The Function of Dendritic Spines: Devices Subserving Biochemical Rather Than Electrical Compartmentalization

Home , Dendrite, Dendritic spine, Neuropil, Spine apparatus, Synapse, Synaptic weight

The Journal of Neuroscience, February 1993, 13(2): 413422

Feature Article

Christof Koch’ and Anthony Zador* ‘Computation and Neural Systems Program, California Institute of Technology, Pasadena, California 91125 and *Neuroscience Program, Yale University School of Medicine, New Haven, Connecticut 06510

Dendritic spines are tiny, specialized protoplasmic protuber- (2) spinesshape the membranepotential in responseto synaptic ances that cover the surface of many neurons. First described input, and (3) spinesdetermine the dynamics of intracellular by Ramon y Cajal(199 1) in light microscopic studies of Golgi- second messengerssuch as calcium. In this article we review stained tissue, they are among the most striking subcellular fea- the current status of each of these proposals with particular tures of many neurons. Spines serve as the major target for emphasison the putative role of spinesin the induction of a excitatory synaptic input onto principal neurons in the hippo- cellular model of synaptic plasticity in cortical structures, long- campus, the neocortex, and other brain regions. Their intimate term potentiation (LTP). association with synaptic traffic suggests some critical role in It may well be possiblethat dendritic spinesserve somecrucial synaptic transmission and plasticity. We here review experi- role in normal synaptic transmission(D. Purves, personalcom- mental data and theoretical models with respect to the putative munication). However, in this article we focus on their possible role of dendritic spines in the induction and retention of synaptic role in synaptic plasticity. Furthermore, we will not discussthe plasticity. electrical behavior of that minority of spinesin neocortex that The ubiquity of spines demands explanation, yet their small carry both an excitatory and an inhibitory synapse(see Koch size-near the limit of resolution of light microscopy-impedes and Poggio, 1983a; Qian and Sejnowski, 1989, 1990; Dehay et an experimental frontal assault. Until recently, most theoretical al., 199l), nor will we consider the role of dendrodendritic syn- studies focused on the role of the spine neck geometry in reg- apses,such as those found on the spines of olfactory granule ulating the amplitude of the EPSP received at the soma. How- cells (Rall and Shepherd, 1968; Shepherd and Greer, 1989). ever, recent experimental evidence suggests that the spine shape may not be able to modulate the “synaptic weight” effectively. The Natural History of Spines Consequently, both theoretical models and calcium-imaging ex- We first summarize some of the pertinent facts about dendritic periments are now focusing on the role of spines in amplifying spines,with particular emphasison neocortex and hippocam- and isolating calcium signals, particularly those involved in the pus, before discussingtheir functional role. induction of a calcium-dependent form of long-term synaptic plasticity. Until recently, physiological hypotheses about the function The distribution of spines of the dendritic spines could only be explored indirectly, through In neocortex, hippocampus, and olfactory cortex, neurons are analytical and computational studies based on morphological classifiedaccording to whether their dendrites are studded with data. Recent technical advances in the direct visualization of spines.Spiny neuronsinclude pyramidal and stellate cells. They calcium dynamics in dendritic structures are now permitting account for about three quarters of neurons in the neocortex. direct tests of some of these theoretical inferences. Smooth neurons, whose dendrites carry few or no spines,make Three principal hypotheses have been advanced to explain up the remainder. Smooth neurons include the basket cell, the the function of spines: (1) spines connect axons with dendrites, chandelier or axoaxonic cell, and the double-bouquet cell; they stain for the inhibitory neurotransmitter GABA (Douglas and Martin, 1990). It hasnot beenexplained why one classof cortical [Key words: dendritic spines, voltage attenuation, bio- cells, inhibitory interneurons, should have so few spines,while chemical compartmentalization, calcium dynamics, pyra- excitatory cells have so many. midal cells, long-term potentiation] A large, layer V pyramidal cell in the visual cortex may have as many as 15,000 spines,averaging about two spinesper mi- Some of the research reported here is supported by the Office ofNaval Research, the National Science Foundation. the James S. McDonnell Foundation. and the crometer of dendrite (Larkman, 199 1; see also Schiiz, 1976) National Institute of Mental Health Center for cell and molecular signalling. C.K. while the reported density for CA1 pyramidal cells varies from thanks the Aspen Center of Physics for its hospitality during the preparation of about one to five spinesper micrometer of dendrite, depending this review, and A.Z. thanks Ed Kairiss for generously making his computer facilities available. We thank Idan Segev and Rodney Douglas for helpful com- on the staining method used(Harris and Stevens, 1989; Amaral ments. et al., 1990). The record is held by cellsin the human cerebellum, Correspondence should be addressed to Dr. Christof Koch, Computation and Neural Systems Program, 216-76, Division of Biology, California Institute of where individual Purkinje cells are studded by up to 200,000 Technology, Pasadena, CA 9 1125. spines,each spine carrying a single excitatory synapsefrom a Copyright 0 1993 Society for Neuroscience 0270-6474/93/130413-10$05.00/O parallel fiber (Braitenberg and Atwood, 1958). 414 Koch and Zador * Function of Dendritic Spines

