MEC PV-positive fast-spiking interneuron network generates theta-nested fast oscillations

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Accession:267338
We use a computational model of a network of Fast-Spiking Parvalbumin-positive Basket Cells to study its synchronizing properties. The intrinsic properties of neurons, properties of chemical synapses and of gap junctions are calibrated using electrophysiological recordings in mice Medial Entorhinal Cortex slices. The neurons synchronize, generating Fast Oscillations nested in an external theta drive. We show how gap junctions are necessary for the generation of the oscillations, how hyperpolarizing chemical synapses give rise to more robust fast oscillations, compared to shunting ones, and how short-term depression in the chemical synapses confine the fast oscillation on a narrow range of phases from the external theta drive.
Model Information (Click on a link to find other models with that property)
Model Type: Connectionist Network;
Brain Region(s)/Organism: Entorhinal cortex; Mouse;
Cell Type(s): Entorhinal cortex fast-spiking interneuron;
Channel(s): I Na,t; I K;
Gap Junctions: Gap junctions;
Receptor(s): GabaA;
Gene(s):
Transmitter(s): Gaba;
Simulation Environment: Brian 2;
Model Concept(s): Brain Rhythms; Excitability; Gamma oscillations; Theta oscillations; Short-term Synaptic Plasticity;
Implementer(s): Via, Guillem; Baravalle, Roman;
Search NeuronDB for information about:  GabaA; I Na,t; I K; Gaba; 
import numpy as np
from scipy.signal import cwt, morlet2
import matplotlib.pyplot as plt
from funcs import *


Nnets = 30;
Ncycs = 30;
fsin = 8
gsin=7.


dt = .1;

Ess = [-75.]#[-75.,-55.];

for glMin in [1.,15.,2.]:
	#color =["b","g","r","y","c"]

	Ntcyc = int(np.round(125./dt)); # Number of points per theta cycle
	phases = np.linspace(-np.pi,+np.pi,Ntcyc); # Values of phases within ones cycle. -PI and +PI for minima of externl input, 0 for the maxima.
	fs = np.arange(50.,450.1,3.);

	rateses = [ [ np.loadtxt("RatesFig7/gLMin%d_Esm%d_cm%d_%dHzgChR%d_Fact%d.dat" % (int(glMin),int(np.round(-Es)),kcm,int(fsin),int(gsin), int(1))) for kcm in range(Nnets) ] for Es in Ess ];
	cwtPowses = [ [ compPWT(rateses[kEs][kcm][-Ncycs*Ntcyc:],dt=dt*1.e-3,fs=fs) for kcm in range(Nnets) ] for kEs in range(len(Ess)) ];
	max_powers = [ [ np.max(cwtPowses[kEs][kcm]) for kcm in range(Nnets) ] for kEs in range(len(Ess)) ];
	maxPowses = np.array([ np.array([ np.array([ np.max( cwtPowses[kEs][kcm][:,kcyc*Ntcyc:kcyc*Ntcyc+Ntcyc] ) for kcyc in range(Ncycs) ]) for kcm in range(Nnets) ]) for kEs in range(len(Ess)) ]);
	kcycs_act_hyp = [ [ kcyc for kcyc in range(Ncycs) if np.max(cwtPowses[0][kcm][:,kcyc*Ntcyc:kcyc*Ntcyc+Ntcyc])>.3*max_powers[0][kcm] ] for kcm in range(Nnets) ];


	fpmaxes_hyp = [ [ np.min( fs[np.where( cwtPowses[0][kcm][:,kcyc*Ntcyc:(kcyc+1)*Ntcyc] > (1.-1.e-6)*np.max(cwtPowses[0][kcm][:,kcyc*Ntcyc:(kcyc+1)*Ntcyc])  )[0]] ) for kcyc in kcycs_act_hyp[kcm] ] for kcm in range(Nnets) ];
	#fpmaxes_shu = [ [ np.min( fs[np.where( cwtPowses[1][kcm][:,kcyc*Ntcyc:(kcyc+1)*Ntcyc] > (1.-1.e-6)*np.max(cwtPowses[1][kcm][:,kcyc*Ntcyc:(kcyc+1)*Ntcyc])  )[0]] ) for kcyc in range(Ncycs) ] for kcm in range(Nnets) ];

