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 perform the motion discrimination task by eye saccades. For each neuron, a response field (RF) is determined Shadlen & Newsom, 2001, J.Neurosci.

Electrodes are inserted into the lateral intraparietal cortex Shadlen & Newsom, 2001, J.Neurosci.

Single neurons favoring a specific direction of the eye movement are found Shadlen & Newsom, 2001, J.Neurosci.

Activity elevated on a decision to move the eye to a specific direction Activity attenuated on a decision to move the eye away from a specific direction Shadlen & Newsom, 2001, J.Neurosci.

The neural activity follows the strength of the information The neural activity reaches the maximum just before the saccadic eye movement Shadlen & Newsom, 2001, J.Neurosci.

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 V L, firing threshold V th, and reset potential V reset 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), V E = 0 the reversal potential of excitatory connectivity, and V I = −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.

Wong & Wang, 2006, J. Neurosci In units of μS, g rec,AMPA = , g ext,AMPA = , g NMDA = , and g rec,AMPA = , g ext,AMPA = , g NMDA = to the interneurons. For inhibitory synapses to pyramidal cells and interneurons, g GABA, are μS and 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. Wong & Wang, 2006, J. Neurosci S is the synaptic gating variable ~ open probability

Wong & Wang, 2006, J. Neurosci 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 excitatory populations, I is the inhibitory population. r i (t) is the instantaneous mean firing rate of the presynaptic excitatory population i, r I (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 S i. Wong & Wang, 2006, J. Neurosci

the firing rate r of a leaky integrate-and-fire (LIF) neuron receiving noisy input r = I syn is the total synaptic input to a single cell, and c E,I is the gain factor. g E,I is a noise factor that determines the shape of the “curvature” of. If g E,I is large, would act like a linearthreshold function with I E,I /c as the threshold current. The values are, for pyramidal cells, I E = 125 Hz, g E = 0.16 s, and c E = 310(VnC) -1 ; and for interneurons, I I =177Hz, g I = s, and c I = 615(VnC) -1 Wong & Wang, 2006, J. Neurosci

Assuming the interspike intervals to be nearly Poisson, the average gating variable can be fitted by a simple function where and r is the presynaptic firing rate. Then F  r))=  r Wong & Wang, 2006, J. Neurosci

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 g 2 = 2 and r 0 = 11.5 Hz. Wong & Wang, 2006, J. Neurosci Further reduction is achieved if approximations, r is time independent and NMDA receptors have a decay time constant much longer than others, are made.

Assuming that all other variables achieve their steady states much faster than the NMDA gating variable S NMDA, which dominates the time evolution of the system. where i 1, 2 labels the two excitatory populations

Wong & Wang, 2006, J. Neurosci After approximations, only two equations are left for solving

the standard set of parameters for the two-variable model is as follows: J N,11 = nA = J N,22, J N,12 = nA = J N,21, J A,11 = *10 -4 nC = J A,22, J A,12 = *10 -5 nA Hz-1 = J A,21 and I 0 = nA. Wong & Wang, 2006, J. Neurosci

where   noise is the variance of the noise, and is a Gaussian white noise with zero mean and unit variance. Unless specified, noise is fixed at nA. where J A,ext = * nA * Hz -1 is the average synaptic coupling with AMPARs and c’ is the degree of coherence Wong & Wang, 2006, J. Neurosci Input signal are applied to 15% of the total excitatory neurons

Wong & Wang, 2006, J. Neurosci A decision is made when the threshold the reached

The theoretical model reproduces the experimental results Error takes Longer time To act Stimulation Coherence Increases The accuracy Wong & Wang, 2006, J. Neurosci

The coherence dependent responses are also demonstrated

Stronger stimulation results in shorter reaction time Wong & Wang, 2006, J. Neurosci

Working memory Wong & Wang, 2006, J. Neurosci

Stimulation induces disturbance on the state of the network and creates transient unstable Wong & Wang, 2006, J. Neurosci

Coherent stimulation separate two nullclines and reduce the number of attractors Wong & Wang, 2006, J. Neurosci

Stronger recurrent current reduces the reaction time and accuracy Wong & Wang, 2006, J. Neurosci

Increase the AMPA Component in the Recurrent current Results in shorter Reaction time but Less accuracy Wong & Wang, 2006, J. Neurosci

Decision Without Working Memory (instinct ?) Wong & Wang, 2006, J. Neurosci

A logical elaboration of the decision making process In 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 ensemble redundancy noise reduction (higher precision) The biological evidence of theoretical derivation of w is still ambiguous. The abrupt rise and drop of neural activity near the sccadic movement have not been simulated (interneuron factor ?)