The Interplay Between Excitation and Inhibition in a Timing Network

Department of Mathematics Zirve University

Gaziantep, Turkey

Mustafa Zeki, Fuat Balcı

Tuesday, February 5, 2013

Objectives

• Designing a realistic neural model with response unit that can learn time through trials and conditioning.

• Obtaining response time distributions that express scalar variability property.

• Obtaining inverse-U shaped learning performance vs dopamine curve.

MODEL

• All neurons are modeled as single compartment modeled using Hodgkin-Huxley type dynamics.

• Model consists of three neuron layers each have the same number of neurons: Inhibitory layer (IL), excitatory counter neuron (CN) layer, and finally, response unit (RU) layer neurons.

Network Architecture

• Excitatory connections. CN to RU excitation increases depending on the neuron index.

Network Architecture

• Inhibitory connections from IN layer to RU layer is non-local.

Typical Behavior

CN neurons

• CN layer neuron wave. CN 10 to CN 13.

Spike time distribution

Constant CV

Overlap of normalized spike time distributions

Performance

• prf=(isn/ts)*(isn/maxsp)

• Isn=number of spikes in one std of target time.

• ts= total spikes.

• maxsp=maximum possible spike number (no inhibition) in one std of target time.

Inverse-U shaped dopamine dependence

• Learning performance dependence to dopamine.

MECHANISM UNDERLYING LEARNING TIME

1. Lurching wave behavior of CN layer neurons.

2. Strengthening of inhibitory synapses with dopamine and dependence to the trial number.

3. Constitution of the learning window.

4. Dependence of the width of the learning window to the target time.

Lurching wave behavior of CN layer neurons.

• The lurching wave behavior of the CN layer neurons appears as a result of the joint work of CN and IN layer neurons.

• The local CN to CN NMDA synaptic current and the local IN to CN fast inhibition plays the basic roles in the construction of the wave.

Strengthening of inhibitory synapses with dopamine and dependence to the

trial number• Persistence of the inhibition from IN to RU layer

neurons plays the major role in the learning process.

• Strengthening of an inhibitory synapse from an IN layer neuron to a RU layer neuron depends on the mutual activation of the neurons, dopamine and the trial number.

• Synaptic variable increases if both neuron become active and dopamine is present.

Constitution of the learning window

• Co-works of non-local graded inhibition around target neuron and graded maximal conductances from CN layer neurons onto RU neurons constructs the learning window.

• The total inhibition from the strengthened inhibitory synapses around target IN is least around target RU neuron and increases with respect to the distance to the target RU neuron.

Constitution of the learning window

• At the start of the trial, RU layer neurons do not respond to this excitation since inhibition is high away from target RU neuron.

• But, as wave approaches to the target CN neuron, inhibition decays and RU unit neurons response to CN layer excitation.

• When wave passes the target RU neuron, inhibition begin to increase again and at some distance from RU target neuron, and RU neurons become silent again.

Constitution of the learning window

• The frequence of RU neurons in the learning window is maximum near target RU neuron and decays as approached to the peripheral of the learning window.

• This is because, the inhibition is least around the RU target neuron.

Dependence of the width of the learning window to the target time

• Width of this learning window increases linearly with target time.

• This, in what follows, cause coefficient of variation (CV) of spike time distribution of RU neurons become constant for changing target times.

• The variation of the difference between excitation and inhibition onto the RU neurons in changing target times is the basic element that controls the width of the learning window.