Guillaume Lenoir
email: glenoir@axiom-genetics.com

Loïc Flatres-Grall

Rafael Muñoz-Tamayo
email: rafael.munoz-tamayo@inrae.fr

Ingrid David
email: ingrid.david@inrae.fr

Nicolas C Friggens
email: nicolas.friggens@agroparistech.fr

Disentangling the dynamics of energy allocation to provide a proxy of robustness in fattening pigs

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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The pig industry faces new challenges related to rapidly changing environmental conditions, especially related to global warming [START_REF] Hansen | Perception of climate change[END_REF], and to growing societal concerns. For several decades, breeding objectives were mainly focused on increasing animal productivity (growth, feed efficiency…) at the expense of non-productive functions, i.e., fitness [START_REF] Puillet | Disentangling the relative roles of resource acquisition and allocation on animal feed efficiency: insights from a dairy cow model[END_REF][START_REF] Rauw | Undesirable side effects of selection for high production efficiency in farm animals: a review[END_REF]. These unfavorable consequences could be explained by trade-offs in resource allocation between biological functions [START_REF] Rauw | Introduction[END_REF]. Indeed, when animals cannot obtain more resources, i.e., in limiting environments, allocation of these resources to a high priority function must be to the detriment of another function [START_REF] Stearns | The Evolution of Life Histories[END_REF]. In this situation the animal is unable to maximize the expression of each biological function simultaneously. This changing context requires having animals able to adapt to new environmental conditions with more limiting resources, which can be associated with an improvement of robustness. [START_REF] Knap | Breeding robust pigs[END_REF] defined robustness as "the ability to combine a high production potential with resilience to stressors, allowing for unproblematic expression of a high production potential in a wide variety of environmental conditions". Generally, the production potential is associated to a phenotype of interest, such as growth, feed efficiency or milk production, egg production. Incorporating one or several traits to evaluate robustness of growing pigs in genetic evaluation would therefore be of value for the development of more sustainable breeding goals (Berghof et al., 2019b). Accordingly, when targeting robustness as a breeding objective, it is important to maintain simultaneously a high level of production to meet industry's economic expectations. However, until recently to it was very difficult to phenotype traits such as robustness in farm animals and therefore on the way to improve it.

In parallel, the increasingly common use of sensors in farms, especially automatic feeding system (AFS) in pig industry, allows continuous individual recording of weight or feed intake over a long period. This offers the possibility to characterize the dynamics of those phenotypes for each individual in the face of variations in the environment. Several studies have used such longitudinal data to quantify resilience indicators based on deviation between an expected trajectory of each individual for a given non-perturbed environment and its observed trajectory on feed intake [START_REF] Nguyen-Ba | A procedure to quantify the feed intake response of growing pigs to perturbations[END_REF] or body weight [START_REF] Revilla | Quantifying growth perturbations over the fattening period in swine via mathematical modelling[END_REF]. Definition and modelling of individual potential trajectory are challenging issues in these approaches. Other studies developped several resilience indicators based on the within individual variance of time series mesurments related to production, such as feed intake of growing pigs [START_REF] Putz | Novel Resilience Phenotypes Using Feed Intake Data From a Natural Disease Challenge Model in Wean-to-Finish Pigs[END_REF], milk yield for dairy cows [START_REF] Poppe | Validation of resilience indicators by estimating genetic correlations among daughter groups and with yield responses to a heat wave and disturbances at herd level[END_REF] or egg production in laying hens [START_REF] Bedere | Using egg production longitudinal recording to study the genetic background of resilience in purebred and crossbred laying hens[END_REF]. These modeling approaches have mainly addressed the characterization of robustness or resilience through the analysis of one production variable. They are a substantial contribution in the phenotyping of resilience but do not address the underlying biological mechanisms and the potential trade-offs in the use of available resources between production and other functions. A robust animal can be considered as an animal able to allocate a proportion of its resources to the right function at the right time [START_REF] Friggens | Review: Deciphering animal robustness. A synthesis to facilitate its use in livestock breeding and management[END_REF]. To our knowledge, the characterization of robustness based on the temporal evolution of the allocation pattern has been little explored in growing pigs.

The acquisition of temporal data of feed intake and weight in growing pigs made it possible to consider the development of allocation model based on these two variables to caracterize robustness. With this objective, we developed a conceptual model to represent the temporal pattern of allocation of energy intake to growth in fattening pigs (Lenoir et al., 2022).

In the present study, the first objective was to develop a robustness indicator on the basis of modelling of longitudinal energetic allocation coefficient to growth for fattening pigs.

Consequently, the environmental variance of this allocation coefficient was considered as a proxy of robustness. This proxy should reflect the ability of an animal to express or adapt its production potential in the face of changes in the environment relative to other animals that have been raised under the same conditions. Our objective was to estimate its genetic parameters and correlation with traits under selection as well as with phenotypes routinely collected on farms and associated to robustness or heatlh status.

Methods

Study population

A total of 25745 pigs from Piétrain NN Français paternal line (Pie NN), free from halothanesensitivity, of the AXIOM company were used in this study. Individuals from the Pie NN line were born in 3 different farms integrated into the AXIOM breeding scheme and that comply with AXIOM's biosafety and health requirements. A part of the males were selected before weaning and then raised at the boar testing station of the breeding company AXIOM Genetics (Azay-sur-Indre, France). The animals considered in the present dataset were 6885 entire males and 13012 females raised and individually tested at their farm of birth from April 2014 to April 2022 and 5848 entire males raised from September 2015 to April 2022 at the boar testing station.

The animals raised on their birth farm were born from 3943 litters, 6.5±2.9 piglets per litter, and from 321 sires, 80±53.8 piglets per sire. To limit the risk of confounding between environmental (i.e., fattening group) and genetic effects, the sires were used at least in two mating groups in each farm and in two different farms. Animals were transferred to fattening rooms when they were 75.7 ±3.4 days of age (33.8±7.8 kg body weight (BW)). Pigs were raised in fattening rooms for 68.6 ±4.9 days until the individual testing at around 142.4±4.6 days of age (103.4±11 kg BW).

For males raised at the boar testing station, they were transferred every three weeks from birth farm to the station at an average age of 27.3±2.2 days with an average BW of 8.5±1.7 kg. They were raised in pens of 14 animals from the same birth farm. These groups of 14 pigs were never modified at the different stages of breeding. Each fattening group consisted of animals sourced from between one or three farrowing farms. These animals came from 2048 litters, 2.6±1.5 piglets per litter, and were born from 238 sires, 22.1 ±15 piglets per sire. They were raised in quarantine and postweaning rooms for five and two weeks respectively and transferred to fattening rooms when they were 76.4±2.9 days of age (34.4±5.4 kg BW). These pigs were raised in fattening rooms for 69 ±4.7 days until the individual testing at around 145.4 ±3.6 days of age (104.5±11.1 kg BW). Fattening rooms were equipped with AFS: Nedap pig performance testing feeding station (Nedap N.V.;

Groenlo, the Netherlands). Animals were fed ad-libitum with commercial diets adapted to their physiological needs. The provided diets were non-limiting in amino acids. The boar testing station environmental and technical conditions are described in detail in Lenoir et al. (2022a). The pedigrees contained 27276 animals across 20 generations.

Information recorded during the fattening period

The performances recorded were the same in farrowing farms testing and boar testing station. Each animal was individually weighed on arrival in the fattening room (initial body weight: IBW). When the average weight of the group was approximately 100 kg, individual tests were performed for animals weighing more than 70 kg (Institut Technique du Porc, 2004). Measurements made during the test were: body weight (TBW), average ultrasonic backfat thickness (BF = mean of three measurements in mm) and ultrasonic longissimus dorsi thickness (LD = one measurement in mm).

The BF and LD measures were transformed to correspond to their values at 100 kg liveweight (BF100 and LD100 respectively) to compare animals at equivalent weight. This transformation was done by applying linear coefficients that multiply the difference between 100 kg and TBW.

Coefficients used are 0.04 mm/kg for BF100 and 0.27 mm/kg for LD100 [START_REF] Sourdioux | Estimation des paramètres génétiques pour des critères de croissance et carcasse en race Piétrain et en lignée composite Piétrain négative halothane[END_REF].

The average daily gain (ADG) was calculated as the difference between TBW and IBW divided by the number of days elapsed between the two weighings.

Additionally, at the boar testing station, BW (kg) and feed intake (FI; kg per visit) were recorded each time the animal went into the AFS. The feed conversion ratio (FCR) was calculated as the ratio between the total FI during the fattening period and the weight gain (TBW-IBW), expressed in kg/kg. The average daily feed intake (DFI) was calculated as the total FI during the period divided by the number of days elapsed. The residual feed intake (RFI) was also estimated for each animal as the deviation between the recorded DFI and the potential average daily feed intake (PDFI) predicted from requirements for maintenance and production. Based on the method proposed by [START_REF] Labroue | Consommation résiduelle chez le porc en croissance alimenté à volonté Méthode de calcul et variabilité génétique[END_REF], the PDFI was estimated by linear regression, with the lm function in R (R Core Team, 2018), of DFI on average metabolic weight (AMW), ADG and BF100. The AMW was estimated for each animal using the formula proposed by [START_REF] Noblet | Influence of growth potential on energy requirements for maintenance in growing pigs[END_REF], ܹܯܣ ൌ ሺ்ௐ భ.ల ିூௐ భ.ల ሻ ଵ.ሺ்ௐିூௐሻ . In addition, all medical treatments received by the animal were recorded. A visual observation of the animals was carried out by the technician in charge of the measurements in order to note any morphological defects, anomalies and clinical signs of disease according to a frame of reference (Institut Technique du Porc, 2004), noted as "observable defects". These observations were made by the same person within any given fattening group. The medical treatments and individual observations were recorded from January 2019 to April 2022 on 3028 males fattened at the boar testing station.