can branch from a single dendritic protrusion. The exact morphology of spines can only be appreciated by means of three- dimensionalreconstructions of serialelectron micrographic sections, as first reported by Wilson et al. (1983) in the neostriatum and later by Harris and Stevens (1988a,b, 1989) in cerebellum and cortex (see Fig. 3). For CA1 pyramidal cells in the rat hippocampus,Harris and Stevens(1989) found wide variability in the dimensionsof spines,with spinenecks ranging in length from 0.08 to 1.6 pm (0.45 f 0.29 pm) and in diameter from 0.04 to 0.46 pm (0.15 f 0.06 pm). The total volume of neck plus head was 0.062 rt 0.08 pm3. Larger spine headswere associated with larger synapses,as measuredby the size of the associatedpostsynaptic density, and by the number of vesicles in the presynaptic axonal varicosity. These dimensionsempha- size that spines bridge the gap between the cellular and the molecular scales.For example, at a resting concentration of 80 nM only about three unbuffered Ca2+ ions are present in the average spine head of volume 0.05 hum’. Dendritic spines are characterized by an absenceof mito- chondria, microtubules, or ribosomes,and by the presenceof a specialized form of smooth endoplasmic reticulum termed the “spine apparatus.” The membranes making up the spine apparatus are closelyapposed to the plasmamembrane of the spine neck and appear to sequestercalcium (Burgoyne et al., 1983; Fifkova et al., 1983). Although spineslack neurofilaments,spine headscontain a densenetwork of actin filaments (F&ova and Delay, 1982). In the neck, actin filaments are oriented lengthwise along the spineapparatus (F&ova, 1985). A number of proteins known to be involved in actin-mediated activities, including neuronal myosin (Drenckhahn and Kaiser, 1983), fodrin (Carlin et al., 1983) and calmodulin (Cacereset al., 1983), have been found in dendritic spines. The closeassociation of spineswith terminal boutons of axons prompted early speculationthat spinesmight conduct impulses Figure 1. A pyramidal cell in layer 2 of cat visual cortex. The cell was between neurons, although at the time little was known about filled intracellularly with HRP. Dendritic spines are seen on the apical the basic mechanismsof synaptic transmission.EM studieshave and basal dendrites (see Martin and Whitteridge, 1984, their Fig. 7A). since confirmed that spines are indeed the major postsynaptic target of excitatory (asymmetric, type I) synaptic input (Gray, 1959). In cat visual cortex, over 90% of the afferent geniculate The microanatomy of spines terminals in layer IV are located on spines(White and Rock, Spinesare found in a wide variety of shapes (Jones and Powell, 1980; LeVay, 1986; Martin, 1988). This associationis limited 1969; Petersand Kaiserman-Abramof, 1970; seealso Figs. l- to excitatory synaptic traffic. Inhibitory (symmetric, type II) 3) ranging from the short and stubby, through the archetypal synaptic input is observed only at a small fraction (between 5% “mushroom-shaped,” to the long and thin. In general, spines and 20%) of spinesin the neocortex, and always in conjunction can be described as having a “neck” that emergesfrom the with excitatory input (Jonesand Powell, 1969; see Fig. 1C in dendrite and ends with a “head.” Sometimesmultiple spines Dehay et al., 1991). In hippocampus, no inhibitory terminals

