1. Dayan Abbot Ch 5.1-4,9

2. Membranes
Different ion channels have different Nernst (reversal) potentials. Opening and closing of channels regulates this flow.
Na and Ca have positive reversal potentials. Opening these channels depolarizes the membrane.
K has negative reversal potential and depolarizes the membrane.
Membrane current thus approximately given by
I= g(V-E)
Where g and E channel specific. G is time dependent conductance.
Channels maintain cell resting potential, spike generation, and synaptic contacts
Resting potential is given by ratio of ion concentrations by Nernst equation for K.
E=RT/F ln [outside]/[inside]

3. Single comparment model linearizes current voltage relation around resting potential.
S is synapse
G_l is leak
V is voltage dependent conductance

4. Integrate-and-fire neuron driven by current input I_e.
For constant current I, the IF neuron spikes regularly with a rate inverse the ISI time:
T_ISI=tau ln(R I + E-V_r)/(RI + E – V_th)
C_m dV/dt = -1/R (V-E)+I
Tau dV/dt= E-V+R I
When V reaches a threshold V_th, V is reset to V_r.
Solid: pyramidal cell first ISI
Open: pyramidal cell adapted ISI
Line: IF model
Adaptation can be included (5.14).

5. Synapes and coupled IF Tau dV/dt = E_l – V - g P (V-E) + R I
P=P_max t/tau_s exp(1 - t/tau_s)
Is alpha function, has max at t=tau_s
V_r = -80 mV
E_l=-70 mV
V_th= -54 mV
Tau=20 ms
G=0.05
RI=25 mV
Tau_s=10 ms
P_max=1
A: Excitatory connection. E=0 mV. Out of phase response
B: Inhibitory connection. E=-80 mV. In phase response

6. IF neuron driven by 1000 excitatory and 200 inhibitory inputs
IF neuron driven by 1000 excitatory and 200 inhibitory inputs. Each input is an independent Poisson spike train driving a synaptic conductance.
Top. Membrane potential in absence of spike generation mechanism. Bottom, with spike generation mechanism.
Left: when total input drives the neuron above the firing threshold, IF fires at high rate and regular (CV=0.3)
Right: when total input drives the neuron below or around the threshold, IF fires irregularly. (CV=0.84).