Figures and data
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 in a pairwise fashion.
(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 
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. The effect of TIMP-1 is known to decay after 5 days [37], and as expected the most notable effects were recorded during the first half of the experiment. (B) The model-inferred interactions Jij for each day of the experiment, both before (top panel) and after TIMP-1 treatment (bottom panel). (C) Interaction parameters (mean and standard deviation, respectively top and bottom) before (blue) and after TIMP-1 treatment (red). The mean of the interaction strength is similar, but the variability increases for the first few days after TIMP-1 treatment. Error bars are the standard deviation across random halves of the duration of the experiment. (D) Preference for the compartments containing food Δhi for each day of the experiment, both before (top panel) and after TIMP-1 treatment (bottom panel). Data points corresponding to the same mouse are connected with gray line segments. (E) Mean (top panel) and variability (bottom panel) of the preference for the compartments containing food, Δhi, for each day of the experiment, before (blue) and after TIMP-1 treatment (red). The preference for the compartments containing food immediately increases after injection of TIMP-1, and decays to a control level after 6 days. Error bars are the standard deviation across random halves of the duration of the experiment. (F) Conditional log-likelihood of mouse locations, predicted by the pairwise model (blue / red), the independent model (black), and the null model (gray dashed) assuming no compartment preference or interactions, averaged across all mice. for before (top panel) and after TIMP-1 treatment (bottom panel). After impairing neuronal plasticity in the PL, individual compartment preferences, represented by the independent model, explain most of the prediction power. Error bars are the standard deviation across all N = 15 mice.
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 pair-wise interactions. Dissatisfaction reduces the space of preferable states due to competitive interactions. (B) The global dissatisfaction triplet index (DTI), F, as a function of time, computed using the inferred interaction Jij matrix learned each day. The level of dissatisfaction F increases in the first few days after TIMP-1 treatment for both male and female mice, and recovers to the level of the control group after five days. In the control cohort M4 (male treated with BSA), there is no significant difference of the global DTI before and after drug treatment. In the male cohort M1, day 2 after TIMP-1 injection shows a significantly greater value of global DTI compared to the baseline from before drug application (p = 0.0019, for day 1, p = 0.0054, see Materials and Methods for details of the significance test). In the female cohort M1, the global DTI increases significantly for day 1 (p = 6.7 × 10−8) and day 2 (p = 4.8 × 10−10) after TIMP-1 injection. (C) Global DTI 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.
Stability of the data, given by the time evolution across 10 days of the experiment (A-D) 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 (E-H).
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.
Experiments used in this study. The column NP indicates the load of the injected nanoparticles.
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.
The specific pairwise interaction Jij is unstable across different days of the experiment. Results shown for cohort M1.
(A) The preference for the compartments containing food, Δhi, the inferred pairwise interaction strength, Jij, and the partial sum of inferred interaction strength, Ji ≡ ∑ j≠i Jij, vary over the 10 days of the experiment. (B) We measure the consistency of the inferred parameters using the Pearson’s correlation coefficient. (C) Bar plot for the correlation coefficient of the inferred parameters across various days. The compartment preference and Ji are more consistent compared to the pair-specific pairwise interaction.
Box plot for how much is each mouse influenced by its peers, measured by the difference of the conditional log-likelihood, given by the pairwise model vs. the independent model.
top: The difference in conditional log-likelihood for each day. bottom: The difference of conditional log-likelihood for each mouse shows some mice are consistently more social than others.
The inferred socialbility is consistent across different cohorts of mice of the same strain.
Plotted as a function of days of the experiment is (A) the mean of the inferred interaction strength, ⟨Jij ⟩and (B) the variablilty of interaction, measured by the standard deviation of the inferred interaction σJ. Error bars are the standard deviation across random halves of the duration of the experiment.
The conditional log likelihood is different for each cohort of C57BL6/J male mice (N = 13 in cohort M2, and N = 10 in cohort M3), 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). This figure follows Figure 3, now for cohort M4 (N = 9).
In panel (B), no significant deviation from the baseline is detected for both the mean interaction and the variability of interaction in the data after BSA treatment.
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).
In panel (B), the asterisks indicate day 1 and day 2 after TIMP-1 injection, the variability of interaction, σJ is significantly increased compared to the baseline (p = 0.0014 for day 1, p = 0.0010 for day 2, see Materials and Methods for details of the significance test).
Mutual information between single mouse position and the rest of the network, given by the inferred pairwise model, for the male cohort M1 before and after TIMP-1 treatment.
(A), the control male cohort M2 before and after BSA treatment (B), the female cohort F1 before and after TIMP-1 treatment (C). In panel (D), day-averaged MI value shows that TIMP-1 treatment either does not change the mutual information for the male cohort M1, or increases for the female cohort F1 (two-sample t -tests: p = 0.012 for comparison between day-averaged MI values before and after TIMP-1 injection, and p = 8 × 10−5 comparing to the first 5-days after TIMP-1 injection).
Interaction analysis for 5-day aggregated data, for the male and female cohort injected with TIMP-1, and the male cohort injected with the BSA control.
(A) Inferred interaction Jij for cohort M1 for the first and the last 5 days of the experiment, before and after TIMP-1 treatment. Two-sample F-test was performed to test whether the distributions have the same variance. The interaction strength learned from mice location in the first five day after TIMP-1 treatment has a significantly different variance compared to both before treatment, and day 6 to day 10 after treatment. The increase of interaction variability is also observed in the female cohort, although only when comparing the first 5 days after treatment with the first 5 days before treatment, and is not observed for the male BSA cohort. (B) Pearson’s correlation coefficient between inferred interaction Jij from different days. Asterisks indicate statistical significance. Almost no correlation is detected between the inferred Jij. (C) Mutual information between single mouse position and the rest of the network given by the inferred pairwise model. Consistent with single-day results from Fig. S12, the mutual information does not change for the male cohorts M1 and M4, and increases for the female cohort F1 after TIMP-1 treatme.
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.
