Alexander Punter

Paola Nava

Pseudopotential-Fragment Spectroscopy for Organic Molecules and Carbon Allotropes

Following on from a previous work (Punter et al., IJQC 2019, 119, 23), pseudopotential sets are developed and tested for a variety of sp 2 and sp 3 carbon fragments. These fragments contain only one or two explicit protons and electrons, and make use of non-atom-centred potentials. They are tested with Density Functional Theory calculations in a selection of chemical environments in which several physical characteristics, including orbital and first ionisation energies, are found to be well-reproduced. They are then employed in the reproduction of molecular absorption spectra for large organic molecules and carbon allotropes, and are found to recreate both absorption and electronic circular dichroism spectra to a high accuracy. They are also found significantly to increase the computational efficiency of TDDFT calculations in which they are used.

I. INTRODUCTION

In most pseudopotential methods, the techniques have revolved around separating the electrons of an atom into core and valence electrons, and replacing the core. This remains true whether they are plane-wave or molecular pseudopotentials, whether they are shape or energy consistent, whether they are norm-conserving or ultrasoft, or indeed if they follow the alternate model core potential formulation of Huzinaga. [START_REF] Igel-Mann | Pseudopotentials for main group elements (IIIa through VIIa)[END_REF][START_REF] Hay | Ab initio effective core potentials for molecular calculations. Potentials for the transition metal atoms Sc to Hg[END_REF][START_REF] Hay | Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals[END_REF][START_REF] Wadt | Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi[END_REF][START_REF] Hamann | Norm-conserving pseudopotentials[END_REF][START_REF] Vanderbilt | Soft self-consistent pseudopotentials in a generalized eigenvalue formalism[END_REF][START_REF] Bonifacic | Atomic and molecular calculations with the model potential method[END_REF] There are several excellent reviews of these methods. [START_REF] Dolg | Effective core potentials[END_REF][START_REF] Dolg | Pseudopotentials and Model Potentials[END_REF][11] In our formulation, the goal is to reproduce electronic behaviour accurately, while replacing not only the core electrons of small molecular fragments, but also to replace specific valence electrons that do not take part in the electronic behaviour in which we are interested, as well as any unnecessary nuclei and protons. In a recent paper [START_REF] Punter | Atomic pseudopotentials for reproducing π-orbital electron behavior in sp2 carbon atoms[END_REF] , we created a set of pseudopotentials designed to emulate an sp 2 -hybridised carbon fragment, eliminating all but one electron and one proton from the whole fragment.

In this paper we describe the most recent developments of the method. We begin in Section II by recalling briefly the defining features of our pseudopotential method, before setting out the new additions made since the previous work. In Section III we derive and test some new pseudopotentials across a series of simple but varied molecules. This involves creating new pseudofragment geometries for different hybridisations of carbon some of which, unlike the originals, have no σ-π separation. In Section IV, we derive and test a new pseudopotential with the aim of reproducing the absorption and electronic circular dichroism (ECD) spectra of π systems. Then, in Section V, we take the pseudopotentials created in previous sections and test them in several much larger and more complicated molecules, with a view to seeing how well the pseudopotentials are able to reproduce the spectroscopy of each. Some final remarks and thoughts are then presented in the conclusion.

II. METHODOLOGY A. Pseudopotential Form

We restrict ourselves to an 'out of the box' approach, where no modification of quantum chemistry package source code should be necessary. This was done so as to keep the potentials independent of the quantum chemistry package used. The main quantum chemistry package we use is Turbomole. [START_REF]a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989-2007[END_REF] Our potentials are of the standard form

k A k (r n k -2 )e -α k r 2 l m |Y l,m k Y l,m | k (1)
where n k is an integer and where the total number of expressions k can run across multiple such expressions for each angular momentum l. [START_REF] Mcmurchie | Calculation of integrals over ab initio pseudopotentials[END_REF] From Equation 1 we see that we have a choice of three variables per potential function, A k , n k and α k . Throughout this work, the value of n k is fixed at 1. We limit ourselves to a maximum of one potential function per angular momentum l for each potential centre. This is done only for the sake of simplicity and the possibility of increasing this limit is discussed in Section VII. There is however a well-known precedent for the main group elements being sufficiently well-described by a single potential function per angular momentum. [START_REF] Igel-Mann | Pseudopotentials for main group elements (IIIa through VIIa)[END_REF] We stated above that we remove whole atoms from the molecular fragments for which we create potentials, as well as some further protons. We also make use of non-atom-centred potentials. In full, the multi-centred pseudopotential operator can be written as

Ŵ = A r exp(-αr 2 ) m |Y 1,m Y 1,m | atom-centred potentials + J C J r -r 0 J exp(-γ J (r -r 0 J ) 2 ) |Y 0,0 Y 0,0 | non-atom-centred potentials (2)
with Y 0,0 the s spherical harmonic, Y 1,m the p spherical harmonics (across all m) and r 0 J the relative fixed position of the J th potential with respect to the origin of the pseudoatom to which the potentials are assigned.

B. Pseudopotential Setups

In keeping with our philosophy described in Section II A of retaining only the chemically-relevant parts of the system, we designed three new potential set-ups that kept only the bonding atoms. These consisted of a further sp 2 carbon fragment, and two sp 3 carbon fragments, termed β, γ and δ potentials respectively. In the previous work, we designed a set of pseudopotentials for an sp 2 -hybridised carbon atom containing only one proton and one electron, to which we shall now refer as the α potential set-up, with the original potential parameters of the previous work referred to as the set1 potentials. All four set-ups, α, β, γ and δ, are summarised in Table I. It was shown in the previous work that α pseudopotentials could accurately reproduce absorption spectra for the excitations of the remaining electrons in the systems (as the pseudopotential calculations contain only π orbitals, excitations to or from σ orbitals cannot be reproduced). The pseudosystem spectra were however consistently shifted by a 30-40 nm as compared to the all-electron spectra.