Figure 2. A reconstruction from serial EM sections of a proximal dendrite of an HRP-filled spiny stellate neuron in layer 4a of cat visual cortex. sp, spine; sn, spine neck; bl, symmetrical synapsing bouton on spine neck; b2, symmetrical synapsing bouton on branch point; b3, asymmetrical synapsing bouton on spine; b4, symmetrical synapsing bouton on dendritic shaft; d, dendritic shaft. Scale bar, 1 pm (from Anderson et al., in press, with permission). The Journal of Neuroscience, February 1993, 13(2) 415 are observed on dendritic spines (K. Harris, personal commu- nication). Changes in spine morphology Both the absolute number as well as the shape of spines can change dramatically with a number of external variables. For instance, in the CA1 region of the hippocampus, the dendritic spine density varies by 30% or more over the 5 d estrus cycle of the adult female rat, while spines on pyramidal cells in the CA3 region showed little statistical significant variation (Wool- ley et al., 1990). Other studies have shown that the shape of spines-in particular the length and diameter of the neck- changes during the course of neuronal development (Harris et al., 1989, 1992) and in response to behavioral or environmental cues such as light, social interaction, or exploratory motor activity (Purpura, 1974; Coss and Globus, 1978; Bradley and Horn, 1979; Brandon and Goss, 1982; Rausch and Scheich, 1982). Other studies have found a correlation between changes in spine shape and brief high-frequency electrical stimulation of specific hippocampal pathways sufficient to induce LTP (Van Harrefeld and Filkova, 1975; Lee et al., 1980; F&ova et al., 1982; Gree- nough and Chang, 1985). Some of the reported changes include larger spine heads, changes in the shape of the spine stem, an increased incidence of concave spine heads, and an increase in the number of shaft synapses. It is not known what role-if any-these changes in spine shape play in the increase in synaptic efficacy. Furthermore, the interpretation of the data is itself problematic (Desmond and Levy, 1988). Figure 3. Three-dimensionalreconstruction of an 8.5-pm-longden- drite from a CA1 pyramidalcell of the rat hippocampus.The dendritic First Hypothesis: Spines Only Connect diameterranges from 0.51 to 0.73pm. Thereare about three spines per micrometer.The diversity of spineshapes and dimensions is especially Spines as connecting tissue striking(from Harrisand Stevens,1989, with permission). The earliest view of spines focused on an anatomical rather than a physiological role (Ramon y Cajal, 199 1). One specific hypothesis was that spines provide sufficient surface area on the One method (Stratford et al., 1989)transforms the spiny den- dendrite for synapse formation. However, the three-dimension- drite into a single “equivalent” (and smooth) cylinder, whose al EM reconstructions by Harris and Stevens (1988a) argue diameter and length are larger than those of the parent dendrite against this view. By graphically removing all spines from their by someappropriate fraction. A secondmethod (Holmes, 1989; computer reconstructions of spiny dendrites, they estimated that Claibome et al., 1992; Segevet al., 1992) preservesthe dimen- only 29-45% of the dendritic membrane area of Purkinje cells sions of the dendrite but increasesthe membrane capacitance would have been covered by synapses if all spines were deleted C,,,and decreasesthe membraneresistance R, appropriately. A and the associated synapses moved to the dendrites. Applying novel analytical method to incorporate spinesinto cable theory the same technique to five reconstructed CA1 pyramidal cell was developed by Baer and Rinzel (1991). Although the effect dendrites, they found that only about 5-9% of the remaining that the increased spine membrane area has on the electrical dendritic surface area would have been covered by the synapses properties of the cell provides no insight into the function of from the spines. Thus, it does not appear that spines are required spines,it may ironically be the only one that we can infer with for lack of dendritic membrane area. These results do not, how- confidence to be important (seealso Jaslove, 1992). ever, preclude a role for spines in simplifying the connectivity between axonal and dendritic processes in the three-dimensional Second Hypothesis: Spines Play an Electrical Role neuropil (Swindale, 198 1). Chang(1952) wasthe first to point out that the spineneck might sculpt the electrical signal generatedby the synapse:“If the end Effect of spines on properties of dendrites bulbs of the gemmules[spines] are the receptive apparatus for Given the high density of spines per micrometer of dendrites the presynaptic impulses,the processof postsynaptic excitation (up to 14 spines/pm on Purkinje cells; Harris and Stevens, 1988b), initiated there must be greatly attenuated during its passage a substantial fraction of the total membrane area of many neu- through the stems of the gemmuleswhich probably offer con- rons resides in spines. It is therefore important to account for siderable ohmic resistancebecause of their extreme slender- this additional area in the analysis of the passive propagation ness.” This observation was extended by Rall (1970; seealso of electrical signals within the dendritic tree; In particular, from Diamond et al., 1970) who proposedthat “. . . the spine stem the vantage point of a somatic recording site, both the total resistancecould be an important variable which might be used capacitance and the electrotonic length of the dendrite increase physiologically to changethe relative weightsof synaptic inputs while the resistance decreases when spines are added to “smooth” from different afferent sources.”Bliss and Lomo (1973) invoked membrane. A number of techniques have been devised to sim- this as a possiblemechanism for LTP in their original descrip- plify the analysis of this effect. tion of that phenomenon. 416 Koch and Zador l Function of Dendritic Spines

