What is the appropriate description level forsynaptic plasticity?Harel Z. Shouval1

Department of Neurobiology and Anatomy, University of Texas Medical School at Houston, Houston, TX 77030

The hypothesis that learningmemory and some aspects ofdevelopment are mechanisticallyimplemented by synaptic plastic-

ity has gained significant experimentalsupport (1, 2). At the cellular and molec-ular level synaptic plasticity is a verycomplex phenomenon, involving hundredsof molecular species, depending on thestructure of dendrites and on ion channelconcentrations. If we are to understandhow high-level processes arise from syn-aptic plasticity, and not simply that theyarise from synaptic plasticity, we mustknow how to best characterize plasticitytheoretically. Such a characterizationshould account for key experimental re-sults, yet at the same time it should be assimple as possible so that we can use itto explain how plasticity can lead tolearning and memory. The article byGjorgjieva et al. (3) in PNAS argues thata sufficient model of synaptic plasticity candepend only on spike pairs and tripletsand that more-complex biophysical andmolecular processes might not be needed.It also shows a correspondence betweenthis triplet-based rule and the well-knownphenomenological Bienenstock CopperMunro (BCM) learning rule (4).Many of the early theories of synaptic

plasticity were not formulated on the basisof low-level experimental evidence. In-stead, they were motivated by the con-sequences of plasticity observed at ahigher level, for example receptive fieldplasticity in visual cortex. To accountfor such high-level plasticity, theoristspostulated phenomenological low-levelmechanisms that can account for suchhigher-level phenomena. In the mid-1970svon der Malsburg (5) proposed rate-basednetwork models that included synapticplasticity and competition between cells toaccount for the formation of orientationselectivity and ocular dominance maps invisual cortex. The plasticity model heused was very simple: synaptic potentia-tion that is proportional to the product ofpresynaptic and postsynaptic activity vari-ables, coupled with a normalization of thetotal synaptic weight. Later work hasshown the limitations of this plasticitymodel (6). The BCM model (4) was alsoformulated to explain receptive field plas-ticity in visual cortex, and like other rate-based phenomenological models, is for-mulated in terms of abstract pre- andpostsynaptic activity variables. The BCM

theory (Fig. 1A) is based on two principles,formulated by two equations. First, theplasticity equation:

dwi

dt¼ xiϕðy; θmÞ [1]

states that the change of the synaptic ef-ficacy (wi) in synapse i is a product ofthe presynaptic activity (xi) and a non-linear function (ϕ) of the postsynaptic ac-tivity (y). The ϕ function is negative atlow values of y and becomes positive wheny exceeds the modification threshold (θm).The second principle, metaplasticity (7),

which states the modification threshold

(θm) is modifiable, serving as a negativefeedback, is implemented in the equation:

θm ¼ �y1þμ

�t; [2]

where the angled brackets denote a slidingtemporal average, and μ > 0 ensures sta-bility (4). In Fig. 1A we show the formof the ϕ function for two different levels ofthe modification threshold.The BCM theory can indeed account for

the formation of orientation selectivityand ocular dominance of cortical neuronsin natural image environments and forvarious different deprivation experiments(6). Furthermore, the assumptions ofBCM have influenced experimental stud-ies of synaptic plasticity (8). However,it is difficult to tightly link BCM to physi-ological and biochemical experiments,owing to the abstract nature of the varia-bles BCM uses.In the late 1990s several experimental

studies indicated that the precise timing ofpre- and postsynaptic spikes have significantinfluence on the sign and magnitude ofsynaptic plasticity (9, 10) (Fig. 1B). Accord-ing to this experimental observation, calledspike timing-dependent plasticity (STDP),when a presynaptic spike comes before apostsynaptic spike [Δt = (tpost − tpre) > 0],long-term potentiation (LTP) is induced,and if the order is reversed (Δt= <0), long-term depression (LTD) is induced. Suchresults cannot be accounted for by rate-based theories, which are designed to beindependent of single spike times.Because of the complexity of the mech-

anisms inducing synaptic plasticity, it wastempting to assume that all of synapticplasticity can be captured by this simplecurve and that plasticity that is induced bycomplex pre- and postsynaptic spike trainscan be simply explained by the superposi-tion of the plasticity induced by all spikepairs (11, 12). Such a theory does not pro-vide a mechanistic description of synapticplasticity; instead it postulates that thecurve in Fig. 1B (Left) can be used tosummarize all that needs to be known ofplasticity. This curve is also called a two-point kernel. Kempter et al. (1999) (11)analyzed the correspondence between

Fig. 1. Models of synaptic plasticity. (A) In BCM,a rate-based model of synaptic plasticity, the signand magnitude of plasticity is determined bypostsynaptic activity (Left). If activity is lower thanθm, LTD is induced; otherwise, LTP is induced. Themodification threshold changes as a function ofthe history of postsynaptic activity. BCM can ac-count for receptive field plasticity in visual cortex(Right). (B) Pair-based kernel model of synapticplasticity. LTD (red) is induced if the postsynapticspike comes before the presynaptic spike; other-wise, LTP (blue) is induced. This rule is consistentwith a rate-based rule that is linear in postsynapticactivity. (C) In a triplet-based theory, pair-basedLTD plus triplet-based LTD can together accountfor various experimental results and for the rate-based BCM model. (D) CaDP, a biophysical modelof synaptic plasticity, assumes that the level ofpostsynaptic calcium determines synaptic plastic-ity. Moderate calcium levels produce LTD, higherlevels LTP. It can account for rate-based plasticityinduction protocols and STDP; however, STDP hasa second LTD region.

