Nicolas Humbert

Lesia Kovalenko

Francesco Saladini

Alessia Giannini

Manuel Pires

Thomas Botzanowski

Sergiy Cherenok

Christian Boudier

Kamal K Sharma

Eleonore Real

Olga A Zaporozhets

Sarah Cianférani

Carole Seguin-Devaux

Federica Poggialini

Maurizio Botta

Maurizio Zazzi

Vitaly I Kalchenko

Mattia Mori

Yves Mély
email: yves.mely@unistra.fr

Nucleocapsid Protein with a New Binding Mode and Multitarget Antiviral Activity

Keywords: Nucleocapsid protein, HIV-1, Fluorescence, 55 calixarenes, NC inhibitors 56 57 -2.0 -

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

that plays key roles in HIV-1 replication through its nucleic 29 acid chaperone properties mediated by its two zinc fingers and 30 basic residues. NC is a promising target for antiviral therapy, 31 particularly to control viral strains resistant to currently 32 available drugs. Since calixarenes with antiviral properties 33 have been described, we explored the ability of calixarene 34 hydroxymethylphosphonic or sulfonic acids to inhibit NC 35 chaperone properties and exhibit antiviral activity. By using 36 fluorescence-based assays, we selected four calixarenes 37 inhibiting NC chaperone activity with sub-micromolar IC50 38 values. These compounds were further shown by mass 39 spectrometry, isothermal titration calorimetry and 40 fluorescence anisotropy to bind NC with no zinc ejection, and 41 to compete with nucleic acids for the binding to NC. 42 Molecular dynamic simulations further indicated that these 43 compounds interact via their phosphonate or sulfonate groups 44 with the basic surface of NC, but not with the hydrophobic 45 plateau at the top of the folded fingers. Cellular studies 46 showed that the most soluble compound CIP201 inhibited the 47 infectivity of wild-type and drug-resistant HIV-1 strains at 48 low micromolar concentration, primarily targeting the early

INTRODUCTION 58 2
During the last two decades, the number of drugs acting as inhibitors of entry/fusion, reverse transcription, integration, and protease cleavage developed to fight HIV disease has gradually increased. Though being endowed with efficient antiviral activity, all these compounds select for resistant strains, as a result of the ability of HIV-1 to rapidly mutate 1 .

Even in the classical treatment scheme, namely the Highly Active Anti-Retroviral Therapy (HAART), which combines anti-retroviral drugs of different classes, treatment failures due to drug resistance are still observed.

Thus, new compounds targeting novel and highly conserved viral targets such as the nucleocapsid protein (NC) could be helpful to limit or prevent the emergence of drug resistance. NC exhibits a chaperone activity which enables the structural rearrangement of nucleic acids (NAs) into their most stable conformation. This activity relies on the ability of NC to bind and dissociate rapidly from its NA targets, to destabilize moderately stable NA secondary and tertiary structures and to promote the annealing of complementary NA sequences 2-5 .

This NC activity is thought to be critical in the reverse transcription process, where NC likely chaperones the annealing of the primer tRNA to the primer binding site (PBS) and the two strand transfers that are required for the synthesis of the proviral DNA by reverse transcriptase [START_REF] De Rocquigny | Viral RNA Annealing 45 Activities of Human Immunodeficiency 46 Virus Type 1 Nucleocapsid Protein 47 Require Only Peptide Domains Outside 48 the Zinc Fingers[END_REF][START_REF] Bampi | The 52 42 Heterologous TRNA(Phe) Binding: A 43 Steady-State and Time-Resolved 44 Fluorescence Study[END_REF] . NC is a small basic protein that binds with high affinity (10 13 -10 14 M -1 ) 8 two zinc ions on two strictly conserved finger motifs (CCHC) through their cysteine and histidine residues (Figure 1a).Upon zinc binding, the NC protein adopts its functional folding leading to the formation at the top of the folded fingers of a hydrophobic plateau that involves the amino acids Val13, Phe16, Thr24, Ala25, Trp37, Gln45 and Met46 9-14 . This plateau is critical for interaction with target NAs, notably through a stacking of the Trp37 residue with the nucleobases [15][16][17] . This key role of the plateau is further illustrated by the fact that single mutation of any of its residues results in non-infectious viral particles 18 .

Due to its key functions in HIV-1 replication and its high conservation, NC appears as an ideal target for antiretroviral therapy. Several strategies, including zinc ejectors, noncovalent NC binders and noncovalent NA binders of different chemical classes (see Discussion section for more details) have been developed, but were not fully successful, due to low specificity or to limited antiviral activity or therapeutic index [19][START_REF] Sancineto | NCp7: Targeting a 74 Multitasking Protein for next-75 Generation Anti-HIV Drug 76 Development Part 1: Covalent 77 Inhibitors[END_REF][START_REF] Iraci | NCp7: Targeting a 83 Multitask Protein for next-Generation 84 Anti-HIV Drug Development Part 2. 85 Noncovalent Inhibitors and Nucleic 86 Acid Binders[END_REF] . In order to develop new compounds directed against NC, we have focused our interest on calixarenes, a large family of macrocyclic aromatic compounds bearing phenolic groups, widely used in supramolecular chemistry [START_REF] Gutsche | Calixarenes 91 Revisited[END_REF][START_REF] Böhmer | Macrocycles 94 with (Almost) Unlimited Possibilities[END_REF] . Calixarenes are rigid vase-like macrocycles with a well-established chemistry. These molecules can be obtained through accessible and relatively cheap organic synthesis routes, which also allow the versatile functionalization of their macrocyclic core [24][25][26] . Calixarenes are also receptors in supramolecular recognition studies 27,[START_REF] Ghirga | In 22 Calixarenes and Beyond[END_REF] that can bind and/or host small molecules through their cavity 29,[START_REF] Perret | 31 Biochemistry of Anionic 32 Calix[n[END_REF] making them suitable for drug delivery purposes. 31- 33 . Calixarenes have been investigated among others as biologically-active molecules in a number of applications, and are recently emerging as candidate therapeutics against multiple diseases [34][START_REF] Yousaf | Applications of 63 Calixarenes in Cancer Chemotherapy: 64 Facts and Perspectives[END_REF][START_REF] Nimse | Biological 68 Applications of Functionalized 69 Calixarenes[END_REF] . However, their mechanism of action is generally poorly elucidated, so that calixarenes are mostly used as tool compounds in chemical biology studies.

We have also considered this family for two reasons. First, 62 calixarenes endowed with antiviral activity were first 63 described in the patent of Hwang et al. [START_REF] Hwang | Inhibition 74 and Treatment of Infection by 75 Enveloped Virus with Calix(n)Arene 76 Compounds[END_REF] , in which the para-64 sulfonatocalix [4]arene and its analogs were characterized as 65 anti-HIV agents. Thereafter, synthetic strategies were 66 developed by inserting carboxylate substituents on the 67 calixarene backbone leading to antiviral molecules that have 68 been tested on humans [START_REF] Harris | Preparation of 80 Calixarene-Based Compounds Having 81 Antibacterial, Antifungal, Anticancer, 82 and Anti-HIV Activity[END_REF][START_REF] Harris | Preparation of 85 Calixarenes as Anti-Viral Compounds[END_REF][START_REF] Coveney | 89 Preparation of Alkylated Pyrogallol 90 Calixarene Type Compounds as Anti-91 Viral Compounds[END_REF][41] . Additional calixarene derivatives 69 with anti-HIV activities were further developed [42][43][START_REF] Luo | Synthesis and Anti-Integrase 27 Evaluation of Novel Calix[4]Arene 28 Derivatives Containing the Triazolyl 29 1,3-Diketo Moiety[END_REF] and 70 recently reviewed. [START_REF] Rodik | Calixarenes in Biotechnology and 35 Bio-Medical Researches[END_REF] Their mechanism of action revealed that 71 they may act as inhibitors of HIV fusion, integration and viral 72 protease cleavage 25,[46][47][48] . Second, calixarene 73 hydroxymethylphosphonic acids [49][50][51] have been shown to form 74 host-guest complexes with free amino acids 52,53

87

In this manuscript, we tested the ability of a series of 88 calixarene hydroxymethylphosphonic or sulfonic acids 89 (Figure 1b-f) to interact with NC and inhibit the binding of 90

cTAR C C C G T G C ̶ G G ̶ C A ̶ T G ̶ C G A A C G ̶ C A ̶ T C ̶ G C ̶ G T G ̶ C A ̶ T T ̶ A C . A G ̶ C T ̶ A T ̶ A C ̶ G A C ̶ G T ̶ A G T ̶ A G ̶ C G ̶ C G G C G C A C ̶ G G ̶ C A ̶ T G ̶ C C T T G G ̶ C A ̶ T C ̶ G C ̶ G A G ̶ C A ̶ T T ̶ A T . G G ̶ C T ̶ A T ̶ A C ̶ G T C ̶ G T ̶ A C T ̶ A G ̶ C G ̶ C dTAR C131 R = OH C932 R = P(O)(OH)2 C931 R1 = H, R2 = OH C933 R1 = H, R2 = P(O)(OH)2 C934 R1 = OH, R2 = P(O)(OH)2 C935 C145 R = P(O)(OH)(ONa) CIP200 R = SO3Na CIP201 R = CH2P(O)(OH)(ONa)

RESULTS

Inhibition of NC chaperone properties: selection of the most active compounds

A series of calixarenes was synthetized and characterized as described in supplementary information (Figures S1 andS2). In order to confirm the ability of the four selected compounds 91 to inhibit the NC chaperone properties, we checked their 92 effect on the NC(11-55)-promoted cTAR/dTAR annealing 93 reaction (Figure 3), which relies on both the nucleic acid 94 destabilizing and aggregating activities of NC 61,[START_REF] Vo | HIV-1 Nucleocapsid 84 Protein Switches the Pathway of 85 Transactivation Response Element 86 RNA/DNA Annealing from Loop-Loop 87 "Kissing" to "Zipper[END_REF] . We used in 95 this test a cTAR sequence labelled with Alexa488 96 (fluorophore) and Dabcyl (quencher) at its 5' and 3' ends, 97 respectively. In the absence of NC, the fluorescence signal is 98 low (Figure 3a) due to the close proximity of both cTAR ends 99 and the strong fluorescence quenching of the Alexa488 100 emission by the Dabcyl group. Of note, Alexa 488 was 101 preferred to Rh6G, due to its lower tendency to bind to 102 calixarenes at the high concentrations used in this assay (data 1 not shown). After addition of NC(11-55) at 8 eq, we observed 2 an increase of the fluorescence signal as a result of the 3 destabilization of cTAR by NC(11-55) (Figure 3a) [START_REF] Shvadchak | 32 H. Identification by High Throughput 33 Screening of Small Compounds 34 Inhibiting the Nucleic Acid 35 Destabilization Activity of the HIV-1 36 Nucleocapsid Protein[END_REF] . A further 4 increase in the fluorescence signal was observed when both 5 NC-coated sequences were mixed together in order to allow 6 the annealing reaction to proceed (Figure 3a andb). Real-time 7 annealing kinetics were monitored in pseudo-first order 8 conditions by following the increase of the Alexa488 9 fluorescence at 519 nm. The same plateau was reached in the 10 absence and in the presence of calixarenes, indicating that the 11 same final product (extended duplex) was formed. However, 12 the reaction was slowed down in the presence of all four 13 selected calixarenes (Figure 3b), clearly indicating that they 14 efficiently counteract the NC-chaperoned annealing reaction. 15

The kinetic traces were fitted using 61,[START_REF] Avilov | Characterization 93 of the Inhibition Mechanism of HIV-1 94 Nucleocapsid Protein Chaperone 95 Activities by Methylated 96 Oligoribonucleotides[END_REF] The absence of zinc ejection with CIP200 and CIP201 was checked by monitoring the time-dependence of their inhibition of the NC(11-55)-induced cTAR destabilization. A fast inhibition was observed with both compounds (Figure S3) in sharp contrast with the slow time-dependent inhibition observed with zinc ejectors (see WDO-217, Figure S3), as a consequence of the time requested to chemically react with the zinc fingers and eject zinc [START_REF] Vercruysse | A Phenyl-Thiadiazolylidene-Amine Derivative Ejects Zinc from Retroviral Nucleocapsid Zinc Fingers and Inactivates HIV Virions[END_REF] . This fast inhibition further suggests that CIP200 and CIP201 do not eject zinc, but rather compete with nucleic acids for binding to NC(11-55).

