Phenomenological models of NaV1.5: Hodgkin-Huxley and kinetic formalisms (Andreozzi et al 2019)

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Accession:257747
"Computational models of ion channels represent the building blocks of conductance-based, biologically inspired models of neurons and neural networks. Ion channels are still widely modelled by means of the formalism developed by the seminal work of Hodgkin and Huxley (HH), although the electrophysiological features of the channels are currently known to be better fitted by means of kinetic Markov-type models. The present study is aimed at showing why simplified Markov-type kinetic models are more suitable for ion channels modelling as compared to HH ones, and how a manual optimization process can be rationally carried out for both. ..."
Reference:
1 . Andreozzi E, Carannante I, D'Addio G, Cesarelli M, Balbi P (2019) Phenomenological models of NaV1.5. A side by side, procedural, hands-on comparison between Hodgkin-Huxley and kinetic formalisms Scientific Reports 9:17493 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Channel/Receptor;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s): I Sodium;
Gap Junctions:
Receptor(s):
Gene(s): Nav1.5 SCN5A;
Transmitter(s):
Simulation Environment: NEURON; Python;
Model Concept(s): Markov-type model;
Implementer(s): Carannante, Ilaria [ilariac at kth.se]; Balbi, Pietro [piero.balbi at fsm.it]; Andreozzi, Emilio [emilio.andreozzi at unina.it];
Search NeuronDB for information about:  I Sodium;
from neuron import h, gui
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.colors as colors
import matplotlib.cm as cmx

dtype = np.float64

# one-compartment cell (soma)
soma        = h.Section(name='soma')
soma.diam   = 50         # micron
soma.L      = 63.66198   # micron, so that area = 10000 micron2
soma.nseg   = 1          # adimensional
soma.cm     = 1          # uF/cm2
soma.Ra     = 70         # ohm-cm

soma.nseg   = 1
soma.insert('na15')      # insert mechanism
soma.ena    = 65
h.celsius   = 24         # temperature in celsius
v_init      = -120       # holding potential   
h.dt        = 0.01       # ms - value of the fundamental integration time step, dt, used by fadvance().

# clamping parameters
dur         = 500        # clamp duration, ms
step        = 3          # voltage clamp increment
st_cl       = -120       # clamp start, mV
end_cl      = 1          # clamp end, mV
v_cl        = -120       # actual voltage clamp, mV

#number of elements of the vector containing the values from st_cl to end_cl with the fixed step
L=len(np.arange(st_cl, end_cl, step))

# vectors for data handling
t_vec       = h.Vector() # vector for time
v_vec       = h.Vector() # vector for voltage
v_vec_t     = h.Vector() # vector for voltage as function of time
i_vec       = h.Vector() # vector for current 
ipeak_vec   = h.Vector() # vector for peak current
inorm_vec   = h.Vector() # vector for normalized current

# saving data (comment the following 4 lines if you don't want to save the data)
f1 = open('2_f_inact_v_vec.dat', 'w')
f2 = open('2_f_inact_inorm_vec.dat', 'w')
f1.write("voltage=[\n")
f2.write("normalized_current=[\n")


# a two-electrodes voltage clamp
f3cl = h.VClamp(soma(0.5))
f3cl.dur[0] = 40	     # ms
f3cl.amp[0] = -120	     # mV
f3cl.dur[1] = dur        # ms
f3cl.amp[1] = v_cl       # mV
f3cl.dur[2] = 20         # ms
f3cl.amp[2] = -10        # mV


# finding the "initial state variables values"
from state_variables import finding_state_variables
initial_values = [x for x in finding_state_variables(v_init,h.celsius)]

print('Initial values [C1, C2, O1, I1, I2]=  ', initial_values)


for seg in soma:
    seg.na15.iC1=initial_values[0]
    seg.na15.iC2=initial_values[1]
    seg.na15.iO1=initial_values[2]
    seg.na15.iI1=initial_values[3]
    seg.na15.iI2=initial_values[4]


