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2000 Nature America Inc httpllneuroscinaturecom 2000 Nature America Inc httpIneuroscinaturecom review Synaptic plasticity taming the beast L F Abbott and Sacha B Nelson Department ofBz oIogy and Volen enter lVahham V FA 0quot USA Synaptic plasticity provides the basis for most models of learning memory and development in neural circuits To generate realistic results synapsespecific Hebbian forms of plasticity such as longterm potentiation and depression must be augmented by global processes that regulate overall levels of neuronal and network activity Regulatory processes are often as important as the more intensively studied Hebbian processes in determining the consequences of synaptic plasticity for network function Recent experimental results suggest several novel mechanisms for regulating levels of activity in conjunction with Hebbian synaptic modification We review three of them synaptic scaling spike timing dependent plasticity and synaptic redistribution and discuss their functional implications Activityadependent modification of synapses is a powerful mech anism for shaping and modifying the response properties of neua rons but it is also dangerous Unless changes in synaptic strength across multiple synapses are coordinated appropriately the level of activity in a neural circuit can grow or shrink in an uncontrolled manner Hebbian plasticity in the form of longaterm potentiation LTP and depression LTD provides the basis for most models oflearning and memory as well as the development of response selectivity and cortical maps These models often invoke ad but mechanisms to stabilize levels of activity Here we review a number of recent developments both experimental and theoretical that suggest how changes of synaptic efficacy can be distributed across synapses and over time so that neuronal circuits can be modi ed exibly yet safely Hebb originally conjectured that synapses effective at evokin a response should grow stronger but over time Hebbian plasticity has come to mean any longalasting form ofsynaptic modi cation strengthening or weakening that is synapse speci c and depends on correlations between pre and postsynaptic ring By acting independently at each synapse Hebbian plasticity gains great power but also acquires stability problems To avoid excessively high or low ring rates the total amount of excitatory drive to a neuron or within a network must be tightly regulated which is difficult to do ifsynapses are modified independently What is needed is a mechanism that maintains an appropriate level of total excitation but allows this to be distributed in different ways across the synapses of a network by Hebbian processes Bienenstock Cooper and Munro suggested one such mechaa nisml In the BCM model correlated pre and I I 39 39 ity evokes LTP when the postsynaptic firing rate is higher than a threshold Value and LTD when it is lower To stabilize the model the threshold shifts or slides as a function of the average post synaptic ring rate For example the threshold increases ifthe postsynaptic neuron is highly active making LTP more difficult and LTD easier to induce Althou h this idea is attractive as a ooma putational model experimental evidence for the sliding threshold is largely indireth hree other candidate mechanisms for regulating neuronal activity during synaptic modificationisynaptic scaling spike of stabilizing Hebbian plasticity but touching brie y on other functional implications Our primary aim is to show that it is now possible to build models of synaptic plasticity based directly on experimental data that provide both exible and stable mecha7 nisms for shaping neuronal responses Synaptic scaling Hebbian plasticity is a positiveafeedback process because effective to destabilize postsynaptic firing rates reducing them to zero or increasing them excessively An effective way of controlling this instability is to augment Hebbian modi cation with additional processes that are sensitive to the postsynaptic ring rate or to the total level of synaptic efficacy A frequent approach in neural net work models is to globally adjust all the synapses onto each post synaptic neuron based on its level of activitys The adjustment can take two forms depending on whether the synapses to a particu7 lar neuron are changed by the same amount subtractive or by an amount proportional to their strength multiplicative Hebbian plasticity is often used to model the development and activityadependent modi cation of neuronal selectivity to Various aspects ofa sensory input for example the selectivity of Visually responsive neurons to the orientation ofa Visual image This typ ically requires competition between synapses so that the neuron becomes unresponsive to some features while growing more responsive to others Many of the mechanisms designed to stabilize Hebbian plasticity introduce such competition Both subtractive and 39I quot adiu tment lead