To further characterize the binding of the calixarenes to NC(11-55), we next determined their binding parameters by ITC (Figure S4). The titration curves were adequately fitted to equation (5), giving Kd values ranging from 0.7 to 2 µM (Table 1), close to the IC50 values determined for the inhibition of NC chaperone activity (Figures 2 and3). We found that the reaction of NC(11-55) was accompanied by a favorable enthalpy contribution, ranging from -2.8 to -5.7 kcal/mol that represents roughly half of the total binding energy (Table 1). The positive S values found for all compounds indicated favorable entropic contributions, suggesting that the formation of the complexes is partly driven by a release of water molecules and/or ions.

S (cal.mol -1 .K - 1 ) C933 11-55 1-55 0.7 ± 0.2 0.15 ± 0.1 -3.8 ± 0.5 -4.4 ± 0.3 15 ± 2 16 ± 1 C934 11-55 1-55 1.8 ± 0.6 0.12 ± 0.1 -2.8 ± 0.3 -2.5 ± 0.2 17 ± 2 23 ± 2 CIP200 11-55 1-55 2 ± 1 0.7 ± 0.1 -5 ± 2 -3.1 ± 0.1 8 ± 3 17.7 ± 0.5 CIP201 11-55 1-55 (1-55)S3
1.1 ± 0.5 0.2 ± 0.1 1.7 ± 0.2 -5.7 ± 0.9 -7.3 ± 0.4 -4.7 ± 0.9 8 ± 2 5.5 ± 0.3 10 ± 3

Buffer: 25 mM Tris (pH = 7.5), 30 mM NaCl and 0.2 mM MgCl2, T = 20°C. The thermodynamic parameters are reported as means ± standard error of the mean for at least three independent measurements.

To investigate the contribution of the strong basic N-terminal domain of the peptide on calixarene binding, we performed ITC titrations with the full length NC. We found that Kd values are 3 to 15 times lower (Table 1) than those determined with the NC(11-55) mutant, suggesting that the basic N-terminal domain of NC significantly contributes to calixarene binding.

Moreover, the basic residues between the two zinc fingers play an important role too in the binding of CIP201 to NC, as 45

indicated by the about one order of magnitude change in the 46 Kd value when these residues were replaced by Ser residues in 47 the NC(1-55)S3 mutant (Table 1). 48

To provide further information on the binding process, the 49 electrostatic and non-electrostatic binding contributions were 50 determined from the variation of Kd with the concentration of 51

Na + ions [START_REF] Record | Ion Effects on Ligand-Nucleic Acid Interactions[END_REF] . The number m' of ion pairs and the non-52 electrostatic binding constant Kd(1M) between NC(11-55) and 53 the calixarenes were derived from: 54 55

log 𝐾 𝑑 = log 𝐾 𝑑 (1𝑀) +  𝑁𝑎 + 𝑚 ′ log [𝑁𝑎 + ]
(2) 56 57

The value of the fraction of Na + ions thermodynamically 58 bound per negatively charged moiety,  𝑁𝑎 + ,was assumed to 59 be 0.71 as for single-stranded DNA [START_REF] Record | Ion Effects on Ligand-Nucleic Acid Interactions[END_REF][START_REF] Mély | Binding of the HIV-1 Nucleocapsid Protein to the Primer TRNA, InVitro, Is Essentially Not Specific[END_REF] .The plots of log Kd 60 versus log [NaCl] were found to be linear in the 10-100 mM 61 salt concentration range (Figure 5). Interestingly, the 62 contribution of the non-electrostatic interactions deduced 63 from the Kd(1M) values was found to be dominant, 64 representing 80 % to 90 % of the binding energy at 30 mM 65 NaCl. Moreover, the number m' of ion pairs between NC(11-66 55) and the calixarenes was about 1 in all the complexes. Of 67 note, a similar distribution of electrostatic and non-68 electrostatic contributions was observed for the binding of 69 NC(12-53) to a small d(AACGCC) oligonucleotide 13,[START_REF] Vuilleumier | Nucleic Acid Sequence 50 Discrimination by the HIV-1 51 Nucleocapsid Protein NCp7: A 52 Fluorescence Study[END_REF] . 70 71 ). As expected, NC(11-55) was found to markedly increase 1 the fluorescence anisotropy of TMR-5'-cTAR, as a result of 2 the formation of the NC(11-55)/cTAR complex. All four 3 selected calixarenes were observed to shift the titration curves 4 toward higher NC(11-55) concentrations as compared to the 5 curve in the absence of calixarenes (Figure 6, black curve). 6 Thus, all four calixarenes compete with cTAR for the binding 7 to NC(11-55), which explains their ability to inhibit the NA 8 chaperone properties of the peptide. It should be noted that the 9 C145 used as negative control has, as expected, a marginal 10 impact on the binding of NC (11-55) with cTAR (Figure 6, 11 compare orange and black curves). Moreover, a control 12 experiment was performed to check both by ITC and 13 fluorescence titrations that calixarenes do not bind to cTAR 14 (Figure S5A andB). Thus, the calixarenes hinder the binding 15 of NC(11-55) to cTAR, only by their binding to the peptide. 16 17 bridged by water molecules (Figure 7). In particular, 79 phosphonate groups at the upper rim of calixarenes C933, 80 C934, and CIP201 bind preferentially the side chain of Arg32 81 by both H-bond interactions and cation-π stacking. The Arg32 82 residue is well included in the calixarene core of C933 (Figure 83 7A), and partially included in the core of C934 (Figure 7B). 84

In CIP201, the Arg32 residue is located at the upper rim of the 85 calixarene molecule because the inner core is occupied by a 86 Na + ion (Figure 7C), whereas CIP200 targets the side chain of 87 Lys47, which is well included in the calixarene core (Figure 88 7D). 89 C933 and C934 proved to bind the NC in a highly comparable 90 manner by interacting with Arg32, as well as with Lys26, 91 Arg29, Lys34, and Lys47. C933 further interacts with Asn17 92 (Figure 7A), whereas C934 interacts with Lys3 and Gln45 93 (Figure 7B), this latter being also involved in the binding of 94 other NC inhibitors [START_REF] Mori | Use of Virtual Screening for Discovering Antiretroviral Compounds Interacting with the HIV-1 Nucleocapsid Protein[END_REF][START_REF] Mori | Functional and Structural Characterization of 2-Amino-4-Phenylthiazole Inhibitors of the HIV-1 Nucleocapsid Protein with Antiviral Activity[END_REF][START_REF] Mori | Predicting the Binding Mode of Known 93 NCp7 Inhibitors To Facilitate the 94 Design of Novel Modulators[END_REF] . Besides Arg32, CIP201 establishes 95 H-bonds with Arg7, Lys14, Lys33, Lys34, and Glu42 (Figure 96 7C). In the case of CIP200, in addition to Lys47, the 97 compound interacts with Ile1, Gln2, Lys3, Arg10, Lys11, 98 Lys38, and Gln45 (Figure 7D). 99 Finally, to provide a structural explanation to the noticeable 100 entropic effect observed by ITC (Table 1), the change of NC 101 hydration associated to the binding of CIP200 was evaluated 102 to NC, with a significant change in the balance between the 124 enthalpy and entropy contributions (Table 1). Indeed, we 125 observed a two-fold less favourable H value together with a 126 two-fold increase in the S value. These changes in H and 127 S values strongly suggest that the binding of CIP201 is less 128 specific with the NC mutant as compared to NC [START_REF] Doyle | 1 Biocalorimetry 2 : applications of 2 calorimetry in the biological sciences -3 Colby College Libraries[END_REF] . Thus, the 129 binding data with NC(1-55)S3 are fully in line with the MD 130 simulations and confirm the key role played by the [START_REF] Rodik | Virus-Sized 44 DNA Nanoparticles for Gene Delivery 45 Based on Micelles of Cationic 46 Calixarenes[END_REF] 3) and the Kd values (Table 1). These similar values determined by different independent experiments strongly suggest that the antiviral activity of CIP201 may be related to its ability to target NC. The cytotoxicity of CIP201 was very low (CC50 > 5 mM), giving an excellent selectivity index for this compound. However, it cannot be excluded at this step that the low toxicity might be related to a limited cell permeability of the compound. 3). CIP201 showed an antiviral activity against these representative resistant HIV-1 viral strains in the low 48 micromolar range, similar to that against the wild-type virus 49 (strain 114 i.e. NL4-3, Table 3). These data indicate that the 50 resistance mutations to drugs currently employed in clinical 51 practice do not affect the susceptibility to CIP201, reinforcing 52 the conclusion that NC could be the main target of the 53 calixarenes. Due to its favourable IC50 values and low toxicity, 54 CIP201 appears as a good starting point for the development 55 of new anti-HIV agents. 56

Mechanism of action of calixarenes 63

As CIP201 was found to be active in the early steps of HIV 64 replication, we performed complementary investigation to 65 further characterize its mode of action. As a first step, we 66 investigated the effects of CIP201 on the production of viral 67 nucleic acid intermediates. The data in Figure 8 suggests that 68 inhibition of HIV replication occurred mainly during pre-69 integration events. In particular, the amount of total HIV-1 70 DNA (Figure 8A) produced after reverse transcription 71 (approximately 16 h post infection) was significantly 72 decreased in presence of CIP201. This decrease was similar 73 to that measured in the presence of rilpivirine (RPV), 74 indicating an impairment of reverse transcription or earlier 75 events. In contrast, CIP201 did not affect the levels of 2-LTR 76 circles (Figure 8B). This absence of effect is in contrast with 77 the approximately 3 times higher amount of 2-LTR circles 78 observed with the integrase inhibitor raltegravir (RAL) as 79 compared to "no drug" control culture. This suggests that 80 CIP201 does not impair viral DNA integration. In addition, 81 the levels of intracellular HIV-1 RNA were comparable to 82 those measured in presence of RPV, reinforcing the 83 hypothesis of an early inhibitory activity for CIP201 (Figure 84 8C). Its effect was similar to that of Nevirapine, a non-nucleoside RT inhibitor (NNRTI) that binds non-competitively to RT allosteric sites 77,78 . By fitting the dependence of RT inhibition as a function of the concentration of CIP201 with equation ( 4), an IC50 value of 0.9 (± 0.1) µM was determined for CIP201 (Figure S9b), as compared to 49 (± 4) nM for Nevirapine in the same assay 76 . Altogether our data suggest that CIP201 106 may have multiple molecular targets in HIV-1. However, as 107 CIP201 is also active on RT resistant strains, it is believed that 108 RT is not a major target of CIP201 in cellular assays and/or 109 that CIP201 inhibits RT via a novel binding mode that is 110 different from that of the established inhibitors. 111

To further decipher the mode of action of CIP201, we used a 112

Multi-Dosing Time protocol to test its effect comparatively to 113 reference inhibitors of entry (maraviroc), RT (lamivudine and 114 didanosine) and integrase (raltegravir) (Table 4). 115 In the standard protocol, CIP201 was incubated with the cells for 2 h during spinoculation and then, again for 48 h. 118 119 When CIP-201 was pre-incubated with the cells for 2 hours and then washed out before HIV-1 incubation, no effect was observed on virus infection, suggesting that CIP201 likely does not bind with high affinity to the plasma membrane in order to protect the cells against HIV-1 infection. In contrast, CIP201 protected U373-CD4-CCR5 cells against virus infection when incubated together with the pseudotyped viruses for 2 h (IC50 = 19 ± 2 µM) or in the standard protocol where CIP201 was added both during spinoculation (for 2 h) and at 2 h post-infection (for 48 h) (IC50 = 20 ± 3 µM).