#figure definition
fig = plt.figure(figsize=(20,15))
fig.suptitle('2. Fast inactivation availability', fontsize=15, fontweight='bold')

ax1 = plt.subplot2grid((2, 4), (0, 0), colspan=2)
ax1.set_xlim(0,560)
ax1.set_ylim(-121,10)
ax1.set_xlabel('Time $(ms)$')
ax1.set_ylabel('Voltage $(mV)$')
ax1.set_title('Time/Voltage relation')

ax2 = plt.subplot2grid((2,4), (0, 2))
ax2.set_xlim(538,548)
ax2.set_ylim(-1.5,0.1)
ax2.set_xlabel('Time $(ms)$')
ax2.set_ylabel('Current density $(mA/cm^2)$')
ax2.set_title('Time/Current density relation - zoom in')

ax3 = plt.subplot2grid((2,4), (0, 3))
ax3.set_xlim(538,548)
ax3.set_ylim(-0.015,0.001)
ax3.set_xlabel('Time $(ms)$')
ax3.set_ylabel('Current density $(mA/cm^2)$')
ax3.set_title('Time/Current density relation - zoom in')

ax4 = plt.subplot2grid((2,4), (1, 0), colspan=2)
ax4.set_xlim(0,560)
ax4.set_ylim(-1.5,0.25)
ax4.set_xlabel('Time $(ms)$')
ax4.set_ylabel('Current density $(mA/cm^2)$')
ax4.set_title('Time/Current density relation')

ax5 = plt.subplot2grid((2,4), (1, 2), colspan=2)
ax5.set_xlim(-125,3)
ax5.set_ylim(-0.05,1.05)        
ax5.set_xlabel('Voltage $(mV)$')
ax5.set_ylabel('Normalized current')
ax5.set_title('Voltage/Normalized current relation')



fig.subplots_adjust(wspace=0.5)
fig.subplots_adjust(hspace=0.5)

# to plot in rainbow colors
values=range(L)
rbw = cm = plt.get_cmap('rainbow') 
cNorm  = colors.Normalize(vmin=0, vmax=values[-1])
scalarMap = cmx.ScalarMappable(norm=cNorm, cmap=rbw)

# clamping definition
def clamp(v_cl):

    f3cl.amp[1] = v_cl
    h.finitialize(v_init)  # calling the INITIAL block of the mechanism inserted in the section.

    # parameters initialization
    peak_curr = 0
    dens = 0
    t_peak = 0
    
    while (h.t<h.tstop): # runs a single trace, calculates peak current
        dens = f3cl.i/soma(0.5).area()*100.0-soma(0.5).i_cap # clamping current in mA/cm2, for each dt
        t_vec.append(h.t)       # code for store the current
        v_vec_t.append(soma.v)  # trace to be plotted
        i_vec.append(dens)      # trace to be plotted
        
        if ((h.t>=540)and(h.t<=542)):     # evaluate the peak (I know it is there)
            if(abs(dens)>abs(peak_curr)):
                peak_curr = dens        
                t_peak = h.t
                
        h.fadvance()

    # updates the vectors at the end of the run        
    v_vec.append(v_cl)             
    ipeak_vec.append(peak_curr)


### start program

def start():
    h.tstop = 40 + dur + 20 
    v_vec.resize(0)
    ipeak_vec.resize(0)


    k=0     # counter    
    for v_cl in np.arange(st_cl, end_cl, step): # iterates across voltages

        print('Voltage Clamp:    ', v_cl,'mV')

        # resizing the vectors
        t_vec.resize(0)
        i_vec.resize(0)
        v_vec_t.resize(0) 
       

        clamp(v_cl)
            
        # code for showing traces
        colorVal1 = scalarMap.to_rgba(v_cl-st_cl-k*(step-1)) 
        k=k+1

        ln1,=ax1.plot(t_vec, v_vec_t,color=colorVal1)
        ln2,=ax2.plot(t_vec, i_vec,color=colorVal1)
        ln3,=ax3.plot(t_vec, i_vec,color=colorVal1)
        ln4,=ax4.plot(t_vec, i_vec,color=colorVal1)

    ipeak_min = ipeak_vec.min()           # normalization of peak current with respect to the min since the values are negative

    for i in range(0, len(ipeak_vec), 1):
         colorVal2 = scalarMap.to_rgba(i)
         inorm_vec.append(ipeak_vec.x[i]/ipeak_min)
         ln5,=ax5.plot(v_vec.x[i], inorm_vec.x[i], 'o', c=colorVal2)

         #printing and saving data (comment the following line if you don't want to print the data)
         print('Voltage:   ', v_vec.x[i],'mV', ',   Normalized current:   ', inorm_vec.x[i])
         # comment the following 2 lines if you don't want to save the data)
         f1.write("%s ,\n" % v_vec.x[i]) 
         f2.write("%s ,\n" % inorm_vec.x[i]) 

    #saving the figure (comment the following line if you don't want to save the figure)   
    plt.savefig('2. Fast inactivation availability', format='pdf', dpi=300, orientation='portrait')    

    # comment the following 4 lines if you don't want to save the data
    f1.write("];")
    f2.write("];")
    f1.close()
    f2.close()

    plt.show()


start()





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