quotquot because they weaken all the synapses to a given neuron if any subset of synapses evokes a high level of activity In general multiplicative global adjustment is less competitive than subtractive adjustment and it may be insuf ciently competitive for some applicationss Competition can be enhanced under a multiplicative scheme 39 synapses that are weakened below a threshold level are eliminate ed These global adjustment schemes were introduced into the models ad hat but future models can be constructed on the basis of recent data A biological mechanism that globally modifies 39 le 39 quot occurs in cultured net C I p m tiri STDP and I 39 JUuLlUl have been characterized experimentally and theoretically We review these recent developments focusing primarily on the issue 1178 r c c works of neocortical hippocampal5 and spinalacord6 neurons n 1 1 C C CIact1v1tyin nature neuroscience supplement 39 Volume 3 39 november 2000 2000 Nature America Inc httpllneuroscinaturecom 2000 Nature America Inc httpIneuroscinaturecom ig 1 S naptic scaling is multiplicative Quanta amplir TTX of miniature EPSCs o BIC r 00 m 1 o E a i m o z m a g E 2 0 o m i 1 5 E Amplitude pA tudes recorded in sister culr tures in Which activity Was either locked With sodium channel blocker tetrototoxin or enhanced by blocking inhibition With bicuculline BIC for two days Activity blockade scales up mEPSC amplitude Whereas activity enhance ment scales it down The plots are Well t by straight lines indicating that in both cases the scaling is multiplicative Adapted from ref 4 720 40 760 780 Control amplitude pA es synaptic strengths characterized by the amplitudes ofminiaa ture excitatory postsynaptic currents mEPSCs to increase in a multiplicative manner Fig 1 Conversely enhancing activity by blocking inhibition scales down mEPSC amplitudes Fig 1 Some iophysical mechanisms responsible for the bidirectiona al and multiplicative properties of synaptic scaling are understoo Direct application of glutamate4 and uorescent labeling of recepa tors5398 show that synaptic scaling is due to a postsynaptic change in the number offunctional glutamate receptors Furthermore increasing synaptic strength during reduced activity is associated with a decrease in the turnover rate of synaptic AMPAatype glue tama ferentially scaled by activity this can produce multiplicative changes in synaptic stren 7 Synaptic scaling in combination with LTP and LTD seems to generate something similar to a synaptic modi cation rule analyzed by Oja8 that illustrates the power of stable competitive Hebbian plasticity see Math Box The Oja rule combines Hebbian plastic ity with a term that multiplicatively decreases the efficacy of all synapses at a rate proportional to the s uare of the postsynaptic re ing rate In simple neuron models this generates an interesting form of input selectivity related to a statistical method called prina cipal component analysis in which neurons become selective to the linear combination of their inputs with the maximum variance This is in some sense the most interesting and informative com bination of inputs to which the neuron can become responsive Activity manipulations scale both AMPAa and NMDAareceptora mediated forms ofglutamatergic synaptic transmissiong Scaling of the NMDA receptor component has implications for Hebbian plasticity because LTP and LTD are produced by calcium entry through NMDA receptors The standard view is thatlarge amounts of calcium entry induce LTP whereas smaller amounts cause LTD lf neurons scale down NMDA receptor currents in response Fig2 The amount and type of synaptic modification STDP evoked by repeated pairing of prey and postsynaptic action potentials in different preparations The horizontal axis is the difference rpm 7 ifpost between the times of these spikes The numerical labels on this axis are approximate and are only intended to give an idea of the general scale Results are for slice recordings of neocortex layer 5 and layer 23 pyramidal and layer 4 spiny stellate cells in viva recordings of retinor tectal synapses in Xenopus tadpoleslg in mm recordings of excitatory and inhibitory synapses from hippocampal neurons 8 Ganguly et aI Soc Neumsci Abstr 25 29161999 and recordings from the electrosenr sory lobe ELL a cerebellumrlike structure in mormyrid electric shls nature neurosa encesupplement 39 Volume 3 39 november 2000 review to enhanced activity this may make it more difficult to evoke LTP and easier to induce LTD Thus in addition to multiplicatively adjusting synaptic strengths synaptic scaling may modify Hebe bian plasticity in a manner functionally similar to the BCM model39s sliding threshold Spiketiming dependent synaptic plasticity Synaptic scaling is a nonaHebbian orm of plasticity because it acts across many synapses and seems to depend primarily on the post synaptic firing rate rather than on correlations between pre and postsynaptic activity Purely Hebbian forms of plasticity can