BioModels Database logo

BioModels Database

spacer

BIOMD0000000302 - Wang1996_Synaptic_Inhibition_Two_Neuron

 

 |   |   |  Send feedback
Reference Publication
Publication ID: 8815919
Wang XJ, Buzsáki G.
Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model.
J. Neurosci. 1996 Oct; 16(20): 6402-6413
Physics Department, Brandeis University, Waltham, Massachusetts 02254, USA.  [more]
Model
Original Model: BIOMD0000000302.xml.origin
Submitter: Lukas Endler
Submission ID: MODEL1101240000
Submission Date: 24 Jan 2011 00:39:46 UTC
Last Modification Date: 17 Mar 2011 01:47:34 UTC
Creation Date: 24 Jan 2011 00:42:22 UTC
Encoders:  Lukas Endler
set #1
bqbiol:occursIn Brenda Tissue Ontology BTO:0000601
Brenda Tissue Ontology BTO:0000920
set #2
bqbiol:occursIn Taxonomy Rattus norvegicus
set #3
bqbiol:hasVersion Gene Ontology synaptic transmission, GABAergic
Notes

This is a model of one presynaptic and one postsynaptic cell, as described in the article:
Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model.
Wang XJ, Buzsáki G. J Neurosci. 1996 Oct 15;16(20):6402-13. PMID: 8815919 ;

Abstract:
Fast neuronal oscillations (gamma, 20-80 Hz) have been observed in the neocortex and hippocampus during behavioral arousal. Using computer simulations, we investigated the hypothesis that such rhythmic activity can emerge in a random network of interconnected GABAergic fast-spiking interneurons. Specific conditions for the population synchronization, on properties of single cells and the circuit, were identified. These include the following: (1) that the amplitude of spike afterhyperpolarization be above the GABAA synaptic reversal potential; (2) that the ratio between the synaptic decay time constant and the oscillation period be sufficiently large; (3) that the effects of heterogeneities be modest because of a steep frequency-current relationship of fast-spiking neurons. Furthermore, using a population coherence measure, based on coincident firings of neural pairs, it is demonstrated that large-scale network synchronization requires a critical (minimal) average number of synaptic contacts per cell, which is not sensitive to the network size. By changing the GABAA synaptic maximal conductance, synaptic decay time constant, or the mean external excitatory drive to the network, the neuronal firing frequencies were gradually and monotonically varied. By contrast, the network synchronization was found to be high only within a frequency band coinciding with the gamma (20-80 Hz) range. We conclude that the GABAA synaptic transmission provides a suitable mechanism for synchronized gamma oscillations in a sparsely connected network of fast-spiking interneurons. In turn, the interneuronal network can presumably maintain subthreshold oscillations in principal cell populations and serve to synchronize discharges of spatially distributed neurons.

The presynaptic and postsynaptic cell have identical parameters and the variables in each cell are identified by using _pre or _post as a postfix to their names. The presynaptic cell influences the postsynaptic one via the synapse (variables and parameters: I_syn, E_syn, g_syn, F, theta_syn, alpha, beta). The applied current to the presynaptic cell, I_app_pre, is set to 2 microA/cm 2 for 10 ms as in figure 1C of the article. The dependence of the postsynaptic cell on directly applied current can be investigated in isolation by setting I_app_pre to 0 and altering I_app_post.

