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Intrinsic Dynamics and Neural Implementation of a Hypothalamic Line Attractor Encoding an Internal Behavioral State - PubMed

  • ️Mon Jan 01 2024

Intrinsic Dynamics and Neural Implementation of a Hypothalamic Line Attractor Encoding an Internal Behavioral State

Amit Vinograd et al. bioRxiv. 2024.

Abstract

Line attractors are emergent population dynamics hypothesized to encode continuous variables such as head direction and internal states. In mammals, direct evidence of neural implementation of a line attractor has been hindered by the challenge of targeting perturbations to specific neurons within contributing ensembles. Estrogen receptor type 1 (Esr1)-expressing neurons in the ventrolateral subdivision of the ventromedial hypothalamus (VMHvl) show line attractor dynamics in male mice during fighting. We hypothesized that these dynamics may encode continuous variation in the intensity of an internal aggressive state. Here, we report that these neurons also show line attractor dynamics in head-fixed mice observing aggression. We exploit this finding to identify and perturb line attractor-contributing neurons using 2-photon calcium imaging and holographic optogenetic perturbations. On-manifold perturbations demonstrate that integration and persistent activity are intrinsic properties of these neurons which drive the system along the line attractor, while transient off-manifold perturbations reveal rapid relaxation back into the attractor. Furthermore, stimulation and imaging reveal selective functional connectivity among attractor-contributing neurons. Intriguingly, individual differences among mice in line attractor stability were correlated with the degree of functional connectivity among contributing neurons. Mechanistic modelling indicates that dense subnetwork connectivity and slow neurotransmission are required to explain our empirical findings. Our work bridges circuit and manifold paradigms, shedding light on the intrinsic and operational dynamics of a behaviorally relevant mammalian line attractor.

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Conflict of interest statement

Competing interests: Authors declare that they have no competing interests.

Figures

Extended Data 1 |
Extended Data 1 |. Shared line attractor dynamics in engaging and observing aggression.

a. Implantation of miniscope, field of view (top) and fluorescence image showing histology (bottom) with jGCaMP7s expression in VMHvl. b. Experimental paradigm to record VMHvlEsr1 activity in mice engaging in aggression. c. Left: neural & behavioral raster of example mouse 1 when engaging in aggression. Right: example neurons. d. Experimental paradigm to record VMHvlEsr1 activity in same mice in Ex. Data 1c during observation of aggression. e. Left: neural & behavioral raster of example mouse 1 during observation of aggression. Right: example neurons. f. Overview of rSLDS analysis. g. Left: rSLDS time constants in example mouse 1. Right: Neural activity projected onto two dimensions (x1 & x2) of dynamical system. h. Behavior triggered average of x1 and x2 dimensions, aligned to introduction of male intruder (n = 5 mice) i. Behavior triggered average of x1 dimensions, aligned to first attack onset (n = 5 mice). j. Left: rSLDS time constants in example mouse 1 during observation of aggression. Right: Neural activity projected onto two dimensions (x1 & x2) of dynamical system. k. Behavior triggered average of x1 and x2 dimensions from observation of aggression, aligned to introduction of Balb-c into resident’s cage (n = 5 mice). l. Behavior triggered average of x1 dimensions from observation of aggression, aligned to first bout of watching attack (n = 5 mice). m. rSLDS time constants across mice engaging in aggression (n = 5 mice). n. Line attractor score across mice engaging in aggression (n = 5 mice). o. rSLDS time constants across mice during observation of aggression (n = 5 mice). p. Line attractor score across mice during observation of aggression (n = 5 mice).

Extended Data 2 |
Extended Data 2 |. Single cell comparison of integration neurons across conditions.

a. Single cell contribution of x1 dimension (rSLDS weights) from engaging in aggression in example mouse. b. Z-score activity of weighted neurons from Ex. Data 2a during engaging in aggression from same mouse. c. Z-score activity of weighted neurons from Ex. Data 2a during observation of aggression from same mouse. d. Single cell contribution of x1 dimension (rSLDS weights) from observation of aggression in example mouse. e. Z-score activity of weighted neurons from Ex. Data 2d during engaging in aggression from same mouse. f. Z-score activity of weighted neurons from Ex. Data 2d during observation of aggression from same mouse. g. Overlap in neurons contributing to line attractor (x1) & x2 dimension from rSLDS performing independently in engaging versus observing aggression. Left: Example mouse, Right: Average across 5 mice.

