HIPPOCAMPUS 00:000–000 (2013)

COMMENTARY
The Conjunctive Trace
Blake A. Richards1 and Paul W. Frankland1,2,3,4*
ABSTRACT:
Memories serve to establish some permanence to ourinner lives despite the fleeting nature of subjective experience. Most
neurobiological theories of memory assume that this mental permanence reflects an underlying cellular permanence. Namely, it is assumed
that the cellular changes which first occur to store a memory are perpetuated for as long as the memory is stored. But is that really the case?
In an opinion piece in this issue of Hippocampus, Aryeh Routtenberg
raises the provocative idea that the subjective sense of memory persistence is not in fact a result of persistence at the cellular level, rather,that ‘‘supple synapses’’ and multiple ‘‘evanescent networks’’ that are
forever changing are responsible for our memories. On one level, his
proposal could be construed as a radical challenge to some of our mostfundamental theories of the neurobiology of memory, including Donald
Hebb’s proposal that memories are stored by networks that strengthen
their connections to increase the likelihood of the same activity patterns
being recreated at a later date. However, it could also be seen as amoderating call, a call for a greater acknowledgement of the dynamic,
stochastic, and distributed nature of neural networks. In this response to
Routtenberg’s article, we attempt to provide a clarification of the dividing line between these two interpretations of his argument, and in doing
so, we provide some overview of the empirical evidence that bears on
this subject. We argue that the data that exists to date favors the more
moderate interpretation: that memory storage involves a process inwhich activity patterns are made more likely to reoccur, but that anunder-appreciated reality is that mnemonic traces may continue tochange and evolve over time. V 2013 Wiley Periodicals, Inc.
C

KEY WORDS:
memorystorage;consolidation;
amygdala;hippocampus; conjunctive encoding; disjunctive encoding; stable trace;
dynamic trace‘‘You cannot step into the same river twice.’’ (Heraclitus)
Memories must be stored somewhere. For us to remember anything
there must be a process whereby alterations to our nervous system
ensure that later activity patterns reflect earlier activity patterns (by notrecognizing this, we would veer off into dualism). However, the exact
manner in which later activity patterns reflect earlier ones is not obvious.
Memories could be stored by increasing the likelihood that a particular
activity pattern would reappear. Alternatively, memories could be stored
by decreasing the likelihood that a particular activity pattern would reap1

Program in Neurosciences and Mental Health, The Hospital for Sick
Children, Toronto, Ontario, Canada, M5G 1X8; 2 Department of Psychology, University of Toronto, Toronto, Ontario, Canada M5S 3GM;
3
Department of Physiology, University of Toronto, Toronto, Ontario,
Canada M5S 1A8; 4 Institute of Medical Science, University of Toronto,
Toronto, Ontario, Canada M5S 1A8
Grant sponsor: Wellcome Trust Senior Research Fellowship in Basic
Biomedical Science*Correspondence to: Paul Frankland, Program in Neurosciences andMental Health, The Hospital for Sick Children, Toronto, Ontario, Canada,
M5G 1X8. E-mail: paul.frankland@sickkids.ca
Accepted for publication 12 December 2012
DOI 10.1002/hipo.22089
Published online in Wiley Online Library (wileyonlinelibrary.com).
C 2013 WILEY PERIODICALS, INC.
V

