Léa Briard

Jean-Louis Deneubourg

Odile Petit

Group behaviours and individual spatial sorting before departure predict the dynamic of collective movements in horses

INTRODUCTION

Animals that live in groups face the daily challenge to decide where and when the group should move. By moving together, they maintain group cohesiveness which brings them several advantages: protection from predators, information about feeding sites, resources defence [START_REF] Alexander | The Evolution of Social Behavior[END_REF]Danchin et al. 2008). Therefore, group members need to seek a consensus by making a decision collectively. Consensus decision can be either shared or unshared [START_REF] Conradt | Consensus decision making in animals[END_REF]. In shared consensus decision, all group members contribute to the decision outcome, either equally (regardless of individual characteristics) or partially (some individuals have a greater influence, [START_REF] Pyritz | Reaching a Consensus: Terminology and Concepts Used in Coordination and Decision-Making Research[END_REF]. In unshared consensus, one particular individual decides systematically where and when the group should go. It is, however, more interesting to consider a spectrum from shared consensus to unshared consensus rather than a binary distinction.

In the study of mechanisms underlying such collective decisions, a frequent approach is to identify the type of consensus by seeking for individuals that could play a key role during decision-making processes [START_REF] Petit | Collective decision-making in white-faced capuchin monkeys[END_REF]. Specific individuals, either old, high-ranking or of a specific sex, have been reported to occupy the position of leaders in various species [START_REF] King | Dominance and Affiliation Mediate Despotism in a Social Primate[END_REF][START_REF] Schaller | The mountain gorilla: Ecology and behavior[END_REF]. However, there are as many studies, if not more, that found that leadership is rather distributed among group members [START_REF] King | The Origins and Evolution of Leadership[END_REF][START_REF] Petit | Decision-making processes: the case of collective movements[END_REF]. Moreover, what one calls a leader is usually the individual that took the vanguard position during collective movements although there is no evidence that this individual decided for others [START_REF] Bourjade | Is Leadership a Reliable Concept in Animals? An Empirical Study in the Horse[END_REF]. For instance, in one of the most cited examples of despotic leadership (i.e. unshared consensus decision), the dominant male in mountain gorillas (Gorilla gorilla berengei [START_REF] Schaller | The mountain gorilla: Ecology and behavior[END_REF], the departure of the silverback has been reported to be preceded by grunts emitted by other group members suggesting a rather shared decisional process [START_REF] Stewart | Gorillas vocalizations during rest periods: signals of impending departure[END_REF]. However, this requires looking beyond the time of departure as decision-making processes may occur beforehand and the influence of all group members measured.

Indeed, studies on collective movements rarely took into account the events preceding hamadryas, [START_REF] Kummer | Social organization of hamadryas baboons: a field study (1st Editio)[END_REF]). In domestic geese, sheep, cattle and bison, the number of participants increased with the number of individuals heading in the direction of the movement [START_REF] Ramseyer | Patterns of group movements in juvenile domestic geese[END_REF]Ramseyer, Boissy, Dumont, & Thierry, 2009;Ramseyer, Thierry, Boissy, & Dumont, 2009;[START_REF] Ramos | Collective decision making during group movements in European bison, Bison bonasus[END_REF]. In some species, this number increased with the number of vocalizers (meerkat, Suricata suricatta: (Kummer, 1968a;[START_REF] Seltmann | The Organization of Collective Group Movements in Wild Barbary Macaques (Macaca sylvanus): Social Structure Drives Processes of Group Coordination in Macaques[END_REF][START_REF] Strandburg-Peshkin | Shared decision-making drives collective movement in wild baboons[END_REF][START_REF] Sueur | Sequence of quorums during collective decision making in macaques[END_REF].

Such predeparture behaviours have been viewed as a preparation for collective movements (Ramseyer, Boissy, Dumont, et al., 2009). However, to be valid, this assumption must be tested by at least verifying that the observed behaviours are specific to the context of collective movements. One solution, for instance, is to compare predeparture behavioural patterns with behavioural patterns exhibited during control periods that did not precede a collective movement. Such method is commonly used in studies on the function of postconflict behaviours that compare matched-control periods with post-conflict periods to deem the observed behavioural pattern, a reconciliation process (e.g. white-face capuchins: [START_REF] Leca | Aggression and reconciliation in Cebus capucinus[END_REF]domestic horses: Cozzi, Sighieri, Gazzano, Nicol, & Baragli, 2010).

However, so far, such an approach has never been used in the context of collective movements and predeparture behaviours. In this study, we applied it to this context using domestic horses, Equus ferus caballus, as a model.

Horses are highly-social species that form long-lasting bonds (Waring, 2003).

Distributed leadership has been reported with an influence of individual characteristics (age:

Tyler, 1972; dominance rank: [START_REF] Krueger | Movement initiation in groups of feral horses[END_REF]personality: Briard, Dorn, & Petit, 2015). However, in both Przewalski (Equus f. przewalskii, [START_REF] Bourjade | Is Leadership a Reliable Concept in Animals? An Empirical Study in the Horse[END_REF] and domestic horses [START_REF] Briard | Personality and Affinities Play a Key Role in the Organisation of Collective Movements in a Group of Domestic Horses[END_REF][START_REF] Briard | How stallions influence the dynamic of collective movements in two groups of domestic horses, from departure to arrival[END_REF], the characteristics of the initiator did not explain variation in recruitment success (e.g. number of followers or joining speed). Moreover, predeparture behaviours such as moving away from the group or maintaining a peripheral position occur in Przewalski horses [START_REF] Bourjade | Decision-Making in Przewalski Horses (Equus ferus przewalskii) is Driven by the Ecological Contexts of Collective Movements[END_REF][START_REF] Bourjade | Is Leadership a Reliable Concept in Animals? An Empirical Study in the Horse[END_REF] and may indicate negotiation processes due to higher conflict of interests as they correlate with longer recruitment phase [START_REF] Bourjade | Decision-Making in Przewalski Horses (Equus ferus przewalskii) is Driven by the Ecological Contexts of Collective Movements[END_REF]. In such a context, exploring the predeparture period appears necessary to understand the collective decision-making of horses. This study aimed to investigate whether: (1) predeparture behaviours can be observed in domestic horses and if so, whether the observed behavioural patterns (2) are specific to the context of collective movements by comparing them to control periods and (3) can explain the dynamic of ensuing collective movements. Based on previous studies in Przewalski horses [START_REF] Bourjade | Is Leadership a Reliable Concept in Animals? An Empirical Study in the Horse[END_REF] and other ungulates (e.g. Ramseyer, Boissy, Dumont, & Thierry, 2009;Ramseyer, Thierry, Boissy, & Dumont, 2009), we expect to see, as departure gets closer, an increase in the arousal of the group. This could manifest itself through an increase in activity, a decrease in group dispersion or the alignment of group members towards the direction of the future collective movement. If such behavioural patterns exist and are specific to predeparture periods, we do not expect to observe them in control periods. However, if we do not find any differences between predeparture and control periods, then predeparture behaviours cannot be deemed as preparatory (i.e. an anticipation of a future collective movement).

MATERIAL AND METHODS

Animals and Environment

The focal groups were bred at La Ferme de Bonjacques, a horse husbandry located in eastern France (48 06 00.0 N, 6 06 01.0 E, 305 ). B h g e e c ed f 9 mares of various breeds aged from 9 to 28 years old for group 1 and 3 to 22 years old for group 2 (see SI Appendix A for more details). All horses were individually recognisable by their morphology, coat colours and white markings. Both groups were kept on hilly pastures (group 1: 8 ha, group 2: 11 ha) composed of large grassland areas with vegetation forming natural, shaded shelters. Due to the relief and the vegetation, individuals were never able to see the entire pasture from any given point. A river, allowing individuals to have free access to water crossed both pastures increasing the number of distinct zones. Both groups had access to a salt lick stone and group 1 had access to a hayrack (2x2m) but spent less than 10% of the total observation period eating from it. Both groups had been accustomed to human presence during a preliminary observation month.

Observation Procedure

Groups were observed and filmed for about two months for a total of 184 hrs for group 1 and 112 hrs for group 2. Two observers approached horses on foot up to a maximal distance of about 20m and used handheld two-way radios to communicate when separated. Each of them had a camera to ensure that the entire group was continuously filmed. Over the observation period, one of the observers also recorded every 5 min by instantaneous scan sampling [START_REF] Altmann | Observational Study of Behavior: Sampling Methods[END_REF] the position of every individual using a pair of telemetric binoculars (precision: 1m) and a compass (precision: 1°). The observer stayed still throughout the scan and attributed for each horse a distance in meter (horse-observer distance) and an angle in degree by pointing the compass towards each horse and placing the orienting arrow on the magnetic needle to read the value. During those scans, the observer also recorded the activity (inactive: at rest -standing with a flexed foot or recumbent-or active: all other activities) and the orientation of each individual according to four noticeable and fixed points in the environment at 90° or 180° of one another.

Data Scoring

Two persons watched the videos and recorded the identity and the behaviour of every individual initiating or joining a collective movement. Before they could score different videos, we ensured inter-observer concordance by asking them to score the same videos and comparing their results until they reached 95% concordance [START_REF] Caro | Inter-observer reliability[END_REF].

