Journal of Computational Neuroscience

, Volume 17, Issue 1, pp 13–29 | Cite as

The Influence of Spike Rate and Stimulus Duration on Noradrenergic Neurons

  • Eric Brown
  • Jeff Moehlis
  • Philip Holmes
  • Ed Clayton
  • Janusz Rajkowski
  • Gary Aston-Jones


We model spiking neurons in locus coeruleus (LC), a brain nucleus involved in modulating cognitive performance, and compare with recent experimental data. Extracellular recordings from LC of monkeys performing target detection and selective attention tasks show varying responses dependent on stimuli and performance accuracy. From membrane voltage and ion channel equations, we derive a phase oscillator model for LC neurons. Average spiking probabilities of a pool of cells over many trials are then computed via a probability density formulation. These show that: (1) Post-stimulus response is elevated in populations with lower spike rates; (2) Responses decay exponentially due to noise and variable pre-stimulus spike rates; and (3) Shorter stimuli preferentially cause depressed post-activation spiking. These results allow us to propose mechanisms for the different LC responses observed across behavioral and task conditions, and to make explicit the role of baseline firing rates and the duration of task-related inputs in determining LC response.

locus coeruleus response dynamics phase density phase oscillators cognitive performance neuromodulator phasic and tonic states conductance-based neuron models 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alvarez V, Chow C, van Bockstaele E, Williams J (2002) Frequency dependent synchrony in locus coeruleus: Role of electronic coupling. Proc. Nat. Acad. Sci. USA 99: 4032-4036.Google Scholar
  2. Arnold L (1974) Stochastic Differential Equations. John Wiley, New York.Google Scholar
  3. Aston-Jones G, Akaoka H, Charlety P, Chouvet G (1991) Serotonin selectively attenuates glutamate-evoked activation of locus coeruleus neurons in vivo. J. Neurosci. 11: 760-769.Google Scholar
  4. Aston-Jones G, Chen S, Zhu Y, Oshinsky ML (2001a) A neural circuit for circadian regulation of arousal. Nature Neurosci. 4: 732-738.Google Scholar
  5. Aston-Jones G, Rajkowski J, Cohen J (2000) Locus coeruleus and regulation of behavioral flexibility and attention. Prog. Brain Res. 126: 165-182.Google Scholar
  6. Aston-Jones G, Rajkowski J, Kubiak P, Alexinsky T (1994) Locus coeruleus neurons in the monkey are selectively activated by attended stimuli in a vigilance task. J. Neurosci. 14: 4467-4480.Google Scholar
  7. Aston-Jones G, Zhu Y, Card P (2001b) Gabaergic afferents to locus coeruleus (LC) from the peri-lc region: Possible LC interneurons. Soc. Neurosci. Abst. 27: 373.8.Google Scholar
  8. Brown E, Moehlis J, Holmes P (2004) On the phase reduction and response dynamics of neural oscillator populations. Neural Comp. 16(4): 673-715.Google Scholar
  9. Chow C, Kopell N (2000) Dynamics of spiking neurons with electrotonic coupling. Neural Comp. 12: 1643-1678.Google Scholar
  10. Clayton E, Rajkowski J, Cohen JD, Aston-Jones G (2004) Decisionrelated activation of monkey locus coeruleus neurons in a forced choice task. In preparation.Google Scholar
  11. Connor J, Walter D, McKown R (1977) Neural repetitive firing: Modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons. Biophys. J. 18: 81-102.Google Scholar
  12. Eriksen BA, Eriksen CW (1974) Effects of noise letters upon the identification of target letters in a non-search task. Perception and Psychophysics 16: 143-149.Google Scholar
  13. Ermentrout B (1996) Type I membranes, phase resetting curves, and synchrony. Neural Comp. 8: 979-1001.Google Scholar
  14. Evans L (1998) Partial Differential Equations. American Mathematical Society, Providence.Google Scholar
  15. Fetz E, Gustaffson B (1983) Relation between shapes of postsynaptic potentials and changes in firing probability of cat motoneurones. J. Physiol. 341: 387-410.Google Scholar
  16. Foote SL, Bloom FE, Aston-Jones G(1983) Nucleus locus coeruleus: New evidence of anatomical and physiological specificity. Physiol. Rev. 63(3): 844-914.Google Scholar
  17. Freidlin M, Wentzell A (1998) Random Perturbations of Dynamical Systems. Springer, New York.Google Scholar
