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

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"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. ..."
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]
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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:
Gene(s): Nav1.5 SCN5A;
Simulation Environment: NEURON; Python;
Model Concept(s): Markov-type model;
Implementer(s): Carannante, Ilaria [ilariac at]; Balbi, Pietro [piero.balbi at]; Andreozzi, Emilio [emilio.andreozzi at];
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 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     = 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         = 20        # clamp duration, ms
step        = 2         # voltage clamp increment, the user can 
st_cl       = -90       # clamp start, mV
end_cl      = 11        # clamp end, mV
v_cl        = -90       # 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
gpeak_vec   = h.Vector()  # vector for peak conductance
gnorm_vec   = h.Vector()  # vector for normalized conductance

# saving data (comment the following 4 lines if you don't want to save the data)
f1          = open('1_V_G_relation_v_vec.dat', 'w')
f2          = open('1_V_G_relation_norm_conductance.dat', 'w')
f2.write("normalized conductance=[\n")

# a two-electrodes voltage clamp
f3cl = h.VClamp(soma(0.5))
f3cl.dur[0] = 5	      # ms
f3cl.amp[0] = -120	  # mV
f3cl.dur[1] = dur     # ms
f3cl.amp[1] = v_cl    # mV
f3cl.dur[2] = 5       # ms
f3cl.amp[2] = -120    # 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:

# figure definition
fig, ax     = plt.subplots(1, 3,figsize=(18,6))  
fig.suptitle('1. Voltage-Normalized conductance relation', fontsize=15, fontweight='bold')

ax[0].set_xlabel('Time $(ms)$')
ax[0].set_ylabel('Voltage $(mV)$')
ax[0].set_title('Time/Voltage relation')

ax[1].set_xlabel('Time $(ms)$')
ax[1].set_ylabel('Current density $(mA/cm^2)$')
ax[1].set_title('Time/Current density relation')

ax[2].set_xlabel('Voltage $(mV)$')
ax[2].set_ylabel('Normalized conductance')
ax[2].set_title('Voltage/Normalized conductance')

# 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):
    curr_tr = 0  # initialization of peak current
    cond_tr = 0  # initialization of peak conductance

    h.finitialize(v_init) # calling the INITIAL block of the mechanism inserted in the section.

    # initialization of variables used to commute the peak current and conductance    
    pre_i  = 0     
    dens   = 0

    f3cl.amp[1] = v_cl    # mV

    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 storing the current
        v_vec_t.append(soma.v)  # trace to be plotted
        i_vec.append(dens)      # trace to be plotted

        if ((h.t>5)and(h.t<=10)):       # evaluate the peak 
                cond_tr = soma.g_na15   # updates the peak conductance
                curr_tr = dens          # updates the peak current

        pre_i = dens

    # updates the vectors at the end of the run        

### start program

def start():

    h.tstop = 5 + dur + 5       # time stop

    # resizing the vectors

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

            # resizing the vectors

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

            colorVal1 = scalarMap.to_rgba(v_cl-st_cl-k*(step-1)) # rainbow printing setting

            ln0,=ax[0].plot(t_vec, v_vec_t,color=colorVal1)
            ln1,=ax[1].plot(t_vec, i_vec,color=colorVal1)
    gpeak_max = gpeak_vec.max()           # maximum value of the conductance used to normalize the conductance vector
    for i in range(0, len(gpeak_vec), 1):

         colorVal2 = scalarMap.to_rgba(i) # rainbow printing setting

         gnorm_vec.append(gpeak_vec.x[i]/gpeak_max) # normalization of peak conductance
         ln2,=ax[2].plot(v_vec.x[i], gnorm_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 conductance:   ', gnorm_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" % gnorm_vec.x[i])            

    #saving the figure (comment the following line if you don't want to save the figure)   
    plt.savefig('1. Voltage-Normalized conductance relation', format='pdf', dpi=300, orientation='portrait')    

    # comment the following 4 lines if you don't want to save the data