Persistent activity and match effects are widely regarded as neuronal correlates of short-term storage and manipulation of information, with the first serving active maintenance and the latter supporting the comparison between memory contents and incoming sensory information. The mechanistic and functional relationship between these two basic neurophysiological signatures of working memory remains elusive. We propose that match signals are generated as a result of transient changes in local network excitability brought about by persistent activity. Neurons more active will be more excitable, and thus more responsive to external inputs. Accordingly, network responses are jointly determined by the incoming stimulus and the ongoing pattern of persistent activity. Using a spiking model network, we show that this mechanism is able to reproduce most of the experimental phenomenology of match effects as exposed by single-cell recordings during delayed-response tasks. The model provides a unified, parsimonious mechanistic account of the main neuronal correlates of working memory, makes several experimentally testable predictions, and demonstrates a new functional role for persistent activity.

Over short time periods, memories are stored by sustained patterns of spiking activity which, once initiated by the stimulus, persist over the entire retention interval. How the information stored by such persistent activity is later retrieved is presently unclear. Here we propose that, besides temporarily storing memories, persistent activity is also instrumental in their retrieval by transiently modifying the tuning properties of the underlying neuronal networks. We show that the mechanism proposed parsimoniously recapitulates the extensive experimental phenomenology on match effects observed in delayed-response tasks, where the information held in memory has to be compared with incoming, sensory-related information to act appropriately. The theory makes very specific, straightforwardly testable predictions.

Funding: EMT and NB acknowledge the financial support of the SI-CODE project of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, under FET-Open grant number: FP7-284553. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

( A ) The different network states—spontaneous (i.e., before stimulus presentation) and memory (i.e., following stimulus offset)—are characterized by different distributions of recurrent inputs. In the spontaneous state, neurons in all memory representations are receiving, on average, the same input and are thus firing at the same low, baseline rate (pink). In the memory state, neurons belonging to the memory representation associated with the presented stimulus receive stronger recurrent inputs and thus fire at enhanced rates (red). The activity of neurons belonging to the other memory representations is reduced due to global inhibition (grey). High-firing neurons are more responsive to external inputs, due to increased recurrent inputs, and see their transient response enhanced upon subsequent stimulus presentations (red sigmoidal-like transfer function). Low-firing neurons are less responsive to external inputs, due to reduced recurrent inputs, and see their transient response suppressed upon subsequent stimulus presentations (grey sigmoidal-like transfer function). ( B ) Network architecture. ( C ) Distribution of firing rates upon stimulus presentation in the spontaneous state. Neurons in the memory representation associated with the presented stimulus are shown in red; neurons in the other memory representations are shown in orange. The overlap between the two distributions is labelled in dark red. The inset shows the corresponding distributions of the additional inputs, whose means are indicated by the two arrows. ( D ) Histogram of the sparseness indices in the spontaneous state.

Here, we propose an alternative to the parallel mechanisms theory, where match enhancement and suppression both result from a single mechanism: the modulation of network excitability brought about by the persistent activity. Information about the presented stimulus is stored across the delay period by a pattern of persistent activity in which, depending on the stimulus, some neurons increase their spiking rate while others decrease it. Changes in the spiking rate must be accompanied by changes in the neuron’s responsiveness to inputs, whereby, upon presentation of a subsequent stimulus, more active neurons will be more depolarized and thus more excitable, while less active neurons will be more hyperpolarized and thus less excitable [ 25 ] ( Fig. 1A ). Changes in single neuron’s responsiveness entail modifications of the tuning properties of the network, which depend on the ongoing pattern of persistent activity. In our account the differential stimulus-evoked activity depending on previously presented stimuli—i.e., the match effects—is a result of those modifications. We show that the above described mechanism, when implemented in a spiking model network, can reproduce consistently and quite naturally, most of the experimental phenomenology about match effects observed in short-term memory tasks, with no need for fatigue mechanisms nor functional differentiation among neurons.

