mit jelentenek a szavak? - cneuro.rmki.kfki.hucneuro.rmki.kfki.hu/files/oszc.pdf · 2006. 11....

Motto:

Harmonikus oszcillator, hidrogenatom.Van-e mas is a vilagon? En nem tudhatom,De ha netan volna mas, azt rugja meg a lo,Az csak perturbacio.

Reszlet a Fizikus Indulobol

Idegi oszcillaciok

– Typeset by FoilTEX – 1

Mit jelentenek a szavak?

• Oszcillacio: valamilyen mennyiseg (pl. membranpotencial, kalcium koncentracio, stb.) pe-riodikus (itt csak idoben periodikus) valtozasa. (Kulcsszavak, amikre gondolni erdemes meg:dinamikai rendszer, fazister, trajektoria, hatarciklus).

• Idegi: periodikusan ismetlodo jelensegeket az idegrendszer sok szervezodesi szintjen, szamosreszeben es sokfele mennyiseggel kapcsolatban megfigyeltek. Pl. az alvas – ebrenlet ciklustolaz egesz agyra kiterjedo makroszkopikus elektromos aktivitas mintazatokon (gorog betukkeljeloltek) keresztul az idegsejteken belul lejatszodo folyamatokig (ioncsatornak nyitas – zarasa).

Valojaban megkulonboztetest tehetunk az agyi es az idegi oszcillacio fogalma kozott: mıgaz elobbit altalaban az agykergen merheto elektroenkefalogrammban (EEG) megmutatkozoperiodikus jelre ertik, utobbi valamilyen belsobb beavatkozassal (egyes idegsejtek extra-, vagyintracellularis merese, helyi terpotencial, stb.) nyert adatokra vonatkoznak.


EEG ritmusok I.

Tortenetileg az agyi oszcillaciokat frekvenciajuk alapjan kategorizaljak. Az alabbi lista rovidbemutato csupan (mely az EEG ritmusokat osztalyozza), a kepet arnyalja, hogy pontosan milyenallatban, annak is melyik agyteruleten es pontosan milyen tulajdonsagu egy adott frekvenciajuritmus.

• Gamma (γ): 30 – 100 Hz-es ritmus, mely az erzekelesben, megismeresben jatszhat szerepetemberben es patkanyban egyarant.

• Beta (β): 12 – 30 Hz. A kis amplitudoju beta oszcillaciot az aktıv viselkedesi allapottalkapcsoljak ossze (munka, jatek, stb.). Kulonfele szerekkel, melyek altalaban stimulansok (pl.kis mennyisegu alkohol, nikotin a cigarettaban, koffein, stb.) is kivalthato.

• Szenzorimotoros ritmus (SMR): 12 – 16 Hz-es oszcillacio, melyet a”fizikai jelenlet er-

zesevel” kapcsolnak ossze. A mozgas gatolja ezt az oszcillaciot, nyugalomban lehet merni.Alacsony SMR lehet autizmusra, vagy figyelemzavarra (Attention Deficit Disorder) utalo jel.

• Alfa (α): 8 – 12 Hz. Nyugodt, koncentralt allapottal kapcsoljak ossze emberben. Legkife-jezettebb a latokereg felett, csukott szemu emberben. Elalvaskor, vagy a szem kinyitasakorcsokken az erossege. Hasonlo a mu (µ) ritmus, melyet a motoros kereg felett lehet merni.Mestersegesen is kivalthato kannabisszal (kulcsszavak meg: ’60-as evek, vızonto, stb.)


EEG ritmusok II.

• Theta (θ): 4 – 8 Hz. Emberben elalvashoz, illetve az alvas bizonyos szakaszaihoz (pl. REM)kotik, de hallucinaciok, illetve hipnozis alatt is merheto. Hallucinogen szerekkel, pl. LSDvalthato ki. Patkanyban az egyik leginkabb kutatott oszcillacio, mert szerepet jatszik a olyanfontos esetekben, mint a tanulas, illetve affektıv es kognitıv folyamatokban. A vizsgalatokatszinte minden agyi szinten, a szinapszisoktol a tobb agyteruletet atfogo vizsgalatokig vegzik.

• Delta (δ): 4 Hz-ig. A leglassabb oszcillacio, melyet mely alomban (az alvas alatt hosszuperiodusokban), vagy egyes teruletek serulesekor figyelnek meg. Altatokkal, eros nyugtatokkalvalthato ki delta allapot.

Az elektroenkefalogramm, elektroenkefalografia kifejezesek Hans Berger nemet fiziologustol szar-maznak, aki az 1920-as evekben kezdte kıserleteit (bar vele egyidoben mar sokan foglalkoztak askalpon vegzett elektromos vizsgalati technikaval, sot az elso EEG-nek tekintheto merest VladimirVladimirovics Pravdics-Neminsky publikalta 1913-ban kutyabol).


Alvasfazisok

• Egy ejszaka soran a koponyarol elvezet-heto EEG aktivitas mintazata ciklikusanvaltozik.

