Journal of Computational Neuroscience

, Volume 36, Issue 3, pp 321–337

On parsing the neural code in the prefrontal cortex of primates using principal dynamic modes

  • V. Z. Marmarelis
  • D. C. Shin
  • D. Song
  • R. E. Hampson
  • S. A. Deadwyler
  • T. W. Berger


Nonlinear modeling of multi-input multi-output (MIMO) neuronal systems using Principal Dynamic Modes (PDMs) provides a novel method for analyzing the functional connectivity between neuronal groups. This paper presents the PDM-based modeling methodology and initial results from actual multi-unit recordings in the prefrontal cortex of non-human primates. We used the PDMs to analyze the dynamic transformations of spike train activity from Layer 2 (input) to Layer 5 (output) of the prefrontal cortex in primates performing a Delayed-Match-to-Sample task. The PDM-based models reduce the complexity of representing large-scale neural MIMO systems that involve large numbers of neurons, and also offer the prospect of improved biological/physiological interpretation of the obtained models. PDM analysis of neuronal connectivity in this system revealed “input–output channels of communication” corresponding to specific bands of neural rhythms that quantify the relative importance of these frequency-specific PDMs across a variety of different tasks. We found that behavioral performance during the Delayed-Match-to-Sample task (correct vs. incorrect outcome) was associated with differential activation of frequency-specific PDMs in the prefrontal cortex.


Multi-input/multi-output (MIMO) neuronal systems Prefrontal cortex Dynamic nonlinear modeling Principal dynamic modes Modeling of neural systems Neural coding Volterra-Wiener modeling 


  1. Abbott, L. F. (1999). Lapique’s introduction of the integrate-and-fire model neuron. Brain Research Bulletin, 50, 303–304.PubMedCrossRefGoogle Scholar
  2. Aftanas, L. I., & Golocheikine, S. A. (2001). Human anterior and frontal midline theta and lower alpha reflect emotionally positive state and internalized attention: high-resolution EEG investigation of meditation. Neuroscience Letters, 310, 57–60.PubMedCrossRefGoogle Scholar
  3. Anderson, C. H., & Eliasmith, C. (2004). Neural engineering: Computation, representation, and dynamics in neurobiological systems (computational neuroscience). MIT Press.Google Scholar
  4. Anderson, C., & Horne, J. A. (2003). Prefrontal cortex: links between low frequency delta EEG in sleep and neuropsychological performance in healthy, older people. Psychophysiology, 40, 349–357.PubMedCrossRefGoogle Scholar
  5. Baker, S. N., Kilner, J. M., Pinches, E. M., & Lemon, R. N. (1999). The role of synchrony and oscillations in the motor output. Experimental Brain Research, 128, 109–117.PubMedCrossRefGoogle Scholar
  6. Benchenane, K., Tiesinga, P. H., & Battaglia, F. P. (2011). Oscillations in the prefrontal cortex: a gateway to memory and attention. Current Opinion in Neurobiology, 21, 1–11.CrossRefGoogle Scholar
  7. Berger, T. W., Eriksson, J. L., Ciarolla, D. A., & Sclabassi, R. J. (1988). Nonlinear systems analysis of the hippocampal perforant path-dentate system. II. Effects of random train stimulation. Journal of Neurophysiology, 60, 1077–1094.Google Scholar
  8. Berger, T. W., Song, D., Chan, R. H., & Marmarelis, V. Z. (2010). The neurobiological basis of cognition: identification by multi-input, multi-output nonlinear dynamic modeling. Proceedings of the IEEE, 98, 356–374.PubMedCentralPubMedCrossRefGoogle Scholar
  9. Berger, T. W., Hampson, R. E., Song, D., Goonawardena, A., Marmarelis, V. Z., & Deadwyler, S. A. (2011). A cortical neural prosthesis for restoring and enhancing memory. Journal of Neural Engineering, 8, 046017.PubMedCentralPubMedCrossRefGoogle Scholar