pear. Neuroscientists often assume the former, but thisis not a given, as Routtenberg points out.
To distinguish between these two possibilities, wewill develop a simple mathematical formulation. Consider the concrete example of a contextual fear memory experiment wherein the circuits of the amygdala
are involved in encoding fearful memories (Fanselow
and LeDoux, 1999). When the animal is first placed in
the conditioning chamber, it experiences the pairing of
the cues with a shock, which we will refer to as experience A1. During A1, a particular set of neurons in the
amygdala will be active, which we will call a1. What
happens now if the animal is placed back in the chamber? Specifically, what set of neurons in the amygdala,a2, are activated during the experience A2 (Fig. 1)? In
the case where no memory has been stored, the probability of any given cell, i, being a member of a2 will be
independent of its being active during A1:
Pði 2 a2 ji 2 a1 Þ ¼ Pði 2 a2 Þ ðNo memoryÞ
It should be recognized that, as given, this is notstrictly speaking a guarantee of no memory storage.
When considering a distributed code the probabilityof individual cells being activated is not enough tocompletely capture the situation. No memory storage
occurs when P(a2 | a1) 5 P(a2), because the mutual
information between a1 and a2 is equal to zero inthis circumstance (Brunel and Nadal, 1999). Although
this would imply that P(i e a2 | i e a1) 5 P(i e a2),
the converse is not always true. Nonetheless, we will
utilize this simplified, cell-by-cell framework to aid
the discussion while recognizing the mathematical limitations of doing so.
The situation of no memory allows us to then distinguish two possible manners in which a memory
could be stored. In the first, which we will refer to as‘‘conjunctive encoding,’’ the probability of a neuron in
the amygdala being active during exposure A2
increases if it was active during A1:
Pði 2 a2 ji 2 a1 Þ > Pði 2 a2 Þ ðConjunctive encodingÞ
Note that a conjunctive code is ultimately what is
implied by the Hebbian aphorism that ‘‘neurons thatfire together wire together (Hebb, 1949).’’ Therefore,
it is worth noting that conjunctive encoding lies at
the heart of most modern theorizing about the neurobiology of memory. The extreme version of this is the

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FIGURE 1.
Conjunctive versus disjunctive encoding of a fear memory. During a fear conditioning experience, A1, a particular subset ofcells, a1, is activated in the amygdala. Here, for illustrative purposes we show a schematic of the circuit with a total of twelve cells, six ofwhich are contained in a1 (top right). When the animal is placed back in the conditioning chamber, this experience A2 will lead to the activation of a new subset of cells, a2. If no memory was stored then a2 will be independent of a1, and the new subset of cells that is activated will
randomly overlap with the subset that was active during conditioning (bottom middle). In contrast, if a memory is stored then a2 must be
dependent on a1, but this can be in one of two ways. Either the cells that were active during conditioning are more likely to be reactivatedduring recall (conjunctive encoding, bottom left) or the cells that were active during conditioning are less likely to be reactivated during
recall (disjunctive encoding, bottom right). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com]

situation in which the exact same activity pattern is recreatedduring retrieval [i.e., P(i e a2 | i e a1) 5 1].
In contrast, another way in which a memory could be stored
would be by ‘‘disjunctive encoding.’’ In this scenario, the probability that a neuron will be active during A2 is actually lowered as a result of its being active during A1:
Pði 2 a2 ji 2 a1 Þ < Pði 2 a2 Þ ðDisjunctive encodingÞ
The extreme case of disjunctive encoding is when the cells
that were active during encoding are never reactivated [i.e., P(ie a2 | i e a1) 5 0]. Although disjunctive encoding is often notconsidered by researchers when thinking about the neurobiology of memory, it is in fact a perfectly legitimate method for
information storage.
Some initial observations are important. First, this basic mathematical framework can, of course, be applied to other tasks beyond
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fear conditioning and to other circuits beyond the amygdala. Second, in describing these two encoding methods we are assumingthat roughly the same number of cells get activated during A1 andA2, which means that we are not considering the degenerative cases
where the entire population’s activity is ramped up or down (i.e., asituation where either all cells become more likely to be in a2 or
all cells become less likely to be in a2). This assumption is basedon evidence that retrieval and encoding activate similar numbersof neurons (Guzowski et al., 1999; Han et al., 2007). Third, giventhat neural networks exhibit a great deal of stochasticity (Faisal etal., 2008; Shadlen and Newsome, 1994; Shadlen and Newsome,
1998; Faisal et al., 2008), the two extreme scenarios (exact reactivation or complete exclusion of an activity pattern) are almost certainly not how brain circuits operate and also not something which
any neuroscientist would advocate. As such, we suggest that any
argument against them is ultimately an argument against a straw
man. Fourth, there is nothing preventing the brain from combin-