Moreover, CIP201 showed only residual activity when incubated with cells 2 h post-infection (Figure S10 and Table 4). Thus, CIP201 resembles to the entry inhibitor maraviroc, 133 but differs from RT inhibitors that remain fully active when 134 provided for 2 or 48 h at 2 h post-infection. Therefore, our 135 data suggest that CIP201 mainly targets the HIV-1 entry step 136 during the first two hours of infection. The low activity of 137 CIP201 when provided 2 h after infection, in spite of its high 138 activity on NCp7 and RT in molecular assays, suggests that 139 CIP201 might not enter efficiently into cells. The lack of 140 activity on HIV-1 infection after cell pre-treatment wth 141 CIP201 and subsequent wash, confirms that CIP201 does not 142 enter efficiently into cells, and may primarily act by binding 143 to viral particles. Finally, its residual activity when added 2 h 144 after infection (Figure S10) may tentatively be attributed to 145 CIP201 molecules that have been shuttled into cells through 1 viral particles docked on the cell surface, in order to inhibit 2 HIV-1 replication possibly by acting on RT and NCp7. available to date, no zinc ejection was observed for these 35 molecules, making them valuable candidates for antiviral 36 therapy. Moreover, NC inhibition in the low to sub-37 micromolar range places these calixarenes within the most 38 potent non-zinc-ejecting NC inhibitors reported to date 80,[START_REF] Tang | HIV-1 9 Antiretroviral Resistance: Scientific 10 Principles and Clinical Applications[END_REF] . 39 By using ITC, the calixarenes were found to bind to NC with 40 affinity in the low to sub-micromolar range in agreement with 41 the NC inhibition data. Moreover, the binding was found to 42 rely on balanced entropy and enthalpy contributions. This was 43 further corroborated by MD simulation for each molecule, 44 showing that the recognition between NC and calixarenes is 45 driven by long-range electrostatic forces, and that calixarenes 46 bind basic residues at NC surface by means of H-bond and 47 cation-π interactions, in line with the strong observed enthalpy 48 energy changes. Moreover, according to the binding mode 49 observed in the most populated cluster of MD frames, a 50 number of water molecules are released from NC residues 51 upon binding of calixarenes, consistent with the favourable 52 entropy changes deduced from ITC. This release of water may 53 compensate for the loss of overall NC flexibility induced by 54 calixarene binding. From the ionic strength dependence of the 55 affinity of calixarenes for NC, we further showed that the 56 binding of calixarenes C933, C934, CIP200 and CIP201 to 57 NC(11-55) involved about 1 ion pair and that non-58 electrostatic interactions represented 80% to 89% of the 59 binding energy at 30 mM NaCl. This suggests that long-range 60 electrostatic interactions are likely required for recognition 61 between the two interacting species, but as suggested by MD 62 simulations, the complex is mainly stabilized by H-bonds, 63 cation-π interactions and water release. Calixarenes C933, 64 C934, and CIP201 that bear phosphonate groups at the upper 65 rim show a similar interaction pattern. They recognize and 66 bind basic residues of the NC linker (and notably Arg32) by 67 H-bond and cation-π interactions, and establish a number of 68 H-bond contacts with basic residues at the top of zinc-fingers, 69 a region of NC that is crucial for its biological functions. 82,83 70 The key role of the basic residues of the NC linker in binding 71 to CIP201 was clearly confirmed using a NC mutant where 72 these residues were replaced by Ser residues (NC(1-55)S3, 73 Figure 1a). Different from the other active calixarenes, 74 CIP200 is functionalized with sulfonate groups at the upper 75 rim, and targets the Lys47 by means of cation-π interactions 76 through inclusion of the residue's side chain in its aromatic 77 core. CIP200 also interacts with a cluster of residues within 78 the N-terminal domain of NC, suggesting that the binding site 79 of calixarenes on NC may be modulated by specific 80 functionalization at the upper rim of the aromatic core. 81

Importantly, the binding mode predicted for calixarenes was 82 not observed before for any type of NC inhibitors. The main 83 hypothesis that emerged by coupling computational with 84 biophysical and biochemical data is that this new binding 85 poor tissue distribution likely due to its highly polar nature [START_REF] Kerns | Drug-like 16 Properties: Concepts, Structure Design 17 and Methods ; from ADME to Toxicity 18 Optimization[END_REF] . 112 113 114

CONCLUSION 115

In this study, we identified the CIP201 calixarene as an 116 antiviral compound active against both HIV-1 reference virus 117 and resistant viral strains, mainly by inhibiting the HIV-1 118 entry step. CIP201 was also found to inhibit the nucleic acid 1 chaperone activity of the HIV-1 NC as well as the flipping 2 and polymerisation activity of RT in molecular assays. The 3 inhibition of NC was predicted to result from the interaction 4 of CIP201 via its phosphonate or sulfonate groups with the 5 basic surface of NC, which blocks the binding of NC to its 6 nucleic acid targets. This binding mode differs from that of 7 most other noncovalent NC inhibitors that target the 8 hydrophobic platform at the surface of the NC zinc fingers 9 (Mori et al, 2015). Importantly, due to its low permeability 10 the antiviral activity of this multi-target compound is certainly 11 underestimated. Thus, CIP201 appears as a very promising 12 candidate for the development of anti-HIV drug candidates 13 targeting the NC. 14 However, efforts are still needed to further increase its 15 efficacy and improve its ADME and pharmacokinetic 16 properties. To this aim, hit-to-lead optimization of CIP201 17 could be driven by the necessity to tune the hydrophilic-18 hydrophobic balance in order to ensure a better 19 pharmacokinetics profile and to enhance in vivo activity. This 20 could be accomplished by chemical modifications at the lower 21 (narrow) rim or the upper (wide) rim of the macrocycle. 22 Interestingly, thiacalixarenes offer almost unlimited 23 possibilities for chemical modifications, including the 24 derivatization of the hydroxyl groups at the lower rim, or the 25 four reactive para-positions of benzene rings at the upper rim 26 by the inclusion of different functional groups with specific 27 chemical or physicochemical features. In the specific case of 28 CIP201, the phosphonate groups could be replaced by 29 bioisosters or other negatively charged groups such as for 30 instance the carboxylic acid, sulfone, triazole, and tetrazole 31 rings. In addition, sulfur atoms can be oxidized to convert the 32 thiacalixarenes into calixarene sulfoxides or calixarenes 33 sulfone with four or six valent sulfur atoms respectively. 34

Besides chemical modifications, conformational changes to 35 the macrocyclic core can be designed in order to achieve 36 optimal interaction with NC. Thanks to the accessible 37 chemistry of calixarenes, and the reliable computational 38 protocol developed in this work, a large number of 39 thiacalixarene derivatives could be preliminarily screened and 40 prioritized in silico for their interaction with NC, although this 41 will be the subject of future works. 42

EXPERIMENTAL SECTION

43 Materials 44 All solvents for spectroscopic measurements were from 45 Sigma-Aldrich (Darmstadt, Germany). Acetonitrile was 46 purchased from Sigma-Aldrich (Darmstadt, Germany) with 47 high degree of purity for the HPLC analysis. 48

The synthesis and the characterization of the calixarenes used 49 in this study are described in the supplementary information. 50 Calixarenes C145 and CIP201 were directly solubilized in 51 water while the other calixarenes were first dissolved in 52 DMSO. Unless mentioned otherwise, experiments were 53 carried out in Tris buffer (25 mM Tris-HCl pH 7.5, 30 mM 54 NaCl, and 0.2 mM MgCl2) 59 . The percentage of DMSO was 55 between 1.3 and 2 % v/v in the final reaction mixtures. Fresh 56 calixarene solutions were prepared before all experiments. 57

Proteins 58

In order to reduce the NA-aggregating properties 58,101,102 of the 59 full-length NC which causes substantial light-scattering, we 60 performed the majority of experiments with the NC(11-55) 61 peptide (Figure 1a). This truncated peptide possesses the zinc 62 finger domain and aggregates NAs only at high 63 concentrations 58,103 . NC, NC(1-55)S3 and NC(11-55) peptides 64 were synthesized by solid-phase peptide synthesis on a 433A 65 synthesizer (ABI, Foster City, CA), as previously 66 described [START_REF] Shvadchak | 32 H. Identification by High Throughput 33 Screening of Small Compounds 34 Inhibiting the Nucleic Acid 35 Destabilization Activity of the HIV-1 36 Nucleocapsid Protein[END_REF]104 . Peptides were stored lyophilized. The zinc-67 bound form of the peptides was prepared by dissolving them 68 in water, adding a 2.5-fold molar excess of zinc sulphate, and 69 raising the pH to its final value by adding buffer. The pH was 70 increased to its final value only after addition of zinc to avoid 71 the oxidation of the zinc-free peptide. The peptide 72 concentration was determined by using an extinction 73 coefficient of 5.7 × 10 3 M -1 cm -1 at 280 nm for NC and NC(11-74 55). 75

Isothermal Titration Calorimetry (ITC)

The

Cell-based antiviral assay with replication competent HIV-1 strains

The antiviral activity of calixarene CIP201 was evaluated by measuring its IC50 values against the HIV-1 wild-type reference strain NL4-3 and a panel of viruses with resistance mutations to approved HIV-1 drugs (supplementary data, Table S1) in a TZM-bl cell line based phenotypic assay 113 . TZM-bl cells are characterized by luciferase and galactosidase reporter genes integrated in the cell genome under the control of an HIV-1 LTR promoter. The expression of reporter genes is regulated by the viral Tat protein, which is produced following transcription of the integrated provirus.

Since the NC viral protein is thought to be involved in both early and late events of HIV-1 life cycle, we adopted a re-

85 Figure 1 .

 851 Figure 1. NC peptides (a), calixarene compounds (b to f), and 86

  its target nucleic acids, preventing the promotion of the destabilization and annealing of the complementary sequences. Molecular modelling and mutational studies indicated that calixarenes exhibit a new binding mode where their phosphonate or sulfonate groups interact with the basic surface of NC. The antiviral activity and cellular cytotoxicity of the most efficient compound were tested using HIV pseudoviruses, as well as replicationcompetent wild-type (WT) and drug-resistant strains. This compound was also tested in humanized mice infected with HIV-1. Finally, the mechanism of action of this calixarene was investigated through biochemical and cell-based assays.

56 Figure 2 .

 562 Figure 2. Inhibition of the NC(11-55)-induced cTAR 57

66 N

 66 no fluorescence change was induced by C935, 69 indicating that it is unable to inhibit the NC(11-55)-induced 70 destabilization of cTAR. Notably, this compound differs from 71 the other tested calixarenes by the fact that it possesses four 72 propyl chains at the lower rim and two bromine substituents 73 at the upper rim of the calixarene core. Assuming that the OH 74 groups may be solvent exposed when calixarenes are bound 75 to NC 60 , the O-propyl chains become then unfavorably 76 solvent-exposed. Moreover, the two bromine substituents 77 may sterically hinder the inclusion of NC residues in the 78 calixarene central core cavity or form a steric obstacle for the 79 binding of C935 to the NC. Determination of the IC50 values 80 revealed that the other tested calixarenes could be divided into 81 two classes (Figure 2, table). The first class comprising the 82 four most active compounds (C933, C934, CIP200 and 83 CIP201) is characterized by IC50 values in the range 3-5 µM, 84 close to the concentration of the NC peptide used in the assay. 85 The second class (C131, C932, C145 and C931) is 86 characterized by IC50 values in the range 40-90 µM and is thus 87 far less efficient. Based on the difference in activities of the 88 two classes, we focused our next efforts only on the 89 compounds of the first class. 90

33 34Figure 3 . 65 Figure 4 .

 333654 Figure 3. Inhibition of NC(11-55)-promoted cTAR/dTAR 35

Figure 5 . 81 Finally

 581 Figure 5. Dependence on Na + ion concentration of the 72

6

 6

Figure 6 .Figure 7 .

