Modeling Rhythms_from Physiology to Function_SfN09

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Modeling Rhythms:from Physiology to Function

Nancy Kpll, PhD,1 Rgr D. Traub, MD,2and Mils A. Whittingtn, PhD3

1Center for Biodynamics

Department of Mathematics and Statistics, Boston UniversityBoston, Massachusetts

2Department of Physical Sciences, IBM T. J. Watson Research Center

Yorktown Heights, New York3Institute of Neuroscience

The Medical School, University of Newcastle-upon-TyneNewcastle-upon-Tyne, United Kingdom


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Mdling Rhythms: frm Physilgy t Functin

IntroductionThe central issues o this course are the roles thatneocortical rhythms play in health and sickness.This and the previous chapter, by R. Traub and M.

Whittington, deal with computational modeling,

but rom dierent perspectives. Although much oRoger Traubs work has been devoted to very detailedmodels o biophysical phenomena, some o the work

he is describing in this course, and the work in thischapter, can be considered reduced; that is, it ocuseson specic aspects o the extraordinary complexity o

neural circuits that give rise to brain rhythms. In theprevious chapter, the main aim was to understand the

origins o very ast oscillations (VFOs). The authorsmade the case that the centrally important details

concern network topology and that the physiologicalunderpinnings o the dynamics have less importance.This chapter aims to connect mechanisms o lower

requency rhythms with unctions o brain rhythms.Here the properties o the intrinsic and synaptic

currents turn out to be the heart o the story, withthe anatomy playing a much smaller role.

I ocus here on cell assemblies, a phrase that denotescollections o neurons that re in approximate

synchrony or a short period o time, whether or notthese cells have direct synaptic connections. About

20 years ago, W. Singer and C. Gray presented datasuggesting that the gamma oscillation is related to

the binding o dierent kinds o input in early sensoryprocessing (Gray et al., 1989; Singer and Gray, 1995).

Since then, a burgeoning literature has appearedthat discusses the association o brain rhythms withvarious tasks and the biophysical underpinnings o

the various kinds o brain rhythms. Thus, it is timelyto reconsider how brain rhythms (considered more

broadly than just the gamma rhythm) can participatein binding, that is, the creation, protection, andinteraction o cell assemblies. Modeling plays an

essential role in this reconsideration by ocusingattention on those properties o brain circuitry

and physiology that are most important or issueso binding.

Brain Rhythms and MechanismsBrain rhythms cannot be completely characterizedby their requencies, nor can any given unction be

mapped to a single requency (see the chapter by C.Tallon-Baudry, Rhythms in Cognitive Processing).

The classical requency ranges delta (14 Hz),theta (48 Hz), alpha (911 Hz), beta1 (1218

Hz), beta2 (1930 Hz), and gamma (3090 Hz)were taken rom EEG studies o human patients invarious experimental paradigms; as such, they were

associated with topography and behavior as well as

requency. For example, the classical alpha rhythmis ound in the posterior part o the brain when the

subject has eyes closed. Now that many more waysare available to probe or rhythms in animal as well

as human subjects, the boundaries among requency

bands has blurred, creating conusion about whatshould be considered dierent rhythms.

I suggest that a better way to distinguish among

rhythms is to consider the dynamical mechanismsunderlying any given oscillatory pattern. (Later on,

I will give examples o what I mean by dynamicalmechanism.) In dierent animals, or even withindierent brain structures, the same mechanism can

correspond to diverse requencies. Further, the samerequency rhythms may be produced by multiple

mechanisms. Mechanisms give important clues tounction, allowing us to see why dierent rhythms

may be used or dierent unctions. The physiologyassociated with the dierent dynamical mechanismsis taken largely rom in vitro work (as discussed in

the chapter by M. Whittington, Diverse Originso Network Rhythms in Cortical Local Circuits).

However, what is known about in vivo rhythms iscompletely consistent (Atallah and Scanziani, 2009;

Cardin et al., 2009). The computational modelingbridges the data we have rom the in vitro modelswith the behavioral data rom in vivo models.

Excitation, Inhibition, and

Synchronization at GammaFrequenciesBecause the ormation o cell assemblies involves

synchronization o neurons, the latter is a goodplace to start. Both excitation and inhibition cangive rise to synchronization, though in dierent

ways. A large pulse o excitation resets cell spikingby causing the cells to spike almost immediately.

Counterintuitively, however, it is inhibition thatis more eective, especially in the context o noisy

inputs. The inhibition hyperpolarizes or shuntsinputs or a relatively xed period that depends on

the baseline excitability o the cell and the size o

the IPSPs, determining the time until the nextspikes (Ermentrout and Kopell, 1998). Noisy inputs

have much less eect than they would have had ithe synchronization were by excitation. This eect

o common inhibition is likely the basis o phaseresetting, which is seen when excitation triggers a

pulse o inhibition (Talei Franzesi et al., 2009).