In some cases, however, the reported experimental phenomenology does not appear to be fully consistent with the parallel mechanisms theory. In delayed paired-associate tasks, the response is conditional on whether the test stimulus matches the pair-associate of the sample stimulus. No repetition occurs. According to the theory, only match enhancement (or no effect, depending on the identity of the test stimulus) should be observed. Experiments report both enhancement and suppression [ 11 ]. In delayed match-to-category tasks where stimuli also do no repeat within a trial, similarly both enhancement and suppression are observed when the test matches the category of the sample [ 12 ]. In a recent study using a delayed cue-instructed go/nogo tasks with distractors, differential responses to neutral stimuli depending on the cue stimulus have been reported [ 13 ]. The theory would rather predict no response modulation, since neutral stimuli have no behavioral relevance nor they repeat during the trial. Finally and importantly, both match enhancement and selective delay-period activity (together with match suppression) have been observed in passive fixation tasks [ 14 , 20 – 24 ], where the theory would predict only match suppression. In fact, in such a task none of the stimuli has behavioral relevance and, thus, there is no need for active repetition detection, let alone memory maintenance.

It is presently unclear how the information stored in the pattern of persistent activity is retrieved and compared with incoming stimuli. One theory holds that match enhancement and persistent activity on one hand, and match suppression on the other hand, are neuronal manifestations of two distinct, parallel mechanisms supporting memory storage and retrieval [ 1 , 18 ]. Enhancement reflects the operation of an active detector which signals the appearance of behaviorally relevant stimuli, stored by persistent activity during the delay period. Suppression, instead, reflects the operation of an automatic detector which signals stimulus repetitions regardless of their behavioral relevance, and its functioning is assumed to be independent of persistent activity. Current mechanistic modeling fully embraces this notion of parallel mechanisms (see, e.g., [ 19 ]). Match suppression, which is generally the most prominent effect, is understood as the result of activity-dependent fatigue, either at the single-cell or at the synaptic level, produced by the sample presentation. Match enhancement, on the other hand, is understood as the result of selective inputs from a different area, or from a functionally different neuronal sub-population within the same area, carrying information about the stimulus actively held in memory.

Persistent delay activity, together with match effects, are basic neuronal hallmarks of temporary maintenance and manipulation of information. Persistent activity has been primarily associated with short-term storage, while match effects are thought to reflect the outcome of the comparison between stored and incoming information. Consistently with these putative roles, they have been observed across different short-term memory protocols besides the DMS task, such as DMS with intervening distractors [ 8 , 9 ], delayed non-match-to-sample [ 10 ], delayed paired-associate [ 11 ], delayed categorization [ 12 ] and delayed cue-instructed go/nogo tasks [ 13 ], and with different class of stimuli, such as natural images, fractal images, spatial locations, motion directions and pure tones. Persistent activity and match effects have also been observed across diverse cortical regions and, interestingly, the basic phenomenology exposed in regions traditionally associated to memory function, such as the pre-frontal, infero-temporal and parietal cortices [ 8 , 9 , 14 ], is qualitatively very similar to the phenomenology observed in regions traditionally associated to sensory processing, such as auditory cortex [ 15 ], area V4 [ 16 ] and area MT [ 17 ].

Memory allows an organism to store information about past events and then use it to modify its behavior in response to future ones. As a simple example, consider the classic delayed match-to-sample (DMS) task, where the appropriate behavior upon presentation of the test stimulus is conditional on the sample stimulus (the past event). What are the mechanisms that support the storage of information about the sample stimulus and its retrieval upon the presentation of the test stimulus? Electrophysiological studies have exposed two neuronal correlates of those mechanisms: (i) sample-selective persistent activity during the delay period (see, e.g., [ 1 – 3 ]); (ii) differential test-period activity depending on whether the test stimulus matches or not the sample (see, e.g., [ 1 , 4 – 7 ]). Specifically, some neurons show enhanced responses in the match as compared to the non-match condition (match enhancement), while others show the opposite pattern (match suppression), despite the fact that stimuli are physically identical in the two conditions.

Results

We model a local cortical circuit involved in memory storage and retrieval using a standard attractor network architecture [26, 27] (Fig. 1B). The network is composed of all-to-all connected excitatory and inhibitory leaky integrate-and-fire neurons. The excitatory sub-network contains p = 6 non-overlapping memory representations, each corresponding to a different stimulus, as well as neurons that do not participate in the task (non-selective neurons). Each memory representation consists of a fraction f = 0.05 of neurons. Synapses between neurons in the same memory representation are stronger than synapses between neurons in different memory representations. Synaptic connectivity in the rest of the network is unstructured. This synaptic organization results in an effective inhibitory interaction among the memory representations. Excitatory recurrent inputs have both a fast and a slow component (mimicking NMDA-Rs kinetics), while inhibitory inputs have only a fast component [28]. All neurons also receive non-selective, noisy excitatory inputs from outside the local network (background input).

