Sara Sartini

Elisabetta Levati

Martina Maccesi

Matteo Guerra

Gilberto Spadoni

Stéphane Bach

Monica Benincasa

Marco Scocchi

Simone Ottonello

Silvia Rivara

Barbara Montanini
email: barbara.montanini@unipr.it

New Antimicrobials Targeting Bacterial RNA Polymerase Holoenzyme Assembly Identified with an in Vivo BRET-Based Discovery Platform

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

INTRODUCTION

Antibiotic resistance is becoming a major health problem worldwide. According to the World Health Organization, we will soon be facing a so-called 'post-antibiotic era', in which common infections and minor injuries can once again kill [START_REF] Cima | WHO warns of 'post-antibiotic era[END_REF].

Multiple mechanisms, such as masking or modification of the target to make it resilient to antibioticmediated inhibition, as well as increased efflux, impaired internalization and/or enzymatic modification of antimicrobial compounds are involved in the development of antibiotic resistance [START_REF] Allen | Call of the wild: antibiotic resistance genes in natural environments[END_REF][START_REF] Brown | Antibacterial drug discovery in the resistance era[END_REF][START_REF] Lewis | New approaches to antimicrobial discovery[END_REF][START_REF] Marston | Antimicrobial Resistance[END_REF][START_REF] Ventola | The antibiotic resistance crisis: part 1: causes and threats[END_REF]. Two other major determinants of the antibiotic crisis are the abuse/misuse of antimicrobials and the 'unproductivity' of the antibiotic discovery pipeline. In fact, most of the presently available antibiotics have been discovered decades ago and are focused on a relatively small number of biological targets, most notably the ribosome, cell wall biosynthesis and, to a lower extent, DNA replication.

A somewhat underexploited, but fully validated antibiotic target is bacterial RNA polymerase (RNAP), which in response to the need for new antibiotics is re-gaining momentum as an attractive antimicrobial target, also thanks to the increasing availability of novel inhibitory compounds and high-resolution RNAP as well as RNAP-inhibitor structures. The potential of RNAP as a valuable antibiotic target stems from its essential biological function and high degree of conservation across bacterial species, yet with a sufficient divergence from its eukaryotic counterpart that makes cross-inhibition and toxicity fairly rare events. Indeed, two RNAP inhibitors, rifampin and lipiarmycin, targeting distinct RNAP active site regions [START_REF] Boyaci | Fidaxomicin jams Mycobacterium tuberculosis RNA polymerase motions needed for initiation via RbpA contacts[END_REF][START_REF] Campbell | Structural mechanism for rifampicin inhibition of bacterial RNA polymerase[END_REF][START_REF] Lin | Structural Basis of Transcription Inhibition by Fidaxomicin (Lipiarmycin A3)[END_REF], have been approved for clinical use. Despite their undisputable efficacy, mutations can lead to acquired drug resistance and failure of antibiotic treatment to cure infections. Resistance-conferring mutations can also affect the treatments with newly discovered RNAP inhibitors, including multiple compounds, in addition to lipiarmycin, that target the RNAP switch region, and the recently discovered natural nucleoside analog pseudouridimycin (PUM) [START_REF] Aristoff | Rifamycins--obstacles and opportunities[END_REF][START_REF] Ho | Structures of RNA polymeraseantibiotic complexes[END_REF][START_REF] Maffioli | Antibacterial Nucleoside-Analog Inhibitor of Bacterial RNA Polymerase[END_REF][START_REF] Srivastava | Frequency, spectrum, and nonzero fitness costs of resistance to myxopyronin in Staphylococcus aureus[END_REF][START_REF] Srivastava | New target for inhibition of bacterial RNA polymerase: 'switch region[END_REF].

In bacterial cells RNAP is present as both a catalytically active, but promoter-blind, core enzyme (RNAPc) formed by five subunits (2, , ', and ) and a holoenzyme form (RNAPh), which upon sigma factor incorporation (e.g., the primary house-keeping Escherichia coli factor  70 ) gains the ability to recognize promoter sequences and to transcribe RNA in a promoter-specific manner. Because of its absolute requirement for productive and specific transcription, the RNAPc- 70 interaction represents another attractive target for RNA synthesis inhibition. This relies on a specific protein-protein interaction (PPI), centered on the clamp helix (CH) region of the RNAPc '-subunit and the 2.2 region of the  factor. Key amino acid residues likely involved in such interaction have been revealed by site-directed mutagenesis experiments [START_REF] Arthur | Mutational analysis of β' 260-309, a  70 binding site located on Escherichia coli core RNA polymerase[END_REF][START_REF] Johnston | The interaction of Bacillus subtilis  A with RNA polymerase[END_REF][START_REF] Ma | Inhibitors of bacterial transcription initiation complex formation[END_REF][START_REF] Sharp | The interface of σ with core RNA polymerase is extensive, conserved, and functionally specialized[END_REF] and by the multiple 3D structures of bacterial RNAP holoenzymes (1L9U, 1Iw7, 4YG2 and references within) [START_REF] Murakami | X-ray crystal structure of Escherichia coli RNA polymerase  70 holoenzyme[END_REF][START_REF] Murakami | Structural basis of transcription initiation: an RNA polymerase holoenzyme-DNA complex[END_REF][START_REF] Vassylyev | Crystal structure of a bacterial RNA polymerase holoenzyme at 2.6 A resolution[END_REF]. These include both polar amino acids (E. coli amino acid residues Arg275, Arg278 and Arg281 in the '-subunit and Asp403 and Glu407 in  70 ) as well as hydrophobic amino acid residues (Leu282 and Met298 in the '-subunit and Ile410 and Leu402 in  70 ). Compensatory amino acid substitutions in both RNAP subunit regions are thus presumably required for the acquisition of resistance while preserving bacterial cell viability.

Following the proof-of-principle demonstration that designed peptides mimicking the 2.2 region can prevent RNAPh formation and inhibit in vitro transcription [START_REF] Husecken | Peptidebased investigation of the Escherichia coli RNA polymerase  70 :core interface as target site[END_REF], the construction of a structure-based pharmacophore model led to the identification of two compounds (GKL003 and C5, 1 and 2 in Table 1) that by binding to the '-subunit interfere with in vitro transcription initiation at nM concentrations [START_REF] Ma | Inhibitors of bacterial transcription initiation complex formation[END_REF][START_REF] Ma | Bacterial Transcription Inhibitor of RNA Polymerase Holoenzyme Formation by Structure-Based Drug Design: From in Silico Screening to Validation[END_REF]. However, when tested for their ability to inhibit bacterial growth, both compounds were found to exhibit antimicrobial activity at 500-100,000 fold higher concentrations, an observation that may be explained by their poor solubility and/or permeability properties. Therefore, while confirming the '- 70 interaction as a viable target for the development of novel antimicrobials, these results, which have been primarily derived from in vitro-based screenings, leave room for a number of improvements. Considering the sub-optimal properties of known '- interaction inhibitors, and in particular their very poor (or lack of) antibacterial activity [START_REF] Ma | Inhibitors of bacterial transcription initiation complex formation[END_REF][START_REF] Ma | Bacterial Transcription Inhibitor of RNA Polymerase Holoenzyme Formation by Structure-Based Drug Design: From in Silico Screening to Validation[END_REF], we decided to explore an expanded chemical space, searching for inhibitors belonging to new chemical classes with more promising antibacterial properties.

With this goal in mind, we developed and optimized a Bioluminescence Resonance Energy Transfer assay in yeast (yBRET) as an in vivo tool for the screening of large candidate compound libraries [START_REF] Corbel | Screening for Protein-Protein Interaction Inhibitors Using a Bioluminescence Resonance Energy Transfer (BRET)-Based Assay in Yeast[END_REF][START_REF] Corbel | First BRET-based screening assay performed in budding yeast leads to the discovery of CDK5/p25 interaction inhibitors[END_REF][START_REF] Corbel | Tamoxifen inhibits CDK5 kinase activity by interacting with p35/p25 and modulates the pattern of tau phosphorylation[END_REF]. yBRET is based on resonance energy transfer between a "donor" luciferase and an "acceptor" fluorescent protein fused to the proteins of interest, both expressed inside yeast cells. If the two proteins interact, energy transfer between the two partners takes place, leading to acceptor fluorophore excitation and the emission of a quantifiable fluorescence (BRET) signal, which will decrease in the presence of an interaction inhibiting compound. yBRET has two favorable features, which are particularly advantageous for the screening of candidate antimicrobial compound libraries: i) the capacity to select for potentially cell-permeant compounds due to its intracellular mode of operation; ii) the ability to immediately detect compounds that are toxic to eukaryotic cells based on the loss of luciferase luminescence.

In this study, yBRET screening of about 5,000 candidate compounds, in silico selected from a larger (≈34,000) compounds library, allowed the identification of seven new hits interfering with the RNAP '- 70 interaction. Four of these hit compounds were independently validated in ELISA and proved to preferentially bind 'subunit. Two derivatives of one of these hits displayed an in vitro RNAP inhibitory activity slightly lower than that of the best available compound (1), but inhibited E. coli and Staphylococcus aureus growth at a more than one order of magnitude lower concentration (50-100 M vs 2 mM) [START_REF] Ma | Inhibitors of bacterial transcription initiation complex formation[END_REF]. Based on the diverse molecular structures of these newly discovered '- 70 interaction inhibitors, we designed a pharmacophore ligandbased model and delineated its mode of binding to the CH region of the RNAP '-subunit.

RESULTS AND DISCUSSION

Reconstitution of the '- 70 interaction in a yBRET format Available 3D structures of the E. coli RNAPh [START_REF] Murakami | X-ray crystal structure of Escherichia coli RNA polymerase  70 holoenzyme[END_REF] and knowledge of the amino acid residues involved in the '- 70 interaction (17) guided the design of the two protein partner constructs for the BRET assay. Given the lack of prior studies using the isolated  70 2.2 domain for RNAPh reconstitution, we initially focused on fulllength  70 and on two different portions of the ' clamp domain overlapping the ' CH region comprised between amino acid residues 1-334 and 220-334, respectively.

In our yBRET set-up the engineered deep-sea shrimp luciferase NanoLuc® (NLuc) is utilized as donor protein and the Yellow Fluorescent Protein (YFP) as acceptor: the protein targeted by the inhibitor (') is fused to the acceptor (YFP) and is constitutively expressed, while expression of the donor-fusion protein ( 70 -NLuc) is under the control of the yeast GAL1 promoter and induced after the addition of the candidate inhibitor compound, to allow for binding of the inhibitor to its target before interaction reconstitution and complex formation (Figure 1A).

BRET signals were measured in the hyper-permeable erg6 yeast strain in order to maximize luciferase substrate and candidate compound internalization. The YFP-' fusion proteins always gave weaker signals compared to the oppositely oriented '-YFP fusions, whereas the orientation of the NLuc donor relative to  70 affected yBRET signal strength to a much lower extent. The shorter (aa. 220-334) ' CH region fragment yielded lower BRET signals compared to the longer (aa. 1-334) fragment. This is likely due to the lack of the ' portion comprised between aa. 41-47, which being also involved in the interaction with the aa. 446-453 region of  70 (E. coli 4YG2), might strengthen the overall interaction but might also be required for a correct folding and positioning of the CH region. Thus, the NLuc- 70 / '(1-334)-YFP pair, which produced the highest BRET signal, was chosen as the best combination for subsequent experiments (Figure 1A).

