# Short-term plasticity optimizes synaptic information transmission.

**ABSTRACT** Short-term synaptic plasticity (STP) is widely thought to play an important role in information processing. This major function of STP has recently been challenged, however, by several computational studies indicating that transmission of information by dynamic synapses is broadband, i.e., frequency independent. Here we developed an analytical approach to quantify time- and rate-dependent synaptic information transfer during arbitrary spike trains using a realistic model of synaptic dynamics in excitatory hippocampal synapses. We found that STP indeed increases information transfer in a wide range of input rates, which corresponds well to the naturally occurring spike frequencies at these synapses. This increased information transfer is observed both during Poisson-distributed spike trains with a constant rate and during naturalistic spike trains recorded in hippocampal place cells in exploring rodents. Interestingly, we found that the presence of STP in low release probability excitatory synapses leads to optimization of information transfer specifically for short high-frequency bursts, which are indeed commonly observed in many excitatory hippocampal neurons. In contrast, more reliable high release probability synapses that express dominant short-term depression are predicted to have optimal information transmission for single spikes rather than bursts. This prediction is verified in analyses of experimental recordings from high release probability inhibitory synapses in mouse hippocampal slices and fits well with the observation that inhibitory hippocampal interneurons do not commonly fire spike bursts. We conclude that STP indeed contributes significantly to synaptic information transfer and may serve to maximize information transfer for specific firing patterns of the corresponding neurons.

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**ABSTRACT:**Bistability within a small neural circuit can arise through an appropriate strength of excitatory recurrent feedback. The stability of a state of neural activity, measured by the mean dwelling time before a noise-induced transition to another state, depends on the neural firing-rate curves, the net strength of excitatory feedback, the statistics of spike times and increases exponentially with the number of equivalent neurons in the circuit. Here we show that such stability is greatly enhanced by synaptic facilitation and reduced by synaptic depression. We take into account the alteration in times of synaptic vesicle release, by calculating distributions of inter-release intervals of a synapse, which differ from the distribution of its incoming inter-spike intervals when the synapse is dynamic. In particular, release intervals produced by a Poisson spike train have a coefficient of variation greater than one when synapses are probabilistic and facilitating, whereas the coefficient of variation is less than one when synapses are depressing. However, in spite of the increased variability in postsynaptic input produced by facilitating synapses, their dominant effect is reduced synaptic efficacy at low input rates compared to high rates, which increases the curvature of neural input-output functions, leading to wider regions of bistability in parameter space and enhanced lifetimes of memory states. Our results are based on analytic methods with approximate formulae and bolstered by simulations of both Poisson processes and of circuits of noisy spiking model neurons.Journal of mathematical neuroscience. 12/2013; 3(1):19. - Amanda E Hernan, Abigail Alexander, Kyle R Jenks, Jeremy Barry, Pierre-Pascal Lenck-Santini, Elena Isaeva, Gregory L Holmes, Rod C Scott[Show abstract] [Hide abstract]

**ABSTRACT:**There is a well-described association between childhood epilepsy and pervasive cognitive and behavioral deficits. Often these children have not only ictal EEG events, but also frequent interictal abnormalities. The precise role of these interictal discharges in cognition remains unclear. In order to understand the relationship between frequent epileptiform discharges during neurodevelopment and cognition later in life, we developed a model of frequent focal interictal spikes (IIS). Postnatal day (p) 21 rats received injections of bicuculline methiodine into the prefrontal cortex (PFC). Injections were repeated in order to achieve 5 consecutive days of transient inhibitory/excitatory imbalance resulting in IIS. Short-term plasticity (STP) and behavioral outcomes were studied in adulthood. IIS is associated with a significant increase in STP bilaterally in the PFC. IIS rats did not show working memory deficits, but rather showed marked inattentiveness without significant alterations in motivation, anxiety or hyperactivity. Rats also demonstrated significant deficits in social behavior. We conclude that GABAergic blockade during early-life and resultant focal IIS in the PFC disrupt neural networks and are associated with long-term consequences for behavior at a time when IIS are no longer present, and thus may have important implications for ADHD and autism spectrum disorder associated with childhood epilepsy.Neurobiology of Disease 11/2013; · 5.62 Impact Factor - Xiao-Sheng Wang, Chun-Zi Peng, Wei-Jun Cai, Jian Xia, Daozhong Jin, Yuqiao Dai, Xue-Gang Luo, Vitaly A Klyachko, Pan-Yue Deng[Show abstract] [Hide abstract]

**ABSTRACT:**Transcriptional silencing of the Fmr1 gene encoding fragile X mental retardation protein (FMRP) causes fragile X syndrome (FXS), the most common form of inherited intellectual disability and the leading genetic cause of autism. FMRP has been suggested to play important roles in regulating neurotransmission and short-term synaptic plasticity at excitatory hippocampal and cortical synapses. However, the origins and mechanisms of these FMRP actions remain incompletely understood, and the role of FMRP in regulating synaptic release probability and presynaptic function remains debated. Here we used variance-mean analysis and peak-scaled nonstationary variance analysis to examine changes in both presynaptic and postsynaptic parameters during repetitive activity at excitatory CA3-CA1 hippocampal synapses in a mouse model of FXS. Our analyses revealed that loss of FMRP did not affect the basal release probability or basal synaptic transmission, but caused an abnormally elevated release probability specifically during repetitive activity. These abnormalities were not accompanied by changes in excitatory postsynaptic current kinetics, quantal size or postsynaptic α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor conductance. Our results thus indicate that FMRP regulates neurotransmission at excitatory hippocampal synapses specifically during repetitive activity via modulation of release probability in a presynaptic manner. Our study suggests that FMRP function in regulating neurotransmitter release is an activity-dependent phenomenon that may contribute to the pathophysiology of FXS.European Journal of Neuroscience 03/2014; · 3.75 Impact Factor

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Cellular/Molecular

Short-TermPlasticityOptimizesSynapticInformation

Transmission

ZivRotman,Pan-YueDeng,andVitalyA.Klyachko

DepartmentofBiomedicalEngineering,DepartmentofCellBiologyandPhysiology,CenterforInvestigationsofMembraneExcitabilityDisorders,

WashingtonUniversitySchoolofMedicine,St.Louis,Missouri63110

Short-termsynapticplasticity(STP)iswidelythoughttoplayanimportantroleininformationprocessing.ThismajorfunctionofSTPhas

recentlybeenchallenged,however,byseveralcomputationalstudiesindicatingthattransmissionofinformationbydynamicsynapsesis

broadband, i.e., frequency independent. Here we developed an analytical approach to quantify time- and rate-dependent synaptic

informationtransferduringarbitraryspiketrainsusingarealisticmodelofsynapticdynamicsinexcitatoryhippocampalsynapses.We

found that STP indeed increases information transfer in a wide range of input rates, which corresponds well to the naturally occurring

spikefrequenciesatthesesynapses.ThisincreasedinformationtransferisobservedbothduringPoisson-distributedspiketrainswitha

constantrateandduringnaturalisticspiketrainsrecordedinhippocampalplacecellsinexploringrodents.Interestingly,wefoundthat

the presence of STP in low release probability excitatory synapses leads to optimization of information transfer specifically for short

high-frequencybursts,whichareindeedcommonlyobservedinmanyexcitatoryhippocampalneurons.Incontrast,morereliablehigh

release probability synapses that express dominant short-term depression are predicted to have optimal information transmission for

singlespikesratherthanbursts.Thispredictionisverifiedinanalysesofexperimentalrecordingsfromhighreleaseprobabilityinhibitory

synapsesinmousehippocampalslicesandfitswellwiththeobservationthatinhibitoryhippocampalinterneuronsdonotcommonlyfire

spikebursts.WeconcludethatSTPindeedcontributessignificantlytosynapticinformationtransferandmayservetomaximizeinfor-

mationtransferforspecificfiringpatternsofthecorrespondingneurons.

