Mice were tested in Eco-HAB, a system for automated, ecologically-relevant assessment of voluntary behavior in groups of mice. Animals were tested for 10 days.

(A) Schematic of the Eco-HAB system, where four compartments are connected with tunnels. Food and water are available ad libitum in compartments 2 and 4. (B) Time series of the location of 15 mice over 10 days, as aligned to the daylight cycle. (C) The activity of the mice is affected by the circadian clock. Error bars represent standard deviation across all mice (mouse-mouse variability, in blue) or across all days for the mean activity level for all mice (day-day variability, in orange). The two curves are slightly shifted horizontally for clearer visualization. We focus the following analysis on the data collected during the first half of the dark phase, between 13:00 and 19:00 (shaded region).

Mice in Eco-HAB interact pairwisely.

(A, B) The schematics showing pairwise interactions: two mice are more likely to be found in the same compartment than the sum of their individual preference implies (A); also, the probability for three mice being in the same compartment can be predicted from the pairwise interactions (B). (C) From pairwise correlation Cij, defined as the probability for mouse i and mouse j being in the same compartment (subtracted by the prediction of the independent model), and the probability for mouse i to be found in compartment r (subtracted by the model where each mouse spends equal amount of time in each of the four compartments), mir − 1/4, pairwise maximum entropy model learns the interaction strength between a pair of mice, Jij, and the local field , which gives the tendency for each mouse in each compartment. The data shown is the aggregated 5-day data from day 1 to day 5 of the C57 males (cohort M1). The pairwise maximum entropy model can predict higher order statistical structures of the data (schematics in panel B), such as the probability for triplets of mice being in the same compartment (subtracted by the prediction of the independent model, mathematically fijk(r, r, r) − fi(r)fj(r)fj(r)) (D), and the probability of K mice being found in the same compartment (E). (F) Conditional log-likelihood of mouse locations, predicted by the pairwise model (l(1,2)), the independent model (l(1)), and the null model assuming no compartment preference or interactions (l(0), the yellow line), for each mice (cohort M1 before TIMP-1 treatment, N = 15).

Summary of experiments used in this study.

The column Nmice gives the number of mice in the cohort used for the analysis, with cohort M4 and F1 containing dead or inactive mice after injection. The original number of mice is included in the parenthensis, and the exclusion procedure is described in Materials and Methods: Exclude inactive and dead mice from analysis. The column “NP” indicates the load of the injected nanoparticles. The column “Day 1” indicates the first day of observation in each of the 10-day experiment.

Quantification of sociability, and the impact of the impaired neuronal plasticity in the prelimbic cortex (PL).

(A) The schematic of the experiment, in which neuronal plasticity in the PL of the tested subjects was impaired with TIMP-1 treatment. A cohort of C57BL6/J male mice (N = 15) was tested in Eco-HAB for 10 days, and then removed from the cages for neuronal plasticity manipulation procedures. After a recovery period, they were placed back in Eco-HAB for another 10 days. For each of the five-day aggregate of the experiment, both before and after TIMP-1 treatment, we plot (B) the model-inferred interactions Jij, (C) preference for food compartments Δhi, (D) conditional log-likelihood for the pairwise model, l(1,2, the independent model, l(1), and the baseline null model, l(0), (E) mutual information between single mouse position and the rest of the network given by the inferred pairwise model.

Effect of TIMP-1 on the structure of the interaction network.

(A) Schematics of how triplets of mice may enter a state of “dissatisfaction” due to competitive pairwise interactions. Dissatisfaction reduces the space of preferable states due to competitive interactions. (B) The global dissatisfaction triplet index (DTI), F, computed using inferred interaction from 5-day segments of the data shows that for both male and female mice treated with TIMP-1, the global DTI is significantly increased after drug treatment. Two-sided Welch’s t -test is performed to test the significance for the difference of the global DTI between the first 5 days after drug injection against the other 5-day segments of the data. Error bars estimate the data variability, which is generated by taking random halves of the data (see Materials and Methods for details).

Stability of the data, given by the time evolution across 10 days of the experiment and the scatter plot between the observables measured using the first 5 days of the data vs. the last 5 days of the data for cohort M1 (N = 15).

The observables plotted include (A, E) mir, probability of mouse i being found in compartment r, (B, F) Cij, the (connected) pairwise correlation, or the in-cohort sociability, between mouse i and mouse j, (C, G) the sum of observed in-cohort sociability, Ci ≡ ∑j≠i Cij, which gives a proxy for how mouse i is effected by the social interaction, and (D, H) the activity rate, measured by the number of transition event per second. The error bars in panels E-H are extrapolated by bootstrapping random halves of the data.

The pairwise maximum entropy model is trained such that the model reproduces the probability for each mouse in each compartment, mir, and the probability for pairs of mice in the same compartment, Cij, as given by the data.

Error bars are generated by bootstrapping random halves of the data.

Learned parameters in the pairwise interaction model versus the observed statistics, plotted for the 5-day aggregate data from the first 5 days of the experiment on male cohort M1 before TIMP-1 treatment.

(A) The inferred interaction Jij versus the connected correlation Cij ; (B) the inferred individual compartment preference hir versus the in-compartment probability for each mouse mir - 1/4.