• NREM: lassu hullamu alvas. A leglas-sabb δ oszcillacio a kereg es a thalamusosszjatekakent keletkezik.

• A REM alvas EEG-je az ebrenleti EEG-hez hasonlıt.

• Mi hatarozza meg, hogy mikormelyik allapot kovetkezik?

• Hogyan keletkeznek? Hol es ho-gyan jon letre a ritmus, mi szink-ronizal? Milyen aramokat me-runk?

• Mi a funkciojuk?

Forras: Kognitıv idegtudomany Osiris, 2003 Budapest


Oszcillaciok keletkezese – egysejt

Neuralis ritmusok generalasaban a kulonfele agyi szervezodesi szinteken levo elemek hatnak kol-cson:

Az EEG-vel, vagy makroszkopikus elektrodaval merheto ritmikus viselkedes mogott periodikus,szinkronizalt egysejt viselkedes all.

A ritmusgeneralas vizsgalatahoz ket kerdest kell targyalni: 1., hogy mi okozza a periodikusviselkedest; 2., hogy mi okozza a szinkronizaciot.

Lattuk, hogy egyedulallo idegsejtek kepesek periodikus membranpotencial oszcillacio, vagy peri-odikus akcios potencial generalasara. Ezek pontos tulajdonsagait a membranba agyazott ioncsa-tornak fajtai, tulajdonsagai, illetve a sejt passzıv tulajdonsagai, morfologiaja szabja meg.

[vol

t]

Küszöb alatti MPO

[másodperc]

Periodikus akciós potenciálok

[vol

t]

[másodperc]

[vol

t]

Periodikus börsztök

[másodperc] 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

−0.06

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Oszcillaciok keletkezese – egysejt

A sejtszintu oszcillacio leırasara szamtalan modell alkalmas, pl.:

• A Hodgkin – Huxley modell konstans aram hatasara periodikusan general akcios potenci-alokat. A HH modell, illetve annak kulonfele aramokkal, reszletes morfologiaval kiegeszıtettutodai igen celszeru eszkozok arra, hogy az oszcillacio sejtszintu generalasanak kerdeset vizs-galjuk (pl. egy adott aram hatasara hogyan valtozik a sejt altal generalt oszcillaciok frekvenciatartomanya).

• Az integrate & fire modell, illetve annak variansai lehetseges eszkozok arra, hogy egy-szeru periodikus viselkedest vizsgaljunk. Itt termeszetesen nem a sejtszintu mechanizmusokrakoncentralunk, hanem a populacios viselkedesre.

• A rata es a fazis modellek pedig kimondottan periodikusan viselkedo sejtek leırasara ke-szultek.

φ (t)

φ (t=0)

A fazismodellt egy egyszeru esetben a kovetkezo matematikai konst-rukcio ırja le: θi(t) = ωi, θi(t) ∈ [0..2π]

Ennek az egyenletnek a megoldasat jol ismerjuk:

θi(t) = (ωit + θi(t = 0) mod 2π


Oszcillaciok keletkezese – halozat

Milyen mechanizmusok jatszhatnak szerepet abban, hogy egy neuralis halozat szinkronizaltaktivitast mutasson?

(késleltetéssel)Kölcsönös serkentés S SGSSerkentés − Gátlás

Csacsogó sejtGKölcsönös gátlás G

Háttér serkentés

Termeszetesen egy valodi agyteruleten egyszerre tobb mechanizmus is szerepet jatszhat.


Kozponti mintazat generator (CPG) I.

Elolenyek mozgasahoz szukseg lehet izmok periodikus vezerlesere (helyvaltoztatas, legzes, ragas,vakarodzas). Ezt vezerelheti egy jol elkulonıtheto neuralis szerkezet a CPG. Ezek allhatnaknehany, vagy sok idegsejtbol, es kepesek kulzo kontroll nelkul ritmikus viselkedest generalni.Ugyanakkor a kulso ingerekre, illetve belso hatasokra kepesek tobbfele ritmus letrehozasara. ACPG-k leırasanak egy nagyon egyszeru modja a fazismodellel tortenhet.

8.3. Four-Neuron Oscillators 145

LH

LF

RH

RF

WALK

LH

LF

RH

RF

TROT

LH

LF

RH

RF

LH

LF

RH

RF

GALLOP

PACE

Figure 8.3 Idealized diagram of the stepping movements of the cat for different characteristic gaits. Openbars represent a lifted foot, and closed bars denote a planted foot. Figure adapted from Pearson (1976).

that required for a trotting gait. A similar architecture, where the roles of the left and rightforelimbs are switched, provides the pattern of activity required for a pace. In some ofthe exercises that follow we outline changes in oscillator frequency, initial conditions, andcoupling which provide additional gaits and demonstrate some of the ways that these factorscan influence the network activity.

