Recordings from brain regions involved in memory ... formation of autoassociative LTM requires .... networks that integrate the STM and LTM networks. (A).
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Physiologically realistic formation of autoassociative memory in networks with theta/gamma oscillations: role of fast NMDA channels. O Jensen, M A Idiart and J E Lisman Learn. Mem. 1996 3: 243-256
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Physiologically Realistic Formation of Autoassociative Memory in Networks with Theta/Gamma Oscillations: Role of Fast NMDA Channels Ole Jensen, ~ Marco A.P. Idiart, 2 and J o h n E. Lismanl'3 lV01en Center for Complex Systems Brandeis University Waltham, Massachusetts 02254 2Institut0 Fisica UFRGS 91501-970 Porto Alegre, RS Brazil cortex. This is the first p r o p o s a l for the special role of these fast NMDA c h a n n e l s . The STM for novel items m u s t d e p e n d o n activity-dependent c h a n g e s intrinsic to neurons rather than recurrent connections, w h i c h have n o t d e v e l o p e d the r e q u i r e d selectivity. Because these intrinsic m e c h a n i s m s are n o t error-correcting, STM will b e c o m e slowly c o r r u p t e d by noise. This limits the accuracy with w h i c h LTM can b e c o m e e n c o d e d after a single p r e s e n t a t i o n . Accurate e n c o d i n g of items i n LTM can be achieved by m u l t i p l e p r e s e n t a t i o n s , provided different m e m o r y items are p r e s e n t e d in a varied i n t e r l e a v e d order. O u r results indicate that a limited m e m o r y - c a p a c i t y STM m o d e l can be integrated in the same n e t w o r k with a high-capacity LTM m o d e l .
Abstract Recordings f r o m b r a i n regions involved in m e m o r y f u n c t i o n s h o w dual oscillations in w h i c h each cycle of a l o w - f r e q u e n c y theta oscillation (5-8 Hz) is subdivided into a b o u t seven subcycles by h i g h f r e q u e n c y g a m m a oscillations (20-60 Hz). It has b e e n p r o p o s e d (Lisman a n d Idiart 1995) that such n e t w o r k s are a m u l t i p l e x e d s h o r t - t e r m m e m o r y (STM) buffer that can actively m a i n t a i n a b o u t seven m e m o r i e s , a capability of h u m a n STM. A m e m o r y is e n c o d e d by a subset o f principal n e u r o n s that fire s y n c h r o n o u s l y in a particular g a m m a subcycle. Firing is m a i n t a i n e d by a m e m b r a n e process intrinsic to each cell. We n o w e x t e n d this m o d e l by i n c o r p o r a t i n g r e c u r r e n t c o n n e c t i o n s with modifiable synapses to store l o n g - t e r m m e m o r y (LTM). The r e p e t i t i o n p r o v i d e d b y STM gradually modifies synapses in a physiologically realistic way. Because different m e m o r i e s are active in different g a m m a subcycles, the f o r m a t i o n of autoassociative LTM r e q u i r e s that synaptic modification d e p e n d o n N-methyl-D-aspartate (NMDA) c h a n n e l s having a time constant of deactivation that is of the same o r d e r as the d u r a t i o n of a g a m m a subcycle (15-50 msec). Many types of NMDA c h a n n e l s have l o n g e r time constants (150 msec), as for instance those f o u n d in the h i p p o c a m p u s , b u t b o t h fast a n d slow NMDA c h a n n e l s are p r e s e n t in
Introduction Insights into the mechanisms of memory have come from several different fields. Psychophysical work indicates the existence of a short-term memory (STM) mechanism of limited capacity (7---2 items) (Miller 1956) and a long-term memory (LTM) mechanism of much higher capacity. Physiological work indicates that STM is maintained by persistent cell firing (Fuster and Jervey 1982; Goldmann-Rakic 1995), whereas LTM appears to be maintained by modifications of synaptic strength (Bliss and Collingridge 1993; Morris et al. 1986). Theoretical analysis of neural networks has indicated how recurrent collaterals with modifiable synapses can lead to distributed storage of
3Corresponding author.