injected current, this synaptic saturation increasesthe effective attenuation betweenthat site and the synapse.Ifthe conductance changeis large enough, the driving potential approacheszero and the spine synapseacts as a voltage source(see below). What biophysical factors determine whether the spine oper- ates in the voltage or current regime? We can quantify this question by analyzing the electrical circuit corresponding to a highly simplified model of a spine attached to a dendrite (Fig. 4; for more details, seeKoch and Poggio, 1983a). The steady- Spine neck state case is particularly simple [the analysis of the transient case is more involved, but the result is essentially the same, becausedue to the extremely small capacitanceC, of the spine head membrane (~0.0 1 pF), the spineinput impedancechanges little at high frequencies; Jack et al., 1975; Koch and Poggio, 1983a]. Any current injected into the spinehead must flow either out Dendrite I acrossthe spinehead resistanceR, or in through the spineneck resistanceR, and along the dendritic input resistanceR,. How- ...... ever, given the very small spine membrane area of < 1 pm2 (Harris and Stevens, 1989) R, is so large (> 1O6 MB) that it can be assumedto be infinite. The spine input resistanceR+, is therefore simply the sum of the neck resistanceand the dendritic input resistancejust below the spine: J-Line= Rv + R,. (1) Figure 4. Simplified electrical model of a passive spine. The leak through We can expressthe current flowing acrossthe synapseat the the spine neck membrane is so small that it has not been included. spine head as

This basic idea was analyzed and refined in subsequentyears &n = gsyn(Esyn- 0, (2) by many authors (Rall and Rinzel, 1971; Rall, 1974, 1978; Jack where g,,, is the synaptic input conductance at the spine head, et al., 1975; Rinzel, 1982; Koch and Poggio, 1983a,b; Turner, E,,, is the synaptic reversal potential, and V, is the amplitude 1984; Wilson, 1984; Perkel and Perkel, 1985; Shepherd et al., of the EPSP at the spinehead (Fig. 4). Applying Ohm’s law, we 1985; Brown et al., 1988b; Segevand Rail, 1988). In a radical multiply Equation 2 by the input resistanceR,,,,, and solve for extension of this original idea, Crick (1982) advanced the I’,. By a simple algebraic manipulation, we obtain “twitching spinehypothesis”-the notion that spines,using actin-based contractile machinery in the spine neck, could sub- (3) serve very fast changes(less than a second)in synaptic efficacy, and that this might provide a mechanismfor short-term mem- Similarly, the amplitude I’, of the EPSP at the dendrite just ory. Let us review the main argument in the caseof a passive, below the spine is given by voltage-independent spine membrane. v = gsynR& d (4) Passive electrical properties of spines 1 + gsynRspine ’ Theoretically, spinescould attenuate the synaptic signal in two Let us consider theseequations in the limits of very small and ways. First, they could reduce the current reaching the parent large synaptic inputs. dendrite by allowing current loss through the spine neck mem- If the synaptic input conductance gsynis small relative to the brane. While this is possible in principle, analysisover a wide spine input resistanceR,,,,, (i.e., gsy,,RSpine< l), then the de- range of spine geometries and passive membrane parameters nominator in Equations 3 and 4 is close to unity and the spine suggeststhat current lossacross the spineneck is negligible.The and dendritic EPSPs can be expressedas explanation is simply that current loss is proportional to membrane surfacearea, and the spineneck areais very small (Harris and Stevens, 1989). In the analysis that follows we will show and that when a synapsebehaves as a current source,the spineneck v, = provides very little electrical isolation between the spine head g&L&n. (6) and the parent dendrite. That is, under these conditions, the action of the synapsecan However, spinescould also attenuate the synaptic signal via be approximated by a current sourceof amplitude g,,,E,,,. Since a second mechanism. Becausethe spine has a greater input the dendritic EPSP depends on R, but not on R,,,,,, it follows resistancethan the parent dendrite, the same synaptic conduc- that V, is independent of spine geometry, which affects only tance changeproduces more depolarization at the spinethan at R,,,,,. In other words, the synapsecan be thought of as injecting the dendrite. As a consequence,the driving potential at the spine the current g,,,E,,, into the spine head, almost none of this head decreasesmore than at the parent dendrite, such that a current will leak out through the tiny spineneck and head mem- smaller synaptic current is generated at the spine head. Since brane and therefore almost all of the current will reach the the depolarization at any remote site is proportional to the dendrite, regardlessof the size of the spine neck. However, The Journal of Neuroscience, February 1993, 73(2) 417 because of the difference in input resistance between the spine head and the dendrite, the dendritic EPSP will be attenuated with respect to the spine EPSP by a factor of V,l V, = Rd/(Rd + R,). If, on the other hand, gsynis large relative to Rspine(i.e., gSynRSplne 1.0 > l), then the spine EPSP begins to approach the synaptic reversal potential (V, - Esyn). The dendritic EPSP then con- verges to 0.5 (7)