Longitudinal data pre-treatment

A pre-treatment process was performed on BW and FI, recorded each time the animal went into the AFS, to validate them, identify quality issues and convert them on a daily scale. This process followed the procedure proposed by [START_REF] Revilla | Quantifying growth perturbations over the fattening period in swine via mathematical modelling[END_REF] and modified by Lenoir et al. (2022a). In summary, on the scale of the visit, a quadratic regression of BW on age + age² for each animal was applied to eliminate aberrant BW. For a given animal and a given visit, if the ratio between the residual value and the fitted value was > 0.15, the BW measurement was considered to be null. This step was repeated a second time. Following this step, the body weight (BW it ; kg) was estimated from the median of the non-null weights for each pig (i) and each fattening day since the transfer to fattening room (t). For feed intake, if for a given animal the feed intake rate at a visit was lower or higher than its mean take rate over the fattening period ±4 standard deviations, the FI measurement was considered to be missing. This missing value was estimated using a linear regression of FI on feeding duration. The daily feed intake (FI it ; kg) was calculated as the intakes during the visits of the day t. Then BW it and FI it were validated at the pen scale to detect inconsistencies linked to the AFS machine. When a control day was missing (due to a mechanic problem of AFS or loss of a RFID tag), the missing BW it and FI it were estimated separately by using local regression model, "proc loess" implement in SAS (SAS Institute Inc., 2013). Data recorded on day t=0 were excluded from the dataset due to AFS calibration and animal adaptation. After data pre-treatment, the file included 405983 daily records associated to the 5848 males fattened at the testing station.

Model for analysis

Modelling energetic allocation coefficient to growth

As shown on Figure 1, the feed intake, i.e input of the system, is transformed in net energy intake and allocated to several functions: maintenance, body development (protein deposition), body reserves (lipid deposition) and other functions [START_REF] Van Milgen | InraPorcU: un modèle pour analyser les performances et évaluer les stratégies alimentaires chez le porc en croissance[END_REF]. The body weight gain, i.e., output of the system, is directly related to the protein and lipid depostion. Resource allocation is regulated during the fattening period for each individual according to deterministic factors: genetic potential and degree of maturity [START_REF] Lewis | The relationship between feed intake and liveweight in domestic animals[END_REF]. Over the time, resource allocation coefficient is also impacted by changes in environmental conditions, i.e., pertubations [START_REF] Friggens | Review: Deciphering animal robustness. A synthesis to facilitate its use in livestock breeding and management[END_REF].

A dynamic regression model (DLM; [START_REF] West | Bayesian forecasting and dynamic models[END_REF] was used to estimate daily energetic allocation coefficient to growth (α it ; Lenoir et al., 2022b). First, FI it was converted in net energy intake in MJ (EI it ), using the net energy density of the feed of 9.85 MJ of NE/kg. Then, the net energy available for growth at day t (NEA it ) was calculated as the difference between EI it and the net energy maintenance requirements at day t (MR it ), estimated according to [START_REF] Noblet | Etat des lieux et perspectives sur la nutrition du porc[END_REF].

The DLM to estimate the allocation coefficient of energy to weight gain for a given pig i at day t (α it ) was built with two equations : an observation equation ( 1), relating cumulative weight gain at day t (CW it in kg) and cumulative net energy available at day t-1 (CNEA it-1 in MJ), a system equation ( 2), describing the changes in α it (unobserved state variable) from day to day according to a stochastic process.

CW ௧ ൌ α ௧ כ CNEA ௧ିଵ ݒ ௧ ܞ ܑ ~Nሺ0, Iσ ௩ ଶ ሻ (1) α ௧ ൌ α ௧ିଵ ݓ ௧ ܟ ܑ ~Nሺ0, Iσ ௪ ଶ ሻ (2)
Where ݒ ௧ was a random observation error for animal i; σ ௩ ଶ is the observational variance i; ݓ ௧

represented random and unpredictable changes in level between time t-1 and t; and σ ௪ ଶ was the system variance. The model was built using the R package dlm [START_REF] Petris | Dynamic Linear Models with R, Use R[END_REF]. The values of α it were calculated independently for each animal with a Kalman smoother algorithm. The value of α it at t=1 was not estimated because the consumption at t-1 was unknown.

Estimation of genetic variance in environmental variance

Longitudinal energetic allocation coefficients (α it ) were analyzed with ASReml 4.2 software [START_REF] Gilmour | Genetic Parameters for Resistance to Non-specific Diseases and Production Traits Measured in Challenging and Selection Environments; Application to a Rabbit Case[END_REF] to estimate both its genetic variance and the genetic variance in the residual variance (i.e., environmental variance) using a two-step approach [START_REF] Sancristobal-Gaudy | Prediction of the response to a selection for canalisation of a continuous trait in animal breeding[END_REF][START_REF] Garreau | Results of four generations of a canalising selection for rabbit birth weight[END_REF].

First step: estimation of genetic variance in the energetic allocation coefficient

The energetic allocation coefficient was analyzed by a random regression model (RR) with first order Legendre polynomials [START_REF] Robson | A Simple Method for Constructing Orthogonal Polynomials When the Independent Variable is Unequally Spaced[END_REF] for the genetic and permanent environmental effects.

The common litter was significant as a random effect, tested using likelihood ratio (LRT) test, ߙrisk of 5%, and included in the model, in addition to additive genetic and permanent environmental effects. Fixed effects included in the model were selected at an p-value of 5% using the Wald F statistic. The significant fixed effects were the fattening group (103 levels), as contemporary group, and the joint effect of fattening group and the fattening pen (517 levels). The age k in days of the animal at day t was include as a covariate. The residual variance was assumed constant over time.

Second step: estimation of genetic variance in residual variance

In the second step of the analysis, the residuals (݁ ௧ , residuals of animal ݅ at time ݐሻ of the RR model were used to compute log transformed squared residuals: ܴܵܮ ௧ ൌ ݈݊ሺ݁ ௧ ଶ ሻ as an indicator of animal robustness. A lower LSR value is assumed to be an indication of a higher animal robustness to environmental perturbations, related to a smaller deviation from expected allocation of energy to growth. To follow the assumption of the BLUP (best linear unbiased prediction; [START_REF] Henderson | Best Linear Unbiased Prediction of Breeding Values Not in the Model for Records[END_REF] method, which should be applied to a non-selected base population, and to estimate the covariance between traits, a multi-traits animal model including the four traits under selection (ADG, BF100, LD100 and FCR, single measurement for all the animals) and the non-selected traits LSR (repeated data for animal in station) and RFI was applied. For the LSR trait, the same fixed effects were fitted as for α it and the random effects included were common litter, permanent environmental and animal additive genetic effects. For the four traits under selection, the fixed effects tested at an α-risk of 5% using the Wald F statistic were the gender (2 levels), the fattening farm (4 levels) and the fattening group within the fattening farm (443 levels). The significant random effects were common litter and animal additive genetic. At this step, heritability (h²) was calculated as the ratio of animal genetic variance to the total phenotypic variance, i.e., the sum of the genetic additive variance, environmental variances (common litter, permanent environmental if necessary) and the residual variance.

Relation between LSR and routinely collected phenotypes

To evaluate whether the LSR phenotype could be considered as a robustness proxy, the relationship between estimated breeding value (EBV) for LSR and health phenotypes was studied. The 3028 males with LSR phenotype and known information over the fattening period (observations, injections…) were divided into 4 quartiles according to their EBV for LSR, from Q1 for the most favorable values (lower EBV LSR) to Q4 for the most unfavorable values (higher EBV LSR). We studied the distribution of other phenotypes associated with animal health and robustness according to the EBV LSR quartile. To compare the differences and frequencies in the scores among the four EBV LSR classes, a Chi-square was performed. Statistical significance was set a priori at P less than or equal to 0.05. These phenotypes are derived from measurements made during the animals performance evaluations, and from the medical treatments recorded during the testing period. In each class, we differentiated animals that can be selected (Selectable) from those that are dead or weighing less than 70 kg at the day of the individual test or weighing 70 kg or more and with an observable defect on the day of testing. We considered as an observable defect on the day of testing, factors such as weak development and similar that were estimated to relate to the robustness of the animal (Appendix 1). A second trait differentiated pigs that received at least one antibiotic or antiinflammatory injection during the testing period from those that didn't receive any injection (No injection). We also differentiated pigs that were "Selectable" without receiving any antibiotic or anti-inflammatory injection during the testing period (Selectable without injection) from the others.