 67 Figure 6. Binding of NC(11-55) to TMR-5'-cTAR in the 19

  along MD trajectories. The comparison of the solvation of NC 103 target residues in the free protein (Figure S8A) with that in the 104 complex (Figure S8B) clearly shows that CIP200 displaces a 105 large number of water molecules from solvent-exposed NC 106 residues such as for example Lys47, in full line with the 107 measured increase in entropy. 108 Overall, MD simulations suggest that the phosphonate and 109 sulfonate groups of calixarenes are responsible for NC 110 recognition through long-range electrostatic interactions and 111 for the stabilization of the final NC/calixarene complexes, 112 mainly through H-bond and cation-π interactions with NC 113 basic residues. As a result, these molecules may inhibit NC by 114 competing with NAs for the binding to the protein and 115 occluding the accessibility to its hydrophobic pocket from the 116 solvent area. 117 To validity of the MD simulations is substantiated by the ITC 118 data with the NC(1-55)S3 mutant where the three positively 119 charged basic residues ( 32 RKK 34 ) of the linker acting as a 120 binding site for CIP201 are replaced by non-charged Ser 121 residues. ITC titration of NC(1-55)S3 by CIP201 revealed an 122 about one order of magnitude decrease in affinity as compared 123

  RKK34 131 sequence in the binding of CIP201. 132Antiviral activity of CIP201 against wild-type and drug-resistant HIV-1 strainsNext, our objective was to determine the antiviral activity of the water soluble calixarene CIP201 acting as NC inhibitor. Indeed, we selected this compound, as it remains highly soluble in water (up to 100 mM) while the others calixarenes were low soluble in aqueous solutions in the absence of DMSO (solubility limits of C933, C934 and CIP200 were measured at 400 µM, 6.5 mM and 150 µM respectively). To determine the antiviral activity of CIP201, we used two cellular assays. The first one being based on Hela cells infection with non-replicative pseudo-particles (antipseudovirus assay in Table 2) monitors only the inhibition of the early steps of infection. The second one being based on cell infection by a wild-type HIV virus (NL4-3) is sensitive to inhibition in either the early phase of HIV infection (MonoCycle) or both the early and late phases of HIV infection (BiCycle). In both the anti-pseudovirus and MonoCycle assays, CIP201 was found to inhibit HIV infection with IC50 values of 3.3 -21 µM with comparable values in both MonoCycle and BiCycle assay, indicating that this compound inhibited mainly, if not only, the early phases of HIV replication. These IC50 values were found to be close to the IC50 values of the NC chaperone assays (Figures 2 and

Table 2 .a

 2 Antiviral activity and cytotoxicity of CIP201. Inhibition activity of CIP201 on the infection of Hela cells by viral pseudoparticles. IC50 corresponds to the concentration at which the infection is decreased by 50%. b CC50: concentration required to cause 50% of cell death. c Selectivity index SI = CC50/IC50. d Inhibitory activities tested on HIV-1 wild-type reference strain NL4-3. The compound CIP201 was then tested on a series of mutant strains resistant to reference protease inhibitors (PI, strain 11808), nucleoside reverse transcriptase inhibitors (NRTI, strain 7406), non-nucleoside reverse transcriptase inhibitors (NNRTI, strain 12231) and integrase inhibitors (INI, strain 11845) (Table

Figure 8 .

 8 Figure 8. Quantification of HIV-1 nucleic acid intermediates produced in the presence of CIP201 (100 µM), or reference compounds

  was tested in humanized NSG mice79 and 7 compared with the triple regimen Triumeq (abacavir, 8 dolutegravir, lamivudine) on viral replication and CD4 9 depletion after 7 weeks of treatment. After 5 weeks of HIV 10 infection, although the mice have drunk the same volume of 11 sucralose solution among the three groups, we did not find any 12 effect of CIP201 on plasma viral load (FigureS10A) and on 13 the CD4/CD8 ratio (FigureS10B) after 6 weeks of treatment. 14In contrast, the mice treated with Triumeq reached 15 undetectable viral load and restored CD4 cell count. The 16 concentrations of CIP201 was further measured in the plasma, 17 spleen, liver and kidneys but was found to be below the LOD 18 (i.e. 10 µg/mL). These results indicate that the lack of efficacy 19 of CP201 in infected humanized mice was probably due to 20 poor absorption, distribution, metabolism, and excretion 21 (ADME) and/or pharmacokinetic properties. Thus,CIP201 22 needs to be optimized for further development in therapy. 23 24 DISCUSSION 25 Following our strategy to develop antiretroviral drug 26 candidates targeting the HIV-1 NC protein 19 , we evaluated the 27 NC inhibitory properties and antiretroviral activity of a 28 number of functionalized calixarenes by means of an 29 integrated multidisciplinary approach. Using fluorescence-30 based methods, calixarenes C933, C934, CIP200 and CIP201 31 proved to inhibit efficiently the NC(11-55)-induced 32 destabilization of cTAR and subsequent annealing with 33 dTAR. Different from the largest class of NC inhibitors 34

  mode efficiently prevents NC to bind to its nucleic acid 86 targets. Moreover, the water soluble compound CIP201 was 87 found to inhibit replication of wild-type and drug-resistant 88 HIV-1 strains in a cellular model at low micromolar 89 concentration, by targeting the early steps of HIV-1 90 replication. Time of addition assays further revealed that 91 CIP201 has low cell permeability, likely due to its high 92 amount of negative charges, and mainly targets the viral entry 93 step. In addition, the residual activity observed after the HIV-94 1 entry step suggested that CIP201 molecules could have 95 entered cells when bound to viral particles and exerted their 96 antiviral activity on RT and NCp7 molecules. Both modes of 97 action are fully consistent with the low levels of HIV-1 DNA 98 and intracellular HIV-1 RNA measured in cells infected by 99 HIV-1 in the presence of CIP201. 100 Finally, CIP201 showed low cytotoxicity that can be at least 101 partly ascribed to the low cell permeability of the compound. 102 The low toxicity of CIP201 was further confirmed on infected 103 humanized mice, which showed no evidence of acute toxicity 104 during the treatment. Therefore, CIP201 stands as a very 105 interesting lead, since its efficacy in inhibiting HIV-1 106 replication is highly comparable to other NC inhibitors (Mori 107 et al, Sancineto et al, Iraci et al). Unfortunately, CIP201 was 108 found to be inactive in this animal model. This lack of efficacy 109 in vivo was related to the low compound's concentration in 110 blood and different organs, suggesting a high clearance and 111

  labelled oligodeoxynucleotides (ODNs)77 were synthesised and purified by IBA GmbH Nucleic Acids 78 Product Supply (Göttingen, Germany). Their concentrations 79 were determined by UV absorbance at 260 nm. For the doubly 80 labelled cTAR, the 5' terminus was labelled with 6-81 carboxyrhodamine (Rh6G) or with Alexa Fluor 488 via an 82 amino linker with a six carbon spacer arm. The 3) at its 5' terminus. The 88 ODNs were purified by reverse-phase high performance 89 liquid chromatography (HPLC) and polyacrylamide gel 90 electrophoresis. Extinction coefficients at 260 nm of 5.15 × 91 10 5 M -1 cm -1 , 5.56×10 5 M -1 cm -1 , 5.775 ×10 5 M -1 cm -1 , and 5.73 92 ×10 5 M -1 cm -1 were used to determine the concentration of 93 dTAR, TMR-5'-cTAR, Rh6G-5'-cTAR-3'-Dabcyl, and 94 Alexa488-5'-cTAR-3'-Dabcyl, respectively. 95Absorption and fluorescence spectroscopy96 Absorption spectra were recorded with a Cary 400 or a Cary 97 4000 spectrophotometer (Agilent). Fluorescence spectra and 98 anisotropy measurements were recorded at 20°C with a 99 Fluorolog or a Fluoromax 3 spectrofluorometer (Horiba 100 Jobin-Yvon) equipped with a thermostated cell compartment. 101 Excitation wavelengths were 520 nm for Rh6G-5'-cTAR-3'-102 Dabcyl, 550 nm for TMR-5'-cTAR, and 480 nm for 103 Alexa488-5'-cTAR-3'-Dabcyl. The spectra were corrected 104 for dilution, buffer fluorescence and wavelength-dependent 105 response of the optics and detectors. 106 To screen calixarenes (Cal), we used an assay in which we 107 tested their ability to inhibit the NC-induced destabilization of 108 cTAR 59 . The percentage of inhibition (% inh) obtained for 109 each calixarene concentration was calculated with equation 110 (3): 111 %𝑖𝑛ℎ = 𝐼 (𝑐𝑇𝐴𝑅+𝑁𝐶) -𝐼 (𝑐𝑇𝐴𝑅+𝑁𝐶+𝐶𝑎𝑙) 𝐼 (𝑐𝑇𝐴𝑅+𝑁𝐶) -𝐼 (𝑐𝑇𝐴𝑅) cTAR), I(cTAR+ NC), and I(cTAR+ NC+ Cal) correspond to the fluorescence intensity of cTAR alone, cTAR in the presence of the NC(11-55)peptide, and cTAR in the presence of both NC(11-55) and calixarene, respectively. To determine the IC50 values, we plotted the percentage of inhibition against the calixarene concentration (C) and fitted it with a modified version of the dose-response equation 105 : % 𝑖𝑛ℎ = 𝐴 1 + (𝐴 2 -𝐴 1 ) 1 + 10 (log(𝐼𝐶 50 )-log ( 𝐶))× 𝑝) (4) where, A1 and A2 represent the percentage of inhibition in the absence and with saturating concentrations of calixarene, respectively. IC50 represents the half maximal inhibitory concentration, and p denotes the Hill coefficient. Annealing kinetics were measured in pseudo-first order conditions by adding a 10-fold excess of unlabelled dTAR to the doubly labelled complementary sequence Alexa488-5'-cTAR-3'-Dabcyl. Excitation and emission wavelengths were set at 480 nm and 519 nm, respectively to monitor the Alexa 488 fluorescence. NC(11-55) was added at a 8:1 molar ratio to each reactant separately, and then the reaction was initiated by mixing the peptide-coated ODNs together. Calixarenes (C933, C934, CIP200 and CIP201) were added at different concentrations to monitor their ability to perturb the NCpromoted cTAR/dTAR annealing rate constants kobs. All fitting procedures were carried out with Origin 8.6 software using nonlinear least-squares methods and the Levenbergspectrometry (ESI-MS) analysis was performed in the positive ion mode on an electrospray time-of-flight mass spectrometer (LCT, Waters, Manchester, UK) equipped with an automated nanoESI source (TriversaNanomate, Advion, Ithaca, NY). Calibration of the instrument was performed using a 2 µM horse heart myoglobin solution prepared in a mixture of water:acetonitrile (1:1) acidified with 1% of formic acid. MS data were acquired and analysed using the MassLynx 4.1 software (Waters, Manchester, UK). For mass spectrometry experiments in nondenaturing conditions, NC(11-55) was prepared in water with 2.2 molar equivalents of ZnSO4 and the concentration was measured using an extinction coefficient of 5700 M -1 cm -1 at 280 nm. Before use, the protein was buffered with 50 mM ammonium acetate (AcONH4) at pH 7.0. NC(11-55) protein (20 µM) was incubated with 200 µM of calixarenes(10 fold excess, 1% of DMSO v/v in the final volume) at 20 °C for 15 min, before recording the mass spectra. In order to balance the weak ionization due to the presence of DMSO, the analyses under non-denaturing conditions were carried out with an accelerating voltage (Vc) of 100 V, and the pressure in the first pumping stage (backing pressure) of the instrument was fixed to 6 mbar.