THE CONJUNCTIVE TRACE
ing conjunctive and disjunctive encoding strategies, both within
and across different networks; these encoding strategies are notmutually exclusive though they do lead to very different experimental predictions.
We can now begin to clarify some of Routtenberg’s arguments by identifying two important questions he raises: Q1. To what extent are conjunctive versus disjunctive encoding strategies used by the brain?
 Q2. If we consider additional recall experiences beyond asingle event (i.e., experiences A3, A4, . . ., AN) is there a consistent set of cells engaged in encoding the memory across all
experiences or does the memory trace change over time?
A critical point of clarification is that these two questions are
distinct. We could have a scenario wherein the brain utilizes
conjunctive codes to store memories, but over time and acrossmultiple retrieval events the traces are gradually altered, suchthat there is no overlap between the initial activity pattern andthe memory traces underlying retrieval at distant time-points.
We will remain agnostic as to exactly how Routtenberg would
answer the two questions above phrased in this way. Some of hisarguments seem to promote the idea of disjunctive codes overconjunctive codes, while others seem to be a demand for a greater
recognition of the dynamic nature of memory traces. We would
argue that the existing literature suggests that the primary modeof encoding is conjunctive. Although disjunctive encoding is aninteresting possibility that may be employed by the brain sometimes, we are not convinced by Routtenberg’s arguments that it istime to abandon this central conception of conjunctive memorystorage. However, Routtenberg may well be correct that there is agreat deal of dynamism to mnemonic engrams, such that longterm memory traces are ever-changing.

EVIDENCE FOR CONJUNCTIVE MEMORY
ENCODING
Perhaps the clearest illustration of conjunctive memory encoding comes from a study by Reijmers et al. (2007). They generated
a transgenic mouse model (the TetTag mouse), wherein theexpression of tetracycline-transactivator is driven by the activityregulated c-Fos promoter, allowing doxycycline controlled conditional tagging of active cells via tau-LacZ. Using this approach,the authors conducted a study to examine exactly the situation
described by our basic framework. Mice were trained in a contextual fear memory task while temporarily not receiving doxycycline, leading to LacZ expression in those cells active during theinitial fear memory encoding (i.e., providing a tag of cells in a1).
Following this, doxycycline was reintroduced and 3 days later the
animals were tested in the context. One hour after testing, mice
were sacrificed and their brains were stained for the activitydriven gene Zif268/Egr-1(i.e., providing a tag of cells in a2). By
examining double tagged cells, Reijmers et al. (2007) were able
to determine whether the number of cells that were incorporated
into both a1 and a2 was above chance (indicating a conjunctive