Initiation and joining latencies

Departure was defined by the movement of an initiator, that is, any individual that first travels at least 20 m in less than 20 s outside the group without pausing and with its neck kept above the horizontal position [START_REF] Bourjade | Decision-Making in Przewalski Horses (Equus ferus przewalskii) is Driven by the Ecological Contexts of Collective Movements[END_REF][START_REF] Briard | Personality and Affinities Play a Key Role in the Organisation of Collective Movements in a Group of Domestic Horses[END_REF]. Then, any horse moving away from the group with its neck kept above the horizontal position and in the same direction as the initiator was identified as a follower. For each follower, we defined a joining latency by calculating the time between an initiation and the moment an individual joined it (i.e. first step taken in the same direction as the initiator). Using these latencies, we determined the joining rank of individuals for each collective movement (i.e. from 1, the initiator, to 9, the last follower). A collective movement begins with a start attempt and ends with the arrival of the last follower [START_REF] Petit | Decision-making processes: the case of collective movements[END_REF][START_REF] Briard | Personality and Affinities Play a Key Role in the Organisation of Collective Movements in a Group of Domestic Horses[END_REF]. We defined the goal area as sites in which all animals stopped walking and started a new activity such as foraging or resting. We defined a predeparture period as those corresponding to the period between the end of the preceding collective movement and the initiation of the focal movement. However, we decided to stop only up to 60 minutes before departure because the sample size for more distant scans was too small (less than 5 events per group). We recorded for group 1 and 2, 56 and 73 initiations respectively, 43 and 50 of them involving the entire group and with all individuals always visible from 60 minutes before initiation to the end of the collective movement. So, the analysis focused on these 43 and 50 events.

Group behaviour before departure

During these 60 minutes preceding initiation, we measured five different group behaviours using scans performed every 5 minutes: number of inactive individuals, number of goal-oriented individuals, distance to goal area, dispersion, and density at the front of the group (see Table 1 for definitions). Since initiation is relatively unpredictable, we never had a scan of the group performed at the exact moment the initiator started to move. Therefore, the scans at 0 min (i.e. first step of the initiator) were completed using video recordings. Then,

preceding

Statistical analysis

The effect of time on the five different group behaviours was investigated using Linear Mixed-Effects Models for dispersion (after a log-transformation due to a right-skewed distribution) and distance to goal area (LMM, R package nlme v. 2002). Given the relationship between the distance to goal area and time, we used a quadratic fit (y ~x + I(x 2 )). Finally, we used as a random factor the identity of each collective movement nested within the group identity and added a correlation structure (corAR1) to take into account the sequential dependence of observations.

To assess if group behaviour could predict the imminence of a collective movement, we compared the predeparture periods with control periods. These control periods were taken off scans performed at least 60 minutes away from any collective movements. We only there is no initiation to be used as a referential, we randomly assigned a fifth of the scans to the time category 0 min. Then, based on their timing, preceding scans were assigned to one of the four remaining time categories, i.e. [15-10[, [30-25[, [45-40[ or [60-55[ min before category 0 min. Isolated scans, that could not be connected to a time category 0 min, were discarded. For orientation, because we did not have any referential direction for the control periods, we used the direction adopted by the majority in each time category 0 min to then look at the number of individuals that had adopted this direction over the previous time categories (i.e. from 10 min to 60 min before). Finally, since front density and group distance to the goal area were measures that rely on the existence of a goal area, they were not compared to control periods. We compared the effect of time on these three behaviours during control periods using similar models than for the predeparture period (see above for details).

As independent variables, we used time (from 0 to 60 min before departure) with an interaction with a binary variable called period type (0 = predeparture; 1 = control).

To assess the influence of predeparture behaviours on the dynamic of the collective movements (i.e. the speed and joining order), we conducted two types of analyses. For the duration of the joining phase, we used a linear mixed-effect model (LMM) with the five group behaviours as independent factors (i.e. dispersion, density, activity, orientation and distance to the goal area; Table 1) and the log-transformed latency of the last follower as the dependent variable (continuous data with a right-skewed distribution). Dispersion and density at the front were log-transformed to linearize their relationship with the dependent variable and faci i a e he i e e a i f he de c efficie . We tested this model at 3 different moments: at initiation, 25-30 min and 55-60 min before departure. We used the multimodel inference method (R package MuMIn v.1.43.6; Barton 2019) to determine which candidate model best explained the dynamic of the joining phase. Models were first compared according hei A ai e i f a i c i e ion (AIC) corrected for small sample size (AICc) and then ranked by their weights (AICw; [START_REF] Burnham | Model selection and multimodel inference: a pratical information-theoretic approach[END_REF]. When the AICc of the candidate models differed by less than 2 units, we accepted the one with the lowest AICc as the best-fit model. We also calculated the evidence ratio between the presented models with the lowest AICc score and that of interest following the formula described in [START_REF] Burnham | Model selection and multimodel inference: a pratical information-theoretic approach[END_REF]. For the joining order, we used a linear model approach to study the temporal link between topological ranks before departure (i.e. topological distance to goal area) and joining ranks during collective movements (R package lme4 v.1.1-21; [START_REF] Bates | Fitting linear mixed-effects models using lme4[END_REF]. We particularly looked at the evolution of the slope.

Before conducting analysis, all variables when included in the same model were screened for excessive correlations (r > 0.7) and collinearity (VIF > 10, [START_REF] Dormann | Collinearity: A review of methods to deal with it and a simulation study evaluating their performance[END_REF].

All statistical analyses were performed in R version 3.6.1 (R Core Team 2019). The significance threshold was set at α=0.05.

Ethical Statement

Our observations were carried out in full accordance with the ethical guidelines of our research institution and comply with the European legislation for animal welfare. This study has been conducted with the approval of our local ethical committee (reference:

AL/19/17/02/13).

RESULTS

Evolution of predeparture behavioural patterns over time

To assess variations during the 60 min period preceding departure, we compared various behaviours that were recorded every 5 minutes. We found that all analysed variables displayed significant changes over time (Figure 1). The number of goal-oriented individuals and the density at the front increased over time during the predeparture period (GLMM, orientation: SE = 0.019 0.002, t584 = 8.690, P < 0.001; GLMM, density: SE = 0.008 0.002, t584 = 5.351 P = 0.02; Figure 1) while dispersion and the number of inactive individuals decreased (LMM, dispersion: SE = -0.093 0.035, t584 = -2.62, P = 0.01; GLMM, group activity: SE = -0.019 0.003, t584= -5.638, P < 0.001, Figure 1). Group distance to goal area exhibited a quadratic relationship with time. Groups moved away from the future destination before getting closer (LMM, distance to goal area, (time) SE = -0.342 0.102, t584 = -3.364, P < 0.001, (time 2 ) SE = -0.004 0.002, t584 = -2.595 P = 0.01). This means that before departure and as the initiation is getting closer, individuals become more active, oriented towards the future goal, reduce interindividual distances, notably at the front of the group, and starts to move towards the goal.

Comparison with control periods

To assess if the above variables could indicate the imminence of a collective movement, we compared predeparture periods with control periods. We found that similarly to predeparture periods, the number of individuals oriented in the same direction increased over time during the control period (ANOVA, time x period type: Chisq = 2.577, P = 0.11) and within the same range (ANOVA, period type: Chisq = 0.0385, P= 0.844). Contrary to orientation, during control periods, time did not have the same effect on the number of individuals of inactive individuals (ANOVA: Chisq = 22.005, P < 0.001), which stayed constant (GLMM, time x period type: SE = 0.024 0.005, P < 0.001; Figure 2). In addition, control periods were characterized, on average, by more inactive individuals than during predeparture periods (GLMM, period type: SE = 0.77 0.24, t537 = 4.678, P < 0.001; Figure 2). The temporal pattern of group dispersion during control periods did not significantly differ from predeparture period (ANOVA, time x period type: Chisq = 0.0012, P = 0.97). However, dispersion in control periods was, on average, three-times higher than in predeparture periods suggesting a much lower group cohesion outside the context of collective movements (LMM, period type: SE = 55.60 4.18, P < 0.001; Figure 2).

Finally, we also observed that during the predeparture period, the number of inactive

Predeparture behaviours predict the duration of the joining phase

At initiation, multimodel inference showed that the best model to explain the duration of the joining phase (i.e. latency of the last follower) included dispersion alone (conditional average LMM: SE = 0.740 ± 0.141, z = 5.172, p < 0.001, RVI = 1; Table S2). The more dispersed the individuals were, the longer it took for group members to follow (Figure 3a). At 25-30 min, the best model for the latency of the last follower included the density at the front alone (conditional average LMM: SE = -0.633 ± 0.303, z = 2.090, p = 0.037; relative variable importance, RVI=0.61; Figure 3b, Table S2), meaning that the more individuals gathered at the front during the predeparture period, the faster the joining phase was (Figure 3b). However, the two next models could not be excluded from the top-ranked models ( AICc < 2) a d he ef e di e ion was also a good predictor of the duration of the joining phase (conditional average LMM: SE = 0.596 ± 0.289, z = 2.066, P = 0.039; RVI = 0.60;

Figure 3c, Table S2). At 55-60 min, the best model included the dispersion alone (conditional average LMM: SE = 1.098 ± 0.316, z = 3.473, P < 0.001, RVI=0.98; Table S2) meaning that the more gathered the individuals were 60 minutes before departure, the faster the joining phase was (Figure 3d). The three other variables, i.e. activity, orientation and distance to the goal area, were never included in the top-ranked models (activity RVI < 0.14, orientation RVI < 0.06, distance to the goal area RVI < 0.01).