Parameters are chosen so that the network exhibits multi-stability between a spontaneous activity state, where all memory representations are active at the same, low firing rate and p different memory states, where one of the memory representation is active at high rate, while the others are quiescent. The different steady states are attractors of the collective network dynamics. See Methods for details.

Network response in the spontaneous state Cortical neurons typically show visual responses to a large faction of stimuli, even after such stimuli have become fairly familiar [29, 30]. To reproduce this feature, we consider that the presentation of a stimulus elicits additional inputs (on top of the background input) to all neurons in the memory representations. Such inputs, for each neuron and for each stimulus, are drawn independently at the beginning of the simulation—and kept fixed thereon—from two Gaussian distributions with same variance but different means. Inputs to neurons in the memory representation associated to the stimulus presented are drawn from the Gaussian with larger mean, while inputs to neurons in the remaining representations are drawn from the Gaussian with smaller mean (inset in Fig. 1C). Means and variance of the two distributions are chosen to qualitatively reproduce the statistics of evoked cortical responses. The resulting firing rates distribution is shown in Fig. 1C. Evoked responses vary in a wide range, from quiescence to relatively high firing rates. The high-rates tail is mostly constituted by neurons in the memory representation of the stimulus being presented (red). However, a significant fraction of neurons in the other memory representations (orange) also fires at high rates. For each neuron in the memory representations, we also measure the sparseness of its responses across the stimulus set via the sparseness index (see Methods), which takes on values between 0 (the neuron responds to all stimuli in the same way) and 1 (the neuron responds to a single stimulus). The resulting distribution is shown in Fig. 1D. The average sparseness index as well as its distribution across neurons are consistent with experimental estimates from visual responses evoked in ITC by familiar stimuli [30]. The pattern of stimulus-evoked activity generated by the model reproduces some of the basic features of cortical responses: sparseness at the network level, right-skewed long-tailed distribution of firing rates, and broad tuning curves at the single-cell level [30]. Next, we study how the features of stimulus-evoked activity are modified when the network is in a memory state.

Network response to repeating stimuli We consider the case in which the active memory representation is the one associated with the incoming stimulus. This corresponds to a match trial in the DMS task. Accordingly, we present the same stimulus twice, with the two presentations separated by a delay period. The first presentation strongly activates the corresponding memory representations (black, Fig. 2A) and, to a lesser extent, all the other representations (red, Fig. 2A) due to the broad selectivity of the evoked responses. At stimulus offset, the memory representation activated by the stimulus remains active at high rates, while the others become quiescent due to the increased level of inhibition (blue, Fig. 2A). Such re-organization of the spiking activity following stimulus presentation is due to a (self-sustained) change in the distribution of the recurrent inputs in the network. Neurons in the active representation receive increased inputs as a result of the positive feedback via the strengthened recurrent synapses. The other neurons receive decreased inputs as a result of the negative feedback due to global inhibition. As a consequence, neurons in the active/inactive representation have a higher/smaller response to stimulus repetition (Fig. 2A). Although the basic features of stimulus-evoked activity in the spontaneous state are qualitatively preserved in the memory state, significant quantitative changes occur. In Fig. 2B we plot the response to the first presentation (sample) vs. the second presentation (match) for the neurons in the active (black) and inactive (red) memory representations. All neurons in the active representation show enhanced responses to the second presentation, although to a different extent. Neurons that show the largest relative increase are those that had moderate responses upon sample presentation. Neurons in the inactive representations also show a wide range of suppressed responses to the second presentation. Neurons with weak responses upon sample presentation (i.e. a significant fraction of the responsive neurons—see Fig. 1C) show no response at all or very strong suppression upon match presentation. Neurons with moderate-to-strong responses show modest levels of suppression or no suppression at all. The memory-dependent modulation of single-neuron responsiveness entails a strong increase in the selectivity of the responses evoked by the second presentation (compare the distributions of the sparseness index in Fig. 2C and Fig. 1D). In our model, the best stimulus for a neuron is typically the one for which the neuron exhibits mnemonic activity so that, upon repetition of that stimulus, its response significantly increases. For a different stimulus the neuron does not exhibit mnemonic activity and thus, upon repetition, its response is suppressed. This is clearly seen in Fig. 2D where we show four single-neuron tuning curves. Stimuli are ranked from best to worst according to the evoked response at sample presentation, i.e. when the network is in the spontaneous state (in black). Upon repetition, i.e. when the network is in the corresponding memory state, the response to the best stimulus increases significantly, while those to the other stimuli decrease (in red). Note the amount of sharpening as quantified by the sparseness indices. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 2. Network response to repeating stimuli (match trial). (A) Average activity level in the memory representation associated with the presented stimulus (black), in the other representations (red) and in the inhibitory sub-network (blue). Presentation periods are indicated by the thick horizontal black lines. (B) Scatter plot of average single-neuron responses to the first and the second presentation. Responses are calculated by counting the number of spikes during the first 200ms of stimulus presentation. Color code as in (A). (C) Histogram of the selectivity indices of the responses to the second presentation upon repeating stimuli. (D) Sample single-neuron tuning curves to the first (black) and to the second presentation (red). Stimuli are ranked from best to worst according to the responses to the first presentation (sample). https://doi.org/10.1371/journal.pcbi.1004059.g002