Extended Data 3 |
Extended Data 3 |. Interaction between dimensions and activation of random neurons

a. Neural activity of five x1 neurons selected for grouped optogenetic perturbation during observation of aggression. b. Neural activity of same five x1 neurons in Ex. Data 3a during grouped optogenetic activation. c. Comparison of peak z-score of x1 neurons selected for grouped optogenetic activation during observation of aggression and during optogenetic activation (n = 9 mice). d. Paradigm for examining activity in x2 dimension upon grouped holographic activation of x1 neurons. e. Average z-score activity of neural activity projected onto x2 dimension across mice (n = 8 mice). f. Quantification of activity in unperturbed x2 dimension upon grouped holographic activation of x1 neurons (n.s, n = 8 mice). g. Paradigm for examining activity in x1 dimension upon grouped holographic activation of x2 neurons. h. Average z-score activity of neural activity projected onto x1 dimension across mice (n = 8 mice). i. Quantification of activity in unperturbed x1 dimension upon grouped holographic activation of x2 neurons (*p<0.05, n = 8 mice). j. Effect of grouped holographic activation of randomly selected neurons on activated neurons. k. Average z-score activity of unperturbed x1 dimension upon activation of random neurons (n = 5 mice). l. Average z-score activity of unperturbed x2 dimension upon activation of random neurons (n = 5 mice). m. Left: Quantification of activity in unperturbed x1 dimension upon grouped holographic activation of random neurons (n.s, n = 5 mice). Right: Comparison of grouped activation of x1 neurons (green, reproduced from Fig. 2c, right) and grouped activation of random neurons on activity of x1 dimension (black, reproduced from Ex. Data 3m, left). n. Quantification of activity in unperturbed x2 dimension upon grouped holographic activation of random neurons (n.s, n = 5 mice).

Extended Data 4 |
Extended Data 4 |. Deriving network time constant for model simulations. a. Analytical derivation of network time constant from connectivity matrix of purely excitatory recurrent neural network

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Figure 1 |
Figure 1 |. Attractor dynamics in head-fixed mice observing aggression.

a. Experimental paradigm for 2-photon head-fixed mice observing aggression. 920nm 2-photon laser was used to monitor activity of VMHvlEsr1 neurons in head-fixed mice observing aggression. A dynamical model fit to neural data guided holographic activation of specific neurons expressing ChRmine using a 1035nm 2-photon laser. b. Example field of view in 2-photon setup through a GRIN lens (top). Fluorescence image of a coronal slice showing expression of jGCaMP7s and ChRmine (bottom). Scale bars – 100μm. c. Neural and behavioral raster from example mouse observing aggression in the 2-photon setup. Arrows indicate insertion of submissive BALB/c intruder to the observation chamber for interaction with an aggressive Swiss Webster mouse (SW). Right: Example neurons from left. d. Neural activity projected onto rSLDS dimensions obtained from models fit to 2-photon imaging data in one example mouse. e. rSLDS time constants across mice (n = 9 mice, ****p<0.0001). f. Line attractor score (see methods) across mice (n = 9 mice). g. Behavior triggered average of x1 and x2 dimensions, aligned to introduction of BALB/c into resident’s cage (n = 9 mice). Dark line – mean activity, shaded surrounding – sem. h. Flow fields from 2P imaging data during observation of aggression from one example mouse. Red arrows indicate the direction flow of time. i. Top: Identification of neurons contributing to x1 dimension from rSLDS model. Weight of each neurons shown as absolute value. Bottom: Activity heatmap of five neurons contributing most strongly to x1 dimension. Right: Neural traces of the same neurons and an indication of when the systems enters the line attractor j. Same as i but for x2 dimension. k. Dynamic velocity landscape from 2P imaging data during observation of aggression from one example mouse. Blue color reflects stable area in the landscape, red – unstable. Black line is the trajectory of the neuronal activity. l. Cumulative distributions of autocorrelation half width of neurons contributing to x1 (green) and x2 (red) dimensions (n = 9 mice, 45 neurons each for x1 and x2 distributions). m. Mean autocorrelation half width across mice for neurons contributing to x1 and x2 dimensions (n = 9 mice, **p<0.01).