Spatial organization before departure predicts joining order

We explored the evolution over time of spatial positions before departure as a function of the joining rank during collective movements. As shown by figure 4, there is a relationship between individual distances to the goal area at departure (LM [initiation] SE = 0.46 0.03 , R 2 = 0.21, P < 0.0001) and up to 30-40 minutes before departure (LM [30-35 min], SE = 0.11 0.049, R 2 = 0.01, P = 0.027). The slope starts to increase around 30-35 minutes before departure as well as the match between the linear regression and the mean value, suggesting that the correlation between the spatial position and the future joining rank is increasing over time (see Table S3 in supplemental material). This result also indicates that individual spatial position before departure is likely to predict how quickly a horse will join the ensuing collective movement.

DISCUSSION

We found evidence that the dynamic of collective movements, from direction to joining duration and order could be predicted by group behaviours exhibited before departure.

Our findings support the idea that decision-making begins well before departure. This therefore means that the first departed individual is likely to be the mere catalyser of an already-begun collective phenomenon and highlights the absolute necessity to look beyond the timing of initiation to understand collective decision-making processes in animal societies.

The specificity of pre-departure behavioural patterns

During the hour prior departure, group behaviours changed over time. The number of inactive individuals progressively decreased, traducing a progressive arousal of the group

(see Ward & Zahavi 1973 f a defi i i f he d f he ).
Si a e hi i c ea e, he number of individuals gathered at the front and oriented towards the future collective movement increased over time. We also observed, a reduction of dispersion and distance to the future goal area before departure. The slight increase in group distance to the goal area before its decrease is likely to be due to the configuration of the environment the studied group lived in (i.e. limited space and destinations). Such gathering at the group periphery and synchronisation of behaviours before departure have been reported in many species [START_REF] Boinski | On the move : how and why animals travel in groups[END_REF]Kummer, 1968a;Ramseyer, Boissy, Dumont, et al., 2009;Ramseyer, Thierry, Boissy, et al., 2009;[START_REF] Strandburg-Peshkin | Shared decision-making drives collective movement in wild baboons[END_REF] and were suggested as a preparation to collective movements. However, to be valid, this assumption needed to be tested by at least verifying that these modifications are not found outside the context of collective movements. Thanks to the comparison with control periods and more definitively than previous studies, we can conclude on the specificity of predeparture periods. On one hand, we found that the temporal increase in activity and cohesion was specific to predeparture periods. During control periods, the activity level stayed relatively constant and group cohesion was much lower. Finally, we found that only during predeparture periods did the number of goal-oriented individuals correlate with the number of inactive individuals and the group dispersion. Therefore, the specificity of predeparture periods lies in the cooccurrence of multiple patterns: a progressive decrease in the number of inactive individuals associated with a low dispersion and a high degree of synchronization in terms of orientation.

Nevertheless, the differences between the indices characterizing the states of the group (number of inactive individuals or dispersion) during the control and pre-departure phase raise the question of the temporal evolution of these indices. For example, concerning the dispersion, two extreme hypotheses can be formulated: a monotonic or a sudden decrease when the group passes from the state observed during the control period to the pre-departure

period. An abrupt decrease would suggest that the adoption of a pre-departure configuration is itself a social phenomenon (e.g. governed by mimetism; Sumpter, 2010). This dynamic towards the pre-departure also raises the question of links between the pre-departure state and the probability of initiating a movement and its success : are these probabilities governed by the same cause as that governing the adoption of the predeparture configuration or do they depend on the state/configuration of the group? New observations are needed to decipher between these different hypotheses.

On the other hand, we found that the temporal pattern of group orientation in pre-departure period is not different from the observed patterns during control periods. Such pattern indicates that individuals maintain their orientation over multiple time steps (i.e inertia). As a consequence, the probability that orientations are identical decreases with time (i.e. as we move away from the initiation period). Moreover, social species are known to respond to the behaviours of group members, such as body posture and orientation, by adopting the same behaviours themselves, a process known as social facilitation or allelomimetism [START_REF] Clayton | Socially Facilitated Behavior[END_REF][START_REF] Conradt | Activity synchrony and social cohesion: A fission-fusion model[END_REF][START_REF] Deneubourg | Collective patterns and decision-making[END_REF]. In herbivores, such synchronization has often been observed outside the context of collective movements [START_REF] Benham | Synchronisation of behaviour in grazing cattle[END_REF][START_REF] Côté | Time budgets and synchrony of activities in muskoxen: The influence of sex, age, and season[END_REF][START_REF] Gautrais | Allelomimetic synchronization in Merino sheep[END_REF][START_REF] Rands | Red deer synchronise their activity with close neighbours[END_REF][START_REF] Stoye | Synchronized lying in cattle in relation to time of day[END_REF].

Therefore, during predeparture periods the increasing number of individuals oriented in the same direction predicts the direction of a potential collective movement but not an impending group departure. The absence of difference between the predeparture and the control periods, both in terms of dynamics and magnitude, puts into perspective the interpretation of the progressive orientation of group members before departure. Such phenomenon is often viewed as a preparation if not a negotiation or a voting process [START_REF] Kummer | Social Organization of Hamadryas Baboons[END_REF][START_REF] Ramos | Collective decision making during group movements in European bison, Bison bonasus[END_REF]Ramseyer, Boissy, Dumont, et al., 2009;[START_REF] Ramseyer | Patterns of group movements in juvenile domestic geese[END_REF]Ramseyer, Thierry, et al., 2009;[START_REF] Strandburg-Peshkin | Shared decision-making drives collective movement in wild baboons[END_REF][START_REF] Sueur | Sequence of quorums during collective decision making in macaques[END_REF] and the resulting dynamics as the consequence of the degree of consensus before departure. However, in the absence of control, the causal relationship between the degree of common orientation before departure and recruitment during collective movements should be interpreted cautiously. Here our results suggest that the choice of destination could result from the global dynamics rather than an a priori choice.

Predeparture behaviours and joining dynamic

Interestingly, the behaviours that were specific to the predeparture periods and could predict the imminence of a departure were not the ones that predicted the joining dynamic.

Indeed, the cohesion of the group, i.e. dispersion and density at the front, was the only factor that had a significant impact on the duration of the joining process. Our results confirmed those of previous studies on dispersion and recruitment in primates [START_REF] Leca | Distributed leadership in semifreeranging white-faced capuchin monkeys[END_REF][START_REF] Sperber | Should i stay or should i go? Individual movement decisions during group departures in red-fronted lemurs[END_REF][START_REF] Sueur | Shared or unshared consensus decision in macaques?[END_REF] and birds [START_REF] Ramseyer | Patterns of group movements in juvenile domestic geese[END_REF] but partially matched those in heifers and ewes (Ramseyer, Boissy, Dumont, et al., 2009;Ramseyer, Thierry, Boissy, et al., 2009). In these latter studies, the authors found an effect of dispersion but also of orientation and activity at different times. The methodological differences make the comparison quite difficult since they analysed only collective movements that occurred when the individuals were aggregated within a certain perimeter before departure.

We also showed that before departure individuals that were closer to the front and therefore to the future goal area joined the collective movement earlier. On one hand, the spatial position of individuals may affect their capacity to initiate as demonstrated by [START_REF] Dyer | Leadership, consensus decision making and collective behaviour in humans[END_REF] in groups of humans. They showed that peripheral individuals were more likely to move freely away from the group than central individuals. On the other hand, the progressive movement of an individual towards the front of the group may act both as a conspicuous cue of motivation and help to recruit group members. Similar results have been reported in Przewalski horses [START_REF] Bourjade | Decision-Making in Przewalski Horses (Equus ferus przewalskii) is Driven by the Ecological Contexts of Collective Movements[END_REF] and other animal societies [START_REF] Boinski | On the move : how and why animals travel in groups[END_REF]Kummer, 1968a;Ramseyer, Boissy, Dumont, et al., 2009;Ramseyer, Thierry, et al., 2009;[START_REF] Strandburg-Peshkin | Shared decision-making drives collective movement in wild baboons[END_REF][START_REF] Sueur | Sequence of quorums during collective decision making in macaques[END_REF]. It has been suggested that front-to-back positioning within animal groups can be the consequences of behavioural or motivational differences between group members [START_REF] Couzin | Collective memory and spatial sorting in animal groups[END_REF].

Individual differences in activity level (Homing pigeons, Columbia livia, [START_REF] Pettit | Speed determines leadership and leadership determines learning during pigeon flocking[END_REF], age (red-fronted lemurs, Eulemur rufifrons, [START_REF] Sperber | Should i stay or should i go? Individual movement decisions during group departures in red-fronted lemurs[END_REF], satiation (roach, Rutilus rutilus, [START_REF] Krause | Oecologia shoal of roach (Rutilus rutilus) and chub (Leuciscus cephalus): a field study[END_REF], dominance [START_REF] Hemelrijk | Spatial centrality of dominants without positional preference[END_REF] or in social attraction (domestic horses, Equus f. caballus [START_REF] Briard | Personality and Affinities Play a Key Role in the Organisation of Collective Movements in a Group of Domestic Horses[END_REF] have shown to explain patterns of positioning within the group. In addition to motivational differences, social preferences and/or shared phenotypes (e.g. phenotypic assortativity, Krause, James, Franks, & Croft, 2014) could underlie such spatial positioning and differences in reac i i a i di id a departure. Indeed, it has been shown in numerous social species that social preferences and phenotypic similarities effect on how individuals are spatially organized [START_REF] Briard | Personality and Affinities Play a Key Role in the Organisation of Collective Movements in a Group of Domestic Horses[END_REF][START_REF] Godde | Correcting for the impact of gregariousness in social network analyses[END_REF] and how they influence one another (i.e. selective mimetism, [START_REF] Sueur | Selective mimetism at departure in[END_REF].

