Mathematical model of phase coding of events in the brain

V. D. Tsukerman

Matematičeskaâ biologiâ i bioinformatika, Tome 1 (2006), pp. 97-107.

Résumé

Slow alpha- and theta-resemblance waves generated by coordinated neuronal activity under activity of nonspecific subcortical inputs create conditions for the dynamic change of excitability of neuronal local groups which, in turn, generate high-frequency gamma oscillation because of external inputs' influence. Arrival of these signals in the most vulnerable phase of the slow rhythm creates a good situation for local gamma rhythms generation. On the basis of these positions, an original model of rhythms’ interaction in neuronal networks of the brain was developed and investigated. In computational modeling experiments, management of amplitude and phase of theta waves is shown, that can serve as an effective way of transformation of the psychophysical scale of event perception (patterns of input signals) into micro-time scales of neuronal messages. One of key elements of a new paradigm is a fundamental role of interaction of rhythms in coding, compression and coordination of neuronal messages in brain. The developed model of a neuronal network represents a network of weak linked nonlinear oscillators and every one of them can generate high-frequency packs modulated by a slow oscillation rhythm. In the model, nonlinear interactions of these rhythms allow to obtain an exact understanding of how the spatial organization of neurons and its inputs at the cells level explains such phenomena of fast and slow oscillatory activity of brain interaction as time compression of the coded messages, masking and of some other.

Bibliographie

[1] Eckhorn R., “Neural mechanisms of scene segmentation: recordings from the visual cortex suggest basic circuits for linking field models”, Neural Networks, 10 (1999), 464–479 <ext-link ext-link-type='doi' href='https://doi.org/10.1109/72.761705'>10.1109/72.761705</ext-link>

[2] Gray C. M., “The temporal correlation hypothesis of visual feature integration: still alive and well”, Neuron., 24 (1999), 31–47 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/S0896-6273(00)80820-X'>10.1016/S0896-6273(00)80820-X</ext-link>

[3] Singer W., “Neuronal synchrony: a versatile code for the definition of relations?”, Neuron., 24 (1999), 49–65 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/S0896-6273(00)80821-1'>10.1016/S0896-6273(00)80821-1</ext-link>

[4] Tallon-Baudry C., Bertrand O., “Oscillatory gamma activity in humans and its role in object representation”, Trends Cog. Sci., 3 (1999), 151–162 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/S1364-6613(99)01299-1'>10.1016/S1364-6613(99)01299-1</ext-link>

[5] Brosch M., Budinger E., Scheich H., “Stimulus related gamma oscillations in primate auditory cortex”, J. Neurophysiol., 87 (2002), 2715–2725

[6] Friedman D., Strowbridge B. W., “Both electrical and chemical synapses mediate fast network oscillations in the olfactory bulb”, J. Neurophysiol., 89 (2003), 2601–2610 <ext-link ext-link-type='doi' href='https://doi.org/10.1152/jn.00887.2002'>10.1152/jn.00887.2002</ext-link>

[7] Cunningham M. O., Halliday D. M., Davies C. H., Traub R. D., Buh E. H., Whittington M. A., “Coexistence of gamma and high-frequency oscillations in rat medial entorhinal cortex in vitro”, J. Physiol., 559:2 (2004), 347–353 <ext-link ext-link-type='doi' href='https://doi.org/10.1113/jphysiol.2004.068973'>10.1113/jphysiol.2004.068973</ext-link>

[8] Balu R., Larimer P., Strowbridge B. W., “Phasic stimuli evoke precisely timed spikes in intermittently discharging mitral cells”, J. Neurophysiol., 92 (2004), 743–753 <ext-link ext-link-type='doi' href='https://doi.org/10.1152/jn.00016.2004'>10.1152/jn.00016.2004</ext-link>

[9] Lagier S., Carleton A., Lledo P.-M., “Interplay between local GABAergic interneurons and relay neurons generates oscillations in the rat olfactory bulb”, J. Neurosci., 24 (2004), 4382–4392 <ext-link ext-link-type='doi' href='https://doi.org/10.1523/JNEUROSCI.5570-03.2004'>10.1523/JNEUROSCI.5570-03.2004</ext-link>