In this regime, the synapseacts as a voltage source( =Esyn)and changesin the geometry of the spine neck (changing RN) can affect the amount of synaptic current entering the spine head. 0.0 Therefore, the current reaching the dendrite will differ, depend- 0.0 0.5 1.0 1.5 2.0 2.5 ing on the length and width of the spine neck. If the dendritic L neck (pm) input resistanceis too large (i.e., R, - co), V, + E,,, and varying Figure 5. Peak somatic EPSP amplitude as a function of spine neck R, will have no further effect on the dendritic EPSP (seeEq. 7). length L,, for three different values of the transient, voltage-indepen- In summary, depending on the product of the synaptic con- dent, synaptic input conductance gsY.on the spine head (t,,l, = 1.5 msec) ductance changegsY,, and the spine input resistanceR,,,,,, the in a simulated pyramidal cell. The geometry was varied to keep the spine-synapsecomplex tends to act either as a current or as a spine neck area constant at 0.24 pm2, while the L,,,, was stretched or compressed (making the spine neck resistance R, proportional voltage source. This constrains the extent to which the mor- to L:, J. For small values ofg,,., the synaptic input can be approximated phology of the spinecan modulate the synaptic efficiency. These as a current and the spine geometry has little effect on the dendritic or relations are illustrated in Figure 5, which showsthe simulated somatic EPSP amplitude. Values for both the AMPA as well as the effect of spineneck shapeon the depolarization at the somafor NMDA component of the CA3 synaptic input onto CA1 cells are be- three different synaptic conductances.For small synaptic con- lieved to be ~0.5 nS. The spine in this simulation was located on the proximal portion of the apical tree of an HRP-filled and anatomically ductances (bottom curve), the somatic depolarization is inde- reconstructed layer V pyramidal cell in area 17 of the anesthetized cat pendent of spine shape, but for a large synaptic conductance (Douglas et al., 199 1; for more details, see Bemander et al., 199 1). (top curve) the spineneck can modulate the current over about an order of magnitude. Technical advances in the last decadehave provided tighter changesare substantially larger and spinesthinner and longer bounds on our uncertainty about the spine operating regime. than in hippocampus. Probably the most complete data are available for the region CA3 pyramidal input (the Scha& collateral input) to region Regenerativeelectrical properties of spines CA 1 pyramidal cellsin the hippocampus.This input is mediated Computer simulations show that if the membrane of the spine by at least two pharmacologically distinct postsynaptic gluta- head is endowed with regenerative, voltage-dependentfast so- mate receptor subtypes: the AMPA subtype, which producesa dium or calcium channels,even small synaptic inputs cantrigger fast, voltage-independent conductance increase,and the NMDA electrical spikesin the spinehead, giving rise to sizeableEPSPs subtype, which mediates a slower, voltage-dependent conduc- in the passivedendrite (Perkel and Perkel, 1985; Shepherd et tance increase. Current estimatessuggest that at thesesynapses al., 1985; Segev and Rall, 1988; Baer and Rinzel, 1991). Such g,,,, is about 0.05-0.2 nS (Bekkersand Stevens,1990; Malinow spikes do not occur if the neck is too short or too thick, since and Tsien, 1990) while g,,,, is ~0.5 nS (Bashir et al., 1991). the associatedspine input resistancewill then be too small to Basedon their EM reconstruction of spinesin the sameregion, cause the EPSP to depolarize above spike threshold levels. In Harris and Stevens (1989) estimate the spineneck resistanceto principle, small changesin the spinegeometry can have a dra- lie between about 0.01 and 0.05 GSL,making the critical product matic effect upon V, by enabling or disabling spine action po- grynRspinemuch less than 1 for a very large range of dendritic tentials. Given the high degreeof voltage attenuation to which input resistances.Even the assumptionthat no current can flow high-frequency electrical events-such as slow or fast dendritic through the spine apparatus- thereby effectively restricting the spikes-are subject as they propagate from dendrites to the cell spine neck-will not changethis product appreciably, because body (Rinzel and Rall, 1974; Mel, 1992) electrical spikes oc- the spine apparatus only occludes about 5-25% of the spine curring in more distal spineswould be difficult to record at the neck (Harris and Stevens, 1988b). It therefore appearsthat the cell body. synapsesof the Schaffer collateral inputs to region CA1 spines Little is known about the presenceof voltage-dependentchan- act as current sources, and that changing spine morphology nels in dendritic spinesin cortical or hippocampal cells. How- will not affect the associateddendritic EPSP appreciably (Tur- ever, direct immunocytochemical evidence for fast voltage-de- ner, 1984; Brown et al., 1988; Harris and Stevens, 1989; see pendent calcium channelsin spinesof cerebellar Purkinje cells also Wilson, 1984). This conclusion is consistent with experi- has recently been provided (Hillman et al., 1991; seealso Jones mental evidence: while the mechanismsunderlying the expres- et al., 1989). It may well be that regenerativeelectrical properties sion of LTP at these synapsesremain controversial (Brown et are important to spine function in some cases. al., 1988a; Madison et al., 1991), there is little to suggestthat a postsynaptic changein the electrical impedanceof the spine Third Hypothesis: Spines Play a Biochemical Role is involved (seealso Larson and Lynch, 1991). This conclusion Over the last decade,an alternative view of spineshas emerged is also likely to hold in neocortex, unlesssynaptic conductance that emphasizestheir effect on chemical rather than electrical 418 Koch and Zador * Function of Dendritic Spines