Author contributions: H.Z.S. wrote the paper.

The author declares no conflict of interest.

See companion article on page 19383.1E-mail: Harel.Shouval@uth.tmc.edu.

www.pnas.org/cgi/doi/10.1073/pnas.1117027108 PNAS | November 29, 2011 | vol. 108 | no. 48 | 19103–19104

COMMENTARY

STDP and rate-based plasticity theories. Byusing a simple model neuron and assumingthat presynatic spikes are generated by aPoisson process with a given rate, they wereable to reduce a theory based on linearsuperposition of the STDP curves to a rate-based theory. Their analysis shows thatthe STDP rule corresponds to a rate-basedrule that is linearly dependent on the post-synaptic firing rate (Fig. 1B, Right) and onthe covariance between the different inputs.These results also show that pair-basedSTDP does not correspond to the BCMrule (13). Further inspection of pair-basedSTDP shows that it cannot account formany experimental observations (14). Forexample, experimentally (9) spike timing-dependent LTP was only induced if spikepairs were delivered at a frequency above10 Hz, a result that cannot be explained bypair-based kernel theory (9, 14).Motivated by the failure of the pair-

based kernel model, Pfister and Gerstner(2006) (13) developed a kernel-basedmodel that took into account both pairsand triplets. In other words, plasticity canbe summarized by two- and three-pointkernels. The triplet-based theory couldaccount for more experimental results andin particular the frequency dependence ofSTDP (9, 15). Indeed, pair-based LTDand triplet-based LTP were sufficient toaccount for experimental observations invisual cortex (Fig. 1C).The article by Gjorgjieva et al. (3) fur-

ther analyzes the triplet-based model byadopting the techniques used previouslyfor pair-based STDP (11). The articleshows that triplet-based STDP reduces toa BCM-like rule and additional temporalcorrelation-dependent components. Toobtain metaplasticity the authors postu-lated an additional mechanism wherebythe magnitude of the pair-based STDP is

an increasing function of the temporalaverage of postsynaptic activity. Conse-quently, the triplet-based rule has many ofthe same features as BCM, such as gen-erating selective receptive fields whenpresented with linearly independent inputvectors. The additional components to thelearning rule mean that it can also ac-complish tasks that BCM cannot; for ex-ample, it can separate between patternsthat are separable only because of theircorrelational structure but would seemidentical on the basis of firing rates alone.These results indicate that a triplet-basedtheory of synaptic plasticity may be suffi-cient, because it can account both for cell-based experimental protocols and forhigher-level features.However, various experimental results

have not been accounted for by the triplet-based theory. For example, the rule de-signed to account for the frequencydependence of STDP (15, 16) cannot atthe same time account for plasticity pro-tocols induced directly by spike tripletsand quadruplets in a different synapsewithin a similar neocortical preparation(16). Further, whereas low-frequency pairsdo not cause LTP when the presynapticstimulus is delivered by activating a singlepresynaptic cell, they might if deliveredextracellularlly, thus activating multiplesynapses (15) because in terms of singlesynapse kernel-based theories, these twoconditions are identical.An alternative to kernel-based theories

are mechanistic theories in which plasticityinduced by different induction protocolsarises from a common mechanism.Mechanistic models fall into two catego-ries: biophysical and phenomenological(17, 18). Phenomenological models assumean underlying mechanism that is not ex-plicitly mapped onto biophysical processes,

in contrast to biophysical models, whichassume mechanisms based on realistic as-sumptions; often the boundary betweenthese categories is not sharp.Biophysical models of synaptic plasticity

make specific testable assumptions aboutthe biophysical mechanisms resulting inchanges to synaptic efficacies. For exam-ple, it is well known that calcium ionsflowing into the postsynaptic spinethrough NMDA receptors play a majorrole in synaptic plasticity in many systems.Additionally, experimental observationsand theoretical ideas have led to the no-tion that low levels of calcium elevationlead to LTD, whereas higher levels lead toLTP. Hence, such assumptions have goneinto several calcium-dependent plasticity(CaDP) models of synaptic plasticity (Fig.1D) (14, 19). These assumptions can ac-count for various induction protocols, in-cluding STDP, but surprisingly STDP insuch models has a second LTD region atΔt > 0. A second LTD region exists inhippocampal slices (14) but probably not inneocortical slices. The failure of CaDP toaccount for neocortical plasticity might betraced back to its assumptions, because inneocortex spike timing-dependent LTDdoes not depend on postsynaptic NMDAreceptors. Alternative theories with twocoincidence detectors might fit the databetter (20).The appropriate description level for

synaptic plasticity is still not known andmight depend on what exactly we aretrying to understand. More research isrequired to test whether kernel basedmodels are sufficient for explaining higher-order phenomena, and how they arise fromthe cellular biophysics, or whether bio-physical models must be used instead.

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19104 | www.pnas.org/cgi/doi/10.1073/pnas.1117027108 Shouval