Network response to non-repeating stimuli We consider the case in which the incoming stimulus is associated with a memory representation different from the one currently active. This corresponds to a non-match trial in the DMS task. Accordingly, we present two different stimuli separated by a delay period. This case requires the consideration of three different neuronal sub-populations: neurons belonging to the active representation, neurons belonging to the representation associated to the incoming stimulus, and neurons in the remaining representations. The time course of the average activity in these sub-populations (together with the inhibitory population—blue line) is shown in Fig. 3A. The presentation of the first stimulus (sample) activates the corresponding memory representation (green), which then stays active during the delay period much as before (Fig. 2A). The presentation of the second stimulus (non-match) evokes a strong response in the corresponding memory representation (black), which eventually shuts down the mnemonic activity related to the first stimulus. The response to the second stimulus is, however, smaller than the response to the first stimulus due to the increased level of inhibition when the network is in a memory state. The neurons not belonging to the active representation nor to the one associated with the non-match exhibit suppressed responses to the second presentation (red). This can be also seen in the distribution of red dots in the scatter plot in Fig. 3B. Interestingly, neurons in the representation active during the first delay (green dots) give a strong, transient response to the second stimulus, which is typically larger than the response evoked by the presentation of the associated stimulus (i.e., the sample). During the second presentation, these neurons receive additional inputs which, although smaller than the ones received by neurons in the representation of the stimulus currently presented (black dots), elicit a strong response, due to the increased responsiveness brought about by persistent activity. These additional inputs are statistically the same as the inputs to all the remaining representations, nevertheless, they elicit dramatically different responses (compare green and red dots in Fig. 3B). This most clearly illustrates the importance of the current network state in determining the responses to incoming stimulation. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 3. Network response to non-repeating stimuli (non-match trial). (A) Average activity level in the memory representation associated with the first stimulus (green), with the second stimulus (black), in the other representations (red) and in the inhibitory sub-network (blue). Presentation periods are indicated by the thick horizontal black lines. (B) Scatter plot of average single-neuron responses to the first and the second presentation. Responses are calculated by counting the number of spikes during the first 200ms of stimulus presentation. Color code as in (A). (C) Histogram of the selectivity indices of the responses to the second presentation upon non-repeating stimuli. (D) Single-neuron tuning curves to the first (black) and to the second presentation for neurons in the active representation (green) and in the non-active representations (red). Stimuli are ranked from best to worst according to the responses to the first presentation (sample). https://doi.org/10.1371/journal.pcbi.1004059.g003 In Fig. 3C we report the distribution of the sparseness index measured by taking out the stimulus whose memory representation is active during the delay period. The distribution is bimodal as a consequence of the increased responsiveness of neurons in the active representation, which transiently respond to all stimuli, inducing a loss of selectivity. On the other hand, the selectivity of the neurons not belonging to the active representation is sharpened as a result of the suppression of weak/moderate responses. Such differential changes in selectivity are clearly shown in the two sets of tuning curves in Fig. 3D.

