Structured stabilization in recurrent neural circuits through inhibitory synaptic plasticity

Reviewer #1 (Public review):

Summary:

Festa et al. provide a detailed analysis of the outcome of spike-timing-dependent plasticity acting on inhibitory synapses for distinct shapes of the kernel that governs how pre- and postsynaptic spike times induce synaptic changes. The authors investigate symmetric and asymmetric kernels, providing a theoretical description of the ingredients that give rise to rate- or covariance-dominated plasticity based on a simplified two-neuron circuit. These analyses are confirmed via simulations of large recurrent networks with random excitatory connectivity. For excitatory connections arranged in a one-dimensional ring, the authors show that two distinct classes of inhibitory neurons (distinguished by their plasticity rules) form an effective Mexican-hat weight profile. Furthermore, the authors show that external inhibition of one of the inhibitory neuron types gives rise to the phenomenon of surround modulation.

Strengths:

The analytical description of the two-neuron circuit is robust and accurately captures the qualitative evolution of inhibitory weights in the recurrent network with random excitatory connectivity. The emergence of the Mexican hat from the combination of distinct inhibitory synaptic plasticity rules acting on different neuron types is an important result that reveals how such connectivity can be learned in biologically plausible networks. All the analyses are well done, and the simulation results are convincing, which supports a robust interpretation of the findings.

Weaknesses:

The two-neuron circuit model is a good choice for the analytics, but it may have hidden a covariance effect of the "rate-dominated" symmetric spike-based kernel that would appear when several inhibitory neurons, each sharing a different spike correlation with the postsynaptic neuron, converge onto it. The rate homeostasis achieved by the rate-dominated model arises from adjusting inhibitory weights according to their initial correlation with the output neuron, so that after learning, the weights are distributed such that these correlations are cancelled out (Vogels et al., 2011). In other words, even the rate-dominated rule is covariance-driven under the hood: with a single inhibitory input, the two-neuron circuit cannot expose this, but with several differently correlated inputs, the covariance dependence should reappear.

It is unclear whether the distribution of inhibitory weights has stabilised after 25 minutes of simulation time (Figure 3C), given that a considerable proportion of (mutual) weights reach the maximum allowed weight while (unidirectional) weights appear to vanish. Without a maximum-weight bound, and given sufficiently long simulations, the weights might diverge to infinity or decay to zero, so the apparent stationarity may be imposed by the bound rather than reflecting a true steady state. This could also be a finite-size effect, given the small number of excitatory connections per neuron.

The connections from excitatory neurons to the two inhibitory populations are different in the ring model (exc to PV is wider than exc to SST according to Table 3), and it is not clear whether this width difference, rather than the plasticity rules themselves, is responsible for the emergence of the Mexican hat.

Reviewer #2 (Public review):

Summary:

This study investigates how inhibitory synaptic plasticity can stabilize recurrent neural circuits while also shaping their functional connectivity. The authors analyze inhibitory spike-timing-dependent plasticity rules and show that different temporal kernels promote distinct E/I motifs, including reciprocal E/I connectivity and lateral inhibition. Using reduced circuit analyses and larger spiking network simulations, they demonstrate that inhibitory plasticity can generate structured effective connectivity, including Mexican-hat-like interactions in ring networks, while maintaining stable activity. The work therefore extends the view of inhibitory plasticity from a primarily homeostatic mechanism to one that may contribute to computationally useful circuit organization.

Strengths:

A major strength of the study is that it identifies a concrete mechanism by which the temporal shape of iSTDP rules determines the structure of learned inhibitory connectivity. The comparison between rules favoring reciprocal E/I motifs and those favoring "lateral" inhibition is shown across both reduced circuit models and larger spiking networks. The ring-network simulations further connect these learned motifs to circuit-level outcomes, including Mexican-hat-like effective connectivity, surround-suppression, and modular spontaneous activity.

Weaknesses:

The main limitations concern the extent to which the learned motifs are fully self-organized and how broadly the results generalize. In particular, the ring-network results rely on a pre-specified ring-like excitatory architecture and on two inhibitory populations with distinct plasticity rules, making it important to clarify which aspects of the Mexican-hat effective connectivity emerge from iSTDP itself. The conclusions would also be strengthened by intermediate plasticity rules. Finally, the ring-network simulations provide an interpretable proof of principle, but the authors should clarify whether the PV/SST effects depend on this specific architecture or would also arise in a more generic recurrent or cortex-like connectivity motif.

