The Reversal Potential of Inhibitory Synapses Strongly Impacts the Dynamics of Neural Networks - Foundations on Natural and Artificial Computation - page 101

their synaptic connections were described by biophysical inspired models. In par-
ticular, we investigated the conditions affecting and driving the synchronization
phenomena in this complex network.

2 Methods

2.1 Model Description

The artificial network is composed by N PY pyramidal neurons and N FS FS
interneurons. The pyramidal neuron models are coupled by excitatory synapses
and receive inhibitory inputs from the network of FS interneuron. For either the
pyramidal neuron or the interneuron, a single compartment biophysical model is
employed to describe its spiking activity. In particular, we adopt the pyramidal
and interneuron biophysical models proposed in [8]. The mathematical model of
the j th pyramidal neuron reads:

−

C dV j
dt

g Na m j h j ( V j − g K n j ( V j −

= I P,j −

V Na ) V K ) g M w j (( V j − V M ))

− −

g L ( V j − V L )+ I PP,j + I IP,j + η P ξ P,j ( t ) (1)

−

dm j
dt

= α m,j (1 m j ) β m,j m j (2)

− −

dh j
dt

= α h,j (1 h j ) β h,j h j , (3)

− −

dn j
dt

= α n,j (1 n j ) β n,j n j , (4)

− −

dw j
dt

w j,∞ − w j

= , (5)

τ j,w

where C =1 μF/cm 2 , I P,j = I P ( j =1 , 2 , ..N ) is the external stimulation
t. The maximal specific conductances and the reversal potentials are respec-
tively: g Na = 100 mS/cm 2 , g K =80 mS/cm 2 , g M =1 mS/cm 2 , g L =0.15
mS/cm 2 and V Na =50 mV , V K = -100 mV , V M = -100 mV , V L =-72
mV . The rate variables describing the currents are defined by: α m,j ( V j )=
0 . 32( V j +54) / [1 exp (( V j +54) / 4)], β m,j ( V j )=0 . 28( V j +27) / [ exp (( V j +27) / 5) 1],

− −

α h,j ( V j )=0 . 128 exp ( ( V j + 50) / 18), β h,j ( V j )=4 / [1 + exp ( ( V j + 27) / 5),

− −

α n,j ( V j )=0 . 032( V j + 52) / [1 exp ( ( V j + 52) / 5)], β n,j ( V j )=0 . 5 exp ( ( V j +

− − −

57) / 40), w j,∞ =1 / [1 + exp ( ( V j + 35) / 10)], τ j,w = 400 / [3 . 3 exp (( V j + 35) / 20) +

−

exp ( ( V j + 35) / 20)]. In this model the onset of periodic firing occurs through an

Hopf bifurcation for I P = 3 . 25 μA/cm 2 with a well defined frequency ( ν = 5 Hz ).
The current I PP,j arises from the excitatory coupling of the j

−

th pyramidal

−

neuron with the other cells, while I IP,j describes the inhibitory current due to