80 Molecular

 80 binding of NC, NC(1-55)S3 and NC(11-55) to calixarenes was investigated by Isothermal Titration Calorimetry (ITC), using a Nano ITC microcalorimeter (TA Instruments) at 20°C, in Tris-HCl (25 mM, pH 7.5) containing 58 0.2 mM MgCl2 and 10, 30, 50 or 100 mM NaCl. The titration 59 experiments were performed by incremental injections (each 60 200 or 300s) of2.5 µL aliquots of calixarene solutions(100, 61 150 or 200 µM)in 300 µL of a 8 µM peptide solution 62 contained in the reaction cell. The heat flow (µcal× s -1 ) 63resulting from the interaction between the two partners was 64 continuously recorded. The quantity of heat Q accompanying 65 each injection was integrated over time and corrected for the 66 heat of dilution measured in an independent experiment in 67 which the calixarene solution was injected into the buffer 68 alone. Instrument control, data acquisition, and analysis were 69 done with the NanoAnalyze software provided by the 70 manufacturer. Assuming 1:1 binding stoichiometry, the molar 71 heat of binding H 0 and the binding dissociation constant Kd 72 were obtained by fitting the differential heat dQ/dXtot 106 as a 73function of the total calixarene concentration ([Cal]tot)𝑟 (1 -𝑟) + (1 + 𝑟) 2 ) 1/2 ) r= [Cal]tot/Kd, Xr = Xtot/ [Cal]totand Xtot is the peptide 79 concentration in the reaction cell of volume V0. //www.eyesopen.com/quacpac). Partial charges were 84 then assigned at the am1-bcc level by antechamber from 85 Amber12 107,108 . The full length NC from the NMR structure of 86 its complex with a small molecule (PDB: 2M3Z)98 was used 87 as starting point in MD simulations after removal of the bound 88 ligand. MD simulations were performed with Amber12. The 89 ff12SB force field was used together with custom force field 90 parameters for Zn-binding residues and coordinated Zn ions, 91 as described previously17 . A time step of 2 fs was used. C-H 92 bonds were restrained by the SHAKE algorithm. For each 93 system studied in this work, one molecule of NC and one 94 molecule of calixarene were placed in a rectilinear box of 95 TIP3P water molecules at a random distance higher than 40 Å 96 from each other. Neutrality of the system was achieved by 97 adding the proper number of Na + counter-ions. Each solvated 98 system was then submitted to a two-step energy minimization. 99In the first step, water molecules were minimized around the 100 frozen solute (NC + calixarene), while in the second step the 101 solvated solute was energy minimized until convergence 102 (rmsd = 0.05). Each system was then heated up to 300 K 103 during 55 ps in the NVT ensemble and then equilibrated in 104 density for 110 ps at constant pressure. After these steps, 105 unrestrained MD trajectories were produced for 0.5 μs in the 106 NPT ensemble. Four replicas of MD trajectories of 0.5 μs 107 each were run to enhance statistical significance. Analysis of 108 MD trajectories was performed with cpptraj 109 . Electrostatic 109 surface potential was calculated by the APBS program 110 . 110 Cell-based antiviral assay with replication-111 defective HIV pseudoparticles 112 13 This assay (described in supplementary information) is based on the infection of Hela cells by replication-defective HIV particles pseudotyped with the Vesicular Stomatitis Virus glycoprotein 111 that bypass entry and mimic the early steps of the HIV virus infection cycle (post-entry to integration).For each tested calixarene, the percentage of inhibition (%inh) was calculated with : compound was tested in sextuplicate.The reverse transcriptase inhibitor AZT (1 µM) was used as a positive control. To determine the IC50 values, we plotted the percentage of inhibition against the calixarene concentration and fitted it with the dose-response equation(4).In parallel to the infectivity test, the cytotoxicity of the molecules was quantified in a MTT assay (3-(4,5dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide) 112 .Another plate of HeLa cells was thus prepared and treated in the same conditions as for the infectivity assay. 24 h after infection, the medium was replaced by a mix containing 100 µL of DMEM and 10 µL of 12 mM MTT solution in PBS and cells were incubated during 4 h. In order to dissolve the insoluble purple formazan reduced by living cells, 85 µL of the mix was replaced by 50 µL of DMSO and gently shaken for 10 min. The absorbance was then measured at 540 nm in a spectrophotometer (Safas, Monaco) and expressed in percentage of cytotoxicity, using the DMEM + DMSO solution as the control.

3 Nucleocapsid

 3 infection assay, named BiCycle Assay, consisting in a first cycle of replication in the T-cell derived MT-2 cell line followed by an additional round of replication in TZM-bl cells. MT-2 cells were seeded at a concentration of 50,000 cells/well in a 96-well plate and infected with the viruses at multiplicity of infection (M.O.I.) 0.1 in the presence of fivefold dilutions of the compounds. After 48-72 h, 50 µL of supernatant from each well, containing the virus produced in the first round of infection, were used to infect TZM-bl cells seeded in a 96-plate well at a concentration of 30,000 cells/well. Two days later, cells were lysed by adding 40 µL of Glo Lysis Buffer (Promega) in each well for 5 min, then 40 µL of Bright-Glo Luciferase Reagent (Promega) were added to each well for relative luminescence units (RLU) counting using a Glo-Max Multi Detection System (Promega). RLU values from each well were used to calculate the IC50 value of 60 each compound using the GraphPad v6.0 software. The 61 inhibition of the early events of viral replication was evaluated 62 through a single cycle replication assay in TZM-bl cells, 63 named MonoCycle Assay. The method consists in the 64 infection of TZM-bl cells at M.O.I. 0.1 in presence of serial 65 five-fold dilutions of the drugs, similarly to the first round of 66 infection of BiCycle Assay. After 48 hours, RLUs were 67 counted and IC50 values were calculated using the GraphPad 68 software. The reference drug-resistant viruses were obtained 69 through the NIH AIDS Reagent Program (ARP, 70 www.aidsreagent.org) and have been already characterized by 71 the Phenosense Assay (Monogram Biosciences), considered 72 as the reference assay for phenotypic investigation of HIV 73 drug resistance due to its consistent application in clinical 74 trials. The infectious clones were firstly transfected in 293LX 75 cells and then expanded in MT-2 cells. 76 Impact of CIP201 in the production of viral 77 nucleic acid intermediates 78 The mechanism of action of calixarene CIP201 was evaluated 79 through the quantification of viral nucleic acid intermediates 80 produced during HIV-1 replication in cell culture. MT-2 cells 81 were infected with NL4-3 wild-type strain at M.O.I 0.1 in 82 presence of 100 µM of CIP201, or the reference integrase 83 inhibitor raltegravir, the protease inhibitor darunaviror the 84 reverse transcriptase inhibitor rilpivirine, all at 2 µM. The 85 amount of viral cDNA produced after reverse transcription 86 was quantified through a real time PCR targeting the LTR 87 region at 16 h post infection, while 2-LTR circles and 88 intracellular viral polyadenylated RNA transcripts were 89 quantified with a specific real time protocol at 30 h post 90 infection. Each of the three HIV-1 nucleic acids species was 91 measured in two separate experiments and the values obtained 92 with CIP201 were compared pairwise with the values 93 obtained with each of the reference drugs considered, by 94 Student t test. 95 SUPPLEMENTARY DATA 96 Calixarene synthesis and characterization, CIP200 and 97 CIP201 do not eject zinc from NC(11-55), Binding of 98 calixarenes to NC(11-55), Absence of interaction of CIP201 99 with cTAR Molecular dynamics, Impairment of reverse 100 transcription by CIP201, Effect of CIP201 on cell infection 101 with the pseudotyped viruses, Evaluation of CIP201 in NSG 102 humanized mice infected with HIV-1, Antiviral assay with 103 replication-defective HIV pseudoparticles, Description of 104 HIV-1 resistant strains. 105 FUNDING 106 This work was supported by the European Project THINPAD 107 "Targeting theHIV-1 Nucleocapsid Protein to fight 108 Antiretroviral Drug Resistance", FP7 Grant Agreement 109 601969, by the Agence Nationale de la Recherche (ANR) and 110 the French Proteomic Infrastructure (ProFI, ANR-10-INBS-111 08-03) and by a PhD fellowship from Institute de Recherche 112 Servierto T. Botzanowski. YM is grateful to the Institut 113 Universitaire de France (IUF) for support and providing 114 additional time to be dedicated to research. 115 116 DEDICATION 117 (12) De Guzman, R. N.; Wu, Z. R.; Stalling, 1 C. C.; Pappalardo, L.; Borer, P. N.; 2 Summers, M. F. Structure of the HIV-1 /doi.org/10.1006/jmbi.1998.2098.

  17

(

  14) Spriggs, S.; Garyu, L.; Connor, R.; 18 Summers, M. F. Potential Intra-and 19 Intermolecular Interactions Involving 20 the Unique-5′ Region of the HIV-1 5′-21 UTR. Biochemistry 2008, 47 (49), 22 13064-13073.

  23 https://doi.org/10.1021/bi8014373. 24 (15) Lam, W. C.; Maki, A. H.; Casas-Finet, 25 J. R.; Erickson, J. W.; Kane, B. P.; 26 Sowder, R. C.; Henderson, L. Mély, Y.; Piémont, E.; Sorinas-Jimeno, 35 M.; de Rocquigny, H.; Jullian, N.; 36 Morellet, N.; Roques, B. P.; Gérard,

4 https: 3 Synthesis

 43 //doi.org/10.1016/j.bmc.2004.09./doi.org/10.1016/j.bmc.2009.11.Tsou, L. K.; Dutschman, G. E.; Gullen, 16 E. A.; Telpoukhovskaia, M.; Cheng, Y.-17 C.; Hamilton, A. D. Discovery of a 18 Synthetic Dual Inhibitor of HIV and 19 HCV Infection Based on a Tetrabutoxy-20 (87) Turpin, J. A.; Song, Y.; Inman, J. K.; 1 Huang, M.; Wallqvist, A.; Maynard, A.; 2 Covell, D. G.; Rice, W. G.; Appella, E.

  9 https://doi.org/10.1021/jm9802517. 10 (88) Bombarda, E.; Morellet, N.; Cherradi, 11 H.; Spiess, B.; Bouaziz, S.; Grell, E.; 12 Roques, B. P.; Mély, Y. Determination 13 of the PKa of the Four Zn2+-14 Coordinating Residues of the Distal 15 Finger Motif of the HIV-1 Nucleocapsid 16 Protein: Consequences on the Binding 17 of Zn2+1. J. Mol. Biol. 2001, 310 (3), 18 659-672.

22 G

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Table 1 .

 1 Thermodynamic parameters for the binding of calixarenes to NC peptides.

	Cmpd	NC	Kd	H
			(µM)	(kcal.mol -1 )

Table 3 .

 3 Antiviral activity of CIP201 against drug-resistant 57

	58	strains.
			a Strain	IC50 (µM)	b Fold Change
			114 (NL4-3)	1.7 ± 0.2	1.0
			11845 (INI)	2.3 ± 0.4	1.3
			11808 (PI)	1.8 ± 0.1	1.1
		12231 (NNRTI)	1.0 ± 0.5	0.6
			7406 (NRTI)	1.5 ± 0.3	0.9
	59	a Reference number of the drug resistant strains obtained
	60	through	the	NIH	AIDS	Reagent	Program
	61	(ARP,www.aidsreagent.org). b Ratio of the resistant virus
	62	IC50 to wild-type reference virus IC50.

Table 4 .

 4 IC50 values obtained in the Multi-Dosing Time protocol using the pseudotype virus assay. 116

	Compounds IC50

Authors wish to dedicate this work to their friends and 1 collaborators Prof. Maurizio Botta and Prof. Olga 2 Zaporozhets, who passed away prematurely in 2019. 3

CONFLICT OF INTERESTS


Dr Pierre Croisille

Dr M Viallon

Dr L Fanton

Dr G Michalowicz

P S Jouk

Y Usson

Y M Zhu

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 

Keywords: Diffusion tensor estimation, diffusion tensor imaging, fiber orientation constraint, human cardiac, tensor smoothing. I

Objective:

The purpose of this study is to increase the accuracy of human cardiac diffusion tensor (DT) estimation in diffusion magnetic resonance imaging (dMRI) with a few diffusion gradient directions. Methods: A structure prior constrained (SPC) method is proposed. The method consists in introducing two regularizers in the conventional nonlinear least squares estimator. The two regularizers penalize the dissimilarity between neighboring DTs and the difference between estimated and prior fiber orientations, respectively. A novel numerical solution is presented to ensure the positive definite estimation. Results: Experiments on ex vivo human cardiac data show that the SPC method is able to well estimate DTs at most voxels and is superiors to the state-of-art methods in terms of the mean errors of principal eigenvector, second eigenvector, helix angle, transverse angle, fractional anisotropy, and mean diffusivity.