Results

Observed allocation coefficients and robustness indicators

The descriptive statistics for the dataset used in this study are shown in Table 1. The observed means and LSR were 0.099±0.027 kg/MJ NE and -12.62±2.50, respectively. The phenotypic correlations, estimated with cor.test function on R (R Core Team, 2018), for trait α t were positive with ݁ ௧ (0.241±0.002) and LSR (0.23±0.002), which means that a higher energetic allocation rate to growth was related to a higher variability. The phenotypic coefficients of variation were greater than 20% for IBW, α t and LSR, and between 10 and 20% for TBW, ADG, DFI and BF100, indicating large phenotypic variation for these traits. (Figure 2a), its average LSR value for was -14.6±1.7. The second animal on Figure 2b had higher deviation between smoothed allocation and prediction likely in response to an environmental perturbation, its average LSR value was higher than for the first individual (-12.3±1.9).

Accordingly, the parameter LSR looks to be a useful indicator to quantify the effect of perturbation of an animal and allows comparison within a population.

Genetic parameters of allocation coefficients, production and robustness indicator traits

The changes in heritability for α t over time estimated with the RR model are shown in Figure 3, ranging from 0.20±0.03 to 0.30±0.03. The heritabilities obtained with the RR model were stable from 67 to 100 days of age, around 0.30±0.03, then decreased up to 150 days of age and then stabilized around 0.20±0.03 toward the end of the control period. The permanent environmental ratios ranged from 0.51±0.03 to 0.64±0.03. The estimates obtained decreased up to 128 days of age and then increased again toward the end of the period.

Heritability estimates of the traits under selection, ADG, BF100, LD100 and FCR, were moderate, ranging from 0.27±0.03 to 0.45±0.02 (Table 2). Heritability estimates for RFI and FCR were not significantly different from each other, 0.29±0.03 and 0.27±0.03 respectively. The robustness indicator LSR was lowly heritable, 0.05±0.01. The proportion of variance due to common litter effects was similar for all traits, ranging from 0.04±0.01 to 0.06±0.01, except in the LSR estimation, which had a proportion of phenotypic variance explained by litter effect close to 0. The proportion of phenotypic variance explained by permanent environment effect for LSR was moderate, 0.22±0.01.

The trait LSR had high negative genetic correlations with ADG, FCR and RFI, ranging from -0.83±0.06 to -0.71±0.06 (Table 3). Estimates of genetic correlations of LSR with BF100 were low and negative, and not significantly different than from 0 with LD100. The trait FCR had a high genetic correlation with RFI, 0.90±0.02, and moderate genetic correlations with ADG and BF100, 0.52±0.06 and 0.50±0.05, respectively. Estimates of the genetic correlations of ADG with BF100

and RFI were positive and moderate to high, 0.43±0.04 and 0.61±0.05 respectively.

Relation between EBV LSR classes and collected phenotypes

The percentage of "Selectable" animals was significantly related to the EBV LSR quartile (Figure 4). The quartile Q1, including animals with the lowest EBV LSR value, had the highest value with 91.7% of "Selectable" animals, and the quartile Q4 had the lowest percentage, 61.2%. The difference between each quartile were significant. In the quartile Q1, 75% of the animals didn't receive any antibiotic or anti-inflammatory injection ("No injection") over the control period. This percentage was not significantly different than those observed for Q2 and Q3, 74.1% and 70.9%

respectively. The difference of percentage animals with "No injection" was significant between Q4, 68.7%, and Q1 or Q2. The proportion of animals "Selectable without injection" was significantly higher in Q1 than in Q3 and Q4, 69.3%, 58.3% and 43.3% respectively. In summary, a lower EBV LSR, i.e., a higher robustness level, was associated with a better chance of being in good health, of being "selectable" and with a lower use of medicines.

Discussion

Our objective was to propose a robustness indicator for fattening pigs from the characterization of the energy allocation of the animal. This indicator is expected to be associated with the ability to cope with different types of environment perturbations encoutered, allowing optimal expresion of production potential. The originality of this work was to use two time-series variables measured in order to model longitudinal an energetic allocation coefficient, α t , over the fattening period. The LSR trait was estimated as the daily deviation of α between the observed values (i.e., calculated with the DLM) and the fitted values estimated by the RR model. Then, we studied the genetic background of LSR in order to assess its potential as selection trait for robustness in fattening pigs.

This study indicated that LSR had a low heritability trait and showed strong favorable genetic correlation with growth and unfavorable with FCR and RFI.

Energetic allocation to growth, from concept to model

When faced with one or more environmental disturbances, we can assume that a fattening pig has two types of responses: a change in feed intake pattern or a modification in energy allocation, that is to say a trade-off. These modifications in feed intake or in allocation patterns can affect or not the body weight gain pattern of the animal. This study focused on the second hypothesis with the objective to quantify robustness with a proxy estimated from variations in the energetic allocation over time. To our knowledge, this approach has been little studied in pigs with a selection purpose.

The effects of environmental conditions on feed intake have been widely studied in pigs, mainly the effects of temperature [START_REF] Quiniou | Voluntary feed intake and feeding behavior of grouphoused growing pigs are affected by ambient temperature and body weight[END_REF] and diseases [START_REF] Kyriazakis | Towards a functional explanation for the occurrence of anorexia during parasitic infections[END_REF]. The quantification of robustness or resilience through the analysis of variations in feed intake have also been studied [START_REF] Putz | Novel Resilience Phenotypes Using Feed Intake Data From a Natural Disease Challenge Model in Wean-to-Finish Pigs[END_REF][START_REF] Nguyen-Ba | A procedure to quantify the feed intake response of growing pigs to perturbations[END_REF][START_REF] Homma | Estimation of genetic parameter for feed efficiency and resilience traits in three pig breeds[END_REF]. With respect to robustness, the effect of disturbances on growth pattern has been studied on pigs after weaning [START_REF] Revilla | Towards the quantitative characterisation of piglets' robustness to weaning: a modelling approach[END_REF] or during the finishing period [START_REF] Revilla | Quantifying growth perturbations over the fattening period in swine via mathematical modelling[END_REF].

Conceptually, for a fattening pig, it can be assumed that net energy is allocated between several functions: maintenance, growth (daily protein and lipid deposition) and other functions such as health or thermoregulation (Figure 1). We can assume that the proportion of the total available net energy allocated to each function was regulated by a "valve" which increases or decreases allocation over time. This modulation supposed that there would be a regulation in the allocation of the net energy which would be linked on the one hand to a "desired allocation", dependent on the characteristics of the individual (genotype, age), and on the other hand to an "allocation permitted by the environment".

The model structure does not detail the full process as described in Figure 1, but provides a simple and biological way to represent energy allocation. Based on these assumptions and on data available in the context of the study, we built the model to estimate α t based on daily feed intake and live weight measurements over time. Energy allocation to maintenance was estimated from the metabolic body weight based on the equation proposed by [START_REF] Noblet | Metabolic utilization of energy and maintenance requirements in growing pigs: effects of sex and genotype[END_REF], although this is an average estimate and we thus ignored any variability between sexes, breeds and individuals. The mobilization of lipid reserves, allowing an increase in the net energy available, was not integrated into the model. Indeed, the mobilization of body reserves, apart from glycogen, is rare in growing animals [START_REF] Van Milgen | Partitioning of energy intake to heat, protein, and fat in growing pigs[END_REF]. In this context, we used a pragmatic approach to estimate the energy available for growth at time t. This pragmatic approach is linked to the fact that it is not possible, in a large population, to evaluate precisely for a given pig at a given time, the net energy allocated to maintenance, to additional thermoregulation or physical activity, to protein deposition and to lipid deposition.

In this study, we use DLM regression to model the relation between CNEA it-1 and CW it over time because the DLM makes it possible to characterize allocation coefficient dynamics by a stochastic process, without the requirement for a strong deterministic assumption. With this method, it is possible to determine whether the allocation coefficient was increasing, decreasing or stagnating, without assuming that it followed any given analytical trend, such as a linear, quadratic or cubic trend [START_REF] Michel | Comparison of Statistical Models for Analyzing Wheat Yield Time Series[END_REF]. Our approach takes advantage of the available dlm package in R [START_REF] Petris | Dynamic Linear Models with R, Use R[END_REF] which enabled processing of the full data in a small computation time (around 35 min for the 405104 measurements). In addition, this simple DLM approach could ultimately be expanded to the development of multivariate models or the implementation of fixed (batch, herd…) or random effects [START_REF] Stygar | Monitoring growth in finishers by weighing selected groups of pigs -A dynamic approach[END_REF]. Another property of DLM is to produce one-stepahead forecasts of one or several variables especially to provide early warning to the farmer when forecast error increases [START_REF] Jensen | A multivariate dynamic linear model for early warnings of diarrhea and pen fouling in slaughter pigs[END_REF]. Dynamic linear models look to be powerful tools for analyzing time-series variables.

Estimation of genetic variance in allocation coefficient α t

We assumed that the "desired allocation" of net energy to growth was driven by two components:

the animal's genetic potential and its degree of maturity. In the first step, the objective was to estimate the genetic variance in allocation coefficient α as affected by degree of maturity, which evolves with the age of the pig. To achieve this, we used a RR model to estimate the genetic variance α t and the slope of allocation coefficient to growth over time for each individual. Random regression using orthogonal polynomials models have been widely used in genetics, for example to model feed intake or RFI in pigs or in rabbits [START_REF] David | Genetic modeling of feed intake[END_REF][START_REF] Shirali | Joint analysis of longitudinal feed intake and single recorded production traits in pigs using a novel Horizontal model1[END_REF]. The random regression of order one was chosen to fit the additive genetic and permanent environmental effects, there was no significant improve of the model, based on LRT test, with polynomials of higher order. If the end of the measurement period had been at a weight closer to the maturity weight, a quadratic random regression would probably be more suitable [START_REF] Lewis | The relationship between feed intake and liveweight in domestic animals[END_REF].