In each case, there are many other architectures that will exhibit the same patterns ofactivity as those mentioned for the various gaits described above and in the exercises. Atpresent, there is little known regarding the mechanisms employed by CPGs in behavinganimals. Thus, it is impossible to determine which architectures most closely model thesebiological mechanisms. Experiments that study CPG-produced locomotion in the cat usetreadmill speed to demonstrate that sensory input can lead to gait changes. The stimulationof the mesencephalic locomotor region in these experiments shows that descending drivefrom higher centers of the nervous system can lead to gait changes as well. Therefore, itseems likely that biological systems may use various methods or combinations of methods

A macska kulonfele jarasmodjai. Feher negy-szog: felemelt lab, fekete negyszog: foldon levolab. Ref.: Pearson, K. The control of walking,Scientific American 235: 72–86

Forras: The Book of GENESIShttp://www.genesis-sim.org/GENESIS/iBoG/iBoGpdf/index.html


Kozponti mintazat generator (CPG) II.

hij csatolassal csatolt oszcillatorok: θ1(t) = ω1 + h12(θ1, θ2)θ2(t) = ω2 + h21(θ2, θ1)

Bevezetjuk a faziskulonbseget: Φ(t) = θ1(t)− θ2(t)Ekkor: Φ(t) = θ1(t)− θ2(t) =

= (ω1 − ω2) + (h12(θ1, θ2)− h21(θ2, θ1))Tegyuk fel, hogy hij(θi, θj) = h′(Φ), hij(θi, θj) = 0, ha θi = θj

Peldaul: hij = aij sin(Φ)Ezzel a peldaval: Φ(t) = (ω1 − ω2)− (a12 + a21) sin (Φ(t))

Akkor kapunk 1:1 faziscsatolt megoldast, ha az oszcillatorok kozotti faziskulonbseg nem valtozik az idoben, azaz,

ha Φ(t) = 0, vagyis Φ(t) = Φ = arcsin

„ω1 − ω2

a12 + a21

«.

Minthogy az arcus sinus fuggveny -1 es 1 kozott vesz fel valos ertekeket, ha a fenti

hanyados ebbe az intervallumba esik, faziscsatolt a ket oszcillator, frekvenciajuk

azonos, a koztuk levo faziskulonbseget az arcus sinus adja radianban.

Ha ellenben a hanyados erteke nagyobb egynel, vagy kisebb mınusz egynel, nincs

faziscsatolas, az oszcillatorok”sodrodnak”egymashoz kepest z

arcs

in(z

)

−2

−1.5

−1

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0

0.5

1

1.5

2

−1 −0.5 0 0.5 1

Hasonloan targyalhato tobb neuron kulonfele halozatokba kapcsolt rendszere.


Alvas-ebrenlet: thalamo-kortikalis ritmusok

Spindle oscillations in reticular thalamic(RE), thalamocortical (Th-Cx, ventrolate-ral nucleus), and cortical (Cx, motor area)neurons. A, circuit of three neuronal ty-pes. B, two rhythms (7-14 Hz and 0.1-0.2 Hz) of spindle oscillations in corticalEEG. C, intracellular recordings in cats un-der barbiturate anesthesia. Note rhythmicspike-bursts of RE neuron during a spindlesequence and concomitant IPSPs leadingto post-inhibitory rebound bursts in Th-Cxneuron.

Forras: Mircea Steriade: THE CORTICOTHALAMIC SYSTEM IN

SLEEP Frontiers in Bioscience 8, 878-899, 2003


Thalamo-kortikalis ritmusok II.

The cortical slow oscillation groups thala-mically generated spindles. CAT 1, int-racellular recording in cat under urethaneanesthesia from area 7. Note slow oscil-lation of neuron and related EEG waves.One cycle of the slow oscillation is fra-med in dots. Part marked by horizontalbar below the intracellular trace (at left)is expanded above (right) to show spindlesfollowing the depolarizing envelope of theslow oscillation. CAT 2, dual simultane-ous intracellular recordings from right andleft cortical area 4. Note spindle duringthe depolarizing envelope of the slow os-cillation and synchronization of EEG whenboth neurons synchronously display prolon-ged hyperpolarizations.




Thalamo-kortikalis ritmusok III.

The slow oscillation during natural SWSand its obliteration during transition to wa-kefulness. (from top to bottom: depth-EEG from left area 5; intracellular activityof RS neuron from left area 7; and elect-romyogram (EMG)). Note phasic hyper-polarizations in area 7 neuron, related todepth-positive EEG field potentials, duringSWS, tonic firing upon awakening markedby EEG activation and increased musculartone, and slight depolarization occurringonly after a few seconds after awakeningand blockage of hyperpolarizations.




Egy konkret pelda – MSDB (kıserletek)

Forras: E.S. Brazhnik and S.E. Fox. Exp. Brain Res. (114) 1997


Egy konkret pelda – MSDB (modell I.)

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Forras: Ujfalussy B. es Kiss T. Journal of Comp. Neurosci. 21(3) 2006


Egy konkret pelda – MSDB (modell II.)