Figure 1 displays a series of singlet excitations for a range of polycyclic aromatic hydrocarbon (PAH) systems using a new set of α potentials, which we call set2, optimised specifically with the reproduction of UV spectra in mind. A detail should be noted in the benzene spectra. The all-electron spectrum contains two peaks at 100 nm, and the pseudomolecular spectrum contains two smaller peaks at 60 nm. The peaks in the all-electron spectrum represent excitations between σ orbitals, meaning that they cannot be reproduced by the pseudo-system. But since we instruct the chemistry package to calculate the same number of excitations in both systems, the pseudosystem produces two additional excitations at a higher energy. These excitations are not unphysical. This phenomenon is present in many of the pseudopotential spectra to follow. The grey zones are used to indicate the energy ranges for which no all-electron excitations are calculated.

The new pseudopotential parameters reported in Table II are not dissimilar to those of the original set1 potentials. The coefficients and exponents are all within 0.5 of those of set1, and incorporating the distances d and c (see Figure 2) into the optimisation procedure has resulted in the non-atom-centred s potentials being moved by less than 0.1 a 0 in both directions.

The significant difference between the potentials of the previous work and the set2 potentials is in the optimisa-Table II. List of optimisation criteria and results for the set2 pseudopotential set. This is an α potential using ethylene as a reference. Column 'Carbon l' shows the angular momenta of the atom-centred-potentials. The 'Criteria' column lists the reference values supplied to the program, as well as their weighting. The Mean Absolute Error (MAE) gives a normalised total error for the best result found by the minimisation procedure, and is the mean error of the values specified in the 'Criteria' column. c and d refer to distances in Figure 2.

Carbon tion criteria. Rather than the HOMO, 1 st ionisation and singlet-triplet gap energies chosen for the original potentials, the set2 potentials are optimised on the HOMO energy, as well as the first two virtual orbitals. This includes the π * orbital.

β, γ and δ pseudopotentials

In creating the β potentials, we wished to have explicit, all-electron systems interact successfully with neighbouring pseudosystems, meaning that the bonding electrons are required. The easiest way to do this from the original α potentials is to add one more electron and proton to the setup, allowing it to form both a σ and a π bond with a neighbouring atom. This means that one of the s potential sets can be removed, as these were intended to recapture the effect of σ electrons which, in the α potential setup, are no longer there. In the α and β set-ups, the planar distance to each potential set is denoted by d, and the distance above and below the xy plane by c. Figure 2 illustrates this.

The γ potential setup has a p-shaped potential on the central carbon, along with three s-shaped potentials replacing the hydrogen atoms at a distance from the central carbon of 0.5 a 0 .

In the δ pseudopotential setup there are two explicit electrons, thus it is able to act as a bridge between two other all-electron, bonding atoms. The central carbon not only has a p-shaped potential, but also its own sshaped potential, and we have s potentials replacing two of the all-electron bonds at a distance from the pseudocarbon of d=0.5 a 0 . In the γ and δ set-ups, the distance from central pseudocarbon to non-atom-centred potentials is denoted by d.

The optimisation code

We generalised the method of the previous work by creating a general minimisation program, the Multiple Orbital Optimiser (MOO), which minimises the error between all-electron and pseudosystems on selected criteria including molecular orbital energies, TDDFT excitation energies, UV spectra fitting and total energy differences, such as ionisation energies, singlet-triplet energy gaps, or even alternate geometries.

The program MOO can be used to alter the coefficients and exponents of the pseudopotentials, and the position of the non-atom-centred potentials. These optimisations are carried out at the Hartree-Fock level, but can be transferred to other levels of calculation. This code is publicly available 14 . III are the details of the β, γ and δ optimisations. Most of the various criteria on which the potentials are optimised can be written in terms of energy, which allows us to normalise the final MAE error by dividing it by the number of criteria (multiplied by any individual weighting applied to them). Various combinations of criteria were tested, and the potentials that produced the smallest overall errors were chosen.

Contained in Table

For these β, γ and δ potentials, the aim was to reproduce bonding structure similarly to the α potentials of the previous paper. This meant reproducing the electronic density took priority over reproducing the virtual space excitations. These potentials are thus optimised on occupied orbitals of highest energies. The importance of the virtual orbitals in the reproduction of absorption spectra was not realised until later.

The β optimisation used the top three occupied orbitals in a closed-shell Hartree-Fock calculation on ethylene as a reference, with a 3× weighting on the HOMO orbital, and the normalised total error is 0.9067 eV . Overall, this pseudopotential setup does not differ greatly from the α pseudopotentials, other than that these potentials are slightly weaker and more diffuse than the α potentials.

The γ optimisation was carried out on an eclipsed ethane molecule, using s and p central potentials, with the top two occupied orbitals as a reference (with the HOMO doubly-weighted). These s potentials are far more concentrated than those of either of the sp 2 potentials. In the relaxed, staggered geometry of ethane, the electrons at either end of the ethane molecule experience each others' influence less strongly. Therefore eclipsed ethane was chosen for this optimisation, in the hopes of creating a more accurate potential.

The δ potentials are optimised on propane and use both a p potential and an s potential on the central pseudocarbon, in addition to the non-atom-centred s potentials. The reference criteria used are the six highestoccupied molecular orbitals of an Unrestricted Hartree-Fock calculation.

In summary then, we have created and optimised four new pseudopotential setups, summarised in Table I, for different carbon fragments.