The trait α t , describing the allocation of net energy in growth during fattening period, has moderate heritabilities in the same range as those estimated for FCR or RFI and was strongly correlated with them. In a previous study [START_REF] Lenoir | Towards the characterisation of animal robustness by dynamic energy allocation indicators in fattening pigs[END_REF], the trait considered was the average value of α t and not the repeated estimates, the heritability obtained was lower (0.16±0.05) but was estimated from a different dataset. For the trait RFI, the study of [START_REF] David | New residual feed intake criterion for longitudinal data[END_REF] showed heritabilities ranging from 0.19±0.06 to 0.28±0.06, using a RR model with weekly estimation over 10 weeks in pigs.

Genetic parameters for LSR and production traits

The heritability of the trait LSR, which characterizes the environmental variance of α t , was low but non null. Generally, the heritability of environmental variance is lower than 0.10 [START_REF] Mulder | Prediction of Breeding Values and Selection Responses With Genetic Heterogeneity of Environmental Variance[END_REF]. This estimate for LSR was in the same range as those published on different traits but with a similar REML method such as: 0.012±0.004 for rabbits birth weight [START_REF] Garreau | Results of four generations of a canalising selection for rabbit birth weight[END_REF], 0.024±0.002 for litter size in pigs [START_REF] Sell-Kubiak | Evaluation of the phenotypic and genomic background of variability based on litter size of Large White pigs[END_REF], 0.029±0.003 to 0.047±0.004 for broiler chicken body weight [START_REF] Mulder | Estimation of genetic variation in residual variance in female and male broiler chickens[END_REF]. Other studies have been based on the analysis of the logtransformed variance (LnVar) of residuals resulting from a modeling of one time-series variable.

This LnVar trait seems to have higher heritabilities than LSR: from 0.20 to 0.24 for milk production [START_REF] Poppe | Validation of resilience indicators by estimating genetic correlations among daughter groups and with yield responses to a heat wave and disturbances at herd level[END_REF] or from 0.10 to 0.12 for egg production [START_REF] Bedere | Using egg production longitudinal recording to study the genetic background of resilience in purebred and crossbred laying hens[END_REF]. Some authors have used the double hierarchical generalized linear model (DHGLM) allowing in the same structural model to estimate the mean of the trait and its residual variance [START_REF] Rönnegård | Genetic heterogeneity of residual variance -estimation of variance components using double hierarchical generalized linear models[END_REF].

In order to perform the multi-trait analysis, we chose to use a 2-step approach rather than the DHGLM. In theory, the DHGLM model would make it possible to estimate a residual genetic variance close to the results obtained by our two-step approach. However, it is much more complex mathematically and has convergence issues, making it difficult to use in an operational breeding program (Berghof et al., 2019a).

Heritability estimates for ADG and RFI were consistent with those reported in literature for Pietrain or Large-White pigs raised in similar environmental conditions, which varied from 0.33 ±0.03 to 0.48 ±0.06 and from 0.21 ±0.03 to 0.34 ±0.05 [START_REF] Saintilan | Genetics of residual feed intake in growing pigs: Relationships with production traits, and nitrogen and phosphorus excretion traits[END_REF][START_REF] Déru | Impact of a highfibre diet on genetic parameters of production traits in growing pigs[END_REF]. For carcass traits (BF100 and LD100), heritabilities were also consistent with the values estimated by [START_REF] Sourdioux | Estimation des paramètres génétiques pour des critères de croissance et carcasse en race Piétrain et en lignée composite Piétrain négative halothane[END_REF] and [START_REF] Saintilan | Genetics of residual feed intake in growing pigs: Relationships with production traits, and nitrogen and phosphorus excretion traits[END_REF] in the Pietrain breed (BF100: 0.38 to 0.48; LD100: 0.25 to 0.34). Our estimate of heritability for FCR was lower than the heritabilities presented by [START_REF] Saintilan | Genetics of residual feed intake in growing pigs: Relationships with production traits, and nitrogen and phosphorus excretion traits[END_REF], [START_REF] Gilbert | Review: divergent selection for residual feed intake in the growing pig[END_REF] and [START_REF] Déru | Impact of a highfibre diet on genetic parameters of production traits in growing pigs[END_REF], which varied from 0.30 ±0.0 to 0.47 ±0.08.

Genetic correlations between robustness and production traits

The growth trait ADG was strongly correlated with LSR. In the present rearing conditions, an animal's ability to be robust, i.e., to have low LSR value, is strongly linked to its ability to express optimal growth regardless of the environment. Growth has been a major selection trait in the Pietrain breed for over 20 years, and lack of growth was a major cause of culling at testing or of non-selection. Nonetheless, even if the correlation was strong, it was not equal to 1, which implies that the trait LSR added an additional information regarding the robustness of the animal compared to ADG. Thus, if selection is made using these traits, they would allow us to improve animal's robustness more than if the selection is made only on growth traits.

There were strong and unfavorable relationship between LSR and feed efficiency traits, FCR and RFI. This could be related to the positive correlation between ADG and FCR, which was affected by the way these two traits were estimated (Lenoir et al., 2022a). The traits ADG and FCR used in selection were measured over an identical period for all pigs but were not standardized between starting and finishing weights. Accordingly, some of the animals tested reached their mature weight before testing, which led to a drop in feed conversion or residual feed intake even if they had previously a strong growth. Thus, there were two different types of finisher pigs with low FCR or RFI: those which had a strong growth but did not approach their mature weight during the testing period, and those with a low daily feed intake associated with a low, near maturity, growth (Lenoir et al., 2022a). We performed an additional analysis where we standardized the trait FCR between 40 and 100kg, the genetic correlation with LSR remained unfavorable but less strong, -0.34±0.14. The standardization of the trait FCR modified the genetic correlation with ADG from moderately unfavorable, 0.52±0.06, to close to zero or slightly favorable, -0.08±0.09. The correlation between LSR and FCR or RFI could indicate that the most robust pigs during the testing period were not the most efficient because they allocate a part of energy to other functions or maintenance. Indeed, a selection for low RFI could impact the ability of the animals to modify their allocation of energy to other functions to cope with environmental challenges [START_REF] Gilbert | Review: divergent selection for residual feed intake in the growing pig[END_REF]. This antagonism between short-term efficiency and resilience has been put forward by [START_REF] Friggens | Review: Deciphering animal robustness. A synthesis to facilitate its use in livestock breeding and management[END_REF]. In this situation, it would seem that there is a compromise that does not make it possible to increase robustness relatively easily without loss of selection response in feed efficiency. In contrast, several studies have shown through divergent selection experiments on RFI, that animals from Low RFI line (LRFI) adapted better to environmental challenges or at least are not disadvantaged compared to animals from High RFI line (HRFI). [START_REF] Chatelet | Impact of hygiene of housing conditions on performance and health of two pig genetic lines divergent for residual feed intake[END_REF] showed that the health, growth performance and feed intake of animals from the LRFI line were less impacted than those of animals born from the HRFI line under poor hygienic conditions. In the same selection experiment, the risk of being culled between 70 days of age and slaughter was 1.8 times less in the LRFI line compared to the HRFI line [START_REF] Gilbert | Review: divergent selection for residual feed intake in the growing pig[END_REF]. In another experience of selection [START_REF] Dunkelberger | Response of pigs divergently selected for residual feed intake to experimental infection with the PRRS virus[END_REF] suggested that pigs for LRFI were more robust to PRRSV challenges; their growth was less affected and they was less affected. These results seem to contradict the resource allocation theory and the genetic correlation estimated in our study. This study was carried out on Pie NN line, a sire line, and the different selection experiments on RFI were realized with animals from Large-White (or Yorkshire), a dam line. The Pietrain sire line had been created and selected for several generations on objectives of improving feed efficiency, growth and carcass characteristics, potentially to the detriment of the other traits, such as robustness. Due to these characteristics and orientations, it can be assumed that there is a different allocation pattern between these lines.

Genetic correlations between robustness and BF100 were slightly unfavorable. We can suppose that the capacity to be robust could be associated with more important body reserves allowing the animal to face perturbations.

Relation between EBV LSR classes and collected phenotypes

Our study shows that model longitudinal energetic allocation to growth offers the opportunity to develop a proxy of robustness that is heritable. Further, this proxy has to meet the expectations of pig farmers, that is to say, it should identify animals that faced to environmental disturbances and were present for testing in good health and with the least amount of medical injections. The analysis of the relationship between EBV LSR quartiles and phenotypes routinely collected on farms shows the most favorable situation for the most robust animals, i.e., those from the quartile with the weakest EBV LSR (Q1). Including LSR in the breeding goal would be an opportunity to improve the robustness qualities of Pie NN line for the fattening period, in spite of the low heritability of LSR. However, these results are evaluated over a short period of animal's life, it would be appropriate to investigate the effects of a selection on the LSR trait over the whole lifespan of related animals (dam, sire, pure or crossbred offspring). In a following step, it could be relevant to study the link between the LSR trait and the reproductive performances of boars (spermatic production) or females (fertility, productive longevity, survival).

