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Complex temporal patterns processing by a neural mass model of a cortical column

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Abstract

It is well known that neuronal networks are capable of transmitting complex spatiotemporal information in the form of precise sequences of neuronal discharges characterized by recurrent patterns. At the same time, the synchronized activity of large ensembles produces local field potentials that propagate through highly dynamic oscillatory waves, such that, at the whole brain scale, complex spatiotemporal dynamics of electroencephalographic (EEG) signals may be associated to sensorimotor decision making processes. Despite these experimental evidences, the link between highly temporally organized input patterns and EEG waves has not been studied in detail. Here, we use a neural mass model to investigate to what extent precise temporal information, carried by deterministic nonlinear attractor mappings, is filtered and transformed into fluctuations in phase, frequency and amplitude of oscillatory brain activity. The phase shift that we observe, when we drive the neural mass model with specific chaotic inputs, shows that the local field potential amplitude peak appears in less than one full cycle, thus allowing traveling waves to encode temporal information. After converting phase and amplitude changes obtained into point processes, we quantify input–output similarity following a threshold-filtering algorithm onto the amplitude wave peaks. Our analysis shows that the neural mass model has the capacity for gating the input signal and propagate selected temporal features of that signal. Finally, we discuss the effect of local excitatory/inhibitory balance on these results and how excitability in cortical columns, controlled by neuromodulatory innervation of the cerebral cortex, may contribute to set a fine tuning and gating of the information fed to the cortex.

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References

  • Abeles M (1982a) Local cortical circuits. An electrophysiological study, studies of brain function, vol 6. Springer, Berlin

    Book  Google Scholar 

  • Abeles M (1982b) Quantification, smoothing, and confidence limits for single-units’ histograms. J Neurosci Methods 5(4):317–325

    Article  CAS  PubMed  Google Scholar 

  • Abeles M (2014) Revealing instances of coordination among multiple cortical areas. Biol Cybern 108(5):665–75

    Article  CAS  PubMed  Google Scholar 

  • Abeles M, Gerstein GL (1988) Detecting spatiotemporal firing patterns among simultaneously recorded single neurons. J Neurophysiol 60(3):909–924

    Article  CAS  Google Scholar 

  • Abeles M, Bergman H, Margalit E, Vaadia E (1993) Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. J Neurophysiol 70(4):1629–1638

    Article  CAS  Google Scholar 

  • Abeysuriya RG, Hadida J, Sotiropoulos SN, Jbabdi S, Becker R, Hunt BAE, Brookes MJ, Woolrich MW (2018) A biophysical model of dynamic balancing of excitation and inhibition in fast oscillatory large-scale networks. PLoS Comput Biol 14(2):e1006007

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Akam T, Kullmann DM (2010) Oscillations and filtering networks support flexible routing of information. Neuron 67(2):308–20

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Albéri L, Lintas A, Kretz R, Schwaller B, Villa AEP (2013) The calcium-binding protein parvalbumin modulates the firing properties of the reticular thalamic nucleus bursting neurons. J Neurophysiol 109(11):2827–2841

    Article  CAS  PubMed  Google Scholar 

  • Andrzejak RG, Lehnertz K, Mormann F, Rieke C, David P, Elger CE (2001) Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: dependence on recording region and brain state. Phys Rev E Stat Nonlinear Soft Matter Phys 64(6 Pt 1):061907

    Article  CAS  Google Scholar 

  • Asai Y, Villa AEP (2008) Reconstruction of underlying nonlinear deterministic dynamics embedded in noisy spike trains. J Biol Phys 34:325–340

    Article  PubMed  PubMed Central  Google Scholar 

  • Asai Y, Villa AEP (2012) Integration and transmission of distributed deterministic neural activity in feed-forward networks. Brain Res 1434:17–33

    Article  CAS  PubMed  Google Scholar 

  • Asai Y, Guha A, Villa AEP (2008) Deterministic neural dynamics transmitted through neural networks. Neural Netw 21(6):799–809

    Article  PubMed  Google Scholar 

  • Benes FM, Taylor JB, Cunningham MC (2000) Convergence and plasticity of monoaminergic systems in the medial prefrontal cortex during the postnatal period: implications for the development of psychopathology. Cereb Cortex 10(10):1014–27

    Article  CAS  PubMed  Google Scholar 

  • Bonzon P (2017) Towards neuro-inspired symbolic models of cognition: linking neural dynamics to behaviors through asynchronous communications. Cogn Neurodyn 11(4):327–353

