Drift of neural ensembles driven by slow fluctuations of intrinsic excitability

Reviewer #1 (Public Review):

Current experimental work reveals that brain areas implicated in episodic and spatial memory have a dynamic code, in which activity representing familiar events/locations changes over time. This paper shows that such reconfiguration is consistent with underlying changes in the excitability of cells in the population, which ties these observations to a physiological mechanism.

Delamare et al. use a recurrent network model to consider the hypothesis that slow fluctuations in intrinsic excitability, together with spontaneous reactivations of ensembles, may cause the structure of the ensemble to change, consistent with the phenomenon of representational drift. The paper focuses on three main findings from their model: (1) fluctuations in intrinsic excitability lead to drift, (2) this drift has a temporal structure, and (3) a readout neuron can track the drift and continue to decode the memory. This paper is relevant and timely, and the work addresses questions of both a potential mechanism (fluctuations in intrinsic excitability) and purpose (time-stamping memories) of drift.

The model used in this study consists of a pool of 50 all-to-all recurrently connected excitatory neurons with weights changing according to a Hebbian rule. All neurons receive the same input during stimulation, as well as global inhibition. The population has heterogeneous excitability, and each neuron's excitability is constant over time apart from a transient increase on a single day. The neurons are divided into ensembles of 10 neurons each, and on each day, a different ensemble receives a transient increase in the excitability of each of its neurons, with each neuron experiencing the same amplitude of increase. Each day for four days, repetitions of a binary stimulus pulse are applied to every neuron.

The modeling choices focus in on the parameter of interest-the excitability-and other details are generally kept as straightforward as possible. That said, I wonder if certain aspects may be overly simple. The extent of the work already performed, however, does serve the intended purpose, and so I think it would be sufficient for the authors to comment on these choices rather than to take more space in this paper to actually implement these choices. What might happen were more complex modeling choices made? What is the justification for the choices that are made in the present work?

The two specific modeling choices I question are (1) the excitability dynamics and (2) the input stimulus. The ensemble-wide synchronous and constant-amplitude excitability increase, followed by a return to baseline, seems to be a very simplified picture of the dynamics of intrinsic excitability. At the very least, justification for this simplified picture would benefit the reader, and I would be interested in the authors' speculation about how a more complex and biologically realistic dynamics model might impact the drift in their network model. Similarly, the input stimulus being binary means that, on the single-neuron level, the only type of drift that can occur is a sort of drop-in/drop-out drift; this choice excludes the possibility of a neuron maintaining significant tuning to a stimulus but changing its preferred value. How would the use of a continuous input variable influence the results.

Result (1): Fluctuations in intrinsic excitability induce drift
The two choices highlighted above appear to lead to representations that never recruit the neurons in the population with the lowest baseline excitability (Figure 1b: it appears that only 10 neurons ever show high firing rates) and produce networks with very strong bidirectional coupling between this subset of neurons and weak coupling elsewhere (Figure 1d). This low recruitment rate need may not necessarily be problematic, but it stands out as a point that should at least be commented on. The fact that only 10 neurons (20% of the population) are ever recruited in a representation also raises the question of what would happen if the model were scaled up to include more neurons.

Result (2): The observed drift has a temporal structure
The authors then demonstrate that the drift has a temporal structure (i.e., that activity is informative about the day on which it occurs), with methods inspired by Rubin et al. (2015). Rubin et al. (2015) compare single-trial activity patterns on a given session with full-session activity patterns from each session. In contrast, Delamare et al. here compare full-session patterns with baseline excitability (E = 0) patterns. This point of difference should be motivated. What does a comparison to this baseline excitability activity pattern tell us? The ordinal decoder, which decodes the session order, gives very interesting results: that an intermediate amplitude E of excitability increase maximizes this decoder's performance. This point is also discussed well by the authors. As a potential point of further exploration, the use of baseline excitability patterns in the day decoder had me wondering how the ordinal decoder would perform with these baseline patterns.

Result (3): A readout neuron can track drift
The authors conclude their work by connecting a readout neuron to the population with plastic weights evolving via a Hebbian rule. They show that this neuron can track the drifting ensemble by adjusting its weights. These results are shown very neatly and effectively and corroborate existing work that they cite very clearly.

Overall, this paper is well-organized, offers a straightforward model of dynamic intrinsic excitability, and provides relevant results with appropriate interpretations. The methods could benefit from more justification of certain modeling choices, and/or an exploration (either speculative or via implementation) of what would happen with more complex choices. This modeling work paves the way for further explorations of how intrinsic excitability fluctuations influence drifting representations.

Reviewer #2 (Public Review):

In this computational study, Delamare et al identify slow neuronal excitability as one mechanism underlying representational drift in recurrent neuronal networks and that the drift is informative about the temporal structure of the memory and when it has been formed. The manuscript is very well written and addresses a timely as well as important topic in current neuroscience namely the mechanisms that may underlie representational drift.