All the network-based versions o the gamma rhythm

appear to depend on this property o commoninhibition (Whittington et al., 2000). I will discuss


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only those or which excitation plays an importantrole, since these are the ones most relevant to cell

assemblies. Pyramidal interneuronal network gamma(PING) is induced in vitro by tetanic stimulation o

hippocampal slices. In PING, the stimulation is higherrequency than gamma; when the stimulation is over,

the network keeps ring at a gamma requency or ashort time. During this brie period, the excitatory

pyramidal cells re on each cycle, as do the inhibitoryast-spiking interneurons (Whittington et al., 2000).Although this gamma requency was produced in

the hippocampus, it is believed that the essentialelements are the same in neocortex.

In its most basic incarnation, PING is a simple

interaction o an excitatory cell (pyramidal) and aninhibitory cell (ast-ring interneuron, e.g., basketcell). We reer to these as E-cells and I-cells. The

excitation rom the pyramid causes the I-cells to spike,which inhibits both cells, and the cycle begins again

when the inhibition wears o. The only currentsother than synaptic ones that are important here are

the standard spiking currents. This is partly becausethe high-voltage regime in which gamma rhythmoccurs makes inhibition-induced currents such as

Ih and IT irrelevant, and because other currents aremuch smaller than the spiking and synaptic currents.

This oscillation has also been studied in larger sparse,heterogeneous networks (Borgers and Kopell, 2003).

The I-cells synchronize their target population, theE-cells; in turn, the E-cells synchronize the I-cells

more crudely, but enough to add to the process.

Another kind o gamma rhythm is induced in vitro,

not by tetanic stimulation but by bath applicationo kainate, a glutamatergic agonist, and/or carbachol,

a cholinergic agonist. The result is a network statein which E-cells re once in a while, rather noisily,but the rhythm is kept going by the I-cells, with the

help o some E-cells during each cycle (Traub etal., 2005). This state can be achieved when there

is a signicant amount o noise in the system, thecells are relatively excitable, but there is no massive

input to a subset o cells. A very similar state is

achieved with acetylcholine in the bath. This kindo gamma rhythm has been modeled by R. Traub

and colleagues, using axo-axonal gap junctions (seethe previous chapter by Traub and Whittington).

In the simpler model used in this chapter, the cellsare one-compartment (no plexus), and the needed

noise is described phenomenologically, rather thanconstructed rom a more detailed network (Borgerset al., 2005). Some o us associate this state with a

background attentional state, or a state o vigilance,whereas the PING state is associated with cell

assemblies within this background state. Modelinghas shown that activating a background rhythm

allows smaller input to create cell assemblies (Borgerset al., 2005).

Gamma Oscillations andCell AssembliesMany researchers, starting with Wol Singer, have

related gamma rhythms to the ormation o cellassemblies. Indeed, gamma oscillations appearprominently exactly at the time and place binding

would be highly desirable, e.g., during early sensoryprocessing. An understanding o the physiological

origin o PING shows why gamma rhythmicity isperectly suited to the creation o cell assemblies.

E-cells with enough excitability to re in a givencycle do so, activating the inhibitory cells, whichthen suppress the other E-cells. This sequence o

events creates a cell assembly, which does not changeas long as the input is the same. The essential reason

is that the PING mechanism o gamma rhythmicityis tied to the decay time o inhibition, which is

the longest time constant in the network duringgamma oscillations. (Other subthreshold currentsplay a much smaller role in the high-voltage ranges

associated with PING.) From cycle to cycle, there isno memory, and the same cells that are activated in

one cycle remain activated as long as the input is thesame (Olusen et al., 2003).

Cell assemblies that are ormed in this way competewith one another i they share interneurons, a

property that is very useul or the involvement ogamma rhythms in attention (Borgers et al., 2005,

2008; Borgers and Kopell, 2008). I some streamo input is given to a subset o E-cells in a network

displaying background gamma, then that set canorm a cell assembly. I a somewhat larger input is

subsequently given to another subset o E-cells, thering o the rst subset is suppressed. The competitiontakes place via the inhibitory cells that are shared in

the network. Although such lateral inhibition canbe done without rhythms, modeling work shows

why gamma rhythms make this competition moreecient (Borgers et al., 2005).

