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nature neuroscience • volume 4 no 3 • march 2001 223

Network oscillations of neuronshave a dual role in neurobiology: forthe investigator, probing from theoutside, they are a sign of brainstate, and they also have functionalrelevance to the organism itself.Thus, network oscillations can sig-nal a stage in the sleep/wake cycle1,2,or the occurrence of a spatiallystructured response to sensoryinput3. Network oscillations alsoprovide a rhythmic output to bedelivered to a motor system4. Anexample of the latter is the lobsterstomatogastric ganglion, a structurewith a limited number of neurons,each with extensively studied intrin-sic properties. Considerable infor-mation is also available on theintercellular connectivity of the net-work, both in terms of chemicalsynapses and gap junctions. As isthe case for many, if not all, physi-ologically useful network oscilla-tions, the output of thestomatogastric ganglion dependscritically (but not necessarily exclu-sively) on synaptic inhibition.

To understand the mechanismsgoverning a network oscillator, it isnecessary to proceed on two levels.First, one needs to consider thedynamics of the system when para-meters such as cellular membraneproperties and maximal synapticconductances are held constantover time. What determines thedegree of synchrony in such a sys-tem (how many cells fire per cycle),the phase relationships between thedifferent neurons, and whether or notthe same circuit generates multiple

the subject of a modeling paper by Soto-Treviño and colleagues5 in this issue.

The authors present data suggestingthat plasticity in hyperpolarizinginhibitory conductances could con-tribute to the functionally useful pat-terning of neurons participating in anetwork oscillation5. The authors con-sider a three-cell representation of a neu-ronal network in the lobsterstomatogastric ganglion (the pyloric net-work). Two of the model cells corre-spond to real neurons in the ganglion,whereas one of the model cells is a lump-ing together of two real neurons. The

basic intrinsic properties of theneurons (for example, whether ornot they tonically depolarize whenisolated) are built into the model.All of the synaptic connections areinhibitory. Some simplifications aremade, such as the removal of actionpotentials and the use of purelyvoltage-graded transmitter release.The problem for the model to‘solve’ is to reproduce the knownphase relationships that the realneurons produce during an oscilla-tion, under conditions where thesynapses are plastic. Such phaserelationships are important to theanimal, because the output of thissystem is used to drive a mechani-cal system—part of the digestivesystem—whose pieces must movetogether in a functionally efficientmanner.

The authors construct a learn-ing rule, that is to say, a scheme formodifying the synaptic conduc-tances at contacts between neurons.This learning rule is implementedas a differential equation for modi-fying each synaptic conductance,which depends upon calcium cur-rents and concentrations (‘targetvalues’ of these quantities are set inadvance by the modeler), and onmembrane potentials; learningtakes place on a time scale slowerthan that of the oscillation per se.The assumptions are biologicallyplausible. For example, intracellu-lar calcium signals are known to beinvolved in mediating plasticitysuch as long-term potentiation

(LTP) and depression (LTD)6. Second,transient spontaneous increases in intra-cellular calcium, occurring on two dif-ferent time scales, seem to be critical forneuronal differentiation in embryonicXenopus spinal cord7, implying that slowmodifications in cell properties, medi-

rhythms? Next, one needs to ask whathappens when some of the above para-meters vary over time: is it possible that,in a self-organizing fashion, physiologi-cally relevant features in the oscillationdynamics will emerge, and in a stableand robust way? This latter question is

Could plasticity ofinhibition pattern pattern generators?Roger D. Traub

A modeling study shows that inhibitory synapse plasticity,guided by simple activity-dependent rules, can lead toappropriate phase relationships within an oscillating network.

The author is at the University of BirminghamMedical School, Division of Neurosciences,Birmingham, B15 2TT, UK.email: r.d.traub@bham.ac.uk

Fig. 1. Evidence for synaptic plasticity during an afferent-evoked network oscillation in the hippocampal slice.Oscillations were evoked by stimulating simultaneously at twosites in CA1, about 2 mm apart, and they appeared at a latencyof 50–150 ms after the end of the stimulus. (a) Simultaneouslyrecorded field potentials at the two sites. The initial oscillationis at 36 Hz (gamma frequency), which then switches to aslower rhythm at about 15 Hz (beta frequency). Both phasesare synchronized between sites, to within 1.2 ms. (b) Simultaneous recordings from two hyperpolarized pyrami-dal cells, one at each site, during an oscillation such as that in(a), showing oscillatory EPSPs. The EPSPs grow in amplitudeduring gamma, then remain approximately fixed during beta.Pharmacological blockade of these EPSPs prevents the switchto beta15. Reprinted with permission from ref. 12, copyright(1997) National Academy of Science, USA.

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224 nature neuroscience • volume 4 no 3 • march 2001

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ated by calcium, can indeed occur bio-logically. Finally, transmitters such asGABA and glycine, which are inhibito-ry in the adult, act in neural circuitsearly in development to generate popu-lation oscillations; it must be noted,however, that at early stages these trans-mitters are excitatory. Examples of thislatter phenomenon include the hip-pocampus8 and the spinal cord9. Theoscillations in hippocampus, occurringspontaneously over just a few days inneonatal rats, are associated with largetransient fluctuations in intracellular cal-cium10, and are believed to be importantin development.

What is remarkable is that, from awide basin of initial conditions of thesynaptic conductances, the system con-verges to a stable oscillatory pattern withphase relationships that match thoseobserved in the real animal. The resulthas implications for how this system,and perhaps other oscillating networks,could develop as the individual animalitself develops: fix the intrinsic proper-ties of the neurons, and then let thesynaptic conductances find their appro-priate values emergently.