LEARNING & MEMORY 3:243-256 © 1996 by Cold Spring Harbor Laboratory Press ISSN1072-0502/96 $5.00
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LTM (Hopfield 1982; Amit 1989; Hertz et al. 1991). Most recently it has been found that networks involved in memory storage show complex oscillatory dynamics. The hippocampus and some regions of cortex have dual oscillations in which a low-frequency oscillation in the theta frequency range ( 5 - 8 Hz) is subdivided into subcycles by a high-frequency oscillation in the gamma ( 2 0 - 6 0 Hz) range (Biedenbach 1966; Bressler 1984; Soltesz and Deschenes 1993; Bragin et al. 1995). We have been interested in synthesizing the results from these fields. Our initial work focused on the relationship between network oscillations and the psychophysical properties of STM (Lisman and Idiart 1995). We proposed that dual oscillations serve as a multiplexing mechanism by which multiple short-term memories can be actively maintained in the same network. A STM is assumed to be encoded by a subset of cells that fire synchronously during a given gamma subcycle, an assumption consistent with previous work indicating the importance of synchrony (Gray et al. 1989; Abeles et al. 1993). Because there are about seven gamma cycles in a theta cycle, this could explain why STM is limited to seven items. Further support for this view is that tb~ Sternberg number (Sternberg 1966), which is a psychophysical measurement of the temporal separation of memories, approximately equals the period of a gamma oscillation. The proposition that different information is stored at different phases of a theta cycle (i.e., in different gamma subcycles) is made plausible by studies of hippocampal place cells (O'Keefe and Recce 1993; Skaggs et al. 1996) showing that different cells fire with different phases during the theta cycle. A second feature of our previous model is the mechanism by which the firing that underlies STM is maintained. Action potentials triggered at the time of information input to the network trigger an after-depolarization (ADP) that is intrinsic to each neuron (Lisman and Idiart 1995). An ADP of this kind has been observed in hippocampal and cortical neurons (Andrade 1991; Caeser et al. 1993; Storm 1989; Libri et al. 1994). The ADP has sufficient duration to trigger firing on subsequent theta cycles and thereby maintains STM. This mechanism for maintaining firing stands in contrast to reverbatory mechanisms involving loops of interconnected cells (Hebb 1949). In our previous STM model (Lisman and Idiart 1995) there was no mechanism for LTM (Fig. 1A). In contrast standard neural network models (Hopfield 1982; Amit
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InformationalInput Modifiable Synapses"-4-, ;~ - Recurrent ,I _-Collaterals Osfilla[°rY~] F e ~1 d]i d [L1l ~]l (gam~imC°a~ ( t h e t a ~ InformationalInput
C Modifiable InformationalInput Synapses / (NMDA/AMPA).L' ..t. - Recurrent - Collaterals
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>-----3----- > - -- ~
Feedback Inhibition (gamma)
Figure 1 : The goal of this series of papers is to examine networks that integrate the STM and LTM networks. (A) STM network in which information is stored using the ADP that is intrinsic to each pyramidal cell. Dual oscillations occur because of external theta-frequency input and because of feedback inhibition from an inhibitory interneuron, which generates the gamma cycles. (B) Autoassociative network in which LTM is encoded in modifiable recurrent synapses. (C) Integrated network that has both STM and LTM. Synaptic modification is governed by fast NMDA channels. Synaptic transmission is mediated by AMPA channels.
1989; Hertz et al. 1991) have recurrent collaterals with modifiable synapses (Fig. 1B) for storing LTM, but no mechanism for storing novel STMs. Our goal in this and the subsequent papers in this series is to examine networks that have both STM and LTM. As shown in Figure 1C, the ADP feature of our STM model and the modifiable synapses of standard LTM models are compatible and integrated models can be analyzed. By studying the interaction of STM and LTM, we have attempted to capture temporal complexities of real learning situations and the kinetic properties of the cellular processes that underlie learning. It is a general assumption of our work that synaptic modification similar to long-term potentiation (LTP) and long-term depression (LTD) underlies the storage of LTM (Morris et al. 1986), even though this is not firmly established. Experimental evidence indicates that LTP occurs slowly and requires repetitive firing (Larson et al. 1986; Hanse and Gustafsson 1994). Specifically, experiments on hippocampal LTP show that induction
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a p h o n e n u m b e r ) . W e s h o w that learning seq u e n c e s of k n o w n items can o c c u r after a single presentation. Therefore, this is a m o d e l of episodic memory. Because h i p p o c a m p a l synapses have only slow NMDA c h a n n e l s (Forsythe and W e s t b r o o k 1988; Jahr and Stevens 1990), an i m p l i c a t i o n is that the h i p p o c a m p a l CA3 region, long thought to b e an autoassociative network, m a y actually be a heteroassociative n e t w o r k specialized for seq u e n c e learning. The ability of such heteroassociative m o d e l s to quantitatively a c c o u n t for important properties of h i p p o c a m p a l p l a c e cells is described in a final p a p e r in this series ( J e n s e n and Lisman 1996a, this issue).