Introduction

Short-term plasticity (STP) acts on millisecond-to-minute time-

scales to modulate synaptic strength in an activity-dependent

manner. STP is widely believed to play an important role in syn-

aptic computations and to contribute to many essential neural

functions, particularly information processing (Abbott and Re-

gehr, 2004; Deng and Klyachko, 2011). Specific computations

performed by STP are often based on various types of filtering

operations (Fortune and Rose, 2001; Abbott and Regehr, 2004).

This generally accepted role of STP in information processing has

been challenged recently by several computational studies aimed at

directlycomputingSTPinfluenceoninformationtransferusingan

information-theoretic framework (Lindner et al., 2009; Yang et al.,

2009). Although earlier studies have shown that information trans-

fer is dependent on release probability (Zador, 1998), which is di-

rectly modified by STP, Lindner et al. (2009) used a generalized

model of STP to show that information transfer by dynamic syn-

apsesisfrequencyindependent,nomatterwhethersynapsesexpress

dominant facilitation or depression. Similar results obtained using

moredetailedmodelsofthecalyxofHeldsynapsealsodemonstrated

that information transmission is predominately broadband

(Yang et al., 2009). These studies suggested that STP does not

contribute to frequency-dependent information filtering and

raised the question of what specific roles STP plays in synaptic

information transmission.

One common feature of these computational studies, how-

ever, is that they considered only steady-state conditions that

synapses reach after prolonged periods of high-frequency stimu-

lation. Although this is a physiologically plausible condition, it

reflects the strained state of the synapses when significant

amounts of their resources, such as the readily releasable pool

(RRP)ofvesicles,havebeenexhausted.Thisisnotrepresentative,

for instance, of excitatory CA3–CA1 synapses, which typically

experience rather short 15- to 25-spike-long high-frequency

bursts separated by relatively long periods of lower activity (Fen-

tonandMuller,1998).Infact,lessthanhalfoftheRRPistypically

used at any time during such naturalistic activity (Kandaswamy

et al., 2010) with nearly complete RRP recovery between the

bursts. This discrepancy between the strained state of synapses

used in analytical calculations of information transmission and

the realistic state of the synapses during natural activity suggests

that more representative conditions need to be considered to

evaluate STP contributions to information processing.

We therefore developed an analytical approach to calculate

the time and rate dependence of synaptic information transmis-

ReceivedJune24,2011;revisedJuly29,2011;acceptedAug.15,2011.

Author contributions: Z.R. and V.A.K. designed research; Z.R. and P.-Y.D. performed research; Z.R. and V.A.K.

contributedunpublishedreagents/analytictools;Z.R.,P.-Y.D.,andV.A.K.analyzeddata;Z.R.andV.A.K.wrotethe

paper.

ThisworkwassupportedinpartbyagranttoV.K.fromtheWhitehallFoundation.WethankDr.ValeriaCavalli

andDianaOwyoungfortheirconstructivecommentsonthemanuscript.

CorrespondenceshouldbeaddressedtoVitalyA.Klyachko,DepartmentofCellBiologyandPhysiology,Depart-

mentofBiomedicalEngineering,425S.EuclidAvenue,CampusBox8228,WashingtonUniversitySchoolofMedi-

cine,St.Louis,MO63110.E-mail:klyachko@wustl.edu.

DOI:10.1523/JNEUROSCI.3231-11.2011

Copyright©2011theauthors 0270-6474/11/3114800-10$15.00/0

14800 • TheJournalofNeuroscience,October12,2011 • 31(41):14800–14809

Page 2

sion using a realistic model of STP in excitatory hippocampal

synapses. Indeed, using more realistic conditions, we found that

STP contributes significantly to increasing information transfer

over a wide frequency range. Furthermore, our time-dependent

analysis indicated that STP optimizes information transmission

specifically for short high-frequency spike bursts in low release

probability synapses, and that this optimization shifts from

bursts to single spikes in high release probability synapses. We

verified these predictions using recordings in excitatory and in-

hibitory hippocampal synapses with corresponding properties.

OurstudythusdirectlyestablishestheroleofSTPininformation

transmission within the information-theoretic framework and

shows that STP works to optimize information transmission for

specific firing patterns of the corresponding neurons.

MaterialsandMethods

Animals and slice preparation. Horizontal hippocampal slices (350 ?m)

were prepared from 15- to 25-d-old mice using a vibratome (VT1200 S,

Leica). Both male and female animals were used for recordings. Dissec-

tions were performed in ice-cold solution that contained the following

(in mM): 130 NaCl, 24 NaHCO3, 3.5 KCl, 1.25 NaH2PO4, 0.5 CaCl2, 5.0

MgCl2, and 10 glucose, saturated with 95% O2and 5% CO2, pH 7.3.

Slices were incubated in the above solution at 35°C for 1 h for recovery

and then kept at room temperature (?23°C) until use. All animal pro-

cedures conformed to the guidelines approved by the Washington Uni-

versity Animal Studies Committee.

Electrophysiological recordings. Whole-cell patch-clamp recordings

were performed using an Axopatch 200B amplifier (Molecular Devices)

from CA1 pyramidal neurons visually identified with infrared video mi-

croscopy (BX50WI, Olympus; Dage-MTI) and differential interference

contrast optics. All recordings were performed at near-physiological

temperatures (33–34°C). The recording electrodes were filled with the

following (in mM): 130 K-gluconate, 0.5 EGTA, 2 MgCl2, 5 NaCl, 2

ATP2Na, 0.4 GTPNa, and 10 HEPES, pH 7.3. The extracellular solution

contained the following (in mM): 130 NaCl, 24 NaHCO3, 3.5 KCl, 1.25

NaH2PO4,2CaCl2,1MgCl2,and10glucose,saturatedwith95%O2and

5%CO2,pH7.3.Inallexperiments,NMDAreceptorswereblockedwith

AP5 (50 ?m) to prevent long-term effects. EPSCs were recorded from

CA1pyramidalneuronsataholdingpotentialof?65mVbystimulating

Schaffer collaterals with a bipolar electrode placed in the stratum radia-

tum ?300 ?m (range ?200–500 ?m) from the recording electrode.

EPSCs recorded in this configuration represent an averaged synaptic

response across a population of similar CA1–CA3 synapses. The same

recording configuration was previously used to provide experimental

supportfortherealisticmodelofSTP(Kandaswamyetal.,2010)usedin

thecurrentstudy.Notethatunderourexperimentalconditions,receptor

desensitization and saturation are insignificant, and voltage-clamp er-

rorsarealsosmallanddonotprovideasignificantsourceofnonlinearity

(WesselingandLo,2002;KlyachkoandStevens,2006b).Therefore,post-

synapticresponsescanbeusedasalinearreadoutoftransmitterreleasein

the relevant frequency range.

