Joint work with Philip Eckhoff and Phil Holmes

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 • 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 • Neuronal model: Leaky integrate-and fire • Recurrent excitatory synapses: AMPA, NMDA • Inhibition: GABAA • External inputs (background, stimulus): AMPA • Task difficulty depends on: (I1 - I2) /(I1 + I2) Decision time Choice 1 made I1 I2 X.-J. Wang (2002)

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 RT RT … … … … n trial RSI n+1 trial Time

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

9. Standard Too high Too low Neural dynamics under tonic modulationof E and I cells Unmotivated Increasing LC-NE Standard/Optimal Firing rate Time Impulsive

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

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.

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