Integrate and fire networks

Networks of integrate-and-fire neurons with axonal delays and refractory period

Model parameters:

• tau [ms]: membrane time constant (RC)
• tref [ms]: absolute refractory period
• delay [ms]: axonal delay
• tspike: reserved variable for storing past spike times when monitoring spikes

Monitoring spikes in DynaSim:

• how to: include the statement monitor VAR.spikes(threshold) or monitor VAR.spikes(threshold,buffer_size) with the equations defining the dynamics of state variable VAR.
• threshold: spike detection threshold for upward crossing of state variable VAR (e.g., V). value: numeric or parameter name.
• buffer_size: number of spikes to store in spike buffer (default: 2). value: numeric.
• spike times from the buffer can be incorporated into equations using the reserved variable names tspike in intrinsic population dynamics or tspike_pre and tspike_post in the equations of connection mechanisms. tspike has dimensions [buffer_size x num_cells].

1 E-cell (excitatory, e.g., pyramidal cell) driving 1 I-cell (inhibitory, e.g., interneuron):

LIF={
    'dV/dt=(E-V+R*I+noise*randn-@isyn)/tau; V(0)=-65'
    'if( any(t<tspike + tref, 1) )(V=reset)'
    'tau=10; tref=10; E=-70; thresh=-55; reset=-75; R=9; I=1.55; noise=100'
    'monitor V.spikes(thresh,2)'
     };

iampa={
  'gSYN=.5; ESYN=0; tauD=2; tauR=0.4; delay=15'
  'f(x) = (exp(-x/tauD)-exp(-x/tauR)).*(x>0)'
  'Isyn(V) = gSYN.*sum(f(t-tspike_pre-delay)).*(V-ESYN)'
  '@isyn += Isyn(V_post)'
};

s=[];
s.populations(1).name='E';
s.populations(1).equations=LIF;
s.populations(2).name='I';
s.populations(2).equations=LIF;
s.populations(2).parameters={'I',0,'noise',0};
s.connections(1).direction='E->I';
s.connections(1).mechanism_list='iampa';
s.mechanisms(1).name='iampa';
s.mechanisms(1).equations=iampa;

data=dsSimulate(s,'time_limits',[0 200], 'solver','rk1', 'dt',.01);
dsPlot(data);

For more examples, including STDP, see: https://github.com/DynaSim/DynaSim/blob/master/demos/examples/dsLIFnetwork.m