Environmental conditions

This studied was carried out in a higher biosecurity environment than regular farms, related to the fact that a breeding company cannot take any risks with a purebred nucleus. The other environmental conditions (feed characteristics, barn design, density…) were close to those found in production farms in France, that is, designed to minimize exposure to environmental challenges.

When designing the selection conditions there is a need to balance between conditions that allow full expression of performance and meet sanitary requirements versus conditions that favor expression of robustness. Even though these environments are qualified as favorable, the animals are subjected to stresses which can be chronic (social stress, heat wave). Rear animals under challenging conditions seems to allow better phenotyping of the robustness of the animals [START_REF] Gilmour | Genetic Parameters for Resistance to Non-specific Diseases and Production Traits Measured in Challenging and Selection Environments; Application to a Rabbit Case[END_REF]. The difficulty of having conditions to evaluate robustness while evaluating production 21 potential could be partly overcome by the use of short-term challenges, such as feeding challenges.

Indeed, offspring of these purebred pigs, selected in one type of environment, are likely to be reared in harder and more variable environments impacting robustness expression. This relationship between the robustness expression and diverse rearing conditions cannot be dissociated from Genotype x Environment (GxE) interaction [START_REF] Falconer | Introduction to Quantitative Genetics[END_REF]. This interaction that may cause reranking of sires, has a greater impact on traits based on variances than on traits based on means [START_REF] Bedere | Using egg production longitudinal recording to study the genetic background of resilience in purebred and crossbred laying hens[END_REF]. The acquisition of data on related animals reared in farms newly equipped with AFS makes it possible to consider evaluating the effects of the GxE interaction.

In this study, we proposed an approach for characterizing the robustness through the variability in the allocation. However, when studying the allocation pattern, it is important to also assess the acquisition trajectory (van Noordwijk and [START_REF] Van Noordwijk | Acquisition and Allocation of Resources: Their Influence on Variation in Life History Tactics[END_REF][START_REF] Friggens | Review: Deciphering animal robustness. A synthesis to facilitate its use in livestock breeding and management[END_REF]. In a routine selection approach, it would be relevant to add to the LSR trait, a trait making it possible to characterize the robustness on acquisition

Conclusions

The trait LSR could be interpreted as an indicator of the response of the animal to perturbations/stress, that is to say a robustness proxy. This study shows that LSR has a low heritability but that it is possible to set up a selection on this trait. We found that this trait is favourably genetically correlated with a growth trait (ADG) and unfavourably with feed efficiency traits (FCR and RFI). Estimation of the economic value of LSR trait is a key issue before adding this trait in breeding goals. Furthermore, improving robustness qualities also meets societal expectations, the economic value of which is difficult to quantify.

List of abbreviations

Figure 2

 2 Figure 2 displays the α t trajectories of two animals exhibiting different patterns. The first animal on

FiguresFigure 1 .Figure 2 .Figure 3 .

 123 Figures

Figure 4 .

 4 Figure 4. Distribution of percentages of pigs that can be selected (Selectable), that didn't receive any antibiotic or anti-inflammatory injection (No injection) or that were "Selectable" without receiving any antibiotic or anti-inflammatory injection during the testing period (Selectable without injection) depending of their estimated breeding value for robustness indicator (LSR) quartile. Q1: pigs with lowest EBV LSR values, i.e., higher robustness genetic potential; Q4: pigs with highest EBV LSR values, i.e., lower robustness genetic potential. Bars with different letters are significantly different (P < 0.05).

Table 1 .

 1 Descriptive statistics of the variables recorded or estimated on fattening pigs

	Tables
	738
	739
	740
	741
	742
	743
	744
	745
	746
	747
	748

1 IBW: initial body weight; TBW: terminal body weight; ADG: average daily gain; FCR: feed conversion; DFI: daily feed intake; RFI: residual feed intak; BF100: backfat thickness estimated at 100kg liveweight; LD100: longissimus dorsi thickness estimated at 100 kg liveweight; α t : allocation coefficient to growth; e t : residual of RR model; LSR= log-squared residual, robustness indicator.

Table 2 .

 2 Estimates of heritability (h²), common litter effect ratio (c²), permanent environmental effect ratio (p²) and phenotypic variance (Vp) for the traits recorded (± standard error)

	755
	756
	757
	758
	759
	760
	761
	762
	763

Table 3 .

 3 Estimates of genetic correlations (r²a ± standard error) between robustness trait (LSR) and

	production traits
	769
	770
	771
	772
	773
	774
	775
	776

BF100= backfat thickness estimated at 100kg liveweight; LD100= longissimus dorsi thickness estimated at 100 kg liveweight; ADG= average daily gain; FCR= feed conversion ratio; LSR= log-squared residual, robustness indicator

Acknowledgements

The authors would like to acknowledge the breeding company Axiom for funding GL's Ph.D thesis.

We also acknowledge the technicians of AXIOM's testing station at La Garenne for their implication for data collection. We also thank Céline Lebeux and Kambiz Kashefifard for managing data collection on farm and development of the database to store and share the data.

Funding

This project was supported by ANRT (Association Nationale Recherche Technologie) with a CIFRE Doctoral fellowship (2019/0705).

Availability of data and materials

The datasets analysed during the current study are not publicly available because they are part of the commercial breeding program of AXIOM. However, they are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate Specific Experimental Animal Care and Use Committee approval was not needed because all the data used in this study were obtained from preexisting databases provided by AXIOM. The data used were from animals raised under commercial conditions that were cared for according to EU-Council directive 2008/120/EC of 18 December 2008 laying down minimum standards for the protection of pigs (http://data.europa.eu/eli/dir/2008/120/oj).

Consent for publication

Not applicable

Competing interests

RMT, NF and ID declare that they have no competing interests. GL and LFG are employed by AXIOM. The datasets are of interest to commercial targets of AXIOM, but this interest did not influence the results in this manuscript in any matter.

Authors' contributions


Santiago Lascano

Arie Van Der Lie

Marie Lopez
email: marie.lopez@cnrs.fr

Unexpected one-pot formation of lactam oximes from amino-hydroxamic esters

Keywords: step one-pot cyclisation, Fmoc deprotection, amino-hydroxamic esters

Unexpected one-pot intramolecular formation of lactam oximes from the corresponding aminohydroxamic ester in presence of amine is described. Several reaction parameters were studied and the importance of the base and the size of the resulting cycle were shown. This reaction, proceeding in high yield in described conditions, and can thus be considered as a new synthetic approach to prepare lactam oximes in a one-pot manner and in mild conditions.

We thank La Maison de la Chimie for the post-doctoral fellowship for SL.

Keywords: Lactam oximes • two

Introduction

In the context of our work on hydroxamic acids for medicinal chemistry purposes, we identified serendipitously a new synthesis pathway to prepare lactam oximes from easily accessible linear protected alkyl amino-hydroxamic acid derivatives. Several classes of lactam oximes were previously reported and mainly carbohydrate-based lactam oximes. For instance, such derivatives were shown of high interest for selective inhibition of Cex class of xylanases [1] and for -amylase inhibition, [2] e.g. GIHL compound [3]. More recently, D-gluconhydroximo-1,5-lactam and its oxime substituted derivatives were described as potent chaperone of β-glucocerebrosidase in Gaucher disease. [1] Interestingly, glucolactam oxime was identified as transition-state mimic for glucosidases. [4] Synthesis of such carbohydrate-based lactam oximes, mainly proceeded through thiol derivatives and via carbohydrate synthesis methodology in more than 10-steps. Several lactam oximes other than carbohydrate were also described. Synthesis of lactam oxime from quinolinone, leading to 6-and 7-membered ring derivatives, [5] and from N-oxide pyridines [6] were also reported. Lactam oxime were also reported as potent HSP90 inhibitors. [START_REF] Chen | Ton-Nu Oxim derivatives as HSP90 inhibitors[END_REF] Finally, an eleven-steps synthesis of lactam oxime squalene and its interest as squalene-hopene cyclase compare to amidoxime analogue was described. [START_REF] Ganem | [END_REF] Therefore, despite their potential interest, little is described about lactam oxime synthesis and reported synthesis occur in numerous steps or in harsh conditions. Thus, in this work, we reported a new synthesis pathway of lactam oximes derivatives and studied various synthesis parameters. Interestingly, we identified optimised conditions for 5-, 6-and 7-membered ring derivatives and obtained crystal structure for 5 and 6-membered ring derivatives, compounds 7 and 8, respectively.

Results and discussion

Synthesis

In our synthetic pathway to prepare enzymatic inhibitors bearing hydroxamic acid moieties, one step was a routine Fmoc deprotection of compounds 1-3 to the corresponding amines 4-6 with piperidine in dichloromethane (Scheme 1). However, isolated yields of the free amine were surprisingly low, in particular for amine 5. LC-MS analysis of the reaction mixture showed an unidentified side-product in large amount for the deprotection of compound 2 and in lesser amount for deprotection of compounds 1 and 3. Scheme 1. Initial reaction conditions for Fmoc deprotection.