Protocols with intervening stimuli We ask next whether the basic mechanism illustrated above is also able to account for the patterns of neural responses observed in DMS tasks in which other stimuli (distractors) are presented in between the sample and the test stimulus. In one of such protocols, the so-called ABBA protocol [9, 18], the behavioral response is conditional upon the repetition of the sample stimulus (A) while the repetition of the distractor (B) has to be ignored. In this case, cells were found that showed an enhanced response to the repetition of A—the behaviorally relevant match—while they showed suppressed responses (as compared to the match response) for the repeating distractor B. At the same time, cells exhibiting match suppression showed larger responses (as compared to the match response) for the repeating distractor [9, 18]. It is worth pointing out that the parallel mechanisms hypothesis was formulated in order to account for these experimental observations, in particular for the observation that match enhancement was apparent only upon the repetition of the behaviorally-relevant stimulus [18]. Our model is able to reproduce the experimental findings described above in a regime where the mnemonic representation activated by the sample stimulus survives the presentation of a distractor with high probability, but is occasionnally disrupted by it. This regime can be obtained by reducing the amplitude of the external inputs during stimulus presentation [32] (see Methods for details). Fig. 5A shows the neural activity in the mnemonic representation associated to the sample stimulus (left panel) and in the remaining representations (right panel). The presentation of the sample activates the corresponding mnemonic representation but also, to a smaller extent, other representations (see Fig. 2). The subsequent presentation of a distractor fails to abolish the mnemonic activity related to the sample (unlike in Fig. 3), although it evokes responses in both the active and the inactive representations. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 5. Protocol with repeating distractors. (A) Average activity level in the memory representation associated with the sample stimulus (left panel) and in the other representations (right panel). Presentation periods are indicated by the thick horizontal lines: the black lines indicate the sample and the match, while the gray lines indicate the non-match and the repeated non-match i.e. repeating distractors. (B) Average response of neural population showing match enhancement (left panel) and match suppression (right panel) for a given stimulus when it is presented as sample, match, non match and repeated non-match (see main text for details). The amplitude of the external inputs are chosen so that the persistent activity elicited by the sample is rarely disrupted by the distractor presentation. We run 20 trials for each stimulus configuration. The error bars indicate the s.e.m. https://doi.org/10.1371/journal.pcbi.1004059.g005 We then proceed as in the experiment [9, 18]. For each stimulus presented as a sample, we separate the neurons which show enhancement upon repetition (i.e., the ones in the corresponding mnemonic representation) from the neurons which show suppression (i.e., the ones in the remaining representations). Next, we average the activity in these neuronal populations across all trials (with distractors) where the corresponding stimulus is presented as match, non-match and repeated non-match. The results of this analysis are shown in Fig. 5B. As can be seen, neurons eventually showing match enhancement exhibit suppressed responses, as compared to the match response, to repeating distractor presentations (left panel). Similarly, neurons eventually showing match suppression exhibit enhanced responses, again as compared to the match response, to repeating distractor presentations. Another common observation in protocols with distractors is that suppression wanes with increasing number of distractors [8]. This finding can also be replicated in the regime where persistent activity survives distractor presentation most of the time, but is occasionally disrupted by it. The amplitude of the population-averaged response depends on whether the mnemonic representation active upon test presentation is the one corresponding to the sample. In particular, if the persistent activity survives the presentation of the distractors, significant suppression will be observed in the majority of cells upon test presentation (see Match-Non Match effects). On the other hand, if the persistent activity is disrupted by the distractor presentation, the fraction of cells exhibiting match suppression will be smaller. The probability that the mnemonic representation associated to the sample is still active upon test presentation is a decreasing function of the number of distractors. In Fig. 6 we plot the average response of cells exhibiting match suppression (i.e. belonging to the mnemonic representations inactive following sample presentation) as a function of the number of intervening distractors. As can be seen, the response in match and non-match trials becomes more similar, i.e. the level of suppression decreases with increasing number of distractors. The same parameter regime can reproduce “standard” match, non-match effects, i.e. when no distractors intervene between sample and match or non-match (“0 distractors” in Fig. 6). Hence, importantly, in our model a unique set of parameters can account for standard match non match protocols, as well as for protocols with intervening stimuli. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 6. Protocol with non-repeating distractors. Match and non-match responses averaged over the populations of cells exhibiting match suppression as a function of the number of intervening stimuli, i.e. non-repeating distractors. As in Fig. 5, the amplitude of the external inputs are chosen so that the persistent activity elicited by the sample is rarely disrupted by the distractor presentation. We run 20 trials for each protocol. The error bars indicate the s.e.m. https://doi.org/10.1371/journal.pcbi.1004059.g006