To be reliably employed for compound screening, the BRET platform must be optimized for signal sensitivity and the specificity of the interaction has to be verified. In the yeast co-transformant expressing NLuc- 70 and '(1-334)-YFP, the BRET signal increased with increasing galactose concentrations up to saturation (not shown) and the minimum galactose concentration (0.5%) yielding the most stable BRET signal (114.1 ± 6.9 mBRET) was thus chosen for subsequent experiments. To verify the specificity of the BRET-reconstituted '- 70 interaction, we mutated specific amino acid residues previously shown to be critical for this interaction [START_REF] Arthur | Mutational analysis of β' 260-309, a  70 binding site located on Escherichia coli core RNA polymerase[END_REF][START_REF] Johnston | The interaction of Bacillus subtilis  A with RNA polymerase[END_REF][START_REF] Ma | Inhibitors of bacterial transcription initiation complex formation[END_REF][START_REF] Sharp | The interface of σ with core RNA polymerase is extensive, conserved, and functionally specialized[END_REF][START_REF] Murakami | X-ray crystal structure of Escherichia coli RNA polymerase  70 holoenzyme[END_REF]. As shown in Figure 1B, the  70 Q406K-E407A double-mutant caused an almost complete loss of the BRET signal, and a 60% reduction of the BRET signal was observed with the ' R275A-R278A double-mutant.

Next, we ran a donor saturation assay to determine whether the observed BRET signal results from random (non-specific) contacts or from a specific PPI. To this end, we swapped the promoters previously utilized for NLuc- 70 and '(1-334)-YFP expression, in order to achieve inducible, galactose concentration-dependent expression of graded amounts of the '-YFP acceptor partner in the presence of a fixed (constitutively expressed) amount of the NLuc donor- 70 partner. Under these conditions, the BRET signals measured in the presence of increasing inducer concentrations fitted a hyperbolic curve, as expected for a specific PPI [START_REF] Bacart | The BRET technology and its application to screening assays[END_REF], with both the wild type and the R275A-R278A mutated versions of the 1-334 '-subunit fragment (Figure 1C). Altogether, these results demonstrate the specificity of the '- 70 interaction reconstituted inside BRETengineered yeast cells.

Functional evaluation of the yBRET screening platform

To validate the yBRET screening platform, we initially used GKL003 and C5 (1 and 2 in Table 1) as reference compounds previously shown to interfere with the '- 70 interaction [START_REF] Ma | Inhibitors of bacterial transcription initiation complex formation[END_REF][START_REF] Ma | Bacterial Transcription Inhibitor of RNA Polymerase Holoenzyme Formation by Structure-Based Drug Design: From in Silico Screening to Validation[END_REF]. The results, however, were largely unsatisfactory, since compound 1 was poorly soluble and displayed a milky consistence when dissolved in yeast synthetic medium at concentrations higher than 10 M, while compound 2 absorbed at 480 nm and emitted at 530 nm, with a significant overlap to the NLuc and YFP spectra that made BRET measurements unreliable. To evaluate the ability of yBRET to specifically identify compounds that inhibit the '- 70 interaction, and given the presence of an indole ring in GKL003 and its in vitro active derivatives, we screened an in-house mini library of 27 indole derivatives (10 mono-indoles and 17 bis-indoles, compounds 3-29 in Supplementary Table 1) (28-31) which were assayed under optimized yBRET conditions and compared with the corresponding results obtained with the use of ELISA. As shown in Supplementary Figure 1A, six of the tested compounds caused BRET signal reduction (up to 50%) without any sign of toxicity.

The yBRET-positive compounds 5 and 15-18, along with two inactive compounds from the same mini-library (the mono-indole 3 and the bis-indole 21) and the reference compounds 1 and 2 were thus tested for their ability to interfere with the '- 70 interaction in a cell-free assay based on ELISA. yBRET-positive molecules inhibited the '- 70 interaction also in ELISA, whereas 3 and 21 were almost completely inactive, thus indicating the reliability of our yBRET-based discovery platform (Supplementary Figure 1B). Compounds 5 and 15 were further evaluated and compared with reference compound 1 in a dose-response ELISA. As shown in Supplementary Figure 1C, they were found to be approximately three-times less potent, with IC50 values of 43.8 μM (5) and 54.5 μM (15), compared to an IC50 of 17.6 μM for compound 1.

Virtual screening campaign for the pre-selection of candidate '- 70 interaction inhibitors

The 'Open Collection Scaffolds' library from Compounds Australia (Griffith University) [START_REF] Simpson | An overview of Australia's compound management facility: the Queensland Compound Library[END_REF], comprising a total of 33,999 commercially available compounds, was used as a repository for the in silico selection of approximately 5,000 candidate '- 70 interaction inhibitors to be subjected to the yBRET screening. Since low MW compounds are less likely PPI inhibitors [START_REF] Villoutreix | A leap into the chemical space of protein-protein interaction inhibitors[END_REF], the library was first filtered by retaining compounds with MW≥ 250. Next, we performed multiple virtual screening runs on the filtered library by applying ligand-based and structure-based selection methods according to the workflow reported in Supplementary Figure 2A. Given the limited information on the key structural elements that are critical for '- 70 interaction disruption, and the medium resolution of the available crystal structures, different selection methods were applied to maximize the possibility of retrieving biologically active compounds. A structure-based selection was first performed by evaluating the fitting of individual compounds to a pharmacophore model built on the 2.2 region of  70 . This pharmacophore model contains seven sites corresponding to the most important amino acid residues of the '- 70 contact region, as revealed by 3D structure and mutagenesis data [START_REF] Arthur | Mutational analysis of β' 260-309, a  70 binding site located on Escherichia coli core RNA polymerase[END_REF][START_REF] Johnston | The interaction of Bacillus subtilis  A with RNA polymerase[END_REF][START_REF] Ma | Inhibitors of bacterial transcription initiation complex formation[END_REF][START_REF] Sharp | The interface of σ with core RNA polymerase is extensive, conserved, and functionally specialized[END_REF][START_REF] Murakami | X-ray crystal structure of Escherichia coli RNA polymerase  70 holoenzyme[END_REF] (Supplementary Figure 2B and2C). A major difference between the present model and the pharmacophore reported by Ma et al. [START_REF] Ma | Inhibitors of bacterial transcription initiation complex formation[END_REF] is that the last one was based on a homology model of Bacillus subtilis RNAP while our pharmacophore was built on the crystal structure of E. coli RNAPh (PDB: 4YG2). Compared to the 4-site model by Ma, our model has additional sites placed on  70 residues Gln406, Leu402 and Asp403. Ligandbased selection was then carried out taking into account four different criteria: i) Shape-screening performed using reference compound 1 in a minimum-energy extended conformation as query (Supplementary Figure 2D). ii) Mutagenesis data indicated the importance of 2.2 acidic residue Glu407 [START_REF] Sharp | The interface of σ with core RNA polymerase is extensive, conserved, and functionally specialized[END_REF] for the interaction with '. Further to this point, reference inhibitor 2, which binds to the '-subunit, contains a carboxylic group. Therefore, a sub-structure search was conducted to retrieve the 367 compounds bearing a carboxylate group. iii) Given the presence of an indole ring in several '- 70 interaction inhibitors [START_REF] Mielczarek | Synthesis and biological activity of novel mono-indole and monobenzofuran inhibitors of bacterial transcription initiation complex formation[END_REF], comprising reference compound 1, the 876 indole derivatives present in the library were also selected. iv) 2D similarity screening based on linear fingerprints using inhibitor 1 as reference structure. Combined use of the above selection criteria led to a final subset of 4960 unique candidate compounds to be subjected to yBRET screening as potential '- 70 interaction inhibitors.

yBRET screening of the in-silico selected compound library

The 4960 compounds selected and retrieved from the 'Open Collection Scaffolds' library were initially screened by yBRET at a fixed concentration of 20 μM, the highest possible concentration allowed by the limited amounts at which the compounds were supplied. Compounds that reduced the BRET signal by at least 15% were retained and re-assayed at the same concentration as well as at a 10 μM concentration. This led to the identification of seven hits belonging to different chemical classes (Table 1). To avoid potential batch-to-batch inconsistencies, independent production batches of the seven hits were acquired and subjected to yBRET assay confirmation and ELISA validation (Table 1). Four of the seven yBRETpositive compounds (31, 33, 34 and 36) were confirmed as inhibitors of the '- 70 interaction in ELISA (Table 1), while compounds 30, 32 and 35 turned out to be insoluble in PBS at concentrations higher than 40 M and did not display any inhibitory activity when tested at a 40 M (or lower) concentrations, and were thus not further pursued. The binding inhibition capacity of the four soluble hits was further assessed in a doseresponse ELISA, which in the case of compounds 31, 33 and 34 revealed IC50 values, ranging from 11.0 μM (34) to 16.7 μM [START_REF] Mantenuto | One-pot synthesis of biheterocycles based on indole and azole scaffolds using tryptamines and 1, 2-diaza-1, 3-dienes as building blocks[END_REF], very similar to the IC50 of the reference compound 1 (17.6 μM), but with higher efficacies (98-100% vs. 80%) (Table 1 and Supplementary Figure 3). Under the same experimental conditions, compound 36 proved to be the least potent (IC50 = 91.3 μM).

Compound 31, bearing an indol-3-yl-urea scaffold, was further investigated through the acquisition and ELISA testing of 12 commercially available structural analogs (listed in Supplementary Table 2) to evaluate their relative potencies and obtain preliminary information on structure-activity relationships. All indol-3-yl-urea derivatives proved to be active as inhibitors of the '- 70 interaction (Supplementary Table 2), and nine of them reduced the PPI-associated ELISA signal by more than 80% (Supplementary Table 2). Analysis of the data obtained at a fixed compound concentration suggests that a phenyl substituent on the amide group is preferred to a benzyl substituent at the same position, and that lipophilic substituents linked to the phenyl ring are well tolerated. Likewise, the presence of a 3-or a 4-pyridyl ring at position 2 of the indole ring leads to similar potencies. A dose-response ELISA analysis of three of the best indol-3-yl-urea derivatives (41, 43 and 47) showed very similar potencies (IC50 ≈10 M) for compounds 41 and 43, which differ only for pyridyl ring substitution, and an IC50 of 20.8 M for compound 47 (Supplementary Table 2 and Supplementary Figure 3).

We then verified the target specificity of the yBRET hits 31, 33, 34 and 36 and of the indole containing molecules 5, 15, and 41, by replacing ' with  70 as primary interactor in ELISA; compound 1, previously shown to specifically target the RNAP '-subunit [START_REF] Ma | Inhibitors of bacterial transcription initiation complex formation[END_REF], was used as an internal reference for this analysis. As shown in Figure 2, a significant (2-4-fold) reduction of binding inhibition compared to the oppositely arranged ELISA format (i.e., using ' as primary interactor) was observed for all compounds, except for the bis-indole 15. In accordance with our experimental design, this indicates that the newly discovered inhibitors interfere with the '- 70 interaction by binding to the RNAP ' subunit.