3code) or below chance (indicating a disjunctive code). The result
was that animals given the training and the recall experience (butnot control groups who were only exposed to the environment
without shock) exhibited a number of cells activated by both theinitial experience and the retrieval experience that was significantly greater than chance. This provides a very clear indicationthat a conjunctive code is used in the amygdala for storing fear
memories.
Evidence of a conjunctive code for fear memories in the
amygdala also comes from a 2009 paper by Han et al. (2009).
Previous studies had demonstrated that overexpression of
CREB (cAMP response element-binding protein) in lateral
amygdala pyramidal cells increased the likelihood of those cells
being active during encoding (i.e., a1) and subsequent recall(i.e., a2) of a fear memory (Han et al., 2007). One possible
interpretation for this observation is that the CREB overexpressing cells are preferentially incorporated into a conjunctive
memory trace (Josselyn, 2010). If this interpretation is correct,
then selective elimination of cells that express high levels of
CREB during encoding should also selectively eliminate theassociative memory stored in the amygdala. To determine
whether this was the case, Han et al. used an inducible diphtheria
toxin receptor strategy to selectively ablate either CREB overexpressing cells or a random, similar-sized, subpopulation of lateral
amygdala cells. When CREB overexpressing cells were selectively
ablated, the fear memory (measured by freezing levels) was eliminated. In contrast, when randomly selected cells were ablated thememory was intact. Hence, ablation of CREB overexpressing
cells, which are active during encoding, leads to forgetting. This
provides a clear, causal demonstration of a conjunctive code in
the amygdala, because a disjunctive code would in fact predict
the opposite effect, that is, ablating cells that are active during
encoding (i.e., ablating a1) should have little to no effect on thememory (since a2 would not contain the ablated cells).
What about memory systems other than the amygdala? Thereis also evidence for conjunctive codes in the hippocampus. An
early demonstration of conjunctive coding was reported by
Guzowski et al. (1999). In this article, the authors described athen new immediate early gene mapping technique that they had
developed known as cellular compartment analysis of temporal
activity by fluorescent in situ hybridization (catFISH). Thismethod takes advantage of the fact that the immediate early gene
Arc exhibits an intracellular shift in the location of its expression
following cellular activation, enabling comparisons of cells activated at two different time points. Guzowski et al. examined the
distribution of active cells in the CA1 region of hippocampus inanimals placed into two different contexts or the same context
twice. Roughly, the same number of cells were activated in eachgroup, but animals placed in the same context twice had 90%
overlap in the activity patterns compared to only 26% for animals placed into different contexts (corresponding to chance levels). Therefore, this greater than chance probability of reactivation is indicative of a conjunctive code for contextual memories
in CA1. Similar results were obtained by Vazdarjanova andGuzowski (2004) when they used catFISH to examine this issue
in more depth (Vazdarjanova and Guzowski, 2004). In this study,
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the percentage of coactivated cells in the animals placed in thesame context twice was slightly lower but still accounted forroughly 70% of the total number of active cells in CA1. A similar
pattern was observed in CA3, indicating that both regions
employ conjunctive encoding for memory storage.
In his article, Routtenberg suggests that Vazdarjanova andGuzowski’s (2004) results are evidence of a disjunctive encoding scheme in the hippocampus, because 30% of the active
cells were only activated by one but not both of the experiences. However, this is an attack on the straw man of the extreme
conjunctive encoding scenario, wherein the exact same set ofcells is reactivated. In both Guzowski et al. (1999) and Vazdarjanova and Guzowski (2004) the number of coactivated cells
observed was above chance. Mathematically speaking, this tells
us that even though the exact pattern was not recreated, since
30% of the cells were not coactivated, the probability of agiven cell being a member of a2 is higher than chance (andnot lower than chance) if it was in a1; this places us explicitly
into a conjunctive encoding framework for contextual memories. There are several reasons why the original pattern ofactivity is unlikely to be faithfully recreated. First, the stochastic
nature of neural activity would make it highly unlikely for theexact same pattern to reappear (Tomko and Crapper, 1974;
Shadlen and Newsome, 1994; Faisal et al., 2008). Second, eachcontextual experience is unique, with slightly different sensory
inputs, endogenous circumstances, and so forth, and one of theexperiences involves a recall event while the other does not.
Instead of asking whether all or most of the cells are activatedby both experiences, the critical question that must be asked is
this: is the number of coactivated cells above or below chance?
A recent study by Liu et al. (2012) provides causal evidence
for the conclusion that conjunctive encoding is used to store contextual memories in the hippocampus (Liu et al., 2012). Theseauthors used viral infection of channelrhodopsin-2 (ChR2) in
the TetTag mouse described above to tag and reactivate cells inthe dentate gyrus (DG) that were active during fear conditioning.
Conditioning was performed in one context, following which theanimals were placed in a different, previously encountered, neutral context. What predictions would conjunctive versus disjunctive encoding have for the effects of optical activation of thetagged cells in this neutral context? In a conjunctive encoding situation, one would expect that the DG cells that were active during fear memory encoding would be part of the memory trace forthe conditioning context. Therefore, we would predict that activating these cells would in fact artificially induce recall, which
would lead to fearful behavior in the neutral context. In contrast,
in a disjunctive encoding situation, the neurons in the DG thatwere active during fear memory encoding would not be a part ofthe memory trace for the conditioning context. As such, activating these cells would not induce recall, so the animals’ behavior
in the neutral context would not indicate any sense of fear. The
findings from Liu et al. (2012) were very clearly those predictedby conjunctive encoding: when the ChR2 expressing cells were
optically activated the animals exhibited significant freezing
behaviour in the otherwise neutral context.
Hippocampus