Datawerefilteredat2kHz,digitizedat20kHz,acquiredusingcustom

software written in LabVIEW, and analyzed using programs written in

MATLAB. EPCSs during the stimulus trains were normalized to an av-

erage of five low-frequency (0.2 Hz) control responses preceding each

traintoproviderelativechangesinsynapticstrength.Eachstimulustrain

waspresentedfourtosixtimesineachcell,andeachpresentationwassepa-

rated by ?2 min of low-frequency (0.2–0.1 Hz) control stimuli to allow

completeEPSCrecoverytothebaseline.TocorrectfortheoverlapofEPSCs

atshortinterspikeintervals(ISIs),anormalizedtemplateofEPSCwaveform

was created for each stimulus presentation by averaging all EPSCs within a

given train that were separated by at least 100 ms from their neighbors and

normalized to their peak values. Every EPSC in the train then was approxi-

matedbyatemplatewaveformscaledtothepeakofthecurrentEPSC,andits

contributiontosynapticresponsewasdigitallysubtracted.

The natural stimulus trains used in this study represent the firing

patterns recorded in vivo from the hippocampal place cells of awake,

freelymovingrats(generouslyprovidedbyDrs.A.FentonandR.Muller,

StateUniversityofNewYork,Brooklyn,NY)(FentonandMuller,1998).

Spikes with ISIs ?10 ms were treated as a single stimulus, because the

delay between the action potential firing and the peak of postsynaptic

currents/potentials prevented resolution of individual synaptic re-

sponses at shorter ISIs. Such treatment does not significantly affect syn-

aptic responses to natural stimulus trains, as we have shown previously

(Klyachko and Stevens, 2006a).

Analytical framework for analysis of information transmission by dy-

namic synapses. Information theory provides a general framework to

quantify information transfer in any system based on the principles of

Shannon (1948). Our approach described below is an extension of the

previousworkofZador(1998)toanalyticallycomputethecontributions

of STP to information transfer based on these principles. Synaptic infor-

mation transmission can be measured by how much information the

output spike train provides about the input train, which is termed “mu-

tual information” (Shannon, 1948). Within the information-theoretic

framework,thispropertyisdefinedformallyintermsofensembleentro-

pies.Theentropyisabasicmeasureininformationtheoryandisgivenby

the following:

H?x? ? ??P?xi?log2?P?xi??,

where P?xi? is the probability of variable x to have the value xi. The

synaptic mutual information Imdepends on the input (also termed

“source”) spike train’s entropy, H?s?, the entropy of output spike trains

(or of synaptic responses) H?r?, and their joint entropy H?r, s?, and by

definition is given by the following:

(1)

Im ? H?r? ? H?s? ? H?r, s? ? H?r? ? H?r ? s?, (2)

where H?r ? s? is a conditional entropy of the output given the inputs,

whichreflectsvariabilityofoutputforrepeatedpresentationsofthesame

input. In practical terms, this means that variability of synaptic output

for the multiple presentations of the same input represents an inherent

“noise” in transmission and does not carry information, because it can-

not distinguish between two different inputs.

The realistic model of STP we used to describe synaptic dynamics in

the hippocampal synapses (Kandaswamy et al., 2010) is formulated to

predict changes in synaptic release probability during a random spike

input. The term “release probability” (Pr) is commonly used to describe

probability of vesicle release given a presynaptic spike. If we describe the

existing/nonexisting presynaptic spike as s ? 1/0, and denote a vesicle

that is released/not released as r ? 1/0, then the release probability is

Pr? P?r ? 1 ? s ? 1?.Inourcalculationswewilldistinguishbetween

the term Pr, the synaptic release probability, and another probability

variable, p ? P?r ? 1?, which simply represents the probability of

synaptic response at a given time. The relation between these two vari-

ables is determined by the stimulation rate, p ? R ? Pr, where R is the

presynaptic firing rateP?s ? 1?. The advantage of chosen STP formula-

tion is that it allows direct comparison to experimental measurements

(Kandaswamy et al., 2010) and provides a useful framework for the cal-

culationoftheinformationtransmission.Specifically,whenanensemble

ofsourcespiketrainswiththesameproperties(e.g.,constantrate)isused

as an input to the STP model, a resulting distribution of release proba-

bilities, f?p, t?, at each point in time can be calculated. The output of

individual synapses is determined by the release of a vesicle, which is

controlledstochasticallybythereleaseprobabilitypatanygivenpointin

time.Sincethesynapseeitherreleasesavesicleoritdoesnot,thesynaptic

response (r) is thus a binary-state system at each point in time. Applica-

tion of Equation 1 to calculate mutual information for this simplified

binary-state system gives the following:

H ? ? plog2?p? ? ?1 ? p?log2?1 ? p?, (3)

wherepistheprobabilitytobeinonestateand(1?p)istheprobability

to be in the other (notice that the expression is symmetrical regarding

assignment of the two states ?p 3 1 ? p?. Also note that the above

formulation is derived in assumption of a monovesicular release. Our

previous computational analyses (Kandaswamy et al., 2010) indicated

Rotmanetal.•InformationTransferbySynapticDynamics J.Neurosci.,October12,2011 • 31(41):14800–14809 • 14801

Page 3

that models of STP in hippocampal synapses described the experimental

data equally well in assumption of either a monovesicular release or

multivesicular release in case the number of active release sites does not

change significantly during elevated activity levels. Given these previous

results, and because the extent of multivesicular release in hippocampal

synapsesandthequantitativerelationshipbetweenmultivesicularrelease

and release probability have not been established, we will limit our anal-

ysis to the monovesicular release framework.

For synaptic transmission, the entropy of vesicle release and thus of

synaptic response, H?r?, is determined by the release probability of the

synaptic ensemble, and is given by the following:

H?r? ? ? R?Pr?log2?R ? ?Pr?? ? ?1 ? R ? ?Pr??

log2?1 ? R ? ?Pr??,(4)

where ?. . .? denotes the ensemble averaged value, and R is the input

stimulus rate.

To calculate the second term, H?r ? s?, in Equation 2, we take into

accountthatforeachindividualresponseinagiventrain,asinglevalueof

p is drawn from the distribution. Therefore, the expression for H?r ? s? is

the average of Equation 3 with the distribution function f?p, t?. This

means that for each point in time a different distribution f?p, t? is

calculated,thereleaseprobabilitypisrandomlyselectedforthattime,

and then the binary-state entropy (Eq. 3) is calculated for that time

point. The resulting expression for conditional entropy is then given

by the following:

H?r ? s? ??f?p, t?? ? plog2?p? ? ?1 ? p?log2?1 ? p??dp.

(5)

Note that the averaging in Equation 5 is the ensemble averaging over

available input spike trains. Expression 5 can be further simplified by

noticing that if p ? 0 is randomly selected, then H(r) in Equation 4 is

exactly 0; then we can exclude the case of no stimulation from Equa-

tion5.Formally,thiscanbedonebyexpressingthereleaseprobability

distribution function f?p, t? as a sum of two contributions given by

the following:

f?p, t? ? ?1 ? R??p,0 ? R ? f˜?p ? s ? 1, t?,(6)

where the first component represents a contribution when there is no

stimulation and the second component represents a contribution when

stimulation is present. From Equations 5 and 6 a simplified expression

for the conditional entropy can thus be derived as follows:

H?r ? s? ? ? R ??f˜?p, t??plog2?p? ? ?1 ? p?log2?1 ? p??dp.