RNAP inhibitory and antibacterial activity

Next, we investigated the ability of the indol-3-yl-urea derivatives (41, 43 and 47), together with the monoindole 5 and the bis-indole 15 from the in-house mini library, to inhibit promoter-specific RNA transcription.

Compound 1, plus rifampin, served as reference compounds for single-round in vitro transcription assays, performed with E. coli RNAP under non-competitive inhibition conditions. In the single-round transcription assays the transcription signal is directly proportional to the number of RNAPc- 70 active complexes formed, so the signal decrease measured in the presence of the test compounds is strictly correlated with the inhibition of  70 binding. As shown in Figure 3A, all compounds, except 15, almost completely inhibited transcription at 50 M. Dose-response curves were determined for the compounds 43 and 47, which yielded IC50 values (28.6 ± 1.0 M; and 32.8 ± 1.1 M, respectively) approximately three times higher than that of reference compound 1 (11.5 M) (Figure 3B). In the in vitro transcription assay, in the case of reference compound 1 we measured an apparent IC50 three orders of magnitude higher than that reported by Ma et al [START_REF] Ma | Inhibitors of bacterial transcription initiation complex formation[END_REF]. This was likely due to the use in our assay of a 20-fold lower RNAPc enzyme:  70 ratio, an experimental parameter previously shown to critically influence the sensitivity and outcome of in vitro transcription inhibition assays [START_REF] Ma | Inhibitors of bacterial transcription initiation complex formation[END_REF]. Despite this methodological interstudy difference, overall internally consistent results were obtained for the in vitro inhibition capacity (both ELISA and transcription) of reference compound 1 and the newly identified inhibitors.

The same subset of in vitro transcription-validated inhibitors, plus the four yBRET hits [START_REF] Mantenuto | One-pot synthesis of biheterocycles based on indole and azole scaffolds using tryptamines and 1, 2-diaza-1, 3-dienes as building blocks[END_REF][START_REF] Villoutreix | A leap into the chemical space of protein-protein interaction inhibitors[END_REF][START_REF] Mielczarek | Synthesis and biological activity of novel mono-indole and monobenzofuran inhibitors of bacterial transcription initiation complex formation[END_REF][START_REF] Klahn | Bifunctional antimicrobial conjugates and hybrid antimicrobials[END_REF] and reference compound 2, were then assayed for antibacterial activity. This was initially tested on the Grampositive B. subtilis WB800N strain and on the Gram-negative non-pathogenic E. coli DH10 T1R strain by monitoring microbial growth in the presence of a fixed concentration of each compound (200 M; 8 h treatment). As shown in Supplementary Table 3, three compounds (2, 43 and 47) displayed a nearly complete growth inhibitory effect (88-99%) on B. subtilis, whereas a much lower growth inhibition (ranging from 28% to 36% for compounds 47, 43 and 41) was observed in the case of E. coli. This bacterial group-specific difference in efficacy was largely offset by the addition of the outer membrane permeabilizer polymyxin B nonapeptide (PMBN; a non-bactericidal derivative of polymyxin B), suggesting that reduced effectiveness against E. coli is likely due to defective compound internalization. In fact, in the presence of 2 gml PMBN, the inhibitory activity on E. coli of compounds 41 and 43 raised to 81% and 100%, respectively (Supplementary Table 3). As shown in Supplementary Figure 5, PMBN, at this concentration, did not affect bacterial growth.

Overall, compounds 41, 43 and 47 proved to be the most active. Compounds 43 and 47 displayed preferential inhibitory activity against E. coli and B. subtilis, respectively, whereas 41 inhibited growth of both bacteria with a milder efficacy. Importantly, the three compounds retained a significant (33%-60%) inhibitory activity upon prolonged (22 h) culture (not shown) and displayed no (41, 43) or a negligible (5%; 47) growth inhibition on the unicellular eukaryote Saccharomyces cerevisiae, when tested at the same concentration (Supplementary Table 3).

The antibacterial activity of the most potent inhibitors (43 and 47) was further assayed at different compound concentrations, monitoring growth inhibition on the same E. coli and B. subtilis strains every 30 min for 8 h (Figure 4). In this assay, compound 43 proved again to be the most potent against E. coli, with a complete growth inhibition down to a 100 M concentration and a well detectable inhibitory effect even at the lowest (50 M) concentration (Figure 4A). A significant but somewhat reduced effect, i.e., with a marked drop of inhibitory activity at 50 M, was observed also on B. subtilis (Figure 4D). Compound 47, instead, displayed a relatively weak inhibitory activity against E. coli (Figure 4B) but a high efficacy against B. subtilis, with a complete growth inhibition down to a 50 M concentration and a smaller but still significant effect at 25 M (Figure 4E). The results of a comparison of the inhibitory capacity of the indol-3-yl-urea derivatives 43 and 47 with reference compounds 1 and 2, using rifampin as a positive control, are also shown in Figure 4 (panels C-F). All compounds were employed at a fixed concentration (100 M), and in accordance with previous data [START_REF] Ma | Inhibitors of bacterial transcription initiation complex formation[END_REF][START_REF] Ma | Bacterial Transcription Inhibitor of RNA Polymerase Holoenzyme Formation by Structure-Based Drug Design: From in Silico Screening to Validation[END_REF], neither of the reference compounds exerted any appreciable inhibitory effect on E. coli and only a weak growth inhibition was observed with compound 2 in the case of B. subtilis. As expected, rifampin completely blocked both bacteria and displayed a time-dependent growth inhibition identical to that of compounds 43 and 47 in the case of B. subtilis, and to that of compound 43 in the case of E. coli. These results are in agreement with those reported for the reference compounds, previously identified solely on the basis of in vitro screenings, which failed to inhibit bacterial growth (1) or did so (2) with low efficacy. To further investigate the antibacterial activity of the two best compounds (43 and 47), additional antibacterial assays were performed. We first determined the Minimum Inhibitory Concentration (MIC) for both compounds against E. coli DH10 T1R and B. subtilis WB800N, and also against the Gram-positive pathogens S. aureus ATCC 25923 and Listeria monocytogenes DSM 20600 (Supplementary Table 4). The four bacterial strains were all found to be susceptible to compounds 43 and 47, with MIC values ranging from 25 to 100 μM (9.5-43 µg/ml). To gain insight on (and distinguish between) a bactericidal vs. a bacteriostatic activity of the compounds, we performed a killing assay using as readout the number of residual viable cells after 8 h of treatment. As shown in Figure 5 (A), both compounds effectively killed E. coli at a 50 µM and 100 M concentration after treatment. Both compounds were also bactericidal against B. subtilis and the pathogen L. monocytogenes (Figure 5B, C) at 100 µM, and particularly compound 47 reduced the number of viable cells also at 50 M concentration (Figure 5B,C). On the other hand, both compounds only displayed a bacteriostatic effect on S. aureus (Figure 5D). Gridlines mark the CFU/ml at t0. Bactericidal effect, that is evidenced by a decrease in the number of viable cells after treatment compared to initial inoculum, is reported under the histograms as Fold reduction vs t0. Growth inhibition values, relative to the DMSO vehicle (Fold reduction vs 8 h), are also reported under the histograms. Data are the mean ±SD of at least three replicates.

As shown by the need for the membrane permeabilizer PMBN in order to achieve an antibacterial effect against E. coli and as pointed out by many other studies, in which hyper-permeable E. coli mutants were used for testing antibacterial activity [START_REF] Maffioli | Antibacterial Nucleoside-Analog Inhibitor of Bacterial RNA Polymerase[END_REF][START_REF] Zhang | GE23077 binds to the RNA polymerase 'i' and 'i+1' sites and prevents the binding of initiating nucleotides[END_REF], inhibitor internalization likely represents the main bottleneck in the discovery of new effective antibiotics. Indeed, despite the presence in 2.2 of an acidic residue (Glu407) critically involved in the '- 70 interaction [START_REF] Sharp | The interface of σ with core RNA polymerase is extensive, conserved, and functionally specialized[END_REF], and the inclusion of 367 carboxylate group-containing compounds in our candidate compound library, no inhibitor bearing a negatively charged group at physiological pH, and thus presumably unable to cross the hydrophobic core of the membrane, was retrieved by the yBRET screening.

To obtain initial information on cytotoxicity against mammalian cells, we tested the hemolytic activity of compounds 43 and 47 on human erythrocytes. In keeping with the lack of cytotoxicity previously observed in the lower eukaryote S. cerevisiae, no or only negligible (less than 2%) hemolysis was detected at the highest tested concentration (200 µM), indicating that both compounds are indeed non-toxic at antibacterial effective concentrations (Supplementary Table 5).

Ligand-based pharmacophore model and ' binding hypothesis

A pharmacophore model was built based on a subset of the active compounds identified through yBRET (5, 15, 33, 36 and 41), plus reference compound 1, representative of the structural diversity of '- 70 interaction inhibitors. These compounds share the presence of aromatic portions variably combined with polar groups not ionizable at physiological pH. Active compound 34 was excluded because of the presence of a basic group, not found in any of the other compounds, which could affect binding mode. The pharmacophore model thus obtained is characterized by five pharmacophore sites: two ring sites that accommodate aromatic portions of the compounds, a hydrophobic site, a hydrogen bond acceptor, and a hydrogen bond donor site (outlined in Figure 6 A, B and in Supplementary Figure 6A). All six '- 70 inhibitors fulfill the requirements of the pharmacophore model, with functional groups chemically consistent with the nature of the pharmacophore sites and proper spatial arrangements. Interestingly, compared to the structure-based pharmacophore built on  70 residues and used for compound selection (Supplementary Figure 2C), this ligand-based model lacks negatively charged sites. This might be explained by the use of yBRET as a primary screening, which requires compound internalization into yeast cells, a process that may be hindered by the presence of negatively charged groups. Likewise, ionized groups might also hamper access to the bacterial cytoplasmic compartment and may thus explain the limited antibacterial activity of compound 2.

