Marc Bouji

Anthony Lecomte

Yannick Hode

René De Seze

Anne-Sophie Villégier

Effects of 900 MHz radiofrequency on corticosterone, emotional memory and neuroinflammation in middle-aged rats

Keywords: Middle-age, Radiofrequency, Interleukin-1β, Interleukin-6, Corticosterone, Fear conditioning

The widespread use of mobile phones raises the question of the effects of electromagnetic fields (EMF, 900 MHz) on the brain. Previous studies reported increased levels of the glial fibrillary acidic protein (GFAP) in the rat's brain after a single exposure to 900 MHz global system for mobile (GSM) signal, suggesting a potential inflammatory process. While this result was obtained in adult rats, no data is currently available in older animals. Since the transition from middle-age to senescence is highly dependent on environment and lifestyle, we studied the reactivity of middle-aged brains to EMF exposure. We assessed the effects of a single 15 min GSM exposure (900MHz; specific absorption rate (SAR) = 6 W/kg) on GFAP expression in young adults (6 week-old) and middle-aged rats (12 month-old). Brain interleukin (IL)-1β and IL-6, plasmatic levels of corticosterone (CORT), and emotional memory were also assessed.

Our data indicated that, in contrast to previously published work, acute GSM exposure did not induce astrocytes activation. Our results showed an IL-1β increase in the olfactory bulb and enhanced contextual emotional memory in GSM-exposed middle-aged rats, and increased plasmatic levels of CORT in GSM-exposed young adults. Altogether, our data showed an age dependency of reactivity to GSM exposure in neuroimmunity, stress and behavioral parameters. Reproducing these effects and studying their mechanisms may allow a better understanding of mobile phone EMF effects on neurobiological parameters.

Introduction

Over the last several decades, the rapid development of mobile phone technology has raised concerns about the cerebral effects of global system for mobile communications (GSM) 900 MHz microwaves. While older people represent an increasing share of cell phone users, aging-related vulnerability/the relationship between aging and vulnerability to electromagnetic fields (EMF) has rarely been assessed experimentally [START_REF] Vecchio | Mobile phone emission modulates inter-hemispheric functional coupling of EEG alpha rhythms in elderly compared to young subjects[END_REF].

The transition from adulthood to senescence seems closely dependent on life style and environmental factors, particularly during middle-age, its early onset. Indeed, middle-aged biological systems are particularly sensitive to toxicological factors, as shown by exacerbated behavioral impairments in middle-aged animals, when compared to younger animals, in response to lipopolysaccharide administration and traumatic brain injury [START_REF] Hoane | Middle age increases tissue vulnerability and impairs sensorimotor and cognitive recovery following traumatic brain injury in the rat[END_REF][START_REF] Kohman | Differential sensitivity to endotoxin exposure in young and middle-age mice[END_REF]. In addition, enrichment or self food-restriction diet during middle-age may postpone the appearance of age-related memory decline and neurochemical modifications [START_REF] Frick | Effects of environmental enrichment on spatial memory and neurochemistry in middle-aged mice[END_REF][START_REF] Kollen | Preserved memory capacities in aged Lou/C/Jall rats[END_REF].

As a consequence, the onset of age-related deficits in middle-aged rodents shows great variability. These deficits include modified neurobiological parameters such as an increase in plasmatic levels of corticosterone (CORT), memory decline, elevation of interleukins (IL) levels, and astrocytes activation [START_REF] Hayakawa | Age-related changes of astorocytes, oligodendrocytes and microglia in the mouse hippocampal CA1 sector[END_REF][START_REF] Lynch | Age-related neuroinflammatory changes negatively impact on neuronal function[END_REF][START_REF] Murray | Evidence that increased hippocampal expression of the cytokine interleukin-1 beta is a common trigger for age-and stress-induced impairments in long-term potentiation[END_REF]. Cytokines, like the two immune mediators IL-1β and IL-6, are secreted by activated microglia and are known to trigger astrocytes activation [START_REF] Woiciechowsky | Brain-IL-1 beta triggers astrogliosis through induction of IL-6: inhibition by propranolol and IL-10[END_REF][START_REF] Zhang | Astrogliosis in CNS pathologies: is there a role for microglia?[END_REF]. Astrocytes are non-neuronal central nervous system cells, implicated in neuronal synaptic plasticity [START_REF] Vernadakis | Glia-neuron intercommunications and synaptic plasticity[END_REF]. Their activation, may lead to an astrogliosis phenomenon, characterized by an increased expression of glial fibrillary acidic protein (GFAP), the main intermediate filament of astrocytes [START_REF] Eng | Astrocytic response to injury[END_REF].

Such biological responses are also elicited following exposure to toxicological or environmental factors. A transitory astroglial reactivity was observed 48 h to 72 h following an acute local exposure to GSM signal at high specific absorption rate (SAR) of 6 Watts/kg (W/kg) [START_REF] Brillaud | Effect of an acute 900MHz GSM exposure on glia in the rat brain: a time-dependent study[END_REF][START_REF] Mausset-Bonnefont | Acute exposure to GSM 900-MHz electromagnetic fields induces glial reactivity and biochemical modifications in the rat brain[END_REF].This response was shown in several structures of the limbic system, a circuitry involved in both memory and emotional processes [START_REF] Fanselow | Are the dorsal and ventral hippocampus functionally distinct structures?[END_REF]. GSM effects on IL expression have only been assessed in one in vitro study [START_REF] Thorlin | Exposure of cultured astroglial and microglial brain cells to 900 MHz microwave radiation[END_REF], while no in vivo animal studies have been published yet. GSM exposure was shown to affect plasmatic CORT levels [START_REF] Mostafa | Effects of exposure to extremely lowfrequency magnetic field of 2 G intensity on memory and corticosterone level in rats[END_REF] and to impair learning and memory [START_REF] Fragopoulou | Whole body exposure with GSM 900MHz affects spatial memory in mice[END_REF][START_REF] Narayanan | Spatial memory performance of Wistar rats exposed to mobile phone[END_REF].

Because common neurobiological parameters are affected by the ageing process and EMF exposures, we hypothesized a possible interaction between GSM exposure and middleage-related vulnerability in these biological responses.

Thus, the aim of the present study was to assess GFAP levels in the cortex, striatum and hippocampus of young adult (6 week-old) and middle-aged male rats (12 month-old), 48 h after the same exposure parameters used in Brillaud's study: single, 15 min, 900 MHZ GSM exposure (brain average SAR = 0 and 6 W/kg). We also evaluated pro-inflammatory cytokines (IL-1β and IL-6) expression in several brain structures (cortex, sub-cortex nuclei, olfactory bulb and cerebellum) and plasmatic levels of CORT. Emotional memory was assessed in the fear conditioning paradigm.

Materials and methods

Animals

Male Sprague Dawley rats (6 week-old and 12 month-old) were purchased from Charles Rivers (France). Animals/The animals were kept in a controlled environment (12-h light/dark cycle, room temperature: 22°C) and received food and tap water ad libitum. Rats were housed two per cage. The cage's environment was enriched with plastic cylinders identical in size, shape and appearance to GSM exposure rockets [START_REF] Brillaud | Effect of an acute 900MHz GSM exposure on glia in the rat brain: a time-dependent study[END_REF]. Rats were handled and weighed daily for one week before the experiments began. The protocols were approved by the French State Council guidelines for the care and use of laboratory animals (Decree n° 87-849, October 19, 1987).

Experimental groups

-Age groups: For both ages, rats were randomly assigned to 2 independent exposure groups at SAR values of 0 or 6 W/kg (n = 8-9/group). On the first day of the experiment, the rats were subjected to the fear conditioning training. 48 h later, they were consecutively exposed to a single GSM signal for 15 min, and tested for sound memory. Contextual memory was tested 48 h after GSM exposure and was immediately followed by anesthesia, blood collection and sacrifice (Figure 1). Exposure doses and ages were counterbalanced over three independent experimental sessions to perform exposures and tests between 9:00 am and 12:00 pm.

-"Time schedule" control groups: Six week-old rats were randomly assigned to 12 independent groups (n = 6/group). Rats were sacrificed 30 min, 5h or 24h following (a) daily handling (cage control (CC) group) (b) a single, 15 min, 6 W/kg GSM-exposure (c) a single, 15 min, sham (0W/kg GSM)-exposure, or (d) a single 15 min sham (0W/kg GSM)-exposure followed by a fear conditioning session (FC group). Treatments and exposure doses were counterbalanced over three independent experimental sessions to perform exposures and tests between 9:00 am and 12:00 pm.

Radiofrequency exposure system

Exposure set-up was performed as previously described [START_REF] Dubreuil | Does head-only exposure to GSM-900 electromagnetic fields affect the performance of rats in spatial learning tasks?[END_REF]. A radio frequency power source (900-64 type, Radio Frequency Power Amplifier, France) emitting a 900 MHz EMF (1/8 duty factor) pulse modulated at 217 Hz was connected to a four-output divider. Each output was connected to a loop antenna allowing local exposure of four animal's heads simultaneously in an anechoic chamber. During exposure, each animal was placed in a Plexiglas rocket capped with a truncated cone on which an individual loop antenna was fixed. The rocket body was lined with air holes to facilitate breathing and minimize the rise in body temperature.

Fear Conditioning

Apparatus

Fear conditioning is a Pavlovian conditioning, in which a neutral conditioned stimulus is paired with an aversive unconditioned stimulus (in the present study, a sound and a foot shock, respectively). The measured responses were freezing and high activity. Freezing was defined as the complete immobilization of the animal except for respiratory movement for a minimum of 1 sec. High activity was used to evaluate locomotor activity and was defined as animal's movement generating a pressure higher than 15 arbitrary unit (corresponding to 3 fold/times the pressure generated by the animal's weight). Conditioning and tests occurred in two standard fear conditioning boxes purchased from Bioseb (France) and controlled by specific software (Panlab, Barcelona). As age differences were observed during conditioning on the last 60 sec of freezing (MaxFreezing) (figure 5b), the freezing response to the sound and the contextual tests was expressed as a percentage of MaxFreezing/as MaxFreezing percentage for each animal.