In each case, the optimisations were made on Hartree-Fock calculations, and this was done to keep the potentials correlation-independent. In the following sections, all calculations use DFT-PBE0/def-SV(P) unless otherwise specified. It was found possible to remove the s basis functions of the def-SV(P) set2 pseudocarbon without altering any of the set2 results. Hereafter in this work, the set2 potentials use the def-SV(P) basis set without s functions.

III. RESULTS: SIMPLE SYSTEMS

The optimised potentials were tested across a sample of molecules chosen to expose the pseudopotentials to a range of different chemical environments. These molecules, along with the sites of the pseudopotentials, are shown in Table IV. In each case the properties measured are the HOMO, first ionisation, singlet-triplet gap and TDDFT first excitation energies.

The results are broken down by pseudofragment type in Figures 3, 4 and5, with average differences in the various properties laid out in Table V. In most of these test

C β CH 2 O CHOH CHNH 2 C β NH C 2 H 4 H 2 CO CH 2 CHOH CH 2 NH CH 2 CHNH 2 C β C β C β * * * * * γ Test Molecules CH 3 OH NH 2 C OH O C O O COOH H C H O P Au Cl CH 4 C 2 H 6 eclipsed CH 3 OH CH 3 NH 2 CH 3 COOH Aspirin C 9 H 8 O 4 ClAuP(CH 3 ) 3 C 2 H 4 CO C γ C γ C γ C γ C γ C γ C γ C γ C γ C γ * * * * * * * * * * δ Test Molecules H H COOH F CH 3 H 3 C OH H 3 C NH 2 H 3 C CHO OHC NH OHC CHO CH 4 FCH 2 COOH CH 3 CH 2 CH 3 C 2 H 5 OH C 2 H 5 NH 2 CHOCH 2 CHO malonaldehyde CHONH 2 CH 2 CHO C δ C δ C δ C δ C δ C δ C δ * * * * * * *
molecules, the pseudocarbon is bound to an all-electron carbon, however among the test molecules are included several in which the pseudocarbon is bound to an allelectron heteroatom i.e. not a carbon. This was done to gauge how sensitive the potentials were to being placed in systems for which they were not optimised.

Looking across the results for sp 2 -hybridised carbon systems (i.e. the molecules containing β pseudofragments) shown in Figure 3 and Table V, we see that all molecules with homoatomic pseudofragment bonds have at most a difference of 5.9% between all-electron and pseudosystems. This is a good accuracy and is consistent with the results of the previous work. The differences between all-electron and pseudopotential systems for heteroatomic pseudofragment bonds however, are substantially larger, particularly in the case of a pseudofragment/oxygen bond. In the case of CH 2 O, the molecular orbitals emerge in the wrong order energetically, includ- ing the HOMO, explaining why its results are uniquely poor.

Turning to the sp 3 -hybrids (i.e. systems containing γ or δ pseudofragments) with their results displayed in Figures 4 and 5 and percentage differences shown again in Table V, it is seen that those systems with homoatomic pseudofragment bonds have maximum differences between all-electron and pseudopotential systems of 5.3%, a similar result to the above. When considering the systems with heteroatomic pseudofragment bonds the differences are once again larger, particularly for pseudofragment/oxygen and pseudofragment/hydrogen bonds. δ pseudofragments allow for two bonds between allelectron atoms and the pseudofragment, and we see that the all-electron/pseudosystem differences in the one test molecule with two pseudofragment/heteroatom bonds, methane, are correspondingly large. In the particular case of the C * γ -P results, it is also worth noting that the pseudosystem is built with three separate sets of γ potentials, which would likely have compounded any error in the potentials themselves. One notes throughout though that the errors on sp 3 systems are much smaller than those of the sp 2 systems. Overall, we deduce that the more polarised the bond between a pseudofragment and a heteroatom, the worse the result. This is to be expected, given that the pseudopotentials are optimised on carbon-carbon bonds, and given the different character of bonds between carbon atoms as compared to those between carbon and oxygen or nitrogen atoms. It is also found that the sp 2 β potentials are more sensitive to a change in the atom to which the pseudofragment is bound. Again this is not surprising, given that the β pseudofragment forms both a σ and a π bond to its all-electron neighbour. Meanwhile, carbon-bound pseudofragments performed consis-tently well across all molecules tested and all properties measured (that is, the HOMO, first ionisation, singlettriplet gap and TDDFT first excitation energies), with errors smaller than 6.0% in all cases. It can therefore be said that these pseudopotentials reproduce the basic properties of the test systems well, and to a degree consistent with the previous work. Particularly impressive to us is the accurate reproduction of the ionisation energies for so many of these systems, as most of the electron relaxation which takes place in all-electron systems after ionisation clearly cannot not happen in the pseudofragments.

IV. RESULTS: ABSORPTION SPECTRA

The set2 pseudopotentials were tested for the same helicene molecules as in the previous work. The UV spectrum of the helicene molecules are improved, as the comparison for the [6]helicene reveals (Figure 6). One sees that the set2 potentials do not require a shift in wavelength in order to line up the pseudosystem spectra with the all-electron spectra, which is an improvement on the previous work. Spectra for a range of pseudo[n]helicenes are included in the Supplementary Information (SI), along with an analysis of transition densities for excitations visible in the [10]helicene ECD spectrum.

These spectra show that we can be confident that our potentials can retain much of the physics of complex π systems, even allowing for some distortion of the molecular plane. Using the definition of dihedral torsion shown in Figure 7, [6]helicene has a maximum dihedral torsionper-ring of 14.5 • . These calculations show that the ECD spectra of helicenes are mainly due to the π-like electrons and that our pseudopotentials allow for the reproduction of properties which are much more difficult to reproduce than UV spectra as they are much more sensitive to the environment. We can also say that the set2 pseudopotentials prove to be more accurate than the set1 potentials for the reproduction of helicene spectra. Overall then, it can be said that the use of virtual orbitals as reference criteria for optimisation improves the UV spectra produced.

