Flexible resonance in prefrontal networks with strong feedback inhibition

[EN] Oscillations are ubiquitous features of brain dynamics that undergo task-related changes in synchrony, power, and frequency. The impact of those changes on target networks is poorly understood. In this work, we used a biophysically detailed model of prefrontal cortex (PFC) to explore the effects of varying the spike rate, synchrony, and waveform of strong oscillatory inputs on the behavior of cortical networks driven by them. Interacting populations of excitatory and inhibitory neurons with strong feedback inhibition are inhibition-based network oscillators that exhibit resonance (i.e., larger responses to preferred input frequencies). We quantified network responses in terms of mean firing rates and the population frequency of network oscillation; and characterized their behavior in terms of the natural response to asynchronous input and the resonant response to oscillatory inputs. We show that strong feedback inhibition causes the PFC to generate internal (natural) oscillations in the beta/gamma frequency range (>15 Hz) and to maximize principal cell spiking in response to external oscillations at slightly higher frequencies. Importantly, we found that the fastest oscillation frequency that can be relayed by the network maximizes local inhibition and is equal to a frequency even higher than that which maximizes the firing rate of excitatory cells; we call this phenomenon population frequency resonance. This form of resonance is shown to determine the optimal driving frequency for suppressing responses to asynchronous activity. Lastly, we demonstrate that the natural and resonant frequencies can be tuned by changes in neuronal excitability, the duration of feedback inhibition, and dynamic properties of the input. Our results predict that PFC networks are tuned for generating and selectively responding to beta- and gamma-rhythmic signals due to the natural and resonant properties of inhibition-based oscillators. They also suggest strategies for optimizing transcranial stimulation and using oscillatory networks in neuromorphic engineering.This material is based upon research supported by the U. S. Army Research Office under award number ARO W911NF-12-R-0012-02 to N. K., the U. S. Office of Naval Research under award number ONR MURI N00014-16-1-2832 to M. H., and the National Science Foundation under award number NSF DMS-1042134 (Cognitive Rhythms Collaborative: A Discovery Network) to N. K. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Sherfey, JS.; Ardid-Ramírez, JS.; Hass, J.; Hasselmo, ME.; Kopell, NJ. (2018). Flexible resonance in prefrontal networks with strong feedback inhibition. PLoS Computational Biology. 14(8). https://doi.org/10.1371/journal.pcbi.1006357148Whittington, M. A., Traub, R. D., & Jefferys, J. G. R. (1995). Synchronized oscillations in interneuron networks driven by metabotropic glutamate receptor activation. Nature, 373(6515), 612-615. doi:10.1038/373612a0Randall, F. E., Whittington, M. A., & Cunningham, M. O. (2011). Fast oscillatory activity induced by kainate receptor activation in the rat basolateral amygdala in vitro. European Journal of Neuroscience, 33(5), 914-922. doi:10.1111/j.1460-9568.2010.07582.xRoux, F., Wibral, M., Mohr, H. M., Singer, W., & Uhlhaas, P. J. (2012). Gamma-Band Activity in Human Prefrontal Cortex Codes for the Number of Relevant Items Maintained in Working Memory. Journal of Neuroscience, 32(36), 12411-12420. doi:10.1523/jneurosci.0421-12.2012Buschman, T. J., Denovellis, E. L., Diogo, C., Bullock, D., & Miller, E. K. (2012). Synchronous Oscillatory Neural Ensembles for Rules in the Prefrontal Cortex. Neuron, 76(4), 838-846. doi:10.1016/j.neuron.2012.09.029Buzsáki, G. (2002). Theta Oscillations in the Hippocampus. Neuron, 33(3), 325-340. doi:10.1016/s0896-6273(02)00586-xCannon, J., McCarthy, M. M., Lee, S., Lee, J., Börgers, C., Whittington, M. A., & Kopell, N. (2013). Neurosystems: brain rhythms and cognitive processing. European Journal of Neuroscience, 39(5), 705-719. doi:10.1111/ejn.12453Rotstein, H. G., & Nadim, F. (2013). Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents. Journal of Computational Neuroscience, 37(1), 9-28. doi:10.1007/s10827-013-0483-3Rotstein, H. G. (2015). Subthreshold amplitude and phase resonance in models of quadratic type: Nonlinear effects generated by the interplay of resonant and amplifying currents. Journal of Computational Neuroscience, 38(2), 325-354. doi:10.1007/s10827-014-0544-2Akam, T., & Kullmann, D. M. (2010). Oscillations and Filtering Networks Support Flexible Routing of Information. Neuron, 67(2), 308-320. doi:10.1016/j.neuron.2010.06.019Ledoux, E., & Brunel, N. (2011). Dynamics of Networks of Excitatory and Inhibitory Neurons in Response to Time-Dependent Inputs. Frontiers in Computational Neuroscience, 5. doi:10.3389/fncom.2011.00025Whittington, M. ., Traub, R. ., Kopell, N., Ermentrout, B., & Buhl, E. . (2000). Inhibition-based rhythms: experimental and mathematical observations on network dynamics. International Journal of Psychophysiology, 38(3), 315-336. doi:10.1016/s0167-8760(00)00173-2Börgers, C., & Kopell, N. (2005). Effects of Noisy Drive on Rhythms in Networks of Excitatory and Inhibitory Neurons. Neural Computation, 17(3), 557-608. doi:10.1162/0899766053019908Buzsáki, G., & Draguhn, A. (2004). Neuronal Oscillations in Cortical Networks. Science, 304(5679), 1926-1929. doi:10.1126/science.1099745Hahn, G., Bujan, A. F., Frégnac, Y., Aertsen, A., & Kumar, A. (2014). Communication through Resonance in Spiking Neuronal Networks. PLoS Computational Biology, 10(8), e1003811. doi:10.1371/journal.pcbi.1003811Womelsdorf, T., Ardid, S., Everling, S., & Valiante, T. A. (2014). Burst Firing Synchronizes Prefrontal and Anterior Cingulate Cortex during Attentional Control. Current Biology, 24(22), 2613-2621. doi:10.1016/j.cub.2014.09.046Buschman, T. J., & Miller, E. K. (2007). Top-Down Versus Bottom-Up Control of Attention in the Prefrontal and Posterior Parietal Cortices. Science, 315(5820), 1860-1862. doi:10.1126/science.1138071Miller, E. K., & Buschman, T. J. (2013). Cortical circuits for the control of attention. Current Opinion in Neurobiology, 23(2), 216-222. doi:10.1016/j.conb.2012.11.011Haegens, S., Nacher, V., Hernandez, A., Luna, R., Jensen, O., & Romo, R. (2011). Beta oscillations in the monkey sensorimotor network reflect somatosensory decision making. Proceedings of the National Academy of Sciences, 108(26), 10708-10713. doi:10.1073/pnas.1107297108Siegel, M., Donner, T. H., & Engel, A. K. (2012). Spectral fingerprints of large-scale neuronal interactions. Nature Reviews Neuroscience, 13(2), 121-134. doi:10.1038/nrn3137Thut, G., & Miniussi, C. (2009). New insights into rhythmic brain activity from TMS–EEG studies. Trends in Cognitive Sciences, 13(4), 182-189. doi:10.1016/j.tics.2009.01.004Herrmann, C. S., Rach, S., Neuling, T., & Strüber, D. (2013). Transcranial alternating current stimulation: a review of the underlying mechanisms and modulation of cognitive processes. Frontiers in Human Neuroscience, 7. doi:10.3389/fnhum.2013.00279Dowsett, J., & Herrmann, C. S. (2016). Transcranial Alternating Current Stimulation with Sawtooth Waves: Simultaneous Stimulation and EEG Recording. Frontiers in Human Neuroscience, 10. doi:10.3389/fnhum.2016.00135Moliadze, V., Atalay, D., Antal, A., & Paulus, W. (2012). Close to threshold transcranial electrical stimulation preferentially activates inhibitory networks before switching to excitation with higher intensities. Brain Stimulation, 5(4), 505-511. doi:10.1016/j.brs.2011.11.004Renart, A., de la Rocha, J., Bartho, P., Hollender, L., Parga, N., Reyes, A., & Harris, K. D. (2010). The Asynchronous State in Cortical Circuits. Science, 327(5965), 587-590. doi:10.1126/science.1179850Wang, X.-J. (1999). Synaptic Basis of Cortical Persistent Activity: the Importance of NMDA Receptors to Working Memory. The Journal of Neuroscience, 19(21), 9587-9603. doi:10.1523/jneurosci.19-21-09587.1999Tegnér, J., Compte, A., & Wang, X.-J. (2002). The dynamical stability of reverberatory neural circuits. Biological Cybernetics, 87(5-6), 471-481. doi:10.1007/s00422-002-0363-9Giulioni, M., Camilleri, P., Mattia, M., Dante, V., Braun, J., & Del Giudice, P. (2012). Robust Working Memory in an Asynchronously Spiking Neural Network Realized with Neuromorphic VLSI. Frontiers in Neuroscience, 5. doi:10.3389/fnins.2011.00149Compte, A. (2000). Synaptic Mechanisms and Network Dynamics Underlying Spatial Working Memory in a Cortical Network Model. Cerebral Cortex, 10(9), 910-923. doi:10.1093/cercor/10.9.910Ardid, S., Wang, X.