Conclusion:

The SPC method is a practical and reliable alternative to current denoising-or regularization-based methods for the estimation of human cardiac DT. Significance: The SPC method is able to accurately estimate human cardiac DTs in dMRI with a few diffusion gradient directions.

microstructures of the tissues. Diffusion tensor imaging (DTI) [START_REF] Basser | MR diffusion tensor spectroscopy and imaging[END_REF] is a dMRI technique proposed to describe quantitatively the diffusion information and fiber features of tissues. It has been largely used for the microstructure investigation of tissues or organs such as brain [START_REF] Assaf | Diffusion tensor imaging (DTI)-based white matter mapping in brain research: a review[END_REF], [START_REF] Alexander | Diffusion tensor imaging of the brain[END_REF] and heart [START_REF] Edelman | In vivo measurement of water diffusion in the human heart[END_REF]- [START_REF] Stoeck | Second-order motion-compensated spin echo diffusion tensor imaging of the human heart[END_REF].

In DTI, accurate and reliable estimation of diffusion tensor (DT) is a major prerequisite for fiber tracking or DT-derived metrics calculation and analysis. A number of DT estimation methods were proposed in recent literature. Among them, the linear least squares (LLS) estimator [START_REF] Kingsley | Introduction to Diffusion Tensor Imaging Mathematics : Part III . Tensor Calculation , Noise , Simulations , and Optimization[END_REF] is widely used in dMRI due to its usability and high computational efficiency. Its weighted variants (WLLS) [START_REF] Kingsley | Introduction to Diffusion Tensor Imaging Mathematics : Part III . Tensor Calculation , Noise , Simulations , and Optimization[END_REF]- [START_REF] Collier | Iterative reweighted linear least squares for accurate, fast, and robust estimation of diffusion magnetic resonance parameters[END_REF] with well-defined weights usually produce more reliable results compared to the LLS (unweighted). Nonlinear methods include nonlinear least squares (NLS) [START_REF] Kingsley | Introduction to Diffusion Tensor Imaging Mathematics : Part III . Tensor Calculation , Noise , Simulations , and Optimization[END_REF], [START_REF] Koay | A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging[END_REF] and least median/trimmed squares (LMS/LTS) [START_REF] Maximov | Robust tensor estimation in diffusion tensor imaging[END_REF] are also used in DT estimation, in which the solution requires an iterative numerical algorithm (such as Levenberg-Marquardt) suffering computational complexity. Their corresponding constrained counterparts, which will be denoted respectively as cLLS, cWLLS, cNLS, and cLMS/cLTS [START_REF] Kingsley | Introduction to Diffusion Tensor Imaging Mathematics : Part III . Tensor Calculation , Noise , Simulations , and Optimization[END_REF]- [START_REF] Veraart | Weighted linear least squares estimation of diffusion MRI parameters: Strengths, limitations, and pitfalls[END_REF], [START_REF] Koay | A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging[END_REF]- [START_REF] Collier | Iterative reweighted linear least squares for accurate, fast, and robust estimation of diffusion magnetic resonance parameters[END_REF], employ the positive definite constraint to ensure the every eigenvalue of estimated DT be positive. In [START_REF] Chang | RESTORE: Robust estimation of tensors by outlier rejection[END_REF] and [START_REF] Chang | Informed RESTORE: A method for robust estimation of diffusion tensor from low redundancy datasets in the presence of physiological noise artifacts[END_REF], robust estimators, called RESTORE and iRESTORE, were proposed to reduce the sensitivity to the presence of outliers. All of the above methods are voxel-based estimators that make minimal assumptions and constraints on diffusion data acquisitions. They are however highly sensitive to noise and commonly require a higher number (>30) of diffusion gradient directions (DGDs) to achieve robust estimation.

In vivo cardiac DTI acquisitions are often severely hampered by cardiac and respiratory motion. To minimize the effect of the motions, respiratory gated [START_REF] Gamper | Diffusion imaging of the in vivo heart using spin echoes-considerations on bulk motion sensitivity[END_REF], [START_REF] Nielles-Vallespin | In vivo diffusion tensor MRI of the human heart: Reproducibility of breath-hold and navigator-based approaches[END_REF] and/or breath-holding [START_REF] Nielles-Vallespin | In vivo diffusion tensor MRI of the human heart: Reproducibility of breath-hold and navigator-based approaches[END_REF]- [START_REF] Delattre | In Vivo Cardiac Diffusion-Weighted Magnetic Resonance Imaging Quantification of Normal Perfusion and Diffusion Coefficients With Intravoxel Incoherent Motion Imaging[END_REF] techniques were used, and longer acquisition time was needed. Despite several advanced acquisition strategies proposed under free-breathing condition [START_REF] Wei | Free-breathing diffusion tensor imaging and tractography of the human heart in healthy volunteers using wavelet-based image fusion[END_REF], [START_REF] Moulin | In vivo free-breathing DTI and IVIM of the whole human heart using a real-time slice-followed SE-EPI navigator-based sequence: A reproducibility study in healthy volunteers[END_REF], the number of DGDs in in vivo acquisitions can rarely be more than 12. Hence, accurate and robust estimation of DTs from resulting raw diffusion-weighted (DW) data becomes an important issue and constitutes a challenging work in cardiac DTI.

Since these DT estimators are sensitive to noise, it is often convenient to adopt denoising techniques for improving the DT estimation. Recently, a number of denoising methods [START_REF] Chu | Estimating Intravoxel Fiber Architecture Using Constrained Compressed Sensing Combined with Multitensor Adaptive Smoothing[END_REF], [START_REF] Zhang | Feature-Preserving Smoothing of Diffusion Weighted Images Using Nonstationarity Adaptive Filtering[END_REF], [START_REF] Coupe | An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images[END_REF], [START_REF] Tabelow | Diffusion tensor imaging: structural adaptive smoothing[END_REF], [START_REF] Bao | Denoising human cardiac diffusion tensor magnetic resonance images using sparse representation combined with segmentation[END_REF]- [START_REF] Ding | Reduction of noise in diffusion tensor images using anisotropic smoothing[END_REF] have been proposed to remove noise from DW images. Some of them have already been used for cardiac DW image filtering, such as nonstationarity adaptive

Structure Prior Constrained Estimation of Human Cardiac Diffusion Tensors

Chun-Yu Chu * , Chang-Yu Sun, Zi-Xiang Kuai, Feng Yang, and Yue-Min Zhu

C

filtering [START_REF] Zhang | Feature-Preserving Smoothing of Diffusion Weighted Images Using Nonstationarity Adaptive Filtering[END_REF] and sparse denoising [START_REF] Bao | Denoising human cardiac diffusion tensor magnetic resonance images using sparse representation combined with segmentation[END_REF], [START_REF] Bao | Structure-adaptive sparse denoising for diffusion-tensor MRI[END_REF] methods. Additionally, a principal component analysis based method [START_REF] Zhang | Two-stage image denoising by principal component analysis with local pixel grouping[END_REF] was also used to process in vivo cardiac DW images [START_REF] Wei | Free-breathing diffusion tensor imaging and tractography of the human heart in healthy volunteers using wavelet-based image fusion[END_REF]. Alternatively, regularization techniques, which regularize DT fields after estimation [START_REF] Frindel | Comparison of regularization methods for human cardiac diffusion tensor MRI[END_REF], [START_REF] Castano-Moraga | A Riemannian approach to anisotropic filtering of tensor fields[END_REF], [START_REF] Filiard | Clinical DT-MRI estimation, smoothing, and fiber tracking with log-euclidean metrics[END_REF] or introduce a regularizer in the procedure of estimation [START_REF] Tschumperle | Variational frameworks for DT-MRI estimation, regularization and visualization[END_REF]- [START_REF] Liu | A robust variational approach for simultaneous smoothing and estimation of DTI[END_REF], were also used to enhance noise immunity. These regularization approaches involve some kind of weighted averaging over corresponding local or non-local voxels, where smoothing operators are defined in terms of variational principles, total Kullback-Leibler divergence, or other prior information of images.

In this paper, we propose a structure prior constrained (SPC) method to estimate human cardiac DTs in dMRI with a few DGDs. The method consists in introducing two regularizers in the conventional nonlinear least squares estimator. The two regularizers penalize respectively the dissimilarity between neighboring DTs and the difference between estimated and prior fiber orientations, which allows for more accurate estimation of DTs with a few DGDs.

II. METHODOLOGY

A. Regularized DT Model

In classical DT model, the diffusion-weighted signal i S in the ith DGD is given by

  T 0 exp i i i S S b  g Dg , (1)
where 0 S is the nondiffusion-weighted signal, b the diffusion sensitization factor, i g the ith DGD, and D the second-order symmetric diffusion tensor. The six independent components of the DT can be calculated using non-linear least squares method with the minimizing objective function f expressed as

  2 0 1 exp N ii i f S S        Hd , ( 2
)
where In the present study, we introduce two regularizers in [START_REF] Basser | MR diffusion tensor spectroscopy and imaging[END_REF], and rewrite the objective function as

N
      2 T 12 1 0 exp N i c i i m i S f b REG REG S            g Dg d V , ( 4
)
where m V is the principal eigenvector (which corresponds to the greatest eigenvalue) of diffusion tensor D ,

B. Constraint of Tensor Smoothness

Inheriting the idea of test statistic between two tensors in [START_REF] Tabelow | Diffusion tensor imaging: structural adaptive smoothing[END_REF], we define the tensor smoothness constraint

1 REG at a voxel p as         1 T T 1 1 U REG w Z       p p pq p q p q q d d d H H d d , (5)
where the weighting factor

C. Constraint of Cardiac Fiber Orientation

The myocardium is a complex tissue composed mainly of myocytes having approximately 25 µm in diameter and 100 µm in length. Current MRI systems do not allow us to image the (a) (b) (c) individual myocytes. Instead, only an aggregate of individual myocytes is observed in an image voxel. Nevertheless, the myocyte aggregate is highly structured and oriented. When tracking the orientation of the myocyte aggregate at each voxel, the voxels form preferential patterns in three-dimensional (3D) space and give rise to the so-called myocardial fibers. Such fibers however should not be understood in the same sense as in brain or musculo-skeletal tissue, because they are actually the image representation of mean myocyte orientations within a voxel in 3D space and the term "fiber" is employed just for simplicity. The statistical study of the human cardiac fiber architecture [START_REF] Lombaert | Human atlas of the cardiac fiber architecture: Study on a healthy population[END_REF] has shown that the helix angle of human cardiac fibers in left ventricle (LV) varies approximately linearly along transmural depth and the transverse angle is approximately parallel to the epicardium. In this study, the helix angle is defined as the angle between the projection of the fiber onto the epicardium and the short-axis plane.

Based on this prior information of the human heart, we derive the prior cardiac fiber orientation of the LV's short-axis slices as follows (Fig. 1):

1) For each voxel p of the slice, we estimate the diffusion tensor using Iterative Reweighted Linear Least Squares (IRLLS) [START_REF] Collier | Iterative reweighted linear least squares for accurate, fast, and robust estimation of diffusion magnetic resonance parameters[END_REF] method in a voxel-by-voxel way, and then extract their main fiber orientations by eigen decomposition.

2) Compute the helix angle of these fiber orientations, and fit an ellipse to the points having the absolute helix angle less than 10 degrees.

3) Compute the distance d p from p to the ellipse.

Specifically, we define the distance as negative value if the voxel located outside of the ellipse. 4) Fit a line to the helix angles of all voxels, and achieve the fitted helix angles. At the same time, we set the fitted transverse angles equal to zero.

