COMMENTARY

What is the appropriate description level for ?

Harel Z. Shouval1 Department of Neurobiology and Anatomy, University of Texas Medical School at Houston, Houston, TX 77030

he hypothesis that learning (θm) is modifiable, serving as a negative memory and some aspects of feedback, is implemented in the equation: development are mechanistically T 1þμ θ ¼ ; [2] implemented by synaptic plastic- m y t ity has gained significant experimental where the angled brackets denote a sliding support (1, 2). At the cellular and molec- temporal average, and μ > 0 ensures sta- ular level synaptic plasticity is a very A complex phenomenon, involving hundreds bility (4). In Fig. 1 we show the form of the ϕ function for two different levels of of molecular species, depending on the fi structure of dendrites and on ion channel the modi cation threshold. concentrations. If we are to understand The BCM theory can indeed account for how high-level processes arise from syn- the formation of orientation selectivity aptic plasticity, and not simply that they and ocular dominance of cortical neurons arise from synaptic plasticity, we must in natural image environments and for know how to best characterize plasticity various different deprivation experiments (6). Furthermore, the assumptions of theoretically. Such a characterization fl should account for key experimental re- BCM have in uenced experimental stud- ies of synaptic plasticity (8). However, sults, yet at the same time it should be as fi simple as possible so that we can use it it is dif cult to tightly link BCM to physi- to explain how plasticity can lead to ological and biochemical experiments, learning and memory. The article by owing to the abstract of the varia- Gjorgjieva et al. (3) in PNAS argues that bles BCM uses. fi Fig. 1. Models of synaptic plasticity. (A) In BCM, In the late 1990s several experimental a suf cient model of synaptic plasticity can a rate-based model of synaptic plasticity, the sign depend only on spike pairs and triplets studies indicated that the precise timing of and magnitude of plasticity is determined by pre- and postsynaptic spikes have significant and that more-complex biophysical and postsynaptic activity (Left). If activity is lower than influence on the sign and magnitude of molecular processes might not be needed. θm, LTD is induced; otherwise, LTP is induced. The It also shows a correspondence between modification threshold changes as a function of synaptic plasticity (9, 10) (Fig. 1B). Accord- this triplet-based rule and the well-known the history of postsynaptic activity. BCM can ac- ing to this experimental observation, called phenomenological Bienenstock Copper count for receptive field plasticity in visual cortex spike timing-dependent plasticity (STDP), Munro (BCM) learning rule (4). (Right). (B) Pair-based kernel model of synaptic when a presynaptic spike comes before a plasticity. LTD (red) is induced if the postsynaptic Δ − > Many of the early theories of synaptic postsynaptic spike [ t =(tpost tpre) 0], spike comes before the presynaptic spike; other- plasticity were not formulated on the basis long-term potentiation (LTP) is induced, wise, LTP (blue) is induced. This rule is consistent and if the order is reversed (Δt = <0), long- of low-level experimental evidence. In- with a rate-based rule that is linear in postsynaptic stead, they were motivated by the con- activity. (C) In a triplet-based theory, pair-based term depression (LTD) is induced. Such sequences of plasticity observed at a LTD plus triplet-based LTD can together account results cannot be accounted for by rate- higher level, for example receptive field for various experimental results and for the rate- based theories, which are designed to be plasticity in visual cortex. To account based BCM model. (D) CaDP, a biophysical model independent of single spike times. for such high-level plasticity, theorists of synaptic plasticity, assumes that the level of Because of the complexity of the mech- postulated phenomenological low-level postsynaptic calcium determines synaptic plastic- anisms inducing synaptic plasticity, it was ity. Moderate calcium levels produce LTD, higher mechanisms that can account for such tempting to assume that all of synaptic levels LTP. It can account for rate-based plasticity plasticity can be captured by this simple higher-level phenomena. In the mid-1970s induction protocols and STDP; however, STDP has von der Malsburg (5) proposed rate-based a second LTD region. curve and that plasticity that is induced by network models that included synaptic complex pre- and postsynaptic spike trains plasticity and competition between cells to can be simply explained by the superposi- account for the formation of orientation theory (Fig. 1A) is based on two principles, tion of the plasticity induced by all spike selectivity and ocular dominance maps in formulated by two equations. First, the pairs (11, 12). Such a theory does not pro- visual cortex. The plasticity model he plasticity equation: vide a mechanistic description of synaptic used was very simple: synaptic potentia- plasticity; instead it postulates that the dwi tion that is proportional to the product of ¼ xiϕðy; θmÞ [1] curve in Fig. 1B (Left) can be used to presynaptic and postsynaptic activity vari- dt summarize all that needs to be known of ables, coupled with a normalization of the states that the change of the synaptic ef- plasticity. This curve is also called a two- fi total . Later work has cacy (wi) in synapse i is a product of point kernel. Kempter et al. (1999) (11) shown the limitations of this plasticity the presynaptic activity (xi) and a non- analyzed the correspondence between model (6). The BCM model (4) was also linear function (ϕ) of the postsynaptic ac- formulated to explain receptive field plas- tivity (y). The ϕ function is negative at ticity in visual cortex, and like other rate- low values of y and becomes positive when Author contributions: H.Z.S. wrote the paper. The author declares no conflict of interest. based phenomenological models, is for- y exceeds the modification threshold (θm). mulated in terms of abstract pre- and The second principle, metaplasticity (7), See companion article on page 19383. postsynaptic activity variables. The BCM which states the modification threshold 1E-mail: [email protected].