(7)

In an individual input train, there will be R stimuli per unit of time, and

each of these will contribute according to the release probability at that

time. In the case of ensemble entropy, each time point contributes

equally,becausewithinthecompleteensembleofinputsthereisanequal

probabilitytorandomlypickaninputspiketrainthatcontainsaspikeat

that time point. The main difference between full ensemble entropy and

conditional entropy is then determined by the choice of specific firing

times.Thismeansthatinthiscalculationthemainsourceofinformation

carriedbytheinputtrainisdeterminedbythespiketimingwithinatrain.

The mutual information, a measure of transferred information, can

now be simply calculated using Equations 4 and 7 as follows:

Im?t? ? ? R?Pr?log2?R ? ?Pr?? ? ?1 ? R ? ?Pr??log2?1 ? R ? ?Pr??

? R ??f˜?p, t??p log2?p? ? ?1 ? p?log2?1 ? p??dp. (8)

To verify this derivation, we can check our formalism for a few simple,

time-independent cases. For the perfectly reliable synapse (Pr? 1),

f˜?p, t? ? ??p ? 1?, which leads to zero conditional entropy. This is

exactlytrueforthissimplecasebecausetheoutputisexactlydetermined

by the input, and although different trains produce different responses,

single stimulation produces only one and the same single response.

The mutual information is then the full entropy of the input given by

Im? H?r? ? H?s? ? ? Rlog2?R? ? ?1 ? R?log2?1 ? R?.

FortheoppositecaseofPr?0,theresponseentropyiszerosincethere

is only one response to any input. When?Pr? ? 0 is used in Equation 4,

the resulting entropy is 0.

For any other constant release probability Pr? p0, we can calculate

the rate-dependent entropy as H?r? ? ? ?p0? R?log2?p0? R? ?

?1 ? p0? R?log2?1 ? p0? R?. The conditional entropy has a sim-

plified expression in this case, because the integration of Equation 7 can

be performed exactly as follows: H?r?s? ? ?R??p0?log2?p0? ? ?1 ?

p0?log2(1 ? p0?].

Because all of the above analysis was performed for a single point in

time (binned time), the resulting Equation 8 thus measures the mutual

information per unit time. We can also define mutual information per

spike by dividing Equation 8 by the stimulation rate R and define the

average cumulative mutual information as the following:

Icumulative?

1

T ? R?

0

T

Im?t?dt,(9)

which measures the average information transfer per unit time,

within a period of time from 0 to T. It is important to point out that in

the case of a static, constant Prsynapse mutual information and av-

erage cumulative mutual information are exactly the same because

they are time independent.

Note that the exact values of bits of information transmitted are de-

pendent on the chosen bin width of time and the release probability, so

that if we assume a more precise Pror spike-timing measurements, their

information contents will increase. We will therefore consider relative

changesinfunctionalbehaviorduetothepresenceofSTPbycomparing

information transmission in a model of a dynamic synapse to informa-

tion transmission by a synapse with a constant Pr(i.e., no STP); both are

analyzed using exactly the same procedures.

Inaddition,thechosenmodeldoesnotconsidermultivesicularrelease

orthenaturalvariabilityintheamountofreleasedneurotransmitterbya

single vesicle. Because there are no clearly established mechanisms that

control these processes, they can only be modeled as randomly distributed

effects. All such processes therefore would not contribute to information

transfer,andintheinformationtheoryformalismtheircontributionwillbe

subtractedaspartofH?r? s?.

Computational analysis. For simulation of the effects of STP on the

information transfer of the CA3–CA1 excitatory synapse, we used our

recentlydevelopedrealisticmodelofSTP,whichshowsacloseagreement

with experimental measurements at this synapse in rat hippocampal

slices (Kandaswamy et al., 2010). This model accounts for three compo-

nents of short-term synaptic enhancement (two components of facilita-

tion and one component of augmentation) and depression, which is

modeled as the depletion of the ready releasable vesicle pool using a

sequential two-pool model. To determine the model parameters in a

wide frequency range, we performed an extensive set of recordings of

synaptic responses in the CA1 neurons in mouse hippocampal slices at

stimulus frequencies of 2–100 Hz. Model parameters were then deter-

minedbyfittingthisexpandedexperimentaldatasetasdescribedbyKan-

daswamy et al. (2010). The model was then able to successfully predict

synaptic responses for arbitrary stimulus patterns.

In the first part of our study, constant-rate Poissonian spike trains

were used. An ensemble of 6400 short trains was simulated for each rate.

Train duration was chosen to achieve the ensemble average number of

spikes in the train equal to 100. This timescale was chosen to match the

existingexperimentaldataonconstantfrequencyandnaturalspiketrain

14802 • J.Neurosci.,October12,2011 • 31(41):14800–14809Rotmanetal.•InformationTransferbySynapticDynamics

Page 4

responses(KlyachkoandStevens,2006a;Kandaswamyetal.,2010).Since

the quantitative information theory analysis requires discretization of

continuousparameters,wechosereleaseprobabilitystepsof0.1andtime

steps of 3 ms. Time steps were chosen to limit the minimum allowed ISI

to experimentally and physiologically realizable cases.

Results

Analyticalcalculationofinformationtransmissionbya

dynamic synapse

Careful experimental analysis of synaptic information transmis-

sion requires testing a prohibitively large number of possible in-

putspiketrains.Asaresult,directexperimentalmeasurementsof

information transfer are not currently feasible. Rather, studies of

synaptic information transmission are performed mostly by com-

puter simulations using models of synaptic dynamics (Markram et

al., 1998b; Zador, 1998; Fuhrmann et al., 2002; Silberberg et al.,

2004b; Lindner et al., 2009; Yang et al., 2009). Computationally,

synaptic information transmission can be estimated within the

information-theoretic framework by calculating the mutual infor-

mation (Shannon, 1948) that reflects how much information the

output spike train provides about the input train. To examine the

contributionsofSTPtosynapticinformationtransfer,wedeveloped

an analytical approach to calculate both the rate and time depen-

dence of mutual information in a dynamic synapse in terms of the

entropy of the synaptic response itself H(r) (Eq. 4) and the condi-

tionalentropyofthesynapticresponsegiventheinput(Eq.7).This

approach is an extension of the earlier formalism originally devel-

opedbyZador(1998).

To examine synaptic dynamics that closely approximate the

experimental data, we derived the entropy terms as a function of

the input spike rate and synaptic release probability (Eq. 8). The

release probability during input spike trains was determined

basedonarealisticmodelofSTPthatwedevelopedpreviouslyfor

excitatory hippocampal synapses (Kandaswamy et al., 2010). To

determinethemodelparametersinawide

frequency range, we performed a set of

recordings of synaptic responses in the

CA1 neurons in mouse hippocampal

slicesatstimulusfrequenciesof2–100Hz.

The observed synaptic dynamics closely

followed our previous recordings in the

rat slices (Klyachko and Stevens, 2006a,b)

(data not shown). Parameters of the

model were determined as we previously

described (Kandaswamy et al., 2010).

