INTRODUCTION OF INTEGRATE AND FIRE MODEL Single neuron modeling By Pooja Sharma Research Scholar LNMIIT-Jaipur

FORMAL NEURON MODEL  McCulloch-Pitts model(1943)  Perceptron model  Hopfield Neuron model

Biophysical Neuronal model  INTEGRATE-FIRE MODEL(1907)  HODGKIN-HUXELY MODEL(1952)  HINDMARSH-ROSE MODEL  FITZHUGH-NAGUMO MODEL(1962)

INTRODUCTION  Most biological neurons communicate by short electrical pulses call action potentials or spikes.  In contrast to standard neuron model used artificial neuron networks IFNdo not rely on a temporal average over the pulses.  In IFN the pulsed nature of the neuronal signal is taken into account and considered as potentially relevant for coding and information processing.

Contd…..  On IFN model pulses are treaded as formal events.  This in no real drawback since in biological spike train,all action potentials of the neuron have roughly the same form.  The time course of the action does not carry any information.

Contd…..  IFN model is phenomenological description on an intermediate level of detail.  Compare to other single-Cell models they offer several advantages.  Moreover dynamics in networks of IFN can be analyzed mathematically.

Single compartment model This is the basic model for all single compartment models. Rate of change of the membrane potential is proportional to rate at which charge builds up inside cell = current entering into neuron Current in = membrane current + external current from electrode

If the voltage hits the threshold at time t 0 : 1) a spike at time t 0 will be registered 2) The membrane potential will be reset to a reset value (V reset ) t0t0 t V V th V reset How spikes can be modeled ??????

Passive Integrated and Fire model Proposed by Lapicque in 1907 Where taum is the membrane time constant, When I e = 0,the membrane potential relaxes exponentially with time constant taum to V=E L Multipling by r m =1/g L we get V Cm Reset Threshold Output Ie A EL gL Stable node Saddle node Unstable node Separatrix E L is the resting potential potential of model cell.

Sub threshold potential Condition to occur next action potential If action potential is fired at t=0,we have V(0)=Vreset

Interspike interval firing rate This expression is valid if R m I e >V th -E L Otherwise r isi =0 For large values of I e,by using linear approximation It shows that for large Ie firing rate grows linearly with I e

This leads to the prediction that the firing rate is a linear function of current (fig A above). However, while the model fits data from the inter-spike intervals from the first 2 spikes well, it cannot match the spike rate adaptation which occurs in real neurons. For this to occur, we need to add an active conductance (fig C) A recording of firing of cortical neuron under cont. current injection,showing spike rate adaption. Spikes for an IF model with an added current. Taum=30ms,E L =V reset =- 65mV,R m =90Mᾫ

Integrate and fire neuron with Active conductance Cm Vm Rm Erev Input Reset Threshold Output To simulate non linear ion channels we add an active resistor. Their conductance depend on voltage. For instance, an action potential occurs when the membrane potential becomes depolarized enough that voltage controlled sodium channels open, initiating the fast positive feedback event of a spike.

Integrate and fire neuron with Active conductance Include an additional current in the model Spike-rate adaptation: The conductance g sra relaxes exponentially to 0 Whenever the neuron fires a spike g sra is increased

Conceptually similar to ANN neuron 16  Weak input Analog inputs specified by rate Strong input Output rate is a function of sum of inputs.