  18. Gardiner C (1985) Handbook of Stochastic Methods. Springer, New York.Google Scholar
  19. Gilzenrat MG, Holmes BD, Rajkowski J, Aston-Jones G, Cohen JD (2002) Simplified dynamics in a model of noradrenergic modulation of cognitive performance. Neural Networks 15: 647-663.Google Scholar
  20. Grant SJ, Aston-Jones G, Redmond DE (1988) Responses of primate locus coeruleus neurons to simple and complex sensory stimuli. Brain Res. Bull. 21(3): 401-410.Google Scholar
  21. Guckenheimer J, Holmes PJ (1983) Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag, New York.Google Scholar
  22. Herrmann A, Gerstner W (2001) Noise and the PSTH response to current transients: I. General theory and application to the integrate and-fire neuron. J. Comp. Neurosci. 11: 135-151.Google Scholar
  23. Jodo E, Aston-Jones, G (1997) Activation of locus coeruleus by prefrontal cortex is mediated by excitatory amino acid inputs. Brain Res. 768: 327-332.Google Scholar
  24. Jodo E, Chiang C, Aston-Jones G (1998) Potent excitatory influence of prefrontal cortex activity on noradrenergic locus coeruleus neurons. Neuroscience 83: 63-80.Google Scholar
  25. Moore RY, Bloom FE (1979) Central catecholamine neuron systems: Anatomy and physiology of the norepinephrine and epinephrine systems. Ann. Rev. Neurosci. 2: 113-168.Google Scholar
  26. Nykamp D, Tranchina D (2000) A population density approach that facilitates large-scale modeling of neural networks: Analysis and application to orientation tuning. J. Comp. Neurosci. 8: 19-50.Google Scholar
  27. Omurtag A, Knight BW, Sirovich L (2000) On the simulation of large populations of neurons. J. Comp. Neurosci. 8: 51-63.Google Scholar
  28. Rajkowski J, Lu W, Zhu Y, Cohen J, Aston-Jones G (2000) Prominent projections from the anterior cingulate cortex to the locus coeruleus (LC) in rhesus monkey. Soc. Neurosci. Abst. 26: 838.15.Google Scholar
  29. Ritt J (2003) A Probabilistic Analysis of Forced Oscillators, with Application to Neuronal Response Reliability. PhD thesis, Boston University.Google Scholar
  30. Rose R, Hindmarsh J (1989) The assembly of ionic currents in a thalamic neuron I. The three-dimensional model. Proc. R. Soc. Lond. B 237: 267-288.Google Scholar
  31. Rush M, Rinzel J (1995) The potassium A-current, low firing rates and rebound excitation in Hodgkin-Huxley models. Bull. Math. Biol. 57: 899-929.Google Scholar
  32. Servan-Schreiber D, Printz H, Cohen JD (1990) A network model of catecholamine effects: Gain, signal-to-noise ratio, and behavior. Science 249: 892-895.Google Scholar
  33. Stein R (1965) Atheoretical analysis of neuronal variability. Biophys. J. 5: 173-194.Google Scholar
  34. Tass P (1999) Phase Resetting in Medicine and Biology. Springer, New York.Google Scholar
  35. Usher M, Cohen JD, Servan-Schreiber D, Rajkowsky J, Aston-Jones G (1999) The role of locus coeruleus in the regulation of cognitive performance. Science 283: 549-554.Google Scholar
  36. Usher M, Davelaar EJ (2002) Neuromodulation of decision and response selection. Neural Networks 15: 635-645.Google Scholar
  37. Valentino RJ, Foote SL (1987) Corticotropin-releasing factor disrupts sensory responses of brain noradrenergic neurons. Neuroendocrinology 45(1): 28-36.Google Scholar
  38. Whitham GB (1974) Linear and Nonlinear Waves. Wiley, New York.Google Scholar
  39. Williams J, North R, Shefner A, Nishi S, Egan T (1984) Membrane properties of rat locus coeruleus neurons. Neuroscience 13: 137-156.Google Scholar
  40. Williams JT, Bobker DH, Harris GC (1991) Synaptic potentials in locus coeruleus neurons in brain slices. Prog. Brain Res. 88: 167-172.Google Scholar
  41. Winfree AT (2001) The Geometry of Biological Time. 2nd edition. Springer, New York.Google Scholar
  42. Zhu WQ (1988) Stochastic averaging methods in random vibration. Appl. Mech. Rev. 41: 189-199.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Eric Brown
    • 1
  • Jeff Moehlis
    • 1
  • Philip Holmes
    • 1
  • Ed Clayton
    • 2
  • Janusz Rajkowski
    • 2
  • Gary Aston-Jones
    • 2
  1. 1.Program in Applied and Computational MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of Psychiatry and Laboratory of Neuromodulation and BehaviorUniversity of PennsylvaniaPhiladelphiaUSA

Personalised recommendations