also be used to regulate total levels of synaptic drive but this requires a delicate balance between LTP and LTD The sensitivity of synapa tic plasticity to the timing of postsynaptic action potentials STDP can provide a mechanism for establishing and maintaining this balance It has long been known that presynaptic activity that precedes postsynaptic firing or depolarization can induce TP whereas reversing this temporal order causes LTD 13913 Recent experimena tal results have expanded our knowledge of the effects of spike time ing on LTP and LTD inductionM39Zl Although the mechanisms that make synaptic plasticity sensitive to spike timing are not fully understood STDP seems to depend on an interplay between the dynamics of NMDA receptor activation and the timing of action potentials backpropagating through the dendrites of the postsya naptic neuron1 392239 3 The type and amount of longaterm synaptic modification induced by repeated pairing of pre and postsynaptic action potena tials as a function oftheir relative timing varies in different prepaa rations Fig 2 In general synaptic modi cation is maximal or 39 neocortexelayer 5 a Xenopus tectum LIP hippocampus LTD neocortexrlayer 23 ippoca mpus C ELL of electric fish GABArergic neurons in hippocampal culture neocortexrlayer 4 spiny stellates tpre tpost m5 1179 2000 Nature America Inc httpllneuroscinaturecom 2000 Nature America Inc httpIneuroscinaturecom review Fig 3 Time dependence of the normalized average transmission amplir tude for a model synapse shoWing shortrterm depression and synaptic redistribution based on the model described in the Math Box FolloWing activation a a presynaptic rate of 100 Hz the average transmission amp itude decreases rapidly The control case brown shows a synapse With a maximum transmission probability of po 02 The parameter 91 is used to characterize the relative strength of the postsynaptic conducr redistribution that changes p0 to 04 but leaves 9 unchanged the average initial amplitude is increased but the ultimate average steadyrstate amplitude remains unchanged green If instead the napse is strengthened by an increase in the postsynaptic conductance Which changes 9 to 2 but leaves p0 at its initial value of 02 both the average inir tial and steadyrstate amplitudes increase orange 0 p0 02 g 1 control a 04 g 1 redistribution 08 P0 02 g 2 conventional LTP 3 Normalized average amplitude 0 50 100 150 200 Time ms small differences between pre and postsynaptic spike times and no plasticity is induced 39 this difference grows too large In some cases the sign of the time difference that is whether the presynaptic spike precedes or follows the postsynaptic spike determines whether the protocol induces LTP or LTD Fig Zaic In other cases synaptic plasticity depends on the relative timing of the pre n postsynaptic spikes but not on their order Fig 2d and e In the cerebellumelike structure of electric fish LTP and LTD are reversed relative to other systems Fig 20 perhaps because the postsynaptic neuron is inhibitory rather than excitatory We do not consider these cases further but concentrate instead on the form of plasticity observed in retinotectal connections and neoe cortical and hippocampal pyramidal cells Fig 2a and b This form of LTP timin dependence provides a mechanism for realizing Hebb s original hypothesis that synapses are strength ened only when resynaptic activity causes postsynaptic ring Such a causal relationship clearly requires the preethenepost teme poral ordering that increases synaptic ef cacy under STDP The amount of LTP falls off roughly exponentially as a function of the difference between pre and postsynaptic spike times with a time constant at is ofthe same order as a typical membrane time con stant This assures that only those presynaptic spikes that arrive within the temporal range over which a neuron integrates its inputs are potentiated further enforcing the requirement of causality STDP weakens inputs that re shortly after a postsynaptic action potential and therefore do not contribute to evoking it When presynaptic spikes occur randomly in time with respect to post synaptic action potentials both LTP and LTD can be induced and it is interesting to ask which dominates In the case oflayer 23 pyramidal neurons Fig 2b random pairings lead to an overall reduction in synaptic strength in other words LTD dominates over LTP in this case This makes functional sense because it weak ens inputs that accidentally39 fire in approximate coincidence with postsynaptic action potentials but that do not consistently con tribute to evoking them STDP is a synapseespeci c Hebbian form of plasticity and although we might expect that the ringerate instabilities that plague purely Hebbian models would also occur with STDP this is not the case STDP can regulate both the rate and Variability of postsynaptic ring243925 For this to occur synaptic strengths must be bounded between zero and a maximum allowed Value but