V. RESULTS: COMPLEX SYSTEMS

Thus far, all potentials have been tested on systems related closely to those for which they have been optimised. In this section, potentials are tested in more complex systems, selected from recent literature, involving metal atoms, distorted π systems, and neighbouring π rings.

A. Twistacene

The phrase 'twisted acene', later 'twistacene', was introduced in 2004 [START_REF] Lu | A Pentacene with a 144 • Twist[END_REF] , then more thoroughly described in 2006 [START_REF] Pascal | Twisted Acenes[END_REF] . The electronic and optical properties of their parent acenes are altered by this twisting [START_REF] Xiao | Synthesis and structure characterization of a stable nonatwistacene[END_REF] , which introduces chirality to the molecule [START_REF] Bedi | Helically Locked Tethered Twistacenes[END_REF] . A study by Bedi et al. [START_REF] Bedi | Helically Locked Tethered Twistacenes[END_REF] describes a system allowing the 'helical-locking' of an acene at a specific torsion angle, and it is to this publication that we turn for geometric data. Figure 8 shows the Ant-cn molecule (where n=3-6 is the length of the carbon bridge at the top of the molecule), which allows the helical locking of anthracene. The increasing length n of the carbon bridge at the top of the molecule allows the anthracene partially to relax back toward a planar alignment.

This molecule is of specific interest to us for similar reasons to the helicene described in Section IV, i.e. that the distorting of π rings starts to break the separation of σ and π orbitals, which will in turn make our α potentials less and less physically descriptive of the system. With a systematic test of increasingly distorted π rings therefore, we can gain some idea of the limits of the pseudopotentials used.

As our interest was solely in the part of the molecule we wished to model with pseudopotentials, i.e. the twisted anthracene itself, we first optimised the molecular geometries (at the DFT-PBE0 level, with def-SV(P) basis sets) before removing the atoms surrounding the central anthracene. This way, we could calculate the anthracene spectra alone.

Figure 9 displays the spectra for Ant-cn, for n = 3 -6, using all-electron structures as well as the set2 pseudopotential set. The all-electron UV spectra are very similar to one another and have peaks in approximately the 120 nm to 400 nm range, with most of the peaks clustered between roughly 120 nm and 280 nm, and the main peak at around 240 nm in each molecule.

The pseudopotentials reproduce in detail the shapes of the all-electron spectra. For the pseudopotentials, all of the peaks in the all-electron systems appear to be present in the pseudosystems. The relative intensities of the peaks also seem broadly correct. Turning to the ECD results we see a similar picture. The set2 potential spectra peaks are spread across a similar range to those of the all-electron spectra. We see once again that all of the peaks are consistently identifiable in both all-electron and pseudosystem spectra, except for the positive peak at 160 nm in the all-electron spectra. The transition density of this peak shows that it is a σ-σ excitation, meaning that it is not possible for the pseudopotentials to reproduce. In the pseudosystems we instead see a negative peak at this wavelength. The intensity of the peaks is also broadly correct, albeit that main peak at around 260 nm is several times higher for the pseudosystem than for the all-electron system. We also see that the negative-to-positive shift indicative of chirality is found in this range, and remains clear even for the most dis-torted system, Ant-c3.

An important and interesting feature of these spectra is that while the incorrect negative peak at 160 nm increases slightly in intensity as the system becomes more distorted, we do not see any additional unphysical peaks appear, nor do we see much further distortion in the peaks present. There is also no shifting of the pseudosystem spectra relative to the all-electron spectra, even for the most distorted systems. We can say then that errors in the pseudopotential spectra remain fairly consistent as the system becomes more distorted. We found this surprising, as we expected the pseudosystem spectra to degenerate as the π rings were distorted. An analysis of some transition densities for all-electron and pseudosystem excitations is presented in the SI.

These results are consistent with the helicene results of Section IV. Table VI shows the maximum and mean distortion angles per benzene unit across both helicene and twistacene molecules used in this work. The distortion per benzene unit is defined in Figure 7. Both maximum and average distortion rates per benzene unit are similar for [6]helicene and for the Ant-cn, with [6]helicene falling roughly in the middle. We see that for all the helicene and Ant-cn molecules, both UV and ECD spectra reproduced, albeit with flaws introduced by the distortion.

Table VI. Maximum and mean distortions per benzene unit for helicene and twistacene molecules used in this work. The maximum distortion per benzene unit is chosen to be the largest dihedral torsion angle in the molecule (see Figure 7).

System

Distortion ( • ) Mean Maximum [6] In conclusion then, we can say that the pseudosystems were successful at recreating the UV spectra of the distorted anthracene π systems, up to and including a distortion of around 14.0 • per benzene unit (Ant-c3), with the set2 potentials proving the most successful. We can also say that while even at the comparatively low rate of twisting of around 6.2 • per benzene unit (Ant-c6), at least one spurious excitation is introduced into the ECD spectra of twistacene, the ECD spectra of the pseudosystems are also very accurate, even up to the maximum distortion of the systems.

B. Dodecaphenyltetracene

This molecule is taken from a synthesis performed by Xiao et al. 19 Its complexity, along with the fact the team had reported a UV spectrum to which theoretical spectra could be compared, made this an attractive challenge. The molecular structure is shown in Figure 10.