Formation of lactam oximes from the corresponding linear di-protected amino-hydroxamic acids is interesting as it is the only example, to our knowledge, of this kind of condensation reaction happening in a one-pot manner. The described formation of these compounds from an amino compound and a hydroxamic ester involves the use of harsh chlorinating reagents such as PCl5 [9] or POCl3 [10], while the condensation of a lactam with an alkoxyamine has been described with triethyloxonium tetrafluoroborate, [5] or by thionation, [11][12] both cases corresponding to a formal activation of the carbonyl. In order to facilitate the synthesis of lactam oxime derivatives, there is an interest of developing a two-step one-pot cyclisation of amino-hydroxamic esters and we decided to further investigate this unexpected reaction.

NMR analysis and X-ray crystal structures

To ascertain the identity of the side-product, compounds 7 and 8, 5-and 6-membered rings, respectively, were isolated and characterised by NMR analysis. While 1 H NMR spectra of linear 5 and cyclic 8 where fairly similar, only displaying slight shifts, 13 C NMR spectra of cyclic compounds showed an important upfield shift of the quaternary sp 2 hydroxamate/lactam oxime carbon of around 20 ppm, consistent with a less electronegative nitrogen replacing the oxygen, resulting in a more shielded carbon (Figure S1). Finally, correlation of the protons at the end of the chain with the sp 2 carbon, was observed in the HMBC spectra of 8 (Figure 1) but absent in the case of 5 (Figure S2). This is a clear indication of the cyclic nature of compound 8. To confirm the structure of compounds 7 and 8, a lot of effort was put to obtain crystals for both cyclic derivatives 7 and 8 and their structures was definitely confirmed by the crystal structure (Figure 2 and3). The 7-membered ring 9 was detected by LC-MS, but was produced in very low amounts and could not be isolated nor characterised.

Interestingly, x-ray crystal structure shows that exocyclic C-N bonds are shorter (1.289(2), 1.288(2) and 1.294(2) Å for 7 and 8 respectively) than endocyclic ones (1.345(2), 1.341(2) and 1.353(2) Å for 7 and 8 respectively), indicating that exocyclic C-N bond has a stronger double bond character. Intramolecular N-H•O distances (2.341, 2.288 and 2.160 Å for 7 and 8, respectively) are consistent with weak hydrogenbonding, but the torsion angles (-143.85/-179.15° and -167.02° for 7 and 8 respectively) seem to indicate that, at least in solid state, this bond is very weak (Table S1). A standard geometry check against structures with similar fragments in the Cambridge Structural Database [13] using MOGUL program [14] shows that almost all bond distances, valence and torsion angles can be considered to be normal, except N2-C3-C7(122.53(1)°) and N28-C29-C33 (123.04(1)°) valence angles in the structure of 7 (Figure 2A). These angles are considerably smaller than the one of similar fragments, approximately 130°, notably those with a similar pyrrolidine motif in the structure. Intramolecular N-H…O bonds seem to play an important role here in enlarging the N-C-C angles, since by enlarging the relevance criterion in the MOGUL query slightly a small cluster was found with similar fragments without pyrrolidine rings containing N-C-C angles close to those encountered in 7, but with a neighbour oxy group similar to O1 and O27 in Figure 2A (see SI for more details). The structural cohesion in 7 originates from one weak intermolecular NH…N interaction (2.58(2) Å and ∠ N-H…N=132.5(1) °) and a number of even weaker CH… and NH… interactions. Structure of 8 does not have any classical intermolecular hydrogen bond, and its structural cohesion appears to arise from very weak CH… interactions only.

Influence of reaction conditions

After having ascertained the identity of the cyclic compounds, and in order to evaluate the influence of different parameters in the deprotection and cyclisation steps, the reaction was tested on analytical scale (typically around 2 mg of compound 2 in 1.2 ml of a 2:1 solvent/base mixture) and followed by LC-MS. The figures show the progression of the percentage of the cyclized compounds over the sum of cyclic and linear deprotected compound, as measured by the integration of the peaks obtained on the 214 nm UV chromatogram. Unless otherwise noted, reaction occurred from protected compound 2 to linear and cyclic compounds 5 and 8 (6-membered ring), respectively, solvent is dichloromethane, base is piperidine (~1200 equivalents), and temperature is 30 °C.

Influence of the solvent

A selection of solvents was tested, based on their polarity, proticity and miscibility with water, namely toluene, chloroform, dichloromethane (DCM), tetrahydrofuran (THF), methanol, acetonitrile and N,Ndimethylformamide (DMF) (Table 1). In all cases, the deprotection was complete in the first measurement, i.e. after 30 minutes and proportion of proportion of cyclic vs linear compounds over time was measured. The results are shown in Figure 4. Importantly, in all solvents full conversion was observed after 30 min. Regarding the cyclisation reaction, the slowest cyclisation rates were observed for DMF (t50≈ 90 h), acetonitrile (t50≈ 60 h) and chloroform (t50≈ 40 h) with a linear kinetic. In DCM, methanol, toluene and THF, cyclisation rates were much faster with little effects of the solvents and t50 values varying from 12 h to 16 h.

Considering solvent parameters (Table 1), it appears that high dipole moment () and high dielectric constant () unfavoured cyclisation. [a] ref. [15]; [b] ref. [START_REF] Reichardt | Welton Empirical Parameters of Solvent Polarity[END_REF]; [c] ref. [START_REF] Kumari | [END_REF] Influence of the temperature Temperature-dependence experiments were carried out in DMF rather than in DCM in order to have access to a large range of temperature. This also gave more room for improvement in the cyclisation reaction. Reaction from 2 were carried out at 30 °C, 60 °C and 90 °C (Figure 5). Unsurprisingly, an increase of the temperature accelerates cyclisation rate. Increasing temperature from 30 °C to 60 °C strongly accelerate the reaction whereas almost no difference was observed between 60 °C and 90 °C. Therefore, in DMF, optimal temperature for cyclisation reaction is 60 °C.

Influence of the base

To study the impact of the base in deprotection and cyclisation reaction, a selection of cyclic, acyclic, secondary and tertiary nitrogenous bases, namely piperidine, morpholine, N,N-diisopropylethylamine (DIPEA), and N,Ndiisopropylamine (DIPA), were selected. In order to avoid side-reactions from the dibenzofulvene side-product, inorganic bases and non-nucleophilic bases such as DBU were discarded. Unlike solvent and temperature, the choice of base has an important effect on the deprotection step (Figure 6). While piperidine leads to extremely fast reaction, with complete Fmoc deprotection under 30 min, morpholine leads to slightly longer reaction times and both DIPEA and DIPA lead to low amounts of deprotected compound 5 (Figure 6 dotted lines), which is consistent with literature. [START_REF]Fields Methods for Removing the Fmoc Group[END_REF] Notably, regarding cyclisation kinetics (Figure 6 plain lines), it also depends on the base. With piperidine and morpholine fast cyclisation rates with similar kinetics were observed. Using DIPEA, cyclisation rate is low but considering the low deprotection yield, this might not be representative. However, interestingly, with DIPA, an initial induction time was observed with low amount of cyclic compound until about 50 h before cyclisation actually occurred whereas the deprotection rate was regularly increasing up to 90%. Thus, aliphatic base used for the deprotection step has a crucial impact on this two-step one-pot reaction. Independently of the pKa (Figure 7), a cyclic aliphatic base led to a higher deprotection yield and favour the cyclisation compare to non-cyclic bases that seems to hinder cyclisation.

Influence of the chain length

As mentioned previously, influence of chain length in cyclisation reaction was first observed when identifying the side-product, hypothesising that the formation of a cyclic compound could explain the differences for 7, 8 and 9. In order to quantify this difference, deprotection and cyclisation of compounds 1, 2 and 3 were followed (Figure 8). As for the previous results using piperidine as a base, complete deprotection of 1-3 was observed after 30 min. Cyclisation rates of compounds 4-6 indicate very clearly that the 6-membered ring 8 is formed much faster (t50≈ 12 h) than its 5-and 7-membered analogues compounds 7 and 9, respectively with t50> 76 h. This is obviously due to the higher stability of the 6-membered ring but very interestingly, these results showed that 5-and 7-membered lactam oximes can be obtained although after longer reaction time.

Cyclisation from starting from deprotected analogues

In order to decipher this one-pot deprotection/cyclisation synthesis and to better understand lactam oxime formation, we decided to follow the condensation starting directly from a Fmoc deprotected linear analogue.

Compound 5 was first considered but its isolation proved to be particularly difficult, as it tended to readily cyclise to 8 during the purification steps. Therefore, in order to overcome this problem, and considering that a slower reaction is easier to follow, we decided to conduct these experiments starting from deprotected linear compound 4 (Scheme 2).

Scheme 2. Synthesis of lactam oxime 7 from Fmoc-deprotected amino-hydroxamic esters 4.