Since no structural information is available on the interaction of ' with a '- 70 PPI inhibitor, the ligandbased pharmacophore model was used to formulate a hypothesis for inhibitor binding to the RNAP 'subunit. Attempts to identify a common binding mode for this subset of compounds through standard automated docking on the surface of the ' CH region did not provide any useful result. Multiple solutions were identified for each ligand, with different orientations and amino acid counterparts for hydrophobic and polar interactions. This is likely due to several reasons such as the flat surface of the ' CH region that lacks any recognizable cavity or shaped structural motif capable of accommodating the ligands, and the particular crystal structure utilized for docking experiments in which ' was crystallized with  70 . Therefore, based on the features revealed by the pharmacophore model and their spatial arrangement, we sought to identify a binding site on the surface of the '-subunit that could provide appropriate binding interactions for the different pharmacophore elements, while also allowing a proper arrangement of the portions of each compound not comprised in the pharmacophore model. We identified Asn294 and Glu295 as ' residues geometrically suitable to act as hydrogen bond donor and acceptor sites for the corresponding acceptor and donor groups of the inhibitors. As highlighted by site-specific mutagenesis studies [START_REF] Arthur | Mutational analysis of β' 260-309, a  70 binding site located on Escherichia coli core RNA polymerase[END_REF][START_REF] Ma | Inhibitors of bacterial transcription initiation complex formation[END_REF], these residues play an important role in the '- 70 interaction. Moreover, at the top of the CH region, not far from residues Asn294 and Glu295, there is a hydrophobic region potentially capable of accommodating the aromatic moieties of the inhibitors. Individual compounds were thus manually docked on the surface of the '-subunit in the conformation pointed out by the pharmacophore model and the resulting complexes were energyminimized in order to remove steric clashes and optimize hydrophobic and polar interactions. As shown in Figure 6C for compound 41, H-bonds are formed between its carbonyl group and the amide group of Asn294 and between the urea nitrogen and the acidic side chain of Glu295. The hydrophobic 6-fluoro-indole portion is accommodated in the hydrophobic cavity near to the helix-turn-helix motif of '. The ' portion involved in the interaction with the compound overlaps the region occupied by  70 in the E. coli RNAP crystal structure, thus interfering with this essential PPI, RNAPh assembly and transcription. Details on the binding mode of the other '- 70 inhibitors are reported in Supplementary Figure 6B. There is no obvious relationship between the amino acid sequence of the 2.2 and ' CH RNAP regions of the four tested bacteria (E. coli, S. aureus, B. subtilis and L. monocytogenes) and the antibacterial activity of the indol-3-yl-urea derivatives 43 and 47. In fact, the ' CH and 2.2 regions are conserved among bacteria, and the species-specific residues of the ' CH region (A286, D289, R293 and L307 in E. coli RNAP) are not involved in the '- PPI, nor in the proposed binding mode of the newly discovered PPI inhibitors. Conversely, other amino acid residues within the 2.2 region (Q400, I410 and M413 in E. coli RNAP) are involved in the '-PPI and their different chemical identities in the RNAPs from the different tested bacteria might influence the affinity between the two proteins. However, compound internalization, rather than subtle differences in the '- interaction region, is likely to play a more significant (and perhaps dominant) role in affecting the antibacterial activity of the compounds. Regarding the pharmacophore model and the structural hypothesis we propose, it should be noted that, while all the active compounds here identified can interact with Asn294 and Glu295, their precise mode of interaction with RNAP remains to be confirmed by structural data.

CONCLUSION

The virtual screening pipeline coupled with a highly productive yBRET assay, allowed, for the first time, the exploration of an extensive chemical space of candidate interfering compounds and the identification of seven hits, preferentially targeting '-subunit, out of approximately 5000 candidates selected from a repertoire of ≈34,000 compounds. This experimental set-up, in addition to its sizeable screening throughput (≈800 compounds/day), is also instrumental to: i) pinpointing from the very beginning compounds with at least a minimal capacity to cross biological boundaries (membrane and cell wall) and ii) the early detection of compounds displaying eukaryotic cell toxicity. We believe that the ability to interrogate large compound libraries and to provide early clues as to the potential biological relevance of the identified compounds are the most attractive features of the yBRET technology. In fact, all of the primary hits identified by yBRET, except the insoluble ones, were confirmed in ELISA, and two out of four displayed at least a minimal growth inhibition capacity. Ultimately, one of these hits led to the identification of two indol-3-yl-urea derivatives (compounds 43 and 47) that proved highly effective in blocking the growth of Gram-positive bacteria (including the human pathogens S. aureus and L. monocytogenes) but also E. coli upon supplementation of the non-bactericidal membrane permeabilizer PMBN.

A potential improvement of this work would be the targeted modification of some of the present hits in order to improve compounds permeability and to increase their potency. This might be achieved by tailored modulation of chemical structures through synthetic medicinal chemistry, taking advantage of the versatility of the indol-3-yl-urea scaffold. In parallel with chemical modification guided by the ' surface binding hypothesis we have generated, this issue could be addressed by chemical conjugation of '- 70 PPI inhibitors: i) with antimicrobial peptides or with proteins engaged by bacterial active transport systems (e.g., siderophore transporters) [START_REF] Klahn | Bifunctional antimicrobial conjugates and hybrid antimicrobials[END_REF][START_REF] Schalk | Siderophore-antibiotic conjugates: exploiting iron uptake to deliver drugs into bacteria[END_REF] to increase the compound permeability, ii) with other RNAP-directed antibiotics targeting distinct regions of the '-subunit to enhance antibacterial potency while reducing resistance development. Interestingly, a similar dual antibiotic fusion approach has been applied previously to two RNAP-targeting antibiotics [START_REF] Zhang | GE23077 binds to the RNA polymerase 'i' and 'i+1' sites and prevents the binding of initiating nucleotides[END_REF].

Also worth of future investigation will be the identification of novel inhibitors using our ligand-based pharmacophore model as a guideline.

Figure 1 .

 1 Figure 1. yBRET reconstitution of the '- 70 interaction and evaluation of BRET signal specificity. (A) Outline of the different fusion constructs and of the corresponding BRET signals. ' (dark green: aa. 1-334; light green: aa. 220-334) and  70 (orange) were joined to the N-and the C-terminus of NLuc and YFP (light gray); (B) BRET signal decrease associated to mutant versions of  70 (Q406K-E407A;  70 m) and ' (R275A-R278A; 'm) compared to the wild-type form of both interactors ('- 70 ). Donor fusion proteins were induced in the presence of 2% (A) or 0.5% (B) galactose. (C) Donor saturation assay of the '- 70 interaction. In the latter assay, the promoters were swapped to obtain the inducible expression of the YFP fusion proteins (using the indicated galactose concentrations) and the constitutive expression of NLuc- 70 . Black: wild-type '(1-334)-YFP; grey: 'm(1-334)-YFP. Data are the mean of three replicates; error bars represent SD.

Figure 2 .

 2 Figure 2. Target specificity of the interaction inhibitors. Comparative forward (' first, grey bars) and reverse ( 70 first, white bars) ELISA analysis of '- 70 binding inhibition by a subset of preselected compounds. All compounds were tested at a fixed 100 M concentration. Data, reported as percent binding relative to the DMSO vehicle, are the mean of three replicates; error bars represent SD; ***: two-tailed t-test p-value < 0.001; ns: not significative (p-value > 0.05).

Figure 3 .

 3 Figure 3. Transcription inhibition. (A) In vitro transcription activity measured in the presence of a subset of prevalidated compounds, including reference compound 1, and Rifampin as a positive control, assayed at a 50 M concentration. (B) Dose-response curves for a selected subset of compounds. Inhibition curves for hit compounds 43 () and 47 () are shown in blue and light blue, respectively; reference compound 1 (O) is in black. In vitro transcription activity is reported as percent relative to the DMSO vehicle. Data are the mean of three replicates; error bars represent SD. See Supplementary Figure 4A and 4B for representative gel images.

Figure 4 .

 4 Figure 4. Antibacterial activity. Growth inhibition assays conducted in the presence of different concentrations of compounds 43 (A, D) and 47 (B, E) against E. coli DH10 T1R (A, B, C) and B. subtilis WB800N (D, E, F), as indicated. Multiple compounds, including Rifampin and reference compounds 1 and 2, were assayed at a fixed concentration (100 M) in panels C and F. All assays performed on E. coli were supplemented with 2 μg/ml PMBN as indicated; data for the DMSO vehicle only are also reported.

Figure 5 .

 5 Figure 5. Effect of compounds on bacterial viability. Bacterial cell viability, expressed as CFU/ml, was measured at t0 and after 8 h culture of E. coli DH10 T1R (A), B. subtilis WB800N (B), L. monocytogenes DSM 20600 (C), and S. aureus ATCC 25923 (D) in the presence of fixed concentrations (50 M and 100 M) of compounds 43 and 47, or DMSO vehicle. Assays performed on E. coli were supplemented with 2 μg/ml of PMBN.Gridlines mark the CFU/ml at t0. Bactericidal effect, that is evidenced by a decrease in the number of viable cells after treatment compared to initial inoculum, is reported under the histograms as Fold reduction vs t0. Growth inhibition values, relative to the DMSO vehicle (Fold reduction vs 8 h), are also reported under the histograms. Data are the mean ±SD of at least three replicates.

Figure 6 .

 6 Figure 6. Ligand-based pharmacophore model. (A) Overview of the pharmacophore model. Pharmacophore sites are shown as colored spheres: ring site, orange; hydrophobic site, green; acceptor site, pink; donor site, blue. '- 70 inhibitors are aligned to the pharmacophore sites. (B) Compound 41 aligned to the pharmacophore model. The indole scaffold matches the two ring sites, the fluorine atom in position 5 occupies the hydrophobic site and the acceptor and donor groups correspond to the urea in the side chain in position 3 of the indole ring. (C) Binding model of compound 41 to the CH region of the RNAP '-subunit (green ribbons and carbons). The helix corresponding to region 2.2 of the  70 subunit is shown in shaded orange to highlight the portion of the '-subunit involved in the interaction

Table 1 :

 1 Structure and '-

70 binding inhibition capacity of reference and hit compounds

			yBRET %	ELISA %
	Compound	Structure	inhibition of binding	inhibition of binding	ELISA IC50 (M)
			(20 M)	(250 M)
	1 a (GKL003)		n.a.	84±14	17.6±1.3
	2 a (C5)		n.a.	46±1 b	n.a.
	30		18±2	0 c	n.a.
	31		28±1	87±4	16.1±1.1
	32		23±2	0 c	n.a.
	33		21±6	99±4	11.4±1.1
	34		28±3	93±1	11±1.1
	35		22±1	0 c	n.a.
	36		16±5	82±6	91.3±1.2

a Compounds 1 (GKL003; (17)) and 2 (C5; (23)) were used as references. b Compound 2 was assayed at a 500 M concentration. c Compounds 30, 32 and 35 were assayed at a 40 µM concentration. n.a.: not assayed.

ACKNOWLEDGMENTS

This work was supported by a University of Parma FIL 2014-Young Investigator grant to BM and a grant from the Regione Emilia-Romagna, Italy (Programma di Ricerca Regione-Università 2010-2012; PRUa1RI-2012-006) to SO. We thank the HPC (High Performance Computing) center of the University of Parma for access to the computational facilities and the Interuniversity Consortium for Biotechnologies (CIB) for technical support. The help of M. Simpson (Griffith University) with the handling and delivery of the Compounds Australia selected compound library and technical advice on the in vitro transcription assay by C. Rivetti (University of Parma) are also gratefully acknowledged.

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SUPPORTING INFORMATION

The Supporting Information is available free of charge on the ACS Publications website at DOI:… Supporting Information include descriptions of chemicals, yBRET assay, recombinant protein production, ELISA, molecular modelling, in vitro transcription assay, antimicrobial activity assays and statistical analysis. Supplementary figures show: the yBRET and ELISA results for the indole derivatives from the in-house mini library; workflow of the virtual screening procedure, the interaction between the CH region of the ' subunit and region 2.2 of  70 , the pharmacophore model and the minimum energy conformation of reference compound 1; dose-response curves for the primary hit molecules and the indol-3-yl-urea derivatives; representative gel images documenting the results of in vitro transcription inhibition assays; the effect of different concentrations of PMBN on the growth of E. coli; ligand-based pharmacophore model and the binding model for hit-compounds interacting with the ' subunit. Reported in supplementary tables are: structures of the indole derivatives from the in-house mini library; the chemical structure and inhibition capacity of indol-3-yl-urea analogs measured by ELISA; compound activity determined by microbial growth inhibition assays; minimum inhibitory concentrations; the results of hemolysis experiments for the two bestperforming indol-3-yl-urea analogs; a list of the oligonucleotides employed in this study.