no further global noneHebbian mechanisms or adhuc constraints are require To see how STDP can stabilize postsynaptic ring rates image ine a neuron that initially receives excessively strong uncorrelated excitatory drive from many synapses making it fire at an u ceptably high rate The strong multiesynaptic input to such a neue 1180 ron is effectively summed into a relatively constant input current In response to such input a neuron will fire in much the same way as it would in response to the injection of the equivalent constant current through an electrode by ring rapidly and regularly In such a situation the neuron acts as an integrator and there is lit tle correlation between the timing of its spikes and those of its inputs lf LTD dominates over LTP for random pre and post synaptic spike pairings this leads to an overall weakening of synaptic efficacy As STDP weakens the synaptic drive the neuron eventually moves into a regime where the average synaptic cur rent is either barely able or unable to make the postsynaptic neue ron fire In this case action potentials are primarily generated by chance clusterings in the timing of presynaptic spikes The neue ron acts somewhat like a coincidence detector and produces an irre ular pattern of postsynaptic ring Presynaptic spikes are more likely to occur slightly before than slightly after postsynaptic action potentials in thi it iatirm t of I I 39 rquot are required to evoke a postsynaptic response The dominance of pre followed by postsynaptic spiking causes synapses to be potene tiated more often than they are depressed which compensates for ing This ultimately leads to a nonuniform distribution of synape tic strengths and a postsynaptic neuron that res at a reasonable rate but irregularly25 Thus STDP not only stabilizes Hebbian modi cation it drives neurons to a noisy but temporally sensitive state that resembles what has been suggested to exist 13911 Vii02 DP so introduces competition into Hebbian plasticie ty19 2439253927 Groups of synapses that are effective at rapidly genera ating postsynaptic spikes are strengthened by STDP making them even more effective at controlling the timing of postsynaptic spikes Synapses from other inputs that fire at random times with respect to this dominant group will then be weakened ifLTD dominates over LTP for random temporal pairin s If two neurons are reciprocally connected and have correlated activities Hebbian plasticity will typically strengthen the synapses between them in a bidirectional manner This can produce strong excitatory loops that cause ecurrently 2000 Nature America Inc httpllneuroscinaturecom 2000 Nature America Inc httpIneuroscinaturecom MATH Box Although space does not permit a full discussion of the tech niques used to model the phenomena discussed in the text we present some basic approaches 1 Synaptic scaling can be implemented along with Hebbian syna tic modification by using something similar to the Oja rule of artificial neural network theory8 If the presynaptic neuron fires at a rate rpm and the postsynaptic neuron at a rate rpm the normal assumption of Hebbian plasticity is that the synaptic strength changes at a rate proportional to prerpwp Synaptic scaling can be modeled by including an additional noneHebbian term so that the synapse modifie cation rate is proportional to prerpm 7 rm W where is some function and Wis the synaptic weight parameter that characterizes the strength of the synapse In the case of the Oja rule rpgst rpm but the experimental data sup port a function that is either positive or negative depending on the postsynaptic firing ratei39s Z STDP can be modeled25 most easily by making the approxie mation that each pre and postsynaptic spike pair contributes to synaptic modi cation independen y and in a similar manner although the data show deviations from these simplifying assumptions 3918 We assume that the curves appearing in Fig 2 in particular Fig 2a and b can be approximated by two expo nential functions Ar expT with Ar gt 0 for tlt 0 and A exp ii7 with A lt 0 for 2 0 A simple way to keep track In keeping with the emphasis of this review on stability we have focused on this aspect of STDP but incorporating sensitivity to timing into Hebbian plasticity has a host of other interesting implie cations STDP can act as a learning mechanism for generating neue ronal responses selective to input timing order and sequence For example STDPelike rules have been applied to coincidence detection2 sequenoe learning28 30 ath learnin in nav39 ationsl39sz and direction selectivity in visual responsessz393 In general STDP greatly expands the capability of Hebbian learning to address teme porally sensitive computational tasks Synaptic redistribution A synapse can be strengthened postsynaptically by increasing the number or efficacy of receptor channels or presynaptically by increasing the probability or amount of transmitter release These mechanisms can have quite different functional