5) Convert the fitted helix angle and fitted transverse angle to the fitted fiber orientation f V (prior fiber orientation). Based on the prior fiber orientation, we define the orientation regularizer

2 REG as     T 2 1 arccos m m f REG   V V V . ( 6

) D. Numerical Solution

Using eigen decomposition, the diffusion tensor can be expressed as

T  DR ΛR , (7)
where

  1 2 3 ,,  R V V V is a rotation matrix whose columns, 1 V , 2 V and 3
V ( 1 V may not always be the principal eigenvector), are the eigenvectors of D , and Λ is a diagonal matrix whose diagonal elements 1  , 2  and 3  are the corresponding eigenvalues.

In spherical coordinates, we can express the eigenvector 1 V as

  T 1 sin cos ,sin sin ,cos       V , ( 8
)
where  is the polar angle and  the azimuth angle.

Constructing a unit vector

t V satisfying T 1 0 t  VV , the eigenvector 2 V can then be expressed as   21 , t   V T V V , (9)
where  

1 , TV is a rotation matrix by an angle of  about an axis in the direction of 1 V . Given a unit vector

T 1 ,, x y z v v v    V
, the matrix T can be described as

      T 1 1 1 1 , cos sin 1 cos          T V I V V V , ( 10
)
with I indicating the identity matrix and  

1  V the cross product matrix of 1 V given by   1 0 0 0 zy zx yx vv vv vv          V . ( 11
)
According to the orthogonality of matrix R , we get

3 1 2    V V V . ( 12
)
Introducing ( 7)-( 12) in ( 4), c f can be expressed as a function of six variables  ,  ,  , 1  , 2  , and 3  . Their values can be estimated by solving the following constrained nonlinear optimization problem

    1 2 3 1,2,3 arg min , , , , t. 0 , s.
c f         , ( 13
)
where 1,2,3 0   ensures the positive definite of the diffusion tensor. In the present study, we solve the optimization problem (13) using the interior-point method.

The proposed method was implemented using in-house program written in Matlab 2016a (Mathworks) and freely available at https://www.creatis.insa-lyon.fr/MOSIFAH/chu/.

III. EXPERIMENTS AND RESULTS

The proposed SPC method was evaluated on synthetic and real human cardiac DW data. The real human cardiac DW data corresponds to ex vivo human hearts, which come from the Grenoble University Teaching Hospital, Grenoble, France. They relate to infants who died after birth up to 14 months of life. The hearts were obtained and processed in compliance with French legal and ethical guidelines. The investigations are conformed to the principles outlined in the declaration of Helsinki [START_REF] Carlson | The revision of the Declaration of Helsinki: Past, present and future[END_REF]. More precisely, after medically pronounced death, cadavers are conserved for a minimum of 24 h at the mortuary at 4°c, in order to give time to the administration to verify there are no contra-indications to the necropsy and to the heirs of the deceased to give the authorization for the autopsy. Those legal formalities being done, the autopsy is performed; the heart are extracted and fixed in a formalin solution to ensure good preservation of cells and tissue as close as possible as living structure.

The proposed method was compared with LLS [START_REF] Kingsley | Introduction to Diffusion Tensor Imaging Mathematics : Part III . Tensor Calculation , Noise , Simulations , and Optimization[END_REF], IRLLS [START_REF] Collier | Iterative reweighted linear least squares for accurate, fast, and robust estimation of diffusion magnetic resonance parameters[END_REF], local principal component analysis (LPCA) [START_REF] Manjon | Diffusion Weighted Image Denoising Using Overcomplete Local PCA[END_REF], and variational framework (VF) based method [START_REF] Tschumperle | Variational frameworks for DT-MRI estimation, regularization and visualization[END_REF].

A. Synthetic DW Data

The DW data was synthesized from the DT model with b-value = 700s/mm 2 and 12 DGDs. The DT eigenvalues were set to (1.2, 0.3, 0.3) × 10 -3 mm 2 /s. The fiber orientation of the simulated data (noise free, Fig. 2, left-up panel) was configured according to the polarized light imaging of an ex-vivo human heart. Usually, in normal hearts, the helix angle varies linearly along the transmural direction and the diffusion tensor varies smoothly in space. However, that may not be true in pathological hearts [START_REF] Khalique | Deranged Myocyte Microstructure in Situs Inversus Totalis Demonstrated by Diffusion Tensor Cardiac Magnetic Resonance[END_REF], [START_REF] Mekkaoui | Myocardial scar delineation using diffusion tensor magnetic resonance tractography[END_REF]. To evaluate how the proposed SPC method behaves in this case, we also simulated a pathological region (marked with red circle in Fig. 2, left-up panel) by introducing a patch with random fiber orientations and DT eigenvalues of (1.2, 0.6, 0.6) × 10 -3 mm 2 /s. This would simulate the situation where the helix angle varies no longer with transmural depth or the diffusion tensor varies no longer slowly in space. Three level Rician noises were added to the simulated data to generate noisy data with different signal-to-noise ratios (SNRs). In this study, the SNR of the DW data was defined as the ratio of mean signal intensity to noise standard deviation.

To evaluate the impact of parameters  and  on DT estimation, simulation experiments were carried out. At different SNRs, we firstly set 0   and varied  to make the SPC method achieve best results, then fixed 0   and varied  to further reduce the error of results.

B. Ex-vivo Human Cardiac DW Data

The real cardiac DW data was taken from five ex-vivo human hearts. The data was acquired on a Siemens Avanto 1.5T MR scanner, using echo planar imaging sequence with one image without diffusion weighting and three different numbers (12, 30, and 64) of DGDs. Specially, the acquisition with 64 DGDs was repeated 20 times. Each DW volume consists of 32 contiguous axial slices of size 140×140, and the spatial resolution is 1.4mm×1.4mm×1.4mm. The main acquisition parameters were: TE = 70 ms, TR = 5100 ms, diffusion sensitivity factor b = 700 s/mm 2 . The SNR of the heart data is about 18.

C. Evaluation

To evaluate quantitatively the proposed method, we perform the average of the 20-times repeatedly acquired data (with 64 DGDs) using a conventional estimator [52]

ik i k S S     , ( 14
)
where ik S is the diffusion signal acquired at the kth acquisition in the ith DGD, and  is the standard deviation of Rician noise, which can be estimated from the non-signal region data in the background corresponding to the air outside the organ [START_REF] Bao | Denoising human cardiac diffusion tensor magnetic resonance images using sparse representation combined with segmentation[END_REF], [START_REF] Nowak | Wavelet-based Rician noise removal for magnetic resonance imaging[END_REF]. Then we estimate the DT using cNLS method on the averaged data, and regard it as the ground-truth (GT). Six DT-derived indices, principal eigenvector (E1), secondary eigenvector (E2), helix angle (HA), transverse angle (TA), fractional anisotropy (FA), and mean diffusivity (MD), were used for the quantitative comparison between different methods. In this work, the E1 error is calculated using arccos( )

es gt e V V  , ( 15
)
where es V is the estimated E1, and gt V the ground-truth.

A LV mask excluding apex was defined manually to extract the region of interest (ROI) as shown in Fig. 5 (red-colored). We evaluated the SPC method on the ROI of the data acquired with different numbers of DGDs, and compared it with IRLLS [START_REF] Collier | Iterative reweighted linear least squares for accurate, fast, and robust estimation of diffusion magnetic resonance parameters[END_REF], local principal component analysis (LPCA) [START_REF] Manjon | Diffusion Weighted Image Denoising Using Overcomplete Local PCA[END_REF], and variational framework (VF) based method [START_REF] Tschumperle | Variational frameworks for DT-MRI estimation, regularization and visualization[END_REF]. For the LPCA, we used the cNLS method to estimate DT from the denoised data. To ensure fairness, we tuned all the parameters of each method for the experiment, and chose the set of parameters yielding the best results. For the proposed SPC method, we set 100   ,   0.15, 0.1, and 0.05 for the experiments on the data acquired with 12, 30, and 64 DGDs, respectively. The parameters  and  were empirically determined by trying a series of values. The criterion for selecting the best value was that the mean E1 error be as small as possible. The six indices (E1, E2, HA, TA, FA, and MD) were calculated from the DTs estimated using the four different methods (IRLLS, LPCA, VF,

D. Results

The experiments on simulated DW data showed that the SPC method produced better results with bigger  and  values in the low SNR case or smaller values in the high SNR case (Fig. 3(a) to (d)). At different SNRs, the mean E1 and FA errors of DT estimation using the five methods (LLS, IRLLS, VF, LPCA, and SPC) are plotted in Fig. 3(e) and (f). It is observed that the proposed SPC method always produces smaller mean E1 errors with respect to the other four methods. Fig. 2 shows the E1 and FA maps derived from DTs estimated using different methods at the SNR of 5. Regarding the E1 maps, obviously, the LLS and IRLLS methods are very sensitive to noise by yielding irregular directions of the principal eigenvectors in the normal regions. The VF, LPCA, and SPC methods produce smoother E1 maps, thus demonstrating the effectiveness of the used regularization or denoising in the DT estimation. But, LPCA clearly shows over-smoothing for E1 map in the pathological region; the arbitrary directions of the principal eigenvectors, which characterize the presence of pathology, have been forced to vary regularly. Visually, VF and SPC led to rather similar results, by preserving the regular and slow variation of the principal eigenvectors in the normal region while not forcing the latters to vary regularly in the pathological region.

Concerning the FA maps, the LLS and IRLLS methods are very sensitive to noise by yielding rather noisy FA maps. The VF, LPCA, and SPC methods produce smoother FA maps. Globally, LPCA under-estimate FA by presenting darker regions with respect to GT whereas the other methods over-estimate FA by exhibiting brighter regions with respect to GT.

To assess more precisely the difference between the different methods, we show in Fig. 4 the error maps of E1 and FA Fig. 7 HA error maps (the left 3 columns) and HA distributions (the right column) derived from DTs estimated using different methods on a short-axis slice data.

The horizontal and vertical axes of HA distributions rerpresent the transmural depth (from epicardium to endocardium) and HA, respectively.

obtained using different methods. We observe that the LPCA method leads to highly inaccurate results in the pathological region by generating big E1 and FA errors. In the normal region, the SPC method also exhibits smaller mean E1 errors than the IRLLS, VF, and LPCA methods. More quantitatively speaking, the SPC method generated smaller mean E1 error (11.7°) than IRLLS (21.5°), VF (15.5°), and LPCA (12.5°) in the normal region. Concerning the FA error maps, there is no obvious difference between the different methods except LPCA that shows severe errors in both normal and pathological regions. to III) that removing one of the regularizers increased the error of DT estimation, which implies that both of the regularizers are necessary to improve the estimation of DT.

As an illustration, we show in Figs. 6 to 8 the E1 and FA maps, the HA error maps with the HA distributions, and the TA error maps with the TA histograms, which were derived from DTs estimated using different methods on a short-axis slice of LV. The position of the slice is marked with the yellow line in Fig. 5. Obviously, the IRLLS method is very sensitive to noise. The E1, FA, HA, and TA obtained using LPCA, VF and SPC methods demonstrated the effectiveness of the used regularization mechanisms in improving the performance of DT estimation. Furthermore, the VF method is inferior to the LPCA and SPC methods in terms of E1. The visual comparison of the E1 obtained using the LPCA and SPC methods on the data acquired with 12 and 30 DGDs shows that the SPC method outperforms the LPCA method at some voxels inside the red rectangle in Fig. 6. In contrast, on the data acquired with 64 DGDs, the SPC and LPCA methods generate very similar E1 results. The comparison of HA (or TA) error maps or HA distributions (or TA histograms) (Figs. 7 and8) obtained using different methods shows that the SPC method generates the smallest HA (or TA) errors among the four methods and its HA distributions (or TA histograms) are more consistent with GT.

From Tables I to III, we also observe that the errors of the six indices increase more or less with the decrease of the number of DGDs, regardless of the methods. For instance, when the number of DGDs decreases from 64 to 30, the E1 errors increase from about 6 to 14 degrees. When the number of DGDs decreases from 30 to 12, the methods exhibit smaller E1 errors increase (about 2 to 4 degrees). Likewise, the FA errors increase from 0.01 to 0.05 when the number of DGDs decreases from 64 to 12.