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Forras: Ujfalussy B. es Kiss T. Journal of Comp. Neurosci. 21(3) 2006


Egy konkret pelda – a hippokampusz I. (anatomia)

Forras: University of Bristol, Center for Synaptic Plasticity Homepage


Egy konkret pelda – a hippokampusz II. (theta ritmus)Neuron326

Figure 1. Voltage-versus-Depth Profile of

Theta Oscillation in the Rat

(Left) A 16-site silicon probe in the CA1-den-

tate gyrus axis. Numbers indicate recording

sites (100 �m spacing). o, str. oriens; p, pyra-

midal layer; r, str. radiatum; lm, str. lacuno-

sum-moleculare; g, granule cell layer; h, hilus.

(Right) Theta waves recorded during explora-

tion. Note gradual shift of theta phase from

str. oriens to str. lacunosum-moleculare.

Gamma waves superimposed on theta oscil-

lation are marked by arrows. Vertical bar: 1

mV. (From Bragin et al., 1995.)

rhinal cortex, perirhinal cortex, cingulate cortex, and and Magoun, 1949) rather than structures specifically

involved in theta rhythm generation. In summary, theamygdala (Adey, 1967; Mitchell and Ranck, 1980; Alonso

and Garcia-Austt, 1987; Leung and Borst, 1987; Pare minimum conditions necessary for the generation of os-

cillating extracellular currents in the theta frequencyand Collins, 2000). These structures are thus the main

current generators of the extracellularly recorded theta band are the proper connections between the hippo-

campus and MS-DBB. Despite 40 years of researchfield. However, none of these cortical structures are

capable of generating theta activity on their own. (Petsche et al., 1962), however, the exact physiological

mechanisms of these interactions have remained unre-Several subcortical nuclei have been postulated to be

critically involved in the rhythm generation of theta. Affer- solved.

ents from these nuclei release neurotransmitters that may

allow for the emergence of network oscillations in the “Classic” Theta Model and Its Inadequacies

In the first and simplest theta model, the MS-DBB hashippocampus and associated structures (“permissive”

action) or may provide a coherent, theta frequency out- been postulated to be the rhythm generator (pace-

maker), which supplies phasic modulation to the hippo-put (“pacemaker” function). Because lesion or inactiva-

tion of medial septum-diagonal band of Broca (MS-DBB) campus (Petsche et al., 1962). Subsequent models

added new components that are summarized in Figureneurons abolishes theta waves in all cortical targets, it

has been regarded as the ultimate rhythm generator of 2. On the assumption that the extracellular field is gener-

ated by the summed activity of IPSPs and EPSPs ontheta (Petsche et al., 1962). The MS-DBB is reciprocally

connected to the supramammillary region (Borhegyi and the somata and dendrites of principal cells, respectively,

these models utilized a single canonical CA1 pyramidalFreund, 1998; Leranth et al., 1999), a second critical

structure involved in pacing the theta rhythm (cf. Vertes cell with passive membrane properties. It has been as-

sumed that all pyramidal cells receive coherent excit-and Kocsis, 1997). Whether the MS-DBB and supra-

mammillary nucleus are true pacemakers or rhythmic atory (from perforant path) and inhibitory (from septum

to feed-forward inhibitory neuron) inputs. The interplayfiring of their neurons depends on the hippocampal and

entorhinal feedback has yet to be determined (Lee et between these two current generators (dipoles) is as-

sumed to be responsible for the unique amplitude/phaseal., 1994; Brazhnik and Fox, 1999; King et al., 1998;

Borisyuk and Hoppensteadt, 1999; Denham and Bo- versus depth profiles of hippocampal theta oscillation.

According to this scheme, the most strongly excitedrisyuk, 2000; Wang, 2002).

Neurons in several other subcortical structures are minority of the population would discharge at the same

time when nonspiking neurons are maximally depolar-phase locked to hippocampal theta oscillation, including

the dorsal raphe nucleus, ventral tegmental nucleus of ized, justifying the “lumped” model. As Figure 1 illus-

trates, theta waves in the waking rat show a gradualGudden, and anterior thalamic nuclei (cf. Bland, 1986;

Vertes and Kocsis, 1997). Finally, stimulation of several phase reversal between CA1 str. oriens and the hippo-

campal fissure (Winson, 1974), consistent with the coor-subcortical nuclei elicits hippocampal theta (cf. Bland,

1986). However, these latter structures also project to dinated activity of at least two current generators (di-

poles). Because the largest amplitude theta waves arethe thalamus and/or neocortex as well, and they are

part of a common ascending activation system (Moruzzi observed at the hippocampal fissure, rhythmic excita-

‘anti-sharp-wave’ neurons, respectively (see Methods). One of theO-LM cells did not reach significance for anti-sharp-wave neurons,because only a small number of ripples (n ¼ 10) could be recorded.Nevertheless, the data confirmed that O-LM cells are silent duringsharp waves.