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

Model
Publication ID: 8815919 Submission Date: 24 Jan 2011 00:39:46 UTC Last Modification Date: 17 Mar 2011 01:47:34 UTC Creation Date: 24 Jan 2011 00:42:22 UTC
Mathematical expressions
Rules
Assignment Rule (variable: tau_0) Assignment Rule (variable: I_Na_post) Assignment Rule (variable: m_inf_post) Rate Rule (variable: h_post)
Rate Rule (variable: V_post) Assignment Rule (variable: alpha_m_post) Assignment Rule (variable: beta_m_post) Assignment Rule (variable: alpha_h_post)
Assignment Rule (variable: beta_h_post) Assignment Rule (variable: I_K_post) Rate Rule (variable: n_post) Assignment Rule (variable: alpha_n_post)
Assignment Rule (variable: beta_n_post) Assignment Rule (variable: I_L_post) Assignment Rule (variable: I_syn) Rate Rule (variable: s)
Assignment Rule (variable: F) Rate Rule (variable: V_pre) Assignment Rule (variable: I_app_pre) Assignment Rule (variable: I_Na_pre)
Assignment Rule (variable: m_inf_pre) Rate Rule (variable: h_pre) Rate Rule (variable: n_pre) Assignment Rule (variable: alpha_n_pre)
Assignment Rule (variable: beta_n_pre) Assignment Rule (variable: alpha_h_pre) Assignment Rule (variable: beta_h_pre) Assignment Rule (variable: alpha_m_pre)
Assignment Rule (variable: beta_m_pre) Assignment Rule (variable: I_K_pre) Assignment Rule (variable: I_L_pre)  
Physical entities
Compartments Species
pre_synaptic_cell      
post_synaptic_cell      
Global parameters
Cm gL gK gNa
E_K E_L E_Na phi
tau_0 I_app_post I_Na_post m_inf_post
h_post V_post alpha_m_post beta_m_post
alpha_h_post beta_h_post I_K_post n_post
alpha_n_post beta_n_post I_L_post I_syn
g_syn s E_syn alpha
F beta V_pre theta_syn
I_app_pre I_Na_pre m_inf_pre h_pre
n_pre alpha_n_pre beta_n_pre alpha_h_pre
beta_h_pre alpha_m_pre beta_m_pre I_K_pre
I_L_pre      
Reactions (0)
Rules (31)
 
 Assignment Rule (name: tau_0) tau_0 = Cm/gL
 
 Assignment Rule (name: I_Na_post) I_Na_post = gNa*m_inf_post^3*h_post*(V_post-E_Na)
 
 Assignment Rule (name: m_inf_post) m_inf_post = alpha_m_post/(alpha_m_post+beta_m_post)
 
 Rate Rule (name: h_post) d [ h_post] / d t= phi*(alpha_h_post*(1-h_post)-beta_h_post*h_post)
 
 Rate Rule (name: V_post) d [ V_post] / d t= (I_app_post-(I_Na_post+I_K_post+I_L_post+I_syn))/Cm
 
 Assignment Rule (name: alpha_m_post) alpha_m_post = (-0.1)*(V_post+35)/(exp((-0.1)*(V_post+35))-1)
 
 Assignment Rule (name: beta_m_post) beta_m_post = 4*exp((-(V_post+60))/18)
 
 Assignment Rule (name: alpha_h_post) alpha_h_post = 0.07*exp((-(V_post+58))/20)
 
 Assignment Rule (name: beta_h_post) beta_h_post = 1/(exp((-0.1)*(V_post+28))+1)
 
 Assignment Rule (name: I_K_post) I_K_post = gK*n_post^4*(V_post-E_K)
 
 Rate Rule (name: n_post) d [ n_post] / d t= phi*(alpha_n_post*(1-n_post)-beta_n_post*n_post)
 
 Assignment Rule (name: alpha_n_post) alpha_n_post = (-0.01)*(V_post+34)/(exp((-0.1)*(V_post+34))-1)
 
 Assignment Rule (name: beta_n_post) beta_n_post = 0.125*exp((-(V_post+44))/80)
 
 Assignment Rule (name: I_L_post) I_L_post = gL*(V_post-E_L)
 
 Assignment Rule (name: I_syn) I_syn = g_syn*s*(V_post-E_syn)
 
 Rate Rule (name: s) d [ s] / d t= alpha*F*(1-s)-beta*s
 
 Assignment Rule (name: F) F = 1/(1+exp((-(V_pre-theta_syn))/2))
 
 Rate Rule (name: V_pre) d [ V_pre] / d t= (I_app_pre-(I_Na_pre+I_K_pre+I_L_pre))/Cm
 
 Assignment Rule (name: I_app_pre) I_app_pre = piecewise(2, (time >= 10) && (time <= 20), 0)
 
 Assignment Rule (name: I_Na_pre) I_Na_pre = gNa*m_inf_pre^3*h_pre*(V_pre-E_Na)
 
 Assignment Rule (name: m_inf_pre) m_inf_pre = alpha_m_pre/(alpha_m_pre+beta_m_pre)
 
 Rate Rule (name: h_pre) d [ h_pre] / d t= phi*(alpha_h_pre*(1-h_pre)-beta_h_pre*h_pre)
 
 Rate Rule (name: n_pre) d [ n_pre] / d t= phi*(alpha_n_pre*(1-n_pre)-beta_n_pre*n_pre)
 
 Assignment Rule (name: alpha_n_pre) alpha_n_pre = (-0.01)*(V_pre+34)/(exp((-0.1)*(V_pre+34))-1)
 