Another way in which gamma oscillations createcompetition is by allowing individual cells to

respond only to inputs that are highly coherent andlocking out other inputs o similar amplitude that are

less coherent. The reason or this selectivity comes,as beore, rom the ne timing o the inhibition

within the target E-I network: The inputs rom thedistractor come when there is a signicant amounto inhibition locked to the primary input, and the


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eects are shunted (Borgers and Kopell, 2008). Thelarger the distractor, the more inhibition is needed.

This eect happens only when the inputs all withinthe gamma requency range, since the gamma band

is tied to the decay time o inhibition. Each time the

chosen E-cells re, they create a bath o inhibitionthat lasts the length o the gamma cycle. Thus,

gamma is excellent or creating cell assemblies thatlock out competing cell assemblies that share ast-

ring interneurons. However, this property makes thegamma rhythm less useul or situations in which it is

important to bind multiple kinds o inormation.

The Dynamical Mechanisms ofSomatosensory Beta1To understand what other rhythms might be doing

in the creation, protection, and interaction o cellassemblies, it is useul to look at the physiology

underlying the rhythms. For the beta rhythm,Im going to ocus on the versions o the beta1and beta2 requency bands ound in the rodent

secondary somatosensory system (S2) (discussed inthe chapter by M. Whittington, Diverse Origins o

Network Rhythms in Cortical Local Circuits). S2 isparticularly interesting because it is a parietal regime

associated with multimodal interactions. Here, too,an understanding o the dynamical mechanisms

underlying the rhythms helps to illuminate theunctional properties o those rhythms.

As discussed by Whittington, the supercial layers oS2 produce a persistent gamma rhythm in vitro, with

kainate in the bath. This is modeled as describedearlier, though we also add other interneurons known

to be ound in the supercial layers, specically, low-threshold spiking (LTS) neurons. These tend to bealmost silent in the supercial mini-slices during

gamma rhythm, but when input rom the deep layerscauses them to re, they can interere with gamma

rhythm. The beta2 rhythm in the deep layers survivesthe blocking o all synaptic receptors, so it is not a

network phenomenon like gamma (Roopun et al.,2006). Thus, the beta2 rhythm is essentially a single-

cell phenomenon, with the gap junctions helpingto coordinate the cells. The deep 25 Hz rhythm isbursty, and its period is governed by an M-current

that builds up and shuts o the burst (Roopun et al.,2006; Kramer et al., 2008).

In the model, intrinsically bursting (IB) cells in thedeep layers connect to both kinds o inhibitory cells;

these are the ascending connections. The descendingconnections go rom the LTS cells to the apical

dendrites o the deep IB cells. The connections areweak enough to allow the two rhythms to coexist

without much disturbance. The layers do disturbone another and, in both experiment and model,

the power is somewhat attenuated when the twolayers interact. The nonspiking currents in the

various compartments play a more important role

in the beta rhythms than in the gamma rhythms.This is especially true o the h-currents in the IB

cell dendrites, the regular spiking (RS) neurons, andthe LTS cells. Inhibition turns on these currents and

encourages rebound bursting, which is critical or thebeta1 rhythm as we understand it.

What causes the switch rom supercial gamma/deepbeta2 dynamics to beta1 dynamics in all the layers?

We suggest that, during the ast gamma and beta2o the oscillation, there is plasticity, increasing the

recurrent excitatory connections o the deep IB cells.However, the plasticity by itsel does not cause the

switch, which also requires the later removal o thedrive to cells. We model the removal o the kainateby hyperpolarizing axons and dendrites o IB cells,

and all the supercial cells, because all these areknown to be depolarized by kainate. The eect o the

removal is to create a concatenation o gamma andbeta2, and a disappearance o the individual rhythms

(also discussed in the Whittington chapter). Theburst o IB cells, now more coherent because o theplasticity, activates the supercial inhibitory cells.

The E-cells re on a rebound rom this inhibition aterabout 25 ms. This causes the LTS cells to re, which

inhibits the dendrites, and the IB cells then re rom

a rebound about 40 ms later. As in the experiments,the 40 ms period o the beta2 portion o the beta1requency is determined by dendritic dynamics o theIB cells rather than by the axonal dynamics or the

deep layer beta2 when the slice was more activated.Although this sequence o events seems extremely

complicated, the model and experiments haveyielded matching conclusions (Kramer et al., 2008).