Protocol

The conditioning session occurred in environment 1 of the fear conditioning boxes. It began with a habituation period with no stimulus (no sound or foot shock, 3 min), followed by three conditioning cycles. One cycle included four consecutive steps: sound presentation (2 kHz; 80 db; 20 sec), no stimulus (10 sec), foot shock (0.25 mA; 1 sec), no stimulus (40 sec).

To test contextual memory, animals were replaced for 2 min in environment 1.To perform the sound memory test, animals were introduced in boxes with a modified environment, defined as environment 2 (different box size, walls color, floor texture, scent and cleaning disinfectant) for 2 min and were exposed to the sound presentation (2 min).

Figure 1

Experiment design. On day 1, rats were subjected to the conditioning session of the fear conditioning test. 48 h after, they were tested for the sound memory immediately after GSM exposure. 48h later, rats were tested for the contextual memory. Then, blood was collected and rats were sacrificed. Exposure and behavior tests were conducted between 9:00 and 12:00 pm.

Plasma and brain sample preparation

Plasmatic CORT was assessed on sacrifice day to avoid the stress induced by blood collection during behavioral tests. Rats were anesthetized with isoflurane. Blood was collected from venae cavae in EDTA and centrifuged (10000 rpm/10 min/4°C). Plasma was stored at -80°C until assayed. The rats were subjected to an intra-cardiac perfusion with 0.1% phosphate buffered saline (PBS).The brains were quickly removed and the two hemispheres were separated and randomly assigned to Enzyme Linked Immuno Sorbant Assay (ELISA) or immunohistochemistry samples preparation. For immunohistochemistry, the brain hemispheres were fixed/placed in 4 % paraformaldehyde (PFA) for 4 days, incubated in 30% sucrose solution, frozen in isopentane at -50°C, and stored at -80°C. Using a cryostat microtome, 25 μm sagittal brain slices were obtained and stored at -20°C in cryoprotectant solution until processing as free-floating sections. For ELISA, the olfactory bulb, cortex, subcortex nuclei and cerebellum of the other hemispheres were dissected on ice and stored at -80°C.

Plasmatic corticosterone

A CORT competitive assay was performed with a commercially available kit (assay designs, correlate-EIA CORT, R&D) according to the manufacturer's instructions. Briefly, polyclonal anti-CORT antibody and alkaline phosphatase-labeled CORT were added to the pre-coated wells. After 2h incubation at room temperature, the excess reagents were washed away and substrate was added. After 1h incubation, the enzymatic reaction was stopped with trisodium phosphate solution. CORT concentrations (ng/ml) were inversely proportional to the intensity of the yellow color read at 405 nm.

GFAP Immunohistochemistry

Brain slices were incubated in 30% H 2 O 2 for 20 min before addition of normal goat serum blocking solution. Sections were incubated overnight at 4°C with the primary antibody anti-GFAP (rabbit antibody, Abcam ab7260), then with the secondary biotinylated antibody (anti-rabbit IgG, ABC kit Abcam ab8627). Sections were incubated with an Avidine Biotine Solution (ABC kit Abcam ab 8627), and staining revealed with 3,3'-diaminobenzidine tetrahydrochloride (Sigma tabs), 30% H 2 O 2 . Sections were washed in PBS to stop the reaction.

GFAP image analysis was performed using Visilog 6.8 imaging software (Noesis, France), by measuring the percentage of stained surface over a manually defined area (optical density), excluding the interface of adjacent tissues (10 × objectives). GFAP was assessed in the cortex, striatum and hippocampus, the structures where an effect of GSM exposure was previously described [START_REF] Brillaud | Effect of an acute 900MHz GSM exposure on glia in the rat brain: a time-dependent study[END_REF][START_REF] Mausset-Bonnefont | Acute exposure to GSM 900-MHz electromagnetic fields induces glial reactivity and biochemical modifications in the rat brain[END_REF].

IL Enzyme Linked Immuno Sorbant Assay

Structures were homogenized by sonication in an ice-cold Tris/HCl/EDTA buffer containing a 4% protease inhibitor (Roche) and 1% phosphatase inhibitor (Sigma) cocktail.

Samples were centrifuged (9800 rpm/15 min/4°C) and the supernatant was collected. A Lowry test was used to measure total protein content in each sample. IL-1β and IL-6 were quantified using commercialized sandwich ELISA kits (Rat IL-1β /IL-1F2 and Rat IL-6, DuoSet ELISA Development system, R&D systems) according to the manufacturer's instructions. Raw data were presented for controls and sham groups, while GSM effects were presented as percentages of sham group.

Statistics

Statistical analyses were performed using the SPSS 15 software (Inc., Chicago, IL, USA). Values were given as mean ± standard deviation of mean (SEM) per group. Raw data were analyzed after logarithmic transformation and, percentages, after square root transformation. Levene's test was used for variance homogeneity. Analyses were performed using three-way analysis of variance/variance analysis (ANOVA) (for age × exposure dose × time and age × exposure values × structure interaction, with repeated measures on time and structure) and two-way ANOVA (for time × age, time × exposure values, age × exposure values and structure × exposure values interaction, with repeated measure on time and structure). The main effects were analyzed using Bonferroni's or Dunnett's post-hoc corrected t-test. Time and structures were treated as within subject factors while exposure doses were treated as between subject factors. Effects were considered significant when p < 0.05. Grubb's test was used for outlier's detection.

Results

Absence of age or GSM exposure effect on GFAP staining

Figure 2 shows GFAP staining in the cortex, striatum and hippocampus of 6 week-old and 12 month-old rats following GSM exposure. ANOVA analysis showed significant structure effect (F 2,24 = 97, p< 0.001) and structure × age interaction (F 2,24 = 5, p = 0.02).

However, no age effect (F 1,12 = 1.9, p = 0.2), treatment effect (F 1,12 = 0,02 p = 0.9), age × treatment (F 1,12 = 0.9, p = 0.4), structure × treatment (F 2,24 = 0.4, p = 0.6) or structure × age × treatment interaction (F 2,24 = 2.2, p = 0.1) was obtained. Bonferroni's post-hoc corrected t-test showed higher GFAP staining in the hippocampus compared to the other structures (p < 0.05) (Figure 2b).

Effect of age and GSM exposure on cerebral IL-6 and IL-1β

No age differences were obtained regarding basal IL levels in the sham exposed groups (p > 0.94) (Table a). Figure 3 (a andb) shows IL-6 and IL-1β following GSM exposure in the cortex, the sub-cortical nuclei, the olfactory bulb and the cerebellum, in 6 week-and 12 month-old rats following GSM exposure.

Figure 3

GSM effect on (a) IL-6 and (b) IL-1β in the cortex (Cx), the sub-cortical nuclei (S-Cx), the olfactory bulb (OB) and the cerebellum (Crb) in 6 week-and 12 month-old rats. Rats were subjected to GSM exposure (0 and 6 W/kg) and sacrificed two days later to quantify IL. * p < 0.05 significantly increased compared to sham groups of both ages. ## p < 0.01 significantly increased compared to 6 week-old exposed group. N = 8-9/group. (c) IL levels were not modified in the brain of 6 week-old rats sacrificed 30 min, 5h and 24h after daily handling (CC), GSM sham-exposure followed by fear conditioning session (FC), GSM sham-exposure (0 W/kg) or GSM-exposure (6 W/kg).

ANOVA analyses performed on the IL-6 and IL-1β measurements showed, respectively, the absence of structure effect (F 3,96 = 0.3, p = 0.8; F 3,96 = 0.8, p = 0.5), treatment effect (F 1,32 = 2.2, p = 0.1; F 1,32 = 0.7, p = 0.4), structure × age interaction (F 3,96 = 0.14, p = 0.9; F 3,96 = 1.8, p = 0.1), structure × treatment interaction (F 3,96 = 1.4, p = 0.2; F 3,96 = 0.8, p = 0.5), or structure × age × treatment interaction (F 3,96 = 0.04, p = 0.9; F 3,96 = 1.6, p = 0.2).

For IL-6, no age (F 1,32 = 0.2, p = 0.9) or age × treatment interaction (F 1,32 = 0.03, p = 0.9) was observed.

For IL-1β, a significant age effect (F 1,32 = 4.4, p = 0.04) and age × treatment interaction (F 1,32 = 4.6, p = 0.04) were detected. ANOVA analysis performed on separate structures' data showed a significant age effect (F 1,32 = 5.8, p = 0.02) and age × treatment interaction (F 1,32 = 5.2, p = 0.03) for IL-1β only in the olfactory bulb. Bonferroni's post-hoc corrected t-test showed significantly increased IL-1β in the olfactory bulb of GSM-exposed 12 month-old rats compared to 6 week-and 12 month-old sham rats (p = 0.04) and to GSMexposed 6 week-old rats (p = 0.01).

Cerebral IL levels were not modified by a 6 W/kg-exposure as compared to a sham GSM-exposure, and by a sham GSM-exposure or fear conditioning procedure (FC) as compared to the CC group, after 30 min, 5h and 24h (p > 0.9) (Figure 3c).

Corticosterone response to GSM is age-dependent

Figure 4 shows plasmatic levels of CORT in GSM-and sham-exposed 6 week-and 12 month-old groups. ANOVA analyses showed a significant dose effect (F 1,20 = 4.5, p = 0.04), but no age effect (F 1,20 = 0.02, p = 0.8) or dose × age interaction (F 1,20 = 1.9, p = 0.2).

Bonferroni's post-hoc corrected t-test showed that GSM exposure significantly increased CORT in the 6 week-old group (p < 0.05), while it had no effect in middle-aged rats.

The CORT level was significantly increased 30 min, but not 5 or 24 h after the fear conditioning procedure compared to sham-and 6 W/kg GSM-exposed group (p = 0.001; p = 0.006) and the CC group (p = 0.03). However, the CORT level was not modified by 6 W/kg as compared to sham GSM-exposure, and by sham-GSM-exposure compared to the CC group, after 30 min, 5h and 24h (p > 0.9) (Figure 4b).