consequences A dramatic example of this involves the interplay of long and short term synaptic plasticit S naptic depression is a form of shorteterm synaptic plasticity that seems to be a widespread feature of cortical synaptic trans mission which has significant functional implications for neural coding35 39 Shorteterm depression which is thought to arise at least in part from depletion ofthe pool of readily releasable vesie cles at a synaptic release site is a useedependent reduction in the probability that a presynaptic action potential will induce release of transmitter This takes the form of a reduction in the probabilie ty of release with each transmission event followed by an expoe nential recovery to a baseline release probability see Math Box At some cortical synapses LTP modifies the shorteterm plase ticity of synapses 03941 an effect called synaptic redistributionm Although the precise mechanism of synaptic redistribution is not known it is consistent with a form of LTP that acts presynapticale nature neurosa encesupplement 39 Volume 3 39 november 2000 review of all the spike pairs contributing to STDP at a given synapse is to define functions Ppe I and P MU that satisfy the equae and quotLLdPp d 7P 39 past 39 pze terminal receives an action potential Similarly Ppm is decremented by an amount A every time the postsynaptic neuron fires an action potential Ppe I then determines how much the synapse is strengthened ifthe postsynaptic neuron fires an action potential at time I and Ppmt determines ening and weakening are subject to constraints so that the synaptic strength does not go below zero or above a certain maximum value 3 Synaptic redistribution requires that we model the process of synaptic depression and how it is modified by LTP373939 Sup pose that a given synapse transmits a presynaptic action potene tial with probability p If the synapse has been inactive for a sufficiently long period of time p approaches its maximum value p0 When the synapse is active we assume thatp decrease es at a rate proportional to the transmission rate due for exam ple to vesicle depletion When transmission is not occurring p recovers exponentially to pa with a recovery time constant ID The assumption is then that in the case of synaptic redise tribution LTP modifies the value opr The curves in Fig 3 were generated from this model with quotED 300 ms ly to increase the probability of transmitter release This increases the likelihood of transmission occurring early in a sequence of presynaptic action potentials but also decreases the availability of readily releasable vesicles for transmission later in the sequence The overall effect is to enhance the average transmission amplie tude for presynaptic action potentials that occur after a period of inactivity but also to increase the onset rate of synaptic deprese sion Synaptic redistribution can significantly enhance the amplie tude of synaptic transmission for the first spikes in a sequence while having no effect on the ultimate steadyestate amplitude Fig 3 although this figure was generated by a model similar effects are seen experimentally373938 There is no steadyestate effect because the increased probability of release and the increased amount of shorteterm depression cancel each other It is not yet clear if forms of LTD reverse the redistribution found in LTP that is decrease the probability of release and reduce the amount of shorteterm depression After redistribution a synapse is much more effective at cone veying transients but there is no change in its efficacy for steady state transmission As a result synaptic redistribution allows Hebbian modification to act without increasing either the steady state firing rates of postsynaptic neurons or the steadyestate excitabile ity of rem imam men or T quot f r 39 J I 39 allows n 2000 Nature America Inc httpllneuroscinaturecom 5 2000 Nature America Inc httpIneuroscinaturecom review term efficacy of a synapse While decreasing its ability to sustain mule tile quot snatic quotquot39 t t 39 P r W1 exactly the properties that lead to enhancement by STDP The sequenceslearning properties of STDP also couple in interesting Ways to the temporal characteristics of synaptic depression For example synaptic depression has been suggested as a mechanism for generating direction selectivity in simple cells of the primary Visual cortex3 STDP that induces synaptic redistribution can gen erate such responses Buchs et 31 Sat Neurosci Abstr 25 2259 1999 as Well as providing a developmental mechanism for oriens tation selectivity DISCUSSION Modeling studies have clearly demonstrated the utility and power of synaptic scaling STDP and synaptic redistribution as mechanisms of learning and development Properties of these forms of plasticis ty have been shown in studies of cultured neurons and brain slices and also to some extent 13911 Viva Preliminary data suggest that blocks ing Visual input to cortical neurons 13911 Viva