DECLARATION OF INTERESTS

We declare that we have no competing interests.


domain: phys chim spi

text:
Robert F Tournier
email: robert.tournier@lncmi.cnrs.fr

Multiple Glass Transitions in Bismuth and Tin beyond Melting Temperatures

Keywords: Metals, glass transitions, melting enthalpy, Liquid-liquid transitions, density, first-order transitions, configurons, Phase

Liquid-liquid transitions were discovered above the melting temperature (Tm) in Bi and Sn up to 2Tm and viewed as glass transitions at Tg = Tn+ > Tm of composites nucleated at Tx < Tm and fully melted at Tn+. A glassy fraction (f) disappeared at 784 K in Sn. (Tn+) increases with singular values of (f) depending on Tx with (f) attaining 100% at Tg = Tn+ = 2Tm. The nonclassical model of homogeneous nucleation is used to predict Tx, Tn+ and the specific heat. The singular values of (f) leading to (Tn+) correspond to percolation thresholds of configurons in glassy phases. A phase diagram of glassy fractions, occurring in molten elements is proposed. The same value of (Tx) can lead to multiple (Tg). Values of (Tg = Tn+) can be higher than (2Tm) for Tx/Tm < 0.7069. A specific heat equal to zero is expected after cooling from T ≤ 2Tm and could correspond to a fully ordered phase. Weak glassy fractions are nucleated near (Tn+) after full melting at (Tm) without transition at (Tx). Resistivity decreases were observed after thermal cycling between solid and liquid states with weak and successive values of (f) due to Tx/Tm < 0.7069.

Introduction

Liquid-liquid phase transitions occur in glass-forming melts at temperatures Tn+ above Tm, the equilibrium thermodynamic melting transition of crystals [ (1) (2) (3) (4) (5) (6) (7) (8) (9) (10; 11) (12) [START_REF] Kim | Crystallization and high mechanical strengthof Al-based amorphous alloys[END_REF] [START_REF] Hu | Influence of melt temperature on the Invar effect in (Fe71.2B.024Y4.8)96Nb4 bulk metallic glasses[END_REF] [START_REF] Popel | Metastable colloidal states of liquid metallic solutions[END_REF] [START_REF] Jiang | Thermodynamic and kinetic studies of the Cu-Zr-Al(-Sn) bulk metallic glasses[END_REF] [START_REF] Wei | Liquid-liquid transition in a strong bulk metallic glass-forming liquid[END_REF] [START_REF] Lan | Hidden amorphous phase and reentrant supercooled liquid in Pd-Ni-P metallic glass[END_REF] (19; 20; 21) [START_REF] Tournier | Building and breaking bonds by homogenous nucleation in glass-forming melts leading to three liquid states[END_REF]]. These transitions often result from the separation of two liquid states, occurring in all supercooled materials at a temperature Tx < Tm, including pure elements in which two liquid phases of the same composition coexist. A liquid fraction crystallizes at Tx and melts at Tm while the complementary glassy fraction melts at Tn+ = Tg [ (23) (24) [START_REF] Tournier | Building and breaking bonds by homogenous nucleation in glass-forming melts leading to three liquid states[END_REF]]. The purpose of this publication liquid-phase (L) to a metastable, heterogeneous, ordered phase viewed as a glass phase called G-phase was observed. The L-G transition occurred by nucleation of the G-phase from the L-phase. The lowest glass transition temperature of liquid-phase (L) depends on its Lindemann coefficient and is much weaker than the nucleation temperature of G-phase [ [START_REF] Tournier | s rule applied to the melting of crystals and ultra-stable glasses[END_REF] [START_REF] Vopson | The generalized Lindemann Melting coefficient[END_REF] [START_REF] Tournier | Validation of non-classical homogeneous nucleation model for G-glass and L-glass formations in liquid elements with recent molecular dynamics simulations[END_REF] [START_REF] Tournier | Prediction of second melting temperatures already observed in pure elements by molecular dynamics simulations[END_REF]]. Increasing the heating rate increased the glass transition temperature of liquid (L). A first order transition from liquid (L) to G-glass was observed, when a supercooled liquid evolved isothermally below its melting temperature at deep undercooling [ (26)]. Several simulations of G-phases in various elements showed full melting heat Hm at various temperatures Tn+ = Tg in Ag [ [START_REF] Johnson | First-order transition in liquid Ag to the heterogeneous G-Phase[END_REF]], in Zr [ [START_REF] Becker | Glass-forming ability of elemental zirconium[END_REF]], in Cu and in Fe [ [START_REF] Bazlov | Crystallization of FCC and BCC liquid metals studied by molecular dynamics simulation[END_REF]]. The values of Tn+ were determined from singular values of G-phase frozen enthalpy, employing the nonclassical homogeneous nucleation (NCHN) model to predict Tx, Tn+ and the enthalpy. Singular values of (f) leading to (Tn+) correspond to percolation thresholds of broken bonds (configurons) leading to glassy phases up to Tn+ [ (33) (34) (24) (29) [START_REF] Tournier | Prediction of second melting temperatures already observed in pure elements by molecular dynamics simulations[END_REF]].

High undercooling rates of bulk liquid elements are known since many years [ (35)].

Consequently, we plan to confirm, in this publication, that the nucleation of G-phases and their glass transition temperatures above Tm are observable without employing heating and cooling rates of the order of 10 10 to 10 13 K/s to escape from crystallization. A phase diagram of glassy fractions, occurring in molten elements at Tx < Tm, is proposed, completing the diagram already established for Tx > Tm [ [START_REF] Tournier | Prediction of second melting temperatures already observed in pure elements by molecular dynamics simulations[END_REF]] in agreement with previous molecular dynamics simulations [ (25) [START_REF] Johnson | Formation of two glass phases in binary Cu-Ag liquid[END_REF] [START_REF] Becker | Glass-forming ability of elemental zirconium[END_REF] [START_REF] Bazlov | Crystallization of FCC and BCC liquid metals studied by molecular dynamics simulation[END_REF]]. The specific heat values at Tg = Tn+ is predicted up to Tg = 2 Tm where a fully ordered glassy phase is expected. The density far above Tm depends on the formation time of bonds increasing glassy phase fractions. Resistivity decreases are due to the increase in (f) in these liquids [ (4)].

Diagram of glassy phases

Three liquid states are present in all melts with enthalpies equal to lsHm, gsHm and lgHm [ [START_REF] Tournier | Fragile-to-fragile liquid transition at Tg and stable-glass phase nucleation rate maximum at the Kauzmann temperature[END_REF]]. For liquid elements, that are easily crystallized, the liquid enthalpy coefficients obey to the following [ (30), [START_REF] Tournier | s rule applied to the melting of crystals and ultra-stable glasses[END_REF]]:

 ls = ε ls0 (1 - 𝜃 2 𝜃 0𝑚 2 ) = 𝜀 𝑙𝑠0 (1 -2.25 𝜃 2 ), (1)
ε gs = ε gs0 (1 -𝜃 2 𝜃 0𝑔 2 ⁄ ) = 𝜀 𝑔𝑠0 (1 -𝜃 2 ) (2) ∆ε lg (θ) = [ε ls -ε gs ] = [ε ls0 -ε gs0 -θ 2 (2.25 𝜀 𝑙𝑠0 -𝜀 𝑔𝑠0 )], (3)
where Hm is the melting enthalpy, ls and gs are fractions of Hm, 0m = -2/3 and 0g = -1 are the reduced Vogel-Fulcher-Tammann (VFT) temperatures in liquid elements for which the minimum value of Tg is fixed by the Lindemann coefficient (ls) of each element [ (27)]. Eq. ( 3) is transformed into Eq. ( 4) for the minimum value of ls0 = gs0:

∆𝜀 𝑙𝑔 = -1.25 𝜀 𝑔𝑠0 𝜃 𝑔 2 , ( 4
)
where ∆𝜀 𝑙𝑔 (g) is the latent heat coefficient, accompanying the glass transition during the first cooling, the formation of Phase 3 below the percolation threshold of bonds, and the partial breaking of bonds after reheating above Tg, occurring without latent heat [ (30)] Figure 3. These relaxation effects due to the development of bonds below the percolation threshold at Tg are observed after quenching melt in amorphous state and heating at 20 K/min [ ( 37), (38) (39) (40) (41) [START_REF] Hornboll | Enthalpy relaxation in hyperquenched glasses of different fragility[END_REF]].

Coefficient minima (lso = gso) were initially determined to be equal to 0.217 [ (43)]. They were the average of many liquid element coefficients deduced from the undercooling rate of each of them corresponding to the mean value 0.103 of their Lindemann coefficient [START_REF] Qiu | Effect of liqui-liquid structure transition on the nucleation in undercooled Co-Sn eutectic alloy[END_REF][START_REF] Lan | Hidden amorphous phase and reentrant supercooled liquid in Pd-Ni-P metallic glass[END_REF]. The number 2.25, initially equal to 2.5 in Eq. ( 1), had for consequence to fix the VFT temperature to Tm/3 [ (44)]. It appears later that (lg) in Eq. ( 3) is the enthalpy coefficient of a true thermodynamic phase called 'Phase 3' discovered for the first time in supercooled water [ (45) (46) [START_REF]Homogeneous nucleation of phase transformations in supercooled water[END_REF]]. It is now a generic name, attributed to all glassy phases, which are formed through a first-order transition [ [START_REF]First-order transitions in glasses and melts induced by solid superclusters nucleated by homogeneous nucleation instead of surface melting[END_REF]]. Phase 3 could be the congruent bond lattice predicted for disordered oxide systems [ ( 48)], extended later to critical packing density formation applied to broken bonds (configurons) producing the glass transitions at Tg [ ( 33), [START_REF] Ozhovan | Topological characteristics of bonds in SiO2 and GeO2 oxide systems at glass-liquid transition[END_REF]]. An ordered fraction of atoms equal to various percolation thresholds exists up to Tn+, in all glass-forming melts [ (34; 50; 23)]. Phase 3 results from the formation of configuron phases [ (50)]. The NCHN model predicted the formation conditions of glacial phases (Phase 3) in Ag-Cu and Ag liquids at various heating rates as previously described by molecular dynamics (MD) simulations, showing full melting at Tn+ = 1.119Tm for Zr, 1.126Tm for Ag, 1.219Tm for Fe and 1.354Tm for Cu [ (25) (26) (31) [START_REF] Bazlov | Crystallization of FCC and BCC liquid metals studied by molecular dynamics simulation[END_REF]]. These phenomena are governed by singular values of the enthalpy lg of glassy Phase 3, formed at nucleation temperatures TnG [ ( 29), [START_REF] Tournier | Prediction of second melting temperatures already observed in pure elements by molecular dynamics simulations[END_REF]].