Figure 2 |
Figure 2 |. Holographic perturbations reveal line attractor dynamics in the VMHvl.

a. Field of view of five x1 neurons selected for 2-photon activation in example mouse 1. b. Neural activity projected onto x1 dimension after grouped optogenetic activation of five x1 neurons in example mouse 1 (top). Neural activity projected onto x2 dimension from activation of the same x1 neurons (bottom). Blue vertical lines indicate the time of holographic activation of x1 neurons. Dashed blue lines indicate the time of holographic activation on non-activated x2 neurons. c. Left: Average activity projected onto x1 dimension from activation of x1 neurons across mice using 20s inter stimulus interval (n = 8 mice). Right: Quantification of average z-scored activity of projected x1 dimension during baseline or various inter stimulus intervals (n = 8 mice, **p<0.01). d. Same as “c” but for 8s inter stimulus interval. e. Stimulation paradigm for grouped activation of x1 neurons using 20s ISI. f. Data and model prediction of applying stimulation paradigm in 2e to rSLDS model trained on observation of aggression. g. Cartoon showing quantification of perturbation along line attractor in neural state space. The Euclidian distance between time points tinitial (baseline before stimulation) and tstimend (end of stimulation) as well as between tinitial and tpoststim (end of ISI of stimulation) are calculated. h. Flow fields from example mouse 1, showing perturbations along line attractor upon activation of x1 neurons. i. Euclidian distance between time points tinitial and tstimend across mice (*p<0.05, **p<0.01). j. Same as 2i but for time points tinitial and tpoststim across mice (*p<0.05, **p<0.01). k. Field of view of five x2 neurons selected for activation in example mouse 1. l. Neural activity projected onto x1 dimension after grouped optogenetic activation of x2 neurons in example mouse 1 (top). Neural activity projected onto x2 dimension from activation of same x1 neurons (bottom). m. Left: Average of activation of x2 neurons across mice using 20s inter stimulus interval (n = 8 mice). Right: Quantification of average z-scored activity during baseline or inter stimulus intervals (n.s, n = 8 mice). n. Left: Average activity projected onto x2 dimension from activation of x2 neurons across mice using 8s inter stimulus interval (n = 7 mice). Right: Quantification of average z-scored activity of projected x2 dimension during baseline or inter stimulus intervals (n.s, n = 7 mice). o. Stimulation paradigm for grouped activation of x2 neurons using 20s ISI. p. Data and model prediction of applying stimulation paradigm in 2o to rSLDS model trained on observing aggression. q. Same as 2g but for an example perturbation orthogonal to a line attractor. r. Flow fields from example mouse 1, showing perturbations orthogonal to line attractor upon activation of x2 neurons. s. Same as 2i but for x2 activation. t. Same as 2j but for x2 activation.

Figure 3 |
Figure 3 |. Neural implementation of a line attractor guided by functional connectivity.