Age and GSM effect on emotional memory

Figure 5 (a and b) shows the percentage of time spent in high activity and freezing during the conditioning session. ANOVA analyses performed on the data summarized in figure 5a showed a significant time effect (F 12,384 = 88, p < 0.001), age effect (F 1,32 = 12, p = 0.002) but no time × age interaction (F 12,384 = 1.32, p = 0.2). T-test showed a significant increase of high activity in the 12 month-old group as compared to the 6 week-old rats at T90 sec to T210 sec (p < 0.001). ANOVA analyses performed on the data summarized in figure 5b showed a significant time effect (F 12,384 = 134, p < 0.001) but no time × age interaction (F 12,384 = 1.3, p = 2.3) or age effect (F 1,32 = 1.7, p = 0.2). ANOVA performed on MaxFreezing responding showed a significant age effect (F 1,32 = 8.2 p = 0.007). T-test showed that the percentage of time spent freezing was significantly higher in the 6 week-old group as compared to the 12 month-old rats at T360 sec (p = 0.04) and T390 sec (p = 0.03). Figure 6a shows time spent freezing during the first 30 sec in environments 1 and 2 in ''conditioned rats''. ANOVA analyses showed a significant age effect (F 1,62 = 8, p = 0.006), environment effect (F 1,62 = 5, p = 0.03) but no age × environment interaction (F 1,62 = 4, p = 0.06). No difference in freezing was shown between 6 week-old and month-old rats in environment 1 (p > 0.05). The 12 month-old rats spent significantly less time freezing in environment 2 (modified environment) compared to environment 1 (know environment) (p = 0.004), while 6 week-old rats showed no responding differences between the two environments. showed a significant time effect (F 3,90 = 5, p = 0.03) and age × exposure × time interaction (F 3,90 = 3.2, p = 0.03). However, no exposure effects (F 1,30 = 0.74, p = 0.39), time × exposure (F 3,90 = 0.28, p = 0.8), age × time(F 3,90 = 1.2, p = 0.3) or age × exposure (F 1,30 = 0.94, p = 0.87) was obtained. ANOVA analyses performed separately on data for the 6 week-and 12 monthold groups showed no time effect or time × treatment interaction (p > 0.4). No significant treatment effect was found in the 6 week-old group (F 1,15 = 0.8, p = 0.4) or the 12 month-old group (F 1,15 = 0.17, p = 0.67). ANOVA analyses performed separately on data for the shamand GSM-exposed groups showed no time × age interaction (F 3,42 = 2.6, p = 0.06 and F 3,48 = 0.8, p = 0.5, respectively) or age effect (F 1,14 = 1.3, p = 0.27 and F 1,16 = 0.5, p = 0.42) in both groups. A significant time effect (F 3,48 = 6.3, p = 0.001) was shown only in GSM exposed groups. No significant group effect was shown for each time point (p > 0.7).

ANOVA analyses performed on the data summarized in figure 6c showed a significant time effect (F 3,90 = 11, p < 0.001), age effect (F 1,30 = 10, p = 0.003) and age × treatment interaction (F 1,30 = 3.4, p = 0.04). ANOVA analyses performed separately on the 6 week-and 12 month-old groups showed a significant time effect (F 3,48 = 8.7, p < 0.001 and F 3,42 = 3.1, p = 0.03, respectively) in both groups. No exposure effect or time × exposure interaction was obtained in both ages groups (p > 0.6). ANOVA analyses performed separately on sham-and GSM-exposed groups' data showed a significant age effect in the GSM-exposed group (F 1,16 = 11.7, p = 0.004) and significant time effect in both groups (p < 0.001). For each time point, a significant group effect was shown (p < 0.05). Dunnett's post-hoc corrected t-test showed a significant increase in freezing time in middle-aged GSM-exposed rats compared to GSMexposed young adults (p = 0.03, T30 sec and p = 0.002, T60 sec) and to sham-young adults (p = 0.04, T30 sec).

Discussion

The aim of this study was to assess the potential vulnerability of neuro-immunity, stress and emotional systems of middle-aged animals in response to an acute GSM exposure.

Our first data indicated that, conversely to earlier published work, acute GSM exposure did not induce astrocytes activation. Our second result suggested that some biological responses of GSM-exposed rats were age-dependent: we found an increase in olfactory bulb IL-1β and fear memory in GSM-exposed middle-aged rats, and increased plasmatic CORT levels in GSM-exposed young adults.

Middle-aged model

Human middle-age (40 to 65 years old) is characterized by the occurrence of early signs of ageing, such as mood disorders and declarative memory decrease [START_REF] Byers | High occurrence of mood and anxiety disorders among older adults: The National Comorbidity Survey Replication[END_REF].

During this period, the onset of senescence is highly dependent on age, sex, species and strains [START_REF] Frick | Effects of environmental enrichment on spatial memory and neurochemistry in middle-aged mice[END_REF][START_REF] Hebda-Bauer | Female CREBalphadelta-deficient mice show earlier age-related cognitive deficits than males[END_REF]. Since environmental factors and life style also play a key role in the progression of ageing, middle-aged models potentially display measurable reactivity to environmental challenges and may be a useful tool for toxicological investigations [START_REF] Frick | Effects of environmental enrichment on spatial memory and neurochemistry in middle-aged mice[END_REF][START_REF] Hebda-Bauer | Female CREBalphadelta-deficient mice show earlier age-related cognitive deficits than males[END_REF][START_REF] Kohman | Differential sensitivity to endotoxin exposure in young and middle-age mice[END_REF].

In the present study, 12 month-old Sprague Dawley male rats were chosen to model middle-age. They displayed the same phenotype as young adults regarding CORT, GFAP and IL levels. Accordingly, no deficits were reported for CORT levels in 10 month-old Sprague Dawley and for IL in 12 month-old Fisher 344 rats and BALB/c mice [START_REF] Gee | Age-related alterations of Apolipoprotein E and interleukin-1beta in the aging brain[END_REF][START_REF] Kohman | Differential sensitivity to endotoxin exposure in young and middle-age mice[END_REF][START_REF] Rasmussen | Daily melatonin administration at middle age suppresses male rat visceral fat, plasma leptin, and plasma insulin to youthful levels[END_REF]. Deficits in Sprague Dawley and Wistar rats were reported later in the middle-age period (approximately 15 month-old), for micro and macroglia markers (CD11b, MHC II and GFAP) and IL levels, respectively [START_REF] Bilbo | Early-life infection is a vulnerability factor for aging-related glial alterations and cognitive decline[END_REF][START_REF] Hoane | Middle age increases tissue vulnerability and impairs sensorimotor and cognitive recovery following traumatic brain injury in the rat[END_REF][START_REF] Minogue | Modulation of amyloid-beta-induced and age-associated changes in rat hippocampus by eicosapentaenoic acid[END_REF].

Regarding behavioral performances, the assessment of age-related decline (as memory) is hampered in late ageing subjects, as it overlaps with senescence-linked disabilities (such as apathy, sleep disorders, modified locomotor activity) that lead to important interindividual variability [START_REF] Bilbo | Early-life infection is a vulnerability factor for aging-related glial alterations and cognitive decline[END_REF][START_REF] Byers | High occurrence of mood and anxiety disorders among older adults: The National Comorbidity Survey Replication[END_REF][START_REF] Hodes | Learning during middle age: a resistance to stress?[END_REF][START_REF] Moretti | Emotional behavior in middle-aged rats: Implications for geriatric psychopathologies[END_REF]. Therefore, middle-aged models' assets are displaying less intra-group variability, then, requiring fewer experimental subjects [START_REF] Moyer | Impaired trace and contextual fear conditioning in aged rats[END_REF], and mitigating ageingrelated biases in behavioral approaches (such as differences in locomotor activity) [START_REF] Pesic | Changes of behavioral parameters during long-term food restriction in middle-aged Wistar rats[END_REF].

In the present study, on the contrary, we showed increased locomotor activity to novelty and decreased freezing during fear conditioning in middle-aged rats. To allow interpretation of behavior assessments, freezing during tests was expressed as percentage of freezing during conditioning, and the absence of differences in locomotor activity was checked during the test sessions using the high activity parameter. In our protocol, the contextual test was performed four days after conditioning, which did not allow robust contextual memory in young adults. On the contrary, middle-aged rats displayed contextual memory and tended to freeze more to/at the sound than young adults did. A previous study reported that 12 month-old Sprague Dawley rats showed more anxiety-related behavior than young rats, without memory impairment, suggesting that trait anxiety may have determined stronger fear memory in our study [START_REF] Moyer | Impaired trace and contextual fear conditioning in aged rats[END_REF]. Based on anatomy, overlapping brain circuitries mediate memory, stress, fear, anxiety and nociception, involving the prefrontal cortex, hippocampus, amygdala and hypothalamus [START_REF] Fendt | The neuroanatomical and neurochemical basis of conditioned fear[END_REF][START_REF] Ledoux | Emotion circuits in the brain[END_REF]. Thus, additional modalities, including sensory skills, ability to freeze, reactivity to novelty or sensorimotor functions may explain differences between young adults and middle aged rats [START_REF] Hodes | Learning during middle age: a resistance to stress?[END_REF].

GSM exposure and neuro-immune system

An indication of injury progression may be given by pro-inflammatory factors, as IL are secreted within 1 to 8 hours by neurons and microglia and within 2 to 8 days by astrocytes following an acute excitotoxic brain injury [START_REF] Pearson | Excitotoxic brain damage in the rat induces interleukin-1beta protein in microglia and astrocytes: correlation with the progression of cell death[END_REF][START_REF] Taupin | Increase in IL-6, IL-1 and TNF levels in rat brain following traumatic lesion. Influence of pre-and posttraumatic treatment with Ro5 4864, a peripheral-type (p site) benzodiazepine ligand[END_REF].

According to our data, a 15 min acute 6 W/kg GSM-exposure does not seem to influence the neuro-immune and neuro-inflammatory axes in young adults, despite our primarily formulated hypothesis. Indeed, IL-1β and IL-6 were not modified from 30 min to 48 h post exposure and the GFAP response previously shown by [START_REF] Brillaud | Effect of an acute 900MHz GSM exposure on glia in the rat brain: a time-dependent study[END_REF] and Mausset-Bonnefond et al. (2004) was not reproduced, while we used a similar protocol.