    Article  PubMed  PubMed Central  Google Scholar 

  • Brama H, Guberman S, Abeles M, Stern E, Kanter I (2015) Synchronization among neuronal pools without common inputs: in vivo study. Brain Struct Funct 220(6):3721–31

    Article  PubMed  Google Scholar 

  • Brette R (2012) Computing with neural synchrony. PLoS Comput Biol 8(6):e1002561

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Brunel N, Hakim V (1999) Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comput 11(7):1621–71

    Article  CAS  PubMed  Google Scholar 

  • Brunel N, Hansel D (2006) How noise affects the synchronization properties of recurrent networks of inhibitory neurons. Neural Comput 18(5):1066–110

    Article  PubMed  Google Scholar 

  • Buzsáki G, Anastassiou CA, Koch C (2012) The origin of extracellular fields and currents-EEG, ECoG, LFP and spikes. Nat Rev Neurosci 13(6):407–20

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Caillard O, Moreno H, Schwaller B, Llano I, Celio MR, Marty A (2000) Role of the calcium-binding protein parvalbumin in short-term synaptic plasticity. Proc Natl Acad Sci USA 97(24):13372–13377

    Article  CAS  Google Scholar 

  • Carlén M, Meletis K, Siegle JH, Cardin JA, Futai K, Vierling-Claassen D, Rühlmann C, Jones SR, Deisseroth K, Sheng M, Moore CI, Tsai LH (2012) A critical role for NMDA receptors in parvalbumin interneurons for gamma rhythm induction and behavior. Mol Psychiatry 17(5):537–548

    Article  CAS  PubMed  Google Scholar 

  • Celletti A, Froeschlé C, Tetko IV, Villa AEP (1999) Deterministic behaviour of short time series. Meccanica 34:145–152

    Article  Google Scholar 

  • Chen G, Ueta T (1999) Yet another chaotic attractor. Int J Bifurc Chaos 9(7):1465–1466

    Article  Google Scholar 

  • Cutsuridis V (2012) Bursts shape the NMDA-R mediated spike timing dependent plasticity curve: role of burst interspike interval and GABAergic inhibition. Cogn Neurodyn 6(5):421–41

    Article  PubMed  PubMed Central  Google Scholar 

  • David O, Friston KJ (2003) A neural mass model for MEG/EEG: coupling and neuronal dynamics. NeuroImage 20(3):1743–1755

    Article  PubMed  Google Scholar 

  • Deng B, Cai L, Li S, Wang R, Yu H, Chen Y, Wang J (2017) Multivariate multi-scale weighted permutation entropy analysis of EEG complexity for Alzheimer’s disease. Cogn Neurodyn 11(3):217–231

    Article  PubMed  Google Scholar 

  • Ermentrout B (2002) Simulating, analyzing, and animating dynamical systems: a guide to Xppaut for researchers and students (software, environments, tools). Society for Industrial and Applied Mathematics, Philadelphia

    Book  Google Scholar 

  • Ermentrout B (2012) XPPAUT. In: Le Novère N (ed) Computational systems neurobiology. Springer, Berlin, pp 519–531 (chap 17)

    Chapter  Google Scholar 

  • Feldman DE (2012) The spike-timing dependence of plasticity. Neuron 75(4):556–71

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Fries P, Womelsdorf T, Oostenveld R, Desimone R (2008) The effects of visual stimulation and selective visual attention on rhythmic neuronal synchronization in macaque area v4. J Neurosci 28(18):4823–35

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Fukushima Y, Tsukada M, Tsuda I, Yamaguti Y, Kuroda S (2007) Spatial clustering property and its self-similarity in membrane potentials of hippocampal CA1 pyramidal neurons for a spatio-temporal input sequence. Cogn Neurodyn 1(4):305–16

    Article  PubMed  PubMed Central  Google Scholar 

  • Furth KE, Mastwal S, Wang KH, Buonanno A, Vullhorst D (2013) Dopamine, cognitive function, and gamma oscillations: role of d4 receptors. Front Cell Neurosci 7:102–102

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Gao J, Hu J, Tung WW (2011) Complexity measures of brain wave dynamics. Cogn Neurodyn 5(2):171–82

    Article  PubMed  PubMed Central  Google Scholar 

  • García-Ojalvo J, Sancho J (1999) Noise in spatially extended systems. Springer, New York