requires a s e c o n d or m o r e high-frequency stimulation u n d e r standard conditions (Bliss and LOmo 1973). O n c e LTP has b e e n i n d u c e d it takes additional t i m e ( t e n s of s e c o n d s ) to express itself ( H a n s e and Gustafsson 1994). Thus a STM buffer is n e e d e d b o t h to cause the persistent firing r e q u i r e d for transfer of information to LTM and to maintain information until LTM is expressed. An additional c o m p l e x i t y is that m e m o r y items often arrive in streams of m u l t i p l e items p e r s e c o n d rather than as single items. An STM buffer that can capture m u l t i p l e items and actively m a i n t a i n t h e m is capable of dealing w i t h such streams. In this p a p e r w e deal specifically w i t h the learning of n o v e l items. An e x a m p l e w o u l d be the first t i m e one is e x p o s e d to a digit. W e s h o w that this novelty creates special p r o b l e m s for STM and the c o r r e c t f o r m a t i o n of autoassociative LTM. In a different class of STM tasks, the items t h e m s e l v e s are already k n o w n (e.g., the digits); what has to be r e m e m b e r e d is w h i c h items are present and in w h a t order, as for instance in a p h o n e n u m b e r . The fact that the individual items are familiar implies that t h e y are already stored autoassociatively in LTM. In the s e c o n d p a p e r in this series (Jensen and Lisman 1996b, this issue) w e s h o w h o w these representations in LTM can dramatically e n h a n c e the reliability w i t h w h i c h arbitrary lists of such items can b e stored in STM. A critical insight to e m e r g e from our analysis of n e t w o r k s w i t h t h e t a / g a m m a oscillations regards the i m p o r t a n c e of the kinetics of N-methyl-D-aspartate (NMDA) channels. These c h a n n e l s control the i n d u c t i o n of LTP at H e b b i a n synapses (for review, see Bliss and Collingridge 1993). Recent w o r k shows that different subtypes of the NMDA channel have very different time constants of deactivation ( H e s t r i n et al. 1994; M o n y e r 1994; S. Vicini, J.F. Wang, J.S. Poling, and D.R. Grayson, pers. comm.). Fast NMDA c h a n n e l s have a time constant on the same scale as a g a m m a cycle, but other isoforms have m u c h longer time constants. In this p a p e r w e s h o w that fast NMDA channels ('r ~ 25 m s e c ) have kinetics that are appropriate for the f o r m a t i o n of autoassociative LTM. W e s h o w that NMDA c h a n n e l s w i t h a slow time constant for deactivation (a- ~ 150 m s e c ) w o u l d not b e well suited for f o r m i n g autoassociative m e m o r i e s , but are ideally suited for forming heteroassociative m e m o r y sequences. In the third paper in this series ( J e n s e n and Lisman 1996c, this issue), w e s h o w h o w n e t w o r k s w i t h slow NMDA channels can form LTM for s e q u e n c e s of k n o w n items (e.g.,
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Materials and Methods The field of n e u r o n a l m o d e l i n g spans from imp l e m e n t a t i o n of abstract b i n a r y n e u r o n s to detailed c o m p a r t m e n t a l models. An i n t e r m e d i a t e app r o a c h has b e e n used here. The n e u r o n s are simplified to have a single c o m p a r t m e n t , b u t i m p o r t a n t t e m p o r a l characteristics of s o m e m e m brane processes are explicitly m o d e l e d . W e have i m p l e m e n t e d the n e t w o r k using spiking m o d e l n e u r o n s so that STM can be e n c o d e d b y s y n c h r o n y of spikes rather than b y rates ( G e r s t n e r et al. 1993; Hopfield and Hertz 1995). The architecture of the n e t w o r k is illustrated in Figure 1C. The net c u r r e n t to each p y r a m i d a l n e u r o n in the n e t w o r k is a p p r o x i m a t e d b y
inet = ileak + iADP + iA + itheta + iGABA + isyn + iext
(1) For simplicity w e have i g n o r e d the p r o p e r t i e s of the m e m b r a n e capacitance. The m a i n effect of the capacitance is to slow d o w n transients and to filter noise. Because w e have not m o d e l e d the m e m brane capacitance explicitly w e have slightly slowed the kinetics of synaptic currents, so that the resulting synaptic voltage events have reasonable kinetics.
V( t) = Rmembrane( iADp( t ) + iA ( t) + itheta( t) + iGABA( t) + isyn(t) + iexAt)) + Wrest
(2)
The average input resistance in p y r a m i d a l CA3 cells has b e e n found to b e ~ R m e m b r a n e ~- 33 Mfl ( T u r n e r and Schwartzkroin 1983). SPIKING W e have not i m p l e m e n t e d the fast c u r r e n t s involved in action potentials and bursting. A spike
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is m o d e l e d as an instantaneous event that occurs w h e n t h r e s h o l d is reached, Vthres = - - 5 0 mY. The cell is t h e n reset to Wrest~- --60 mY. •:
AFTER-DEPOLARIZATION (ADP) Pyramidal cells e x h i b i t an after-depolarization (ADP) after spiking d u r i n g cholinergic (Storm 1989; Andrade 1991; Caeser et al. 1993; Libri et al. 1 9 9 4 ) or serotonergic m o d u l a t i o n (Araneda and Andrade 1991 ). The ADP provides a r a m p of excitation that builds up after a spike, w i t h i n a time of 200 m s e c and t h e n falls. W e m o d e l iAo P by an alpha function:
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Figure 2: Mechanism of STM network (Fig. 1A). The first memory pattern is introduced at t= 160 msec. The solid line in (B) is the membrane potential from cell 1 that encodes pattern 1. The broken line is the membrane potential from cell 6 that encodes pattern 2. The ramp of excitation, the ADP, is shown for cell 1 and cell 6 in C. The spiking of an activated cell is maintained by the ADP and the frequency of the spiking is locked to the subthreshold theta input (D). At t= 500 msec the second pattern is introduced. As seen in E, the feedback inhibition keeps the memories separated in time.