The authors largely achieve their aim of showing that inhibitory synaptic plasticity can provide structured stabilization of recurrent circuits. The results support this claim within the model framework by demonstrating that different temporal forms of iSTDP lead to distinct learned E/I motifs and can shape effective connectivity and cortical-like response patterns. However, the broader biological interpretation remains more suggestive because some results depend on specific assumptions for the network architecture and plasticity rules.

The work is likely to be valuable for researchers studying inhibitory plasticity, E/I balance, cortical circuit development, and biologically plausible learning because it provides a clear theoretical link between local inhibitory learning rules and circuit-level organization. The combination of analytically tractable motifs, spiking network simulations, and publicly available code makes the framework useful for future research.

The significance of the work lies not in showing that inhibitory plasticity can have functions beyond homeostatic stabilization, which has been established by previous theoretical and experimental studies, but in formalizing how the temporal form of iSTDP rules can bias the emergence of distinct E/I motifs. At present, the work identifies rules that are sufficient to generate these motifs in model networks, while the mapping of these rules onto specific interneuron types remains for future experimental testing.

Author response:

We thank the editors for sending our work for review and the reviewers for their thorough and constructive evaluations. In response to their feedback, we will submit a revised version of the manuscript soon. Below, we provide clarification on several of the concerns raised and outline the changes planned for the revised manuscript.

Reviewer 1, weaknesses

(1) The two-neuron circuit model is a good choice for the analytics, but it may have hidden a covariance effect of the "rate-dominated" symmetric spike-based kernel that would appear when several inhibitory neurons, each sharing a different spike correlation with the postsynaptic neuron, converge onto it. The rate homeostasis achieved by the rate-dominated model arises from adjusting inhibitory weights according to their initial correlation with the output neuron, so that after learning, the weights are distributed such that these correlations are cancelled out (Vogels et al., 2011). In other words, even the rate-dominated rule is covariance-driven under the hood: with a single inhibitory input, the two-neuron circuit cannot expose this, but with several differently correlated inputs, the covariance dependence should reappear.

Reviewer 1  highlights that the rate-homeostatic rule by Vogels et al. (2011) also includes a covariance-dependent component. Thus, in a network with multiple excitatory units, differences in pre-postsynaptic correlations can drive a redistribution of weights, resulting in stronger inhibitory weights for higher correlations. Our two-neuron circuit, which contains only one plastic inhibitory input, cannot reveal this competitive effect. We note, however, that although in the Vogels rule the covariance-dependent term is non-zero, it is typically much smaller than the rate-dependent term (see Methods, Section 4.3). Consequently, covariance-dependent organization may emerge on a slower timescale (a similar effect was also shown by Lagzi and Fairhall 2024; https://doi.org/10.1126/sciadv.adi4350). In the revised manuscript, we will clarify this point and analyze small motifs with multiple excitatory units and heterogeneous correlations, focusing on both the timescale of weight redistribution and the resulting steady-state weights. We will also revise our interpretation of Supplementary Figure S9: within the simulated time window, the rate-dominated rule produces uniform inhibitory connectivity, but this does not exclude slower covariance-dependent reorganization.

(2) It is unclear whether the distribution of inhibitory weights has stabilised after 25 minutes of simulation time (Figure 3C), given that a considerable proportion of (mutual) weights reach the maximum allowed weight while (unidirectional) weights appear to vanish. Without a maximum-weight bound, and given sufficiently long simulations, the weights might diverge to infinity or decay to zero, so the apparent stationarity may be imposed by the bound rather than reflecting a true steady state. This could also be a finite-size effect, given the small number of excitatory connections per neuron.

The reviewer raises the possibility that the apparent stationarity in Figure 3C is influenced by the imposed weight bounds. In the revised manuscript, we will discuss this point and present extended versions of the simulations in Figure 3 where we remove the weight bounds. We will also test whether the observed behavior depends on network size or excitatory connection density. We note that, under different external input regimes, the weights stabilize without reaching the hard bound (Figure S11), suggesting that saturation is not a necessary outcome.

(3) The connections from excitatory neurons to the two inhibitory populations are different in the ring model (exc to PV is wider than exc to SST according to Table 3), and it is not clear whether this width difference, rather than the plasticity rules themselves, is responsible for the emergence of the Mexican hat.

We recognize that we did not fully justify the parametrization used in the ring model. The pre-existing ring architecture determines the spatial correlations available to iSTDP and therefore contributes to the learned connectivity. In the revised manuscript, we will add control simulations in which the excitatory inputs to the PV and SST populations have either identical or markedly different widths, while the plasticity rules are kept fixed. These controls will allow us to assess the relative contributions of these factors to the formation of a Mexican-hat effective-connectivity profile.

