Spatially heterogeneous inhibition projects sequential activity onto unique neural subspaces
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eLife Assessment
This valuable study uses mathematical modeling and analysis to address the question of how neural circuits generate distinct low-dimensional, sequential neural dynamics that can change on fast, behaviorally relevant timescales. The authors propose a circuit model in which spatially heterogeneous inhibition constrains network dynamics to sequential activity on distinct neural subspaces and allows top-down sequence selection on fast timescales. The study convincingly demonstrates how this mechanism could operate and makes predictions about connectivity patterns and dynamics.
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Abstract
Neural activity in the brain traces sequential trajectories on low dimensional subspaces. For flexible behavior, these neural subspaces must be manipulated and reoriented within short timescales of tens of milliseconds. Using mathematical analysis and simulation of a recurrently connected neural circuit for sequence generation, we report that incorporating a subtype of interneurons that provides spatially heterogeneous inhibition enables the projection of sequential activity onto task- or context-specific neural subspaces. Depending on the sparsity of inhibitory projections, neural subspaces could be arbitrarily rotated, without altering the key aspects of sequence generation. Thus, we propose a circuit motif by which inhibitory interneurons can enable flexible switching between neural subspaces on a fast timescale of milliseconds, controlled by top down signals.
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eLife Assessment
This valuable study uses mathematical modeling and analysis to address the question of how neural circuits generate distinct low-dimensional, sequential neural dynamics that can change on fast, behaviorally relevant timescales. The authors propose a circuit model in which spatially heterogeneous inhibition constrains network dynamics to sequential activity on distinct neural subspaces and allows top-down sequence selection on fast timescales. The study convincingly demonstrates how this mechanism could operate and makes predictions about connectivity patterns and dynamics.
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Reviewer #1 (Public review):
Summary:
The authors show that targeted inhibition can turn on and off different sections of networks that produce sequential activity. These network sections may overlap under random assumptions, with the percent of gated neurons being the key parameter explored. The networks produce sequences of activity through drifting bump attractor dynamics embedded in 1D ring attractors or in 2D spaces. Derivations of eigenvalue spectra of the masked connectivity matrix are supported by simulations that include rate and spiking models. The paper is of interest to neuroscientists interested in sequences of activity and their relationship to neural manifolds and gating.
Strengths:
(1) The study convincingly shows preservation and switching of single sequences under inhibitory gating. It also explores overlap across …
Reviewer #1 (Public review):
Summary:
The authors show that targeted inhibition can turn on and off different sections of networks that produce sequential activity. These network sections may overlap under random assumptions, with the percent of gated neurons being the key parameter explored. The networks produce sequences of activity through drifting bump attractor dynamics embedded in 1D ring attractors or in 2D spaces. Derivations of eigenvalue spectra of the masked connectivity matrix are supported by simulations that include rate and spiking models. The paper is of interest to neuroscientists interested in sequences of activity and their relationship to neural manifolds and gating.
Strengths:
(1) The study convincingly shows preservation and switching of single sequences under inhibitory gating. It also explores overlap across stored subspaces.
(2) The paper deals with fast switching of cortical dynamics, on the scale of 10ms, which is commonly observed in experimental data, but rarely addressed in theoretical work.
(3) The introduction of winner-take-all dynamics is a good illustration of how such a mechanism could be leveraged for computations.
(4) The progression from simple 1D rate to 2D spiking models carries over well the intuitions.
(5) The derivations are clear, and the simulations support them. Code is publicly available.
Weaknesses:
(1) The inhibitory mechanism is mostly orthogonal to sequences: beyond showing that bump attractors survive partial silencing, the paper adds nothing on observed sequence properties or biological implications of these silenced sequences. The references clump together very different experimental sequences (from the mouse olfactory bulb to turtle spinal chord or rat hippocampus) with strongly varying spiking statistics and little evidence of targeted inhibitory gating. The study would benefit from focusing on fewer cases of sequences in more detail and what their mechanism would mean there.
(2) The paper does not address the simultaneous expression of sequences either in the results or the discussion. This seems biologically relevant (e.g., Dechery & MacLean, 2017) and potentially critical to the proposed mechanism as it could lead to severe interference and decoding limitations.
(3) The authors describe the mechanism as "rotating a neuronal space". In reality, it is not a rotation but a projection: a lossy transformation that skews the manifold. The two terms (rotation and projection) are used interchangeably in the text, which is misleading. It is also misrepresented in Figure 1de. Beyond being mathematically imprecise in the Results, this is a missed opportunity in the Discussion: could rotational dynamics in the data actually be projections introduced by inhibitory gating?
(4) The authors also refer to their mechanism as "blanket of inhibition with holes". That term typically refers to disinhibitory mechanisms (the holes; for instance, VIP-SOM interactions in Karnani et al, 2014). In reality, the inhibition in the paper targets the excitatory neurons (all schematics), which makes the terminology and links to SOM-VIP incorrect. Other terms like "clustered" and "selective" inhibition are also used extensively and interchangeably, but have many connotations in neuroscience (clustered synapses, feature selectivity). The paper would benefit from a single, consistent term for its targeted inhibition mechanism.
(5) Discussion of this mechanism in relation to theoretical work on gating of propagating signals (e.g., Vogels & Abbott 2009, among others) seems highly relevant but is missing.