Cyclisation of 4 was studied at 30 °C in dichloromethane, toluene, dichloromethane/piperidine 2:1, toluene/piperidine 2:1, as well as at 60°C in toluene and toluene/piperidine 2:1. The results are shown in Figure 9. Starting from Fmoc-deprotected compound, cyclisation is slightly faster in toluene than in DCM. As in temperature dependence experiments for the cyclisation of 5 to 8 (Figure 5), results show that a higher temperature increases dramatically cyclisation rate with 85 % of cyclic compound 7 after 3 h in toluene at 60 °C compare 3 % at 30 °C. However, unexpectedly, the presence of piperidine do not lead to a higher cyclisation rate, but instead prevents the formation of cyclic analogue. This was also observed at higher temperatures, where the presence of piperidine led to 2 % of cyclisation after 2 h, instead of 71 % in toluene without base. Therefore, in the one-pot deprotection/cyclisation reaction, piperidine ensure the Fmoc deprotection but is not involved in the cyclisation step. A hypothesis for the cyclisation mechanism is presented Scheme 3 but is still to be confirmed.

Cyclisation yield

After studying these reaction parameters, we then selected the best identified conditions for the cyclisation (Scheme 4) and carried out the reaction on larger scale to prepare purified cyclic compound 8 in order to determine the yield of the overall reaction. Considering the available reactants, a 100 mg scale was used which is further representative of scales commonly used in medicinal chemistry program. This first trial, led to a surprisingly low yield of 38 %. We hypothesised that this low yield was linked to the presence of a highly apolar side-product, visible by LC-MS. Isolation of the unknown compound proved arduous and we could not come up with a satisfactory hypothesis for its structure, but we speculated that it was the result of the reaction of free dibenzofulvene -released from the reversible adduct formed with piperidine -with the trityl-protected hydroxamic acid. In order to circumvent this problem, the reaction was run in the presence of β-mercaptoethanol, as thiols are known to form more stable adducts with dibenzofulvene. [START_REF] Ueki | [END_REF][20] Deprotection and cyclization in dichloromethane/piperidine/β-mercaptoethanol did indeed result in a higher yield of 54 %, which is an interesting result to consider this reaction as a new way to access lactam oximes. Routine treatment of the resulting protected lactam oxime 8 in TFA in DCM yielded the corresponding deprotected lactam oxime 10 characterised by MS and NMR.

Conclusion

In conclusion a two-step one-pot synthesis for the preparation of trityl-protected lactam oximes was described. The study showed that for optimal conditions were the use of DCM, toluene, THF or methanol as solvent, with piperidine or morpholine and at 60 °C. Further deprotection of the trityl group can then be carried out using routine TFA in DCM to access lactam oximes.

Experimental Section

X-ray crystal structure. Crystal evaluation and data collection for 7 and 8 were performed on a Bruker Venture diffractometer with a micofocus Cu-K source using the APEX3 [21] program. SAINT [21] was used for the integration of the data using default parameters, for the empirical absorption correction using spherical harmonics employing symmetry-equivalent and redundant data, and the correction for Lorentz and polarization effects. The crystal structure was solved using the ab initio iterative charge flipping method with parameters described elsewhere [22] using the SUPERFLIP program [23] and it was refined using full-matrix least-squares procedures on |F| 2 as implemented in CRYSTALS [24] on all independent reflections with I>-3(I). The absolute structure for the noncentrosymmetric structure of 8 could not be determined reliably because of the absence of elements with sufficient anomalous scattering. The H atoms were all located in a difference map, but repositioned geometrically. They were initially refined with soft restraints on the bond lengths and angles to regularize their geometry (C---H in the range 0.93-0.98 Å) and Uiso(H) (in the range 1.2-1.5 times Ueq of the parent atom), after which the positions were refined with riding constraints. [25] CCDC 2143586 (for Cpd 7) and 2143587 (for Cpd 8) contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/structures. General synthesis methods. Briefly, reagents for synthesis were purchased from Fluka, Sigma-Aldrich, and TCI, salts of the best grade available from Fluka or Sigma-Aldrich and used as received. Unless stated otherwise, flash chromatography was carried out Interchim PuriFlash 430 Instrument using 50 µm irregular silica cartridges (40-60 µm). Analytical TLC was performed on silica gel 60 F254 (Merck). Analytical, reversed-phase HPLC was performed on a Thermo Scientific, UltiMate3000 system equipped with a C18 reversed-phase column (Thermo Scientific, Hypersil GOLD aQ, 2.1 x 50 mm, 1.9 μm) eluting with a linear gradient of MeCN in H2O containing 0.1% formic acid at a flow rate of 0.5 ml.min -1 . 1 H and 13 C NMR spectra were recorded on a Bruker 400 MHz spectrometer (Bruker DRX-400) and are reported as chemical shifts (δ) in ppm relative to (residual) solvent signal. Spin multiplicities are reported as a singlet (s), doublet (d), triplet (t), quartet (q), doublet of doublets (dd), doublet of quartets (dq) with coupling constants (J) given in Hz, or multiplet (m). 13 C resonances were assigned with the aid of additional information from DEPT 135, HSQC and HMBC spectra. LCMS analyses were performed on an instrument equipped with a Shimadzu LC-20AD XR pump, SPD-M20A diode array detector. A C18 reversed-phase column (Phenomenex, Kinetex polar C18, 3 x 750 mm, 2.6 μm, 100 Å) was used. Elution was performed using a binary gradient (solvent A: H2O + 0.1% formic acid; solvent B: ACN + 0.1% formic acid). Low resolution mass spectra were acquired using electrospray in positive and negative modes and are reported as mass-per-charge ratio m/z (intensity in %, [assignment]).

Compound 1. To a solution of S4 (202 mg, 621 µmol), EDCI•HCl (178 mg, 927 µmol) and HOBt (98 mg, 730 µmol) in CH2Cl2 (15 ml) and DMF (5 ml), was added DIPEA (280 µl, 1.6 µmol) and then TrtONH2 (213 mg, 772 µmol). The mixture was then left under stirring at rt overnight. The solution was then covered with water and extracted with CH2Cl2. The organic fractions were collected, dried over Na2SO4, filtered, and concentrated. Purification by flash column chromatography (SiO2, CH2Cl2/MeOH 19:1) afforded compound 1 as a colourless solid (152 mg, 42%). 1 Compound 2. To a solution of S5 (255 mg, 750 µmol), EDCI•HCl (143 mg, 750 µmol) and HOBt (144 mg, 1.07 mmol) in DMF (15 ml), was added TrtONH2 (400 mg, 1.45 mmol). The mixture was then left under stirring at rt overnight. The solution was then covered with brine and extracted with CH2Cl2. The organic fractions were collected, dried over Na2SO4, filtered, and concentrated. Purification by flash column chromatography (SiO2, CH2Cl2/MeOH 19:1) afforded compound 2 as a colourless solid (332 mg, 74%). 1 One-pot Fmoc-deprotection and cyclisation in analytical scale. Compound 1, 2 or 3 (exactly ca. 2 mg) was solubilised in the appropriate solvent in LC-MS vial and selected base was added (1 ml final volume). Reaction mixture was incubated at appropriate temperature and was monitored overtime by LC-MS. Deprotection rate as well as proportion of cyclic vs. linear compounds were calculated from HPLC analysis by peak integration on the 214 nm UV chromatogram. Compound 8. Compound 2 (101.5 mg, 178.2 µmol) was solubilised in DCM (6 ml). β-Mercaptoethanol (3 ml) and piperidine (3 ml) were added and the reaction mixture was stirred for 30 h at rt. Reaction mixture was diluted in DCM and washed with NH4Clsat (1). Aqueous layer was back-extracted with DCM (2), organic layers were combined, dried over Na2SO4, filtered and concentrated under vacuum. Purification of the crude product by flash chromatography (2:3 EtOAc/hexane) afforded 8 (34,6 mg, 97.0 µmol) with 54% yield. 1

Figure 1 .

 1 Figure 1. HMBC NMR analysis of cyclic compound (8) showing H-5/C-1 correlation.

Figure 2 .

 2 Figure 2. Molecular structure of compounds 7 (A) and 8 (B) in ORTEP-style. Atomic displacement ellipsoids have been drawn at 50% probability level. Atoms which are referenced to are labelled.

Figure 3 .

 3 Figure 3. Best overlay of both independent molecules in the asymmetric part of the crystallographic unit cell of compound 7 structure. rmsd value is 0.1809 Å and maximum deviation 0.3918 Å. Both molecules are inversionrelated in this view.

Figure 4 .

 4 Figure 4. Solvent dependence of compound 5 cyclisation into compound 8, in solvent/piperidine 2:1 v/v at 30 °C. Ratio of cyclic compound 8 over the sum of linear compound 5 and cyclic compound 8 is measured by HPLC analysis by peak integration on the 214 nm UV chromatogram.

Figure 5 .

 5 Figure 5. Temperature dependence of compound 5 cyclisation into compound 8, in DMF/piperidine 2:1 v/v. Ratio of cyclic compound 8 over the sum of linear compound 5 and cyclic compound 8 is measured by HPLC analysis by peak integration on the 214 nm UV chromatogram.

Figure 6 .

 6 Figure 6. Base dependence of Fmoc-deprotection yield (dotted lines) and compound 5 cyclisation into 8 (plain curves), in DCM/base 2:1 v/v at 30 °C. Ratio of cyclic compound 8 over the sum of linear compound 5 and cyclic compound 8 as well as deprotection yield are measured by HPLC analysis by peak integration on the 214 nm UV chromatogram.

Figure 7 .

 7 Figure 7. Structure and pKa of aliphatic amines using for the two-step one-pot lactam oxime formation (from Broadwell tables).

Figure 8 .