The reader will see that this molecule could encapsulate two different challenges. First are the phenyl groups, i.e. the presence of many π systems facing and overlapping one another at different angles. This is sure to involve the overlapping of many higher-energy orbitals, making for a complicated electronic structure. Second is the fact that the central tetracene is distorted by the phenyl groups. Since we already have both the twistacene molecule in Section V A and the helicene molecules in Section IV to investigate distorted π systems, we decided to 'pseudopotentialise' only the phenyl groups so as not to confuse the results. Figure 10 shows the pseudomolecular system. This setup uses both α potentials, along with β potentials connecting the phenyl rings to the central, all-electron tetracene.

The set2 potentials show five clear peaks in nearagreement with the all-electron peaks, with the possible exception of the peak at around 300 nm (set2) as compared to around 330 nm (all-electron). The relative intensities of these peaks are also similar to those of the allelectron spectrum, although they are somewhat skewed toward the lower-energy excitations by comparison.

The next comparison to be made is that of these theoretical results with the experimental ones in the original synthesis. The experimental spectrum extends from around 650 nm to 250 nm and has a spread of shallow excitations across the 600-450 nm range, a clear and strong peak at 360 nm, and at least one further peak in the 250 nm region. The stronger peaks (below 450 nm) are reproduced in the theoretical spectra, both in allelectron and pseudosystem calculations. The range of peaks between 600 and 400 nm is not reproduced in any of the theoretical spectra. Comparison of theoretical and experimental spectra is complicated by the fact in the experimental results the molecules are in a CH 2 Cl 2 solution.

An experimental spectrum for a simple tetracene molecule, without phenyl groups, has also been added to Figure 11. [START_REF] Bryson | Ground Control Monitoring for the Organics Experiment on the EXPOSE-R Facility on the International Space Station[END_REF] We see that the characteristic shapes of the dodecaphenyltetracene spectrum appear to arise from the central tetracene itself, and that the main result of adding the phenyl groups appears to be that the largest excitations are now at wavelengths roughly 200 nm shorter than in the tetracene. We also see that this 'shift' is faithfully reproduced by the DFT calculations, both allelectron and pseudopotential.

Finally, we note that the HOMO energies of the allelectron and set2 systems are -4.941 eV and -5.476 eV respectively, making for percentage errors that are not dissimilar to those of the higher polyenes modelled previously [START_REF] Punter | Atomic pseudopotentials for reproducing π-orbital electron behavior in sp2 carbon atoms[END_REF] .

In conclusion, these results for dodecaphenyltetracene show that this pseudopotential technique is effective at recreating the UV spectra of overlapping and interacting π systems.

C. Hemi-Cryptophane

The interest in cryptophanes and hemicryptophanes lies in their propensity to form Van der Waals complexes as hosts. Some of these complexes have interesting catalytic properties [START_REF] Ikbal | Bioinspired Oxidation of Methane in the Confined Spaces of Molecular Cages[END_REF][START_REF] Perraud | Hemicryptophane-assisted electron transfer: a structural and electronic study[END_REF][START_REF] Gosse | Synthesis and Structural Studies of Gallium(III) and Iron(III) Hemicryptophane Complexes[END_REF] . Our own interest in such molecules is that they combine a range of different carbon environments with a complex electronic structure. A further consideration is that such 'cage molecules' are often characterised by their UV spectra, and so the ability to produce an accurate UV spectrum with a reduced pseudocage molecule would be useful practically.

The molecule we have adopted as a test subject is a Cu(II)hemicryptophane complex, shown in Figure 12 [START_REF] Ikbal | Bioinspired Oxidation of Methane in the Confined Spaces of Molecular Cages[END_REF] . In order to try to make the investigation as systematic as possible, we decided to group parts of the molecule together as shown in Figure 12, before building up the number of pseudopotentials used.

In light of the results from Section III, where we saw that the results were markedly less accurate when pseudofragments were permitted to bond with heteroatoms, it was decide to institute a 'no-heterobonding' rule, in order to see what the effects might be on the resulting spectra. An example of the 'no-heterobonding' rule for the 'upper π' section of the cage is shown in Figure 13. Figure 13a shows the regular-all-electron upper π section of the cage. Figure 13b shows a version in which all carbon atoms have been replaced by pseudoatoms. Finally, Figure 13c shows the upper π section following the no-heterobonding rule, in which there must be at least one all-electron carbon atom in between pseudofragments and heteroatoms.

Table VII. Structures of pseudohemicryptophane complexes.

Each column represents a part of the molecule (see Figure 12) that has been replaced with potentials. The 'Type' row shows the pseudopotential setups used for each part. The 'rule' column shows whether or not the no-heterobonding rule has been applied, i.e. whether pseudofragments have been placed next to non-carbon atoms in the complex. For those systems with the 'Y (π)' designation, heterobonding is forbidden for carbons which are members of π rings, but has been permitted elsewhere.

upper π upper bridges methyls mid-bridges rule peaks Type

α,β δ γ δ - - A Y N Y N N 2 B Y N Y N Y (π) 1, 2 C Y Y Y N Y (π) 1, 2 D Y Y Y Y Y (π) 1, 2
Several schemes of pseudopotential positioning have been tested. Only some of them are discussed here, where no pseudopotentials are used below the mid-bridges (as the use of pseudopotentials on the lower π degrades the computed spectra). The full results are reported in the SI.

The reference spectra, shown in Figure 14, has two major features, a sharp, intense peak at around 800 nm and a shallower and less intense peak centred at around 1900 nm. They are labelled as peak 1 and 2, respectively. Let us start by comparing A and B. The methyl groups are replaced in both cases by the pseudopotentials. For the upper π, the schemes shown in Figures 13b and13c are adopted for A and B (no-heterobonding rule), respectively. Peak 1 is not reproduced in A, but it is in B. Peak 2 is reproduced in both, even if the setup of B causes a reduced intensity. Two further setups are presented, with an increasing number of pseudopotentials: pseudocomplex C that builds on the setup of B; pseudocomplex D, where the pseudopotentials are applied from the upper bridges all the way down to the mid-bridges, while making sure to respect the no-heterobonding rule for the upper π systems. This makes for an overall reduction in the number of explicit electrons in the complex of 132, from 545 to 413. For both C and D, the UV spectrum is reproduced with an accuracy similar to that of B.

