleotides (dimensionless)"
legend_states[1] = "ATP in component nucleotides (dimensionless)"
legend_constants[4] = "C_m in component membrane (femtofarad)"
legend_algebraic[3] = "I_Ca in component Ca_current (femtoampere)"
legend_algebraic[4] = "I_K in component K_current (femtoampere)"
legend_algebraic[7] = "I_KCa in component Ca_activated_K_current (femtoampere)"
legend_algebraic[8] = "I_KATP in component ATP_sensitive_K_current (femtoampere)"
legend_states[2] = "V in component membrane (millivolt)"
legend_constants[5] = "g_Ca_ in component Ca_current (picosiemens)"
legend_constants[6] = "V_Ca in component Ca_current (millivolt)"
legend_constants[7] = "v_m in component Ca_current (millivolt)"
legend_constants[8] = "s_m in component Ca_current (millivolt)"
legend_algebraic[1] = "m_infinity in component Ca_current (dimensionless)"
legend_constants[9] = "g_K_ in component K_current (picosiemens)"
legend_constants[10] = "V_K in component K_current (millivolt)"
legend_states[3] = "n in component K_channel_activation (dimensionless)"
legend_constants[11] = "g_KCa_ in component Ca_activated_K_current (picosiemens)"
legend_constants[12] = "k_D in component Ca_activated_K_current (micromolar)"
legend_states[4] = "c in component cytosolic_Ca (micromolar)"
legend_algebraic[6] = "omega in component Ca_activated_K_current (dimensionless)"
legend_constants[13] = "g_KATP_ in component ATP_sensitive_K_current (picosiemens)"
legend_constants[14] = "tau_n in component K_channel_activation (millisecond)"
legend_constants[15] = "v_n in component K_channel_activation (millivolt)"
legend_constants[16] = "s_n in component K_channel_activation (millivolt)"
legend_algebraic[2] = "n_infinity in component K_channel_activation (dimensionless)"
legend_algebraic[5] = "J_mem in component Ca_influx (micromolar_per_ms)"
legend_constants[17] = "f in component Ca_influx (dimensionless)"
legend_constants[18] = "alpha in component Ca_influx (micromolar_per_fA_ms)"
legend_constants[19] = "k_c in component Ca_influx (per_millisecond)"
legend_rates[1] = "d/dt ATP in component nucleotides (dimensionless)"
legend_rates[0] = "d/dt ADP in component nucleotides (dimensionless)"
legend_rates[2] = "d/dt V in component membrane (millivolt)"
legend_rates[3] = "d/dt n in component K_channel_activation (dimensionless)"
legend_rates[4] = "d/dt c in component cytosolic_Ca (micromolar)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 1200
constants[1] = 185
constants[2] = 10
constants[3] = 20
states[0] = 0.085817
states[1] = 2.1047
constants[4] = 5300
states[2] = -67.018
constants[5] = 1200
constants[6] = 25
constants[7] = -20
constants[8] = 12
constants[9] = 3000
constants[10] = -75
states[3] = 0.00011
constants[11] = 300
constants[12] = 0.3
states[4] = 0.15666
constants[13] = 350
constants[14] = 16
constants[15] = -16
constants[16] = 5.6
constants[17] = 0.001
constants[18] = 0.00000225
constants[19] = 0.1
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[0] = states[1]*(power(1.00000+constants[3]*states[0], 2.00000))
rates[1] = (constants[2]-algebraic[0])/(1000.00*constants[0])
rates[0] = (algebraic[0]-constants[1]*states[0])/(1000.00*constants[0])
algebraic[2] = 1.00000/(1.00000+exp((constants[15]-states[2])/constants[16]))
rates[3] = (algebraic[2]-states[3])/constants[14]
algebraic[1] = 1.00000/(1.00000+exp((constants[7]-states[2])/constants[8]))
algebraic[3] = constants[5]*algebraic[1]*(states[2]-constants[6])
algebraic[5] = -constants[17]*(constants[18]*algebraic[3]+constants[19]*states[4])
rates[4] = algebraic[5]
algebraic[4] = constants[9]*states[3]*(states[2]-constants[10])
algebraic[6] = 1.00000/(1.00000+constants[12]/states[4])
algebraic[7] = constants[11]*algebraic[6]*(states[2]-constants[10])
algebraic[8] = ((states[2]-constants[10])*constants[13])/states[1]
rates[2] = -(algebraic[3]+algebraic[4]+algebraic[7]+algebraic[8])/constants[4]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = states[1]*(power(1.00000+constants[3]*states[0], 2.00000))
algebraic[2] = 1.00000/(1.00000+exp((constants[15]-states[2])/constants[16]))
algebraic[1] = 1.00000/(1.00000+exp((constants[7]-states[2])/constants[8]))
algebraic[3] = constants[5]*algebraic[1]*(states[2]-constants[6])
algebraic[5] = -constants[17]*(constants[18]*algebraic[3]+constants[19]*states[4])
algebraic[4] = constants[9]*states[3]*(states[2]-constants[10])
algebraic[6] = 1.00000/(1.00000+constants[12]/states[4])
algebraic[7] = constants[11]*algebraic[6]*(states[2]-constants[10])
algebraic[8] = ((states[2]-constants[10])*constants[13])/states[1]
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)