With this optimal set of parameters, the

model has been shown to accurately pre-

dict all key features of synaptic dynamics

duringnaturalspiketrainsrecordedinex-

ploring rodents (Kandaswamy et al.,

2010). The basal Prvalue in the model

was set to 0.2, which represents the

meanreleaseprobabilityinthesesynapses

(Murthy et al., 1997). It is important to

note that although Pris typically low in

these synapses, it is distributed across a

significant range of values in the popula-

tion of hippocampal synapses. We there-

foreassumedtheaveragevalueofPr?0.2

in our first set of calculations, but then

performed a detailed robustness analysis

of the information transmission and of

our results as a function of all major

model parameters, including the range of

Prvalues from 0.05 to 0.4, which includes a large proportion of

the synaptic population (Dobrunz and Stevens, 1997; Murthy

et al., 1997) (see text and Fig. 4).

Previousanalysesofsynapticinformationtransferconsidered

the steady-state conditions that synapses reach after prolonged

high-frequency stimulation (Lindner et al., 2009; Yang et al.,

2009)andwerethustimeindependent.Becausesuchsteady-state

conditions might not be fully representative of the state in which

synapses operate during natural activity levels, the contribution

ofSTPcouldhavebeenobscuredinsuchtime-independentanal-

yses if this contribution has a strong temporal component. We

thus focused on deriving and using a time-dependent formalism

to capture such time-dependent effects.

TheroleofSTPininformationtransferduringconstant-rate

Poissonspike trains

We first applied our time-dependent formalism to examine

information transmission by a dynamic synapse during

constant-rate, Poisson-distributed spike trains. As expected,

the information transmission showed a clear dependence on the

input rate (Fig. 1) similarly to the previous report (Zador, 1998).

Most importantly, we found that information transfer was

greater in the presence of STP than for the constant basal Pr(i.e.,

no STP present) for a wide range of input rates, ?1–40 Hz (Fig.

1).Thisisthecaseforboththemutualinformationperspike(Fig.

1A) and the mutual information per unit of time (Fig. 1B). At

low input rates, 0.01 ? R ? 0.1, at which STP contribution is

small and does not significantly alter release probability, infor-

mation transmission follows the same line as that for constant

basalPr?0.2value;however,asinputrateincreases,information

transfer grows faster in the presence of STP, reaching levels that

nearly double information transmission at basal Prvalue. The

range of input rates at which STP contributes to information

Figure1.

(A)orperunitoftime(B)forastaticsynapseforarangeofPrvaluesshown(blacktraces)andtheaveragecumulativemutual

informationIcumulativeforadynamicsynapsewithabasalPr?0.2(redtraces).Icumulativewasdeterminedfor100-spike-longtrains

ateachrate(seeMaterialsandMethodsfordetails).Notethatinthecaseofastatic,constantPrsynapse,mutualinformationand

Icumulativeare exactly the same since they are time independent. The presence of STP increases information transferred by the

dynamicsynapseinawidefrequencyrangeabovethatofastaticsynapsewiththesamebasalreleaseprobability.

Informationtransmissionforconstant-ratePoisson-distributedinputspiketrains.A,B,Mutualinformationperspike

Rotmanetal.•InformationTransferbySynapticDynamics J.Neurosci.,October12,2011 • 31(41):14800–14809 • 14803

Page 5

transfer is comparable to the range of fre-

quencies found in natural spike trains

(Fenton and Muller, 1998; Leutgeb et al.,

2005). Thus, STP clearly increases infor-

mationtransferinarate-dependentman-

ner, unlike the findings in previous

reports (Lindner et al., 2009; Yang et al.,

2009).Thisresultarisesinpartfromusing

a realistic model of STP that closely ap-

proximates synaptic dynamics in excit-

atory hippocampal synapses and in part

from performing time-dependent analy-

sis. The latter has shown that the steady-

statesynaptic response

analyzed in information transmission

studies may not be representative, at least

in the case of the hippocampal excitatory

synapses,ofthestatethatsynapsesassume

during physiologically relevant activity.

commonly

Optimizationofinformation

transmissionbySTP

inunreliable synapses

IfSTPplaysaroleininformationprocess-

ing, then the time dependence of the in-

formation transfer may determine the

optimal length and structure of the input

spiketrain.Indeed,analysisofshortinput

trainlengths(Fig.2A)showedaclearpeak

of information transmission for trains of

?4–20spikes(withapeakat4to6spikes)

at all rates above ?16 Hz. Lower rates

showed an increase toward the steady-

statemutualinformationvalue,butunder

these conditions mutual information

grew with rate independently of the train

length. Higher rates and long train lengths showed convergence

to a common universal value, suggesting that under the condi-

tions approaching the steady state the mutual information is

broadband, as previously reported (Yang et al., 2009). The same

resultswerealsoobtainedwhencumulativeinformationtransfer

was examined for different input rates (Fig. 2B). For cumulative

informationtransfer,thepeakshiftedto9–12spikes(Fig.2B,D),

as expected when we factored in the added contribution from

the several initial spikes that occurred when information

transfer was low.

To evaluate the benefits of such optimization, we compared

mutual information for the optimal train length at a given firing

ratefordynamicsynapsesversusstaticsynapseswitharangeofPr

values. In the case of dynamic synapses with a basal Pr? 0.2,

information transmission for the optimal length spike train was

equivalent to that of a static synapse with twice higher Pr? 0.4

(Fig. 2C). Together, these results show that STP in low release

probability excitatory synapses not only increases information

transmission in a rate-dependent manner, but it also leads to

optimization of information transfer for short spike bursts that

are indeed commonly observed in excitatory hippocampal neu-

rons (Leutgeb et al., 2005).

Informationtransmissionduringnaturalspike trains

To examine whether these information transmission principles

playaroleinamorerealisticsituation,weexaminedinformation

transmissioninamodelofexcitatoryhippocampalsynapsesdur-

ing natural spike patterns recorded in hippocampal place cells of

freely moving and exploring rodents (Fenton and Muller, 1998).

These spike trains represent the patterns of inputs that the

excitatory hippocampal synapses are likely to encounterinvivo

(Leutgeb et al., 2005). To be able to apply our formalism to an

arbitrary spike train with varying rates, we needed to transform

the input train into a time-dependent rate r(t) and produce a

correspondingensembleofinputspiketrains,makingtheprecise

analysis of information transfer very time intensive. The analysis

of information transfer can be simplified, however, by eliminat-

ing the need for ensemble measurements if the expression for

mutualinformationcanbeformulatedonlyasafunctionofmea-

sured values, such as Pr. We thus used an approximation for the

conditional entropy expression in Equation 7 by replacing the

averaging over values of release probability p, by its average, i.e.,

?Pr?, as follows:

H?r ? s? ? ? R??Pr?log2??Pr?? ? ??1 ? ?Pr??log2?1 ? ?Pr????.

(10)

Wethendeterminedtheaccuracyofthisapproximationbycom-

paring the exact amount of information transfer (given by Eq. 8)

forconstant-ratetrainsusingthepreciseexpressionforH?r ? s?in

Equation 7 versus its approximation in Equation 10. This ap-

proximation resulted in 95% accuracy or better in estimating

information transfer for stimulus trains shorter than ?40 spikes

atallratestested(0.01–72Hz),andfor100-spike-longtrainsatall

Figure 2.

synapse with a basal Pr? 0.2 is plotted versus spike number in the train. Information transmission is optimal for the short

high-frequencyspikeburstsandconvergestoauniversalsteady-statevalueatlongertraindurations.Numbersshownaboveeach

tracerepresenttherateofsynapticinput.B,SameasinAfortheaveragecumulativemutualinformationIcumulative.Thepeakof

optimal train length shifted toward the larger number of spikes, but the same overall optimization behavior is seen. Numbers

shownaboveeachtracerepresenttherateofsynapticinput.C,Thebenefitofoptimizingthetrainlengthforthechosenfiringrate.

