Interplay between homeostatic synaptic scaling and homeostatic structural plasticity maintains the robust firing rate of neural networks

Reviewer #1 (Public Review):

This manuscript investigates how homeostatic structural plasticity and synaptic scaling act under different levels of activity suppression and how this influences the network dynamics during growth and temporary or persistent silencing. To this end, the authors first use electrophysiology and chronic imaging to investigate the influence of different levels of AMPA-receptor blockade. A smaller level leads to reduced activity and up-regulation of synapse size and number, whereas a complete block abolished activity and decreases spine numbers. Along this line, the choice to block AMPAR is unconventional and needs to be better justified as both investigated homeostatic mechanisms are known to be AMPAR dependent.

Second, this finding is transferred into a mathematical rewiring rule, where spine number shrinks, grows, and shrinks again with increasing activity. It is shown that this rule, in contrast to other, simpler rules (grow, shrink), can grow healthy networks from scratch only if additional stimulation is provided. Continuing with these stable networks, the activity of a sub-network is increased, decreased, or silenced by modulating an external stimulation to the neurons. Whereas both activity and connectivity return to a stable state for small alteration, complete silencing leads to disconnection of the silenced network parts. Recovery from this can be achieved by restoring stimulation before the connectivity has completely decayed or by adding sufficiently fast synaptic scaling, although both cases can lead to unhealthy activity. A more systematic assessment of this interaction between scaling and homeostatic rewiring revealed a minimal timescale ratio that is needed for recovery. This is an important step towards disentangling the necessity of multiple, seemingly redundant mechanisms. Yet, in the simulations, the role of recurrent connectivity versus external inputs should be investigated in more detail in order to ensure the generality of the finding that a recovery of the activity is impossible for the presented rewiring rule without synaptic scaling.

Overall, the combination of experiments and simulations is a promising approach to investigating network self-organization. The gradual blocking of activity is especially valuable to inform mathematical models and distinguish them from alternatives. Here, the simulation results clearly demonstrate that the experimentally informed rule exhibits qualitatively different dynamics including the need for another homeostatic mechanism. However, a better connection between the simulations and experiment two would be desirable. In particular, it is unclear whether the model would actually reproduce the experiment, to which other experiments the model results relate, and which experimentally testable predictions the model makes.

In summary, this manuscript makes a valuable contribution to discerning the mathematical shape of a homeostatic structural plasticity model and understanding the necessity of synaptic scaling in the same network. Both experimental and computational methods are solid and well-described. Yet, both parts could be linked better in order to obtain conclusions with more impact and generality.

Reviewer #2 (Public Review):

This manuscript by Lu et al addresses the understudied interplay between structural and functional changes underlying homeostatic plasticity. Using hippocampal organotypic slice cultures allowing chronic imaging of dendritic spines, the authors showed that partial or complete inhibition of AMPA-type glutamate receptors differentially affects spine density, respectively leading to an increase or decrease of spines. Based on that dataset, they built a model where activity-dependent synapse formation is regulated by a biphasic rule and tested it in stimulation- or deprivation-induced homeostatic plasticity. The model matches experimental data (from the authors and the literature) quite well, and provides a framework within which functional and structural changes coexist to regulate firing rate homeostasis.

While the correlation between changes in AMPAR numbers and in spine number/size has been well characterized during Hebbian plasticity, the situation is much less clear in homeostatic plasticity due to multiple studies yielding diverging results. This manuscript adds new experimental results to the existing data and presents a valuable effort to generate a model that can explain these divergences in a unifying and satisfactory framework.

The model and its successive implantation steps are well presented along a clear thread. However, it would have benefited from having an actual timeline of structural changes throughout the three days of AMPAR inhibition, especially as their experimental model allows it. This would have provided additional information on spine dynamics (especially transient spines) and on the respective timescale of the structural and functional changes, and thus led to a better-informed model.

Additionally, the model would have been strengthened by an experimental dataset with homeostatic plasticity induced by higher activity (e.g. with bicuculline). To the best of my knowledge, there is currently no data on structural plasticity following scaling down, and it is also known that scaling up and down are mediated by different molecular pathways. The extension of the model from scaling up (in response to silencing) to scaling down (in response to increased activity) offers an interesting perspective but may be a bit of a stretch.

Finally, the authors are very specific in their definition and distinction of structural and functional homeostatic plasticity for their model. Structural plasticity is limited to spine density and functional plasticity to synaptic scaling, which allows the authors to discuss the interplay between very distinct "synapse number-based structural plasticity" and "synaptic weight-based synaptic scaling", and appears to bypass the fact that spine size regulates the space available for AMPARs at the synapse and thus synaptic weight. The authors are of course aware of the importance of changes in spine size, as they present some intriguing data showing that spine size is differentially affected by partial or complete inhibition of AMPARs and include the putative role of spine size changes in the discussion. However, spine size does not seem to be taken into account in their network simulations, which present synaptic scaling and structural plasticity as completely distinct processes. While the model still offers interesting insights into the interaction of these processes, it would have benefited from a less stringent distinction; this choice and the reasons behind it should be made more explicit in the manuscript.

Author Response:

We sincerely appreciate the recognition from both reviewers regarding the innovative gradual activity-blocking design employing NBQX, as well as the robustness of our approach that integrates experimental and computational approaches to investigate the interplay between homeostatic functional and structural plasticity in response to activity deprivation.

