The Decisive Commanding Neural Network In the Parietal Cortex

1. The Decisive Commanding Neural Network In the Parietal Cortex By Hsiu-Ming Chang (張修明)

2. Shadlen & Newsom, 2001, J.Neurosci.

3. 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.

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

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

6. 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.

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

8. The reaction time is longer than the decay time of NMDA receptor activation The reaction with error decisions takes longer time than with the correct ones Roitman & Shadlen , 2002, J.Neurosci.

9. The decision process is simulated in a theoretical network The resting potential VL, firing threshold Vth, and reset potential Vresetwere set respectively to −70mV, −50mV and −55mV. Else Wong & Wang, 2006, J. Neurosci

10. 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. Wong & Wang, 2006, J. Neurosci

11. In units of μS, grec,AMPA= 0.0005, gext,AMPA= 0.0021, gNMDA= 0.000165, and grec,AMPA= 0.00004, gext,AMPA= 0.00162, gNMDA= 0.00013 to the interneurons. For inhibitory synapses to pyramidal cells and interneurons, gGABA, are 0.0013μS and 0.001μS respectively. Wong & Wang, 2006, J. Neurosci

12. S is the synaptic gating variable ~ open probability 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

13. Approximations are made to simplify calculations For a total of 2000 neurons with 400 Inhibitory ones Wong & Wang, 2006, J. Neurosci

14. F(yi)= Yi /(tNMDA(1-yi)), and yiis the steady state of Si. where i 1, 2, 3 denotes the two selective, and one nonselective excitatory populations, 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. Wong & Wang, 2006, J. Neurosci

15. the firing rate r of a leaky integrate-and-fire (LIF) neuron receiving noisy input r = Isyn is the total synaptic input to a single cell, and cE,Iis the gain factor. gE,Iis a noise factor that determines the shape of the “curvature” of . If gE,Iis 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

16. 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(y(r))=gr Wong & Wang, 2006, J. Neurosci

17. Further reduction is achieved if approximations, r is time independent and NMDA receptors have a decay time constant much longer than others, are made. 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

18. 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

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

20. the standard set of parameters for the two-variable model is as follows: 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

21. Input signal are applied to 15% of the total excitatory neurons where JA,ext = 0.2243 * 10-3 nA * Hz-1 is the average synaptic coupling with AMPARs and c’ is the degree of coherence where s2noise 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. Wong & Wang, 2006, J. Neurosci

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

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

24. The coherence dependent responses are also demonstrated Wong & Wang, 2006, J. Neurosci

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

26. Working memory Wong & Wang, 2006, J. Neurosci

27. Wong & Wang, 2006, J. Neurosci

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

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

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

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

32. Wong & Wang, 2006, J. Neurosci

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

34. 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

35. 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 ?)