    Book  Google Scholar 

  • Gollo LL, Mirasso C, Villa AEP (2010) Dynamic control for synchronization of separated cortical areas through thalamic relay. Neuroimage 52(3):947–955

    Article  PubMed  Google Scholar 

  • Gross J, Hoogenboom N, Thut G, Schyns P, Panzeri S, Belin P, Garrod S (2013) Speech rhythms and multiplexed oscillatory sensory coding in the human brain. PLoS Biol 11(12):e1001752

    Article  PubMed  PubMed Central  Google Scholar 

  • Gruart A, Delgado-García JM, Lintas A (2016) Effect of parvalbumin deficiency on distributed activity and interactions in neural circuits activated by instrumental learning. In: Wang R, Pan X (eds) Advances in cognitive neurodynamics (V). Springer, Singapore, pp 111–117

    Chapter  Google Scholar 

  • Guyonneau R, Van Rullen R, Thorpe SJ (2005) Neurons tune to the earliest spikes through stdp. Neural Comput 17:859–879

    Article  PubMed  Google Scholar 

  • Hénon M (1976) A two-dimensional mapping with a strange attractor. Communi Math Phys 50(1):69–77

    Article  Google Scholar 

  • Iglesias J, Villa AEP (2010) Recurrent spatiotemporal firing patterns in large spiking neural networks with ontogenetic and epigenetic processes. J Physiol Paris 104:137–146

    Article  PubMed  Google Scholar 

  • Iglesias J, Chibirova O, Villa A (2007) Nonlinear dynamics emerging in large scale neural networks with ontogenetic and epigenetic processes. Lect Notes Comput Sci 4668:579–588

    Article  Google Scholar 

  • Jansen BH, Rit VG (1995) Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biol Cybern 73(4):357–366

    Article  CAS  PubMed  Google Scholar 

  • Jansen BH, Zouridakis G, Brandt ME (1993) A neurophysiologically-based mathematical model of flash visual evoked potentials. Biol Cybern 68(3):275–283

    Article  CAS  PubMed  Google Scholar 

  • Korn H, Faure P (2003) Is there chaos in the brain? II. Experimental evidence and related models. C R Biol 326(9):787–840

    Article  PubMed  Google Scholar 

  • Lee AT, Vogt D, Rubenstein JL, Sohal VS (2014) A class of gabaergic neurons in the prefrontal cortex sends long-range projections to the nucleus accumbens and elicits acute avoidance behavior. J Neurosci 34(35):11519–11525

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Lintas A (2014) Discharge properties of neurons recorded in the parvalbumin-positive (pv1) nucleus of the rat lateral hypothalamus. Neurosci Lett 571:29–33

    Article  CAS  PubMed  Google Scholar 

  • Lintas A, Schwaller B, Villa AEP (2013) Visual thalamocortical circuits in parvalbumin-deficient mice. Brain Res 1536:107–118

    Article  CAS  PubMed  Google Scholar 

  • Longtin A (1993) Nonlinear forecasting of spike trains from sensory neurons. Int J Bifurc Chaos 3(03):651–661

    Article  Google Scholar 

  • Makarenko V, Llinás R (1998) Experimentally determined chaotic phase synchronization in a neuronal system. Proc Natl Acad Sci USA 95(26):15747–52

    Article  CAS  PubMed  Google Scholar 

  • Malagarriga D, Villa AEP, García-Ojalvo J, Pons AJ (2014) Excitation/inhibition patterns in a system of coupled cortical columns. In: Wermter S, Weber C, Duch W, Honkela T, Koprinkova-Hristova P, Magg S, Palm G, Villa AEP (eds) Artificial neural networks and machine learning—ICANN 2014. Lecture Notes in Computer Science, vol 8681. Springer, Cham, pp 651–658

  • Malagarriga D, García-Vellisca MA, Villa AEP, Buldú JM, García-Ojalvo J, Pons AJ (2015a) Synchronization-based computation through networks of coupled oscillators. Front Comput Neurosci 9:00097

    Article  Google Scholar 

  • Malagarriga D, Villa AEP, Garcia-Ojalvo J, Pons AJ (2015b) Mesoscopic segregation of excitation and inhibition in a brain network model. PLoS Comput Biol 11(2):e1004007

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Manseau F, Marinelli S, Mendez P, Schwaller B, Prince DA, Huguenard JR, Bacci A (2010) Desynchronization of neocortical networks by asynchronous release of GABA at autaptic and synaptic contacts from fast-spiking interneurons. PLoS Biol 8(9):e1000492