We have shown that three distinct classes of interneuron, as

defined by their synaptic connectivity, contribute to differentaspects of network oscillations in vivo. Therefore, it seems that alarge diversity of GABA interneurons evolved to control pyramidalcells in a temporally distinct and brain-state-dependent manner.During theta activity, CA1 place cells1 are activated primarily by theperforant path19,20. TheO-LMcells, whose axons are co-alignedwiththe perforant path input, fire coincidentally with the strongesthyperpolarization in the distal dendrites of pyramidal cells6. There-fore, O-LM cells might phase-modulate excitatory input from theperforant path21 and/or provide rhythmic hyperpolarization thatcould de-inactivate voltage-sensitive ion channels and facilitatesomatodentritic back-propagation of the action potentials22 andburst discharge23 in active place cells. Axo-axonic cells and basketcells have high discharge probabilities on the descending phase ofthe theta cycle at times when the discharge probability of pyramidalcells is lowest and gamma power is highest2,6,24–26. Such cycle-phasearrangement can facilitate the rhythmic entrainment of pyramidalcell discharge7. During slow-wave sleep, the main driving source toCA1 pyramidal neurons is the sharp-wave-associated discharge ofthe CA3 pyramids5. Transient suppression of O-LM cell activityduring sharpwaves may allow action potentials in pyramidal cells toback-propagate to the most distal dendrites27,28 and facilitate long-term potentiation of those entorhinal input synapses that arecoincidentally active during sharp waves. Basket cells (parvalbu-min-positive) fire at high frequency and phase-locked to rippleoscillation, and can therefore provide an inhibitory temporalstructure for large populations of pyramidal cells3,5. By contrast,axo-axonic cells, which make inhibitory synapses at the site ofaction potential generation, only fire at the beginning of the sharpwave. Such a coordination of distinct inputs could time-lock theactivity of thousands of pyramidal cells to fire together, exactly atthe maximum amplitude of ripple episodes.Different classes of interneuron innervate distinct domains of

pyramidal cells and exhibit specific firing patterns during beha-viourally relevant oscillations. Therefore, they probably evolved totemporally coordinate input–output transformation in the hippo-campal pyramidal cells, and to govern the formation and retrieval ofcell assemblies during hippocampus-dependent behaviour. A

Methods

Electrophysiological recordings

Rats were treated in accordance with the Animals (Scientific Procedures) Act, 1986 (UK)and associated procedures. Fifty-two male Sprague–Dawley rats (250–350 g) wereanaesthetized with 1.25mg kg21 urethane, plus supplemental doses of ketamine andxylazine (20 and 2mg kg21, respectively) as needed, and body temperature was retainedwith a heating pad. Neuronal activity in the hippocampus was recorded extracellularlywith a glass electrode (18–25MQ) filled with 1.5% neurobiotin in 0.5M NaCl, and thelocal field potential (LFP) was recorded with a stationary second electrode in thehippocampal CA1 pyramidal cell layer. Single-unit activity (sampling rate 20 kHz) andLFP (sampling rate 800Hz) were filtered online at 0.8–5 kHz and 0.5–200Hz, respectively.After the collection of a sufficient number of spikes, the electrode was advanced towardsthe cell, which was then labelled juxtacellularly with neurobiotin by applying positivecurrent steps14. The shape and amplitude of spikes were monitored during recording,advancing the electrode and labelling to ensure that recorded spikes originated from asingle neuron only, and that the recorded cell was labelled. Recordings fromnine out of tenputative interneurons resulted in a single labelled interneuron following histological

R Figure 4 Distinct interneuron classes generate different firing patterns during theta and

ripple oscillations in vivo. a, Discharge frequency (mean ^ s.e.m.) of pyramidal cells,

parvalbumin-positive basket cells, axo-axonic cells and O-LM cells during theta (t),

non-theta/non-sharp-wave (n) and sharp-wave-associated ripples (s). b, The mean firing

probabilities of different cell types are shown as grey columns, firing probabilities of each

interneuron as coloured lines. For clarity, two theta cycles are shown; 08 and 3608 mark

the trough of the theta cycles recorded extracellularly in the stratum pyramidale (left

column). The start, maximum amplitude and end of the normalized sharp-wave episodes

are marked as21, 0 and 1, respectively (right column). Note that the phase relationships

of neurons to the network patterns are similar within the same class, despite variation in

discharge probability of individual cells.

letters to nature

NATURE |VOL 421 | 20 FEBRUARY 2003 | www.nature.com/nature 847© 2003 NaturePublishing Group

Forrasok: Buzsaki Gy. Neuron 2002 (bal); T. Klausberger es mtsai. Nature 2003 (jobb)


Egy konkret pelda – a hippokampusz III. (modell)

Forras: Orban G. es mtsai. J. Neurophysiology 2006


Oszcillaciok keletkezese - osszefoglalas

• Mi volt a ritmus-generatos a hippokampalis theta es gamma ritmus eseteben?