The probability of K mice found in the same compartment, predicted by the pairwise maximum entropy model, the independent model, and computed from the 5-day aggregate data for the first 5 days in male cohort M1 before TIMP-1 treatment (N = 15).

The subpanels are arranged in the same order as in the Eco-HAB setup. Error bars for the experiment are extrapolated from 50 random halves of the data, for the independent is generated by 50 random cyclic shuffling of the data, and for the pairwise model is from 50 random MCMC samplings (each with 54000 realizations, the same number of data points as the data) for the pairwise model.

Model predicted in-state probability matches data observation for the aggregate data of first five days of experiment in mice cohort M1 - C57BL6/J male mice (N = 15), which shows the prediction of the inferred pairwise model is unbiased.

Error bars are extrapolated from 20 draws of random halves of the data.

Cross-validation for maximum entropy models with triplet interactions and models with pairwise interactions on combined 10-day data (cohort M1, N = 15).

For the triplet model, L2 regularization βG is applied only to the triplet interactions. For the pairwise model, L2 regularization βJ is applied only to the pairwise interactions. Error bars are standard error from the mean across 6 different training-test set partitions, each containing 1 hour of data as test set and 5 hours of data as training set. The maximum of test-set log likelihood is achieved when the regularization strength βG is large in the triplet model, and when the regularization strength βJ is small in the pairwise model, indicating that the triplet model overfits for the data pulled from all 10 days.

Cross-validation for maximum entropy models with pairwise interactions on combined data from a total of K days (cohort M1, N = 15).

The plotted log-likelihoods are shifted by the training-set log likelihood at L2 regularization strength βJ = 10−1. The L2 regularization strength βJ is applied only to the pairwise interactions. Error bars are standard error from the mean across 6 different training-test set partitions, each containing 1 hour of data as test set and 5 hours of data as training set. For K = 1, the test-set likelihood increases as the regularization strength βJ increases, indicating that the pairwise maximum entropy model overfits if we only consider data from each day; while for K ≥ 4, the test-set likelihood decreases as the regularization parameter increases, indicating no overfitting.

Temporal consistency of inferred parameters from 5-day accumulated data for mice cohorts M1 (N = 15), M2 (N = 13), M3 (N = 10), M4(N = 12)).

(A) Chamber preference for each mouse in each box, hir, between models learned from the accumulated data from day 1-5, compared to the model learned from accumulated data from day 6-10. The Pearson’s correlation coefficient is shown on the plot. (B) Swarm plot for inferred pairwise interactions for each cohort from the first 5 days and the last 5 days. Two-sided t -test for equal mean and two-sided F -test for equal variance are performed. The asterisks encode the following p-values: *, p ≤ 0.05; **, p ≤ 0.01; * * *, p ≤ 0.001. (C) and (D) are the same as (A) and (B) for the pairwise interaction between mouse i and mouse j, Jij.

The conditional log likelihood is different for each cohort of C57BL6/J male mice (N = 13 in cohort M2, N = 10 in cohort M3, and N = 12 in cohort M4 (before BSA injection), exhibiting individuality.

Quantification of sociability, and the impact of the injection of BSA-infused nanoparticles, a control which does not impair neuronal plasticity in the prelimbic cortex (PL), in male C57BL6/J mice.

This figure follows Figure 3, now for cohort M4 (N = 9).

Quantification of sociability, and the impact of the impaired neuronal plasticity in the prelimbic cortex (PL) in female mice.

This figure follows Figure 3, now for cohort F1 (N = 13).

Pearson’s correlation coefficient between inferred interaction Jij from different five-day aggregated data, before and after drug injection, for cohort M1, M4 and F1. Asterisks indicate statistical significance. Almost no correlation is detected between the inferred Jij. The only two comparisons that exhibit statistical significance are between first and last 5 days after TIMP injection for cohort M1 (p-value = 0.033), and between last 5 days before TIMP and last 5 days after TIMP injection for cohort F1 (p-value = 0.028).

Dissatisfaction triplet index F computed using subgroups of mice for cohorts M1 (N = 15, Nsub = 9) and F1 (N = 13, Nsub = 9). Subsampling is performed at the level of inferred interactions, i.e. interactions Jij among all N mice are inferred using the pairwise maximum entropy model, then, 10 random subgroups of Nsub mice are drawn. Top: each colored bar represent 1 realization of the subsampling. Bootstraps of random halves of the data were used in analysis to be consistent Figure 4.Bottom: average over subgroups of the bar plot in the top row. Error bar represents standard deviation across different realizations of subgroups.

Dissatisfaction triplet index computed using subgroups of mice from cohorts M1 and F1. Subsampling is performed at the data level, i.e. the co-localization patterns of Nsub randomly selected mice are used to infer the interaction strengths, which are then used to compute the dissatisfaction triplet index F.

The global dissatisfaction triplet index (DTI) computed using shuffled interaction, Fshuffled vs. the global DTI computed using the inferred interaction, Frandom half.

Each point corresponds to one random half of the data. The two sets of global DTI’s are equal within the range of the error bars, computed by standard deviation across 20 random shuffling of the inferred interaction Jij, which shows the global DTI comes from the value of the inferred interaction, and that there is no additional network structure of the inferred interaction.