Author response:

Public Reviews:

Reviewer #1 (Public review):

Our goal was to propose a possible computational mechanism underlying information integration in the claustrum, not to claim structural or causal equivalence between the model and the biological circuit. We acknowledge that some expressions in the original manuscript may have been interpreted as exceeding this intention, and we will revise the text to explicitly soften such statements.

It is well established that behavior-trained RNNs can admit multiple internal solutions capable of producing the same behavioral output, and we fully agree with this point. Among the many possible solutions, we focused on networks that exhibited dynamical properties consistent with independently obtained behavioral and physiological findings. Thus, in our view, biological plausibility in this study is not grounded in structural isomorphism, but rather in whether the core population-level dynamical properties observed in the model are reproducible in actual claustral population activity.

We also agree with the reviewer that our original qualitative comparison of GPFA-based latent trajectories did not provide sufficient quantitative support. In the revised manuscript, we have therefore added an eigenvalue-based quantitative analysis of the dimensional structure of population trajectories. This analysis does not depend on the identity of the dimensionality-reduction method itself, but instead focuses on quantifying the geometric structure of population-state trajectories as they evolve over time. Applying the same metric to both the RNN and biological claustrum data revealed consistent condition-specific differences in population dynamics.

This quantitative addition strengthens the previous qualitative trajectory comparison and clarifies that the model implements a specific computational dynamical regime that directionally corresponds to claustral population activity. While this does not imply uniqueness of the model, we believe it suggests that the proposed computational principle represents a biologically realizable candidate mechanism.

(1) Tone of model-data correspondence

Numerous statements describe the RNN as "closely mimicking," "recapitulating," or being "nearly identical" to claustral neural dynamics, sometimes extending to claims about causal relationships between neural activity and behavior. Given that neural data were not used to train the model, and that only a small subset of trained networks showed the reported dynamics, these statements should be substantially softened throughout the manuscript. The RNN should be framed as providing one possible computational realization consistent with existing data, not as a close instantiation of the biological circuit.

We agree with the reviewer’s concern. Expressions such as “closely mimicked,” “nearly identical,” and “recapitulate” will be replaced with more moderate language.

(2) Non-uniqueness of RNN solutions

The fact that only a small fraction of trained networks exhibited "claustrum-like" clusters deserves deeper discussion. This observation raises the possibility that the identified solution is fragile or highly specific rather than canonical. The authors should explicitly discuss the non-uniqueness of internal solutions in behavior-trained RNNs, including the range of alternative network dynamics that can reproduce the same behavior. In particular, it should be clarified why the specific network exhibiting "claustrum-like" clusters is informative about claustral computation, rather than representing one arbitrary solution among many.

As the reviewer noted, behavior-trained RNNs can yield multiple internal solutions that generate the same behavioral output, and we acknowledge this non-uniqueness. However, we do not interpret the relatively low success rate (5/100 networks) as evidence of fragility. Rather, we interpret it as suggesting that the emergence of this particular dynamical regime requires stringent structural constraints.

The computational demands of the task—specifically, the integration of temporally separated signals—drive convergence toward networks capable of sustaining persistent activity through recurrent excitatory connectivity. Indeed, all networks exhibiting a claustrum-like cluster shared a strong recurrent excitatory structure within Cluster 1, a structural feature consistent with our slice electrophysiology findings.

Our criterion for selecting RNNs was their ability to reproduce behavioral and physiological observations from the delayed escape experiment. Excluded RNNs may reflect alternative information-processing strategies characteristic of other brain regions or artificial logical solutions. Importantly, claustrum-like dynamics were not explicitly enforced during training; they emerged spontaneously under behavioral constraints, suggesting that this solution is not arbitrary.

Furthermore, the computational principles derived from the RNN were quantitatively consistent with in vivo single-neuron activity. Using an eigenvalue-based metric (λ₃/Σλ), both the RNN and biological claustrum data showed effects in the same direction. Leave-one-neuron-out analyses further demonstrated that this pattern was broadly distributed across neurons in the claustrum. These convergent results suggest that the identified network captures a computational regime that is consistent with claustral population dynamics, rather than representing an arbitrary solution unrelated to the biological observations.

(3) GPFA trajectory comparisons

The qualitative similarity between RNN trajectories and GPFA-derived trajectories from sparse in vivo data is interesting but insufficient to support claims of robustness or population-level structure. Statements suggesting that these patterns are unlikely to arise from noise or random fluctuations are not justified, given the single-trial, pseudo-population nature of the data. Either additional quantitative controls should be added, or the interpretation should be substantially tempered.