Routtenberg cites Liu et al. (2012) in his article, and recognizes that others may construe their results as evidence ‘‘. . .that
memory is stored in selected cells. . .’’ But, he goes on to suggest that this is not a necessary conclusion and that we canreinterpret Liu et al.’s findings if we instead consider a different
possibility. To quote: ‘‘Information is . . . not actually stored in
the sense of an extant residuality. Thus, the physical indeterminancy of the engram is given its biological reality in the retrieval process, as for example the retrieved freezing behavior in
the Liu et al. report which is taken for the fear engram.’’ Here,
Routtenberg seems to be arguing that Liu et al. were not infact inducing recall by activating a fear memory engram.
Rather, the freezing of the animals in the neutral context during optical stimulation was caused by some unspecified mechanism, one that does not involve information having been stored
via persistent modifications to the hippocampal network.
Importantly, Liu et al. conducted control experiments to showthat in the absence of conditioning or the absence of opticalactivation the animals did not freeze, which demonstrated thatboth a fear memory and reactivation of the cells was necessary
to induce freezing. We would therefore argue that Routtenberg’s assessment of this article is incorrect, and it underlines
the problem with his arguments against conjunctive encoding
more generally. Although, a disjunctive encoding scheme formemory retrieval is interesting and theoretically possible it leads
to specific predictions that can be tested. The evidence that wehave reviewed here is clear: in both the amygdala and hippocampus a conjunctive encoding scheme appears to be theprimary mode of encoding and the data does not indicate disjunctive encoding. The situation may be different in other mnemonic circuits, or for other tasks, but this phenomenon must be
demonstrated first to be worthy of further consideration.

STABILITY VERSUS DYNAMISM IN LONGTERM MEMORY TRACES
Despite the fact that some persistent changes must occur inorder to store information there is nothing preventing the brain
from continually inducing new modifications in order to alterand update the substrates of memory storage. To make this concrete, we consider again the mathematical framework introduced
above, but we now expand the experiences and activity patterns
beyond a single encoding and recall event, and instead consider aset of N experiences A1, . . ., AN and their corresponding activity
patters a1, . . ., aN. Even though the existing evidence in the
amygdala and hippocampus suggests that a1 and a2 typicallyoverlap significantly more than chance, the information contained in these altered probabilities could be propagated to later
experiences in two different manners. In one case, which we willcall a ‘‘stable trace’’, a core subset of cells would continue to havea very high probability of being reactivated during each experience, such that these cells would continue to be members of a3,
a4, and so forth, even though other cells may be randomly active
or inactive. The other possibility, which we will call a ‘‘dynamic

THE CONJUNCTIVE TRACE

5

FIGURE 2.
Stable versus dynamic long-term memory traces. Over extended periods of time a conjunctive memory trace may either
stabilize or continue to evolve. In this example, we show the progression of a memory trace in a schematic circuit over three experiences, A1,
A2, and A3. If conjunctive encoding is used to store the memory, then the overlap in the activity patterns for consecutive experiences must be
greater than chance, that is, the overlap between a1 and a2, or a2 and a3, must be above chance. In this schematic, there are twenty-six cells,
and eight are activated during each experience, making the number of coactive cells expected by chance approximately two to three cells (8/26
3 8/26 3 26 cells 5 2.46 cells of overlap on average). However, whether the overlap between non-consecutive activity patterns is greater thanchance depends on whether the memory trace is stable or dynamic. In the case of a stable trace (top right), the heightened probability of being
activated propagates within the same subset of cells that was originally active during A1, leading to a similar degree of overlap in the activity patterns for consecutive and non-consecutive traces (as illustrated by the Venn diagram). The other possible scenario is a dynamic trace (bottom
right), wherein the heightened probability of being activated gradually propagates to a new subset of cells. The result is that although A2 andA3 still exhibit greater than chance overlap (thereby preserving the memory) the overlap between A1 and A3 will diminish (as illustrated by the
Venn diagram). Over extended periods of time this could result in a completely altered trace that does not resemble the original trace that waslaid down during encoding. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com]