www.pnas.org/cgi/doi/10.1073/pnas.1117027108 PNAS Early Edition | 1of2 Downloaded by guest on September 24, 2021 STDP and rate-based plasticity theories. By an increasing function of the temporal in contrast to biophysical models, which using a simple model neuron and assuming average of postsynaptic activity. Conse- assume mechanisms based on realistic as- that presynatic spikes are generated by a quently, the triplet-based rule has many of sumptions; often the boundary between Poisson process with a given rate, they were the same features as BCM, such as gen- these categories is not sharp. able to reduce a theory based on linear erating selective receptive fields when Biophysical models of synaptic plasticity superposition of the STDP curves to a rate- presented with linearly independent input make specific testable assumptions about based theory. Their analysis shows that vectors. The additional components to the the biophysical mechanisms resulting in the STDP rule corresponds to a rate-based learning rule mean that it can also ac- changes to synaptic efficacies. For exam- rule that is linearly dependent on the post- complish tasks that BCM cannot; for ex- fi ple, it is well known that calcium ions synaptic ring rate (Fig. 1B, Right)andon ample, it can separate between patterns flowing into the postsynaptic spine the covariance between the different inputs. that are separable only because of their through NMDA receptors play a major These results also show that pair-based correlational structure but would seem role in synaptic plasticity in many systems. STDP does not correspond to the BCM identical on the basis of firing rates alone. rule (13). Further inspection of pair-based These results indicate that a triplet-based Additionally, experimental observations STDP shows that it cannot account for theory of synaptic plasticity may be suffi- and theoretical ideas have led to the no- many experimental observations (14). For cient, because it can account both for cell- tion that low levels of calcium elevation example, experimentally (9) spike timing- based experimental protocols and for lead to LTD, whereas higher levels lead to dependent LTP was only induced if spike higher-level features. LTP. Hence, such assumptions have gone pairs were delivered at a frequency above However, various experimental results into several calcium-dependent plasticity 10 Hz, a result that cannot be explained by have not been accounted for by the triplet- (CaDP) models of synaptic plasticity (Fig. pair-based kernel theory (9, 14). based theory. For example, the rule de- 1D) (14, 19). These assumptions can ac- Motivated by the failure of the pair- signed to account for the frequency count for various induction protocols, in- based kernel model, Pfister and Gerstner dependence of STDP (15, 16) cannot at cluding STDP, but surprisingly STDP in (2006) (13) developed a kernel-based the same time account for plasticity pro- such models has a second LTD region at model that took into account both pairs tocols induced directly by spike triplets Δt > 0. A second LTD region exists in and triplets. In other words, plasticity can and quadruplets in a different synapse hippocampal slices (14) but probably not in be summarized by two- and three-point within a similar neocortical preparation neocortical slices. The failure of CaDP to kernels. The triplet-based theory could (16). Further, whereas low-frequency pairs account for neocortical plasticity might be account for more experimental results and do not cause LTP when the presynaptic traced back to its assumptions, because in in particular the frequency dependence of stimulus is delivered by activating a single neocortex spike timing-dependent LTD STDP (9, 15). Indeed, pair-based LTD presynaptic cell, they might if delivered does not depend on postsynaptic NMDA and triplet-based LTP were sufficient to extracellularlly, thus activating multiple receptors. Alternative theories with two account for experimental observations in synapses (15) because in terms of single coincidence detectors might fitthedata visual cortex (Fig. 1C). synapse kernel-based theories, these two The article by Gjorgjieva et al. (3) fur- conditions are identical. better (20). ther analyzes the triplet-based model by An alternative to kernel-based theories The appropriate description level for adopting the techniques used previously are mechanistic theories in which plasticity synaptic plasticity is still not known and for pair-based STDP (11). The article induced by different induction protocols might depend on what exactly we are shows that triplet-based STDP reduces to arises from a common mechanism. trying to understand. More research is a BCM-like rule and additional temporal Mechanistic models fall into two catego- required to test whether kernel based correlation-dependent components. To ries: biophysical and phenomenological models are sufficient for explaining higher- obtain metaplasticity the authors postu- (17, 18). Phenomenological models assume order phenomena, and how they arise from lated an additional mechanism whereby an underlying mechanism that is not ex- the cellular biophysics, or whether bio- the magnitude of the pair-based STDP is plicitly mapped onto biophysical processes, physical models must be used instead.