Spine head sistance” (T. Zador and C. Koch, unpublished observations; see also Carnevale and Rosenthal, 1992) as the changein calcium concentration in responseto a current of calcium ions. Both the electrical as well as the calcium spine input resistanceswill be much larger than the associateddendritic input resistances.As a consequence,a given current flowing into the spinegives rise to a much larger local responsethan the samecurrent flowing into the dendrite. A key difference between the electrical and chemical effects of spinesarises from the effect of the spineneck. In our analysis NMDA of the passiveelectrical properties of spinesabove, we concluded x channel that the electrical current loss through the spineneck was negligible. To comparethe lossof calcium current through the spine neck membrane, one can define the equivalent of the space u constant, which describesthe distance over which [Ca2+] at steady state decreasese-fold in an infinite cable. This definition Ca diffusion ---.I requires certain simplifying assumptionsabout the spine Ca2+ I f i dynamics, namely, the presenceof linear nonsaturable pumps ( i in the neck, a constant extracellular [Ca*+], and a simplecalcium ---2=--Ca buffer d ‘y’ buffer scheme.Assuming that a 0.1 -pm-thin spineneck has the parameters used in Zador et al. (1990), the “diffusive space constant” Xc, is x0.3 pm (Zador and Koch, unpublished observations), about three orders of magnitude smaller than the steady-stateelectrical spaceconstant. From this we can estimate Dendritic shaft 1‘f r the calcium concentration at the dendritic shaft in responseto a steady-statecurrent inflow at the spine head. Since for these parameters the dendritic shaft is about three space-constants Figure 6. Schematic of the system controlling intracellular calcium in away from the spinehead, the calcium concentration at the shaft a dendritic spine. The electrical model is similar to Figure 4, except that the synaptic conductance g&t) has been replaced by a voltage- is expected to be at least e3 x 20-fold lower than at the head. dependent NMDA conductance and a voltage-independent AMPA con- This is in dramatic contrast to the almost complete lack of ductance in parallel (not shown). Ca2+ ions enter through the NMDA electrical current attenuation experiencedbetween the spinehead receptor channels, are bound to the four calcium-binding sites on the and the base. calmodulin molecules, diffuse down the neck to the dendrite or can be These principles are illustrated in computer simulations of removed by two different calcium pumps (for more details, see Zador et al., 1990). the fully nonlinear calcium dynamics thought to underlie the induction of LTP (Fig. 7; for details, see Zador et al., 1990; Brown et al., 1991). In the model,calcium entersthrough NMDA signaling.Chemical dynamics may be particularly important in receptor-gated channelson a spinehead and diffusesalong the the induction of LTP. The induction of LTP at the Schaffer spine neck into the dendrite. The model also