The effect of both group cohesion and spatial positioning before departure on the joining dynamic suggests that even in case of high synchronisation in terms of activity or orientation, interindividual distances greatly affect recruitment. As a consequence of spatial sorting and group cohesion, individuals differ in their neighbourhood size (i.e. how many conspecifics an individual interacts with, [START_REF] Farine | Individual variation in local interaction rules can explain emergent patterns of spatial organization in wild baboons[END_REF], which could affect their propensity to react to the initiator departure. In our study, since the initiator is among the closest to the front, it also means that individuals far from the goal area are far from the initiator. Therefore, it is possible that in domestic horses, as in a flock of birds under attack by a peregrine falcon [START_REF] Ballerini | Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study[END_REF], the propagation of information (i.e. departure of the initiator) and the reaction of individuals depended on distances. Such nearest neighbour effect was also found to underlie spatial organisation during collective movement in wild primates [START_REF] Farine | Both nearest neighbours and long-term affiliates predict individual locations during collective movement in wild baboons[END_REF][START_REF] Sperber | Should i stay or should i go? Individual movement decisions during group departures in red-fronted lemurs[END_REF] and activity synchronisation in red deer [START_REF] Rands | Red deer synchronise their activity with close neighbours[END_REF]. Interestingly, until now, such effect was only identified in dense and large groups of animals where one individual is unlikely to see all its conspecifics.

Many questions remain to be addressed concerning the exact rules that underpin decision-making processes during collective movements in domestic horses. First of all, we could not study the effect of predeparture behaviours on the number of followers as the majority of recorded events involved the entire group. However, in numerous species including horses [START_REF] Bourjade | Decision-Making in Przewalski Horses (Equus ferus przewalskii) is Driven by the Ecological Contexts of Collective Movements[END_REF][START_REF] Krueger | Movement initiation in groups of feral horses[END_REF][START_REF] Petit | Collective decision-making in white-faced capuchin monkeys[END_REF][START_REF] Sueur | Shared or unshared consensus decision in macaques?[END_REF], individuals can fail to recruit any group member and often have to renounce to depart from the group. Using such unsuccessful departures as well as control periods that only differ from predeparture periods by one parameter (e.g. dispersion) would provide useful insights on why an initiation succeeds or fails and help understand decision-making processes. Moreover, although it is clear that interindividual distances are at stake, even in this small-scale system, our study did not allow us to disentangle between motivational differences and local information transmission. Indeed, we did not record enough events during which the initiator was not the closest to the goal. Experiments with trained individuals that would depart from the group following a cue [START_REF] Gérard | How does the expressiveness of leaders affect followership in domestic horses (Equus ferus caballus)?[END_REF][START_REF] Pillot | Moving together: Incidental leaders and naïve followers[END_REF] would allow recording a sufficient number of events where the initiator holds various spatial position. It could then be determined which differences in motivation or local information transmission are decisive. Finally, we had to rely on discrete data to study the dynamic of predeparture behaviours. With the rise of technology (e.g. GPS collars, drones, automatic tracking software), continuous data could be collected allowing more advanced statistical analysis, which could help uncover new behavioural patterns.

Conclusion

We demonstrate that decision-making during collective movements is a continuous process that starts before departure in domestic horses. The use of control periods, a first in the context of collective movements and predeparture behaviours, highlights the specificity of periods preceding collective movements and how animals communicate their willingness to move to other group members. Moreover, we showed that a behaviour often presented as preparatory, i.e. interindividual alignment, was not specific to predeparture and occurred just as often in other contexts. Finally, our work suggests that similarly to dense and large groups, interindividual distances are a key aspect of decision-making processes in small and loose groups. Taken together our results clearly emphasise the necessity to look beyond the event of A e di able Table S2 -Model selections with Akaike's information criterion corrected for small sample size (AICc) for the models used to examine the influence of predeparture behaviours on the duration of the joining phase (i.e. latency of the last follower). The degree of freedom (df), the weights (wi) and the evidence ratio (E/R) for each model are also indicated. The full model comprised dispersion, group activity, group orientation, front density and distance to the goal area as independent variables. The identity of the the initiator was used as a random factor. Models in bold represent the best-fit models for each dependent variable (∆AICc < 2).

Model terms df

  the dynamic of the impending collective movements in terms of number of participants or joining duration. For instance, group dispersion has been shown to influence the number of participants in mammals (white-faced capuchin, Cebus capucinus: Leca, Gunst, Thierry, & Petit, 2003; Tonkean macaque, Macaca tonkeana and rhesus macaque, Macaca mulatta: Sueur & Petit, 2008; sheep, Ovis aries and cattle, Bos taurus: Ramseyer, Boissy, Dumont, & Thierry, 2009; Ramseyer, Thierry, Boissy, & Dumont, 2009; European bison, Bison bonasus: Ramos, Petit, Longour, Pasquaretta, & Sueur, 2015) and birds (black-headed gulls, Larus ridibundus: de Schutter 1997; domestic goose, Anser anser: Ramseyer et al. 2008), fish (Damselfish, Dascyllus aruanus: Ward et al. 2013). Some individuals can also display behaviour that indicates their motivation to move, for instance by moving away from group members in the desired direction (Hamadryas baboon, Papio h.

  scans obtained from direct observation were categorized into half-open 5-min time intervals (e.g. ]0-5min], ]5-10min], etc.). From angle and distances values obtained by instantaneous scan sampling using the telemetric binoculars and the compass, we were able to calculate individual xy-coordinates: Xi = cos (αi) × di and Yi = sin (αi) × di with αi the angle in radian and di the distance in meters. Since the goal area could not be anticipated, we defined its angle and distance every 5 minutes based on the video recordings, the individual angle and distance of the focal scan and a cadastral plan of the pasture. The xy-coordinates of the group barycenter were equal to the mean of individual xy-coordinates, Xbc = ∑xi/N, and Ybc = ∑yi /N, with N = 9. The index of group dispersion was equal to the squared deviations from the barycenter divided by N, D = ∑√[ (Xi -Xbc) 2 + (Yi -Ybc) 2 ]/ N. Finally, with a similar formula Dia = √[(Xi -Ya) 2 + (Xi -Ya) 2 ] with Xa and Ya the xy-coordinates of the goal area, we calculated individual distances to the goal area and attributed a topological rank based on topological distances (i.e. rank 1 is attributed to the closest individual). The front of the group was determined using the closest individual to the goal area as a referential. The density at the front of the group was calculated using the number of individuals within a 10-meters radius around the referential.

  used 5 time categories (from 0 to 60 min before departure, with 15-min intervals) to ensure sufficient sample size per time category (N0 = 101, N15 = 103, N30 = 104, N45 = 92, N60 = 70). Since

  individuals was significantly correlated to the number of individuals oriented in the same direction (Pearson r = -0.15, P < 0.001, N = 678) and the dispersion (Pearson r = -0.13, P < 0.001, N = 678) contrary to the control periods (activity -orientation, Pearson r = -0.03, P = 0.59, N = 364; activity -dispersion, Pearson r = -0.09, P = 0.16, N = 470).

Figure 1 -

 1 Figure 1 -Patterns of (a) orientation, (b) density at the group front, (c) dispersion, (d) distance to goal

Figure 2 -Figure 3 -

 23 Figure 2 -Comparison of the evolution of group behaviour, (a) orientation, (b) activity and (c)

Figure 4 -

 4 Figure 4 -Temporal evolution of the relationship between spatial position before departure and

Table S3 -

 S3 Temporal evolution of the link between topological distances before departure and joining order during collective movement

	Time categories	Estimate (slope)	SE		R 2			p-value
	Initiation	0.459	0.031		0.21			< 0.0001
	0 -5 min	0.175	0.041		0.029			< 0.0001
	5 -10 min	0.259	0.038		0.066			< 0.0001
	10 -15 min	0.161	0.041		0.024			0.0001
	15 -20 min	0.146	0.044		0.019			0.0011
	20 -25 min 25 -30 min	0.163 0.158	0.045 0.045	AICc ∆AICc 0.025 0.023	wi	0.0003 E/R 0.0005
	At departure 30 -35 min	0.108	0.049		0.009			0.0269
	Full model 35 -40 min	0.085	8 0.051	309.7	29.51 0.005	0	0.0933
	Log (dispersion) 40 -45 min	-0.025	4 0.056	280.2	-0.003	0	0.785	0.6600	1
	Log (dispersion) + log (front density) 45 -50 min 0.049	5 0.056	284.0	3.77 -0.007	0.119	6.60 0.3806
	Null model (intercept only) 50 -55 min 55 -60 min	0.083 0.064	3 0.061 0.059	300.1	19.83 0.003 0.007	0	0.1724 0.2730
	30 min before departure
	Full model		8	190.0	19.05	0
	Log (front density)		4	170.9		0	0.341		1
	Log (dispersion)		4	171.2	0.30	0.294	1.16
	Log (front density) + Log (dispersion)	5	172.3	1.32	0.071	4.80
	Null model (intercept only)		3	178.0	7.01	0.010	34.1
	60 min before departure
	Full model		8	131.3	27.87	0
	Log (dispersion)		4	103.4		0	0.700		1
	Log (dispersion) + log (front density)	5	106.3	2.91	0.164	4.27
	Null model (intercept only)		3	112.3	8.88	0.008	87.5

ACKNOWLEDGEMENTS

We would like to thank Brigitte Laurent for giving us access to her horses. We are also grateful to our trainees Valentin Julien, Tristan Juette, Sarah Fernique and Amandine Ramos for their valuable help with data collection. Data were collected during L.B.'s doctorate at the Department of Ecophysiology, Physiology and Ethology UMR 7178, Strasbourg, France) and Unit of Social Ecology (Free University of Brussel, Belgium)

FUNDING

This work was financially supported by the French Ministry of Higher Education and Research, the Foundation des Treilles, David et Alice van Buuren, de Meurs-François and Groupement de Recherche en Ethologie 2822 (to LB).

collective movements of Macaca tonkeana : an experimental and theoretical approach.