during the critical peris od through intraocular injection of tetrodotoxin strengthens synapses measured subsequently in slioes in a multiplicative man ner NS Desai SBN and QC Turrigiano unpublished data This effect is similar to the synaptic scaling induced by blocking activity in culture preparations Recordings from hippocampal plaoe cells of behaving rats suggest that STDP may occur during normal behavior323945 Place cells fire when a rat passes through a particus lar location known as the place field in a familiar environment Models that inoorporate STDP predict that plaoe elds located along a path that a rat traverses repeatedly in a xed direction should sh39 backward along the path that is in the direction opposite to the rat s motion as a result of this experiencezglsl The redicted shifts have been observed experimentallysz 45 Finally evidence for t e occurrence of synaptic redistribution 13911 Viva is provided by slice recordings following sensory deprivation in rat somatosensory cortex All three mechanisms We have discussed can contribute to the stability of neuronal firing rates and they might thus appear reduns dant However each has its own distinctive functional roles Synaps tic scaling by realizing something equivalent to the Oja rule can cause a neuron to become selective to the most Variable aspects of its inputs Furthermore among the mechanisms We have discussed synaptic scaling is the only one that does not require postsynaptic activity It can thus rescue a neuron that has become inactive due to insuf cient excitatory synaptic drive Both STDP and synaptic redistribution can produoe interesting temporal effects STDP pros Vides a mechanism for learning temporal sequences but in some e addition of a synaptic scaling mechanism to s to modify transient rather than steady state responses Thus it seems likely that all three forms of plastics ity and other forms that We have not discussed are needed to provide a full repertoire of developmental and learning mechanisms Most excitatory synapses onto excitatory neurons but not onto inhibitory neurons examined to date show some form of long term plasticity The forms of plasticity at least as characterized by their temporal sensitivity Vary considerably across different brain regions and even across layers Within one region Fig 2 Similar ly redistribution occurs at neocortical synapses 03941 but seems not to be a feature of LTP in the CA1 region ofthe hippocampusiglso Given the complexity oflearning and memory it is not surprising to see many forms of synaptic plasticity with different mechanisms of induction and expression Determining hoW these t together 1182 to account for the Wide Variety oflearning and developmental phe nomena is a challenge for theoretical Work in the years ahead ACKNOWLEDGEMENTS quot A U LFVllllH L Theoretical Neurobiology at Brandeis Universin and the WM Keck Foundation We thank Gina Turrigiarlo Eve Marder andlesper Sjostro m for comments RECEIVED 24 M Y39 CCEPTED 26 SEPTEMBER 2000 Bienenstock E L Cooper L N 81 Munro P W Theory for the development of neuron selectivity orientation specificity and binocular interaction in visual cortex Neurosci 2 32748 1982 2 AbrahamW C M tanlxti r Prog Neumbiol 52 3037323 1997 3 Miller K D 81 MacKay D J C The role of constraints in llebbian learning Neural Comput 6 1007126 1994 4 Turrigiano G 3 Leslie K 12 Desai N s Rutherford L C 81 Nelson 3 B W s m 391 8927896 1998 Lrssen D v et a1 Activity differentially regulates the surface expression of synaptic AMPA and NMDA glutamate receptors Proc Natl Acad sci USA 95 709777102 1998 9 O39Brien R J et a1 Activityrdependent modulation of synaptic AMPA receptor accumulation Neuron 21 106771078 1998 7 Turrigiano G G amp Nelson B Thinking globally acting locally AMPA receptor turnover and synapticstrength Neuron21 9337941 1998 ja simplified neuron mo e as a principal component analyzer Math Biol 15 2677273 1982 Watt A J van Rossum M C W MacLeod K M Nelson 3 B amp Turrigiano G G Activity corregulates quanta AMPA and NMDA currents at neocortical synapses Neuron 26 6597670 2000 10 Lisman J The CaMrkinase hypothesis for the storage of synaptic memory TrendsNeurosci 17 4067412 1994 Levy W B amp Steward D emporal contiguity requirements for longrterm associative potentiationdeprexion in the hippocampus Neuroscience 8 7917797 1983 2 Custafson B Wigstrom 1l Abraham W C amp lluang mt Longrterm potentiation in the hippo m s using depolarizing current pulses as the conditioning stimulus to single volley synaptic potentials Neurosci 7 7747780 1987 13 Debanne D Gahwiler B H amp Thompson s M Asynchronous pre and ofthe rathippocampus in vitro PmcNat1Acad Sci USA 91 114871152 1994 Mar am ll Lubke J Frotscher M 81 sakman B Regulation of synaptic ef cacy by coincidence of postsynaptic APs and EPSPs science 275 2137215 1997 15 Magee J C Johnston D A synaptically controlled associative signal for Hebb39 plasticity in hippocampal neurons science275 2097213 1997