By summarising the results of the UV spectra we were able to conclude the following:

1. A heteroatom bond (i.e. a C-O bond) in the upper π region of the molecule is largely responsible for peak 1. In the original article, this peak was attributed only to copper transitions, independent of the cage. Here we see the cage is in fact necessary for peak 1 to be produced. The no-heterobonding rule is necessary to capture this transition correctly, as evident for A and confirmed by other setups in the SI.

2. Peak 2 has a strong upper π component. Its intensity is well-reproduced for A, but it is reduced in the other cases, suggesting that the setup in Figure 13b reproduces the upper π system slightly better than 13c (see the SI for comparison with other setups).

Figure 15 displays the all-electron transition densities for peaks 1 and 2. These provide further evidence that deductions above regarding the nature of the two peaks are correct. Peak 1 broadly shows an electron transfer between upper and lower parts of the molecules, and the density on the upper part is indeed focused on the upper π rings and the oxygen atoms directly below them. Peak 2 similarly contains a transfer of electron density between the top and bottom of the molecule, with a strong upper π component.

The chirality of this molecule arises in the top of the hemicryptophane itself, and so good pseudopotentials will be important for the accurate reproduction of the ECD spectrum. Looking at Figure 14, this is indeed the case. Pleasingly, with the exception of pseudocomplex A, all the ECD spectra retain a clear positive-to-negative shift, i.e. the signature of their chirality is preserved. The most distinctive features of the all-electron system are a positive peak at around 800 nm, leading into a large, shallow negative peak at around 1900 nm. Pseudocomplex spectra B, C and D broadly share these traits, albeit with intensities differing by up to a factor of around three.

In conclusion then, this Cu(II)hemicryptophane complex is reproducible with simple carbon pseudopotentials, as we were able to recreate the key features of the complex's spectrum. This is particularly impressive given the heavy delocalisation of electron density over the whole molecule. However, it should be noted that it was necessary to derive a new rule in order to be sure of retaining the necessary electronic complexity, which is that bonds between pseudocarbons and all-electron atoms should be restricted to carbon-carbon bonds only, and that bonding pseudocarbons to explicit heteroatoms should be avoided. Given the results seen in Section III, and given that all pseudocarbons in this work are optimised on carbon-carbon bonds, this seems reasonable.

VI. TIMINGS

Table VIII. Comparison of time and SCF iterations between

all-electron and pseudosystems. The gain is defined as the ratio of the all-electron system calculation time to the pseudosystem calculation time. The final two columns give the percentage of electrons and basis functions remaining in the pseudosystem respectively. Table VIII displays a comparison of calculation lengths between pseudopotential and all-electron systems, factoring in both the overall computational time and the number of SCF iterations. It can be seen that in every case, that the gain in time per iteration is larger than 1, varying from 2.39 to 21.38. The gain per iteration varies strongly, though not exclusively, according to the proportion of electrons remaining in the pseudosystem as compared to the all-electron system.

SCF

However, we also see that the number of SCF iterations need to converge pseudomolecule calculations varies a lot. For dodecaphenyltetracene many fewer iterations are needed; for the Ant-c3 and [10]helicene molecules the number is similar, and for the cage molecules many more are required, so much so that the overall gain is less than one, the SCF calculations on the pseudomolecules take longer to converge than those on all-electron systems. The reason for this is thought to be the quality of the starting guesses for the molecular orbitals, the oneelectron terms of the Hamiltonians. Finally, we see that across all systems there is a consistent and usually substantial gain in the time taken for TDDFT calculations to be completed.

VII. CONCLUSION

In this work we have developed and extended a previously-reported pseudopotential method 1 .

1. Several new pseudopotential setups were created for different hybridised carbon environments, and found to reproduce electronic structural properties such as HOMO, singlet-triplet and 1 st ionisation energies to a similar degree of accuracy to the previous work.

2. It was found possible to optimise pseudopotentials to improve the absorption spectra produced with pseudomolecules.

3. It was found that these pseudopotentials, used judiciously, were able to reproduce both the UV and ECD spectra of greatly more complex molecules than those on which they were optimised.

Rules derived for the application of these potentials are that in order to produced that best results they should (1) not be bonded to heteroatoms, i.e. that one allelectron carbon should be kept between pseudofragments and non-carbon all-electron atoms, and (2) that beyond a torsion angle of a few degrees α potentials become unreliable at reproducing ECD spectra, though the quality of UV spectra was maintained up to an average torsionper-benzene unit of 14.1 • . A possible future improvement to the method would be the optimisation of custom basis sets for the pseudopotentials. Such basis sets could make them more accurate and may require fewer basis functions, increasing computational efficiency. ). The torsion angle is defined as the angle between the ends of the central anthracene. In each case, the anthracene itself is highlighted in yellow, while the carbon bridge that determines the torsion is highlighted in blue. Figure 12. Labelling scheme for Cu(II)hemicryptophane complex, where oxygen is in red, nitrogen in blue, and copper is pink.

VIII. FUNDING INFORMATION

R 2 O O R 1 R 3 C β C β C α C β C β C α R 2 O O R 1

Figure 1 .

 1 Figure 1. Comparison of the absorption spectra for the 20 first singlet excitations obtained with set2 pseudopotentials and all-electron calculations (def2-SV(P)(s-less)/TD-PBE0) within the RPA framework. The grey zone covers energies for which no all-electron excitations have been calculated.