  10. Berger, T. W., Song, D., Chan, R. H. M., Marmarelis, V. Z., Hampson, R. E., Deadwyler, S. A., et al. (2012). A hippocampal cognitive prosthesis: multi-input, multi-output nonlinear modeling and VLSI implementation. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 20(2), 198–211.PubMedCentralPubMedCrossRefGoogle Scholar
  11. Brandenberger, G. (2003). The Ulradien rhythm of sleep: diverse relations with pituitary and adrenal hormones. Revue Neurologique, 159(11), S5–S10.Google Scholar
  12. Buzsaki, G. (2002). Theta oscillations in the hippocampus. Neuron, 33, 325–340.PubMedCrossRefGoogle Scholar
  13. Buzsaki, G. (2005). Theta rhythm of navigation: link between path integration and landmark navigation, episodic and semantic memory. Hippocampus, 15, 827–840.PubMedCrossRefGoogle Scholar
  14. Canolty, R. T., Ganguly, K., Kennerley, S. W., Cadieu, C. F., Koepsell, K., Wallis, J. D., et al. (2010). Oscillatory phase coupling coordinates anatomically dispersed functional cell assemblies. Proceedings of the National Academy of Sciences of the United States of America, 107, 17356–17361.PubMedCentralPubMedCrossRefGoogle Scholar
  15. Churchland, P. S., & Sejnowski, T. J. (1999). The computational brain. MIT Press.Google Scholar
  16. Courtemanche, R., Fujii, N., & Graybiel, A. M. (2003). Synchronous, focally modulated beta-band oscillations characterize Local Field Potential activity in the striatum of awake behaving monkeys. Journal of Neuroscience, 23, 11741–11752.PubMedGoogle Scholar
  17. Deadwyler, S. A., & Hampson, R. E. (2004). Differential but complementary mnemonic functions of the hippocampus and subiculum. Neuron, 42, 465–476.PubMedCrossRefGoogle Scholar
  18. Dobson, A. J. (2002). An introduction to generalized linear models. CRC Press.Google Scholar
  19. Donoghue, J. P., Sanes, J. N., Hatsopoulos, N. G., & Gaal, G. (1998). Neural discharge and local field potential oscillations in primate motor cortex during voluntary movements. Journal of Neurophysiology, 79, 159–173.PubMedGoogle Scholar
  20. Eeckman, F. H. (1992). Neural systems: Analysis and modeling.Google Scholar
  21. Ekstrom, A. D., Caplan, J., Ho, E., Shattuck, K., Fried, I., & Kahana, M. (2005). Human hippocampal theta activity during virtual navigation. Hippocampus, 15, 881–889.PubMedCrossRefGoogle Scholar
  22. Fetz, E. E., Chen, D., Murthy, V. N., & Matsumura, M. (2000). Synaptic interactions mediating synchrony and oscillations in primate sensorimotor cortex. Journal of Physiology, Paris, 94, 323–331.PubMedCrossRefGoogle Scholar
  23. FitzHugh, R. (1955). Mathematical models of threshold phenomena in the nerve membrane. Bulletin of Mathematical Biophysics, 17, 257–278.CrossRefGoogle Scholar
  24. Fox, S. E., Wolfson, S., & Ranck, J. B. J. (1986). Hippocampal theta rhythm and the firing of neurons in walking and urethane anesthetized rats. Experimental Brain Research, 62, 495–508.PubMedCrossRefGoogle Scholar
  25. Friedrich, R. W., Habermann, C. J., & Laurent, G. (2004). Multiplexingusing synchrony in the zebra fish olfactory bulb. Nature Neuroscience, 7, 862–871.PubMedCrossRefGoogle Scholar
  26. Fries, P. (2005). A mechanism for cognitive dynamics: neuronal communication through neuronal coherence. Trends in Cognitive Sciences, 9, 474–480.PubMedCrossRefGoogle Scholar
  27. Fries, P., Nikolic, D., & Singer, W. (2007). The gamma cycle. Trends in Neurosciences, 30, 309–316.PubMedCrossRefGoogle Scholar
  28. Gabor, S., Hangya, B., Hernadi, I., Winkler, I., Lakatos, P., & Ulbert, I. (2010). Phase entrainment of human delta oscillations can mediate the effects of expectation on reaction speed. Journal of Neuroscience, 30, 13578–13585.CrossRefGoogle Scholar
