Depression and Potentiation of Pyramidal Gamma Rhythms by

Depression and Potentiation of Pyramidal Gamma Rhythms by External Gamma Rhythms Effects of Noisy Drive on Rhythms in Networks of Excitatory and Inhibitory Neurons Börgers and Kopell (2005) Cortical Gamma Rhythms Modulate NMDAR-Mediated Spike Timing Dependent Plasticity in a Biophysical Model Lee, Sen, and Kopell (2009)

Pyramidal Inter-neuronal Gamma Rhythms (PING) • Observed during sensory processsing + memory tasks

Gamma 30 -80 Hz

Pyramidal Inter-neuronal Gamma Rhythms (PING) • • • Generated by networks of I cells and E cells drive and synchronize the I cells gate and synchronize the E cells

PING model • • • Assume all-to-all connectivity Assume no heterogeneity Use Theta model

Theta model of a spiking neuron • • Most currents negligible during PING So, use Theta model (simplification of HH)

Synapses • • Excitatory synapses: AMPAR Inhibitory synapses: GABAA

Connectivity

Intrinsic frequency of the I cells • f. I < f. E for PING

How can PING rhythms be destroyed? • • Phase walkthrough Supression

Phase walkthrough • I cells fire >1 between I cell spikes

Supression • I cells overinhibit the E cells, stopping PING

Phase walkthrough occurs when • • connectivity parameters are not within the phase walkthrough boundary highly stochastic spiking of E cells causes phase walkthrough

Phase walkthrough boundary • • frequency of I group needs to be < freq of E otherwise, I cells improperly gate E cells

Phase walkthrough boundary • • so, f_I = f_P defines the phase walkthrough boundary f_i and f_P are determined by connectivity values

Phase walkthrough occurs when • • • External current to E (I_E) cells is too small I->E connections (g_IE) are too strong Exernal drive to I cells (I_I) is too large

I_E needs to be larger for PING

g_IE needs to be smaller for PING

I_I needs to be lower for PING

Phase walkthrough is harder with I->I synapses

Phase walkthrough occurs when • • connectivity parameters are not within the phase walkthrough boundary highly stochastic spiking of E cells causes phase walkthrough

Stochastic spiking of E cells -> phase walkthrough

How can PING rhythms be destroyed? • • Phase walkthrough Supression

Suppresion

Suppresion occurs when. . . • • Parameters are not within the suppression boundary Highly stochastic spiking of I cells causes suppression

Suppresion boundary • Parameter space that leads to E-cells NOT being dominated by inhibition

Suppresion occurs when. . . • • External drive to E cells (I_E) is too small External drive to I cells (I_I) is too large I->E connection (g_IE) is too strong I->I connectiviy (g_II) is too weak

I_E must be larger for PING

g_IE must be smaller for PING

I_I should be smaller for PING

g_II should be larger for PING

Suppresion occurs when. . . • • Parameters are not within the suppression boundary Highly stochastic spiking of I cells causes suppression

Stochastic I-cell spiking causes supression

Bistable region • • where, depending on init. conditions, can get PING or suppression

Bistable region

Sparse connectivity and heterogeneity

Frequency range for which PING is robust • • Gamma frequencies, thus "PING" As we saw, too low-freq oscillations weren't robust and using the parameter choices we found to lead to stable oscillations, can't really get stable oscillations for frequencies > 90 Hz

I_I

I_E I_I

g_IE I_I

g_II I_I

g_EI I_I

g_EE I_I ? ? ?

Gamma rhythms found during learning + memory tasks

Gamma 30 -80 Hz

Gamma rhythms found during learning + memory tasks • suggests gamma rhythms important for memory

Basic Oscillator with external rhythm input

2 -cell PING oscillator

Input rhythm • • • Regular, discrete spikes varied frequency of input over trials input spikes activated AMPA + NMDA currents

STDP via glutamatergic model

External inputs had Potentiating and depressing effects on PING oscillators

Strict rhythm in external input required for effect

Assymetry in STDP rules also required

Multiple input rhythms • • • With multiple input rhythms, higher coherence -> more potentiation but slightly incoherent inputs -> more potentiation than perfectly coherent ones

Multiple input rhythms

Theta rhythms • • Theta rhythms didn't seem to have an effect But pauses in gamma rhythm at theta durations had potentiating effect

Mechansim for entraining oscillators • • • Authors think this mechanism may be used during tone-training in the auditory system Also, a similar mechanism though to be involved in olfaction (Dmitry Rinberg's lab) Suggests similar mechanisms may be important throughout the brain

Limitations? • • • Only used 2 -cell network No heterogeneity Bistable regions? Didn't test init condits. . .