Two families of nucleation temperatures are given in Eqs. [START_REF] Xu | Folded network and structural transition in molten tin[END_REF][START_REF] Wang | Evidence for the structure transition in a liquid Co-Sn alloy by in-situ magnetization measurement[END_REF] where n-is equal to two opposite values of g because gs is a function of  2 in Eq. ( 2):

𝜃 𝑛-= 𝜃 𝑔 = ±(𝜀 𝑔𝑠 -2) 3 , (5)
𝜃 𝑛+ = ∆𝜀 [START_REF] Wang | Evidence for the structure transition in a liquid Co-Sn alloy by in-situ magnetization measurement[END_REF] where  is equal to singular values of the enthalpy coefficient (-lg) of Phase 3.

There are two methods to produce a glassy phase with an enthalpy coefficient equal to (-). The first one predicts the undercooling temperature for each value of . These nucleation temperatures (x) are calculated using the (NCHN) model applied to Liquid 2:

ε gs (θ = 0) = (3θ 𝑥 + 2 -∆ε)/(1 - 𝜃 𝑥 2 θ 0g 2 ) (7)
Here, 0g 2 = 1. For  = 0, a second order-like phase transition temperature takes place at Tg during heating for the minimum value of gs0. Values of x for various values of  are deduced for the same value of gs0.

Glass phases, formed at x after undercooling, lead to glassy phases with g = n+ =  in agreement with Eq. [START_REF] Wang | Evidence for the structure transition in a liquid Co-Sn alloy by in-situ magnetization measurement[END_REF]. They are accompanied by a crystallized fraction (1-). A composite crystal-glass is built below Tm with a melting enthalpy (1-) Hm and a missing enthalpy ( Hm) recovered at Tn+ [ [START_REF] Tournier | Multiple melting temperatures in glass-forming melts[END_REF]]. The glassy phase fraction is not destroyed at Tm and depends on the sample thermal history and the last value of  obtained at Tx during heating.

The minimum glass transition at Tg is masked by spontaneous crystallization of many liquid elements and determined with Eq. ( 7) using  = 0 and the minimum value of gso = lso, depending on the Lindemann coefficient ls of each element [ [START_REF] Tournier | s rule applied to the melting of crystals and ultra-stable glasses[END_REF]]:

𝜀 𝑔𝑠0 = 𝜀 𝑙𝑠0 = (1 + 𝛿 𝑙𝑠 ) 2 -1 (8)
In Figure 1, a second method is used to calculate new values of x during heating. Each value of g varying from -0.5 to 2 corresponds to a value of Tg/Tm between 0.5 and 3. All ratios Tg/Tm, represented in Figure 1, could be those of phases resulting from a firstorder transition at Tx, with Tx and Tg depending on heating rates. Applying Eq. ( 7), determines the value of gs0 = ls0, (positive or negative [ (23)]), for each (g) and  = 0. Each firstorder transition at x respects  = n+ = g > 0, in agreement with Eq. [START_REF] Wang | Evidence for the structure transition in a liquid Co-Sn alloy by in-situ magnetization measurement[END_REF]. Negative values of g (Tg/Tm < 1) are higher than x because Tg/Tm is always higher than Tx/Tm. The values of (x) obtained with Eq. ( 7) are weaker than those predicted in Figure 1 along the dashed curve. Valuable for all glass transitions due to Lindemann coefficients. For Bi, Tx/Tm = 0.8068 reveals Tg/Tm = 1.8675 as observed from differential thermal analysis (DTA). For Sn, Tx/Tm = 0.71022 reveals Tg/Tm = 1.5523. For Tx/Tm > 0.7069, there are 5 glass transitions. For Tx/Tm < 0.7069, the number of glass transitions is equal to 3. (Tg/Tm) can be higher than 2. Transitions at Tg/Tm = 1.4291 and 1.4384 are initiated by other (Tx/Tm) values. Tg/Tm = 0.5, 1.5 and 3 for Tx/Tm = 0.22451. For Tx/Tm = 1, transitions were observed at Tg/Tm with latent heat much weaker than ( Hm) above Tm.

The two lines between Tg/Tm = 0.5 and 1.5 are symmetrical with respect to 1. There are 5 values of Tg/Tm for Tx/Tm higher than 0.7069, and 3 values of Tg/Tm for Tx/Tm < 0.7069, depending on the singular values of  determined by each thermal history. For Tx/Tm = 0.7069, Tg/Tm = 1.475. Note that the NCHN model predicts nucleation temperatures at Tn+ > 2 Tm, ignoring the structure of these new ordered phases. We assume that glassy phases are formed.

Diagram applications

Liquid-liquid transitions in bismuth were observed along lines [START_REF] Wang | Discontinuous structural phase transition of liquid metal and alloys[END_REF][START_REF] Yue | Experimental evidence for the existence of an ordered structure in a silicate liquid above its liquidus temperature[END_REF][START_REF] Zu | Temperature-Induced Liquid-Liquid Transition in Metallic Melts: A Brief Review on the New Physical Phenomenon[END_REF][START_REF] Xu | Folded network and structural transition in molten tin[END_REF] in Figure 1, by several authors using differential scanning calorimetry (DSC) or differential thermal analysis (DTA) at various heating rates, leading, in fact, to vitreous transitions at Tg/Tm = 1.4291, 1.4384, 1.8675 and 2 for Tx/Tm = 0.70811, 0.70767, 0.80681 and 1 respectively without recovery of the endothermic heat ( Hm) at these temperatures [ (1) (3) (4)]. The value of gs0 for bismuth was equal to 0.1907 corresponding to ls = 0.0912 [START_REF] Zu | Temperature-Induced Liquid-Liquid Transition in Metallic Melts: A Brief Review on the New Physical Phenomenon[END_REF].

The vertical lines [START_REF] Greenberg | Evidence for a temperature-driven structural transition in liquid bismuth[END_REF][START_REF] Xu | Folded network and structural transition in molten tin[END_REF] in Figure 1 are those of tin and correspond to Tg/Tm = 1.5523 (Tg = 783.9 K) and 2 (Tg = 2 Tm). The horizontal line Tx/Tm = 0.71022 determines Tg/Tm = 1.5523. Two liquid-liquid transitions, occurring at Tg/Tm = 1.5523 and 2 are known up to now. Only Tg/Tm = 1.5523 is characterized as a glass transition [ ( 5)].

The Bi glass transition was not reproduced at Tg/Tm = 2 during cooling because all bonds were erased during heating far above Tg/Tm = 2 as observed with heating and cooling rates of 2 K/min [ ( 4)] (Figure 13b).

In contrast, the Sn transition at Tg/Tm = 2.168, during heating, disappeared during cooling and gave rise to a new transition at Tg/Tm = 1.832 characterizing a first-order transition at Tg/Tm = 2 observing that [(2.168+1.832)/2 = 2] with heating and cooling rates of 7.5 K/min [ ( 4)] (Figure 13e). The first-order transition at Tg/Tm = 1.832 (Tg = 652 °C) was reproduced during the second heating and cooling at 10 °C/min and could correspond to  = 0.832.

The resistivity [ (4)] after the second heating were much weaker than those obtained during the first heating of Sn and Bi. At the highest temperature T = 2.28 Tm, the ordered fractions did not disappear because Tg is expected to be on the order of 3 Tm. The resistivity decreases were equal to 22% for tin and 16.7% for Bi.

Singular enthalpy coefficients

We examine the case where the glassy phase is formed at Tx. Characteristic values of lg () = - at various temperatures Tx would correspond to various percolation thresholds of configurons. The enthalpy coefficient (lg = -) of Phase 3 is constant up to Tn+ = Tg.

The transition at Tg leads to a new liquid state with lg linearly decreasing with temperature in agreement with Eq. ( 6). Consequently, the melt specific heat, being proportional to the derivative (lg/dT), undergoes a jump equal to Hm/Tm at Tg = Tn+.

Bismuth

The weakest glass transition temperature of bismuth was predicted at Tg = 202.46 K [ ( 23 4), nucleated at 395 K, without crystallization at Tm, disappears at Tg = 2Tm = 1089 K. We expect, by reversing heating to cooling at a reduced temperature slightly lower than g, that the enthalpy coefficient lg will fall to zero, without forgetting that the glassy fraction is equal to .

The enthalpy coefficient variation of Phase 3 along Line (5) in Figure 2, obeying to Eq. ( 6), is obtained after a transition at Tg = Tn+ followed by continuous heating through the various glass transitions.

Tin

The weakest glass transition temperature of tin is Tg = 185.2 K (g = -0.63332), applying Eq. ( 7) for gs0 = 0.167, (ls = 0.08028). The singular enthalpy coefficients of liquid tin are lg = 0, lg0 = 0.167, -lg (g) = 0.08373, -lg (0m = -2/3) = 0.09278, -lg ( = -1) = 0.20875 and -lg = 1. A sum of all basic coefficients leads to  = 0.5523. Here too, the combination of singular enthalpy coefficients determines the glass transition at Tg/Tm. As a conclusion of this chapter, the existence of singular glassy fractions (f) in liquid Bi and Sn is predicted. Liquid-liquid transitions are observed and occur at the predicted glass transition temperatures.

Experimental densities of Bi and Sn during heating

Density varies linearly with increasing temperature, T (K), above Tm in liquid elements [ (3) (51) (52) (53) (54) [START_REF] Assael | Reference data for the density and viscosity of liquid cadmium, cobalt, gallium, indium, mercury, silicon, thallium, and zinc[END_REF]]:

𝑑 = 𝑑 0 -𝑎𝑇. ( 9
)
where d0 is a density at 0 K. In general, density measurements were made after melting the crystalline phase in the absence of temperature Tx resulting from undercooling and reheating. Nevertheless, liquid-liquid transitions were observed with heating rates between 0.1 and 20°C/min at temperatures (Tn+) [ ( 23)]. Consequently, new atomic bonds are induced by relaxation of liquid state near Tn+ [ [START_REF] Tournier | Building and breaking bonds by homogenous nucleation in glass-forming melts leading to three liquid states[END_REF]]. The singular coefficient  belonging to lower enthalpy phases determines the temperature Tn+ = Tg, and gives rise, at very low heating rate, to relaxation of weak endothermic latent heat in the neighborhood of temperatures Tn+. These relaxation times also have for consequence, to disperse the liquid density measurements and are due to the development of bonds above Tm. Density, d, is expected to be reduced for bismuth and increased for tin by this enthalpy relaxation up to Tg = 2Tm. Then, Eq. ( 9) can be written as a function of  = , applying Eqs. [START_REF] Zu | Temperature-Induced Liquid-Liquid Transition in Metallic Melts: A Brief Review on the New Physical Phenomenon[END_REF][START_REF] Wang | Evidence for the structure transition in a liquid Co-Sn alloy by in-situ magnetization measurement[END_REF]:

𝑑 = 𝑑 0 -𝑎𝑇 𝑚 (1 + 𝜃 𝑛+ ) = 𝑑 0 -𝑎𝑇 𝑚 (1 ± ∆𝜀 𝑙𝑔 ). (10)
Density measurements would lead to dispersed results because they would be dependent on the measurement time and on the amplitude of the relaxed enthalpy.

