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The Decisive Commanding Neural Network In the
Parietal Cortex
By
Hsiu-Ming Chang (張修明 )
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Shadlen & Newsom, 2001, J.Neurosci.
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Monkeys are trained to performthe motion discrimination task byeye saccades.For each neuron, a responsefield (RF) is determined
Shadlen & Newsom, 2001, J.Neurosci.
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Electrodes are inserted into the lateral intraparietal cortex
Shadlen & Newsom, 2001, J.Neurosci.
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Single neurons favoring a specific direction of the eye movementare found
Shadlen & Newsom, 2001, J.Neurosci.
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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
Shadlen & Newsom, 2001, J.Neurosci.
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The neural activityfollows the strengthof the information
The neural activityreaches the maximumjust before the saccadic eye movement
Shadlen & Newsom, 2001, J.Neurosci.
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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.
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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
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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
Wong & Wang, 2006, J. Neurosci
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.
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Wong & Wang, 2006, J. Neurosci
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.
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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.
Wong & Wang, 2006, J. Neurosci
S is the synaptic gating variable ~ open probability
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Wong & Wang, 2006, J. Neurosci
Approximations are made to simplify calculations
For a total of 2000 neurons with 400 Inhibitory ones
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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.
Wong & Wang, 2006, J. Neurosci
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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
Wong & Wang, 2006, J. Neurosci
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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
Wong & Wang, 2006, J. Neurosci
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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.
Wong & Wang, 2006, J. Neurosci
Further reduction is achieved if approximations, r is time independent andNMDA receptors have a decay time constant much longer than others, aremade.
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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
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Wong & Wang, 2006, J. Neurosci
After approximations, only two equations are left for solving
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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.
Wong & Wang, 2006, J. Neurosci
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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
Wong & Wang, 2006, J. Neurosci
Input signal are applied to 15% of the total excitatory neurons
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Wong & Wang, 2006, J. Neurosci
A decision is made when the threshold the reached
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The theoretical model reproduces the experimental results
Error takes Longer timeTo act
StimulationCoherenceIncreasesThe accuracy
Wong & Wang, 2006, J. Neurosci
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Wong & Wang, 2006, J. Neurosci
The coherence dependent responses are also demonstrated
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Stronger stimulation results in shorter reaction time
Wong & Wang, 2006, J. Neurosci
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Working memory
Wong & Wang, 2006, J. Neurosci
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Wong & Wang, 2006, J. Neurosci
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Stimulationinduces disturbance on the stateof the networkand createstransient unstable
Wong & Wang, 2006, J. Neurosci
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Coherentstimulationseparatetwo nullclinesand reducethe numberof attractors
Wong & Wang, 2006, J. Neurosci
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Stronger recurrent current reduces the reaction time and accuracy
Wong & Wang, 2006, J. Neurosci
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Increase the AMPAComponent in the Recurrent currentResults in shorterReaction time butLess accuracy
Wong & Wang, 2006, J. Neurosci
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Wong & Wang, 2006, J. Neurosci
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DecisionWithoutWorkingMemory
(instinct ?)
Wong & Wang, 2006, J. Neurosci
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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
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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 ?)