  29. Hampson, R. E., Song, D., Chan, R. H. M., Sweatt, A. J., Fuqua, J., Gerhardt, G. A., et al. (2012a). A nonlinear model for hippocampal cognitive prosthesis: memory facilitation by hippocampal ensemble stimulation. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 20(2), 184–197. doi:10.1109/TNSRE.2012.2189163. PMID: 22438334.PubMedCentralPubMedCrossRefGoogle Scholar
  30. Hampson, R. E., Song, D., Chan, R. H. M., Sweatt, A. J., Riley, M. R., Goonawardena, A. V., et al. (2012b). Closing the loop for memory prostheses: detecting the role of hippocampal neural ensembles using nonlinear models. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 20(4), 510–525. doi:10.1109/TNSRE.2012.2190942. PMID: 22498704.PubMedCentralPubMedCrossRefGoogle Scholar
  31. Hampson, R. E., Gerhardt, G. A., Marmarelis, V. Z., Song, D., Opris, I., Santos, L., et al. (2012c). Facilitation and restoration of cognitive function in primate prefrontal cortex by a neuroprosthesis that utilizes minicolumn-specific neural firing. Journal of Neural Engineering, 9(5), 056012. doi:10.1088/1741-2560/9/5/056012.PubMedCentralPubMedCrossRefGoogle Scholar
  32. Hasselmo, M. E., Bodelon, C., & Wyble, B. P. (2002). A proposed function for hippocampal theta rhythm: separate phases of encoding and retrieval enhance reversal of prior learning. Neural Computation, 14, 793–817.PubMedCrossRefGoogle Scholar
  33. Hertz, J., Krogh, A., Palmer, R.G. (1991). Introduction to the theory of neural computation. Addison-Wesley.Google Scholar
  34. Hille, B. (2001). Ionic channels of excitable membranes (3rd ed.). Sinauer Associates.Google Scholar
  35. Hindmarsh, J. L., & Rose, R. M. (1984). A model of neuronal bursting using three coupled first order differential equations. Proceedings of the Royal Society of London, Series B: Biological Sciences, 221, 87–102.CrossRefGoogle Scholar
  36. Hobson, J., & Pace-Schott, E. (2002). The cognitive neuroscience of sleep: neuronal systems, con sciousness and learning. Nature Reviews Neuroscience, 3, 679–693.PubMedCrossRefGoogle Scholar
  37. Hodgkin, A., & Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117, 500–544.PubMedCentralPubMedGoogle Scholar
  38. Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences of the United States of America, 79(8), 2554–2558.PubMedCentralPubMedCrossRefGoogle Scholar
  39. Hyman, J., Zilli, E., Paley, A., & Hasselmo, M. (2005). Medial prefrontal cortex cells show dynamic modulation with the hippocampal theta rhythm dependent on behavior. Hippocampus, 15, 739–749.PubMedCrossRefGoogle Scholar
  40. Izhikevich, E. M. (2007). Dynamical systems in neuroscience: Geometry of excitability and bursting. MIT Press.Google Scholar
  41. Izhikevich, E. M., & Edelman, G. M. (2008). Large-scale model of mammalian thalamocortical systems. Proceedings of the National Academy of Science, 105, 3593–3598.CrossRefGoogle Scholar
  42. Jacobs, J., Hwang, G., Curran, T., & Kahana, M. J. (2006). EEG oscillations and recognition memory: theta correlates of memory retrieval and decision making. NeuroImage, 15, 978–987.CrossRefGoogle Scholar
  43. Jacobs, J., Kahana, M. J., Ekstrom, A. D., & Fried, I. (2007). Brain oscillations control timing of single-neuron activity in humans. Journal of Neuroscience, 27, 3839–3844.PubMedCrossRefGoogle Scholar
  44. Jensen, O., et al. (2002). Oscillations in the alpha band increase with memory load during retention in a short-term memory task. Cerebral Cortex, 12, 877–882.PubMedCrossRefGoogle Scholar
  45. Jensen, O., Kaiser, J., & Lachaux, J. P. (2007). Human gamma-frequency oscillations associated with attention and memory. Trends in Neurosciences, 30, 317–324.PubMedCrossRefGoogle Scholar
  46. Jones, M. W., & Wilson, M. A. (2005). Theta rhythms coordinate hippocampal-prefrontal interactions in a spatial memory task. PLoS Biology, 3, e402.PubMedCentralPubMedCrossRefGoogle Scholar