1991; Bragin et al. 1995), e n t o r h i n a l c o r t e x ( G r e e n and Arduini 1954; Mitchell and Ranek 1980), the cingulate c o r t e x (Leung and Borst 1987) and n e o c o r t e x ( B i e d e n b a c k 1966; Silva et al. 1991; Nakamura et al. 1992). The m e d i a l septum provides b o t h cholinergic and GABAergic projections to the e n t o r h i n a l - h i p p o c a m p a l - e n torhinal loop (Stewart and Fox 1990). Furthermore, temporal correlations b e t w e e n active cells in the s e p t u m and the h i p p o c a m p a l system indicate that not only does the s e p t u m p r o v i d e a constant cholinergic m o d u l a t i o n that facilitates oscillations, but it also i n d u c e s a phasic drive (Alonso et al. 1987). Regions in m e d i a l forebrain having the same oscillatory p r o p e r t i e s as the s e p t u m are k n o w n to project to cortical areas (Alonso et al. 1996). W e imagine that the same type of projections drives certain cortical regions at theta fre-
(4)
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Theta oscillations have b e e n identified in the h i p p o c a m p u s ( V a n d e r w o l f 1969; Stewart and Fox
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w h e r e rA = 5 m s e c (see Storm 1990 for approxim a t e values).
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The fast AHP c u r r e n t p r e v e n t s pyramidal cells from fast, repetitive firing. W e m o d e l the current b y a d e c r e a s i n g exponential:
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W h e n e v e r the cell spikes again, the ADP is reset and starts to b u i l d up again. W e have used "rApe = 200 msec. This m e a n s that the ADP starts to d e c l i n e just after a s u b s e q u e n t theta cycle unless the ADP is refreshed. It is this decline that underlies the d r o p o u t of a p r e v i o u s l y inserted m e m o r y w h e n an e i g h t h m e m o r y is i n t r o d u c e d (see Fig. 5 of J e n s e n and Lisman 1996b, this issue). A conseq u e n c e of picking the T of the ADP in this way is that the ADP is fairly flat (Fig. 2c) at the time w h e n the ADP triggers spiking. It is for this reason that the t i m i n g r a m p s p r o v i d e d by the ADP can be disr u p t e d b y low levels of noise. W e suspect that a m o r e c o m p l e x and realistic m o d e l of the ADP w o u l d allow m o r e realistic choices of m e m b r a n e noise.
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pattern #2
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q u e n c y just as the s e p t u m drives the hippocampus. H e n c e the oscillatory i n p u t to cortex and hipp o c a m p u s is m o d e l e d as
itheta(t) = BthetaSin(2ffrft)
SYNAPTIC INPUT The r e c u r r e n t collaterals are all excitatory and make one to one c o n n e c t i o n s w i t h all of the pyramidal cell. The synaptic transmission is m e d i a t e d by synaptically released glutamate b i n d i n g to AMPA and NMDA receptors. The synaptic i n p u t to cell i is
(5)
w h e r e the theta f r e q u e n c y f = 6 Hz.
iisyn(t) = IAMPA(t) .i .i + INMDA(t)
(7)
FEEDBACK INHIBITION w h e r e the AMPA c u r r e n t is m o d e l e d b y an alphafunction
In general, i n t e r n e u r o n s have b e e n found to p r o v i d e a p o w e r f u l i n h i b i t o r y f e e d b a c k to the pyramidal cells, ( A n d e r s e n et al. 1963; A n d e r s e n et al. 1964; C o b b et al. 1995). Furthermore, intracellular recordings, in vivo, from basket cells in the rat h i p p o c a m p u s s h o w that these cells fire at g a m m a f r e q u e n c y (Sik et al. 1995) on the positive p o r t i o n of the theta oscillation. Place cell recordings of rats s h o w that i n t e r n e u r o n s fire at a m u c h h i g h e r f r e q u e n c y than the p y r a m i d a l neurons, and that they have no spatial selectivity Clung et al. 1994). This suggests that the inhibitory feedback c o u l d b e r e s p o n s i b l e for generating the g a m m a oscillations in the following way: The firing of a subset of the p y r a m i d a l n e u r o n s will excite the entire i n t e r n e u r o n a l n e t w o r k through c o n v e r g i n g excitatory inputs. The i n t e r n e u r o n s will t h e n provide an i n h i b i t o r y f e e d b a c k to all pyramidal cells. After the i n h i b i t i o n wears off, a n e w subset of pyramidal n e u r o n s will b e c o m e active and so forth. Because w e assume that all i n t e r n e u r o n s fire in s y n c h r o n y w e s i m p l y m o d e l the net GABAergic i n p u t as
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t--~ire~-tdelaY~TAMPA /_
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h c r e W~y,, ~J is the relative a m p l i t u d e of an EPSC in cell i evoked by cell j. For the t i m e course of the AMPA-mediated EPSCs we have chosen TaMpa = 1.5 m s e c ( W i l l i a m s and J o h n s t o n 1991). In this p a p e r ( b u t not in J e n s e n and Lisman 1996a,c, this issue) w e assume that only AMPA receptors participate in p r o d u c i n g the EPSP; ANMDA = 0 mA. H o w e v e r the fall and rise t i m e for the NMDA c o m p o n e n t is of i m p o r t a n c e for synaptic modification, TNMDAf=7.0 m s e c and TNMDa,r = 1.0 msec. The delay in the r e c u r r e n t feedback is tdelay = 0.5 msec.
