Gamma oscillations in hippocampal interneuron networks (Bartos et al 2002)

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To examine whether an interneuron network with fast inhibitory synapses can act as a gamma frequency oscillator, we developed an interneuron network model based on experimentally determined properties. In comparison to previous interneuron network models, our model was able to generate oscillatory activity with higher coherence over a broad range of frequencies (20-110 Hz). In this model, high coherence and flexibility in frequency control emerge from the combination of synaptic properties, network structure, and electrical coupling.
1 . Bartos M, Vida I, Frotscher M, Meyer A, Monyer H, Geiger JR, Jonas P (2002) Fast synaptic inhibition promotes synchronized gamma oscillations in hippocampal interneuron networks. Proc Natl Acad Sci U S A 99:13222-7 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Hippocampus;
Cell Type(s): Abstract Wang-Buzsaki neuron;
Channel(s): I Na,t; I K;
Gap Junctions: Gap junctions;
Receptor(s): GabaA;
Simulation Environment: NEURON;
Model Concept(s): Activity Patterns; Oscillations; Synchronization; Synaptic Integration;
Implementer(s): Jonas, Peter [Peter.Jonas at];
Search NeuronDB for information about:  GabaA; I Na,t; I K;
gap.mod *
TITLE nethhwbm.mod   interneuron sodium, potassium, and leak channels

 This file is based on the original hh.mod file (see original comment
 below). It was modified to match the model that was used in the
 simulations of Wang and Buzsaki (1996, J. Neurosci. 16).

 This is the original Hodgkin-Huxley treatment for the set of sodium, 
  potassium, and leakage channels found in the squid giant axon membrane.
  ("A quantitative description of membrane current and its application 
  conduction and excitation in nerve" J.Physiol. (Lond.) 117:500-544 (1952).)
 Membrane voltage is in absolute mV and has been reversed in polarity
  from the original HH convention and shifted to reflect a resting potential
  of -65 mV.
 Remember to set celsius=6.3 (or whatever) in your HOC file.
 See squid.hoc for an example of a simulation using this model.
 SW Jaslove  6 March, 1992


  - m is substituted by it"s steady state value: m_inf - see 'BREAKPOINT'
  {as a result mtau is not needed, 'minf' is removed from
  GLOBAL declaration and 'm' is included in the RANGE var list
  otherwise it will be handled as a GLOBAL var and will not be
  evaluated separately for the 'sections'; for 'h' an 'n' this 
  is not a problem}

  - for h and n alpha and beta values are multiplied by 5 
  (see factor "Phi" in the W&B model)

  - USEION removed as we don't want to deal with ions and set eNa and
  eK directly. Rev potentials 'egna' and 'egk' are in the PARAMETERS
  - temp: set to 6.3 Celsius, alpha and beta values are set/manipulated
  directly to simulate characteristic firing pattern

  I. Vida, Nov. 2000

        (mA) = (milliamp)
        (mV) = (millivolt)

? interface

        SUFFIX hh_wbm
        NONSPECIFIC_CURRENT ina,ik,il

        RANGE gnabar,gna,egna,m, gkbar,gk,egk, gl,el
	GLOBAL hinf, ninf, htau, ntau

        gnabar = .035 (mho/cm2)	<0,1e9>
	egna	= 55 (mV)	
        gkbar = .009 (mho/cm2)	<0,1e9>
	egk	= -90 (mV)	
        gl = .0001 (mho/cm2)	<0,1e9>
        el = -65 (mV)
        m h n
        v (mV)
	celsius (degC)

	gna (mho/cm2)
        ina (mA/cm2)
	gk (mho/cm2)
        ik (mA/cm2)
        il (mA/cm2)
        minf hinf ninf
	htau (ms) ntau (ms)
LOCAL mexp, hexp, nexp        
? currents
        SOLVE states METHOD cnexp
	m = minf
        gna = gnabar*m*m*m*h
	ina = gna*(v - egna)
        gk = gkbar*n*n*n*n
	ik = gk*(v - egk)      
        il = gl*(v - el)
	m = minf
	h = hinf
	n = ninf

? states
DERIVATIVE states {  
        h' = (hinf-h)/htau
        n' = (ninf-n)/ntau

? rates
PROCEDURE rates(v(mV)) {  :Computes rate and other constants at current v.
                          :Call once from HOC to initialize inf at resting v.
        LOCAL  alpha, beta, sum
        TABLE minf, hinf, htau, ninf, ntau DEPEND celsius FROM -100 TO 100 WITH 200

        q10 = 3^((celsius - 6.3)/10)

               :"m" sodium activation system
        alpha = .1 * vtrap(-(v+35),10)
        beta =  4 * exp(-(v+60)/18)
        sum = alpha + beta
        minf = alpha/sum

                :"h" sodium inactivation system
        alpha =.35 * exp(-(v+58)/20)
        beta = 5 / (exp(-(v+28)/10) + 1)
        sum = alpha + beta
	htau = 1/(q10*sum)
        hinf = alpha/sum

                :"n" potassium activation system
        alpha =.05*vtrap(-(v+34),10) 
        beta = .625*exp(-(v+44)/80)
	sum = alpha + beta
        ntau = 1/(q10*sum)
        ninf = alpha/sum
FUNCTION vtrap(x,y) {  :Traps for 0 in denominator of rate eqns.
        if (fabs(x/y) < 1e-6) {
                vtrap = y*(1 - x/y/2)
                vtrap = x/(exp(x/y) - 1)