Our study was one of the first to assess these biomarkers, as only one study has been published and showed the absence of EMF-effects on IL secretion in primary astroglial and microglial cultured cells [START_REF] Thorlin | Exposure of cultured astroglial and microglial brain cells to 900 MHz microwave radiation[END_REF]. Regarding the astroglial response to GSM, the literature is characterized by a high variability, as shown by negative [START_REF] Fritze | Effect of global system for mobile communication microwave exposure on the genomic response of the rat brain[END_REF][START_REF] Grafstrom | Histopathological examinations of rat brains after long-term exposure to GSM-900 mobile phone radiation[END_REF] and positive effects [START_REF] Ammari | GFAP expression in the rat brain following sub-chronic exposure to a 900 MHz electromagnetic field signal[END_REF][START_REF] Brillaud | Effect of an acute 900MHz GSM exposure on glia in the rat brain: a time-dependent study[END_REF][START_REF] Mausset-Bonnefont | Acute exposure to GSM 900-MHz electromagnetic fields induces glial reactivity and biochemical modifications in the rat brain[END_REF]. Protocol differences may explain part of this variability, as, GFAP expression can be decreased by stress [START_REF] Laping | Transcriptional control of glial fibrillary acidic protein and glutamine synthetase in vivo shows opposite responses to corticosterone in the hippocampus[END_REF]. In our protocol, the use of fear conditioning in our protocol and the demonstration that it increases CORT after 30 min must be highlighted as a possible interacting parameter.

For the first time, our study investigated the question of a GSM effect on GFAP and IL response in middle-aged rodents. We found that cerebral GFAP and IL-6 were not modified while IL-1β was increased only in the olfactory bulb, 48 h following GSM exposure.

This response may be explained by the fact that this structure is anatomically small and protrudes near the GSM source. A lack of homogeneity in IL-1β secretion through brain regions may also depend on the patterns of neural activation in response to a stimulus [START_REF] Minami | Immobilization stress induces interleukin-1 beta mRNA in the rat hypothalamus[END_REF]. Similar middle aged-related IL hyper-reactivity was demonstrated in response to lipopolysaccharides [START_REF] Kohman | Differential sensitivity to endotoxin exposure in young and middle-age mice[END_REF].

GSM exposure, stress and emotional memory

Fear is an apprehensive arousal response to an explicit threat and refers to the activation of the defensive behavioral system [START_REF] Fendt | The neuroanatomical and neurochemical basis of conditioned fear[END_REF]. Fear conditioning is based on both a Pavlovian conditioning and the induction of fear in response to an aversive unconditioned stimulus. Both processes are complex and rely closely on CORT release.

The increased CORT levels found in GSM-exposed 6 week-old rats were not in accordance with the literature showing the absence of a CORT levels modification relative to EMF exposure in in vivo studies in adult Fischer 344 and Wistar rats [START_REF] Prochnow | Electromagnetic Field Effect or Simply Stress? Effects of UMTS Exposure on Hippocampal Longterm Plasticity in the Context of Procedure Related Hormone Release[END_REF][START_REF] Stagg | Effect of immobilization and concurrent exposure to a pulse-modulated microwave field on core body temperature, plasma ACTH and corticosteroid, and brain ornithine decarboxylase, Fos and Jun mRNA[END_REF]. However, previous studies showed middle-aged related differences in plasmatic CORT or corticotropin-releasing factor responses to different types of stress when compared to young animals [START_REF] Nolan | Chronic ethanol consumption depresses hypothalamic-pituitary-adrenal function in aged rats[END_REF][START_REF] Pisarska | Agerelated alterations in emotional behaviors and amygdalar corticotropin-releasing factor (CRF) and CRF-binding protein expression in aged Fischer 344 rats[END_REF]. Reports of increased CORT levels for 3 days post-stress exist [START_REF] Gaillet | The involvement of noradrenergic ascending pathways in the stress-induced activation of ACTH and corticosterone secretions is dependent on the nature of stressors[END_REF][START_REF] Ottenweller | Repeated stress persistently elevates morning, but not evening, plasma corticosterone levels in male rats[END_REF], however, in most cases, the plasmatic CORT response corresponds to a transitory peak occurring within the first 30 min post (stress) stimulus [START_REF] Xu | Behavioural stress facilitates the induction of longterm depression in the hippocampus[END_REF]. Our experiments showed that the CORT release was significantly increased 30 min but not 5 or 24 hours following fear conditioning, while acute GSM exposure alone did not affect CORT in young adults. These data strongly suggest that acute GSM is not perceived as a stressor. While it is

hazardous to speculate about a potential link between CORT increase and GSM exposure performed 48h before, one may hypothesize that higher CORT levels, observed 3 days post exposure may correspond to increased reactivity of the hypothalamic-pituitary-adrenal axis to sacrifice-induced stress that would be affected by GSM and fear conditioning interaction; however, this hypothesis warrants reproducing adequate experimental groups in a single experiment.

Our data appears to contradict the acute anxiogenic effect of CORT in the fear response [START_REF] Mitra | Acute corticosterone treatment is sufficient to induce anxiety and amygdaloid dendritic hypertrophy[END_REF] as increased CORT level was not linked to an increased fear response in GSM-exposed young adults. Indeed, this group rather displayed a tendency toward a decrease in response to the sound, which may be underlined by the fear-reducing effects of CORT, linked to its ability to inhibit the recall of previously acquired, emotionally arousing information [START_REF] Roozendaal | Stress, memory and the amygdala[END_REF][START_REF] Sartori | Enhanced fear expression in a psychopathological mouse model of trait anxiety: pharmacological interventions[END_REF]. In the same test, exposed middle-aged rats displayed an increased freezing response. One may hypothesize that this increase to results from increased IL-1β in the olfactory bulb. Indeed, olfactory bulbectomy is a model of depression, and has been characterized in 19 month-old Sprague Dawley male rats by emotional and mood-related behavioral impairments, including a tendency toward an increased freezing response [START_REF] Slotkin | Modeling geriatric depression in animals: biochemical and behavioral effects of olfactory bulbectomy in young versus aged rats[END_REF].

Performing tests of depression-like behavior and fear conditioning using a discrete olfactory conditioned stimulus may allow/make it possible to determine behavioral impacts of GSM-induced increased IL in the olfactory bulb [START_REF] Pugh | Role of interleukin-1 beta in impairment of contextual fear conditioning caused by social isolation[END_REF]. Lastly, at both ages, GFAP and IL in the hippocampus and sub-cortical nuclei, including key structures implicated in the fear conditioning paradigm, were not subjected to GSM or age effects. More generally, current literature is characterized by discordant GSM effects on memory (positive effects: [START_REF] Fragopoulou | Whole body exposure with GSM 900MHz affects spatial memory in mice[END_REF][START_REF] Narayanan | Spatial memory performance of Wistar rats exposed to mobile phone[END_REF] ; negative results: [START_REF] Ammari | Effect of head-only sub-chronic and chronic exposure to 900-MHz GSM electromagnetic fields on spatial memory in rats[END_REF][START_REF] Dubreuil | Does head-only exposure to GSM-900 electromagnetic fields affect the performance of rats in spatial learning tasks?[END_REF]), which may be explained by the weakness or specificity of GSM action in particular protocols or types of memory processes.

Conclusion

The present study showed middle-age-related vulnerability to an acute GSM exposure.

Biomarkers of such vulnerability were: enhanced emotional memory and impaired corticosterone response while IL showed only a weak and isolated increase in the olfactory bulb. Reproducing these effects and studying the underlying mechanisms may allow a better understanding of the interaction between mobile phone EMF and the neurobiological tissue through ageing.

Figure 2

 2 Figure 2

  Figure 4

Figure 5

 5 Figure 5

Figure 6

 6 Figure 6

Figure 6 (

 6 Figure 6 (b and c) shows the percentage of time spent freezing in response to the sound and the context. ANOVA analyses performed on the data summarized in figure 6b


Guillaume Fayet

Patricia Rotureau
email: patricia.rotureau@ineris.fr

Vinca Prana

Carlo Adamo

Global and local QSPR models to predict the impact sensitivity of nitro compounds

Keywords: Quantitative Structure-Property Relationships, Density Functional Theory, Validation, Applicability domain, Impact Sensitivity, Nitro Compounds

come

Global and local quantitative structure-property relationship models to predict the impact sensitivity of nitro compounds

INTRODUCTION

Sensitivity is a critical property of energetic materials as it characterizes the tendency of the material to react under the effect of various stimuli: heat, electric spark, friction or impact. In particular, impact sensitivity, denoted h 50% , expresses the sensitivity of materials to a mechanical impact. It is experimentally evaluated by determining the height at which a weight of a defined mass leads to a reaction when falling on a material sample, with a 50% level of probability. It is a standard property of explosive substances not only when evaluating performances but also for safety considerations, since it is part of the regulatory tests within regulatory frameworks, e.g. Globally Harmonized System (GHS) [START_REF]Globally harmonized system of classification and labelling of chemicals (GHS), United Nations[END_REF] or Transport of Dangerous Goods (TDG) [START_REF]Recommendations on the Transport of Dangerous Goods: Manual of Tests and Criteria, United Nations[END_REF].