=
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w h e r e tj refers to the action potential of the j t h p y r a m i d a l cell. W e have c h o s e n TGABA 4 m s e c (Miles 1990). The t e r m a N serves to normalize the GABAergic i n p u t if the n e t w o r k size is changed. N is the n u m b e r of p y r a m i d a l n e u r o n s in the network. The constant a denotes the sparseness of p y r a m i d a l cells c o d i n g for information (i.e., a = M / N w h e r e M is the n u m b e r of cells representing a pattern). In these papers w e always keep M constant: M = a N = 5.
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and the NMDA c u r r e n t b y a d o u b l e e x p o n e n t i a l
iGaeA(t) =
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SYNAPTIC MODIFICATION The repetition of m e m o r y patterns in the short-term m e m o r y buffer allows us to c o n s i d e r
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to travel from the s o m a to the synapses of the r e c u r r e n t collaterals. The first t e r m in the expression is responsible for i m p l e m e n t i n g H e b b i a n LTP. If bglu ( t ) a n d ipost ( t ) peak at the same time, w/j will a p p r o a c h one w i t h the characteristic time "~pp (ass u m i n g "~pp < < "rnpp and Zpp < < If the preand postsynaptic events are slightly a s y n c h r o n o u s , the potentiation is g r a d e d w i t h r e s p e c t to the temporal separation of the events. If the events are fully a s y n c h r o n o u s a d e c r e a s e in synaptic efficacy occurs: LTD (for review, see Christie et al. 1994; Linden 1994). This is m o d e l e d by the s e c o n d term. If a p r e s y n a p t i c e v e n t o c c u r s w i t h o u t a postsynaptic event, the synaptic w e i g h t w# app r o a c h e s zero w i t h a characteristic time "gpnp (pre-, not post-). Similar if only a p o s t s y n a p t i c event occurs, a p p r o a c h e s zero w i t h the time Tnpp ( n o t pre-, post-). W e apply the values Zpp = 50 m s e c and "rpnp=Tnpp = 250 msec. N o t e that the learning rule w e use causes the value at w h i c h synapses saturate to be g r a d e d w i t h r e s p e c t to the convolved pre- and p o s t s y n a p t i c activity no m a t t e r h o w m a n y times stimulation is repeated.
physiological realistic learning rules. Long-term p o t e n t i a t i o n (LTP) is a possible physiological imp l e m e n t a t i o n of the Hebb-rule: Simultaneous preand p o s t s y n a p t i c activity e n h a n c e s synaptic efficacy. The e n h a n c e m e n t has b e e n s h o w n to dep e n d on NMDA r e c e p t o r s that are activated by the binding of glutamate. The activated NMDA receptors allow an i n w a r d c u r r e n t of Ca 2 +, p r o v i d e d t h e r e is sufficient postsynaptic depolarization. T h r o u g h less u n d e r s t o o d mechanisms, the Ca 2+ rise triggers LTP by increasing AMPA- and N M D A - m e d i a t e d synaptic responses (for review, see Bliss and Collingridge 1993). W e assume that the p o s t s y n a p t i c depolarization is attributable to b a c k - p r o p a g a t i n g action potentials or o t h e r dendritic depolarizing events that o c c u r w i t h a small delay relative to the spike initiation in the somatic r e g i o n ( M a r k r a m et al. 1995):
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w h e r e "rpost = 2.0 m s e c is the duration of a backp r o p a g a t i n g spike at the postsynaptic spine. As m e n t i o n e d , the kinetics of the NMDA channels is going to be crucial for the function of the n e t w o r k . W e m o d e l the time c o u r s e of the glutam a t e b o u n d to the NMDA r e c e p t o r s by a double exponential:
NOISE As a c o m p u t a t i o n a l c o n v e n i e n c e w e add Gaussian noise to the firing t h r e s h o l d of e a c h p y r a m i d a l cell at each g a m m a cycle. The standard deviation is (r = 0.05 mV.
,lU,t,:xp(
EXTERNAL INPUT (11)
The external input iex t s e r v e s to excite pyramidal n e u r o n s w h e n m e m o r i e s are i n t r o d u c e d . In the simulations w e always i n t r o d u c e novel patterns at the troughs of theta cycles. We have used the c o n s t a n t s Aaoe = 300 pA, Btheta = 150 pA, A A = -- 120 pA, = -- 180 pA and AAMPA----700 pA. Slightly different p a r a m e t e r s are used in s o m e of the simulations in J e n s e n and Lisman (1996a,b,c this issue). See figure captions for details. W h e n calculating the m e m b r a n e p o t e n tials numerically w e use the time step A t = 0.1 msec. In the simulations w e use a n e t w o r k of 10 to 40 cells. W e use relatively f e w cells in o u r simulations for the sake of fast simulations.
