(A) Mouse in an open field (1 meter diameter), and two-dimensional trajectory of 30 minutes duration. Position of the animal is here digitized at 25 frames per second. (B) Transformation of continuous variables, velocity and position, into binary symbols. A velocity threshold was set to differentiate inactivity (I - White) and activity (A - Black) periods. Sample of trajectories with two enlarged periods corresponding to an inactivity period and to a velocity decrease following a change in direction (marked by an arrow in the velocity graph) and not identified as an inactivity period. Furthermore, the arena was divided into two concentric zones, P (periphery, shaded) and C (center), the radius of the latter being equal to 0.65. (C) Symbolic sequence analysis: Combining symbols leads to the definition of four states PI | PA | CI | CA. The trajectory is then represented by a sequence of symbols (marked by steps) and associated residence times (τ).

(A) Flow diagram: (A1) Transition matrix between the four states can be used to build a flow diagram, where conditional probabilities of transition between states are indicated by number (percentage) and by the thickness of the connecting arrows. Transitions from PI to CA and CI to PA are almost never observed (p<1/1000) and then are not represented in the flow diagram. (A2) Conditional probability of transition from PA to CA depends on previous state. Comparison of P(X|YZ) and P(X|Y) for X = PA, Y = CA (red points) and Z = PA (left) or CI (right) indicates no significant difference (NS). For X = CA, Y = PA (black points) and Z = PA (left) or PI (right) a significant difference appear. (A3) First-order Markov description of the sequence with a distinction between Pap and PAc (see text). (B) First-order Markov description of ß2−/− sequence. Red connecting arrows indicate probabilities of transition that are statistically modified when compared with WT. (C) Comparison of the distributions of time spent within PI, PAp and PAc states respectively (from left to right). Inset: Boxplot of the mean duration of the indicated state. Number of stars indicates statistical level of significance (- p>0.05, * p<0.05, ** p<0.01, *** p<0.001).

(A) Comparison between the number of PI, CI, PAP, CA and PAc states (from left to right) simulated using WT first-order transition matrix and residence time distributions (black circles) and after a transformation consisting in removing a fixed percentage of inactivity (red circles - see Method section and text for the principle of transformation). Note that distributions of experimental and simulated data fit perfectly (see Figure 4A for comparison). (B) First-order Markov description of transformed WT sequence of behaviors. The matrix is similar to those obtained in ß2 KO mice (see Figure 3B). (C) Comparison of the distributions of the time spent within PI, PAp and PAc states respectively (from left to right) for WT (Black, experimental data), simulation (Red) and ß2 (Blue, experimental data). Inset: Boxplot of the mean duration of the indicated state. Number of stars indicates the statistical level of significance (Wilcoxon test, - p>0.05, * p<0.05, ** p<0.01, *** p<0.001).

Sequences are described using 6 states CI, PAp, CA, Pac, defined as previously, and PInsc and PIsc that correspond to PI without or with scanning. Context tree is drawn in landscape mode with the root (X) placed on the left and past dependencies on the right. Probability distribution over the next symbols appears after each context in red (percentages). For example for WT, (0,0,80,0,16,4) indicates that P(X|CI) = 0; 0; 80; 0; 16 and 4% for X = CI , PAp, CA, PAr, Pinsc and PIsc respectively. Each horizontal line indicates a step in the past. {} indicates a choice between different symbols (A) Fitted context tree (Left) for concatenated sequence of n = 14 WT animals. and schematic representation (Right) of the “choice point”, to enter or not in the center after a PI (B) Fitted context tree (Left) for concatenated sequence of n = 11 ß2−/− animals and schematic representation of chaining (Right).

(A) Boxplot of the total traveled distance and (B) time spent in inactive state during a 30 min session in the open-field respectively for wild-type (WT, n = 32) and mutant mice (ß2−/−, n = 33). (C) Relation between the times spent in a given state (PA and CA in red, PI and CI in black) and the distance traveled during this time. Best linear fits were indicated for active and inactive states with the respective slope (µ). Number of stars indicates the statistical level of significance (- p>0.05, * p<0.05, ** p<0.01, *** p<0.001).

(A) Comparison between the total time spent in PI, CI, PAp, CA and PAc states (from left to right) during a 30 min session in the open-field, for WT (black circle) and ß2−/− (red circle) and with the simulation obtained from WT first-order transition matrix and residence time distributions (black triangles) and with the simulation obtained from ß2−/− first-order transition matrix and residence time distributions (red triangles). Note that distributions of experimental and simulated data fit perfectly meaning that the simulations reproduce the dynamics as regards the average time spent in each state. (B) Simulated time spent in PI (left) and PAc (right) obtained by combining transition matrices and distributions of state durations (see text). WT/WT, ß2/WT, WT/ß2 and ß2/ß2 indicate that sequences are simulated using WT or ß2−/− matrices of transition (before /) and WT or ß2−/− state duration distributions (after /). (e.g. WT/ß2 indicates simulation with WT matrix of transition and ß2−/− residence time distribution). “Matrix” and “Time” indicate that the discrepancy originates from the effect of changing the transition matrix and the residence time distribution, respectively.

(A) Ethogram quantifying activity of the mice during the inactivity state. Comparison of the percentage of rearing, scanning, grooming, wall rearing and sniffing in PI behaviors (see Methods) during a 30 min session in the open-field, in WT (empty circles) and in ß2−/− mice (filled black circles). Number of stars indicates the statistical level of significance (- p>0.05, * p<0.05, ** p<0.01, *** p<0.001). (B) Modification of the probability of the next state depending on activity during a PI. (Left) Modification of P(PA|CA) (indicated by first left point and dashed lines) knowing preceding state i.e Undifferentiated PI, Rearing, Scanning, Grooming, Wall rearing, Sniffing (from left to right), for WT (n = 14, above, white circle) and ß2−/− mice (n = 11, black circle, below). Note that probability of CA is only modified when the mouse performs a scanning (***, p<0.001). (Right) Same presentation for P(CI|CA). Note that this probability is not modified by previous states P(CI|CA) = P(CI|PA-CA) = P(CI|PI-PA-CA), nor by activity performed during a PI (Rearing, Scanning, Grooming, Wall rearing, Sniffing, (from left to right)).

Schematic representation of the modulation of the probability to engage a movement in the center of the arena after a stop at the periphery for WT mice (black) and ß2−/− mice (red). Baseline probability (filled circles and dashed lines) is increased (upward arrow) or decreased (downward arrow) by scanning or recent center excursion respectively. Range between the two baselines (dashed horizontal line) marked baseline difference between WT and ß2−/−. Fear and stress (downward left array) are supposed to decrease center excursion while exploration increases (up-ward left array) it.