If optimal train length is chosen, the dynamic synapse with a basal Pr? 0.2 can transfer information as efficiently as a static

synapse with Pr? 0.4. D, Peak position and width (calculated as a half-width above the steady-state level) of the average

cumulativemutualinformationIcumulative.Thepeaklocationcorrespondstooptimalburstlengthandthewidthdeterminesthe

specificityofthisoptimization.

Time dependence of synaptic information transmission. A, Time-dependent mutual information for a dynamic

14804 • J.Neurosci.,October12,2011 • 31(41):14800–14809Rotmanetal.•InformationTransferbySynapticDynamics

Page 6

rates ?56 Hz (Fig. 3A). The only input regimes in which larger

deviations were seen were outside the physiologically relevant

range of stimuli for these synapses. The accuracy of this approx-

imation suggests that the entropy held in the distribution f?p, t?

of p values is relatively small with respect to the main contribu-

tiontoentropy,whichisduetothespiketiminginthetrain.This

is not surprising considering that the probability of an action

potential firing at any given time point is very small. This notion

can be seen more easily using a simple example at a 1 Hz rate.

Sincewechosetimestepsof3msforouranalysis,therewere333

timepointsin1sandtherefore333possibledifferentspiketrains

all having the 1 Hz rate. The synapse can release with 1 of 10

possible values of release probability (since it is quantized with

0.1 steps), and in reality the values are constrained by the model

so the actual spectrum is even smaller. This explains why in our

approximation the variability arising from the spike timing is

much greater than that of the release probability distribution.

Estimation of information transfer during a natural spike train

using this simplification is based on the assumption that the

propertiesofaspecificnaturalspiketrainusedarerepresentative

of an ensemble of natural spike trains and that variability within

this ensemble is relatively small. Under this assumption, our

analysis shows that information transfer by a dynamic synapse

increases several-fold during spike bursts in the presence of STP

(Fig. 3B,C). The synaptic information transfer due to STP in

dynamicsynapseswiththebasalPr?0.2iscomparabletothatof

a static synapse with Pr? 0.4. This effect of STP is very similar to

the results seen for the optimal length spike train (Fig. 2C), sug-

gesting that natural spike trains in hippocampal neurons may be

optimized to transmit maximal information given the specific

dynamicsoftheirsynapses.Itisimportanttopointoutthatareal

synapse with a basal release probability of Pr? 0.4 is more likely

tohavedepression-dominatedSTP(DobrunzandStevens,1997;

Murthy et al., 1997), leading to an overall decrease of transferred

information (see Fig. 5 and text below). It is thus the tuning

between the natural spike train structure and the dynamic prop-

erties of excitatory hippocampal synapses that allows the en-

hancement of information transfer during natural spike trains.

Robustnessofinformationtransfer optimization

Although hippocampal excitatory synapses have a low average

releaseprobability,ithasawidedistributioninthesynapticpop-

ulation (Murthy et al., 1997). The expression of individual STP

components is interdependent with the release probability and

variesinamplitudeasafunctionofPr(ZuckerandRegehr,2002;

AbbottandRegehr,2004).Itisthereforeimportanttodetermine

to what extent our findings are robust regarding changes in re-

lease probability as well as in individual model parameters. We

thus performed the same analysis as described above for a range

ofmodelparameterswithina100%rangeofchanges(from?0.5

to ?2) in facilitation amplitude, augmentation amplitude, the

time course of RRP recovery that effectively controls depression

amplitude,andthesizeoftheRRP(Fig.4A–C).Wefoundthatall

ofourobservationsregardingtheroleofSTPinincreasinginfor-

mationtransfer,aswellastheoptimizationofinformationtrans-

fer for spike bursts, were not strongly dependent on the model

parameterswithintheserangesandheldtrueforallvaluestested.

This analysis also allowed us to examine the roles of different

forms of STP in optimization of information transfer. Specifi-

cally, we used three metrics to quantify information transfer op-

timization: the peak position (Fig. 4A), the peak width (Fig. 4B),

and the peak height (Fig. 4C). We found that the largest decrease

in both the peak position and width occurred when facilitation

amplitudewasincreased.Thiseffectwaspresumablyduetofaster

use of synaptic resources (vesicles) leading to faster and stronger

depression.Oppositeoftheseeffectsoffacilitation,wefoundthat

thelargestincreaseinpeakwidthoccurredwhenvesiclerecycling

time was decreased (Fig. 4A), increasing vesicle availability and

leadingtomuchsloweronsetofdepression.Similarly,increasing

thesizeoftheRRPproducedthelargestincreaseinpeakposition

(Fig. 4B) by effectively extending vesicle availability and thus

delaying the onset of depression. We further considered the con-

tributionsofSTPcomponentstothepeakheight(Fig.4C),which

represents one way of quantifying optimization strength. Our

analysisrevealedthatpeakheightreceiveditslargestcontribution

from the facilitation amplitude. This effect of facilitation is ex-

pectedsincethepeakoccursearlyduringthestimulustrain,when

synaptic dynamics is indeed dominated by facilitation.

Figure3.

imation for mutual information from exact numerical calculations. The approximation pre-

sented holds true with 95% accuracy for all firing rates between 0.01 and 56 Hz and train

durationsof100spikes,aswellasforspiketrainsshorterthan?40spikesatallratestested.For

spiketrainslongerthan?40spikesatratesof64Hzandabove,significantdeviationsappear.

The approximation accuracy is reduced when the model is stressed to the point when the

release probability during prolonged high-rate stimulation approaches zero. B, The average

cumulative mutual information Icumulativefor a natural spike train. Icumulativeshows rapid

changesduringnaturalspiketrainswithpeakscorrespondingtospikeburstsanddecayscorre-

spondingtoperiodsoflowactivity.Informationtransferinadynamicsynapsebasedonmea-

sureddatastartsaslowasforastaticsynapsewithaPr?0.2,butthenincreasesduringbursts,

duetoSTP,toreachtheperformanceofastaticsynapsewithaPr?0.4.C,Mutualinformation

perunittimeforthefirst70spikesinthetrainplottedforadynamicsynapsewithabasalPr?

0.2andstaticsynapsewithPrfrom0.2to0.4.Thedynamicsynapseexpressesawiderangeof

transferredinformationvaluesduringthenaturalspiketrainfromthatsimilartoastaticPr?

0.2synapsetoabovethatofstaticPr?0.4synapse.

Informationtransmissionforanaturalspiketrain.A,Relativedeviationofapprox-

Rotmanetal.•InformationTransferbySynapticDynamics J.Neurosci.,October12,2011 • 31(41):14800–14809 • 14805

Page 7

We also examined the robustness of

informationtransmission

changes in basal release probability in a

range from 0.05 to 0.4 (Fig. 4D), which

includes the majority of excitatory hip-

pocampal synapses (Murthy et al., 1997).

While the optimization of information

transmission was observed at all Prvalues

withinthisrange,wefoundstronginverse

dependence between optimization and Pr

such that the optimal length of the bursts

decreasedrapidlywithincreasingPr(from

35 spikes at Pr? 0.05, to 11 spikes at Pr?