Reviewer 2, weaknesses

(1) The main limitations concern the extent to which the learned motifs are fully self-organized and how broadly the results generalize. In particular, the ring-network results rely on a pre-specified ring-like excitatory architecture and on two inhibitory populations with distinct plasticity rules, making it important to clarify which aspects of the Mexican-hat effective connectivity emerge from iSTDP itself. The conclusions would also be strengthened by intermediate plasticity rules. Finally, the ring-network simulations provide an interpretable proof of principle, but the authors should clarify whether the PV/SST effects depend on this specific architecture or would also arise in a more generic recurrent or cortex-like connectivity motif.

This comment raises an important distinction between the components that are specified and those that emerge through plasticity. In our simulations, the excitatory architecture is fixed, whereas the initially weak and unstructured inhibitory-to-excitatory connections are learned through iSTDP. Thus, in the ring network, the spatial organization of excitation is prescribed, but the inhibitory connectivity and resulting Mexican hat-like effective connectivity emerge from the interaction of this architecture with the two iSTDP rules. Importantly, the central result that symmetric and antisymmetric rules promote distinct reciprocal and lateral E/I motifs is not restricted to the ring network, but is also observed in sparse randomly connected spiking networks and in networks with intrinsically generated irregular activity. The ring network is therefore used to demonstrate how these general motif-forming mechanisms can support specific circuit computations.

Our framework parametrizes a broader family of pairwise iSTDP rules rather than relying exclusively on isolated, preselected rules, allowing the contribution of rule shape and rate-dependent terms to be understood analytically. Intermediate or “mixed” plasticity rules, including those considered by Yang and Doiron (2026) https://doi.org/10.1103/9nv2-y63v, as well as additional network architectures, are valuable directions for extending the framework. We will revise the Discussion to clarify which components are prescribed, which emerge through plasticity, and which conclusions apply beyond the ring-network implementation.

(2) The authors largely achieve their aim [...] by demonstrating that different temporal forms of iSTDP lead to distinct learned E/I motifs and can shape effective connectivity and cortical-like response patterns. However, the broader biological interpretation remains more suggestive because some results depend on specific assumptions for the network architecture and plasticity rules.

This comment points to an important distinction between biological generality and mechanistic insight. Our models are deliberately simplified to isolate how the temporal structure of iSTDP interacts with internally generated correlations to select distinct E/I connectivity motifs, and to make this relationship analytically tractable. The resulting predictions are then reproduced in large conductance-based spiking networks with different connectivity structures and sources of irregular activity. Thus, although we do not claim that the specific biological implementations considered here capture the full diversity of cortical circuits, the conclusions are not restricted to a single minimal model or network architecture. Adding further biological detail would introduce additional parameters and architecture-specific assumptions, but would not by itself establish greater generality or provide the same mechanistic understanding. In the revised Discussion, we will clarify the distinction between the general mechanistic principles established by our framework and the more specific biological interpretations that remain to be tested.

(3) [...] At present, the work identifies rules that are sufficient to generate these motifs in model networks, while the mapping of these rules onto specific interneuron types remains for future experimental testing.

Our use of the PV and SST labels is intended as a biologically motivated implementation rather than as a universal assignment of plasticity rules to these interneuron classes. The symmetric and antisymmetric kernels were motivated by in vitro measurements from PV and SST interneurons in mouse orbitofrontal cortex, respectively (Lagzi et al., 2021; https://doi.org/10.1101/2021.09.06.459211). Because inhibitory plasticity can vary across brain regions, developmental stages, and experimental conditions (Feldman, 2012; https://doi.org/10.1016/j.neuron.2012.08.001), the general conclusion of our work concerns the mapping from the temporal structure of an iSTDP rule to the E/I motif it promotes, rather than a fixed correspondence between a particular rule and an interneuron identity.

Our models therefore establish more than the sufficiency of two isolated rules: the analytical framework explains how features of the plasticity kernel and rate-dependent terms determine whether reciprocal, lateral, or blanket inhibitory connectivity emerges. The specific association of these mechanisms with PV and SST interneurons in other circuits remains an experimentally testable prediction. We will clarify this distinction in the revised manuscript and emphasize that, once cell-type-specific plasticity rules are measured in a given circuit, the framework can predict the E/I connectivity motifs that those rules are expected to promote.