W e apply the values TNMDAf=7.0 m s e c and "~NMDA,r= 1.0 m s e c to characterize the kinetics of the fast NMDA r e c e p t o r s ( M o n y e r et al. 1994; S. Vicini, J.F. Wang, J.S. Poling, and D.R. Grayson, pers. comm.; see Discussion). Finally, the synaptic strength f r o m cell i to cell j is d e t e r m i n e d by:
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GENERAL PROPERTIES OF NETWORK FUNCTION (12) Before p r o c e e d i n g w i t h issues related to LTM, it will be useful to describe h o w the STM n e t w o r k
w h e r e "rdetay is the time it takes an action potential
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FORMATION OF ASSOCIATIVE MEMORY
Figure 2E shows the f e e d b a c k i n h i b i t i o n that follows each action potential. It is this i n h i b i t i o n that serves to restrict firing to discrete phases of the theta oscillation. The order in w h i c h a set of m e m o r i e s is repeated in the STM buffer is i n d e p e n d e n t of the exact phase of i n t r o d u c t i o n of n e w m e m o r i e s . Figure 3 shows w h a t h a p p e n s w h e n a fourth m e m o r y is p r e s e n t e d to a n e t w o r k that already contains three active m e m o r i e s . As can b e seen, the fourth m e m o r y is always stored in the fourth g a m m a cycle. Over a certain range, the exact phase of introd u c t i o n is not i m p o r t a n t (phases d u r i n g active firing of m e m o r i e s already in the buffer w e r e not e x a m i n e d ) . It w o u l d s e e m to b e i m p o r t a n t that a n e w m e m o r y is not i n t r o d u c e d d u r i n g the p e r i o d that previously inserted m e m o r i e s are active and w e imagine that a n e t w o r k earlier in the sensory pathway has the capability of storing information for up to several h u n d r e d m i l l i s e c o n d s and controlling the entry of information into the shortterm buffer. The discretization of sensory processing by oscillations, e v e n at the level of the retina ( N e u e n s c h w a n d e r and Singer 1 9 9 6 ) and the very short-term m e m o r y processes t e r m e d iconic (Long 1980) and e c h o i c m e m o r y p r e s e n t in primary sensory c o r t e x ( W i c k e l g r e n 1969; Lu et al. 1992) m a y fulfill these r e q u i r e m e n t s .
acts as a buffer to capture multiple items as they o c c u r in real time. An STM is r e p r e s e n t e d by the c o i n c i d e n t firing of a subset of n e u r o n s w i t h i n a particular g a m m a cycle. Different m e m o r i e s are e n c o d e d b y different subsets. In Figure 2A,B one m e m o r y is i n s e r t e d into the buffer at 160 m s e c by an external i n p u t that s y n c h r o n o u s l y fires five of the cells shown. This firing triggers a slowly rising ADP. The ADP causes the cells to fire on the subs e q u e n t theta cycle (Fig. 2A,B). W h e n this happens, the ADP r a m p is reset ( r e f r e s h e d ) making it possible for the same processes to occur on the n e x t theta cycle. A s e c o n d m e m o r y is inserted 340 m s e c after the first in the trough of the theta cycle. This leads to s y n c h r o n o u s firing of two other cells. O n s u b s e q u e n t theta cycles, the d y n a m i c s of the n e t w o r k lead to the firing of this m e m o r y in the s e c o n d g a m m a cycle. G a m m a cycles are separated b y 12 m s e c ( 8 0 Hz) in this simulation. The fact that the m e m o r i e s o c c u r r e d 340 m s e c apart, but are r e c r e a t e d w i t h a separation of 12 msec, is w h a t is t e r m e d time c o m p r e s s i o n (Tank and Hopfield 1987; Skaggs et al. 1996). Because multiple m e m ories are actively m a i n t a i n e d in different time slots, w e refer to this as a m u l t i p l e x e d STM buffer. The f u n c t i o n of the n e t w o r k can b e understood in terms of the c o m p o n e n t currents of the p y r a m i d a l cells (Fig. 2C-E). The ADP causes persistent firing and controls the timing of the firing. In the right part of Figure 2C it can be seen that the r a m p s for the two m e m o r i e s are slightly offset in time and it is this offset w h i c h brings cells that e n c o d e the first m e m o r y to threshold before cells that e n c o d e the s e c o n d ( w i t h i n each theta cycle).
LIFETIME OF NMDA CHANNELS COMPARED WITH THE DURATION OF A GAMMA CYCLE W e n o w consider h o w LTM f o r m a t i o n w o u l d occur if the STM buffer d e s c r i b e d above had re-
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Figure 3" The order of memories in the STM buffer is independent of the exact phase at which they are introduced. A new memory (#4) is introduced to the network at different phases. As seen, the new memory always ends up being the last to be activated in the buffer (i.e., the order of the memory items in the STM is independent of when they are presented). The new memory is introduced at the phases 0, 270, 90, and 170. Introduction of new memory during the activity of an old memory was not considered (see text).