[10] Whittington M. A., “Coexistence of gamma and high-frequency oscillations in rat medial entorhinal cortex in vitro”, J. Physiol., 559 (2004), 347–353 <ext-link ext-link-type='doi' href='https://doi.org/10.1113/jphysiol.2004.068973'>10.1113/jphysiol.2004.068973</ext-link>

[11] Lledo P.-M., Gheusi G., Vincent J.-D., “Information processing in the mammalian olfactory system”, Physiol. Rev., 85 (2005), 281–317 <ext-link ext-link-type='doi' href='https://doi.org/10.1152/physrev.00008.2004'>10.1152/physrev.00008.2004</ext-link>

[12] von Stein A., Chiang C., Konig P., “Top-down processing mediated by interareal synchronization”, PNAS USA, 7 (2000), 14748–14753

[13] Kopell N., Ermentrout G. B., Whittington M. A., Traub R. D., “Gamma rhythms and beta rhythms have different synchronization properties”, PNAS USA, 7 (2000), 1867–1872 <ext-link ext-link-type='doi' href='https://doi.org/10.1073/pnas.97.4.1867'>10.1073/pnas.97.4.1867</ext-link>

[14] Tsukerman V. D., Nelineinaya dinamika sensornogo vospriyatiya, ili Chto i kak kodiruet mozg, Izd-vo Rostovskogo Universiteta, Rostov-na-Donu, 2005, 195 pp.

[15] Raghavachari S., Kahana M. J., Rizzuto D. S., Caplan J. B., Kirschen M., Bourgeois B., Madsen J. R., Lisman J. E., “Gating of human theta oscillations by a working memory task”, J. Neurosci., 21:9 (2001), 3175–3183

[16] White J. A., Banks M. A., Pearce R. A., Kopell N. J., “Networks of interneurons with fast and slow g-aminobutyric acid type A (GABAA) kinetics provide substrate for mixed gamma-theta rhythm”, PNAS USA, 97 (2000), 8128–8133 <ext-link ext-link-type='doi' href='https://doi.org/10.1073/pnas.100124097'>10.1073/pnas.100124097</ext-link>

[17] Sederberg P. B., Kahana M. J., Howard M. W., Donner E. J., Madsen J. R., “Theta and gamma oscillations during encoding predict subsequent recall”, J. Neurosci., 23:34 (2003), 10809–10814

[18] Canolty R. T., Edwards E., Dalal S. S., Soltani M., Nagarajan S. S., Kirsch H. E., Berger M. S., Barbaro N. M., Knight R. T., “High gamma power is phase-locked to theta oscillations in human neocortex”, Science, 313 (2006), 1626–1628 <ext-link ext-link-type='doi' href='https://doi.org/10.1126/science.1128115'>10.1126/science.1128115</ext-link>

[19] Tsukerman V. D., Cheshkov G. N., “Osnovy nelineinoi dinamiki sensornogo vospriyatiya. I. Fazovoe kodirovanie v ostsillyatornykh setyakh”, Neirokompyutery: razrabotka i primenenie, 7–8 (2002), 65–72

[20] Tsukerman V. D., “Osnovy nelineinoi dinamiki sensornogo vospriyatiya II. Neirodinamicheskie korrelyaty vnimaniya v pertseptualnoi obrabotke”, Neirokompyutery: razrabotka i primenenie, 7–8 (2002), 73–81

[21] Tsukerman V. D., Kulakov S. V., “Biologicheskie algoritmy kodirovaniya sensornykh sobytii”, Neirokompyutery: razrabotka i primenenie, 11 (2004), 15–25

[22] Tsukerman V. D., Svetlichnyi A. V., Problemy teoreticheskoi biofiziki, eds. Esipova N. G., Kols O. R., Riznichenko G. Yu., Khruschev S. S., Izd-vo Moskovskogo Universiteta, M., 1998, 183

[23] Tsukerman V. D., Proceedings of the 8th ICANN, eds. Niklasson L., Boden M., Ziemke T., Sweden, Skovde, 1998, 1027–1032

[24] Tsukerman V. D., Neiroinformatika-99, eds. Ezhov A. A., Frolov A. A., Shumskii S. A., Izd-vo MIFI, M., 1999, 228–235

[25] Tsukerman V. D., Kozhin O. G., Neiroinformatika-2000, Izd-vo MIFI, M., 2000, 202–208