1. Optimality, robustness, and dynamics of decision making under norepinephrine modulation: A spiking neuronal network model Joint work with Philip Eckhoff and Phil Holmes Sloan-Swartz Meeting 2008

2. Experimental results: Cellular level Norepinephrine (NE) modulates EPSP, IPSP, cellular excitability Locus coeruleus (LC) supplies NE throughout the brain Locus coeruleus (LC) supplies NE throughout the brain LC neurons exhibit tonic or phasic firing rate mode [NE] release approx linear to tonic firing rate of LC | | | || | | | | || | | | || | Tonic mode | | || ||||||| | | | | | Phasic mode Berridge and Abercrombie (1999)

3. Aston-Jones et. al (1999) Aston-Jones and Cohen (2005) Experimental results: Behavioral level Inverted-U shape performance in behavioral tasks

4. Past modeling work (i) Connectionist modeling e.g. Usher et al (1999); Brown et al (2004); Brown et al (2005) (ii) Normative (Bayesian) approach e.g. Yu and Dayan (2005); Dayan and Yu (2006) (iii) Biophysical modeling work are more concerned with signal-to-noise ratio, e.g. Hasselmo (1997); Moxon et al (2007).

5. Goal To link cellular to behavioral level of LC-NE modulation, in the context of a decision-making reaction task task, and study the decision circuit’s performance (reward rate) using a spiking neuronal network model

6. A spiking neuronal network model for 2-alternative forced-choice decision- making tasks X.-J. Wang (2002) I1I1I1I1 I2I2I2I2 Neuronal model: Leaky integrate-and fire Recurrent excitatory synapses: AMPA, NMDA Inhibition: GABA A External inputs (background, stimulus): AMPA Task difficulty depends on: ( I 1 - I 2 ) /  ( I 1 + I 2 ) Neuronal model: Leaky integrate-and fire Recurrent excitatory synapses: AMPA, NMDA Inhibition: GABA A External inputs (background, stimulus): AMPA Task difficulty depends on: ( I 1 - I 2 ) /  ( I 1 + I 2 ) Decision time Choice 1 made

7. Performance in a reaction time task: Rate of receiving reward Reward rate = (Total # of correct trials) / (Total time) Total time = Sum of Reaction time + Response-to-stimulus interval Reaction time = Decision time + non-decision latency Reward rate = (Total # of correct trials) / (Total time) Total time = Sum of Reaction time + Response-to-stimulus interval Reaction time = Decision time + non-decision latency Time n trialn+1 trialRSI … RT

8. Tonic LC-NE modulation of both E and I cells provides robust decision performance Robust performance for modulation of NMDA or AMPA, as long as E and I cells are modulated together “1” denotes standard set of parameters of Wang (2002) Assume linear LC [NE] g syn

9. Neural dynamics under tonic modulation of E and I cells StandardToo lowToo high Increasing LC-NE Unmotivated Impulsive Standard/Optimal Firing rate Time

10. Differential tonic modulation between E and I cells There exists a maximum robustness when synapses of E cells are modulated about half that of I cells

11. Single-cell evoked response under tonic modulation Condition of maximum robustness also results in an inverted-U shape for single-cell evoked response. Since we used linear modulation, inverted-U shape is a pure network effect.

12. Phasic LC-NE modulation [NE] = F(LC) for phasic? dg / dt = G( [NE] ) ? Assume linear. = 100 ms  NE = 100 ms Delay = 200 ms

13. Phasic modulation can provide further improvement in performance… … provided glutamatergic modulation dominates over that of GABAergic synapses

14. Conclusion Inverted-U shape in decision performance Tonic co-modulation of E and I cells provides robust performance (more expt on I cells needed to confirm) Lesser affinity of E to I cells to tonic modulation results in: (i) maximum robust performance; (ii) inverted-U shape of single-cell evoked response (can be a pure network effect) [NE] = F(LC) for phasic LC mode? If F is linear, our work shows that phasic modulation can further improve over tonic when modulation of glutamatergic synapses dominate over GABAergic. Inverted-U shape in decision performance Tonic co-modulation of E and I cells provides robust performance (more expt on I cells needed to confirm) Lesser affinity of E to I cells to tonic modulation results in: (i) maximum robust performance; (ii) inverted-U shape of single-cell evoked response (can be a pure network effect) [NE] = F(LC) for phasic LC mode? If F is linear, our work shows that phasic modulation can further improve over tonic when modulation of glutamatergic synapses dominate over GABAergic.

15. Acknowledgements Barry Waterhouse, Drexel University College of Medicine Jonathan Cohen, Princeton University PHS grants MH58480 and MH62196 AFOSR grant FA9550-07-1-0537 Barry Waterhouse, Drexel University College of Medicine Jonathan Cohen, Princeton University PHS grants MH58480 and MH62196 AFOSR grant FA9550-07-1-0537