Animal Behaviour, 78, 1087 1095. https://doi.org/10. 1016/j.anbehav.2009.07.029 Sumpter, D. J. (2010)). Collective Animal Behaviour. Princeton University Press. Tyler, S. J. (1972). The behaviour and social organization of the new forest ponies.

AUTHORS' CONTRIBUTIONS

LB collected field data, participated in the design of the study, carried out the statistical analysis and drafted the manuscript; OP and JLD supervised and coordinated the study, participated in the data analysis and helped draft the manuscript. All authors gave final approval for publication. 0 [30 25[ [45 40[ [60 55[ [15 10[ 0 [30 25[ [45 40[ [60 55[ [15 10[ 0 [30 25[ [45 40[ [60 [45 40[ [60 55[ [15 10[ 0 [30 25[ [45 40[ [60 55[ [15 10[ 0 [30 25[ [45 40[ [60 Supplementary material


Rossana Fanelli

Dénes Berta

Tamás Földes

Edina Rosta

R Andrew Atkinson

Hans-Jörg Hofmann

Kenneth Shankland

Alexander J A Cobb

Organocatalytic Access to a cis-Cyclopentyl-γ-amino Acid: An Intriguing Model of Selectivity and Formation of a Stable 10/12-Helix from the Corresponding γ/α-Peptide

In this study, we have developed a highly enantioselective organocatalytic route to the (1S,2R)-2-(aminomethyl)cyclopentane-1-carboxylic acid monomer precursor, which has a cis-configuration between the C-and N-termini around the cyclopentane core. Kinetic measurements show that the product distribution changes over time due to epimerization of the C1 center. Computations suggest the cis-selectivity is a result of selective C-C bond formation, whilst subsequent steps appear to influence the selectivity at higher temperature. The resulting γ-amino acid residue was incorporated into a novel γ/α-peptide which forms a well-ordered 10/12-helix with alternate H-bond directionality in spite of the smallest value of the ζ-angle yet observed for a helix of this type. This highly defined structure is a result of the narrow range of potential ζ-angles in our monomer. In contrast, the larger range of potential ζ-values observed for the corresponding trans-system can be fulfilled by several competing helical structures.

Introduction

Foldamers -non-natural oligomers capable of forming secondary structures [START_REF] Martinek | Peptidic foldamers: Ramping up diversity[END_REF][START_REF] Guichard | Synthetic foldamers[END_REF][START_REF] Hill | A field guide to foldamers[END_REF][START_REF] Gellman | Foldamers: A manifesto[END_REF][5][START_REF] Yashima | Helical polymers: Synthesis, structures, and functions[END_REF] -represent an intriguing class of macromolecules whose utilities range from molecular recognition [START_REF] Chandramouli | Iterative design of a helically folded aromatic oligoamide sequence for the selective encapsulation of fructose[END_REF][START_REF] Collie | Molecular Recognition within the Cavity of a Foldamer Helix Bundle: Encapsulation of Primary Alcohols in Aqueous Conditions[END_REF] and peptidomimetics [START_REF] Hill | A field guide to foldamers[END_REF][START_REF] Gellman | Foldamers: A manifesto[END_REF][START_REF] Cheng | β-peptides: From structure to function[END_REF][START_REF] Goodman | Foldamers as versatile frameworks for the design and evolution of function[END_REF][START_REF] Gopalakrishnan | Therapeutic potential of foldamers: From chemical biology tools to drug candidates[END_REF] to catalysis [START_REF] Müller | A rationally designed aldolase foldamer[END_REF][START_REF] Maayan | Folded biomimetic oligomers for enantioselective catalysis[END_REF][START_REF] Nagano | Stabilized α-Helix-Catalyzed Enantioselective Epoxidation of α,β-Unsaturated Ketones[END_REF][START_REF] Lebailly | Refoldable foldamers: Global conformational switching by deletion or insertion of a single hydrogen bond[END_REF] and drug delivery. [START_REF] Douat | A Cell-Penetrating Foldamer with a Bioreducible Linkage for Intracellular Delivery of DNA[END_REF][START_REF] Douat | Hybrid Cell-Penetrating Foldamer with Superior Intracellular Delivery Properties and Serum Stability[END_REF][START_REF] Aguesseau-Kondrotas | Prospect of Thiazole-based g-Peptide Foldamers in Enamine Catalysis: Exploration of the Nitro-Michael Addition[END_REF] Chief amongst these systems are the peptidic foldamers which are comprised of nonnatural amino acid monomers. There are two main reasons for the interest they have garnered. First is their potential to generate new and fascinating architectures, capable of displaying side chains in different ways compared to native structures. Second and important from a biological perspective, is that these systems are resistant to protease degradation -an important facet in peptidomimetics. [START_REF] Giannis | Peptidomimetics for Receptor Ligands-Discovery, Development, and Medical Perspectives[END_REF] One of the most successful approaches to ensuring that these non-natural units are capable of facilitating secondary structure formation is to design them such that they are conformationally restricted. This ensures that the relative arrangement of the C-and N-termini are fixed within the optimal parameters required for secondary structure formation. [START_REF] Baldauf | Helix Formation and Folding inγ-Peptides and Their Vinylogues[END_REF][START_REF] Baldauf | Helix Formation in α, γ-and β, γ-Hybrid Peptides: Theoretical Insights into Mimicry of α-and β-Peptides[END_REF][START_REF] Baldauf | Ab initio MO Theory -An Important Tool in Foldamer Research: Prediction of Helices in Oligomers of ω-Amino Acids[END_REF] For these reasons, the asymmetric synthesis of conformationally restricted β-and γ-amino acids has received a great deal of attention, as has their application to foldamer design. The reason for desiring such diversity is simple -the more monomers one can access, the more secondary structures become available and thus a greater range of exploitable chemical space is accessible, which is of great importance in fields such as peptidomimetics and catalysis.

Several monomers of this type have been utilized to these ends, [START_REF] Guo | Stereospecific Synthesis of Conformationally Constrained γ-Amino Acids: New Foldamer Building Blocks That Support Helical Secondary Structure[END_REF][START_REF] Guo | New Preorganized γ-Amino Acids as Foldamer Building Blocks[END_REF][START_REF] Giuliano | Evaluation of a cyclopentane-based γ-amino acid for the ability to promote α/γ-peptide secondary structure[END_REF][START_REF] Giuliano | A γ-Amino Acid That Favors 12/10-Helical Secondary Structure in α/ γ-Peptides[END_REF] but one that has been particularly elusive, owing to a lack of synthetic access to it has been the cis-cyclopentyl γ-amino acid system. In this report, we describe the organocatalytic development of this simple but challenging monomer, which uncovers an intriguing model of selectivity and we also demonstrate that it forms a highly organised and stable 10/12-helix beyond that observed for the corresponding trans-system. [START_REF] Giuliano | Evaluation of a cyclopentane-based γ-amino acid for the ability to promote α/γ-peptide secondary structure[END_REF] Results and discussion cis-γ-Cyclopentane Amino Acid Synthesis.