Bismuth density

The specific heat of bismuth above Tm, measured point after point [ ( 56)], is strongly dispersed as reproduced in Figure 4. Few singular values of Tn+ are indicated. The deepest one occurs at 862 K ( = 2×0.23838 +0.10594 =0.5827) and the highest ones at 1017 K ( = 0.8675) and 1089 K ( = 1). The specific heat (0.147 J/K/g) at Tm is recovered at 1180 K showing that the transition width at 1089 K is about 100 K in this case. These results show that the dispersion of measurements attains 12 % and that these weak glassy fractions induced by relaxation, have glass transition temperatures equal to Tn+. Consequently, liquid-liquid transitions observed around each temperature Tn+ would correspond to fractions much weaker than the singular value () associated with Tn+. The same dispersion is expected for density measurements below the line defined by Eq. (9}. The density change at Tm corresponds to a melting heat of 1.23838 Hm instead of Hm, because it contains the enthalpy (0.23838 Hm) given by Eq. ( 4), which corresponds to the initial formation of Phase 3. There is no visible transition in Figure 5 at T = 2Tm as shown by the quasi-continuity of the density.

Tin density

The density of tin is represented Lines (1-3) in Figure 6: solid tin, Line (1) [ ( 54 54)]; Line (2) [ ( 53)]; Line (3) [ ( 57)]. Tx = 284 K, the glass formation temperature after undercooling and the melting temperature of gray tin. 2 Tm = 1010 K.

The heat capacities during heating

The specific heat (Cp) is reduced by a contribution (Cp) above Tm during heating in the presence of a glassy fraction f =  after an enthalpy change (- Hm) and a first-order transition at Tx:

𝛿𝐶 𝑝 = 𝑇 (𝛿𝑆 𝛿𝜃) ⁄ 𝑝 (𝛿𝜃 𝛿𝑇 ⁄ ) 𝑝 = -𝑇𝑆 𝑚 𝑇 𝑚 ⁄ (11)
where 𝑆 = -∆𝜀 𝐻 𝑚 𝑇 𝑚 = -𝜃 𝐻 𝑚 𝑇 𝑚 ⁄ ⁄ represents the entropy of the glassy phase fraction at Tn+ with  =  applying Eq. ( 6). There is no specific heat and density added in the absence of glassy fraction for  = 0 in all liquids. Eq. ( 11) is not applied in the absence of first-order transition at Tx. Applying Eq. ( 11) leads to Cp = 0 at Tg = 2 Tm: For Sn:

𝐶 𝑝 = 28.43 -0.0563 × (𝑇 -𝑇 𝑚 ), [START_REF] Zhou | Indication of liquid-liquid phase transition in CuZr-based melts[END_REF] with Hm = 7179 J/mole [ ( 58)] and Tm = 505 K At Tm, Cp = 28.43 J/mole in agreement with Chen's measurements [ ( 59)] after adding 0.9 mJ/mole corresponding to the electronic specific heat contribution of tin [ ( 60)].

For Bi:

𝐶 𝑝 = 30.2 -0.05546(𝑇 -𝑇 𝑚 ), [START_REF] Kim | Crystallization and high mechanical strengthof Al-based amorphous alloys[END_REF] with Tm = 544.5 K. At Tm, Cp = 30.2 J/mole [ ( 61)] is used to determine Hm = 8613 J/mole. The measured melting enthalpy is 1.23838 Hm leading to 10662 J/mole inside an uncertainty of measurements varying from 10480 to 11300 J/mole [ ( 62)].

The constants 28.43 and 30.2 J/K/mole are values of Cp at Tm in the absence of glassy phases. These heat capacities are equal to zero at T = 2Tm and to 28.43 and 30.2 J/mole at temperatures higher than 2Tm as shown for Sn in Figure 7 and bismuth in Figure 8. When a fraction (f) of liquid is no longer in a glassy state above the temperature (T), (Cp) linearly decreases from 28.43 for Sn to zero and from 30.2 J/K/mole to zero for Bi. These specific heat variations, expected during heating, are plotted as a function of temperature for Sn and Bi in Figures 7 and8.

Other experimental observations of glassy states above Tm

Tin

A glass transition was detected for the first time around 783.9 K in agreement with our predictions [ (5)]. This transition induced a specific heat jump of about 1.8 J/K/mole instead of 12.7 J/K/mole corresponding to a glassy fraction f  1.8/28.4 = 6.3 % instead of 55.23 %. This glassy fraction was induced in a stepwise-scanning mode: the temperature during the thermal equilibration stage changed with time and gradually approached a constant value in about 60 minutes. The peak of Cp, observed during this slow heating, accompanied by critical phenomena, could be attributed to the thermodynamic transition of configurons [ (33), [START_REF] Ojovan | Viscosity and glass transition in amorphous oxides[END_REF]]. The jump of Cp measured at 4 K/min was weaker because the nucleation time of new bonds was much lower.

Bismuth

DTA at 0.1 °C/min reveals an endothermic latent heat of the order of 20 to 100 J/mole [ (3)] at Tg =1.8675 Tm. A transition width (T) of 200 K was observed at 1089 K by resistivity measurements with 2°C/min and a width (T = 10 K) expected for R = 0.1°C/min [ (4)]. We attribute this liquid-liquid transition to a glassy fraction of the order of 6.6 % with 20 J/mole and 33 % with 100 J/mole] assuming a transition width of 10 K. A second endothermic heat was observed by DTA at T = 2 Tm = 1089 K corresponding to a second glass transition and to the enthalpy relaxed during 720 min between 1017 and 1089 K.

Configuron thermodynamic transition was revealed by structural changes at the glass transition via radial distribution functions [ ( 64), [START_REF] Ojovan | On structural rearrangement during the vitrification of molten copper[END_REF]]. The first sharp diffraction minimum in the pair distribution function was shown to contain information on structural changes in amorphous materials at the glass transition temperature (Tg). An additional feature of such configuron transition was determined by measuring the temperature dependence of the structure factor of molten bismuth, -S(q). The authors observed, in their neutron diffraction analysis [ (3)] , an additional feature in the measurement that appeared around the melting temperature of bismuth. Pair distribution function curves (g(r)) were calculated for each (S(q)) measurement. At and above melting, both the S(q) and g(r) curves were characterized by a shoulder located on the high q and r side of the first peak, respectively. The temperature dependence of the coordination numbers lead to the number of atoms contributed by the shoulder, NShoulder(T). The derivative of NShoulder with respect to temperature, showed a discontinuity at the transition point at 1089 K, and was associated with this temperature-driven transformation and a structural change. This structural change is a signature of the thermodynamic transition of configurons [ ( 33)].

7.3 BiSb20 wt% DSC revealed that Cp was equal to zero at 1070 °C with a heating rate of 20 °C /min [ (4)] Figure 15b. From our model, we deduce that the glassy fraction (f) was 100 %. The liquidus temperature of this alloy is 425 °C (698 K). The glass transition, occurring at 1070 °C (1343 K), was weaker than 2 Tm = 1396 K. The specific heat increased from 1070 °C to 1123 °C. The transition width (2000 K) is expected to be 10 times wider than at 2 K/min. Consequently, the recovery of Cp, for a temperature increase of 53 K, is of the order of 53/2000  2.6 % of its value at Tm. We conclude that the glassy fraction (f = 100 %) was induced at a temperature Tx < Tm. The rapid increase of the heating rate had for consequence to induce the first order transition at Tx < Tm. This experiment showed for the first time that a glassy phase of 100 % can be obtained with a heating rate of 20 K/min.

InSn80wt%

An internal friction method was used to study the structural changes of InSn80wt% This eutectic composition has a melting temperature of 183 °C (456 K). The highest glass transition temperature is predicted at 912 K (639 °C). The internal friction has a maximum at 670 °C and a minimum at 560 °C with a heating rate of 2.5 °C/min and a maximum at 712 °C and a minimum at 600 °C with 6 °C/min. This liquid -liquid transition temperature increases with the heating rate as observed in all glasses [ (4)].

Another method to stabilize glassy states above (2 Tm)

A process was described by Zu F.Q. [ (4)], ignoring at this time, that resistivity decreases could be due to the formation of glassy fractions, added after several cooling to various temperatures Tx < Tm, followed by successive reheating as shown in Figure 7. Each value of Tx/Tm < 0.7069 lead to a glass transition much higher than 2 Tm as shown by the glassy phase diagram of Figure 1. These various reheating enriched the total glassy fraction as shown by resistivity reductions of 40 % after three heating of Cu-Sb76.5wt%, of 22 % in tin and 16.7% in bismuth after two heating. In addition, depending on heating rate, another glass transition occurs at Tm < Tn+ < 2 Tm in various alloys such as InSn80wt%, InBi32wt% at R = 3°C/min, and CuSb76.5wt% at 5°C/min. They were due to the formation of very weak glassy fractions (f), depending on heating and cooling rates. The residual resistivity is equal to 100 Ω.cm at Tm during the first heating. Consequently, the formation of high glassy fractions with Tg >> 2 Tm could be attained after adding new thermal cycles, leading to a maximum resistivity fall. Reheating cycles could stabilize the glassy phase above (Tn+ = 2Tm). 4)] (Figure 13f).

Conclusions

Liquid-liquid transitions are observed below and above Tm.

First-order transitions, predicted by the NCHN model, occur at Tx < Tm, building glassy phase fractions () after supercooling and crystallized fractions (1-) of melt. Melting of glassy fractions occurs at temperatures Tn+ > Tm at the percolation threshold of configurons (broken bonds). One of them induces a glass enthalpy equal to the melting enthalpy ( = 1), without crystallized fraction, up to a glass transition (Tg = 2Tm). All glassy fractions would have a heat capacity equal to zero, revealed by reversing heating to cooling below Tn+.

Liquid-liquid transitions between the melting temperature (Tm) and (2 Tm) are observed in the absence of first order transition at Tx < Tm and are reminiscent of glassy fractions (f) formed at temperatures (Tx) weaker than (Tm) through first-order transitions. These weak fractions correspond to singular values () of enthalpy coefficients (lg () = -) of a new phase called "Phase 3", and to typical percolation thresholds of configurons at various temperatures (Tn+ = Tg). These fractions are slowly induced near (Tn+) by relaxation in the absence of first order transition prior to melting.

Several situations are encountered in bismuth and tin:

1-After melting Bi and Sn at T = Tm, weak fractions (f) were built by slow heating (0.1°C/min for Bi and one hour between each measurement for Sn) and melted at g = n+ = (Tn+ -Tm)/Tm = . Liquid-liquid transitions were observed at 1.8675 Tm for bismuth and 1.5523 Tm for Sn. The glassy character of these transitions is confirmed by structural transitions that we attribute to melting of configurons. The glass transition in Sn was also characterized by a weak specific heat jump predicted by the NCHN model and a peak at 1.5523 Tm due to the thermodynamic character of a transition obeying to critical exponents associated with configuron percolation. There is no endothermic latent heat equal to ( Hm), only a weak endothermic heat equal to a weak fraction (f << ).

