20100420

notes from attempting to generate upstates :

Upstates/downstates are synchronous in that the population transisions in unison. upstates are asyncronous in that we don't want simple global oscillations. Inhibition must be able to prevent runaway excitation ( to some extent ) to make upstates semi-stable. In the firing rate model, insufficient inhibition causes the mean population current to resemble spikes. Slow, modulatory envelopes of gamma oscillations might be caused by a mistmatch of the refractory / recovery process timescale with the excitation time scale. Can a network have bistable character even if the individual neurons do not ? Results from firing rate models seem to indicate yes, but I have not been able to reproduce this in spiking models.

for some parameters :
even though upstates have variable ength, the time between them is constant and characterized by time-to-recovery from inhibition. the transision to upstate sometimes invovles emergence of small oscillations which gradually amplify. In well connected populations of e-i cells, the population dynamics often resemble single neuron dynamics, with spiking, refractoriness, and bursting characteristics. Random connections with random weights seem sufficient to generate chaotic up-down state switching in firing rates with either a single population or e and i cells. With separate e-i populations upstates seem to have more variability in the field potential amplitude ( but this may just be for the select amplitude ranges investigated ). See if you can generalize this to spiking models.

states observed in a locally connected firing rate model :

all-on
all-off
global oscillations
spiral waves
noisy
sptailly smoothed noise
travelling plane waves
static reaction diffusion patterns
orbits between N=2,3,4 reaction diffusion like patterns

e i noise adaptation driving
on + - -
off -
noise +
smooth + + +
travel + + +
spiral + +
global + + +
pattern + + -
shift + + +


since these seem to cover the parameter space, speculate as to which modes are most similar to asyncronous, chaotic, up-down state dynamics ? :

........propagating spontaneous aperiodic dynamic
on .........- ...........+ ..........- ........-
off ........- ...........- ..........- ........-
pattern ....- ...........+ ..........- ........-
noise ......- ...........- ..........+ ........+
spiral .....+ ...........+ ..........+ ........+
travel .....+ ...........+ ..........- ........+
bistable ...- ...........+ ..........- ........+
smooth .....+ ...........- ..........+ ........+
noise ......- ...........- ..........+ ........+
oscillation - ...........+ ..........- ........+


three likely candidates :
The spiral waves seem promising, travelling waves seem promising if they can be disrupted to become aperiodic and chaotic smoothed noise is promising if it can be created without explicite noise driving. Adding some long range connections to local model does trippy things. Can we represent ei netwok as graph flow ? The notion of e-local connectivity verses i-local connectivity ? observations : purely random without adaptation seems to have two modes :
static mode with weak inhibition
oscillator mode with strong inhibition and excitation
add in adaptation into this mix and you get chaotic up/dpwn like behavior.
the dynamics of a well connected e-i system very often resembles the dynamics of a simple 2D dynamical system.

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