1. Martin SJ, Grimwood PD, Morris RG (2000) Synaptic 8. Bear MF (2003) Bidirectional synaptic plasticity: From 15. Sjöström PJ, Turrigiano GG, Nelson SB (2001) Rate, tim- plasticity and memory: An evaluation of the hypothe- theory to reality. Philos Trans R Soc Lond B Biol Sci 358: ing, and cooperativity jointly determine cortical synap- sis. Annu Rev Neurosci 23:649–711. 649–655. tic plasticity. Neuron 32:1149–1164. 2. Whitlock JR, Heynen AJ, Shuler MG, Bear MF (2006) 9. Markram H, Lübke J, Frotscher M, Sakmann B (1997) 16. Froemke RC, Dan Y (2002) Spike-timing-dependent Learning induces long-term potentiation in the hippo- Regulation of synaptic efficacy by coincidence of post- synaptic modification induced by natural spike trains. – – campus. Science 313:1093 1097. synaptic APs and EPSPs. Science 275:213 215. Nature 416:433–438. fi fi 3. Gjorgjieva J, Clopath C, Audet J, P ster JP (2011) A 10. Bi GQ, Poo MM (1998) Synaptic modi cations in cul- 17. Senn W, Markram H, Tsodyks M (2001) An algorithm – triplet spike-timing dependent plasticity (STDP) model tured hippocampal neurons: Dependence on spike tim- for modifying neurotransmitter release probability generalizes the Bienenstock–Cooper–Munro (BCM) ing, synaptic strength, and postsynaptic cell type. based on pre- and postsynaptic spike timing. Neural rule to higher-order spatiotemporal correlations. Proc J Neurosci 18:10464–10472. Comput 13:35–67. Natl Acad Sci 108:19383–19388. 11. Kempter R, Gerstner W, van Hemmen L (1999) Hebbian 18. Clopath C, Büsing L, Vasilaki E, Gerstner W (2010) 4. Bienenstock EL, Cooper LN, Munro PW (1982) Theory learning and spiking neurons. Phys Rev E 59: Connectivity reflects coding: A model of voltage- for the development of neuron selectivity: Orientation 4498–4514. based STDP with homeostasis. Nat Neurosci 13: specificity and binocular interaction in visual cortex. 12. Song S, Miller KD, Abbott LF (2000) Competitive Heb- – J Neurosci 2:32–48. bian learning through spike-timing-dependent synap- 344 352. fi 5. von der Malsburg C (1973) Self-organization of orien- tic plasticity. Nat Neurosci 3:919–926. 19. Shouval HZ, Bear MF, Cooper LN (2002) A uni ed tation sensitive cells in the striate cortex. Kybernetik 13. Pfister JP, Gerstner W (2006) Triplets of spikes in model of NMDA receptor-dependent bidirectional 14:85–100. a model of spike timing-dependent plasticity. J Neuro- synaptic plasticity. Proc Natl Acad Sci USA 99: 6. Cooper L, Intrator N, Blais BS, Shouval HZ (2004) Theory sci 26:9673–9682. 10831–10836. of Cortical Plasticity (World Scientific, Hackensack, NJ). 14. Shouval HZ, Wang SS, Wittenberg GM (2010) Spike tim- 20. Karmarkar UR, Najarian MT, Buonomano DV (2002) 7. Abraham WC, Bear MF (1996) Metaplasticity: The plas- ing dependent plasticity: A consequence of more funda- Mechanisms and significance of spike-timing depen- ticity of synaptic plasticity. Trends Neurosci 19:126–130. mental learning rules. Front Comput Neurosci 4:19. dent plasticity. Biol Cybern 87:373–382.

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