Acknowledging the raised concerns and insightful advice shared by the reviewers, we provide the the following provisional response:

Why did we focus on activity silencing? Our decision to focus on chronic activity deprivation stems from a robust body of evidence—summarised in the recent review by Moulin and colleagues (2022)—that highlights the consistent occurrence of homeostatic spine loss alongside synaptic downscaling in response to prolonged excitation. In contrast, chronic silencing studies, as outlined in the same review, exhibit inconsistencies and contradictions, with spine loss often manifesting as non-homeostatic. After carefully reviewing the available data, we formulated two hypotheses to account for this heterogeneity: (i) the non-linear nature of activity-dependent structural plasticity, and (ii) the intricate interplay between homeostatic synaptic scaling and structural plasticity influenced by factors such as the extend of activity deprivation, specific dendritic segments, cell phenotypes, brain regions, and even across species. The intricate exploration of these hypotheses necessitated a systematic approach through computational simulations (and suitable experiments). The present manuscript intentionally confines the discussion of heightened activity to a proof-of-concept computer simulation, underscoring our deliberate emphasis on the central theme of activity silencing. Nevertheless, we do concur with the reviewers that an intriguing avenue for future exploration lies in extending the model to encompass homeostatic synaptic downscaling triggered by augmented activity.

Why did we choose NBQX and why didn't we extensively characterise it? We utilised NBQX, a competitive antagonist targeting AMPA receptors, enabling us to finely modulate network activity via dosages (as elucidated by Wrathall et al., 2007), surpassing the control attainable with TTX. Despite its atypical role in studying homeostatic synaptic plasticity, NBQX boasts commendable efficacy in regulating network activity, substantiated by our electrophysiological recordings as well as in vivo and in vitro studies (Follett et al., 2000; Wrathall et al., 2007). However, it's worth noting that NBQX selectively binds to GluA2-containing AMPA receptors, pivotal for TTX-triggered synaptic scaling (Gainey et al., 2009) and glutamate-induced spine protrusion in the presence of TTX (Richards et al., 2005). Importantly, there's no conclusive evidence suggesting that NBQX, when applied in isolation (without TTX), hinders the synthesis or insertion of AMPA receptors. While we acknowledge the interest and value in characterising NBQX separately, such an endeavour extends beyond the immediate scope of our current study.

It's pertinent to also note that the models we employed—activity (calcium) dependent homeostatic synaptic scaling and structural plasticity—are inherently phenomenological in nature. In essence, these models refrain from delving into intricate molecular mechanisms beyond the regulation of calcium concentration by firing rates. Given the highly phenomenological nature of our models, introducing a detailed molecular characterization of NBQX, or expanding into a chronic increase in network activity scenarios targeting different molecular pathways, could potentially create misleading expectations among our readers, implying a level of molecular pathway implementation that is not our immediate focus.

Did the model successfully replicate the experimental findings? Achieving a strong agreement between computer simulations and empirical data is often a sought-after outcome, particularly when both aspects are integrated within a single study. However, this congruence is not always the primary intent. In our present investigation, we introduced three distinct ways in which experimental data merged with computational studies: to provide informative input, to validate hypotheses, and to stimulate novel ideas.

Our experiments primarily aimed to inform the computational model through an analysis of spine density. The computational framework was envisioned to yield insights that could be broadly applicable, extending beyond the mere replication of conducted experiments. In this context, our modelling outcomes effectively mirrored the heterogeneous alterations in synapse numbers observed in various in vivo and in vitro studies following activity deprivation—ranging from homeostatic increases to non-homeostatic synapse loss.

Our model also proposed a plausible mechanism illustrating how synaptic scaling might propel the transition from non-homeostatic synapse loss to the restoration of synapse levels, achieved by maximising inputs from active spines. This supposition found partial confirmation when considering both our experimentally obtained spine sizes and those detailed in the existing literature—pointing to a reduction in spine numbers but a conservation of larger spine sizes during complete activity blockade.

Moreover, our experimental observations unveiled certain aspects that, while not entirely encompassed by our model, have the potential to inspire future modelling studies. For instance, we observed size-dependent changes in spine sizes under complete activity blockade; we also observed inconsistent combinations of spine density and size changes across dendritic segments upon activity deprivation. The prospect of reconfiguring the interplay between structural plasticity and synaptic scaling rules to elucidate the observed heterogeneity in outcomes stands as an intriguing avenue worth revisiting, particularly as the modelling of structural plasticity within a network of intricately detailed neurons becomes feasible.

In summary, while the aspiration to faithfully replicate experimental outcomes exists, achieving an exact correspondence between a purposefully simplified system, like the point neural network we employed in our study, and real-world data should be approached with caution. Striving for such a match carries the risk of overfitting and prematurely advancing conclusions that might not stand the test of broader applications.

Why did we establish strict definitions for functional and structural plasticity? The rationale behind this strategic decision lies in the historical breadth of the term "structural plasticity," encompassing a wide array of high-dimensional alterations in neural morphology throughout development and adulthood. This expansive interpretation contributed to the delayed development of computational models specifically targeting structural plasticity. Moreover, certain elements, like spine sizes, blur the boundaries with the functional facet of synapses as also mentioned by the reviewers. We hope the reviewers and readers concur with our perspective that implementing structural plasticity through the manipulation of synapse numbers—effectively enabling dynamic (re)wiring—provides a high degree of freedom and robustness. Synaptic size seamlessly translates into synaptic weights within the modelling framework. While the distinction between synaptic weight and synapse number may seem stringent, it meticulously prepares the groundwork for addressing a fundamental question: How does the gradual modification of synapse numbers, juxtaposed with the swift modulation of synaptic weights, interact within a perpetually evolving dynamic system? In this respect our study serves as a panoramic vista, unveiling possibilities wherein distinct combinations of these two governing principles can engender divergent outcomes. This contribution not only stands as a benchmark but also extends a welcoming embrace to forthcoming structural plasticity models that embrace the concept of continuous size and number alterations.