CCNExcercises:Neuron

Computational Cognitive NeuroscienceNeuron

Kristína Rebrová

Kristína Rebrová Computational Cognitive NeuroscienceNeuron

Neuron as detector


Dynamics of Integration: tug-of-war


Neurons variables

gi : inhibitory conductanceEi : inhibitory driving potentialΘ: action potential thresholdVm: membrane potentialEe : excitatory driving potentialge : excitatory conductanceEe : leak driving potentialge : leak conductanceg : maximum conductance


Neural integration

Vm(t) = Vm(t−1)+dtvm[ge(Ee−Vm)+gi (Ei−Vm)+gl (El−Vm)]

Ie = ge(Ee − Vm)

Ii = gi (Ei − Vm)

Il = gl (El − Vm)

Inet = Ie + Ii + Il

Vm(t) = Vm(t − 1) + dtvmInet


Equilibrium Membrane Potential

ge(t) =1n

∑i

xiwi

xi = input to the neuronwi = weight of the neurona weight defines how much unit listens to given inputweights determine what the neuron detects = everything isencoded in weights

Vm =gege(t)

gege(t) + gigi (t) + glEe +

gigi (t)

gege(t) + gigi (t) + glEi+

gl

gege(t) + gigi (t) + glEl


Generating Output

If Vm gets over threshold, neuron fires a spike.Spike resets membrane potential back to rest.Vm has to climb back up to threshold to spike again


Rate Code Approximation to Spiking

spikes to ratesinstantaneous and steady – smaller, faster modelsdefinitely lose several important thingsto find an equation* that makes good approximation of actualspiking rate for same sets of inputsX-over-X-plus-1 (XX1) function


The end

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Education

CCNExcercises:Neuron