Figure 2 .

 2 Figure 2. Definition of distances c and d for α and β pseudopotential set-ups

Figure 3 .

 3 Figure 3. DFT-PBE0 and TDDFT-PBE0 comparison of allelectron and pseudosystem energies across a range of β potential systems.

Figure 4 .Figure 5 .

 45 Figure 4. DFT-PBE0 and TDDFT-PBE0 comparison of allelectron and pseudosystem energies across a range of γ potential systems.

Figure 6 .Figure 7 .Figure 8 .

 678 Figure6.[6]Helicene UV and ECD spectra, for all-electron (red), set1 (blue) and set2 pseudopotential (black) systems. Calculations are performed at the TDDFT-PBE0 level. The grey zone covers energies for which no all-electron excitations have been calculated.

Figure 9 .

 9 Figure 9. UV and ECD spectra for twisted anthracenes Antcn (for n = 3 -6), calculated at the TDDFT-PBE0 level for the first 20 singlet excitations. These include the all-electron spectra (red) and the set2 potential spectra (blue). The grey zone covers energies for which no all-electron excitations have been calculated.

Figure 10 .

 10 Figure 10.Pseudododecaphenyltetracene, with α pseudoatoms in green and β pseudoatoms in red. All-electron atoms remain in black.

Figure 11 .

 11 Figure 11. UV spectrum of dodecaphenyltetracene using allelectron (black) and pseudopotential (blue) systems, calculated at the DFT-PBE0 level. The original experimental data19 is also shown (green), along with an experimental spectrum for tetracene (green)[START_REF] Bryson | Ground Control Monitoring for the Organics Experiment on the EXPOSE-R Facility on the International Space Station[END_REF] .

Figure 13 .

 13 Figure13. The 'no-heterobonding' rule for upper π ring pseudopotentials.

Figure 14 .

 14 Figure 14. All-electron and pseudomolecular UV (above) and ECD (below) spectra for Cu(II)hemicryptophane. Peaks 1 and 2 are labelled. Calculations were carried out at the TDDFT-B3LYP level, with the first 20 singlet excitations.

Figure 15 .

 15 Figure 15. Transition densities based on all-electron TDDFT-B3LYP calculations for excitation peaks 1 (top) and 2 (bottom). In both cases, electron density is reduced in the blue zones and increased in the red.

Table I .

 I A summary of different pseudopotential set-ups presented in this work. Non-atom-centred potentials are highlighted in red.

	Diagram	Designation	Description
		α	sp 2 , 1 explicit electron
		β	sp 2 , 2 explicit electrons
		γ	sp 3 , 1 explicit electron
		δ	sp 3 , 2 explicit electrons
	1. α pseudopotentials

Table III .

 III Optimisation criteria and parameters for the best β, γ and δ potential sets.

		Optimisation Criteria
	Carbon l	Basis	Criteria	MAE (eV )
		β potentials
			HOMO(×3);
	p	def-SV(P)	HOMO-1;	0.90670
			HOMO-2
		γ potentials
	p	def-SV(P)	HOMO(×2); HOMO-1	0.4179
		δ potentials
			HOMO;
			HOMO-1;
	s, p	def-SV(P)	HOMO-2; HOMO-3;	0.40067
			HOMO-4;
			HOMO-5
		Optimised Parameters
	Potential A (Ha0) α (a -2 0 ) d (a0)	c (a0)
		β potentials
	p	-2.0031 0.4694	-	-
	s	0.4376 0.4946	0.5	0.25
		γ potentials
	p	-2.0949 0.3951	-	-
	s	38.5052 14.8328	0.5	-
		δ potentials
	p	-6.9569 3.4066	-	-
	s	5.3934 6.4912	0.5	-
	s (carbon)	0.6391 0.9382	-	-

Table IV .

 IV Molecules used to test β, γ and δ pseudopotentials. The pseudofragments are denoted by C * β , C * γ and C *

	δ
	respectively.
	β Test Molecules

Table V .

 V Average errors for molecules using β, γ and δ potentials, arranged by pseudocarbon-X bond type, for DFT-PBE0 and TDDFT-PBE0 calculations. '∆S-T ' is the singlet-triplet gap, and '1 st Ex' is the energy of the first TDDFT-PBE0 excitation.

	Bond Type		Mean Error (%)
	(C sp 2 systems
	β pseudofragments
	All	18.4	18.1	15.2	17.5
	C * β -C C * β -O C * β -N	5.5 60.6 14.7	5.9 43.3 29.4	5.5 35.6 24.1	2.0 63.7 18.1
		sp 3 systems
	γ pseudofragments
	All	5.1	3.9	7.7	4.3
	C * γ -C C * γ -O C * γ -N C * γ -H C * γ -P	5.3 9.5 3.1 4.3 9.0	2.8 7.8 3.8 1.5 2.3	1.7 12.4 4.9 8.8 1.3	4.6 7.7 2.9 9.8 13.7
		δ pseudofragments
	All	8.9	3.1	2.3	10.5
	H-C * δ -H C-C * δ -C C-C * δ -O C-C * δ -N C-C * δ -F	25.0 5.3 12.7 5.5 2.8	9.3 0.2 2.9 2.5 4.2	6.9 0.9 0.3 1.1 4.8	26.8 2.8 25.7 5.9 3.4

* -X) ∆S-T HOMO 1 st I.E. 1 st Ex

The authors acknowledge the french Ministère de l'éducation nationale et de la recherche for providing the PhD grant of A. Punter.