	meansfs_hyp = [ np.mean([ fpmaxes_hyp[kcm][kcyc] for kcyc in range(len(kcycs_act_hyp[kcm])) ]) for kcm in range(Nnets) ];
	stdsfs_hyp = [ np.std([ fpmaxes_hyp[kcm][kcyc] for kcyc in range(len(kcycs_act_hyp[kcm])) ]) for kcm in range(Nnets) ];

	#meansfs_shu = [ np.mean([ fpmaxes_shu[kcm][kcyc] for kcyc in range(Ncycs) ]) for kcm in range(Nnets) ];
	#stdsfs_shu = [ np.std([ fpmaxes_shu[kcm][kcyc] for kcyc in range(Ncycs) ]) for kcm in range(Nnets) ];

	width = 5.2 # in inches
	height = 7.# in inches
	#tmp = plt.figure(figsize=[width,height]);

	# Plot the maximum wavelet powers
	for kEs in range(len(Ess)):
		tmp1 = plt.subplot(2,1,kEs+1);
		tmp = plt.errorbar(range(Nnets), np.mean(maxPowses[kEs],axis=1), yerr=np. std(maxPowses[kEs],axis=1), marker="o", ls="");
		#tmp = plt.ylim(0.,4.e+6);
		tmp1.spines['top'].set_visible(False)
		tmp1.spines['right'].set_visible(False)
		tmp1.spines['bottom'].set_visible(True)
		tmp1.spines['left'].set_visible(True)
		tmp = plt.ylabel("$P_{max}$ (spike$^2$/s$^2$)")
		tmp1.set_xticks([10,20,30])
		tmp1.set_xticklabels([])
		tmp1.set_yticks([0.,1.e+6,2.e+6,3.e+6,4.e+6])
		tmp1.set_yticklabels(["0","","","","4"])

	# Plot the frequencies with maximum wavelet power

	# For hyperpolarizing synapses
	tmp1 = plt.subplot(2,1,2);
	tmp = plt.errorbar(range(len(meansfs_hyp)), meansfs_hyp, yerr=stdsfs_hyp, marker="o", ls="");
	tmp = plt.ylim(0.,450.);
	tmp1.spines['top'].set_visible(False)
	tmp1.spines['right'].set_visible(False)
	tmp1.spines['bottom'].set_visible(True)
	tmp1.spines['left'].set_visible(True)
	tmp = plt.ylabel("$F_{max}$ (Hz)")
	tmp = plt.xlabel("network index")
	tmp1.set_xticks([10,20,30])
	tmp1.set_xticklabels([])
	tmp1.set_yticks([0,200,400])
	# For shunting synapses
	#tmp1 = plt.subplot(2,2,4);
	#tmp = plt.errorbar(range(len(meansfs_shu)), meansfs_shu, yerr=stdsfs_shu, marker="o", color="g", ls="");
	#tmp = plt.ylim(0.,450.);
	#tmp1.spines['top'].set_visible(False)
	#tmp1.spines['right'].set_visible(False)
	#tmp1.spines['bottom'].set_visible(True)
	#tmp1.spines['left'].set_visible(True)
	#tmp = plt.ylabel("$F_{max}$ (Hz)")
	#tmp = plt.xlabel("network index")
	#tmp1.set_xticks([10,20,30])
	#tmp1.set_xticklabels([])
	#tmp1.set_yticks([0,200,400])
plt.legend(["gLmin=1.","gLmin=1.5","gLmin=2."])
plt.savefig("Figures/Supp5_%dHzgChR%dFactor%d.eps" % (int(fsin),int(gsin), int(1)) );plt.savefig("Figures/Supp5_%dHzgChR%dFactor%d.png" % (int(fsin),int(gsin),int(1)) );