includes two sat- collateral input to region CA1 pyramidal neurons requires an urable pumps and the nonlinear calcium buffer protein, cal- increase in the concentration of intracellular calcium, [Ca*+],, modulin. Simulated calcium dynamics following a train of syn- at the postsynaptic site; this increaseis thought to be mediated aptic stimuli are shown in Figure 7. Due to the small volume by Ca2+influx through the NMDA receptor complex (Dunwid- of the spine, the small Ca2+influx following synaptic stimulation die and Lynch, 1979; Collingridge et al., 1983; Lynch et al., leadsto a large transient increasein the spine calcium concen- 1983; Harris et al., 1984; Malenka et al., 1988; reviewed in tration (for the region CA1 spine used in these simulations, Brown et al., 1988a). [Ca2+ls= 10 PM correspondedto only about 300 Ca*+ ions). From a computational point of view, NMDA synapseson Thus, spinescan dramatically amplify the small incoming cal- spines can serve to implement a Hebbian rule (Stent, 1973; cium signal. However, due to the mismatch in volumes, the Brown et al., 1988a). Accordingly, computer models have in- increase in the dendritic [Caz+], is very small (several tens of creasingly focusedon the role of spinesin modulating calcium nanomolesper liter). dynamics following synaptic input (Robinson and Koch, 1984; Figure 8 illustrates both voltage and calcium attenuation along Coss and Perkel, 1985; Pongracz, 1985; Gamble and Koch, the spine neck, that is, the ratio of voltage (or calcium concen- 1987; Holmes and Levy, 1990; Zador et al., 1990; Brown et al., tration) at one location to the voltage (or calcium concentration) 1991; Koch et al., 1992). at another location, for two different manipulations. In one case, Becausethe cable equation governing electrical signal prop- the relative peak calcium increase due to influx through the agation is analogousto the reaction-diffusion equation govern- NMDA receptor channel is illustrated from the spine head to ing passive diffusion and buffering of Ca2+ ions, insights ob- the dendrite, as is the associatedpeak voltage attenuation. In a tained from the analysisof membrane potential can be applied separatesimulation, the concentration of calcium in the den- to the analysisof calcium dynamics. In many respectsthe results drite, [Ca2+ld,was “clamped” to 1 PM. The spinehead, however, are similar, but in others the conclusions are quite different, remained protected from thesehigh calcium values by the pres- owing to differencesin the relevant biophysical parameters. ence of calcium pumps in the membrane of the spine neck The ability of spinesto amplify signals,whether chemical or (Zador et al., 1990), providing a graphic illustration of the tiny electrical, can be understood by defining-by analogy with the size of the associatedspace constant. Becausethe corresponding conventional electrical input resistance-a “chemical input re- electrical leak conductance acrossthe neck is negligible,almost The Journal of Neuroscience, February 1993, 13(2) 419