To evaluate as early as possible potential safety problems when handling energetic materials, notably in development process, the use of computation approaches is of great interest. Computer capabilities are in constant increase and developing accurate predictive methods to estimate the properties of such compounds is now possible. In particular, Quantitative Structure-Property Relationships (QSPR) are increasingly used to predict properties of chemicals [START_REF] Papa | Development, Validation and Inspection of the Applicability Domain of QSPR Models for Physicochemical Properties of Polybrominated Diphenyl Ethers[END_REF][START_REF] Cocchi | Development of Quantitative Structure-Property Relationships Using Calculated Descriptors for the Prediction of the Physicochemical Properties (n D , ρ, bp, ε, η) of a Series of Organic Solvents[END_REF][START_REF] Katritzky | Quantitative Correlation of Physical and Chemical Properties with Chemical Structure: Utility for Prediction[END_REF][START_REF] Gharagheizi | A QSPR model for estimation of lower flammability limit temperature of pure compounds based on molecular structure[END_REF][START_REF] Fayet | Predicting explosibility properties of chemicals from Quantitative Structure-Property Relationships[END_REF][START_REF] Papa | On the Use of Local and Global QSPRs for the Prediction of Physico-chemical Properties of Polybrominated Diphenyl Ethers[END_REF][START_REF] Papa | QSPR as a support for the EU REACH regulation and rational design of environmentally safer chemicals: PBT identification from molecular structure[END_REF][START_REF] Bhhatarai | CADASTER QSPR Models for Predictions of Melting and Boiling Points of Perfluorinated Chemicals[END_REF]. This approach consists in correlating an experimental property with descriptors of the molecular structure. Such models are even recommended into the new European regulation related to the Registration, Evaluation, Authorisation and Restriction of Chemicals (REACH) [START_REF]the European Parliament and of the Council of 18 December 2006 concerning the Registration, Evaluation, Authorisation and Restriction of Chemicals (REACH). 12[END_REF] and rules have been defined by the Organisation for Economic Co-operation and Development (OECD) to clarify their validation for a regulatory use [12]. These rules not only clarify the importance of transparency in the definition of the algorithm, but also in the definition of endpoints (including experimental protocols) and domains of applicability, as well as in the measures of performances of models (e.g. with an external validation to estimate predictivity). Moreover, they encourage their mechanistic interpretation. Some QSPR models have been already devoted to impact sensitivity in the past. Kamlet [START_REF] Kamlet | The Relationship of Impact Sensitivity with Structure of Organic High Explosives[END_REF][START_REF] Kamlet | The relationship of Impact Sensitivity with Structure of Organic High Explosives. II. Polynitroaromatic explosives[END_REF] proposed linear models linking logh 50% to the oxygen balance for nitro compounds with high correlations but without any external validation. Correlations were also proposed with the charge distribution descriptors [START_REF] Rice | A Quantum Mechanical Investigation of the Relation between Impact Sensitivity and the Charge Distribution in Energetic Molecules[END_REF], e.g. empirical molecular electronegativities [START_REF] Mullay | A Relationship between Impact Sensitivity and Molecular Electronegativity[END_REF][START_REF] Mullay | A Relationship between Impact Sensitivity and Molecular Electronic Structure[END_REF], charge of nitro groups [START_REF] Zhang | Investigation of Correlation between Impact Sensitivities and Nitro Group Charges in Nitro Compounds[END_REF][START_REF] Cao | Two Dominant Factors Influencing the Impact Sensitivities of Nitrobenzenes and Saturated Nitro Compounds[END_REF], electrostatic potential at the midpoint of the C-NO 2 bond (V mid ) [START_REF] Rice | A Quantum Mechanical Investigation of the Relation between Impact Sensitivity and the Charge Distribution in Energetic Molecules[END_REF][START_REF] Politzer | Relationships between dissociation energies and electrostatic potentials of C-NO2 bonds: applications to impact sensitivities[END_REF][START_REF] Murray | A relationship between impact sensitivity and the electrostatic potentials at the midpoints of C-NO2 bonds in nitroaromatics[END_REF], or the dissociation energy of this bond [START_REF] Politzer | Relationships between dissociation energies and electrostatic potentials of C-NO2 bonds: applications to impact sensitivities[END_REF][START_REF] Owens | Calculation of energy barriers for bond rupture in some energetic molecules[END_REF][START_REF] Song | Relationship between the Bond Dissociation Energies and Impact Sensitivities of Some Nitro-Explosives[END_REF]. These correlations notably highlighted the critical part of the C-NO 2 bond in the decomposition process of nitro compounds [START_REF] Korolev | Differentiation of the molecular structure of nitro compounds as the basis for simulation of their thermal destruction processes[END_REF].

In more recent works, multivariate approaches were preferred. For instance, Nefati [START_REF] Nefati | Prediction of the Impact Sensitivity by Neural Networks[END_REF], Cho [START_REF] Cho | Optimization of Neural Networks Architecture for Impact Sensitivity of Energetic Molecules[END_REF] and Jun [START_REF] Jun | Neural networks study on the correlation between impact sensitivity and molecular structures for nitramine explosives[END_REF] used artificial neural networks (ANN) with various descriptors. Li [START_REF] Li | A multivariate relationship for the impact sensitivities of energetic N-nitrocompounds based on bond dissociation energy[END_REF] also proposed models based on the C-NO 2 bond dissociation energy and the oxygen balance. A series of multi linear regressions were also proposed by Keshavarz [START_REF] Keshavarz | Prediction of impact sensitivity of nitroaliphatic, nitroaliphatic containing other functional groups and nitrate explosives[END_REF][START_REF] Keshavarz | Novel correlation for predicting impact sensitivity of nitroheterocyclic energetic molecules[END_REF][START_REF] Keshavarz | Investigation of the Various Structure Parameters for Predicting Impact Sensitivity of Energetic Molecules via Artificial Neural Network[END_REF][START_REF] Keshavarz | Simple empirical method for prediction of impact sensitivity of selected class of explosives[END_REF][START_REF] Keshavarz | A simple approach for predicting impact sensitivity of polynitroheteroarenes[END_REF], based on constitutional descriptors for various nitro compounds, or Afanas'ev [START_REF] Afanas'ev | Comparative characteristics of some experimental and computational methods for estimating Impact Sensitivity Parameters of Explosives[END_REF] and Badders [START_REF] Badders | Predicting the Impact Sensitivities of Polynitro Compounds Using Quantum Chemical Descriptors[END_REF], with a larger diversity of descriptors. Most of these models presented remarkable correlations but their predictive powers were in general not evaluated on an external set of molecules.

Only few models were proposed with a transparent validation on an external set. Morrill [START_REF] Morrill | Development of quantitative structure-property relationships for predictive modeling and design of energetic materials[END_REF] proposed MLR models based on quantum chemical descriptors issued from semi-empirical calculations with only low performances in prediction (56% in relative error). Keshavarz [START_REF] Keshavarz | Simple Relationship for Predicting Impact Sensitivity of Nitroaromatics, Nitramines, and Nitroaliphatics[END_REF] also proposed a model dedicated to nitramine, nitroaromatic and nitroaliphatic compounds with a root mean squared deviation in prediction of 23 cm. However, this last model was not checked by internal validation tests (neither cross validation, nor Y-randomization).

In the work of Wang [START_REF] Wang | Prediction of impact sensitivity of nitro energetic compounds by neural network based on electrotopological-state indices[END_REF], various approaches (MLR, partial least squares and ANN) were used to develop models based on electrotopological descriptors to predict the impact sensitivities of nitroaromatic, nitramine and nitroaliphatic compounds. High predictive powers were exhibited (up to R² ext =0.932, for MLR models) but lack in robustness can be noticed, potentially due to overparameterization since models are based on up to 16 descriptors. Moreover, the domains of applicability of the models were not considered. Thus, these models do not achieve all OECD principles for their validation.

In this paper, new models were developed with aim to follow all these principles and, then, be applicable in a regulatory framework. In particular, multilinear models were proposed to predict the impact sensitivities of nitroamine, nitroaliphatic and nitroaromatic compounds using a wide variety of descriptors, including quantum chemical descriptors that are expected to allow interpretation in terms of chemical reactivity. These models were validated based on a series of internal and external validation tests. Nitro compounds were first considered by families to obtain local models and then in the same database to achieve a unique global model.

MATERIALS AND METHODS

Experimental data set

This paper aims to correlate the impact sensitivities (h 50% ) to the chemical structures of nitro compounds. Nevertheless, if the chemical mechanisms involved in the initiation of decomposition by an impact, at a molecular scale, are linked to chemical structures, experimental conditions and physical effects, notably related to granulometry, also influence measurements. Moreover, they are thus not completely reproducible, in particular from an apparatus to another [START_REF] Kamlet | The relationship of Impact Sensitivity with Structure of Organic High Explosives. II. Polynitroaromatic explosives[END_REF].

Therefore, the choice of experimental data is critical since all uncertainties are propagated in the final model during the fitting procedure. So, to ensure at best the compatibility between experimental values, all experimental impact sensitivities were extracted from a single reference [START_REF] Storm | Sensitivity Relationships in Energetic Materials[END_REF], collecting the impact sensitivities of nitro compounds obtained from drop weight impact tests. In practice, logh 50% (with h 50% in cm) was considered since it has been successfully used to exhibit correlations in previous works [START_REF] Kamlet | The Relationship of Impact Sensitivity with Structure of Organic High Explosives[END_REF][START_REF] Kamlet | The relationship of Impact Sensitivity with Structure of Organic High Explosives. II. Polynitroaromatic explosives[END_REF][START_REF] Keshavarz | A simple approach for predicting impact sensitivity of polynitroheteroarenes[END_REF][START_REF] Badders | Predicting the Impact Sensitivities of Polynitro Compounds Using Quantum Chemical Descriptors[END_REF][START_REF] Wang | Prediction of impact sensitivity of nitro energetic compounds by neural network based on electrotopological-state indices[END_REF].

The data set consisted in 60 nitramines, 50 nitroaliphatics and 51 nitroaromatics, i.e. 161 nitro compounds, presented in table 1. To allow the validation of models, it was divided into two sets. A training set was used to develop models and a validation set to estimate their predictive power. To achieve efficient validation, the validation set should be representative of the chemical diversity of molecules in the applicability domain of the model, i.e. included in the training set. Here, the partition between sets was done in each family of nitro compounds (nitramines, nitroaliphatics, nitroaromatics) to ensure the sufficient representativity of each family in the final model and to ensure an adequate number of molecules in each set for the development and validation of specific models. Moreover, sets were built to respect same distribution in experimental values in the training and validation sets. To this end, molecules were ordered by increasing experimental values in each family and validation molecules were selected regularly (one molecule out of three). The remaining molecules constituted the training set.