  47. Kahana, M. J. (2006). The cognitive correlates of human brain oscillations. Journal of Neuroscience, 26, 1669–1672.PubMedCrossRefGoogle Scholar
  48. Kiss, T., Hoffmann, W. E., & Hajós, M. (2011). Delta oscillation and short-term plasticity in the rat medial prefrontal cortex: modelling NMDA hypofunction of schizophrenia. The International Journal of Neuropsychopharmacology, 14, 29–42.PubMedCrossRefGoogle Scholar
  49. Klimesch, W., et al. (1998). Induced alpha-band power changes in the human EEG and attention. Neuroscience Letters, 244, 73–76.PubMedCrossRefGoogle Scholar
  50. Koch, C., & Segev, I. (1989). Methods in neuronal modeling: From synapses to networks. MIT Press.Google Scholar
  51. Lebedev, M. A., & Nelson, R. J. (1995). Rhythmically firing (20–50 Hz) neurons in monkey primary somatosensory cortex: activity patterns during initiation of vibratory-cued hand movements. Journal of Comparative Neuroscience, 2, 313–334.CrossRefGoogle Scholar
  52. Marmarelis, V. Z. (1993). Identification of nonlinear biological systems using Laguerre expansions of kernels. Annals of Biomedical Engineering, 21, 573.PubMedCrossRefGoogle Scholar
  53. Marmarelis, V. Z. (1997). Modeling methodology for nonlinear physiological systems. Annals of Biomedical Engineering, 25, 239.PubMedCrossRefGoogle Scholar
  54. Marmarelis, V. Z. (2004). Nonlinear dynamic modeling of physiological systems. Wiley Interscience & IEEE Press.Google Scholar
  55. Marmarelis, V. Z., & Berger, T. W. (2005). General methodology for nonlinear modeling of neural systems with Poisson point-process inputs. Mathematical Biosciences, 196, 1–13.PubMedCrossRefGoogle Scholar
  56. Marmarelis, P. Z., & Marmarelis, V. Z. (1978). Analysis of physiological systems: The white-noise approach. Plenum Press.Google Scholar
  57. Marmarelis, V. Z., & Orme, M. E. (1993). Modeling of neural systems by use of neuronal modes. IEEE Transactions on Biomedical Engineering, 40, 1149–1158.PubMedCrossRefGoogle Scholar
  58. Marmarelis, V. Z., Zanos, T. P., & Berger, T. W. (2009). Boolean modeling of neural systems with point-process inputs and outputs. Part I: theory and simulations. Annals of Biomedical Engineering, 37, 1654–1667.PubMedCentralPubMedCrossRefGoogle Scholar
  59. Marmarelis, V. Z., Shin, D. C., Song, D., Hampson, R. E., Deadwyler, S. A., & Berger, T. W. (2012). Design of optimal stimulation patterns for neuronal ensembles based on Volterra-type hierarchical modeling. Journal of Neural Engineering, 9(6), 066003. doi:10.1088/1741-2560/9/6/066003. PMID: 23075519.PubMedCentralPubMedCrossRefGoogle Scholar
  60. Marmarelis, V. Z., Shin, D. C., Song, D., Hampson, R. E., Deadwyler, S. A., & Berger, T. W. (2013). Nonlinear modeling of dynamic interactions within neuronal ensembles using Principal Dynamic Modes. Journal of Comparative Neuroscience, 34(1), 73–87. doi:10.1007/s10827-012-0407-7. PMID: 23011343.CrossRefGoogle Scholar
  61. Murthy, V. N., & Fetz, E. E. (1992). Coherent 25- to 35-Hz oscillations in the sensorimotor cortex of awake behaving monkeys. Proceedings of the National Academy of Sciences of the United States of America, 89, 5670–5674.PubMedCentralPubMedCrossRefGoogle Scholar
  62. Murthy, V. N., & Fetz, E. E. (1996). Oscillatory activity in sensorimotor cortex of awake monkeys: synchronization of local field potentials and relation to behavior. Journal of Neurophysiology, 76, 3949–3982.PubMedGoogle Scholar
  63. Opris, I., Hampson, R. E., Stanford, T. R., Gerhardt, G. A., & Deadwyler, S. A. (2011). Neural activity in frontal cortical cell layers: evidence for columnar sensorimotor processing. Journal of Cognitive Neuroscience, 23, 1507–1521.PubMedCentralPubMedCrossRefGoogle Scholar