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Markram H, Lübke J, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275(5297):213–5

    Article  CAS  PubMed  Google Scholar 

  • Mateos DM, Guevara Erra R, Wennberg R, Perez Velazquez JL (2018) Measures of entropy and complexity in altered states of consciousness. Cogn Neurodyn 12(1):73–84

    Article  CAS  PubMed  Google Scholar 

  • Montbrió E, Pazó D, Roxin A (2015) Macroscopic description for networks of spiking neurons. Phys Rev X 5(2):021028

    Google Scholar 

  • Muller L, Chavane F, Reynolds J, Sejnowski TJ (2018) Cortical travelling waves: mechanisms and computational principles. Nat Rev Neurosci 19(5):255–268

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Myers MH, Kozma R (2018) Mesoscopic neuron population modeling of normal/epileptic brain dynamics. Cogn Neurodyn 12(2):211–223

    Article  PubMed  Google Scholar 

  • Ng BSW, Logothetis NK, Kayser C (2013) EEG phase patterns reflect the selectivity of neural firing. Cereb Cortex 23(2):389–98

    Article  PubMed  Google Scholar 

  • Nobukawa S, Yamanishi T, Nishimura H, Wada Y, Kikuchi M, Takahashi T (2019) Atypical temporal-scale-specific fractal changes in Alzheimer’s disease EEG and their relevance to cognitive decline. Cogn Neurodyn 13(1):1–11

    Article  PubMed  Google Scholar 

  • Nunez P (1995) Neocortical dynamics and human EEG rhythms. Oxford University Press, New York

    Google Scholar 

  • Ozaki TJ, Sato N, Kitajo K, Someya Y, Anami K, Mizuhara H, Ogawa S, Yamaguchi Y (2012) Traveling EEG slow oscillation along the dorsal attention network initiates spontaneous perceptual switching. Cogn Neurodyn 6(2):185–98

    Article  PubMed  PubMed Central  Google Scholar 

  • Panzeri S, Brunel N, Logothetis NK, Kayser C (2010) Sensory neural codes using multiplexed temporal scales. Trends Neurosci 33(3):111–20

    Article  CAS  PubMed  Google Scholar 

  • Parker TS, Chua LO (1989) Poincaré maps. Springer, New York, pp 31–56

    Google Scholar 

  • Parnavelas JG, Papadopoulos GC (1989) The monoaminergic innervation of the cerebral cortex is not diffuse and nonspecific. Trends Neurosci 12(9):315–9

    Article  CAS  PubMed  Google Scholar 

  • Qu J, Wang R, Yan C, Du Y (2014) Oscillations and synchrony in a cortical neural network. Cogn Neurodyn 8(2):157–66

    Article  PubMed  Google Scholar 

  • Rabinovich MI, Varona P (2011) Robust transient dynamics and brain functions. Front Comput Neurosci 5:24

    Article  PubMed  PubMed Central  Google Scholar 

  • Reinoso JA, Torrent MC, Masoller C (2016) Emergence of spike correlations in periodically forced excitable systems. Phys Rev E 94(3–1):032218

    Article  CAS  PubMed  Google Scholar 

  • Reynolds GP, Abdul-Monim Z, Neill JC, Zhang ZJ (2004) Calcium binding protein markers of GABA deficits in schizophrenia-postmortem studies and animal models. Neurotox Res 6(1):57–61

    Article  PubMed  Google Scholar 

  • Rubino D, Robbins KA, Hatsopoulos NG (2006) Propagating waves mediate information transfer in the motor cortex. Nat Neurosci 9(12):1549–57

    Article  CAS  PubMed  Google Scholar 

  • Schroeder CE, Lakatos P (2009) Low-frequency neuronal oscillations as instruments of sensory selection. Trends Neurosci 32(1):9–18

    Article  CAS  PubMed  Google Scholar 

  • Schwaller B, Tetko IV, Tandon P, Silveira DC, Vreugdenhil M, Henzi T, Potier MC, Celio MR, Villa AEP (2004) Parvalbumin deficiency affects network properties resulting in increased susceptibility to epileptic seizures. Mol Cell Neurosci 25(4):650–663

    Article  CAS  PubMed  Google Scholar 

  • Segundo JP (2003) Nonlinear dynamics of point process systems and data. Int J Bifurcat Chaos 13(08):2035–2116