We have ourselves contributed extensively to the asymmetric synthesis of conformationally restricted unnatural amino acids, including six-membered γ-amino acids or their precursors (e.g. 2, Scheme 1a) [START_REF] Nodes | Enantioselective Intramolecular Michael Addition of Nitronates onto Conjugated Esters: Access to Cyclic gamma-Amino Acids with up to Three Stereocenters[END_REF] as well as other five-membered systems [START_REF] Nodes | Asymmetric Phase-Transfer-Catalyzed Synthesis of Five-Membered Cyclic γ-Amino Acid Precursors[END_REF][START_REF] Al-Ani | Asymmetric Organocatalytic Synthesis of Cyclopentane γ-Nitroketones[END_REF] and linear δ 3 -amino acids. [START_REF] Aitken | O-nitroso aldol synthesis: Catalytic enantioselective route to α-aminooxy carbonyl compounds via enamine intermediate[END_REF] At the same time, Gellman reported a synthesis of the related cis-cyclohexyl system 5 (Scheme 1b) [START_REF] Guo | Stereospecific Synthesis of Conformationally Constrained γ-Amino Acids: New Foldamer Building Blocks That Support Helical Secondary Structure[END_REF] using secondary amine catalysis, and recently used the same approach to access the analogous trans-five-membered system 7 (Scheme 1c). [START_REF] Giuliano | Evaluation of a cyclopentane-based γ-amino acid for the ability to promote α/γ-peptide secondary structure[END_REF] However, we desired access to a five-membered γ-amino acid with a cis-arrangement around the ring as we were curious about what the effect of this more conformationally restrained geometry would be when incorporated into a foldamer. Having successfully demonstrated that an organocatalytic 5-exo-trig can lead to cis-selectivity in a different process, [START_REF] Al-Ani | Asymmetric Organocatalytic Synthesis of Cyclopentane γ-Nitroketones[END_REF] we felt that a similar intramolecular approach would be our best chance of attaining our desired cis-target with good selectivity. The only previous access to this system was achieved by Ley and co-workers who obtained the cis-γ-amino acid residue in 10% enantiomeric excess over 7 steps, using an enzyme-mediated resolution. 31 We therefore decided to return to secondary amine catalysis in order to accomplish this, Scheme 1: (a) Our previous work on unnatural γ-amino acid synthesis. [START_REF] Nodes | Enantioselective Intramolecular Michael Addition of Nitronates onto Conjugated Esters: Access to Cyclic gamma-Amino Acids with up to Three Stereocenters[END_REF] (b) Gellman and coworkers' access to trans-cyclohexane γ-amino acid precursor. [START_REF] Giuliano | A γ-Amino Acid That Favors 12/10-Helical Secondary Structure in α/ γ-Peptides[END_REF] (c) Gellman and co-workers' access to trans-cyclopentane γ-amino acid precursor. 25 (d) We theorized that we would be able to access the cis-system through a stereoselective intramolecular nitro-Michael addition.

with the view of using enamine chemistry to access the desired cis-cyclopentane system via an intramolecular conjugate addition onto a nitro-olefin (Scheme 1d). We began our efforts with the most basic 7-nitro-hept-6-en-1-al system 10, made in 4 steps from cyclohexene (for full technical details, see SI), and were delighted to observe that the substrate was rapidly converted to the desired cyclic structure 11, following an in situ reduction with sodium borohydride to prevent possible epimerization (Table 1).

In these initial screens, the preference for the cis-isomer did not appear to be strong at first. However, we were pleased to see that enantioselectivities were reasonable -particularly with respect to the Ley-Yamamoto-Armuddsen tetrazolic organocatalyst VI (Table 1, Entry 6). [32][33][34][35][36][37][38] It was noted with some interest at this stage that the enantioselectivities of the two isolated cis-and trans-products were markedly different and our rationale for this is discussed later in the manuscript. Nevertheless, in order to continue optimizing both diastereo-and enantioselectivity, we began by lowering the temperature to find to our delight that for the tetrazolic catalyst VI although the enantioselectivity was not affected, the diastereoselectivity was much improved (albeit at the expense of reaction time, Entry 8).

Intriguingly, neither co-catalyst nor organocatalyst loading improved selectivities (see SI for full study) but a major influence was both the solvent (dichloroethane) and the concentration of the reaction, where although a more dilute system made the reaction much slower, both diastereoselectivity and enantioselectivity improved remarkably (Entry 14). Of particular note, with these optimized conditions, the reaction is scalable up to 7 mmol maintaining yields and selectivities.

Pleasingly we were able to deduce the absolute stereochemistry of our product from the single-crystal X-ray diffraction of the corresponding (-)-camphonyl ester 12 which confirmed a (1S,2R)-configuration. (Figure 1).

Although we had now managed to access our desired target for foldamer design in excellent stereoselectivity, we also wished to see if our methodology could be applied to other substrates. In that respect, we were able to access cyclopentylketone 13 from the corre- sponding nitroolefin substrate, as well as the fascinating indane system 14 albeit with a 1:1 diastereomeric ratio. Nevertheless, the excellent enantioselectivities of the isolated cissystems was very pleasing (Figure 2). As briefly mentioned above, during our studies it became apparent that the diastereoselectivity and enantioselectivity of this reaction was not straightforward. To begin with, the enantioselectivity of the cis-conformer was far superior to that of the trans-conformer.

Additionally, it was observed that prolonged reaction times would not only decrease the diastereomeric ratio of the cis-and trans-adducts, but also that the enantiomeric excesses of these were changeable, with the cis-system being degraded and the trans-one being enhanced. We theorized two possibilities for this time dependent selectivity. First, that the simple reverse reaction could be occurring, ultimately resulting in the thermodynamically favourable trans-system becoming more predominant via a less enantioselective transition state. Second that there are two independent and competing pathways to the cis-and trans-adducts that over time are subjected to a catalyst-assisted epimerization through a product enamine. Examining the ratio of the four enantiomers during and after the reaction, one can notice a redistribution driven by thermodynamics converting both cis-products to their respective C1-epimeric trans-products (Figure 3). Figure 3b shows the ratio of each enantiomer at t 1 (2 hours from beginning of reaction) and at t 2 (23 hours from beginning of reaction). Interestingly, the decrease of concentration of the (1S,2R)-cis-enantiomer matches with the increase in concentration of the (1R,2R)-trans-enantiomer, and similarly, the ratio difference of the (1R,2S )-cis enantiomer matches with the ratio difference of the (1S,2S )-trans enantiomer. This suggests that the major (1S,2R)cis-enantiomer is converted to the (1R,2R)-trans-enantiomer and the minor (1R,2S )-cisenantiomer is converted to the (1S,2S )-trans-enantiomer, implying that C1-epimerization is certainly one aspect of the story.

Theoretically, a retro-Michael reaction could also lead to the conversion of cis-enantiomers to the thermodynamically more favoured trans-enantiomers. Interestingly, however, this study shows that the enantiomeric ratio of the trans-product is not maintained as one would expect if this were the case, but instead undergoes an enantioenrichment.

Computational Investigation of Stereoselectivity.

In order to gain a complete understanding of this, we turned to computational studies to ascertain the most energetically likely pathways in the formation of each diastereomer. Calculations were performed for substrate 10 in the presence of catalyst VI. Our goal was to establish a model which accounts for the initial cis-selectivity and its observed change in enantiomeric excess over time. Conformational sampling was carried out using mixed lowmode Monte-Carlo search [START_REF] Chang | An internal-coordinate Monte Carlo method for searching conformational space[END_REF][START_REF] Kolossváry | Low Mode Search. An Efficient, Automated Computational Method for Conformational Analysis: Application to Cyclic and Acyclic Alkanes and Cyclic Peptides[END_REF][41] as implemented in Schrodinger 2017-1 42 based on the OPLS 2005 all atom force field, [START_REF] Jorgensen | The OPLS [optimized potentials for liquid simulations] potential functions for proteins, energy minimizations for crystals of cyclic peptides and crambin[END_REF][START_REF] Jorgensen | Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids[END_REF][45] followed by conformational clustering. Kohn-Sham DFT calculations were done for the mechanistic studies using Gaussian09 Rev.E. [START_REF] Frisch | Gaussian09 Revision E.01[END_REF] The presented result were obtained employing the ωB97XD range separated hybrid functional, [START_REF] Chai | Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections[END_REF] with the basis 6-311G(d,p) for optimization, frequency and solvent calculations and the 6-311++G(3df,3pd) basis for electronic energies. [START_REF] Ditchfield | Self-Consistent Molecular-Orbital Methods. IX. An Extended Gaussian-Type Basis for Molecular-Orbital Studies of Organic Molecules[END_REF][START_REF] Hehre | Self-Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian-Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules[END_REF][START_REF] Hariharan | The influence of polarization functions on molecular orbital hydrogenation energies[END_REF] Thermochemical corrections were calculated according to Grimme's qRRHO 51 approximation as implemented in goodvibes. [START_REF] Lab | IFunes, bobbypaton/GoodVibes: Good-Vibes v3[END_REF] Solvent corrections are determined for DCE using PCM solvent model with Truhlar's SMD parametrization. [START_REF] Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions[END_REF][START_REF] Ribeiro | Use of Solution-Phase Vibrational Frequencies in Continuum Models for the Free Energy of Solvation[END_REF] The proposed catalytic cycle is depicted in Scheme 2. We focused on the carbon-carbon bond forming and the subsequent protonation step as well as the intermediates connecting them as they have been shown to be of paramount importance. The transition states of the addition step shed light on the coordinating nature of the tetrazole moiety of the catalyst. The most stable conformers feature a strong Hbonding interaction between the tetrazole ring which is maximized in the path of the product (1S,2R)-15 (Figure 6), with a small cost of strain in the pyrrolidine ring.