Molecular descriptors

The molecular structures of the 161 nitro compounds of the data set were calculated using the density functional theory (DFT) in Gaussian03 package [START_REF] Frisch | Gaussian03[END_REF]. Geometries were optimized using the PBE0 functional [START_REF] Adamo | Toward reliable density functional methods without adjustable parameters: The PBE0 model[END_REF] and the 6-31+G(d,p) basis set. This method has already been used in QSPR studies [START_REF] Fayet | Predicting the thermal stability of nitroaromatic Compounds using Chemoinformatic Tools[END_REF][START_REF] Fayet | On the use of descriptors arising from the conceptual density functional theory for the prediction of chemicals explosibility[END_REF][START_REF] Fayet | QSPR Modeling of Thermal Stability of Nitroaromatic Compounds: DFT vs. AM1 Calculated Descriptors[END_REF][START_REF] Fayet | Development of a QSPR model for predicting thermal stabilities of nitroaromatic compounds taking into account their decomposition mechanisms[END_REF]. Moreover it was validated from geometrical and energetic considerations for studying the decomposition of nitro compounds [START_REF] Fayet | Theoretical Study of the Decomposition Reactions in Substituted Nitrobenzenes[END_REF][START_REF] Fayet | A theoretical study of the decomposition mechanisms on substituted ortho-nitrotoluenes[END_REF]. Vibrational frequencies were computed at same calculation level to ensure that all stable species presented no imaginary frequency. These molecular structures were then characterized by a series of descriptors. Four classes of descriptors can be considered. Constitutional descriptors exhibit the presence and number of specific features of molecules, e.g. numbers of atoms, bonds or chemical groups. Topological descriptors describe the 2D structure of the molecule based on its connectivity table. They characterize the size and shape of molecules, e.g. the Wiener index is well correlated with the boiling point of alkanes as it mathematically represents their degrees of branching [START_REF] Wiener | Structural Determination of Paraffin Boiling Points[END_REF]. Geometric descriptors stem for the 3Dstructure (e.g. molecular volume). Quantum chemical descriptors include binding, energetic, electronic and thermodynamic information. They are particularly useful to characterize the reactivity of compounds.

Here, most of the descriptors resulted from the DFT calculated structures using CodessaPro software [49]. Detailed definitions and information about these descriptors can be found in [START_REF] Karelson | Molecular Descriptors in QSAR/QSPR[END_REF]. Additional descriptors were also included since they have been identified in previous works to be related to the properties (e.g. their heats of decomposition [START_REF] Fayet | On the use of descriptors arising from the conceptual density functional theory for the prediction of chemicals explosibility[END_REF][START_REF] Fayet | On the prediction of thermal stability of nitroaromatic compounds using quantum chemical calculations[END_REF]) of nitro energetic compounds or to characterize some particular features identified in the dataset. Finally, more than 300 descriptors were computed for each molecule in this study.

QSPR modeling

The QSPR approach relies on the principle that modifications of molecular structures undergo modifications of the properties of chemical compounds. It consists in developing mathematical relationships between experimental properties and descriptors of the molecular structures. To this end, various approaches can be used like genetic algorithms (GA) [START_REF] Leardi | Genetic algorithms in chemometrics and chemistry: a review[END_REF] or artificial neural networks (ANN) [START_REF] Gasteiger | Neural Networks in Chemistry[END_REF]. In this paper, multi linear regressions were computed. Such models follow the mathematic form in Eq. 1.

∑ + = i i i X a a Y 0 (1)
where Y is the property to predict, X i are the molecular descriptors and a i are the corresponding regression constants.

To achieve reliable and meaningful models, the statistical treatment has to select the set of n descriptors, among the more than 300 calculated ones, that leads to the development of the most predictive model. Here, the so-called "best multi linear regression" procedure (BMLR), as implemented in CodessaPro software, was used. This method, already used successfully for the development of predictive models of nitro compounds [START_REF] Fayet | Development of a QSPR model for predicting thermal stabilities of nitroaromatic compounds taking into account their decomposition mechanisms[END_REF] and described in ref [START_REF] Karelson | Molecular Descriptors in QSAR/QSPR[END_REF], is based on the successive addition of descriptors in original two-parameter equations as long as the stability of models, evaluated based on the Fisher criterion F, increases. It finally provides the best model for each number of descriptors. The final model is chosen as the model presenting the best compromise between parameterization (i.e. the number of descriptors) and correlation.

Internal and external validations

To evaluate the performances of models, internal and external validations were performed. The goodness-of-fitting was first characterized by the coefficient of determination (R²) and the root mean squared error (RMSE) between calculated and experimental values for the molecules of the training set. The pertinence of each descriptor in the model was checked based on a student t-test at a 95% level of confidence.

Then, the robustness of models was estimated by leave-one-out and leave-many-out cross validations (Q² LOO , Q² 10CV , Q² 5CV ). Models were expected to present Q² values close to R² ones. Moreover, to ensure against chance correlations, Y-randomization tests [START_REF] Rücker | y-Randomization and Its Variants in QSPR/QSAR[END_REF][START_REF] Lindgren | Model validation by permutation tests: Applications to variable selection[END_REF] were computed. The values of properties were randomized 500 times and, at each iteration, new models were refitted. These new models are expected to present poor correlations compared to original ones. As proposed by Rücker et al. [START_REF] Rücker | y-Randomization and Its Variants in QSPR/QSAR[END_REF], chance correlation was considered at a 1% level of probability, by considering that the difference between the correlation of the original model and the average correlation of the random models issued from Y-randomisation (R² YS ) should not exceed 2.3 times the standard deviation in R² for the new models (SD YS ).

Lastly, the predictive power of models was characterized by external validation on the correlation between predicted and experimental values for the molecules of the validation set. Performances of models were clarified based on the root mean square error (RMSE EXT ), the R² EXT and Q² EXT coefficients obtained from the predictions on the validation set. A summary of used statistical coefficients is proposed in table 2.

Applicability Domain (AD)

The domain of applicability of a model is the domain in which predictions are reliable. Indeed, by construction, a QSPR model is not applicable for all chemicals but only predictions for molecules that are similar to the ones of the training set can be considered as reliable.

In this paper, the domain of applicability of each model was defined by interpolation of the molecules of the training set, in the chemical space defined on the descriptors constituting the model. The Ambit Discovery software [START_REF] Jaworska | Ambit Discovery[END_REF] was used to build these applicability domains to include 95% of the molecules of the training set based on their Euclidean distance to the mean in the descriptors space.

Hence, all external validation statistics have been computed again by excluding the molecules of the validation set that did not belong to the applicability domain of the models. These parameters were noted RMSE IN , R² IN , Q² IN .

Moreover, for final application, it should be noted that models also have to be used in the range of experimental property values for the molecules in the training set. So, predictions calculated out of this range should be considered with particular attention.

Partial Least Squares

To assist discussion, partial least squares (PLS) analyses were also carried out using SIMCA P+ software [START_REF] Simca P+ | [END_REF]. This method consists in projecting an initial set of intercorrelated descriptors into a reduced set of orthogonal variables, called latent variables (LV). By construction, first projection represents the maximum of variance in the data set, taking into account the covariance of each descriptor with the impact sensitivity and additional projections aim to take into account the remaining variance. A LV was considered as necessary if it increased the robustness of the PLS analysis by 0.05. This approach allows the representation of the chemical space by plotting molecules on a 2D-graph based on the first two LVs (score plot) since these two LVs gathered most part of the variance in the dataset.

RESULTS

To predict the impact sensitivity of nitro compounds, two strategies were applied in this paper. In a first step, local models, dedicated to each family of nitro compounds (nitramines, nitroaliphatics and nitroaromatics), were developed. Prediction based on local models was successfully used by Papa et al. for the prediction of physico-chemical properties of polybrominated diphenyl ethers [START_REF] Papa | On the Use of Local and Global QSPRs for the Prediction of Physico-chemical Properties of Polybrominated Diphenyl Ethers[END_REF], Colombo et al. for the prediction of aqueous toxicity [START_REF] Colombo | The proposal of architecture for chemical splitting to optimize QSAR models for aquatic toxicity[END_REF] and by Maunz et al. for chemical toxicity [START_REF] Maunz | Prediction of chemical toxicity with local support vector regression and activity-specific kernels[END_REF]. In particular, Colombo et al. proposed an approach based on the partition of the chemical space in subsets based on structural parameters (e.g. the number of aromatic rings, the maximum bond order for a C atom) and the application of a local model for each identified subset. More recently, Buchwald et al. [START_REF] Buchwald | Using local models to improve (Q)SAR predictivity[END_REF] developed a more complex approach for the treatment of various large datasets (related to toxicological endpoints), in which the predictions are obtained by linear combination of the responses issued from different global and/or local models.

In a second step, a global model was built, to take into account of the whole diversity of compounds in the dataset (nitramines, nitroaliphatics and nitroaromatics) and the performances of this last model were compared to the predictions issued from local models.

Model for nitramines

The first developed model was dedicated to nitramine compounds. So, the BMLR procedure was applied to the 41 ones of the training set that range from 0.70 and 2.51 in logh 50% . Models with up to seven descriptors were computed and the best compromise between the correlation and the number of descriptors in the model was found for the four-parameter equation in Eq. 2.

+ + + - = (2)
where OB is the oxygen balance as defined in the TDG regulation [START_REF]Recommendations on the Transport of Dangerous Goods: Manual of Tests and Criteria, United Nations[END_REF], T 1 E is the topological electronic index (for all pairs of atoms), N O,avg and N N,avg are the average nucleophilic reactivity indices for a O and a N atom, respectively.

The presence of the oxygen balance was expected since it has been already proposed to be correlated with the impact sensitivity [START_REF] Kamlet | The Relationship of Impact Sensitivity with Structure of Organic High Explosives[END_REF][START_REF] Kamlet | The relationship of Impact Sensitivity with Structure of Organic High Explosives. II. Polynitroaromatic explosives[END_REF][START_REF] Cao | Two Dominant Factors Influencing the Impact Sensitivities of Nitrobenzenes and Saturated Nitro Compounds[END_REF][START_REF] Lothrop | The Relationship between Performance and Constitution of Pure Organic Explosive Compounds[END_REF]. In this equation, N O,avg and N N,avg are related to the reactivity of nitro groups that is critical in the decomposition process of nitro compounds [START_REF] Korolev | Differentiation of the molecular structure of nitro compounds as the basis for simulation of their thermal destruction processes[END_REF]. The contribution of topological electronic index T 1 E in the model is less important. Nevertheless, it is not the most important descriptor, particularly regarding OB with a t-test of -15.5 vs. 5.0 for T 1

E

.