IV. DISCUSSION

We have proposed a SPC method to estimate human cardiac DT by introducing two regularizers in the conventional NLL estimator. The first regularizer penalizes the dissimilarity between neighboring DTs, which is based on the assumption that DTs are locally smooth, which is commonly used by spatial regularization methods. The second regularizer introduces a constraint on cardiac fiber orientation, which is motivated by the fact that the helix angle and transverse angle of human cardiac fibers have approximately regular variations with transmural depth on most regions of LV.

To guarantee a positive definite solution, an efficient way based on Cholesky decomposition was used in [START_REF] Maximov | Robust tensor estimation in diffusion tensor imaging[END_REF], [START_REF] Wang | A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex DWI[END_REF], [START_REF] Liu | A robust variational approach for simultaneous smoothing and estimation of DTI[END_REF].

In the present study, we proposed an alternative numerical solution, in which we convert the variable d of the objective function to six variables containing three angles (  ,  , and By applying the proposed SPC method on the LV excluding apex region, we demonstrated that the introduction of the two regularizers is necessary for improving the DT estimation, but the second regularizer ( 2 REG ) exhibits smaller contribution than the first one ( 1 REG ). Such conclusion on ex vivo cardiac data could be extended to the case of in vivo cardiac data. For the apex region, the helix angle and transverse angle have irregular variations with transmural depth [START_REF] Lombaert | Human atlas of the cardiac fiber architecture: Study on a healthy population[END_REF], thus the second regularizer should be removed ( 0   ). The improvements of the proposed SPC method could be obtained using 1 REG only. In the situations where the local smoothness assumption is violated, which is the case with the regions boxed with yellow rectangle in Fig. 6 or the pathological region of the simulated data, the SPC method should be used with caution. Unfortunately, in this case, none of the four methods (IRLLS, LPCA, VF, and LPC) can achieve accurate or simply plausible estimation of DT. Therefore, it is a challenge work and needs further study. In all cases, we should not try to estimate the cardiac DT in irregular regions without sufficient SNR.

For the first regularizer 1 REG , we used the Euclidian distance for the Cartesian coordinate system. Previous studies performed tensor processing in a shape-adaptive (i.e. prolate spheroidal) coordinate system [START_REF] Nielsen | Mathematical model of geometry and fibrous structure of the heart[END_REF], [START_REF] Toussaint | In vivo human cardiac fibre architecture estimation using shape-based diffusion tensor processing[END_REF]. It would be interesting to also consider the regularization of tensor fields in the prolate spheroidal coordinate and compare the results from the two systems.

We observed that SPC FA map is much smoother than the ground-truth FA map (Fig. 6). Note however that, unlike the case for the simulated data, the ground-truth for the in vivo data refers to the average of the 20-times repeatedly acquired data with 64 DGDs (Section III.C). It does not represent the ground-truth of the myocardium (which is unknown), and it is simply a reference for comparison. It would then be interesting to know if such oversmooth effect alters the ground-truth of the myocardium.

Meanwhile, in vivo cardiac DTI acquisitions are a challenging task because of inevitable compromise between spatial resolution and coverage, SNR, and cardiac and respiratory motion. A direct consequence would for example be the fact that there are few points to represent the myocardium. In addition, it is difficult to acquire in vivo DW data for different numbers of DGDs. In all these situations, the performance of the proposed method might be influenced. It then becomes important to obtain a sufficient number of pixels with good quality for representing the myocardium. A solution might be to increase the number of pixels using interpolation [START_REF] Yang | A Comparative Study of Different Level Interpolations for Improving Spatial Resolution in Diffusion Tensor Imaging[END_REF] or superresolution [START_REF] Luo | Fast single image super-resolution using estimated low-frequency k-space data in MRI[END_REF] methods, before applying the proposed method.

V. CONCLUSION

The proposed SPC method allows for the estimation of human cardiac DT in dMRI with a few DGDs. The results on ex vivo human cardiac data showed that the proposed method is able to accurately estimate DTs at the most voxels of LV. Its comparisons with the existing LLS, IRLLS, LPCA, and VF methods demonstrates its lower mean errors of E1, E2, HA, TA, FA, and MD. Furthermore, the proposed numerical solution framework provides a flexible tool for DT estimation, by easily allowing introducing additional constraints on eigenvectors or eigenvalues.

1 REG the smoothness constraint on tensor d , 2 REG

 12 the orientation constraint on m V ,  and  the regularization parameters which provide a tradeoff among the precision of model fitting, tensor smoothness, and main orientation constraint.

  voxels p and q .

Fig. 1 .

 1 Fig. 1. The calculation of prior fiber orientation. (a) Fitting an ellipse (red) to the points (green) having an absolute helix angle (AHA) less than 10 degrees. (b) Fitting a line (red) to the helix angles (blue) along transmural depth. (c) Fitted fiber orientations (prior fiber orientations). The color-coding represents the direction of the principal eigenvector (Green: left-right direction in the image. Red: up-down direction in the image. Blue: direction perpendicular to the image plane).

Fig. 2

 2 Fig. 2 E1 and FA maps derived from DTs estimated using different methods at the SNR of 5 in the case of simulated pathological DW data. The red circle indicates the pathological region. The color-coding represents the direction of the principal eigenvector (Green: left-right direction in the image. Red: up-down direction in the image. Blue: direction perpendicular to the image plane).

Fig. 4 1 REG ), while 0 

 410 Error maps of E1 and FA with different methods at the SNR of 5. (a) E1 error maps. (b) FA error maps. and SPC) on the human cardiac data acquired with different numbers (12, 30, and 64) of DGDs, and compared to the GT. We also evaluated the interest of the two regularizers in the proposed SPC method by setting respectively  and  to zero. 0   means the discarding of the regularization on DT (  means the removal of the regularization on cardiac fiber orientation ( 2 REG ).

Fig. 5

 5 Fig. 5 The region of interest of the heart (red-colored, coronal view). The yellow line indicates the position of the slice used for illustration.

Fig. 6

 6 Fig. 6 E1 and FA maps derived from DTs estimated using different methods on a short-axis slice of the real human heart. The red rectangle indicates the points, at which the proposed SPC outperforms the other methods. Bottom row is ground-truth. The yellow rectangle shows a region where the local smoothness assumption for DTs is violated. The color-coding represents the direction of E1 (Green: left-right direction in the image. Red: up-down direction in the image. Blue: direction perpendicular to the image plane).

  Their mean FA errors are 0.13 (IRLLS), 0.14 (VF), 0.16 (LPCA), and 0.14 (SPC), respectively.Regarding the real cardiac DW data, the mean errors on the five heart of the six indices, E1, E2, HA, TA, FA, and MD are given in Tables I to III for three different numbers of DGDs. Globally, SPC outperforms the other methods except LPCA that shows slightly smaller TA errors. Very occasionally, SPC exhibits slightly greater E2 errors than LPCA or FA error than VF. When discarding the regularization on DT ( 1 REG ) (i.e. 0   ) or the regularization on cardiac fiber orientation ( 2 REG ) (i.e. 0   ), we observe (last two columns of Tables I

Fig. 8

 8 Fig. 8 TA error maps (the left 3 columns) and TA histograms (the right column) derived from DTs estimated using different methods on a short-axis slice data.



  ) and three eigenvalues ( 1  , 2  , and 3  ). The new form of the objective function allows us to add directly constraints on eigenvectors or eigenvalues of DT such as 1,2,3 01   (constraint the eigenvalues in the range [0, 1]). It is more flexible than the Cholesky decomposition.

  H is the ith row of an encoding gradient design matrix H and can be derived from the gradient components

						DT D , and i
						ix g , iy g , and iz g ,
						H	i	2 ix  2 2 2 2 2 ix iy ix iz iy iy iz iz bg bg g bg g bg bg g bg  	. (3)
		is	the	number	of	DGDs,
	d	xx D D D D D D xy xz yy yz zz   	is a vector representation of

, , , , ,

TABLE I MEAN

 I ERRORS OF THE SIX INDICES DERIVED FROM DTS ESTIMATED USING DIFFERENT METHODS ON THE FIVE HEARTS ACQUIRED WITH 64 DGDS.

	Error	LLS	IRLLS	LPCA	VF	SPC	SPC (	0   )	SPC (	0   )
	E1 (degree)	21.2  16.7	20.9  16.9	16.6  12.8	19.6  17.5	15.6  12.9	18.0  15.8	16.5  14.8
	E2 (degree)	32.8  21.9	32.4  21.9	25.7  22.2	29.0  21.5	25.2  20.8	30.3  22.4	26.2  21.8
	HA (degree)	13.1  8.2	12.8  8.0	12.8  7.3	12.9  7.8	11.3  6.1	12.7  7.4	12.1  6.5
	TA (degree)	21.0  11.6	20.7  11.5	16.6  9.9	16.5  8.6	16.9  9.5	18.9  11.0	17.9  10.3
	FA	0.18  0.14	0.18  0.14	0.07  0.06	0.06  0.05	0.07  0.05	0.17  0.14	0.07  0.05
	MD (10 -3 mm 2 /s)	0.18  0.14	0.18  0.14	0.07  0.07	0.09  0.08	0.07  0.08	0.09  0.09	0.08  0.08

TABLE II MEAN

 II ERRORS OF THE SIX INDICES DERIVED FROM DTS ESTIMATED USING DIFFERENT METHODS ON THE FIVE HEARTS ACQUIRED WITH 30 DGDS.

	Error	LLS	IRLLS	LPCA	VF	SPC	SPC (	0   )	SPC (	0   )
	E1 (degree)	35.2  22.2	34.7  22.1	22.1  15.2	27.6  19.9	20.8  16.2	24.3  18.3	21.6  16.3
	E2 (degree)	46.2  22.9	45.8  22.9	30.5  22.7	37.7  22.3	30.3  22.5	38.4  24.0	31.3  22.7
	HA (degree)	23.1  12.5	22.7  12.4	16.8  9.7	16.3  9.3	16.0  8.9	17.7  9.6	15.9  8.9
	TA (degree)	31.3  15.9	31.6  15.9	19.0  11.3	23.5  12.1	19.2  11.0	21.4  12.0	19.8  10.6
	FA	0.20  0.14	0.19  0.13	0.07  0.06	0.09  0.07	0.07  0.05	0.15  0.13	0.07  0.05
	MD (10 -3 mm 2 /s)	0.16  0.12	0.19  0.12	0.10  0.09	0.10  0.09	0.09  0.09	0.11  0.10	0.08  0.10

TABLE III MEAN

 III ERRORS OF THE SIX INDICES DERIVED FROM DTS ESTIMATED USING DIFFERENT METHODS ON THE FIVE HEARTS ACQUIRED WITH 12 DGDS.

	Error	LLS	IRLLS	LPCA	VF	SPC	SPC (	0   )	SPC (	0   )
	E1 (degree)	38.9  23.2	38.6+  22.9	23.5  16.5	28.2  19.1	22.3  17.4	26.5  20.8	22.7  18.1
	E2 (degree)	48.9  23.6	48.7  23.2	29.4  20.6	42.1  23.1	34.5  22.8	36.9  24.4	34.5  23.6
	HA (degree)	27.0  13.2	26.6  13.1	16.4  9.8	20.5  10.6	16.3  9.0	19.5  10.2	17.7  9.4
	TA (degree)	32.9  15.9	32.8  15.9	18.0  11.4	23.8  12.8	20.6  11.2	20.9  11.4	20.0  11.2
	FA	0.22  0.15	0.20  0.15	0.08  0.06	0.11  0.10	0.08  0.06	0.14  0.12	0.08  0.06
	MD (10 -3 mm 2 /s)	0.21  0.12	0.16  0.13	0.11  0.09	0.10  0.09	0.08  0.09	0.11  0.10	0.09  0.09

This work was supported by the National Natural Science Foundation of China (No. 61601057 and No. 81701654), the French ANR under ANR-13-MONU-0009-01, and the Natural Science Foundation of Heilongjiang Province of China (F2015002). We also gratefully acknowledge the support of Dr.