 8 Ring-size dependence of the cyclization of 4-6 into 7-9, in DCM/piperidine 2:1 v/v. Ratio of cyclic compounds 7-9 over the sum of linear 4-6 and 7-9 is measured by HPLC analysis by integration of peaks obtained on the 214 nm UV chromatogram.

Figure 9 .

 9 Figure 9. Temperature and base dependence of the cyclisation of Fmoc-deprotected linear compound 4. Ratio of cyclic compounds 7 over the sum of linear compound 4 and cyclic compound 7 is calculated from HPLC analysis by peak integration on the 214 nm UV chromatogram.

Scheme 3 .

 3 Scheme 3. Mechanism hypothesis of ,-amino-trityl protected hydroxamic acid cyclisation.

Scheme 4 .

 4 Scheme 4. Synthesis of lactam oxime 10 using one-pot deprotection cyclisation reaction.

  H NMR (400 MHz, CDCl3, n/n: stereoisomeric peaks): 8.24/8.00 (s, 1H), 7.80 (d, 3 J (H,H) = 7.5, 2H), 7.65 -7.57 (m, 2H), 7.56 -7.48 (m, 3H), 7.43 (t, 3 J (H,H) = 7.5, 2H), 7.40 -7.30 (m, 14H), 5.05 -4.62 (m, 1H), 4.47 -4.36 (m, 2H), 4.30 -4.18 (m, 1H), 3.12 -2.83 (m, 2H), 1.93 -1.43 (m, 4H); 13 C NMR (101 MHz, CDCl3) δ= 176.7 (C), 156.3 (C), 143.8 (C), 141.3 (C), 141.0 (C), 129.1 (CH), 128.2 CH), 127.9 (CH), 127.7 (CH), 127.1 (CH), 125.1 (CH), 120.0 (CH), 93.5 (C), 66.4 (CH2), 47.3 (CH), 40.5 (CH2), 28.7 (CH2), 23.2 (CH2); Rf (CH2Cl2/MeOH 9:1)= 0.68; ESI-MS m/z= 1187 [2M+Na] + , 605 [M+Na] + , 583 [M+H] + , 243 [Trt] + .

3 .

 3 4 (C), 146.9 (C), 144.0 (C), 141.3 (C), 129.1 (CH), 128.2 (CH), 128.0 (CH), 127.3 (CH), 127.1 (CH), 125.0 (CH), 120.0 (CH), 93.5 (C), 66.5 (CH2), 47.3 (CH), 40.5 (CH2), 30.7 (CH2), 29.2 (CH2), 20.4 (CH2). Rf (CH2Cl2/MeOH 9:1)= 0.75; ESI-MS m/z= 619 [M+Na] + , 243 [Trt] + .Compound To a solution of S6 (201 mg, 569 µmol), EDCI•HCl (164 mg, 855 µmol) and HOBt (88 mg, 648 µmol) in CH2Cl2 (15 ml) and DMF (5 ml), was added DIPEA (260 µl, 1.5 µmol) and then TrtONH2 (198 mg, 719 µmol). The mixture was then left under stirring at rt overnight. The solution was then covered with water and extracted with CH2Cl2. The organic fractions were collected, dried over Na2SO4, filtered, and concentrated. Purification by flash column chromatography (SiO2, CH2Cl2/MeOH 19:1) afforded compound 3 as a colourless solid (159 mg, 46%).1 H NMR (400 MHz, CDCl3) δ= 7.90 (s, 1H), 7.80 (d,3 J (H,H) = 7.4, 2H), 7.64 (d,3 J (H,H) = 7.4, 2H), 7.52 (s, 3H), 7.43 (t,3 J (H,H) = 7.4, 2H), 7.38 (s, 12H), 7.38 -7.32 (m, 2H), 4.90 (s, 1H), 4.44 (d,3 J (H,H) = 6.8, 2H), 4.25 (t, 3 J (H,H) = 6.8, 1H), 3.14 (s, 2H), 1.96 -0.99 (m, 8H).;13 C NMR (101 MHz, CDCl3) δ= 177.1 (C), 156.4 (C), 144.1 (C), 141.4 (C), 141.1 (C), 129.1 (CH), 128.2 (CH), 127.9 (CH), 127.7 (CH), 127.1 (CH), 125.1 (CH), 120.0 (CH), 93.4 (C), 66.5 (CH2), 47.3 (CH), 40.8 (CH2), 31.1 (CH2), 29.5 (CH2), 26.2 (CH2), 23.0 (CH2). Rf (CH2Cl2/MeOH 9:1)= 0.77; ESI-MS m/z= 1243 [2M+Na] + , 633 [M+Na] + , 243 [Trt] + .

  H NMR (400 MHz, CDCl3): 7.42-7.39 (m, 6H), 7.33-7.23 (m, 9H), 3.11 (td, J= 1.6, 6 Hz, 2H), 2.14 (t, J= 6.4 Hz, 2H), 1.71 (m, 2H), 1.58 (m, 2H), 1,29 (s, 1H); ESI-MS m/z= 379 [M+Na] + . Compound 10. Compound 8 (23.2 mg, 65.1 µmol) was solubilised in DCM(3 ml) and TFA (20 µl, 0.26 mmol) was added. Solution turned bright yellow and triisopropylsilane (TIPS), trityl scavenger, was added until disappearance of the yellow colour. Crude mixture was washed with NH4Clsat (1). Aqueous layer was back-extracted with DCM (2), organic layers were combined, dried over Na2SO4, filtered and concentrated under vacuum. Title compound 10 (3,7 mg, 32.4 µmol) was obtained with 50% yield.1 H NMR (400 MHz, CDCl3): 3.23 (t, J= 8.0 Hz,1H), 2.27 (t, J= 8.0 Hz, 1H), 1.75 (m, 2H), 1.29-1.24 (m, 6H), 0.90-0.84 (m, 1H); ESI-MS m/z= 115 [M+H] + .

Table 1 .

 1 Solvent properties

	Solvent	Dipole moment  (D) [a]	H-Bond donor	Relative polarity [b]	Dielectric constant  (F•m -1 ) [c]
	Dichloromethane	1.57	7.1	0.309	9.08
	Methanol	1.71	22.3	0.762	33.1
	Toluene	0.36	2.0	0.099	2.38
	Tetrahydrofuran	1.75	8.0	0.210	7.47
	Chloroform	1.01	5.7	0.259	4.81
	Acetonitrile	3.92	6.1	0.460	37.5
	Dimethylformamide	3.82	11.3	0.386	38.3

  H NMR (400 MHz, CDCl3) δ= 7.88 (s, 1H), 7.80 (d, 3 J (H,H) = 7.5, 2H), 7.63 (d, 3 J (H,H) = 7.5, 2H), 7.51 (s, 3H), 7.43 (t, 3 J (H,H) = 7.5, 2H), 7.37 (s, 12H), 7.37 -7.32 (m, 2H), 4.98 -4.65 (m, 1H), 4.41 (s, 2H), 4.24 (s, 1H), 3.06 (s, 2H), 2.05 -1.05 (m, 6H).; 13 C NMR (101 MHz, CDCl3) δ= 176.9 (C), 156.

Acknowledgements

Entry for the Table of Contents

A one-pot deprotection/cyclisation synthesis was developed to access lactam oxime in mild condition. Reaction parameters were studied and after reaction optimisation, 5-, 6-and 7-membered ring lactam oxime were obtained.

Dr. Santiago Lascano received his Bachelor's and Master's degree at the University of Geneva, after which he obtained his PhD in 2016 in the group of Prof. S. Matile at the same university, working on orthogonal dynamic bonds for complex supramolecular systems. During his post-doctoral stay at the IBMM in Montpellier, he worked on synthesis of epigenetic modulators for anticancer treatments. Since 2019, he joined Syngenta as Process chemist.

Dr. Arie van der Lee graduated from the University of Groningen in experimental physics and completed there a doctoral thesis in 1992 on the properties of crystalline superionic materials. A postdoctoral study at the Institut des Matériaux de Nantes was focused on the structure determination of commensurately and incommensurately modulated inorganic compounds. At the Institut Européen des Membranes in Montpellier his expertise is in the field of thin film reflectometry and structure determination of inorganic and organic compounds by singlecrystal and powder diffraction. He has had over the years a strong commitment within different national and international learned societies such as the International Union of Crystallography and the Association Française de Cristallographie. He is the current Vice President of the European Crystallographic Association.

Dr. Marie Lopez obtained her PhD in 2007 at Grenoble University working on chemoenzymatic synthesis and interaction studies of oligosaccharides under the supervision of Dr. H. Driguez and Dr. A. Buléon. In 2010 she joined the Griffith Institute for Drug Discovery (GRIDD) in Brisbane she worked on glycosylated carbonic anhydrase inhibitors under the supervision of Prof. S.-A. Poulsen. She then worked on anti-infectious agents with Dr. S. Köhler (IRIM) and Prof. J.-Y. Winum (IBMM), in Montpellier. In 2013 she was recruited by the CNRS at the ETaC laboratory in Toulouse (headed by P. B. Arimondo) to work on targeting and understanding DNA methylation through inhibition and chemical probe strategies. In 2018 she moved to the IBMM in Montpellier, where she is managing projects in chemistry and chemical biology to understand and target epigenetic modifications in pathological contexts.