  64. Rizzuto, D. S., Madsen, J. R., Bromfield, E. B., Schulze-Bonhage, A., Seelig, D., Aschenbrenner-Scheibe, R., et al. (2003). Reset of human neocortical oscillations during a working memory task. Proceedings of the National Academy of Sciences of the United States of America, 100, 7931–7936.PubMedCentralPubMedCrossRefGoogle Scholar
  65. Rosenblatt, F. (1962). Principles of neurodynamics. Spartan Books.Google Scholar
  66. Sanes, J. N., & Donoghue, J. P. (1993). Oscillations in local field potentials of the primate motor cortex during voluntary movement. Proceedings of the National Academy of Sciences of the United States of America, 90, 4470–4474.PubMedCentralPubMedCrossRefGoogle Scholar
  67. Siegel, M., Warden, M. R., & Miller, E. K. (2009). Phase-dependent neuronal coding of objects in short-term memory. Proceedings of the National Academy of Sciences of the United States of America, 106, 21341–21346.PubMedCentralPubMedCrossRefGoogle Scholar
  68. Singer, W. (1993). Synchronization of cortical activity and its putative role in information processing and learning. Annual Review of Physiology, 55, 349–374.PubMedCrossRefGoogle Scholar
  69. Singer, W. (1999). Neuronal synchrony: a versatile code for the definition of relations? Neuron, 24(49–65), 111–125.Google Scholar
  70. Song, D., Chan, R. H., Marmarelis, V. Z., Hampson, R. E., Deadwyler, S. A., & Berger, T. W. (2007). Nonlinear dynamic modeling of spike train transformations for hippocampal-cortical prostheses. IEEE Transactions on Biomedical Engineering, 54, 1053–1066.PubMedCrossRefGoogle Scholar
  71. Song, D., Chan, R. H. M., Marmarelis, V. Z., Hampson, R. E., Deadwyler, S. A., & Berger, T. W. (2009). Nonlinear modeling of neural population dynamics for hippocampal prostheses. Neural Networks, 22, 1340–1351.PubMedCentralPubMedCrossRefGoogle Scholar
  72. Vertes, R. P. (2005). Hippocampal theta rhythm: a tag for short term memory. Hippocampus, 15, 923–935.PubMedCrossRefGoogle Scholar
  73. von Stein, A., & Sarnthein, J. (2000). Different frequencies for different scales of cortical integration: from local gamma to long range alpha/theta synchronization. International Journal of Psychophysiology, 38, 301–313.CrossRefGoogle Scholar
  74. Widrow, B., & Lehr, M. A. (1990). 30 years of adaptive neural networks: perceptron, madaline, and backpropagation. Proceedings of the IEEE, 78(9), 1415–1442.CrossRefGoogle Scholar
  75. Zanos, T. P., Courellis, S. H., Berger, T. W., Hampson, R. E., Deadwyler, S. A., & Marmarelis, V. Z. (2008). Nonlinear modeling of causal interrelationships in neuronal ensembles. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 16, 336–352.PubMedCentralPubMedCrossRefGoogle Scholar
  76. Zanos, T. P., Hampson, R. E., Deadwyler, S. A., Berger, T. W., & Marmarelis, V. Z. (2009). Boolean modeling of neural systems with point-process inputs and outputs. Part II: application to the rat hippocampus. Annals of Biomedical Engineering, 37, 1668–1682.PubMedCentralPubMedCrossRefGoogle Scholar
  77. Zhang, Y., Chen, Y., Bressler, S. L., & Ding, M. (2008). Response preparation and inhibition: the role of the cortical sensorimotor beta rhythm. Neuroscience, 156, 238–246.PubMedCentralPubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • V. Z. Marmarelis
    • 1
  • D. C. Shin
    • 1
  • D. Song
    • 2
  • R. E. Hampson
    • 3
  • S. A. Deadwyler
    • 3
  • T. W. Berger
    • 2
  1. 1.Department of Biomedical Engineering and the Biomedical Simulations Resource (BMSR)University of Southern CaliforniaLos AngelesUSA
  2. 2.Department of Biomedical Engineering, Program in Neuroscience, Center for Neural EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  3. 3.Department of Physiology and PharmacologyWake Forest University Health SciencesWinston-SalemUSA

Personalised recommendations