The fit of this model (presented in Figure 1) is very good since the correlation between calculated and experimental values in the training set is high (R²=0.919, RMSE=0.11

O NO Q Q N Q P OB h + + + - - = - (3)
where P Qmax-Qmin is the polarity parameter defined as the difference between the maximum and minimum charges in the molecule, Q 2 NO2,max is the squared maximum charge for a nitro group (calculated from natural population analysis [START_REF] Reed | Natural localized molecular orbitals[END_REF]) and N O,max is the maximum nucleophilic reactivity index for a O atom.

OB remains pertinent for the prediction of impact sensitivity of nitroaliphatic compounds. Moreover, the regression constants and t-test values for this descriptor are very similar in both models (0.017 vs. 0.018 and 15.5 vs. 14.8, for Eqs. 2 and 3 respectively). The three other descriptors are quantum chemical descriptors. In particular, N O,max and Q 2 NO2,max are related to the electronic and reactivity properties of nitro groups, which are critical in the decomposition process of nitro compounds. Besides, the electronic properties of nitro groups also strongly influence the last parameter, P Qmax-Qmin .

The performances of the model are better than the MLR model of Wang for nitroaliphatic compounds [START_REF] Wang | Prediction of impact sensitivity of nitro energetic compounds by neural network based on electrotopological-state indices[END_REF]. The new equation is more correlated with R²=0.929 (vs. 0.801 for Wang). Moreover, the models obtained after Y-randomization demonstrate low correlations (R² YS =0.123 and SD YS =0.076). So, this new model did not result from chance correlation. All property values in the training set, which define the AD of the model, ranged between 0.78 and 2.48 (log unit). Its predictive power, calculated for the 16 nitroaliphatic molecules of the validation set (see. Figure 2), remains high when considering the AD of the model with RSME IN =0.19. Here again, robustness is good (Q² LOO =0.901) when Wang's models clearly failed (Q² LOO =0.512) due to possible overparameterization.

Model for nitroaromatics

The last class of compounds in the data set concerned 51 nitroaromatics. A QSPR model was developed on the 34 nitroaromatic compounds of the training set. Among the 18 models issued from BMLR, the four-parameter equation in Eq. 4 demonstrated the best compromise between correlation and parameterization.

C N LUMO N Q BO h - - - + = ε (4)
where ε LUMO is the energy of the lowest unoccupied molecular orbital (LUMO), BO N,max is the maximum bond order for a N atom, Q min is the minimum partial charge and N C,min is the minimum nucleophilic reactivity index for a C atom.

The performances of this model are less important than the ones for nitramines and nitroaliphatics. Indeed, correlation and robustness are lower, with R²=0.812 and Q² LOO =0.751, and, due to molecules out of the applicability domain, predictivity in terms of RMSE EXT exceeds the domain of values of logh 50% in the data set. Indeed, RMSE EXT of 3.502 was calculated whereas the values for the molecules of the data set are concentrated between 0.70 and 2.51. In particular, the predicted values for 2,4,6trinitrobenzonitrile (aro-40) and 2,4,6-trinitrobenzaldoxime (aro-48) are negative and thus non physical (-9.67 and -0.59, respectively). These important deviations (clearly shown in Figure 3) made the statistical coefficients Q² EXT out of its classic range of values (-71.09). When considering only the applicability domain, this coefficient becomes meaningful, even if performances remain low in terms of prediction (R² IN =0.541, Q² IN =0.508, RMSE IN =0.32). Besides, the models proposed by Wang [START_REF] Wang | Prediction of impact sensitivity of nitro energetic compounds by neural network based on electrotopological-state indices[END_REF] for nitroaromatics presented similar failure in prediction (R² EXT =0.522, Q² EXT =0.457, RMSE EXT =0.27, for its MLR model in Table 4).

The complexity of the mechanisms involved in the decomposition of nitroaromatic compounds offers an explanation to such difficulty. Indeed, different reaction paths have been identified for the decomposition of nitroaromatic compounds upon their molecular structures [START_REF] Brill | Kinetics and mechanisms of thermal decomposition of nitroaromatic explosives[END_REF]. For instance, particular primary paths were exhibited for nitroaromatics presenting a methyl group in ortho position to a nitro group [START_REF] Fayet | A theoretical study of the decomposition mechanisms on substituted ortho-nitrotoluenes[END_REF] compared to nitroaromatics without any ortho groups [START_REF] Fayet | Theoretical Study of the Decomposition Reactions in Substituted Nitrobenzenes[END_REF]. Such consideration was considered by Kamlet [START_REF] Kamlet | The relationship of Impact Sensitivity with Structure of Organic High Explosives. II. Polynitroaromatic explosives[END_REF] who proposed two models as a function of the presence of CH containing groups in ortho position to a nitro leading to good correlations (r=0.97 and 0.96 for the compounds without and with α-CH linkage, respectively). Besides, similar subdivision was proposed in previous work for the prediction of heats of decomposition [START_REF] Fayet | Development of a QSPR model for predicting thermal stabilities of nitroaromatic compounds taking into account their decomposition mechanisms[END_REF]. These two subdivisions were also considered in the present study. However, no reliable model was obtained when considering only non-ortho-substituted or only ortho-substituted nitroaromatic compounds. The development of a model dedicated to the nitro compounds presenting α-CH linkage was not possible since the number of available data (only 17 compounds) was not sufficient for partition between training and validation sets.

Projection methods, e.g. PLS, are efficient tools to identify specific classes of molecules in databases, and were used here to identify possible particular clusters of compounds among nitroaromatics. Indeed, the presence of specific groups of molecules in data sets, generally due to particular molecular features, could explain the difficulty to achieve reliable models. So, a PLS analysis was performed on the entire set of 51 nitroaromatics based on the entire set of descriptors, after exclusion of all descriptors presenting missing values or no variance, i.e. 313 descriptors. The score plot, in Figure 4, obtained by projection of the molecules on the first two LVs, proposes an illustration of the distribution of molecules as a function of the descriptors and their covariance with the impact sensitivity. No distinction was observed between ortho and non-ortho substituted compounds as in previous works [START_REF] Fayet | Development of a QSPR model for predicting thermal stabilities of nitroaromatic compounds taking into account their decomposition mechanisms[END_REF], but clusters were identified as a function of other molecular features: number of aromatic cycles and presence of a C(NO 2 ) 3 fragment. In particular, this last feature could be related to a particular decomposition path during the decomposition process.

To go further in the development of reliable models, a first potential strategy would consist in developing different models for each identified clusters in this PLS analysis. Unfortunately, the available data set was not large enough. Indeed, the largest cluster contained only 27 molecules, which is not sufficient to be divided into sufficiently large training and validation sets.

In another approach, additional experimental measurements may lead to a dataset producing a better distribution of the molecules in the chemical space, by performing. In this paper, the data set was extracted from a single reference taken from literature. But, impact sensitivity is very dependent on experimental apparatus and other data from other sources may not be consistent. Nevertheless, in this paper, the data reported in reference [START_REF] Storm | Sensitivity Relationships in Energetic Materials[END_REF] made it possible to extend the data set to nitramines and nitroaliphatics, as proposed in the following global analysis.

Global model

In the perspective of a more global approach towards the prediction of impact sensitivities of nitro compounds, the complete data set was considered. It contained 161 molecules and was balanced between the three families of nitro compounds: 61 nitramines, 51 nitroaromatics and 50 nitroaliphatics. Thus, this data set could be expected to be adapted to the development of a global model.

Moreover, it could allow further predictions for nitroaromatic compounds by introducing additional compounds that could better represent the diversity of mechanisms that could be involved in the decomposition of nitro compounds as explained in previous section.

This global model was developed on the entire training set, i.e. 108 molecules. Using the BMLR method, regressions with up to 15 descriptors were computed and a five-parameter regression (in Eq. 5) was selected.

NH avg O n WPSA Q N OB h + + - + - = (5)
where OB is the oxygen balance as defined in the TDG regulation [START_REF]Recommendations on the Transport of Dangerous Goods: Manual of Tests and Criteria, United Nations[END_REF], N O,avg is the average nucleophilic reactivity index for a O atom, Q min is the minimum partial charge, WPSA3 is the weighted partial positive charged surface area (order 3) obtained via calculated Mulliken charges [START_REF] Mulliken | Electronic Population Analysis on LCAO-MO Molecular Wave Functions. I[END_REF] and n NH2 is the number of amino groups. Some chemical interpretation can be highlighted. As in the models for nitramines and nitroaliphatics, the significance of OB (t-test=-16.2) is consistent with the correlations made by Kamlet [START_REF] Kamlet | The Relationship of Impact Sensitivity with Structure of Organic High Explosives[END_REF][START_REF] Kamlet | The relationship of Impact Sensitivity with Structure of Organic High Explosives. II. Polynitroaromatic explosives[END_REF] and Lothrop [START_REF] Lothrop | The Relationship between Performance and Constitution of Pure Organic Explosive Compounds[END_REF]. Moreover, N O,avg characterizes the reactivity of the O atoms in nitro groups that are central in the decomposition process of nitro compounds. Moreover, if the pertinence of the descriptors WPSA3 and Q min , are less easy to clarify, they are based on the distribution of charge in molecules, which is strongly influenced by the presence of nitro groups. Lastly, the presence of the number of amino groups did not appear so likely interpretable. Nevertheless, it is the less significant descriptor in the equation (t-test=2.6). The development of a model excluding n NH2 was tested but the performance of the models decreased, in particular for the amino molecules of the validation set.

The performances of this model are satisfactory (as presented in figure 5). Indeed, it is not only well correlated (R²=0.816) and robust (Q² LOO =0.793), but also predictive (R² EXT =0.759), in particular in its applicability domain (R² IN =0.750). In terms of predicted impact sensitivity, predictions between 0.70 and 2.51 (log unit) can be considered as reliable. This model is more predictive than the global MLR model of Wang [START_REF] Wang | Prediction of impact sensitivity of nitro energetic compounds by neural network based on electrotopological-state indices[END_REF] (R² EXT =0.740). It is less reliable than the models developed previously in this paper for nitramines and nitroaliphatics but better than the one for nitroaromatic compounds. The same observations can be made for the models of Wang.

