The document discusses computational cognitive neuroscience and neuron dynamics. It describes neuron variables that determine the neuron's membrane potential and how inputs are integrated over time. The equilibrium membrane potential equation is shown, which depends on excitatory, inhibitory and leak conductances and driving potentials. If the membrane potential exceeds the threshold, the neuron will fire a spike and reset. Spikes can be approximated as rates using functions like X-over-X-plus-1 to model actual spiking behavior from input rates.

1. Computational Cognitive Neuroscience
Neuron
Kristína Rebrová
Kristína Rebrová Computational Cognitive NeuroscienceNeuron

2. Neuron as detector
Kristína Rebrová Computational Cognitive NeuroscienceNeuron

3. Dynamics of Integration: tug-of-war
Kristína Rebrová Computational Cognitive NeuroscienceNeuron

4. Neurons variables
gi : inhibitory conductance
Ei : inhibitory driving potential
Θ: action potential threshold
Vm: membrane potential
Ee: excitatory driving potential
ge: excitatory conductance
Ee: leak driving potential
ge: leak conductance
¯g: maximum conductance
Kristína Rebrová Computational Cognitive NeuroscienceNeuron

5. 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
Kristína Rebrová Computational Cognitive NeuroscienceNeuron

6. Equilibrium Membrane Potential
ge(t) =
1
n
i
xi wi
xi = input to the neuron
wi = weight of the neuron
a weight defines how much unit listens to given input
weights determine what the neuron detects = everything is
encoded in weights
Vm =
¯gege(t)
¯gege(t) + ¯gi gi (t) + ¯gl
Ee +
¯gi gi (t)
¯gege(t) + ¯gi gi (t) + ¯gl
Ei +
¯gl
¯gege(t) + ¯gi gi (t) + ¯gl
El
Kristína Rebrová Computational Cognitive NeuroscienceNeuron

7. 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
Kristína Rebrová Computational Cognitive NeuroscienceNeuron

8. Rate Code Approximation to Spiking
spikes to rates
instantaneous and steady – smaller, faster models
definitely lose several important things
to find an equation* that makes good approximation of actual
spiking rate for same sets of inputs
X-over-X-plus-1 (XX1) function
Kristína Rebrová Computational Cognitive NeuroscienceNeuron

9. The end
Thank you for your attention
kristina.rebrova@gmail.com
Kristína Rebrová Computational Cognitive NeuroscienceNeuron