(6) Schematics throughout give the wrong intuition about the network model: Colors and arrows suggest single E/I neurons that follow Dale's rule and have no autapses. None of this is true (Figure 2b W). Autapses are actually required for the eigenvalue derivation (Equation 11).
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Reviewer #2 (Public review):
Summary:
In "Spatially heterogeneous inhibition projects sequential activity onto unique neural subspaces", Lehr et al. address the question of how neural circuits generate distinct low-dimensional, sequential neural dynamics that can shift to different neural subspaces on fast, behaviorally relevant timescales.
Lehr et al. propose a circuit architecture in which spatially heterogeneous inhibition constrains network dynamics to sequential activity on distinct neural subspaces and allows top-down sequence selection on fast timescales. Two types of inhibitory interneurons play separate roles. One class of interneuron balances excitation and contributes to sequence propagation. The second class of interneuron forms spatially heterogeneous, clustered inhibition that projects onto the sequence-generating portion …
Reviewer #2 (Public review):
Summary:
In "Spatially heterogeneous inhibition projects sequential activity onto unique neural subspaces", Lehr et al. address the question of how neural circuits generate distinct low-dimensional, sequential neural dynamics that can shift to different neural subspaces on fast, behaviorally relevant timescales.
Lehr et al. propose a circuit architecture in which spatially heterogeneous inhibition constrains network dynamics to sequential activity on distinct neural subspaces and allows top-down sequence selection on fast timescales. Two types of inhibitory interneurons play separate roles. One class of interneuron balances excitation and contributes to sequence propagation. The second class of interneuron forms spatially heterogeneous, clustered inhibition that projects onto the sequence-generating portion of the circuit and suppresses all but a subset of the sequential activity, thus driving sequence selection. Due to the random nature of the inhibitory projections from each inhibitory cluster, the selected sequences exist on well-separated neural subspaces, provided the 'selection' inhibition is sufficiently dense. Lehr et al. use mathematical analysis and computational modeling to study this type of circuit mechanism in two contexts: a 1D ring network and a 2D, locally connected, spiking network. This work connects to previous literature, which considers the role of selective inhibition in shaping and restructuring sequential dynamics.
Strengths:
(1) This study makes testable predictions about the connectivity patterns for the two types of interneurons contributing to sequence generation and sequence selection.
(2) This study proposes a relatively simple circuit motif that can generate many distinct, low-dimensional neural sequences that can vary dynamically on fast, behaviorally relevant timescales. The authors make a clear analytical argument for the stability and structure of the dynamics of the sub-sequences.
(3) This study applies the inhibitory selection mechanisms in two different model network contexts: a 1D rate model and a 2D spiking model. Both settings have local connectivity patterns and two inhibitory pools but differ in several significant ways, which supports the generality of the proposed mechanism.
Weaknesses:
(1) Scaling synaptic weights to match the original sequence dynamics is a complex requirement for this mechanism. In the 2D network, the solution to this scaling issue is the saturation of single-unit firing rates. It is unclear if this is in a biologically relevant dynamical regime or to what degree the saturation dynamics of the sequences themselves are altered by the density of selective inhibition.
(2) In the 2D model, although the sequence-generating circuit is quite general, the heterogenous interneuron population requires a tuned connectivity structure paired with matched external inputs. In particular, the requirement that inhibitory pools project to shared but random excitatory neurons would benefit from a discussion about the biological feasibility of this architecture.
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Reviewer #3 (Public review):
Summary:
The study investigates the control of the subspaces in which sequences propagate, through static external and dynamic self-generated inhibition. For this, it first uses a 1D ring model with an asymmetry in the weights to evoke a drift of its bump. This model is studied in detail, showing and explaining that the trajectories take place in different subspaces due to the inhibition of different sets of contributing neurons. Sequence propagation is preserved, even if large numbers of neurons are silenced. In this regime, trajectories are restricted to near-orthogonal subspaces of neuronal activity space. The last part of the results shows that similar phenomena can be observed in a 2D spiking neural network model.
Strengths:
The results are important and convincing, and the analyses give a good further …
Reviewer #3 (Public review):
Summary:
The study investigates the control of the subspaces in which sequences propagate, through static external and dynamic self-generated inhibition. For this, it first uses a 1D ring model with an asymmetry in the weights to evoke a drift of its bump. This model is studied in detail, showing and explaining that the trajectories take place in different subspaces due to the inhibition of different sets of contributing neurons. Sequence propagation is preserved, even if large numbers of neurons are silenced. In this regime, trajectories are restricted to near-orthogonal subspaces of neuronal activity space. The last part of the results shows that similar phenomena can be observed in a 2D spiking neural network model.
Strengths:
The results are important and convincing, and the analyses give a good further insight into the phenomena. The interpretation of inhibited networks as near-circulant is very elucidating. The sparsening by dynamically maintained winner-takes-all inhibition and the transfer to a 2D spiking model are particularly nice results.
Weaknesses:
I see no major weaknesses, except that some crucial literature has not yet been mentioned and discussed. Further, Figure 2c might raise doubts whether the sequences are indeed reliable for the largest amount of sparsening inhibition considered, and it is not yet clear whether the dynamical regime of the 2D model is biologically plausible.
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