In a similar manner to the intermediates observed by Seebach and Hayashi, [START_REF] Patora-Komisarska | Organocatalyzed Michael Addition of Aldehydes to Nitro Alkenes -Generally Accepted Mechanism Revisited and Revised[END_REF] Blackmond, [START_REF] Iwamura | In-situ Catalyst Improvement in the Proline-Mediated α-Amination of Aldehydes[END_REF][START_REF] Iwamura | Probing the Active Catalyst in Product-Accelerated Proline-Mediated Reactions[END_REF][START_REF] Burés | Curtin-Hammett Paradigm for Stereocontrol in Organocatalysis by Diarylprolinol Ether Catalysts[END_REF][START_REF] Burés | Correction to Curtin-Hammett Paradigm for Stereocontrol in Organocatalysis by Diarylprolinol Ether Catalysts[END_REF] Wennemers, [START_REF] Duschmalé | Effects of internal and external carboxylic acids on the reaction pathway of organocatalytic 1,4-addition reactions between aldehydes and nitroolefins[END_REF] Pihko and Papái [START_REF] Sahoo | Dihydrooxazine Oxides as Key Intermediates in Organocatalytic Michael Additions of Aldehydes to Nitroalkenes[END_REF][START_REF] Földes | Stereocontrol in Diphenylprolinol Silyl Ether Catalyzed Michael[END_REF] in studies performed with the Hayashi-Jørgensen catalyst, there are three intermediates the addition step can result in (Figure 4). In a moderately polar solvent as DCE, the zwitterionic structure 10c is thermodynamically unfavoured. The formation of a four-membered ring (10d) in a trans-configuration is rendered impossible due to extreme ring strain, while it is found to be rather stable in the cis-path, (even if the applied level of theory might overestimate its stability). Thus the Nevertheless, the temperature dependence of the qRRHO term of the protonation transition state is considerably higher than that of the first step, which may also account for the temperature dependent selectivity (see SI for full details). Assuming that the addition step determines the selectivity, cis diastereomers form faster and with higher enantioselectivity. This model is in line with the experimental evidence shown in Figure 3 for the C1 epimerization where (1S,2R)-15 and (1R,2S )-15 convert to (1R,2R)-15 and (1S,2S )-15, respectively.

In summary, the existence of two independent pathways to the cis-and trans-adducts has some unexpected consequences. First, for reasons explained in the selectivity model, the ee of the cis-is superior to that of the trans-adduct. Second, that this cis-product can epimerise to the trans-adduct under the reaction conditions.

If the trans-product was solely formed by epimerization of the cis-adduct, the enantiomeric excess would be the same. However, although this C2-epimerization is clearly happening (with the products of this being of the same high enantiopurity), it is also being incorporated into the original trans-selective pathway which is, as mentioned, of a much lower enantioselectivity. As a consequence the overall impression given is that the trans-adduct becomes increasingly enantioenriched as more of the corresponding and purer cis-adduct epimerises to it. On the other hand, the enantioselectivity of the cis-enantiomer decreases with time and this can be simply explained by the fact that the high difference of concentration of the two enantiomers leads to the epimerization in greater quantities of the major cis enantiomer, likely via 1 st order kinetics, and ultimately adversely effecting the er of that system.

Structural Characterisation of γ/α-Foldamers Containing the cis-Cyclopentyl Monomer.

Following both ours, [START_REF] Nodes | Enantioselective Intramolecular Michael Addition of Nitronates onto Conjugated Esters: Access to Cyclic gamma-Amino Acids with up to Three Stereocenters[END_REF] and the Gellman group's [START_REF] Guo | Stereospecific Synthesis of Conformationally Constrained γ-Amino Acids: New Foldamer Building Blocks That Support Helical Secondary Structure[END_REF][START_REF] Guo | New Preorganized γ-Amino Acids as Foldamer Building Blocks[END_REF][START_REF] Giuliano | Evaluation of a cyclopentane-based γ-amino acid for the ability to promote α/γ-peptide secondary structure[END_REF][START_REF] Giuliano | A γ-Amino Acid That Favors 12/10-Helical Secondary Structure in α/ γ-Peptides[END_REF] syntheses of γ-amino acids, their use within foldamer constructs has attracted great interest. In the main these systems have employed a cyclic backbone; a common feature which results in a conformational restriction that is beneficial for foldamer formation. For example, Gellman has accessed foldamers based on cis-and trans-cyclohexyl based γ-systems (A, B and C in Figure 8). [START_REF] Guo | Stereospecific Synthesis of Conformationally Constrained γ-Amino Acids: New Foldamer Building Blocks That Support Helical Secondary Structure[END_REF][START_REF] Guo | New Preorganized γ-Amino Acids as Foldamer Building Blocks[END_REF][START_REF] Giuliano | A γ-Amino Acid That Favors 12/10-Helical Secondary Structure in α/ γ-Peptides[END_REF] Of particular note is also the Balaram and co-workers' α/γ-peptide containing the constrained achiral γresidue gabapentin (D, Figure 8). 63,64 System D allowed the arrangement of the secondary structure which contained, until now, one of the smallest ζ-angles known and leading to a 12/10-helix. The trans-cyclopentyl system has also been exploited (E, Figure 8) but a noticeable absence from these studies have been the cis-cyclopentane γ-amino acids that are the subject of this study (Figure 8) owing to the aforementioned lack of methodology towards them in any enantiopure sense. Having successfully achieved the synthesis of the cis-γ-amino acid precursor 11, our next task was to synthesize the corresponding 1:1 γ/α-hexapeptide for secondary structure analysis and this is summarized in Scheme 3. To begin with, dipeptide precursor 16 was accessed through the PCC oxidation of γnitroalcohol 11 followed by peptide coupling with benzoyl protected l-alanine. The resulting species was then reduced using zinc powder to unmask the primary amine which was protected using Boc anyhydride, giving C-terminus protected NH 2 -dipeptide-OBn 17. Boc protection of dipeptide 17 then allowed us to access to the N-terminus protected BocNHdipeptide-OH derivative 19 using standard reduction conditions. The crystalline nature of intermediate 18 enabled collection of single-crystal X-ray diffraction data, which not only confirmed the configuration of our cyclopentane system, but also allowed us to analyse the internal torsional angles of our γ-residue (Figure 9). With dipeptides 17 and 19 in hand, we were able to couple them to generate tetramer 20. The N-terminus of this was then exposed on treatment with HCl in dioxane, allowing for the coupling of a second dipeptide 19 and finally access to the desired hexapeptide system 21 (Scheme 3). Owing to the short length of tetramer 20, we focused on the structural characterisation of the hexamer 21.

The very good dispersion of proton signals allowed for the near total assignment based on 1 H-1 H COSY, ROESY and TOCSY NMR. Four out of six amide peaks were found at δ > 7 ppm, which is a typical feature of H-bonded protons (Figure 10). A self-aggregation experiment was performed to prove there was no self-association and confirm that the downfield detected amide peaks were due to intramolecular rather than intermolecular interactions (0.04 -4mm in CDCl 3 , see full details in the SI). DMSO titration experiments were then conducted to identify protons that were not engaged in intramolecular H-bonding, thus discriminating free and H-bonded signals giving further structural information. Figure 11b shows the change in chemical shift (∆ δ) of each residue after consecutive additions of DMSO (5, 10, 15, 25, 50, 100 µL). Only the l-Ala (2) amide peak, which is highlighted in red, is strongly shifted downfield after the addition of DMSO and thus is the only residue not involved in H-bonding (Figure 11), giving further support to the proposed helical structure. This was further supported by detailed analysis of the obtained 2-D NMR data, which showed three medium range cross peaks (Types i, ii and iv in Table 2), characteristic of 12/10helices for α/γ-peptides [START_REF] Giuliano | Evaluation of a cyclopentane-based γ-amino acid for the ability to promote α/γ-peptide secondary structure[END_REF][START_REF] Giuliano | A γ-Amino Acid That Favors 12/10-Helical Secondary Structure in α/ γ-Peptides[END_REF]65 (relative positions of interacting amino acids γ 1 → α 2 /γ 1 ← α 4 ) and therefore of a 10/12-helical structure for γ/α-peptides(α 1 → γ 2 /α 1 ← γ 4 , 2). [START_REF] Baldauf | Helix Formation in α, γ-and β, γ-Hybrid Peptides: Theoretical Insights into Mimicry of α-and β-Peptides[END_REF] Like Gellman we do not see interaction iii, [START_REF] Giuliano | Evaluation of a cyclopentane-based γ-amino acid for the ability to promote α/γ-peptide secondary structure[END_REF] however we do see interaction iv, which might be one reason that we see a more ordered structure. [START_REF] Giuliano | A γ-Amino Acid That Favors 12/10-Helical Secondary Structure in α/ γ-Peptides[END_REF]65 In addition, the different sequencing might have led to additional NOE interactions, and therefore we also observed strong interactions between HCα of α residues with HCβ of i +1 α-residues and HCγ of γ-residues with HCα of the i+2 γ-residues (Table 2).

The determined NOE cross peaks were used as molecular restrictions to identify the most populated lowest energy conformations of the γ/α-peptide 21. Based on the NMR data, 55 conformers of the hexapeptide were identified employing Monte-Carlo methods (details in SI) and further optimized with DFT empoying the long range corrected ωB97XD functional together with the 6-311G** basis set. [START_REF] Chai | Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections[END_REF] The overlay of the conformers above 1% population (assuming Boltzmann distribution) is depicted in Figure 12. Five out of six residues correspond clearly to a well defined 10/12-helix with backbone dihedral values listed in Table 3.