• Mily sejtek membran–aramait lehet merni EEG elektroddal? Miert?

• A szinaptikus aramokat vagy az akcios-potencialokat lehet latni?

• Mi a ritmus-generatora az alvasi-orsoknak?

• Az EEG-n lathato alvasi orsok eseteben mely sejtek aktivitasat merjuk?


Oszcillaciok funkcionalis szerepe

Feltetelezheto, hogy az idegi oszcillaciok valammilyen, az idegrendszer mukodesehez, idegi sza-mıtasokhoz kapcsolodo okbol jonnek letre. Egy-egy jellemzo oszcillacios mintazat azt jelezheti,hogy az adott terulet valamilyen tıpusu szamıtasokat vegez. A talamo-kortikalis rendszerbennem ugyanaz tortenik pl. β mint δ aktivitas alatt. Az erdekes kerdes azonban inkabb az, hogymiben es hogyan segıtik ezt a specialis feladatot az idegi oszcillaciok? (Nyılvan nemcsak azert vannak ott, hogy tudassak a vizsgalodo elektrofiziologussal, hogy most valami kulonostortenik.)

• Kozos orajel az egyutt dolgozo idegsejtek szamara (egy periodikus jelhez kepest lehet fazisokatmerni, es ez lehetoseget teremt a fazis-kod kialakıtasara.

• A fazis-kod egyik alkalmazasa a koncentraciotol fuggetlen szagfelismeres.• Gray es mtsai. felvetettek a

”perceptualis binding”hipotezist.

• Szerepet jatszhatnak a tanulasban (tuzelesi ido fuggo szinaptikus valtozas, STDP).• Szerepet jatszhat memorianyomok kialakıtasaban, tarolasaban es visszakereseseben.• A jel/zaj arany novelese (pl. sztochasztikus rezonancia)• Periodikus vezerlese a test valamely reszenek.

A kovetkezokben nehany pelda modellt nezunk meg ezekre.


Szagok koncentracio invarians kodolasa fazisokkal

Tobb sejt tuzelesenek egymashoz viszonyıtott relatıv fazisa kodolhat egy szagot. Ha ezek a relatıvtuzelesi idok fuggetlenek a szag koncentraciojatol, akkor olyan rendszert kapunk, mely barmilyeneros szagot kepes kategorizalni. A kiolvaso (dekodolo) rendszernek olyan, hogy adott tuzeles-mintazatokra erzekeny. (JJ Hopfield: Pattern recognition computation using action potentialtiming for stimulus representation. Nature 376:33–36)Computational theories on the function of theta oscillations 397

3 Models

3.1 Pattern recognition

Pattern recognition is a classical challenge for neural net-works (Rosenblatt 1958; Duda et al. 2001). In its canonicalform, a network has to classify a highly distributed patternof input activity (such as pixel values in an image) into oneof a small number of possible categories (such as houses vs.faces). In the case of regression, the network is also allowedto give answers like ‘70% house, 30% face’. Traditionally, in-puts to a neural network are thought of as distributed patternsof injected current: each neuron is depolarized to a differentlevel, and the output of the network is given in terms of thefiring rates of some of its neurons.

The first two models in this section explore the possi-ble benefits of representing outputs in terms of relative spiketimes (spike phases) rather than firing rates, when there is alsoa synchronous subthreshold oscillating input to all cells of thenetwork. These models use feed-forward networks. The thirdmodel investigates recurrently coupled networks using firingrates codes, and points out that limit cycles can alleviate thetrade-off between effectively amplifying a selected subset ofinputs and avoiding the spontaneous amplification of noiseinto ‘hallucinations’ when there is no meaningful signal inthe input.

3.1.1 Concentration invariant pattern recognition

It was first proposed by Hopfield (1995) purely on theoreticalgrounds that subthreshold membrane potential oscillationsmay endow neurons with a temporal code that can effectivelysupport a specific type of computation apparently importantin olfactory processing: concentration invariant odor recog-nition. In the model, cells receive a subthreshold oscillatoryinput plus a depolarizing current (Fig. 2a). Depending on thelevel of depolarization a cell will fire earlier or later duringthe theta cycle – as long as the depolarization remains in theregime in which the cell fires exactly one spike per cycle. Thisway, the timing of action potentials relative to the theta oscil-lation will depend quasi-logarithmically on the amount ofdepolarizing current (Fig. 2c). If a given odor excites severalsuch cells with different depolarization levels proportional tothe concentration of the odorant, then these cells will fire atdifferent times during the subthreshold oscillation, but due tothe logarithmic mapping from depolarization to spike timing,the timing of spikes fired by different cells relative to eachother will be preserved, independent of odorant concentra-tion. An appropriate decoder, sensitive for a given pattern ofrelative presynaptic spiking times (e.g., by being connectedto presynaptic cells through delay lines of different lengths)would then be able to recognize odors in a concentrationinvariant way. Brody and Hopfield (2003) further elaboratedon this idea, showing that such a network is also capable ofodor segmentation (recognizing individual odors in a mix-ture) and odor recognition in the presence of strong distractorodors. Hopfield (2004) also showed how essentially the same