0.2,to6spikesatPr?0.4).Itisimportant

to note that this analysis represents the

lower bound approximation in the sense

that in real synapses this dependence be-

tween the optimal peak position and Pris

likely to be even stronger. This is because

most of the current STP model parame-

ters have been determined from experi-

mental data that represent the averaged

behavior of CA3–CA1 synapses, i.e., the

synapse with a Pr? 0.2. Since functional

interdependencesbetweenPrandSTPpa-

rameters are not currently known, per-

forming this analysis at significantly

higher Prvalues would require determin-

ing a new set of model parameters based

on the experimental data recorded at

these increased Pr. As Prvalue increases,

the experimentally determined amplitudes of facilitation and

augmentation would decrease and amplitude of depression

would increase. These indirect effects of increasing the Prwould

further accentuate the dependence of optimization on release

probability, but they are not taken into account in our current

analysis,becausewevaryonlyoneparameter(inthiscasePr)ata

time. Based on these considerations, we limited our analysis to a

lower range of Prvalues (0.05–0.4, the range within which syn-

apticdynamicsremainsqualitativelysimilar)beforeitshiftsfrom

facilitation- to depression-dominated mode at higher Prvalues

(Dobrunz and Stevens, 1997).

Together, these results indicate that STP-mediated optimiza-

tion of information transmission in unreliable synapses is robust

within a relevant range of model parameters and within a lower

range of release probabilities that are predominant in excitatory

hippocampal synapses.

regarding

Predictionforinformationtransmissioninhighrelease

probabilitysynapsesandits verification

The above analysis suggests that STP-mediated optimization of in-

formation transmission for spike bursts holds for unreliable syn-

apses,butmightnotbepresentinhighreleaseprobabilitysynapses,

which are expected to have a dominant short-term depression. In-

deed,analysisofdepression-dominateddynamicsynapseswithaPr

? 0.5 (and no facilitation/augmentation) shows strong monoto-

nous decay of average cumulative mutual information with the in-

put rate (Fig. 5A). Even at 2 Hz, depressing synapse with a Pr? 0.5

transfers less information during a 150-spike-long train than the

static synapse with Pr? 0.4, and at 40 Hz the dynamic synapse

transferslessinformationthanastaticsynapsewithaPr?0.2.

Based on the above analysis, we predicted that in high release

probability synapses single spikes rather than bursts would be

expected to carry maximal information as the optimal burst

length would approach a value of 1 (Fig. 4D). To verify this

prediction, we took advantage of the fact that a large proportion

of inhibitory hippocampal synapses in the CA1 area have a high

release probability (Mody and Pearce, 2004; Patenaude et al.,

2005) and express dominant short-term depression (Maccaferri

et al., 2000). To examine information transfer in these synapses,

we used a series of measurements we previously performed in

CA1 inhibitory hippocampal synapses with constant-frequency

stimulation(KlyachkoandStevens,2006a).Theactualmeasured

values of synaptic strength during trains were used in these cal-

culations. We found that the average cumulative mutual infor-

mationdecreasedmonotonicallywiththelengthofthetrain,and

no optimization peak was observed at all frequencies examined

(Fig. 5B). This result confirms the prediction of our analysis and

suggeststhatforinhibitoryhippocampalneurons,optimalinfor-

mation transfer would take place when the train is composed of

singlespikesratherthanbursts.Thisfitswellwiththeobservation

that inhibitory hippocampal interneurons, unlike excitatory py-

ramidal cells, do not typically fire spike bursts (Connors and

Gutnick, 1990).

Discussion

We have examined the role of synaptic dynamics in information

transmissionbyestimatingthemutualinformationbetweensyn-

aptic drive and the output synaptic gain changes in a realistic

model of STP in excitatory hippocampal synapses. Our analysis

shows that the presence of STP leads to an increase in informa-

tion transfer in a wide frequency range. Furthermore, consider-

ations of the time dependence of information transmission

revealed that STP also determines the optimal number of spikes

in a train that maximizes information transmission. Specifically,

Figure 4.

informationwiththe2?changeofmodelparameters(augmentationamplitude,facilitationamplitude,numberofvesiclesinRRP

andrecycling(depression)timescale).Thepeakhalf-widthabovethesteady-statelevelwastakenasameasureforpeakwidth.The

stimulusrateof32Hzwasusedinthisrobustnessanalysis.B,C,SameasAforthechangesinpeaklocation(B)andheight(C).D,

Changesinpeakwidthwiththechangesofbasalreleaseprobability.

Robustness of information transmission optimization. A, Changes in peak width of average cumulative mutual

14806 • J.Neurosci.,October12,2011 • 31(41):14800–14809 Rotmanetal.•InformationTransferbySynapticDynamics

Page 8

in these low release probability synapses, information transmis-

sion is optimal for the short high-frequency spike bursts that are

indeed common in the firing patterns of excitatory hippocampal

neurons. When an optimal spike pattern is used as an input, the

informationtransferbythedynamicsynapseisequivalenttothat

ofastaticsynapsewithtwicegreaterbasalreleaseprobability.Our

analysis further showed strong dependence of this optimization

onthebasalreleaseprobabilityandpredictedthatthisoptimization

will reach unity (so that a single spike is optimal for information

transmission)atlargevaluesofPr,whensynapticdynamicsisdom-

inatedbyshort-termdepression.Weverifiedthesekeyobservations

usinganalysesofexperimentalrecordingsinlowreleaseprobability

excitatoryandhighreleaseprobabilityinhibitoryhippocampalsyn-

apses in brain slices. Our findings thus demonstrate that STP con-

tributes significantly to synaptic information processing and works

to optimize information transmission for specific firing patterns of

thecorrespondingneurons.

TheroleofSTPininformation transmission

The function of STP in information processing has been sug-

gested by numerous studies of visual and auditory processing

(Chance et al., 1998; Taschenberger and von Gersdorff, 2000;

Chung et al., 2002; Cook et al., 2003; DeWeese et al., 2005;

MacLeod et al., 2007) and of cortical/hippocampal circuit oper-

ations (Abbott et al., 1997; Markram et al., 1998a; Silberberg et

al., 2004a; Klyachko and Stevens, 2006a; Kandaswamy et al.,

2010). Specific computations performed by STP are often based

onfrequency-dependentfilteringoperationsandinclude,butare

not limited to, detection of transient inputs, such as spike bursts

(Lisman, 1997; Richardson et al., 2005; Klyachko and Stevens,

2006a) and abrupt changes in input rate (Abbott et al., 1997;

Puccinietal.,2007),synapticgaincontrol

(Abbott et al., 1997), input redundancy

reduction (Goldman et al., 2002), and pro-

cessing of population bursts (Richardson

et al., 2005).

Information theory provides a robust

quantitative framework to analyze the

roleofSTPininformationtransmissionat

synapsesandhasbeensuccessfullyusedin

several studies of synaptic processing

(Tsodyks and Markram, 1997; Varela et

al., 1997; Markram et al., 1998b; Tsodyks

et al., 1998; Zador, 1998; Maass and

Zador, 1999; Natschla ¨ger et al., 2001;

Fuhrmann et al., 2002; Goldman et al.,

2002; Loebel and Tsodyks, 2002). The

main complication of applying infor-

mation theory to address physiological

questions is its reliance on the analysis

of large ensembles of input spike pat-

terns, which require either prohibitively

largesetsofmeasurementsoracommit-

ment to simplifying assumptions. In the

pioneeringworkofZador(1998),calcu-

lations based on ISI distribution were

used to significantly reduce the number

of simulations needed. This simplifica-

tion assumes the time independence of

synapticresponsesandworkswellinap-

proximation of steady-state synaptic

conditions. This methodology, how-

ever, does not allow the correct analysis

of time-dependent information transmission by dynamic syn-

apses with rapidly changing release probability. By developing

an extension of this previous information theory formalism to

include time-dependent analysis, we were able to clearly demon-

strate the role of STP in increasing information transfer in a wide

rangeofinputfrequencies(Fig.1).