Dependence on persistent activity, response selectivity and current dynamics We analyze systematically how match effects depend on persistent activity (PA), selectivity of the visual responses, and currents dynamics via both a simplified rate dynamics (SRD -that converges to the stationary states described by mean field equations; see Methods) and the spiking network dynamics (SND). First, we study the dependence of match effects on the level of PA by manipulating the synaptic strength between neurons in the same memory representations (J + ), keeping all the other parameters fixed. To quantify match effects we use the enhancement (suppression) index, defined as the ratio between match (M) and sample (S) response in the active (inactive) memory representation and the match-non match index, defined as the ratio between M and non-match (NM) response in a memory representation. We find that match effects increase with increasing levels of PA (Figs. 7A–B). Neurons in the active memory representation show larger responses to M than to S, as well as larger responses to M than to NM (black and blue line in Fig. 7B). The amplitude of both suppression and enhancement increases with increasing J + due to the concomitant increase of the level of PA (increasing responsiveness in the active representation) and the level of global inhibition (decreasing responsiveness in the inactive representations). In the absence of PA, all indices are equal to one, i.e. there is no modulation of response. The simplified rate dynamics (SRD-full lines) give results that are very close to the spiking neurons dynamics (SND-dashed lines). PPT PowerPoint slide

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larger image TIFF original image Download: Figure 7. Dependence of match effects on level of persistent activity, selectivity of the responses and current dynamics. (A) Persistent activity (red) and inhibitory activity (blue) as a function of J + . Note for J + below a given value the network is unable to sustain persistent activity. The dotted branch of both curves represents unstable solutions. (B) Match effects indices as a function of J + calculated with SRD (full lines) and SND (dashed lines). Match effects quantitatively increase with increasing J + , that is with increasing levels of persistent activity. (C) Match effect indices vs α. Match effects are quantitatively more important at low/moderate selectivity levels. (D) Match effects indices with SRD (full lines) and SND (dashed lines) vs the fraction of slow recurrent inputs (modulated by NMDA-Rs). On the left, indices are calculated by averaging the response over the first 200ms of stimulus presentation; on the right the response is calculated over 500ms, i.e. the entire stimulus duration. See main text for details. https://doi.org/10.1371/journal.pcbi.1004059.g007 Next, we study the dependence of match effects on the selectivity of the visual responses by manipulating the difference (α) between the average additional input to the memory representation associated to the stimulus presented (α + β) and the average additional input to the other representations (β); all other parameters are kept fixed. We find that match effects are quantitatively more important for low/moderate levels of selectivity, but are nevertheless preserved for strongly selective responses. For α close to zero, the response to stimulus presentation is not selective enough to allow the network to activate the corresponding memory representation. In this regime, all indices calculated via the SRD are equal to one (full lines in Fig. 7C). For moderate α (0.1 mV < α < 0.8 mV), the network is able to activate the memory representation associated with the presented stimulus and, moreover, PA survives the presentation of a NM. As a result enhancement effects are quite strong (compare the blue/black with the red/green curves). In the SND, instead, the stimulus presentation could stochastically activate any of the memory representations, thus yielding high fluctuations on the indices (dashed lines in Fig. 7C) and low agreement with SRD. For larger α, PA is disrupted by the presentation of a NM, and enhancement and suppression effects become more comparable. Note that the range of α for which PA survives the presentation of the NM increases with increasing J + . In our model, match effects result from modifications of the transient network response following stimulus presentation. Accordingly, decreasing the fraction of recurrent inputs with slow dynamics, and thus speeding up transients, reduces both suppression and enhancement effects (Fig. 7D). Nevertheless, even for relatively small fractions of slow recurrent inputs, match effects are still significant when the responses are averaged over the entire duration of stimulus presentation (i.e., 500ms—right panel in Fig. 7D). This is consistent with experiments showing that match effects are mostly evident during the early response phase [33].