 Assignment Rule (name: beta_n_pre) beta_n_pre = 0.125*exp((-(V_pre+44))/80)
 
 Assignment Rule (name: alpha_h_pre) alpha_h_pre = 0.07*exp((-(V_pre+58))/20)
 
 Assignment Rule (name: beta_h_pre) beta_h_pre = 1/(exp((-0.1)*(V_pre+28))+1)
 
 Assignment Rule (name: alpha_m_pre) alpha_m_pre = (-0.1)*(V_pre+35)/(exp((-0.1)*(V_pre+35))-1)
 
 Assignment Rule (name: beta_m_pre) beta_m_pre = 4*exp((-(V_pre+60))/18)
 
 Assignment Rule (name: I_K_pre) I_K_pre = gK*n_pre^4*(V_pre-E_K)
 
 Assignment Rule (name: I_L_pre) I_L_pre = gL*(V_pre-E_L)
 
  Spatial dimensions: 3.0  Compartment size: 1.0
  Spatial dimensions: 3.0  Compartment size: 1.0
Global Parameters (45)
 
 Cm
Value: 1.0   (Units: uF_per_cm2)
Constant
 
 gL
Value: 0.1   (Units: mS_per_cm2)
Constant
 
 gK
Value: 9.0   (Units: mS_per_cm2)
Constant
 
 gNa
Value: 35.0   (Units: mS_per_cm2)
Constant
 
 E_K
Value: -90.0   (Units: mV)
Constant
 
 E_L
Value: -65.0   (Units: mV)
Constant
 
 E_Na
Value: 55.0   (Units: mV)
Constant
 
   phi
Value: 5.0   (Units: dimensionless)
Constant
 
   tau_0
Value: NaN   (Units: ms)
 
   I_app_post
Constant
 
   I_Na_post
Value: NaN   (Units: microA_per_cm2)
 
   m_inf_post
Value: NaN   (Units: dimensionless)
 
   h_post
Value: NaN   (Units: dimensionless)
 
 V_post
Value: -64.0   (Units: mV)
 
   alpha_m_post
Value: NaN   (Units: per_ms)
 
   beta_m_post
Value: NaN   (Units: per_ms)
 
   alpha_h_post
Value: NaN   (Units: per_ms)
 
   beta_h_post
Value: NaN   (Units: per_ms)
 
   I_K_post
Value: NaN   (Units: microA_per_cm2)
 
   n_post
Value: NaN   (Units: dimensionless)
 
   alpha_n_post
Value: NaN   (Units: per_ms)
 
   beta_n_post
Value: NaN   (Units: per_ms)
 
   I_L_post
Value: NaN   (Units: microA_per_cm2)
 
   I_syn
Value: NaN   (Units: microA_per_cm2)
 
 g_syn
Value: 0.1   (Units: mS_per_cm2)
Constant
 
   s
Value: NaN   (Units: dimensionless)
 
   E_syn
Value: -75.0   (Units: mV)
Constant
 
   alpha
Value: 12.0   (Units: per_ms)
Constant
 
   F
Value: NaN   (Units: dimensionless)
 
   beta
Value: 0.1   (Units: per_ms)
Constant
 
 V_pre
Value: -64.0   (Units: mV)
 
   theta_syn
Constant
 
   I_app_pre
Value: NaN   (Units: microA_per_cm2)
 
   I_Na_pre
Value: NaN   (Units: microA_per_cm2)
 
   m_inf_pre
Value: NaN   (Units: dimensionless)
 
   h_pre
Value: NaN   (Units: dimensionless)
 
   n_pre
Value: NaN   (Units: dimensionless)
 
   alpha_n_pre
Value: NaN   (Units: per_ms)
 
   beta_n_pre
Value: NaN   (Units: per_ms)
 
   alpha_h_pre
Value: NaN   (Units: per_ms)
 
   beta_h_pre
Value: NaN   (Units: per_ms)
 
   alpha_m_pre
Value: NaN   (Units: per_ms)
 
   beta_m_pre
Value: NaN   (Units: per_ms)
 
   I_K_pre
Value: NaN   (Units: microA_per_cm2)
 
   I_L_pre
Value: NaN   (Units: microA_per_cm2)
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000302

Curator's comment: (updated: 24 Jan 2011 00:42:00 GMT)

Reproduction of figure 1 C of the original publication using Copasi 4.6.

spacer
spacer