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2 post-syn. membran~ potential
c u r r e n t c o n n e c t i o n s w i t h modifiable synapses. W e assume that all principal n e u r o n s are interconn e c t e d b y r e c u r r e n t s (Fig. 1C). Physiological w o r k o n H e b b i a n synapses allows us to p r e d i c t w h a t will h a p p e n at these r e c u r r e n t synapses. Although as stated by Hebb, s y n c h r o n o u s firing in the presynaptic and postsynaptic cell is the condition for s t r e n g t h e n i n g synapses, the exact m e a n i n g of sync h r o n y was not defined. E x p e r i m e n t s show that LTP can o c c u r even w h e n the postsynaptic depolarization occurs w i t h a delay after presynaptic firing (Levy and Steward 1983; Gustafsson and WigstrOm 1986; Gustafsson et al. 1987; Larson and Lynch 1989). The time constant of deactivation of the NMDA c h a n n e l s d e t e r m i n e s h o w long this delay can be. The d e p e n d e n c e of synaptic modification ( A w ) on the t i m i n g of pre- and postsynaptic activity in t h e t a / g a m m a n e t w o r k s is illustrated in Figure 4. W h e n m e m o r y 1 is activated, glutamate is released from the axons of the pyramidal cells coding for m e m o r y 1. The glutamate b i n d s to the NMDA r e c e p t o r s on all postsynaptic pyramidal cells and leads to an activated state (Fig. 4B1). C h a n n e l s in the activated state can open, but only if the postsynaptic cell depolarizes to relieve the Mg 2+ block. W h e n o p e n i n g occurs, there is an influx of Ca 2+ ( n o t m o d e l e d explicitly) w h i c h leads to LTP. This increases the synaptic strength b y a value ( A w q ) p r o p o r t i o n a l to the convolution of the time course of the activated state of the NMDA c h a n n e l s and the postsynaptic depolarization (see Material and Methods). Figure 4 shows that the synaptic c o n n e c t i o n s that are s t r e n g t h e n e d in a t h e t a / g a m m a n e t w o r k d e p e n d critically on the time constant of deactivation of NMDA c h a n n e l s ( u n b i n d i n g of glutamate). If the NMDA c h a n n e l s have fast deactivation and therefore span only one g a m m a cycle (Fig. 4B1), t h e n cells that fire in different g a m m a cycles (Fig. 4A) and therefore r e p r e s e n t different m e m o r i e s , will not have the synapses b e t w e e n t h e m s t r e n g t h e n e d (Fig. 4B2, Awij ). The only conn e c t i o n s that are s t r e n g t h e n e d are b e t w e e n cells that r e p r e s e n t the same m e m o r y . The synapses that are s t r e n g t h e n e d are thus appropriate for autoassociative LTM. If however, NMDA channels have a slow deactivation that spans several g a m m a cycles (Fig. 4C1 ), c o n n e c t i o n s w o u l d b e strengthe n e d b e t w e e n cells that r e p r e s e n t different memories (Fig. 4C2). This is w h a t w e call heteroassociative m e m o r y . In this p a p e r w e will assume that
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Figure 4: Rulesfor LTP induction indicate that the type of memory formed in networks with theta/gamma oscillations will depend on the time constant of the NMDA channel. (A) Representation of the seven different memories becoming active within a theta cycle. (B1) The time course of fast NMDA channels activated by memory item one. (B2) Strong connections form only between cells that fire in the same gamma cycle. Because these cells encoded the same memory, the fast NMDA channel forms the connections needed for autoassociation. Awij represents the synaptic connections between cell i and j. (Cl) The time course of slow NMDA channels whose time constant spans multiple gamma cycles. (C2) Connections form between memory item one and subsequent memories (i.e., heteroassociations are formed)
the n e t w o r k contains only fast NMDA c h a n n e l s and is therefore specialized for the f o r m a t i o n of autoassociative LTM.