Beta1 Rhythms and CellAssembliesIn vivo beta1 appears to be a rhythm that is displayed

ater the exciting stimulus is gone (Tallon-Baudry etal., 1999; Haenschel et al., 2000). The physiologyassociated with the in vitro beta1 rhythm has many

implications or cell assemblies (Kopell et al.,2009) that t well with what is known about beta2

rhythms ound in vivo in behaving animals. Theseimplications contrast with properties o the PINGoscillation. Unlike the latter, i more (tonic) input is

ed into some cells that are part o a beta1 assembly,the activation o those cells does not lead to a

suppression o the others; rather, they orm a separatecell assembly within the old one, ring at additional


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phases. I dierent streams o input enter dierentsubsets o cells, even at dierent levels o excitation,

these can combine to orm a cell assembly within theold beta assembly. Thus, the beta1 context allows

cell assemblies to represent simultaneously bothpast and present, and to do so in ways that allow or

multimodal inputs.

Another property o cell assemblies ormed ina network displaying beta1 is that the assemblycan build up over time: As a sequence o inputs

comes and goes, leaving behind groups o cellsparticipating in dierent beta rhythms, those cells

can sel-organize into a single assembly. Finally,in the beta1 mode in the rodent S2, the deep and

supercial layers have coherent timing. This eatureis important or a multimodal structure that interactswith other structures in relation to which the deep

and supercial layers o S2 can be either input oroutput layers.

The ability to not compete comes rom the physiology

o the beta1 rhythm. In contrast with the gammarhythm (in which the supercial inhibitory cells aretimed by the supercial excitatory rhythms), in beta1,

the supercial inhibitory cells are timed mainly bythe deep IB cells. The ability to maintain an assembly

ater the initial signal is gone results rom the reboundnature o each part o the concatenation: Once the

pattern is set up, it does not need to be activated anyurther. Since the h-current is modulated by many

substances, this rebound is easily controlled. Allthese properties o the physiology underlying thebeta1 rhythm enable supercial excitatory cells to

interact in a completely dierent way than in PING,allowing or fexible manipulation o cell assemblies.

Coordinating Cell AssembliesSo ar, we have suggested that the PING version ogamma rhythmicity is eective or producing and

protecting cell assemblies, and that the beta1 versiono the multimodal areas is an excellent context or

manipulating such assemblies ater the initial signalis gone. Another aspect o computing with cell

assemblies is coordinating them. Modeling work romthe hippocampus suggests that the theta rhythm canbe involved in coordinating cell assemblies that were

initially created in the context o gamma rhythms.Specically, the oriens-lacunosum moleculare

(O-LM) cells can cause assemblies o cells ring atgamma requencies to synchronize (Tort et al., 2007).

This can occur even i the cell assemblies are notdirectly connected with one another via pyramidalcells or ast-ring interneurons. These O-LM cells

are known to re at theta-range requencies and

to participate in theta requency rhythms in vitroeven in the absence o excitatory input (Gillies et

al., 2002; Rotstein et al., 2005). This observationsuggests a dierent role or the well-known nesting o

gamma oscillations within theta rhythms (Chrobakand Buzsaki, 1998; Harris et al., 2003): Rather

than providing slots or dierent cell assemblies inthe theta period (Jensen and Lisman, 1996), the

gamma system creates cell assemblies that are thencoordinated within the theta oscillation. The LTScells o the neocortex might play a similar role

(Gibson et al., 1999).

The interaction o multiple rhythms is an active eldo study. In vivo studies (Lakatos et al., 2008) have

documented the nesting o neocortical rhythms,especially delta, alpha, and theta rhythms in restinganimals. A hypothesis rom this work is that the

slower rhythms provide windows in which the otherrhythms are activated. How this might work or

coordinating cell assemblies is not yet understood; ata airly crude level, it could certainly allow multiple

inputs to be active simultaneously or to gate thedierent inputs so that they cannot interact (Lakatoset al., 2007; C. Schroeder chapter herein, Aligning

the Brain in a Rhythmic World). The slowerrhythms might also act to coordinate cell assemblies

that display gamma requency rhythms, as in thehippocampal example. Another kind o interaction

is n:m phase coupling (Palva and Palva, 2007),which would coordinate activity without giving rise

to constant phase relationships.

The actual requencies may also be important

or interactions o dierent subsets o cells. Fromsimpler models o oscillations, it is well known that

oscillators with similar requencies can phase-lockin a 1:1 ashion, and that sucient dierences inrequency make this impossible. For large, network-

based oscillations, no theory is yet adequate.However, research seems to suggest that dierences in

requencies associated with various mechanisms mayindeed be important or determining which pathways

are most eective under particular circumstances

(Middleton et al., 2008). Dierences in requenciesthemselves are also thought to be a mechanism or

phase precession (Geisler et al., 2007).

We do not adequately understand many propertieso interacting network oscillators. However, the

more we learn about the physiology o rhythms andthe implications o the physiology or networks,the better we will be able to fesh out the ways

in which the nervous system uses these propertiesor cognition.


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Modeling Rhythms_from Physiology to Function_SfN09