To complete the comparison between local and global models, the difference between the values obtained from Eqs. 2-4 and experimental results was computed for the molecules of the validation set (taking into account ADs) and a better predictive power was observed for a consensus modelling based on local models (R² IN =0.829) than for the global model (R² IN =0.750), as shown in table 5. Moreover, it can be noticed that if the predictive power of the global model is significant, it failed for nitroaromatic compounds with only R² IN =0.227, contrary to the hope of improvement that could be issued from the extension of the dataset in terms of chemical diversity. Local models lead to better predictivity than the global one for nitroaliphatics (R² IN =0.877 vs 0.816) and similar results are obtained for nitramines (R² IN =0.845 vs 0.835). So, these two approaches lead to the same conclusions. In both cases, a failure was observed for nitroaromatic compounds whereas good predictions were obtained for nitramines and nitroaliphatics (with higher reliability for local models than for the global one, as it could have been expected).

Finally, theses two approaches are complementary. Indeed, local models give the best predictions for some molecules, e.g. for the 1,1,1,3-Tetranitrobutane (ali-35) with an error of 0.12 compared with an error of 0.31 for the global model, whereas the global model is more predictive for others, such as trinitroethyl-5,5-dinitro-3-nitrazahexanoate (ami-49) and 2,2,2-trinitroethyl-4,4,4-trinitrobutyrate (ali-40) with deviations of 0.01 and 0.03 vs. 0.19 and 0.14 for the local models, respectively. So, global and local approaches are complementary and they could be used in a consensus by considering the prediction from both models to obtain a more robust estimation of the sensitivity of studied compounds.

CONCLUSION

In this study, four QSPR models were developed and validated in view of predicting the impact sensitivities of nitro compounds, based on multilinear regressions and quantum chemical calculations. The data set used was well balanced between three classes of nitro compounds: nitramines, nitroaliphatics and nitroaromatics. First, three local models were developed for each of the three families. Then, a fourth model was developed on a global approach using all the nitro compounds of the data set.

All models were constructed according to all OECD principles for the validation of QSAR/QSPR models for regulatory use. Indeed, the endpoint was clearly defined as the impact sensitivity from drop weight impact test. Algorithms were completely defined from the model equations to the calculation of initial molecular structures. Moreover, the applicability domain was determined based on the chemical space in the training set and performances were characterized by internal and external validation procedures to measure the goodness-of-fit, the robustness and the predictive power of models. Furthermore, descriptors in models were pertinent from a chemical point of view since most of them are related (directly or indirectly) to the properties of nitro groups that are critical in the reaction mechanisms involved in the decomposition of nitro compounds.

For both nitramines and nitroaliphatics, local models demonstrated high performances, in particular in terms of predictivity (RMSE IN =0.16 and 0.19 respectively), whereas analysis failed for nitroaromatics due to the too large diversity of structures regarding the size of the data set. Concerning the global model, it demonstrated significant predictive power with RMSE IN =0.21 in its applicability domain. Regarding the predictions of impact sensitivities for nitroaromatics, both local and global models failed. Even though the performance of this last model was good, local models could be preferred since their performances were higher in the case of nitramines and nitroaliphatics. A consensus approach based on both local and global approaches could also be pertinent to improve confidence in the predictions.

Figure 4 -

 4 Figure 4 -Identification of clusters of compounds from the score plot of PLS analysis on the 51 nitroaromatic compounds of the data set based on 313 molecular descriptors. The intercalation fragments "A" identified in the data set are: -NH-, -CH 2 -CH 2 -, -CH=CH-, -(C=O)-or absent (no intercalation fragment).

Figure 5 -

 5 Figure 5 -Experimental vs. predicted logh 50% of nitro compounds based on Eq. 5

  ). Moreover, the cross validation correlation coefficients are close to R² and stable when the partition size increases (Q² LOO =0.888, Q² 10CV =0.878, Q² 5CV =0.867), exhibiting good robustness. The model does not result from chance correlation, since the models generated from Y-randomization present low correlations (R² YS =0.103, SD YS =0.071). Finally, predictions realized on the 19 nitramines of the validation set are in good agreement with experimental values (R² EXT =0.878, Q² EXT =0.853, RMSE EXT =0.16), especially in the applicability domain (R² IN =0.845, Q² IN =0.817, RMSE IN =0.16), as demonstrated in Table3.These performances are better than the ones of Wang's models for nitramines[START_REF] Wang | Prediction of impact sensitivity of nitro energetic compounds by neural network based on electrotopological-state indices[END_REF] in table 4. In particular, correlation is better than his MLR model (R²=0.852). Moreover, the robustness and the predictive power of the new model are also significantly higher (Q² LOO =0.888 vs. 0.695, Q² EXT =0.853 vs. 0.670 and RSME EXT =0.16 vs. 0.23). These better results, in particular in robustness, can be attributed to an over-parameterization of the models of Wang, based on 10 descriptors vs. only 5 in the present study for nearly the same number of molecules.

	Model for nitroaliphatics
	A second specific model was developed on the 34 nitroaliphatic compounds of the training set. A
	four-parameter model (in Eq. 3) was proposed to be the best compromise between correlation and
	number of descriptors [63].
	log	% 50	438 . 0	018 . 0	07 . 4	max	min	5 . 28	2	2	max ,	79 . 4	max ,

Table 1 -

 1 Experimental and predicted impact sensitivities (logh 50% ) from local and global models (Eqs 2-5)

			Experimental		Predicted
	ID	compounds	Ref. [39]	Nitramines Eq. 2	Nitroaliphatics Eq. 3	Nitroaromatics Eq. 4	Global Eq. 5
	Training set
	ami-01 N,N'-Dinitro-methanediamine	1.11	1.21	-	-	1.21
	ami-02 N-Nitro-N-methyl-formamide	2.51	2.52	-	-	2.44
	ami-03 Methyl-2,2,2-trinitro-ethylnitramine	0.95	1.00	-	-	0.94
	ami-04 Trinitroethyl-nitroguanidine	1.18	1.00	-	-	0.99
	ami-05 Cyclotrimethylene-trinitramine	1.41	1.35	-	-	1.34
	ami-06 N-Methyl-N,N'-dinitro-1,2-ethanediamine	2.06	2.08	-	-	1.89
	ami-07 Trinitroethyl-cyanomethylnitramine	1.04	1.09	-	-	1.09
	ami-08 Bis-(2,2,2-trinitroethyl)-nitramine	0.70	0.56	-	-	0.60
	ami-09 N,N'-Dimethyl-N,N'-dinitrooxamide	1.90	1.86	-	-	1.93
	ami-10 N-Nitro-N-(trinitroethyl)-glycinamide	1.23	1.17	-	-	1.53
	ami-11 Cyclotetramethylene-tetranitramine	1.46	1.38	-	-	1.28
	ami-12 N,N'-Dinitro-N-[2-(nitramino)ethyl]-1,2-ethanediamine	1.59	1.71	-	-	1.73
	ami-13 1,3,3,5,5-Pentanitropiperidine	1.15	1.16	-	-	1.07
	ami-14 2,2,2-Trinitroethyl-3',3',3'-trinitropropyl-nitramine	0.78	0.80	-	-	0.79
	ami-15 Trinitroethyl-N-ethyl-N-nitro-carbamate	1.28	1.44	-	-	1.54
	ami-16 Trinitroethyl-2-methoxy-ethylnitramine	1.62	1.44	-	-	1.88
	ami-17 N,N'-3,3-Tetranitro-1,5-pentanediamine	1.54	1.59	-	-	1.60
	ami-18 2,2,2-Trinitroethyl-N-(2,2,2-trinitroethyl)-nitramino acetate	0.95	0.91	-	-	1.05
	ami-19 2,2,2-Trinitroethyl-4-nitrazavalerate	1.54	1.46	-	-	1.55
	ami-20 Trinitropropyle-(2,2-dinitropropyl)-nitramine	1.23	1.20	-	-	1.17
	ami-21 2',2',2'-Trinitroethyl-2,5-dinitrazahexanoate	1.18	1.25	-	-	1.39
	ami-22 2,2,2-Trinitroethyl-3,3-dinitrobutyl nitramine	1.30	1.20	-	-	1.17
	ami-23 N,N'-Dinitro-N,N'-bis[2-(nitramino)ethyl]-1,2-ethanediamine	1.72	1.81	-	-	1.87

Table 3 -

 3 Performances of QSPR models value out of the classical range due to non physical prediction values obtained for compounds that were finally out of the applicability domain of the model

		Nitramines	Nitroaliphatics	Nitroaromatics	Global
		Eq. 2	Eq. 3	Eq. 4	Eq. 5
	n TR	40	34	34	108
	n EXT	20	16	17	53
	R²	0.919	0.929	0.812	0.816
	RMSE TR	0.11	0.13	0.16	0.19
	Q² LOO	0.888	0.901	0.751	0.793
	Q² 10CV	0.878	0.893	0.743	0.786
	Q² 5CV	0.867	0.902	0.751	0.789
	R² YS	0.103	0.123	0.127	0.049
	SD YS	0.071	0.076	0.082	0.028
	R² EXT	0.878	0.876	0.013	0.759
	Q² EXT	0.853	0.863	-71.09 a	0.749
	RMSE EXT	0.16	0.19	3.50	0.23
	R² IN	0.845	0.877	0.541	0.750
	Q² IN	0.817	0.871	0.508	0.740
	RMSE IN	0.16	0.19	0.32	0.22

a

Table 4 -

 4 Comparison of the performances of previous and new MLR-based QSPR models References Target compounds n train n valid R² Q² LOO R² EXT Q² EXT RMSE EXT Wang et al. b Nitramines 45 10 0.852 0.695 0.856 0.670 Value out of the classical range due to non physical prediction values obtained for compounds that were finally out of the applicability domain of the model b Experimental values collected from various literature references, including ref [39]. c All experimental values collected from ref [39].

	0.23

a

Table 5 -

 5 Predictive powers in the applicability domain (R² in ) of the new QSPR models by family of nitro compounds

	Models	Nitramines	Nitroaliphatics Nitroaromatics	All
		Eq. 2	0.845	-	-
	Local	Eq. 3	-	0.877	-	0.829
		Eq. 4	-	-	0.541
	Global	Eq. 5	0.835	0.816	0.227	0.750