FORMATION OF LTM FOR NOVEL ITEMS W e n o w consider h o w a n o v e l autoassociative m e m o r y can be i n c o r p o r a t e d into LTM in a physiologically realistic w a y in a n e t w o r k w i t h fast NMDA channels. This physiological realism includes the a s s u m p t i o n that synaptic m o d i f i c a t i o n requires substantial r e p e t i t i o n (see Introduction, Materials and Methods). W e also have a d d e d rand o m m e m b r a n e noise not p r e s e n t in our p r e v i o u s simulations (Figs. 2 and 3; Lisman and Idiart 1995). Our simulation in Figure 5 shows the formation of LTM for m u l t i p l e items p r e s e n t e d in real
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FORMATION OF ASSOCIATIVE MEMORY
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the e x t e n t that s o m e cells participating in a m e m ory r e p r e s e n t a t i o n eventually fire in the w r o n g g a m m a cycle, errors will also b e c o m e synaptically encoded. This is illustrated b y the inset in Figure 5B. The size of each m a t r i x e l e m e n t r e p r e s e n t s the strength of the synapse from cell i to cell j. W e c o n c l u d e that novel m e m o r i e s can b e incorporated into LTM after a single presentation, b u t the e n c o d i n g will inevitably c o n t a i n inaccuracies. Although a novel i t e m c a n n o t accurately b e e n c o d e d into LTM b y a single presentation, w e thought that multiple p r e s e n t a t i o n s of the same s e q u e n c e m i g h t lead to c o r r e c t e n c o d i n g if erroneous information stored d u r i n g a p r e v i o u s presentation could be r e m o v e d d u r i n g a s u b s e q u e n t p r e s e n t a t i o n b y LTD (for review, see Christie et al. 1994; Linden 1994; D e b a n n e and T h o m p s o n 1996). W e m o d e l LTD b y d e c r e a s i n g the synaptic c o n d u c t a n c e if a p r e s y n a p t i c activation occurs w i t h o u t postsynaptic activation or vice versa. The time w i n d o w for w h i c h the pre- and postsynaptic events are c o n s i d e r e d s y n c h r o n o u s is d e t e r m i n e d by the time characteristic of the NMDA c h a n n e l (see Materials and Methods). Hence, if s o m e synapses had b e e n e r r o n e o u s l y strengthened, one could e x p e c t that r e i n t r o d u c t i o n of the m e m o r y patterns will r e d u c e the e r r o n e o u s l y s t r e n g t h e n e d synapses. This is, however, not the case if the same s e q u e n c e of m e m o r y patterns is r e p e a t e d l y presented. Some of the synapses that w e r e erroneously s t r e n g t h e n e d d u r i n g initial p r e s e n t a t i o n s do n o t get w e a k e n e d (Fig. 6A). Correct e n c o d i n g can o c c u r if the o r d e r of the same m e m o r y patterns is varied from p r e s e n t a t i o n to presentation. W e have applied this p r o c e d u r e in Figure 6B. Initially, s o m e errors w e r e e n c o d e d into the synaptic matrix. After the s e q u e n c e was p r e s e n t e d r e p e a t e d l y w i t h the order interchanged, a correct m e m o r y trace builds up.
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Figure 5: (A) Two novel memory patterns are introduced to the network on subsequent theta cycles. Cells 1-5 code for pattern 1 and cells 6-10 code for pattern 2. At each subsequent theta cycle the two memories become reactivated, but are degraded because of noise (become unsynchronized within the gamma cycles). (B) With a physiological learning rule, LTM for the two memories builds up slowly. The synaptic encoding is a measure of the actual synaptic values relative to synaptic values corresponding to perfect encoding. Because of noise the memories are degraded and the errors are encoded, as illustrated by the inset representing the synaptic matrix. The cell number (1-10) is specified on both axes; the size of the square at location i,j denotes the synaptic strength of the connection between cell i (yaxis) and cell j (x-axis).
time to the network. In the example, two novel m e m o r i e s are p r e s e n t e d to the n e t w o r k (arrows in Fig. 5A). The ADP leads to the firing of b o t h memories o n s u b s e q u e n t theta cycles, but w i t h i n a few cycles, the firing is progressively desynchronized. This is b e c a u s e the m e m b r a n e noise generates errors in the ADP t i m i n g ramps and causes cells to fire in the w r o n g g a m m a subcycle. Because the ADP that controls timing is unitary, there is no basis for error correction. Thus, once a t i m i n g error occurs for a cell, the error c o n t i n u e s on subs e q u e n t theta cycles. As seen in Figure 5B, the r e p e t i t i o n of m e m o r i e s in STM gradually leads to the b u i l d up of synaptic strength in LTM. The m e m o r y i n f o r m a t i o n is thus learned. However, to
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Discussion MECHANISM OF STM It has b e e n p r o p o s e d that STM c o u l d rely on reverbatory m e c h a n i s m s ( H e b b 1949), and that the r e c u r r e n t c o n n e c t i o n s of attractor n e t w o r k are an e x a m p l e of such a r e v e r b a t o r y loop (Amit 1989). Specifically, in attractor n e t w o r k s activity is m a i n t a i n e d because cells that r e p r e s e n t a m e m ory selectively excite each other w i t h strong syn-
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A
presentation 1
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Figure 6: Conditions required for establishing error-free autoassociative LTM of individual items. Memories are presented in rapid succession during a learning period. Such presentations are repeated many times and the resulting synaptic weight matrix is shown as a function of the number of presentations. The matrix elements of 1-5 on the x- and y-axis represents the synapses ideally coding for the first memory. The next memory is ideally coded by the elements at 6-10 at the xand y-axis and so forth. (A) If the same eight memories are always introduced in the same order, the memories are never accurately learned, as shown by the inappropriate components of the matrix. (B) If the eight memories are introduced in random order, the matrix becomes accurate. The simulations were done the following way: A sequence of items was selected from a eight-item list and introduced to the system. The sequence was kept active for 20 theta cycles allowing the individual memories to become encoded into the synapses. Then a new sequence was selected and introduced to the network. In A seven consecutive items was select from a list of eight elements and introduced to the network. In B the seven items were selected randomly from the list before each introduction. The final synaptic values ranged from 0 to 0.8.
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