Fig. 2 Encoding depolarization level in firing phase. a The timing ofspikes (top spike trains) within the theta cycle (middle sinusoid trace)depends on the level of depolarizing current (bottom step functions)received by the cell (Hopfield 1995). Spike trains labeled with 1, 2,3 are triggered by increasing input step currents 1, 2, 3, respectively.Relatively low depolarization (1) causes the cell to fire near the peakof theta, increasing input current (2, 3) shifts firing times towards thenegative peak of theta (dotted line). b When depolarization changes, fir-ing times in the first cycle after the change (transient firing phase) maydiffer from firing times in subsequent cycles (asymptotic firing phase)(Lengyel and Érdi 2004). Spike trains labeled with 1, 2, 3 are triggeredby time-shifted input step currents 1, 2, 3, respectively. Timing of thefirst spike depends on the exact phase of current switch-on: for someswitch-on times (1) it is identical to the asymptotic firing phase, forothers (2, 3) the first spike occurs later than the asymptotic firing phase.c Asymptotic firing phase depends logarithmically on the depolarizingcurrent (black solid line). Firing during transients can occur in a broaderphase range (gray shaded area); the size of this range increases withthe level of current (modified from Lengyel and Érdi 2004)

network could be used to recognize brief dynamical patternsin time-varying stimuli, such as syllables in speech.

The biological plausibility of this mechanism has recentlybeen confirmed by Margrie and Schaefer (2003) in in vivorecordings in the mouse olfactory bulb. The existence of astrong theta modulation of mitral cells was demonstrated thatregulated single cell firing, just as predicted by theoreticalstudies. Furthermore, the feasibility of spike latency coding

Computational theories on the function of theta oscillations 397

3 Models

3.1 Pattern recognition

Pattern recognition is a classical challenge for neural net-works (Rosenblatt 1958; Duda et al. 2001). In its canonicalform, a network has to classify a highly distributed patternof input activity (such as pixel values in an image) into oneof a small number of possible categories (such as houses vs.faces). In the case of regression, the network is also allowedto give answers like ‘70% house, 30% face’. Traditionally, in-puts to a neural network are thought of as distributed patternsof injected current: each neuron is depolarized to a differentlevel, and the output of the network is given in terms of thefiring rates of some of its neurons.

The first two models in this section explore the possi-ble benefits of representing outputs in terms of relative spiketimes (spike phases) rather than firing rates, when there is alsoa synchronous subthreshold oscillating input to all cells of thenetwork. These models use feed-forward networks. The thirdmodel investigates recurrently coupled networks using firingrates codes, and points out that limit cycles can alleviate thetrade-off between effectively amplifying a selected subset ofinputs and avoiding the spontaneous amplification of noiseinto ‘hallucinations’ when there is no meaningful signal inthe input.

3.1.1 Concentration invariant pattern recognition

It was first proposed by Hopfield (1995) purely on theoreticalgrounds that subthreshold membrane potential oscillationsmay endow neurons with a temporal code that can effectivelysupport a specific type of computation apparently importantin olfactory processing: concentration invariant odor recog-nition. In the model, cells receive a subthreshold oscillatoryinput plus a depolarizing current (Fig. 2a). Depending on thelevel of depolarization a cell will fire earlier or later duringthe theta cycle – as long as the depolarization remains in theregime in which the cell fires exactly one spike per cycle. Thisway, the timing of action potentials relative to the theta oscil-lation will depend quasi-logarithmically on the amount ofdepolarizing current (Fig. 2c). If a given odor excites severalsuch cells with different depolarization levels proportional tothe concentration of the odorant, then these cells will fire atdifferent times during the subthreshold oscillation, but due tothe logarithmic mapping from depolarization to spike timing,the timing of spikes fired by different cells relative to eachother will be preserved, independent of odorant concentra-tion. An appropriate decoder, sensitive for a given pattern ofrelative presynaptic spiking times (e.g., by being connectedto presynaptic cells through delay lines of different lengths)would then be able to recognize odors in a concentrationinvariant way. Brody and Hopfield (2003) further elaboratedon this idea, showing that such a network is also capable ofodor segmentation (recognizing individual odors in a mix-ture) and odor recognition in the presence of strong distractorodors. Hopfield (2004) also showed how essentially the same

