The Decisive Commanding Neural Network In the Parietal Cortex

The Decisive Commanding Neural Network In the

Parietal Cortex

By

Hsiu-Ming Chang (張修明 )

Shadlen & Newsom, 2001, J.Neurosci.

Monkeys are trained to performthe motion discrimination task byeye saccades.For each neuron, a responsefield (RF) is determined


Electrodes are inserted into the lateral intraparietal cortex


Single neurons favoring a specific direction of the eye movementare found


Activity elevated on a decision tomove the eye to a specific direction

Activity attenuated on a decision tomove the eye away from a specific

direction


The neural activityfollows the strengthof the information

The neural activityreaches the maximumjust before the saccadic eye movement


The reaction with error decisions takes longer time than with the correct ones

The reaction time is longer than the decay time of NMDA receptor activation

Roitman & Shadlen , 2002, J.Neurosci.

The resting potential VL, firing threshold Vth, and reset potential Vreset were set respectively to −70mV, −50mV and −55mV.

Else

Wong & Wang, 2006, J. Neurosci

The decision process is simulated in a theoretical network

where g was the peak synaptic conductance, S the synaptic gating variable (fraction of open channels), VE = 0 the reversal potential of excitatory connectivity, and VI = −70mV the reversal potential for inhibitory synapses. w was a dimensionless potentiation factor due to structured excitatory synapses


The relatively strong synapses, a potentiation factor w = w+ = 1.7 is chosen1. A “depression” factor w = w− = 1−f(w+−1)/(1−f) < 1 for the synapses between two different selective populations, and for synapses between the nonselective population to selective ones. For all other connections, w = 1.


In units of μS, grec,AMPA = 0.0005, gext,AMPA = 0.0021, gNMDA = 0.000165, and grec,AM

PA = 0.00004, gext,AMPA = 0.00162, gNMDA = 0.00013 to the interneurons. For inhibito

ry synapses to pyramidal cells and interneurons, gGABA, are 0.0013μSand 0.001μS respectively.

The time constants were τAMPA = 2ms,τNMDA,decay = 100ms, τNMDA,rise = 2ms, τGABA = 5ms, andα = 0.5ms−1. The rise time for AMPA and GABA (< 1ms) were assumed to be instantaneous. Spikes from external of the network were assumed to go through AMPA receptors.


S is the synaptic gating variable ~ open probability


Approximations are made to simplify calculations

For a total of 2000 neurons with 400 Inhibitory ones

where i 1, 2, 3 denotes the two selective, and one nonselective excitatorypopulations, I is the inhibitory population. ri(t) is the instantaneous mean firing rate of the presynaptic excitatory population i, rI(t) is the mean firing rate of the inhibitory population.S and its associated are the average synaptic gating variable and its corresponding decay time constant, respectively.

F)= i /(NMDA(1-i)), and i is the steady state of Si.


the firing rate r of a leaky integrate-and-fire (LIF) neuronreceiving noisy input

r =

Isyn is the total synaptic input to a single cell, and cE,I is the gain factor. gE,I is a noise factor that determines the shape of the “curvature” of . If gE,I is large, would act like a linearthreshold function with IE,I/c as the threshold current.

The values are, for pyramidal cells, IE = 125 Hz, gE = 0.16 s, and cE = 310(VnC)-1; and for interneurons, II =177Hz, gI = 0.087 s, and cI = 615(VnC)-1


Assuming the interspike intervals to be nearly Poisson, the average gating variable can be fitted by a simple function

where 0.641 and r is the presynaptic firing rate. Then

Fr))= r


Under a wide range of conditions, the firing rate of the nonselective population changes only by a modest amount, assumed at a constant mean rate of 2 Hz.

Applying linear approximation of the input– output transfer function of the inhibitory cell.

where g2 = 2 and r0 = 11.5 Hz.


Further reduction is achieved if approximations, r is time independent andNMDA receptors have a decay time constant much longer than others, aremade.

Assuming that all other variables achieve their steady states much faster than the NMDA gating variable SNMDA, which dominates the time evolution of the system.

where i 1, 2 labels the two excitatory populations


After approximations, only two equations are left for solving

the standard set of parameters for the two-variable model is asfollows: JN,11 = 0.1561 nA = JN,22, JN,12 = 0.0264 nA = JN,21, JA,11

= 9.9026*10-4 nC = JA,22, JA,12 = 6.5177*10-5 nA Hz-1 = JA,21 and I0 = 0.2346 nA.


where noise is the variance of the noise, and is a Gaussian w

hite noise with zero mean and unit variance. Unless specified, noise is fixed at 0.007 nA.

where JA,ext = 0.2243 * 10-3 nA * Hz-1 is the average synaptic coupling with AMPARs andc’ is the degree of coherence


Input signal are applied to 15% of the total excitatory neurons


A decision is made when the threshold the reached

The theoretical model reproduces the experimental results

Error takes Longer timeTo act

StimulationCoherenceIncreasesThe accuracy



The coherence dependent responses are also demonstrated

Stronger stimulation results in shorter reaction time


Working memory


Stimulationinduces disturbance on the stateof the networkand createstransient unstable


Coherentstimulationseparatetwo nullclinesand reducethe numberof attractors


Stronger recurrent current reduces the reaction time and accuracy


Increase the AMPAComponent in the Recurrent currentResults in shorterReaction time butLess accuracy


DecisionWithoutWorkingMemory

(instinct ?)


A logical elaboration of the decision making processIn a neural system is demonstrated

The functional significant neural activity is represented in a form of synchronization.

Decision is made when the neural network reaches a steady state in activity

The purpose for the vast number of neurons in the ensembleredundancynoise reduction (higher precision)

The biological evidence of theoretical derivation of w is stillambiguous.

The abrupt rise and drop of neural activity near the sccadicmovement have not been simulated (interneuron factor ?)

The Decisive Commanding Neural Network In the Parietal Cortex

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