2-After melting Bi and Sn at T = Tm, transitions were also observed at T = 2 Tm by DTA and (or) resistivity that we consider as new glass transitions. The transition was reversible only for Sn. A weak endothermic heat was observed for Bi at 2 Tm, as expected for a weak value of (f).

3-We show that the density variation between Tm and 2 Tm is equal to that from solid to liquid at Tm. The glassy state of Bi has a density equal to that of the liquid at Tm while, that of Sn is equal to that of the solid at Tm.

4-After melting

Bi at T = Tm, high-resolution measurements of the density showed the existence of singular values corresponding to those of the enthalpy of Phase 3. The melting heat at Tm corresponds to 1.23838 Hm instead of Hm including, in addition, the latent heat of glassy phase after the first cooling as predicted by the NCHN model.

5-A glassy phase diagram is proposed for systems having their lowest transition determined by their Lindemann coefficients. Each first order transition at Tx < Tm leads to multiple glass transitions. The possible existence of weak glassy fractions (f) for Tx/Tm < 0.7069, with glass transition temperatures much higher than (2 Tm) is envisaged (beyond (3 Tm) for f < 22.45%). Resistivity measurements showed decreases in Bi and Sn from Tm to 2 Tm and beyond, after thermal cycling between the solid and undercooled liquid states.

6-The glassy phase formations at Tx are accompanied by latent heats, being recovered at Tn+ with (Tm < Tn+ < 2Tm) which decrease the liquid specific heat. Predictions of their contribution equal to (n+ Hm/Tm) are proposed for Tn+ = Tg ≤ 2Tm. The heat capacity linearly decreases down to zero when  increases up to 1 (Tn+ = 2Tm). A specific heat equal to zero, down to Tm, could be induced by reversing heating to cooling from a temperature slightly weaker than Tg = Tn+. We show, for the first time, that the liquid specific heat is constant between Tm and 2Tm in the absence of glassy phase.

7-The stability of glassy fractions for Tx/Tm < 0.7069 can be very high because their (Tg) could be much higher than (2 Tm) as proved by resistivity decreases observed up to 2 Tm and beyond in Bi and Sn. The glassy fraction (f) is enhanced by successive thermal cycles between solid and liquid states. Each new glassy fraction could be added and could reinforce the total glassy fraction at very high temperatures up to f ≤ 100%.

Figure 1 :

 1 Figure 1: Glassy phase diagram (Tg/Tm) resulting from first-order transitions at Tx/Tm during heating of liquid elements.Valuable for all glass transitions due to Lindemann coefficients. For Bi, Tx/Tm = 0.8068 reveals Tg/Tm = 1.8675 as observed from differential thermal analysis (DTA). For Sn, Tx/Tm = 0.71022 reveals Tg/Tm = 1.5523. For Tx/Tm > 0.7069, there are 5 glass transitions. For Tx/Tm < 0.7069, the number of glass transitions is equal to 3. (Tg/Tm) can be higher than 2. Transitions at Tg/Tm = 1.4291 and 1.4384 are initiated by other (Tx/Tm) values. Tg/Tm = 0.5, 1.5 and 3 for Tx/Tm = 0.22451. For Tx/Tm = 1, transitions were observed at Tg/Tm with latent heat much weaker than ( Hm) above Tm.

  )]. The singular enthalpy coefficients  were determined: lg = 0, lg0 = 0.1907, -lg (g) = 0.094065, -lg (0m = -2/3) = 0.10594, -lg ( = -1) = 0.238375 and lg = -1. The experimental coefficients () giving rise to n+ = 778/544.5 -1 = 0.429 and 784.6/544.5-1 = 0.44096 were obtained with a heating rate of 5 K/min and were nearly equal to the theoretical values (0.42908 = 0.1907+0.23838) and (0.43838 = 0.094065+0.10594+0.23838) [ (1)]. In Figure 2, these two transitions are nucleated at Tx = 286.2 and 288 K during undercooling. Only the transition at T = 286.2 K is represented, leading to the horizontal line (2) up to Tg = 778.1 K. The observed coefficient  = 0.8675 [ (3)], nucleated at T = 370 K, was equal to the sum (0.42908+0.43838) up to Tg = 1016 K along Line (3) [ (23)]. The coefficient ( = 1) along Line (

Figure 2 :

 2 Figure 2: Bismuth glassy phase fractions f =  expected after undercooling and reheating. Four liquid-liquid transitions at Tn+ = Tg after reheating were observed. Horizontal lines: 1-lg = 0 of glassy fractions; 2- = n+ = g = 0.42908 up to Tg = 778 K, 0.43838 up to Tg = 783 K, (not represented); 3- = 0.8675 up to Tg = 1016 K; 4- = 1 up to Tg = 1089 K without crystallization at Tm. Vertical lines: Tx = 286.2 K leading to  = 0.42908 and a crystallized fraction (1- = ); Tx =

Figure 3 :

 3 Figure 3: Tin glassy phase fraction f =  expected after undercooling and reheating. Tx = 284 K (x = -0.43757), leading to a liquid-liquid transition at Tn+ = Tg = 783.9 K after reheating. ( = 0.5523) corresponding to the enthalpy coefficient of the gray phase. The crystallized fraction (1-) of the white phase is (). The glassy phase with Tg = 2 Tm = 1010 K and  = 1 is nucleated at Tx = 366.7 K (x = -0.33336) and heated without crystallization at Tm.In Figure3, the transition occurring at Tx = 284 K (x = -0.43757) gives rise to a glassy fraction f = 0.5523 and a glass transition at Tg/ Tm= 1.5523 (Tg = 783.9K) calculated with gs0 = 0.167 and Eqs.[START_REF] Wang | Evidence for the structure transition in a liquid Co-Sn alloy by in-situ magnetization measurement[END_REF][START_REF] He | Liquid-liquid structure transition and nucleation in undercooled Co-B eutectic alloys[END_REF]. The temperature (284 K) separates two crystalline phases corresponding to gray and white tin. The temperature Tx = 284 K, corresponding to the melting temperature Tm  284 K of gray tin, is difficult to observe because of the concomitant formation of a glass phase at the same temperature [ (51)]. Above 284 K, the liquid fraction of gray phase is a glass with Tg = 783.9 K, coexisting with a crystallized fraction (1-0.5523 = 0.4477) of white tin up to Tm. A glass transition temperature was observed in tin at Tg  780 K, confirming the existence of a glassy fraction above Tm [ (5)]. The glass phase corresponding to f =  = 1 would be nucleated at Tx = 366.7 K and heated without crystallization at Tm, up to Tg = 2 Tm = 1010 K. We will see that the glass transition at 1010 K observed by resistivity measurements is reversible [ (4)].

Figure 4 :

 4 Figure 4: Specific heat of bismuth above Tm. Reproduced from [ (56)] with permission of Springer Ed. The line Cp = 0.1464 KJ/ (Kg K) leading to the value of Cp at Tm = 505 K is added. The specific heat is constant from Tm to 2 Tm in the absence of relaxed enthalpy. Tg = 674 K for  = 0.23838+0.09401 = 0.3324, Tg = 778 K for  = (0.42908 = 0.1907+0.23838), Tg = 882 K for  = (0.429+0.23838+0.09456 = 0.761), Tg = 1017 K for  = 0.8675, Tg = 1089 K for  = 1.

Figure 5 :

 5 Figure 5: Bismuth density versus temperature, T (°C). Reproduced with authorization of EPL, EPI [ (3)]. The density variation between Tm (K) and 2 Tm (K) is equal to the density change at Tm while the enthalpy coefficient varies from 0 to 1. Singular values of the enthalpy coefficient are added to the original figure. Line (1) is the density before enthalpy relaxation of glassy phases. A melting heat, 1.23853 Hm includes the latent heat of the glassy fraction occurring for Tg/Tm = 1 in the phase diagram of Figure 1.

  )], and liquid tin, Lines[START_REF] Yue | Experimental evidence for the existence of an ordered structure in a silicate liquid above its liquidus temperature[END_REF] [[START_REF] Alchagirov | Temperature dependence of the density of liquid tin[END_REF]] and (3) [ (57)]. Lines[START_REF] Yue | Experimental evidence for the existence of an ordered structure in a silicate liquid above its liquidus temperature[END_REF][START_REF] Greenberg | Evidence for a temperature-driven structural transition in liquid bismuth[END_REF] are chosen among measurements with only 50 Kg/m 3 of error reviewed byAlchagirov and Chochaeva [ (53)]. The difference in density, 82 Kg/m 3 at 2 Tm is higher than the measurement error. Lines (2,3) could represent two liquid densities that are parallel and separated by approximately 75 Kg/m 3 or less inside the measurement error. This phenomenon, if confirmed, would be associated with the presence of a weak glassy fraction f << 0.20875 from 0 K to 2 Tm and beyond as predicted. The density change at Tm and the melting heat depend on the thermal history and may include glassy fractions that are melted at very high temperatures beyond 3 Tm as predicted by the glassy phase diagram.

Figure 6 :

 6 Figure 6: Tin density (d) in Kg/m 3 , versus T (K). Line (1) [ (54)]; Line (2) [ (53)]; Line (3) [ (57)]. Tx = 284 K, the glass formation temperature after undercooling and the melting temperature of gray tin. 2 Tm = 1010 K.

Figure 7 :

 7 Figure 7: Heat capacities of bismuth in J/K/mole. Cp = 30.2 from T = 544.5 to 1089 K in the absence of glass phase. Cp = 17.2 from Tm = 544.5 to Tg = 778.1 K in the presence of glassy fraction f = 42.908 %. Cp = 4 from Tm = 544.5 to Tg = 1017 K in the presence of a glassy fraction f = 86.75 %. Cp = 0 for f = 100%. Heating beyond Tg, leads to Cp = 30.2 inside the transition width. Cooling from a temperature slightly below Tg leads to the glassy state.

Figure 8 :

 8 Figure 8: Heat capacities of tin in J/K/mole. Cp = 28.43 from T = 505 to 1010 K in the absence of glassy phase. Cp = 12.7 from Tm = 505 to Tg = 783.9 K in the presence of glassy fraction f = 55.23%. Cp = 0 for f = 100%. Heating beyond Tg, leads to Cp = 28.43 inside the transition width. Cooling from a temperature slightly below Tg leads to the glassy state.

[ ( 66 )

 66 ]. This alloy has a melting temperature of about 190°C (463 K) and a glass transition temperature, expected at 2 Tm = 926 K (653 °C). A minimum of internal friction occurs at 625 °C et un maximum at 700 °C. Based on the results of a diffraction experiment around 700 °C, the liquid structures before and after the peak are very different [ (4)]. Before the change, there are residual covalent bonds of solid tin in the melt and during the transition, the residual bonds are broken and at the same time, new atomic bonds build up, with a relatively uniform melt forming. This description given by [ (4)] is known as being due to the percolation threshold of configurons [ (33)]. 7.5 PbSn61.9wt%

Figure 9 :

 9 Figure 9: Resistivity falls of Cu-Sb 76.5 wt% after thermal cycling. Reproduced from [ (4)] (Figure13f).

Author Contributions: only one author.

Funding: This research received no external funding.

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