Fig. 2 Encoding depolarization level in firing phase. a The timing ofspikes (top spike trains) within the theta cycle (middle sinusoid trace)depends on the level of depolarizing current (bottom step functions)received by the cell (Hopfield 1995). Spike trains labeled with 1, 2,3 are triggered by increasing input step currents 1, 2, 3, respectively.Relatively low depolarization (1) causes the cell to fire near the peakof theta, increasing input current (2, 3) shifts firing times towards thenegative peak of theta (dotted line). b When depolarization changes, fir-ing times in the first cycle after the change (transient firing phase) maydiffer from firing times in subsequent cycles (asymptotic firing phase)(Lengyel and Érdi 2004). Spike trains labeled with 1, 2, 3 are triggeredby time-shifted input step currents 1, 2, 3, respectively. Timing of thefirst spike depends on the exact phase of current switch-on: for someswitch-on times (1) it is identical to the asymptotic firing phase, forothers (2, 3) the first spike occurs later than the asymptotic firing phase.c Asymptotic firing phase depends logarithmically on the depolarizingcurrent (black solid line). Firing during transients can occur in a broaderphase range (gray shaded area); the size of this range increases withthe level of current (modified from Lengyel and Érdi 2004)

network could be used to recognize brief dynamical patternsin time-varying stimuli, such as syllables in speech.

The biological plausibility of this mechanism has recentlybeen confirmed by Margrie and Schaefer (2003) in in vivorecordings in the mouse olfactory bulb. The existence of astrong theta modulation of mitral cells was demonstrated thatregulated single cell firing, just as predicted by theoreticalstudies. Furthermore, the feasibility of spike latency coding

Forras: Lengyel M. es mtsai. Biological Cybernetics 2005


Perceptual”binding”

Forras: C.M Gray, Neuron 1999

A.K. Engel et al., Nature Reviews Neurosciences 2001


”Binding” hipotezis

Az idegi oszcillaciok Gray es mtsai. ’90-es evekben, a macska latokergeben vegzett vizsgalataikapcsan valtak kulonosen izgalmas temava (Charles M. Gray, Peter Konig, Andreas K. Engel & Wolf Singer: Oscillatory responses

in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338, 334–337)


7± 2 rovidtavu memoria tarolasa – human kıserletek

Forras: JE. Lisman es MAP. Idiart Science 1995

A, Emberi munkamemoria kapacitas (a teljes lista korrekt elohıvasanak a valoszınusege). B,Valasz latencia az s-edik listaelemnel. C-D: csatolt oszcillaciok emberben es patkanyban. E,After-depolarizacios hullam intracellularisan merve kortikalis piramissejten.


7± 2 rovidtavu memoria tarolasa – oszcillacios modell

”This work suggests that brain oscillations are a timing mechanism for controlling the serial

processing of short-term memories.”

Forras: JE. Lisman es MAP. Idiart Science 1995


Fazis precesszio – a hely kodolasa

A hippokampalis megfigyeltek olyan sejteket (helysejtek, place cells), melyek csak a kornyezet egyadott helyen (hely mezo, place field) aktıvak. Ezek mind aktivitasuk nagysagaval, mind az akciospotencialok, hippokampalis theta oszcillaciohoz viszonyıtott fazisaval kodoljak az allat helyet.




Navigacio: STDP (spike timing dependent plasticity) – az egymas utani helysejtek kozotti szi-napszisok megerosodnek. Az, hogy mikor ki ki utan kovetkezik, az attol fugg, hogy milyen irany-bol jon az allat. A szinapszisokat lehet modulalni az un.

”head-direction sejtek” aktivitasaval.




Felfedezes, a cel iranyanak hozzarendelese a helyhez es mozgas a cel fele

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Forras: O. Trullier and JA Meyer, Biological Cybernetics 2000


A tanıtas es az elohıvas szetvalasztasa

Forras: MA Hasselmo et al., Neural Computation 2002

Tanıtas: eros kulso input, gyenge rekurrens dinamika, rekurrenseken LTP, piramissejtek hiper-polarizalva (csak a nagy serkentest kapok tudjanak tuzelni).Elohıvas: gyenge EC bemenet, rekurrens dinamika dominal, nincs LTP, piramissejteken diszin-hibicio.


Elektromos halak

• Gyengen elektromos halak: zavaros vi-zekben elnek (Amazonasz, Nılus ...)

• Vizibolhakkal taplalkoznak.

• Elektromos szerv: modosult izom vagyidegsejtek, nehany tucat mV-os elekt-romos mezo.

• Nagy axonok egymassal parhuzamosanfutnak, es szinkronizalt aktivitast mu-tatnak.

Forras: Erik Harvey-Girard, http://www.apteronote.com


Elektromos halak

• Erzekeles: π-unitok az egesz borben,de foleg a fejen.

• Ketfele receptor: T a frekvencia es Paz amplitudo detektalasara.

• Mind a denever az ultrahanggal, ok isıgy erzekelik a korulottuk levo vilagot(kepesek elkapni a vizibolhakat).



Elektromos halak

Kommunikacio a halak kozott: JAR jamming avoiding reflex eltekeri a frekvenciajat.Ciripeles: rovid amplitudo es frekvencia-modulalt egysegek, feltehetoen kommunikacios cellal.



mit jelentenek a szavak? - cneuro.rmki.kfki.hucneuro.rmki.kfki.hu/files/oszc.pdf · 2006. 11....

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