Table 5 Proxies available in ncpi for generating extracellular signals

From: A Python toolbox for neural circuit parameter inference

Symbol

Value/definition

Description

firing rate

\({{\rm{\upsilon }}}_{{\rm{X}}}({\rm{t}})\)

Population spike rate

AMPA

\(\sum _{{\rm{u}}}{{\rm{I}}}_{{\rm{AMPA}}}^{\left\langle {\rm{u}}\right\rangle }({\rm{t}})\) for u [1, NE]

Sum of AMPA currents

GABA

\(\sum _{{\rm{u}}}{-{\rm{I}}}_{{\rm{GABA}}}^{\left\langle {\rm{u}}\right\rangle }({\rm{t}})\) for u [1, NE]

Sum of GABA currents

Vm

\(\sum _{{\rm{u}}}{{\rm{V}}}_{{\rm{m}}}^{\left\langle {\rm{u}}\right\rangle }({\rm{t}})\) for u [1, NE]

Sum of membrane potentials

∑ I

\(\sum _{{\rm{u}}}{{\rm{I}}}_{{\rm{AMPA}}}^{\left\langle {\rm{u}}\right\rangle }({\rm{t}})+{{\rm{I}}}_{{\rm{GABA}}}^{\left\langle {\rm{u}}\right\rangle }({\rm{t}})\) for u [1, NE]

Sum of synaptic currents

∑ |I|

\(\sum _{{\rm{u}}}\left|{{\rm{I}}}_{{\rm{AMPA}}}^{\left\langle {\rm{u}}\right\rangle }({\rm{t}})\right|+\left|{{\rm{I}}}_{{\rm{GABA}}}^{\left\langle {\rm{u}}\right\rangle }({\rm{t}})\right|\) for u [1, NE]

Sum of their absolute values

LRWS

\(\sum _{{\rm{u}}}{{\rm{I}}}_{{\rm{AMPA}}}^{\left\langle {\rm{u}}\right\rangle }\left({\rm{t}}-6{\rm{ms}}\right)-1.65\,{{\rm{I}}}_{{\rm{GABA}}}^{\left\langle {\rm{u}}\right\rangle }({\rm{t}})\) for u [1, NE]

LFP reference weighted sum25

ERWS1

\(\sum _{{\rm{u}}}{{\rm{I}}}_{{\rm{AMPA}}}^{\left\langle {\rm{u}}\right\rangle }\left({\rm{t}}+0.9{\rm{ms}}\right)-0.3\,{{\rm{I}}}_{{\rm{GABA}}}^{\left\langle {\rm{u}}\right\rangle }({\rm{t}}-2.3{\rm{ms}})\) for u [1, NE]

EEG reference weighted sum 1 (non-causal)24

ERWS2

\(\sum _{{\rm{u}}}{{\rm{I}}}_{{\rm{AMPA}}}^{\left\langle {\rm{u}}\right\rangle }\left({\rm{t}}+0.6{{\rm{\upsilon }}}_{{\rm{ext}}}^{-0.1}{\rm{ms}}+0.4{\rm{ms}}\right)-\left(1.4{\,{\rm{\upsilon }}}_{{\rm{ext}}}^{-1.7}+0.2\right)\,{{\rm{I}}}_{{\rm{GABA}}}^{\left\langle {\rm{u}}\right\rangle }({\rm{t}}+1.9{{\rm{\upsilon }}}_{{\rm{ext}}}^{-0.6}{\rm{ms}}-3{\rm{ms}})\) for u [1, NE]

EEG reference weighted sum 2 (non-causal)24