‘Or

Figure 7. Spatiotemporaldynamics of Ca2+ in responseto a train of three pre- synapticstimuli (at 100 Hz) while the membranepotential in the spinewas simultaneouslyclamped to -40 mV. Changesin [Ca2+],-inducedby the calcium influx throughthe NMDA receptor channel-are restricted mainly to the spine head. The axis labeled compart- ment indicates distance from the dendritic shaft(at the origin;the spineneck ends at 1.O pm and the NMDA synapse 0 is located just below the membrane at the spinehead at 1.3 pm) (from Zador et al., 1990).

no electrical attenuation occurs when the dendrite is clamped to a fixed potential. In other words, spines may be electrical accessible but chemically isolated. It remains technically impossible to record spine EPSPs directly, so hypotheses about spine electrical function must be evaluated indirectly. Experimental techniques for assessing the more recent theoretical results on the biochemical effects of spines have developed much more rapidly. Chief among these techniques has been the optical measurement of calcium concentration by calcium-sensitive dyes. Two recent reports have usedthe calcium-dependent changesin the fluorescenceof intracellular fura- in hippocampal neuronsto test thesehypoth- eses. Miiller and Connor (199 1) studiedthe isolation ofthe dendrite from chemical changesat presumedspine headsunder conditions of orthodromic stimulation. Using a protocol of strong electrical stimulation to the associative/commissuraldistal input to region CA3 neurons,they found an increasein intraspine calcium concentration ([Ca*+],) from a resting level of about 50 Distance from base of spine (/an) nM to levels in excessof 1 PM (1.3 f 0.5 MM); in contrast, the increase at the parent dendrite was much less (to 370 f 120 Figure 8. Voltageand calciumattenuation under two differentcon- nM). Since the image was acquired over 200 msec, the actual ditions as a function of distance, from the base of the dendrite (at the peak [Ca2+lr may have been underestimated, and becauseof origin) to the head of the spine just below the NMDA channels (at 1.3 laterally projecting spines the actual increase at the dendrite wrn; the spine neck ends at 1.O pm; see arrow). Curve I shows the neak may have been overestimated. The increasewas blocked by the concentration of intracellular free calcium in response to three presyn- antic stimuli (taken from Fig. 7). Curve 2 illustrates the associated___- volt- _._ NMDA receptor antagonist D-2-amino-5phosphonovalerate age attenuation. Both voltage and free calcium attenuate by about one (AP5) suggestingthat entry was directly through NMDA recep- order of magnitude from the spine head to the base of the spine. In a tor-gated channels, possibly localized on the spine head. different simulation illustrating antidromic steady-state behavior, either Guthrie et al. (199 1) employed a similar technique to assess the calcium concentration (curve 3) or the membrane potential (curve 4) is clamped to a fixed value in the dendrite. Due to the presence of the isolation of presumedspine headsfrom [Ca”] changesat calcium pumps in the spine neck membrane, calcium rapidly attenuates the dendrite under conditions of antidromic stimulation in CA 1 and reaches baseline levels at the spine head, while the dendritic mem- pyramidal cells. Using controllable photoinduced damage to brane potential has very effective access to the spine head, since prac- increase the intradendritic calcium concentration ([Ca*+],) to tically no electrical attenuation occurs across the spine neck. 420 Koch and Zador * Function of Dendritic Spines

0.2-l .5 PM, they found that in a significant minority of spines Bliss TVP, Lomo T (1973) Long-lasting potentiation of synaptic trans- the increase in [Ca2+ls lagged behind the increase in [Ca*+ld. mission in the dentate area of the anaesthetized rabbit following stimulation of the perforantpath. J Physiol(Lond) 232:331-356. Control experiments with injected cobalt indicated that the lag Bradley P, Horn G (1979) Neuronal plasticity in the chick brain: was not due to a physical diffusion barrier between the dendrite morphological effects of visual experience on neurons in hyperstria- and the spine, supporting the idea that calcium-dependent pro- turn accessorium.Brain Res162: 1481-153. cesses, such as calcium pumps or other uptake systems, were Braitenberg V, Atwood RP (1958) Morphological observations in the cerebellar cortex. J Comp Neurol 109: l-34. responsible for isolating the spine head. 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