Most interesting is examination of the backbone torsion angle ζ, representing rotation around the bond of the cyclopentane ring that is part of the peptide sequence. The values for this angle are strongly restricted in case of the cis-configuration on this bond. In the case of (1S,2R)-or, alternatively, (1R,2S )-configuration, theoretical studies show that only a relatively small range of values of about 0°, ±30°or ±45°are possible, dependent on which bond of the envelope conformation of the ring is selected to be part of the peptide sequence (pseudorotation). In good agreement, the values for ζ from the NMR analysis are in between 30-45°. Based on quantum chemical calculations, a catalog of all helical folding patterns in conformationally unrestricted α/γ-peptides is available. [START_REF] Baldauf | Helix Formation in α, γ-and β, γ-Hybrid Peptides: Theoretical Insights into Mimicry of α-and β-Peptides[END_REF] Comparing our structure with the catalogue data shows that it corresponds to the most stable mixed 12/10-helix in the The situation is distinctly different in case of a trans-arrangement on the cyclopentane ring with 1S,2S -or 1R,2R-configuration. Here, a much larger range of possible values for the torsion angle ζ are possible, which occur in a greater number of potential helical structures. Thus, competition between these trans-structures may prevent stable secondary structure formation. Indeed, studies on peptides with such constituents by Gellman and coworkers [START_REF] Giuliano | Evaluation of a cyclopentane-based γ-amino acid for the ability to promote α/γ-peptide secondary structure[END_REF] indicate a much weaker tendency to form ordered helical structures, although a tendency in direction of a 10/12-helix found by Sharma and coworkers 65 became visible.

Conclusions

In conlusion, we have developed a highly stereoselective organocatalytic route to the (1S,2R)-2-(aminomethyl)cyclopentane-1-carboxylic acid monomer precursor. This selectivity has been explained computationally and found to be a result of two independent pathways with a favourable kinetic profile towards the cis-system. Prolonged reaction times erode both the enantiopurity of the cis-adduct and the diastereomeric ratio via C2-epimerization that unusually also leads to the apparent enantioenrichment of the trans-adduct. γ/α-Oligomers were then synthesized and it was found that the hexamer populated a 10/12-helix. The cis-γ-residue contains the smallest ζ-angles reported for this type of helix and in contrast to the one reported by Balaram and co-workers 63 the helix seems tighter due to the even smaller ζ-angles. This highly organized secondary structure does not seem to occur in the corresponding trans-system, possibly owing to the greater number of potential conformations in that system resulting in a greater range of helices. [START_REF] Giuliano | Evaluation of a cyclopentane-based γ-amino acid for the ability to promote α/γ-peptide secondary structure[END_REF]

Figure 1 :

 1 Figure 1: X-ray crystal structure of the alcohol derivative (CCDC : 1947228) 12.

Figure 2 :

 2 Figure2: Our methodology could be applied to simple ketones as well as the intriguing indane system 14.

  ee trans = 60% ee cis = 44% ee trans = 66% ee (b)

Figure 3 :

 3 Figure 3: Proportion of enantiomers of the five-membered ring 11 at t 1 and at t 2 performing the reaction in CH 2 Cl 2 at rt for investigative purposes.

Scheme 2 :Figure 4 :

 24 Scheme 2: Mechanistic proposal of the 5-exo-trig cyclisation.

15 Figure 5 :

 155 Figure 5: Calculated energies and Gibbs free energies were obtained at the ωB97XD/6-311G(d,p) level of theory with qRRHO corrections and SMD solvation in dichloroethane.

Figure 6 :

 6 Figure 6: C-C bond forming transition states on the (1S,2S ) (left) and (1S,2R) (right) paths.

Figure 7 :

 7 Figure 7: left: geometry of (1S,2S )-1e ‡ . right: geometry of (1S,2R)-1e ‡ , showing an earlier, less concerted TS.

Figure 8 :

 8 Figure 8: Constrained carbocyclic γ-amino acids that promote helical foldamers.

18 Figure 9 :

 189 Figure 9: Asymmetric unit of the single-crystal X-ray structure of Boc-protected dipeptide 18 (CCDC : 1947227).

Figure 10 :

 10 Figure 10: 1 H NMR spectra in CDCl 3 at a concentration of 0.2 mM for the characterisation of γ/α peptide 21.

Figure 11 :

 11 Figure 11: DMSO titration of 2mm γ/α-peptide 21 in CDCl 3 : (a) H-bonding and solvent exposed amide protons in the proposed γ/α-peptide 10/12-helical structure. The amide proton circled in red are expected to exhibit the largest chemical shift change upon DMSO addition. (b) Change of chemical shift of NH peaks with progressive DMSO addition. (c) Amide peak region of 1 H NMR spectra collected with addition of 0, 10, 25, 50 and 100 µL of DMSO added to a 2mm solution of hexamer 21 in CDCl 3 .

Figure 12 :

 12 Figure 12: Overlap of the 9 lowest energy structures of 21 obtained with a computational study where residue AMCP (1) and side chains have been omitted, as well as simplification of the terminal protecting groups for the purposes of clarity. (a) Backbone of oligomer 21. (b) Top view of helical backbone structure of 21. (c) H-bond directionality for the oligomer 21.

  catalogue. The backbone torsion angles of the idealized helix are φ = 66°, θ = 32°, ζ = 48°, ψ = -129°for the γ-amino acid constituent and φ = -67°and ψ = 148°for the α-amino acid constituent. The same helix type was also found by Balaram and co-workers in α/γ-peptides with the γ-amino acid gabapentine.63

Table 1 :

 1 Optimisation Study (Abridged) a

				O	1. Catalyst (20 mol%)	* *	OH
		O 2 N		H	2. NaBH 4 , MeOH		* *	NO 2
			10							11
						O		Me
		N H	Ph OTMS Ph	N H	Ph OH Ph	Ph	N H 2 N	Cl Me Me	H N	HN N N N
			III	IV			V		VI
	Entry	Catalyst Solvent Conc,	T, °C	Time,	Yield,	dr, d	ee, e %
				m		h b		% c	cis:trans
	1 f	III	CH 2 Cl 2 0.2	rt	0.3		62	1:4	nd,-59
	2 f	VI	CH 2 Cl 2 0.2	rt	1.5		91	1:8	nd, 72
	3	III	CH 2 Cl 2 0.2	0	1			57	1:1	-87, g -27
	4	IV	CH 2 Cl 2 0.2	0	96		5 h	1:1	nd,nd
	5	V	CH 2 Cl 2 0.2	0	72		42	1:6	-68,-74
	6	VI	CH 2 Cl 2 0.2	0	14		62	2:1	83, g 71
	7	III	CH 2 Cl 2 0.2	-20	>24		20	1:1	36, 53
	8	VI	CH 2 Cl 2 0.2	-20	22		62	3:1	82, 22
	9	VI	MeCN	0.2	-20	25		54	1:1	65, 56
	10	VI	THF	0.2	-20	24		52	1:1	50, 38
	11	VI	MeOH	0.2	-20	26		11	3:2	-10
	12	VI	DCE	0.2	-20	50		53	7:1	85, 54
	13	VI	DCE	0.1	-20	48		66	6:1	89
	14	VI	DCE	0.05	-20	168		74	17:2	93
	15	VI i	DCE	0.05	-20	168		43	10:1	92,-11

a See Supporting Information for full optimization study. b Time for complete consumption of aldehyde as observed by tlc. c Isolated yield over two steps. d Determined by 1 H NMR on the crude mixture. e Determined by HPLC analysis using a chiral OD column for the cis diastereomer and a chiral AS column for the trans diastereomer. f Yield, dr and ee were calculated of the aldehyde product without any further reduction with NaBH 4 . g Determined by HPLC analysis using a chiral AD-H column. h Reaction did not go to completion. i 2 mol% of catalyst loading.

Table 2 :

 2 Significant observed NOE cross peaks for hexamer 21 and characteristic NOE cross peaks of 12/10-helical structures.

																	strong
																	medium
																	weak
			AMCP (1)	AMCP (3)	AMCP (5)
	O	HN O	H	H	H	O	N H L-Ala (2) H N O H H H	H	H	O	N H H	O L-Ala (4) H N H H	H	H	O	N H	H O L-Ala (6) O

Table 3 :

 3 Backbone torsion angles of hexamer 21 from NMR analysis [ a] and X-ray data for dipeptide 18.[a] ωB97XD/6-311G** level of density functional theory.

		BocHN	(R) (R) φ	ζ θ	(S) (S) O ψ	H N φ	(S) (S) ψ	O OBn
					18
		Residue			φ	θ	ζ	ψ
	Hexamer 21	AMCP (1)	26.0±75 9.7±50 35.3±23 -103.0±8
		l-Ala (2)		-72.8±8	-	-	128.7±34
		AMCP (3)		61.0±3 43.5±3 41.9±1 -119.0±4
		l-Ala (4)		-72.8±4	-	-	141.7±2
		AMCP (5)		59.0±1 46.2±2 28.4±1 -119.7±3
		l-Ala (6)		-63.9±1	-	-	139.9±10
	X-ray Dipeptide crystal 18 cis-AMCP (1)	-96.3	176.7	29.4	-100.1
		l-Ala(2)		-125.7	-	-	1.1

Acknowledgement

We would like to thank our funders King's College London (to. R. F.) and the ERC (Project No. 757850 BioNet to D. B. and T. F.). We are grateful to the UK Materials and Molecular Modelling Hub for computational resources, which is partially funded by EPSRC (EP/P020194/1). D.B. and E.R. are grateful for the Nuffield Foundation and the summer students Angelo Davis and Fangling Zheng for their commitment.

Supporting Information Available

Experimental procedures and characterization data for all new compounds.

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