-J., Gomez-Cabrero, D., & Compte, A. (2010). Reconciling Coherent Oscillation with Modulationof Irregular Spiking Activity in Selective Attention:Gamma-Range Synchronization between Sensoryand Executive Cortical Areas. Journal of Neuroscience, 30(8), 2856-2870. doi:10.1523/jneurosci.4222-09.2010Bastos AM, Loonis R, Kornblith S, Lundqvist M, Miller EK (2018) Laminar recordings in frontal cortex suggest distinct layers for maintenance and control of working memory. Proceedings of the National Academy of Sciences: 201710323.Shin, D., & Cho, K.-H. (2013). Recurrent connections form a phase-locking neuronal tuner for frequency-dependent selective communication. Scientific Reports, 3(1). doi:10.1038/srep02519Dong, Y., & White, F. J. (2003). Dopamine D1-Class Receptors Selectively Modulate a Slowly Inactivating Potassium Current in Rat Medial Prefrontal Cortex Pyramidal Neurons. The Journal of Neuroscience, 23(7), 2686-2695. doi:10.1523/jneurosci.23-07-02686.2003Bloem, B., Poorthuis, R. B., & Mansvelder, H. D. (2014). Cholinergic modulation of the medial prefrontal cortex: the role of nicotinic receptors in attention and regulation of neuronal activity. Frontiers in Neural Circuits, 8. doi:10.3389/fncir.2014.00017Jimenez-Fernandez, A., Cerezuela-Escudero, E., Miro-Amarante, L., Dominguez-Moralse, M. J., de Asis Gomez-Rodriguez, F., Linares-Barranco, A., & Jimenez-Moreno, G. (2017). A Binaural Neuromorphic Auditory Sensor for FPGA: A Spike Signal Processing Approach. IEEE Transactions on Neural Networks and Learning Systems, 28(4), 804-818. doi:10.1109/tnnls.2016.2583223Lande, T. S. (Ed.). (1998). Neuromorphic Systems Engineering. The Springer International Series in Engineering and Computer Science. doi:10.1007/b102308Liu, S.-C., & Delbruck, T. (2010). Neuromorphic sensory systems. Current Opinion in Neurobiology, 20(3), 288-295. doi:10.1016/j.conb.2010.03.007Richardson, M. J. E., Brunel, N., & Hakim, V. (2003). From Subthreshold to Firing-Rate Resonance. Journal of Neurophysiology, 89(5), 2538-2554. doi:10.1152/jn.00955.2002Chen, Y., Li, X., Rotstein, H. G., & Nadim, F. (2016). Membrane potential resonance frequency directly influences network frequency through electrical coupling. Journal of Neurophysiology, 116(4), 1554-1563. doi:10.1152/jn.00361.2016Lea-Carnall, C. A., Montemurro, M. A., Trujillo-Barreto, N. J., Parkes, L. M., & El-Deredy, W. (2016). Cortical Resonance Frequencies Emerge from Network Size and Connectivity. PLOS Computational Biology, 12(2), e1004740. doi:10.1371/journal.pcbi.1004740Adams, N. E., Sherfey, J. S., Kopell, N. J., Whittington, M. A., & LeBeau, F. E. N. (2017). Hetereogeneity in Neuronal Intrinsic Properties: A Possible Mechanism for Hub-Like Properties of the Rat Anterior Cingulate Cortex during Network Activity. eneuro, 4(1), ENEURO.0313-16.2017. doi:10.1523/eneuro.0313-16.2017Cannon, J., & Kopell, N. (2015). The Leaky Oscillator: Properties of Inhibition-Based Rhythms Revealed through the Singular Phase Response Curve. SIAM Journal on Applied Dynamical Systems, 14(4), 1930-1977. doi:10.1137/140977151Olufsen, M. S., Whittington, M. A., Camperi, M., & Kopell, N. (2003). Journal of Computational Neuroscience, 14(1), 33-54. doi:10.1023/a:1021124317706Durstewitz, D., & Seamans, J. K. (2002). The computational role of dopamine D1 receptors in working memory. Neural Networks, 15(4-6), 561-572. doi:10.1016/s0893-6080(02)00049-7Durstewitz, D., Seamans, J. K., & Sejnowski, T. J. (2000). Dopamine-Mediated Stabilization of Delay-Period Activity in a Network Model of Prefrontal Cortex. Journal of Neurophysiology, 83(3), 1733-1750. doi:10.1152/jn.2000.83.3.1733Nunez, P. L., & Srinivasan, R. (2006). Electric Fields of the Brain. doi:10.1093/acprof:oso/9780195050387.001.0001Sherfey, J. S., Soplata, A. E., Ardid, S., Roberts, E. A., Stanley, D. A., Pittman-Polletta, B. R., & Kopell, N. J. (2018). DynaSim: A MATLAB Toolbox for Neural Modeling and Simulation. Frontiers in Neuroinformatics, 12. doi:10.3389/fninf.2018.0001