We agree that the original GPFA trajectory comparison in the biological claustrum data remained qualitative and did not sufficiently establish robustness or population-level structure. We have therefore added quantitative analyses in the revised manuscript.

Before presenting these analyses, we clarify methodological limitations inherent in pseudopopulation and single-trial data. GPFA estimates latent trajectories based on covariance structure and temporal smoothness assumptions. In pseudopopulations, true simultaneously recorded covariance cannot be fully reconstructed. Although our dataset is based on single trials rather than trial-to-trial variability, we acknowledge that latent-space estimation depends on covariance structure.

Therefore, the additional quantitative metric is not independent of the GPFA estimation stage; rather, it evaluates the geometric structure of single-trial latent trajectories estimated by GPFA.

Specifically, for biological data, we reanalyzed GPFA-estimated latent trajectories in PCA space and computed an eigenvalue-based metric (λ₃/Σλ). Across 20 time bins, a sliding window of 10 bins was applied. For each window, we computed the covariance matrix and extracted eigenvalues for PC1, PC2, and PC3. The third eigenvalue (λ₃) was normalized by total variance (Σλ = λ₁ + λ₂ + λ₃). This metric quantifies the extent to which trajectories deviate from a planar (two-dimensional) structure into a third dimension. An increase in λ₃/Σλ indicates the formation of a higher-dimensional geometric structure.

For RNN data, since all unit activities were simultaneously observed and sufficient trials were available, we directly applied PCA to population activity without GPFA. Mean trajectories across trials were computed, and the same λ₃/Σλ metric was applied. Although the initial dimensionality-reduction steps differ, the final metric definition and computation are identical. Thus, the comparison focuses on geometric dimensional structure rather than the dimensionality-reduction method itself.

Importantly, within the biological dataset, GPFA estimation, preprocessing, pseudopopulation construction, subsampling strategy, temporal alignment, and smoothing were applied identically across the CS and Neutral conditions. Under this common analysis framework, λ₃/Σλ values were consistently higher in the CS condition than in the Neutral condition.

For the RNN data, an identical analysis pipeline was applied across the CS+Open and Open-only conditions. In this case as well, λ₃/Σλ values were significantly higher in the CS+Open condition than in the Open-only condition.

If structural bias arose from covariance estimation or dimensionality reduction, it would be expected to affect conditions similarly within each dataset. The observation that λ₃/Σλ increases selectively in the CS condition in biological data and in the CS+Open condition in the RNN therefore supports the interpretation that the effect reflects a condition-specific dynamical difference rather than an artifact of dimensionality reduction.

To further examine whether the effect was driven by a small subset of neurons, we performed leave-one-neuron-out analyses in the biological dataset. In the CS group, most neurons contributed relatively evenly to the metric, whereas such distributed contribution was not observed in the Neutral group. This suggests that the three-dimensional structure reflects an organized population-level phenomenon rather than covariance dominated by a small number of outlier neurons.

These results indicate that the consistent elevation of λ₃/Σλ in the CS condition (biological data) and in the CS+Open condition (RNN) reflects a genuine dynamical feature rather than an artifact arising from pseudopopulation construction or dimensionality reduction.

Taken together, the three-dimensional geometric structure observed in GPFA-based latent trajectories is unlikely to reflect random noise. The replication of the same quantitative metric in the RNN, using an independent dimensionality-reduction procedure, strengthens the correspondence between the two systems. We appreciate the reviewer’s suggestion for quantitative reinforcement, which has substantially strengthened the manuscript.

(4) Scope of functional claims

The discussion connecting the findings to broad theories of claustral function, global workspace, or consciousness extends well beyond the data presented. These speculative links should be clearly labeled as such and significantly reduced in strength and prominence.

We agree with the reviewer and will clearly indicate that references to broader theoretical interpretations are speculative. We will substantially reduce their strength and emphasis.

(5) Comment on Conceptual Interpretation of the Behavioral Paradigm:

The manuscript repeatedly describes the delayed escape task as an "inference-based behavioral paradigm" and states that animals "infer that a value-neutral alternative space is likely to be safer" when the CS is presented in a novel environment. While I appreciate that the US-CS association was established in a different context and that the CS is then presented in a new environment, I am not convinced that the current behavioral evidence uniquely supports an inference interpretation.

We agree with the reviewer’s concern. We will describe the delayed escape task as “a behavioral paradigm that requires integration of temporally separated task-relevant signals” and remove inference-related terminology throughout the manuscript.

Reviewer #2 (Public review):

We appreciate the reviewer’s constructive and well-balanced comments. We regret that some of our wording and the scope of our introduction and discussion may not have appropriately reflected the contributions of prior studies. We will revise the manuscript accordingly to ensure that previous literature is more accurately and fairly acknowledged. In addition, we will reorganize the figures to more clearly present the hypotheses being tested and will provide additional details regarding both the modeling framework and the experimental procedures.