That synaptic inhibition varies overthe course of several episodes of anoscillation, and probably has function-ally relevant effects, is known fromstudies of the locust olfactory system.In this system, odor presentation leadsto 20–30 Hz network oscillations inantennal lobe projection neurons, aswell as local neurons. Different spa-tiotemporal patterns of firing, super-imposed on the oscillation, are evokedby different odors. With repeated pre-sentation of the same odor, however,there is an alteration in the globalresponse, with reduced overall firing,but with a tighter and more precise tem-poral organization of firing, amongthose neurons that do fire. This changein system dynamics is associated withenhancement of synaptic inhibitorypotentials generated by activity in thelocal neurons11.

An important question concerns howthe ideas of Soto-Treviño and colleagueson self-organization in oscillating net-works, and on possible critical roles ofintracellular calcium, might apply to ver-tebrate network oscillators, whichinvolve much larger population of neu-

distributed network of many neurons—when axonal conduction delays are longenough (over 10 ms), two coupled, butspatially separated, oscillatory subsys-tems tend to oscillate in antiphase. Heb-bian plasticity in this system, however,allows the oscillation to switch abruptlyfrom antiphase to in-phase, a patternthat can then persist. For this switch tooccur, inhibition needs to becomeenhanced. In the model, this plasticityoccurs both in the outputs of local-con-necting interneurons, and in theenhancement of synaptic excitation ofinterneurons by distant principal neu-rons. As in the study of Soto-Treviñoand colleagues, the network expressionof the plastic changes consists of analteration in the relative phases of different neurons participating in theoscillation.

1. Llinás, R. & Ribary, U. Proc. Natl. Acad. Sci.USA 90, 2078–2081 (1993).

2. Steriade, M. Cereb. Cortex 7, 583–604(1997).

3. Singer, W. & Gray, C. M. Annu. Rev.Neurosci. 18, 555–586 (1995).

4. Harris-Warrick, R. M., Marder, E.,Selverston, A. I. & Moulins, M. (eds.)Dynamic Biological Networks. TheStomatogastric Nervous System (MIT Press,Cambridge, Massachusetts, 1992).

5. Soto-Treviño, C., Thoroughman, K. A.,Marder, E. & Abbott, L. F. Nat. Neurosci. 4,297–303 (2001).

6. Cormier, R. J., Greenwood, A. C. & Connor,J. A. J. Neurophysiol. 85, 399–406 (2001).

7. Gu, X. & Spitzer, N. C. Dev. Neurosci. 19,33–41 (1997).

8. Ben-Ari, Y., Cherubini, E., Corradetti, R. &Gaiarsa, J.-L. J. Physiol. (Lond.) 416, 303–325(1989).

9. Nishimaru, H., Iizuka, M., Ozaki, S. &Kudo, N. J. Physiol. (Lond.) 497, 131–143(1996).

10. Garaschuk, O., Hanse, E. & Konnerth, A. J. Physiol. (Lond.) 507, 219–236 (1998).

11. Stopfer, M. & Laurent, G. Nature 402,664–668 (1999).

12. Whittington, M. A., Traub, R. D., Faulkner,H. J., Stanford, I. M. & Jefferys, J. G. R. Proc.Natl. Acad. Sci. USA 94, 12198–12203(1997).

13. Doheny, H. C., Faulkner, H. J., Gruzelier, J. H., Baldeweg, T. & Whittington, M. A.Neuroreport 11, 2629–2633 (2000).

14. Tallon-Baudry, C., Bertrand, O., Peronnet, F.& Pernier, J. J. Neurosci. 18, 4244–4254(1998).

15. Traub, R. D., Whittington, M. A., Buhl, E. H., Jefferys, J. G. R. & Faulkner, H. J. J. Neurosci. 19, 1088–1105 (1999).

rons. One cannot answer this questiondefinitively without considerable furtherwork, but certain data suggests that theideas may be generalizable. For example,certain oscillations in the mammalianbrain could be relevant to memory, andmight have self-organizing propertiesthat result from plasticity in inhibitorycircuits, and calcium is likely to be crit-ical.

Thus, for example, oscillations hav-ing frequencies in the tens of Hz (includ-ing gamma or ‘40 Hz’) may setconditions for synaptic plasticity tooccur11,12, exhibit a pattern that is his-tory dependent13, and be useful forworking memory14. Such memory-likefeatures are likely to be related, bothfunctionally and mechanistically. Forexample, as plasticity of excitatorysynaptic conductances occurs over hun-dreds of milliseconds, during a gamma(30–70 Hz) oscillation, the pattern of theoscillation switches abruptly to a lowerfrequency (10–25 Hz), superimposed ona subthreshold oscillation at the originalgamma frequency15 (Fig. 1). Theseexperimental data show that synapticconductances can actually change dur-ing the course of an oscillation in amammal, and influence the form of theoscillation. At least some of the memo-ry-like features of oscillations are longlasting, relative to the period of the oscil-lation. For example, consider the case ofelectrically evoked gamma/beta oscilla-tions in the hippocampal slice. In thispreparation, a single period of beta oscil-lation, lasting one or two seconds over-all, affects the structure and synchronyof subsequent evoked oscillations formany minutes12,15.

The example described above con-cerns plasticity of EPSPs in principalneurons. In addition, however, plasticityof inhibitory circuits, in principle, couldinfluence the structure of gamma oscil-lations in mammals. Thus, LTP and LTDof both excitatory and inhibitory con-nections have been studied with networksimulations (A. Bibbig & R.D. Traub,Soc. Neurosci. Abstr. 26, 736.3, 2000),motivated by a problem arising withgamma oscillations that are synchro-nized in the human brain over distancesof many centimeters, distances whereinaxonal conduction delays are likely to besignificant. In our model—a spatially

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