    Article  Google Scholar 

  • Singer W (1993) Synchronization of cortical activity and its putative role in information processing and learning. Annu Rev Physiol 55:349–74

    Article  CAS  Google Scholar 

  • Singer W (1999) Neuronal synchrony: a versatile code for the definition of relations? Neuron 24(1):49–65

    Article  CAS  PubMed  Google Scholar 

  • Spiegler A, Kiebel SJ, Atay FM, Knösche TR (2010) Bifurcation analysis of neural mass models: impact of extrinsic inputs and dendritic time constants. Neuroimage 52(3):1041–1058

    Article  PubMed  Google Scholar 

  • Stam CJ (2005) Nonlinear dynamical analysis of EEG and MEG: review of an emerging field. Clin Neurophysiol 116(10):2266–2301

    Article  CAS  PubMed  Google Scholar 

  • Tal I, Abeles M (2016) Temporal accuracy of human cortico–cortical interactions. J Neurophysiol 115(4):1810–20

    Article  PubMed  PubMed Central  Google Scholar 

  • Tal I, Abeles M (2018) Imaging the spatiotemporal dynamics of cognitive processes at high temporal resolution. Neural Comput 30(3):610–630

    Article  CAS  PubMed  Google Scholar 

  • Tetko IV, Villa AEP (2001) A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 2. Application to simultaneous single unit recordings. J Neurosci Methods 105(1):15–24

    Article  CAS  PubMed  Google Scholar 

  • Tewarie P, Hunt BAE, O’Neill GC, Byrne A, Aquino K, Bauer M, Mullinger KJ, Coombes S, Brookes MJ (2018) Relationships between neuronal oscillatory amplitude and dynamic functional connectivity. Cereb Cortex. https://doi.org/10.1093/cercor/bhy136

    Article  Google Scholar 

  • Theiler J, Rapp PE (1996) Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram. Electroencephalogr Clin Neurophysiol 98(3):213–22

    Article  CAS  PubMed  Google Scholar 

  • Villa AEP, Abeles M (1990) Evidence for spatiotemporal firing patterns within the auditory thalamus of the cat. Brain Res 509(2):325–327

    Article  CAS  PubMed  Google Scholar 

  • Villa AEP, Fuster JM (1992) Temporal correlates of information processing during visual short-term memory. Neuroreport 3(1):113–116

    Article  CAS  PubMed  Google Scholar 

  • Vogels TP, Abbott LF (2009) Gating multiple signals through detailed balance of excitation and inhibition in spiking networks. Nat Neurosci 12(4):483–91

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Vogt SM, Hofmann UG (2012) Neuromodulation of STDP through short-term changes in firing causality. Cogn Neurodyn 6(4):353–66

    Article  PubMed  PubMed Central  Google Scholar 

  • von der Malsburg C, Schneider W (1986) A neural cocktail-party processor. Biol Cybern 54(1):29–40

    Article  PubMed  Google Scholar 

  • Wennekers T (2008) Tuned solutions in dynamic neural fields as building blocks for extended EEG models. Cogn Neurodyn 2(2):137–46

    Article  PubMed  PubMed Central  Google Scholar 

  • Whittington MA, Traub RD (2003) Interneuron diversity series: inhibitory interneurons and network oscillations in vitro. Trends Neurosci 26(12):676–82

    Article  CAS  PubMed  Google Scholar 

  • Zaslavsky G (1978) The simplest case of a strange attractor. Phys Lett A 69(3):145–147

    Article  Google Scholar 

  • Zylberberg A, Fernández Slezak D, Roelfsema PR, Dehaene S, Sigman M (2010) The brain’s router: a cortical network model of serial processing in the primate brain. PLoS Comput Biol 6(4):e1000765

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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Acknowledgements

The authors acknowledge the partial support by the Swiss National Science Foundation Grant No. CR13I1-138032. AJP’s work was supported, in part, by the Spanish MINECO FIS2015-66503-C3-2-P. All authors conceived and designed the simulations, which were performed primarily by DM. DM and AEPV wrote the paper, and all authors have read and approved the final manuscript.

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Malagarriga, D., Pons, A.J. & Villa, A.E.P. Complex temporal patterns processing by a neural mass model of a cortical column. Cogn Neurodyn 13, 379–392 (2019). https://doi.org/10.1007/s11571-019-09531-2

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