trace’’, is for the information to be maintained via an updating of
the memory trace over time, such that a2 may overlap with a1 toa large extent, and a3 may overlap with a2 to a large extent, but
a3 and a1 could be quite different (Fig. 2).
We believe that Routtenberg’s proposal can be broadly construed as an objection against trace stability. He presents a series of interesting neurobiological observations that could fit
quite well with a dynamic trace scenario. The malleability ofdendritic spines (Fischer et al., 1998), the continual renewal ofproteins at postsynaptic sites (Gray et al., 2006) and the importance of NMDA receptors beyond the initial encoding eventfor some types of learning (Shimizu et al., 2000; Santini et al.,2001) all fit with a situation wherein the brain continually
updates its memory traces. Routtenberg points to an especiallyinteresting consequence of this model of long-term memorystorage: if memory traces are continually altered over time thenperhaps consolidation is not in fact the crystallization of theoriginal synaptic architecture used to encode the information,
but rather a process of information redistribution and re-encoding. This process could help to protect memories by generating
highly distributed traces or by generating multiple traces, as
Routtenberg suggests. If true, then consolidation could help toprevent interference or memory loss because it effectively‘‘hedges’’ the information storage against conflicts arising fromother changes induced by later experiences. This proposal repre-

sents an important alternative to the idea of a stable trace, and wefeel that it should be carefully considered by researchers who study
long-term memory. Indeed, recent evidence suggests that CA1 utilizes a dynamic trace mechanism, one that could aid in the encoding of elapsed time (Mankin et al., 2012). Furthermore, there isplenty of evidence that as memories mature they are reorganized at
the systems level (Frankland and Bontempi, 2005), with the circuits engaged at the time of encoding (or shortly thereafter) differing from those engaged when the equivalent memory is retrieved
at more remote time-points (Wheeler et al., 2013). This process of
systems consolidation fits quite nicely with Routtenberg’s conceptualization of a dynamic trace. It is conceivable that remote memories are altered, distributed across multiple neural circuits, and possibly even duplicated precisely because the long-term consolidationof memory involves flexible, evanescent traces that encode the information. If so, then synapses must indeed remain supple to provide an effective physical mechanism for propagating memory.

CONCLUSION
The quote from Heraclitus that we included at the beginning of this response captures the transitory nature of any
physical system, including the brain. When we recall our past,
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we can never replicate the internal neural states that we wereoriginally experiencing; this is, perhaps, a truism. Nonetheless,there are different ways in which memory storage and recall
may involve a divergence away from the activity patterns that
occurred during encoding. In his article, Routtenberg challenges
two components of conventional wisdom: (1) that memory storage involves persistent changes that encourage the reactivation ofprevious activity patterns (the conjunctive trace), and (2) that
long-term memory consolidation is a process that stabilizes thecellular or synaptic changes that were originally instigated byencoding (the stable trace). In general, prompting scientists toreconsider these potentially dogmatic assumptions is somethingwhich we applaud. However, we have argued here that the challenge to the first component, although interesting, is not supported by the existing literature—on this point the standard wisdom is likely to be correct. Despite this, Routtenberg’s challenge
to the second component is an important theoretical contribution that deserves further consideration. The apparent permanence of our cherished memories may not in fact be reflected byany long-lasting permanence at the neurobiological level.

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