The study is based on an all-to-all recurrent neuronal network with synapses following Hebbian plasticity rules. On the first day, a cue-related representation is formed in that network and on the next 3 days it is recalled spontaneously or due to a memory-related cue. One major observation is that representational drift emerges day-by-day based on intrinsic excitability with the most excitable cells showing highest probability to replace previously active members of the assembly. By using a day-decoder, the authors state that they can infer the order at which the reactivation of cell assemblies happened but only if the excitability state was not too high. By applying a read-out neuron, the authors observed that this cell can track the drifting ensemble which is based on changes of the synaptic weights across time. The only few questions which emerged and could be addressed either theoretically or in the discussion are as follows:

1. Would the similar results be obtained if not all-to-all recurrent connections would have been molded but more realistic connectivity profiles such as estimated for CA1 and CA3?
2. How does the number of excited cells that could potentially contribute to an engram influence the representational drift and the decoding quality?
3. How does the rate of the drift influence the quality of readout from the readout-out neuron?

Reviewer #3 (Public Review):

The authors explore an important question concerning the underlying mechanism of representational drift, which despite intense recent interest remains obscure. The paper explores the intriguing hypothesis that drift may reflect changes in the intrinsic excitability of neurons. The authors set out to provide theoretical insight into this potential mechanism.

They construct a rate model with all-to-all recurrent connectivity, in which recurrent synapses are governed by a standard Hebbian plasticity rule. This network receives a global input, constant across all neurons, which can be varied with time. Each neuron also is driven by an "intrinsic excitability" bias term, which does vary across cells. The authors study how activity in the network evolves as this intrinsic excitability term is changed.

They find that after initial stimulation of the network, those neurons where the excitability term is set high become more strongly connected and are in turn more responsive to the input. Each day the subset of neurons with high intrinsic excitability is changed, and the network's recurrent synaptic connectivity and responsiveness gradually shift, such that the new high intrinsic excitability subset becomes both more strongly activated by the global input and also more strongly recurrently connected. These changes result in drift, reflected by a gradual decrease across time in the correlation of the neuronal population vector response to the stimulus.

The authors are able to build a classifier that decodes the "day" (i.e. which subset of neurons had high intrinsic excitability) with perfect accuracy. This is despite the fact that the excitability bias during decoding is set to 0 for all neurons, and so the decoder is really detecting those neurons with strong recurrent connectivity, and in turn strong responses to the input. The authors show that it is also possible to decode the order in which different subsets of neurons were given high intrinsic excitability on previous "days". This second result depends on the extent by which intrinsic excitability was increased: if the increase in intrinsic excitability was either too high or too low, it was not possible to read out any information about past ordering of excitability changes.

Finally, using another Hebbian learning rule, the authors show that an output neuron, whose activity is a weighted sum of the activity of all neurons in the network, is able to read out the activity of the network. What this means specifically, is that although the set of neurons most active in the network changes, the output neuron always maintains a higher firing rate than a neuron with randomly shuffled synaptic weights, because the output neuron continuously updates its weights to sample from the highly active population at any given moment. Thus, the output neuron can readout a stable memory despite drift.

Strengths:
The authors are clear in their description of the network they construct and in their results. They convincingly show that when they change their "intrinsic excitability term", upon stimulation, the Hebbian synapses in their network gradually evolve, and the combined synaptic connectivity and altered excitability result in drifting patterns of activity in response to an unchanging input (Fig. 1, Fig. 2a). Furthermore, their classification analyses (Fig. 2) show that information is preserved in the network, and their readout neuron successfully tracks the active cells (Fig. 3). Finally, the observation that only a specific range of excitability bias values permits decoding of the temporal structure of the history of intrinsic excitabililty (Fig. 2f and Figure S1) is interesting, and as the authors point out, not trivial.

Weaknesses:

1. The way the network is constructed, there is no formal difference between what the authors call "input", Δ(t), and what they call "intrinsic excitability" Ɛ_i(t) (see Equation 3). These are two separate terms that are summed (Eq. 3) to define the rate dynamics of the network. The authors could have switched the names of these terms: Δ(t) could have been considered a global "intrinsic excitability term" that varied with time and Ɛ_i(t) could have been the external input received by each neuron i in the network. In that case, the paper would have considered the consequence of "slow fluctuations of external input" rather than "slow fluctuations of intrinsic excitability", but the results would have been the same. The difference is therefore semantic. The consequence is that this paper is not necessarily about "intrinsic excitability", rather it considers how a Hebbian network responds to changes in excitatory drive, regardless of whether those drives are labeled "input" or "intrinsic excitability".

2. Given how the learning rule that defines input to the readout neuron is constructed, it is trivial that this unit responds to the most active neurons in the network, more so than a neuron assigned random weights. What would happen if the network included more than one "memory"? Would it be possible to construct a readout neuron that could classify two distinct patterns? Along these lines, what if there were multiple, distinct stimuli used to drive this network, rather than the global input the authors employ here? Does the system, as constructed, have the capacity to provide two distinct patterns of activity in response to two distinct inputs?

Impact:
Defining the potential role of changes in intrinsic excitability in drift is fundamental. Thus, this paper represents a potentially important contribution. Unfortunately, given the way the network employed here is constructed, it is difficult to tease apart the specific contribution of changing excitability from changing input. This limits the interpretability and applicability of the results.