a. Left: Paradigm for examining activity in unperturbed x1 and x2 neurons upon activation of single x1 neurons. Right: Average z-score activity of perturbed x1 neurons (25 single neurons from n = 8 mice). b. Average z-score activity of unperturbed x1 neurons upon perturbation of single x1 neurons (n = 8 mice). c. Average z-score activity of unperturbed x2 neurons upon perturbation of single x1 neurons (n = 8 mice). d. Quantification of activity in unperturbed x1 neurons upon perturbation of single x1 neurons (**p<0.01, n = 8 mice). e. Quantification of activity in unperturbed x1 neurons upon perturbation of single x2 neurons (n.s, n = 8 mice). f. Left: Paradigm for examining activity in unperturbed x1 and x2 neurons upon activation of single x2 neurons. Right: Average z-score activity of perturbed x2 neurons (18 single neurons from n = 7 mice). g. Average z-score activity of unperturbed x2 neurons upon perturbation of single x2 neurons (n = 7 mice). h. Average z-score activity of unperturbed x1 neurons upon perturbation of single x2 neurons (n = 7 mice). i. Quantification of activity in unperturbed x1 neurons upon perturbation of single x2 neurons (n.s, n = 7 mice). j. Quantification of activity in unperturbed x2 neurons upon perturbation of single x2 neurons (n.s, n = 7 mice). k. Left: Cartoon illustrating either strong but sparse connectivity among x1 neurons (1), or dense and interconnectivity within subnetwork (2). Right: Empirical distribution of pairwise functional connectivity between x1 neurons (green) and from x1 to x2 neurons (red) (n = 99 pairs, n = 7 mice). l. Cartoon illustrating different elements of an excitatory network that can determine network level persistent activity including synaptic conductance time constant (ts) and density of subnetwork connectivity (σ). m. Model simulation result showing network time constant (tn) by varying σ in range 0–20% density values and ts in range 0–20s. The blue portions of the image refer to configurations that result in unstable networks with runaway excitation. n. Zoomed in version of 3m but for glutamatergic networks with synaptic conductance time constant (ts) in range 0.01–0.5s. o. Plot of network time constant (tn) against density of integration subnetwork for slow neurotransmitter networks (ts:10,15,20s). The network time constant tn varies monotonically with density for large values of ts. p. Same as 3o but for glutamatergic networks (ts:0.01,0.1,0.2,0.3s). q. Cartoon showing modified VMHvl circuit with fast feedback inhibition incorporated. r. Left: Plot of network time constant (tn) against density of integration subnetwork for a slow neurotransmitter network with ts=20s, for different values of strength of inhibition (inhibitory gain, ginh:1.25,5,10). Right: Same as left but for a glutamatergic network with ts=0.1s. s. Model simulation of a slow neurotransmitter network with fast feedback inhibition (ts:20s, 36% density of subnetwork connectivity). Top: Input (20s ISI) provided to model, Bottom: Spiking activity in network. The first 200 neurons (20%) comprise the interconnected integration subnetwork. t. Ca2+ activity convolved from firing rate (see Methods) of integration subnetwork (top) and remaining neurons (bottom). u. Same as 3s but for a fast transmitter network (ts:0.1s,36% density of subnetwork connectivity). v. Same as 3t but for a fast transmitter network (ts:0.1s,36% density of subnetwork connectivity).

Figure 4 |
Figure 4 |. Strength of functional connectivity infers line attractor’s decay rate.

a. Example neural activity projected onto x1 (integration) dimension of three mice that display varying rates of decay following removal of a Balb/c intruder from cage while observing aggression (i.e movement down the line attractor). b. Z-score activity on unperturbed x1 neurons upon activation of single x1 neurons in the same mice from 4a. c. Illustration of different quantification approaches to the change in activity of unperturbed x1 neurons from 4b as either mean z-score activity following first stimulus or area under the curve (auc). d. Correlation between rSLDS time constant obtained from observation of aggression and average z-score across unperturbed x1 neurons across 8 mice measured using either average z-score (left) or AUC (right) post first stimulus (r2: 0.59, *p<0.05). e. Correlation between rSLDS time constant obtained from observation of aggression and average z-score across unperturbed x2 neurons across 8 mice measured using either average z-score (left) or AUC (right) post first stimulus (r2: 0.06, n.s). f. Same as 4d but quantified post third stimulus. (r2: 0.87, ***p<0.001) g. Same as 4e but quantified post third stimulus. (r2: 0.0, n.s) h. Cartoon depicting summary of results illustrating intrinsic dynamics of hypothalamic line attractor. i. Cartoon depicting implementation of a hypothalamic line attractor encoding a behavioral internal state.

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