Thisresultwouldnotbeapparentinanalysesofthesteady-state

conditions that were used in previous studies of information trans-

missionbydynamicsynapses(Lindneretal.,2009;Yangetal.,2009)

and indeed led to different conclusions. Both studies, however, as-

sumedtime-independentinformationtransfer,anassumptionthat

we found obscured the contributions of STP, which have a strong

temporal component. In fact, we have shown, in agreement with

Yang et al. (2009), that for the significantly long trains, when syn-

apses reach a steady state, information transmission indeed con-

verges to the same unifying level, and there is a wide range of

stimulation rates that all exhibit the same information transfer.

Analysis of synaptic dynamics during natural spike trains (Fig. 3)

revealedthatthisregimeisnotcommonduringphysiologicallyrel-

evant activity levels, at least in the case of excitatory hippocampal

synapses. In addition, performing simulations under steady-state

conditions reduces the dynamic range of synaptic strength, which

mightcontributetothelackoffrequencydependence.

It is also important to note that our calculations were simpli-

fied by avoiding a postsynaptic neuron firing model, which is

usuallyintroducedasafinalstageofcalculations.Ourgoalwasto

keep our calculations as close to the experimental data as possi-

ble. The most commonly used model in similar studies is the

leak-integrate-and-fireneuron,whichintroducesalargenumber

of free parameters, avoids the nonlinear properties of dendritic

integration, and is difficult to verify experimentally (Burkitt,

Figure5.

tionperspikeforastaticsynapseforarangeofPrvaluesshown(blacktraces)andtheaveragecumulativemutualinformation

Icumulativeforadepression-dominatedhighreleaseprobabilitysynapse(Pr?0.5)(redtrace)plottedasafunctionoftheinputrate.

Icumulativeshowsastrongdecayasinputrateincreased.Atallratesabove1Hzdepressingsynapsewith(Pr?0.5)transfersless

informationduringa150-stimuli-longtrainthanthestaticsynapsewithPr?0.4.B,Averagecumulativemutualinformationwas

calculateddirectlyfromthepreviousexperimentalmeasurementsofsynapticdynamicsinCA1inhibitoryhippocampalsynapses

(KlyachkoandStevens,2006a).Thismutualinformationisplottedasafunctionofspikenumberinthetrainandshowsasteep

decreasewiththetrainlength.Nooptimizationforspikeburstsisobservedatanyofthefrequenciestested(2–40Hz)andmaximal

informationtransmissionisachievedatthefirstspikeinthetrain.

Timeandratedependenceofmutualinformationinhighreleaseprobabilitydepressingsynapse.A,Mutualinforma-

Rotmanetal.•InformationTransferbySynapticDynamics J.Neurosci.,October12,2011 • 31(41):14800–14809 • 14807

Page 9

2006; Brette et al., 2007; Paninski et al., 2007). A more realistic

approachtogeneratingoutputneuronspikingcouldbebasedon

a previous study of dendrite-to-soma input/output function of

the CA1 pyramidal neurons, demonstrating that this input–out-

put relationship could be modeled as a linear filter followed by

adapting static-gain function (Cook et al., 2007). Application of

such an approach would also require precise knowledge of how

multiple heterogeneous synaptic inputs interact and are spatially

integrated in the dendrites. Given the intricate spatiotemporal

dendritic processing (Spruston, 2008) and complexity of inter-

synaptic interactions over various timescales (Remondes and

Schuman, 2002; Dudman et al., 2007), the problem of linking

individual synaptic dynamics to the actual spiking output of a

neuronremainslargelyunresolved.Wethereforechosenottouse

a neuronal-spiking model. Moreover, if any neuronal-spiking

modelchangesinformation-transferpropertiesinarate-ortime-

dependent manner, it would be advantageous to study these ef-

fects independently of the choice of synaptic STP model. It thus

remainstobedeterminedhowinformationtransmissionatindi-

vidual synapses is modified by complex dendritic processing in

thepostsynapticneuron.However,giventhatanSTP-dependent

increase in synaptic information transfer is observed over a wide

frequencyrangeandishighlyrobust,wepredictthattheeffectsof

STP we observed at the level of synaptic output will also be qual-

itatively present at the level of actual spiking output of a neuron,

unlessdendriticfilteringstronglyattenuatessynapticsignalsover

this entire frequency range.

Optimizationofinformation transfer

The key finding of our study is the optimization of information

transmission by STP. In low release probability synapses, informa-

tion transmission is maximal for short high-frequency spike bursts

(Fig. 2). This result demonstrates that the short timescale, ?30

spikes,duringwhichthesynapsereachesitssteadystate,hasanon-

trivialtime-andrate-dependentcontributionofSTPtoinformation

transfer.Ournumericalcalculationsshowthatsynapsescanmodu-

latetheinformationtheytransferwithrespecttothelengthandthe

rateoftheinputspikepattern.Thismayleadtotheoptimizationof

information transfer for variable rate trains, such as natural spike

trains, if they are composed of constant-rate trains of a length that

maximizes information transfer at that rate. Our calculations thus

predictthatamixtureofinputrateswouldbeoptimalforinforma-

tion transmission when low-frequency trains of any length are

mixedwithshortburstsofhigh-ratefiringtomaximizetheinforma-

tion transfer of a synapse. This is indeed in agreement with the ex-

perimentally observed firing patterns of excitatory hippocampal

neurons(FentonandMuller,1998;Leutgebetal.,2005).

Based on the same optimization considerations, our analyses

predictedthathighreleaseprobabilitysynapseswouldhavemax-

imal information transmission when single spikes rather than

bursts are used as synaptic input. This effect arises from the

switch in synaptic dynamics from facilitation/augmentation to

depressionathighreleaseprobabilities(Figs.1,5).Thisinterpre-

tation is in agreement with a previous study (Goldman et al.,

2002) showing that depressing synapses reduces information re-

dundancy in spike trains. Indeed, when natural spike trains were

usedasaninputtodepressingstochasticsynapses,theyexhibited

reduced autocorrelation of spike timing, which is equivalent to

our finding of optimization by single spikes. It is tempting to

speculate that STP expression might have evolved in part to op-

timizeinformationtransmissioninthefiringpatternsofthecor-

responding neurons, as seems to be the case for both excitatory

andinhibitoryhippocampalsynapses.Alternatively,itispossible

thattheadaptationpropertiesofneurons,whichdeterminetheir

bursty firing patterns, might have evolved in part to optimize

informationtransfergiventheexistenceofSTP.Futurestudiesof

informationtransmissionusingmoredetailedmodelsofsynaptic

dynamics in other neural systems will reveal the extent to which

this principle applies to other types of synapses, or whether it is

specific to a subset of circuits or to certain types of information

transmitted.Theseanalyseswillalsorequireabetterunderstand-

ing of information encoding, which currently limits application

of information theory to a wider variety of synapses and circuits.

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