(1) This paper is based on behavioral results and neural recordings from their prior paper (Han et al.), but data, e.g., in Figure 1, are not clearly identified as new or as coming from that source. Figure 1A, for example, appears to be taken directly from Han et al. No methods are given in this manuscript for the behavioral testing or the in vivo electrophysiology.

We will clarify more explicitly which data and methods originate from Han et al. (2024). In the original manuscript, Figure 1 panels A, D, E, F, and L (left) were indicated in the legend as originating from Han et al. (2024). We will further clarify this distinction in the main text. Additionally, we will briefly describe the behavioral experiments and in vivo electrophysiology performed in Han et al. in the Methods section, with appropriate citation.

(2) Many other details are unclear. Examples include model training, the weight matrices and how these changed with training (p. 13), equations 2 and 3 (p. 13), the sources for the constants in the equations (p. 14), the methods (anesthesia, stereotaxic coordinates, injection specifics and details for "sparse expression") for the ChrimsonR injections.

As requested, we will provide additional details regarding model training procedures, weight matrices and their evolution during training, equations (2) and (3), the origin of constants used in the equations, and detailed methods for ChrimsonR injection (anesthesia, stereotaxic coordinates, injection parameters, and clarification of “sparse expression”).

(3) The explorations of model behavior are a catalog of everything tried rather than an organized demonstration of what the model can and cannot do. The figures could be reduced in number to emphasize the key comparisons of the different clusters and the model's behavior under different conditions, intended to "test" the model.

We will reorganize the figures to emphasize core results and clarify that the primary goal is to test and validate the computational model.

(4) On page 6, the E-E connectivity is argued from Shelton et al. (2025) and against Kim et al. (2016), but ignores Orman (2015), which, to this reviewer's knowledge, was the first to demonstrate such connectivity, including the long-duration events and impact of planes of section.

We will cite Orman (2015) as suggested and note that persistent activity has been observed in slices cut at specific angles, consistent with our findings.

(5) Whereas the authors are entitled to their own opinion of prior work (references 3-8), it is inappropriate to misrepresent prior work as only demonstrating a "limited function" of claustum. Additional papers by Mathur's group and Citri's group are ignored.

We will remove wording implying “limited” prior work and appropriately acknowledge contributions from the Mathur and Citri groups.

In summary, the authors have made a computational model that recapitulates the firing of a subset of potentially claustral neurons during a particular behavioral task (delayed escape is certainly not the only behavior that involves claustrum - see e.g., attention, salience, sleep). If the conclusion is that excitatory claustral cells must be connected to other excitatory claustral cells, such a conclusion is not new, and the electrophysiological E-E metrics are not well quantified (e.g., connectivity frequency, strength of connection). If the model is intended to predict how the claustrum might accomplish any other task, there is insufficient detail to evaluate the model beyond the evidence that the model creates a subset of cells that can sustain firing during the delay period in the delayed escape task.

Across all whole-cell recordings, optogenetic responses were observed in 38 out of 43 patched cells (~90%), suggesting that a high proportion of claustral neurons receive intra-claustral excitatory input. However, precise connectivity frequency and strength cannot be determined from the current dataset.

As the reviewer noted, our RNN is specialized for the delayed escape task, and we do not claim direct generalization to other proposed claustral functions such as attention, salience, or sleep. The goal of this study is to computationally characterize the temporal integration mechanism observed in this specific task.

While our model is specific to the delayed escape task, the computational principle identified here—nonlinear trajectory-based temporal integration supported by recurrent excitatory connectivity—may represent a more general mechanism for integrating temporally separated signals. However, testing such generality lies beyond the scope of the present study and will be framed as a future direction in the revised Discussion.

Figures and data

RNN simulation capable of performing the Delayed Escape Test

Comparison of recurrent connectivity in the claustrum and in the RNN simulation

PCA Trajectories, Decoder Accuracy, and Partial Information Decomposition of Cluster 1 RNN Neurons under different simulation conditions.

Trajectory Coding Hypothesis and Biological Neural Trajectories.

RNN activity of Clusters 1–3 under CS and door-opening only conditions

Contribution of each cluster to the output during the delayed escape test

RNN activity of Clusters 2 and 3 under inhibition (left) and escape latency under 180-s delay condition

Slice physiology and pharmacological manipulation of claustral persistent activity

PCA trajectories of Clusters 2 and 3 under various simulation conditions

Model-fit comparison across clusters

Decoding performance and PID analysis across clusters

PCA trajectories of high- and low-synergy neurons