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 = 0.0005, g ext,AMPA = 0.0021, g NMDA = 0.000165, and g rec,AMPA = 0.00004, g ext,AMPA = 0.00162, g NMDA = 0.00013 to the interneurons. For inhibitory synapses to pyramidal cells and interneurons, g GABA, are 0.0013μS 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 = 0.087 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 0.641 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 = 0.1561 nA = J N,22, J N,12 = 0.0264 nA = J N,21, J A,11 = 9.9026*10 -4 nC = J A,22, J A,12 = 6.5177*10 -5 nA Hz-1 = J A,21 and I 0 = 0.2346 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 0.007 nA. where J A,ext = 0.2243 * 10 -3 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
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 ?)