Amel Mhaya

Dominique Bégu

Slim Tounsi

Corinne Arpin
email: corinne.arpin@u-bordeaux.fr

MgrB Inactivation Is Responsible for Acquired Resistance to Colistin

Keywords: Enterobacter cloacae complex, Enterobacter hormaechei subsp. steigerwaltii, colistin resistance, MgrB, PhoPQ regulatory system

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

INTRODUCTION

The genus Enterobacter is a member of the ESKAPE group (Enterococcus faecium, Staphylococcus aureus, Klebsiella pneumoniae, Acinetobacter baumannii, Pseudomonas aeruginosa, and Enterobacter spp.), and is grouped within the Enterobacter cloacae complex (ECC) group [START_REF] Lavigne | Enterobacter spp.: Update on Taxonomy, Clinical Aspects, and Emerging Antimicrobial Resistance[END_REF]. In a seminal work, Hoffmann and Roggenkamp defined 13 genetic clusters (C-I to C-XIII) of ECC according to their hsp60 sequences (hsp, for heat shock protein) [START_REF] Hoffmann | Population genetics of the nomenspecies Enterobacter cloacae[END_REF].

More recently, based on the analysis of 360 whole-genome sequences, ECC was placed into 18 phylogenomic groups (A to R) and two meta-clusters, i.e. Enterobacter hormaechei and Enterobacter cloacae [START_REF] Chavda | Comprehensive Genome Analysis of Carbapenemase-Producing Enterobacter spp.: New Insights into Phylogeny, Population Structure, and Resistance Mechanisms[END_REF][START_REF] Beyrouthy | Novel Enterobacter Lineage as Leading Cause of Nosocomial Outbreak Involving Carbapenemase-Producing Strains. 8[END_REF]. At present, more than 3,000 Enterobacter genomes are available in GenBank databases and the taxonomy of this genus is still evolving [START_REF] Wang | Enterobacter wuhouensis sp. nov. and Enterobacter quasihormaechei sp. nov. recovered from human sputum[END_REF]. ECC species are opportunistic pathogens and, due to their natural and acquired resistance to many antibiotics, they are described as the leading cause of resistant nosocomial infections [START_REF] Lavigne | Enterobacter spp.: Update on Taxonomy, Clinical Aspects, and Emerging Antimicrobial Resistance[END_REF].

Colistin (polymyxin E) is considered as one of the last-resort therapeutic agents for treatment of multidrug-resistant Gram-negative bacteria [START_REF] Baron | Molecular mechanisms of polymyxin resistance: knowns and unknowns[END_REF]. It is a cationic antimicrobial peptide that targets the anionic lipid A phosphate moiety of bacterial lipopolysaccharide (LPS), leading to an altered cell permeability and thereafter to cell death [START_REF] Baron | Molecular mechanisms of polymyxin resistance: knowns and unknowns[END_REF]. The most common resistance mechanism in Enterobacteriaceae is attributed to the covalent modifications of LPS through the incorporation of positively charged groups such as phosphoethanolamine (pEtN) and 4amino-4-deoxy-l-arabinose. These modifications neutralize the negative charges of LPS and subsequently reduce binding affinity of colistin to its target [START_REF] Baron | Molecular mechanisms of polymyxin resistance: knowns and unknowns[END_REF]. Plasmid-mediated colistin resistance, i.e. MCR genes encoding pEtN transferases, were described [START_REF] Kieffer | mcr-9, an Inducible Gene Encoding an Acquired Phosphoethanolamine Transferase in Escherichia coli, and Its Origin[END_REF][START_REF] Yuan | Coproduction Of MCR-9 And NDM-1 By Colistin-Resistant Enterobacter hormaechei Isolated From Bloodstream Infection[END_REF]. However, colistin resistance mechanisms are mostly attributed to chromosomal modifications in twocomponent regulatory systems (TCRS), namely PmrA/PmrB and PhoP/PhoQ, which can cause constitutive expression of LPS modifications and consequently colistin resistance. Such chromosomal modifications were well described in Klebsiella pneumoniae [START_REF] Baron | Molecular mechanisms of polymyxin resistance: knowns and unknowns. 6[END_REF][START_REF] Cannatelli | In vivo emergence of colistin resistance in Klebsiella pneumoniae producing KPC-type carbapenemases mediated by insertional inactivation of the PhoQ/PhoP mgrB regulator. 11[END_REF], but also in E. cloacae complex [START_REF] Kang | Colistin heteroresistance in Enterobacter cloacae is regulated by PhoPQ-dependent 4-amino-4deoxy-l-arabinose addition to lipid A[END_REF]. Moreover, substitution, disruption and inactivation changes in mgrB gene encoding for the negative regulator of PhoP/Q have been identified to play a prominent role in polymyxin resistance in clinical K. pneumoniae isolates [START_REF] Cannatelli | MgrB inactivation is a common mechanism of colistin resistance in KPC-producing Klebsiella pneumoniae of clinical origin[END_REF][START_REF] Olaitan | Mechanisms of polymyxin resistance: acquired and intrinsic resistance in bacteria[END_REF][START_REF] Jayol | National survey of colistin resistance among carbapenemase-producing Enterobacteriaceae and outbreak caused by colistinresistant OXA-48-producing Klebsiella pneumoniae, France[END_REF]. Very few reports have mentioned mgrB mutations and their possible role in colistin resistance of clinical Enterobacter spp. [START_REF] Dagher | Intestinal Carriage of Colistin Resistant Enterobacteriaceae at Saint Georges Hospital in Lebanon[END_REF][START_REF] Chavda | Coidentification of mcr-4.3 and blaNDM-1 in a Clinical Enterobacter cloacae Isolate from China[END_REF], and no studies were performed to confirm its involvement in this genus.

Thus, the aim of this study was to analyze an in vitro mutant of Enterobacter hormaechei subsp. steigerwaltii containing a mutated mgrB gene, and to confirm its role in colistin resistance. Our procedure was validated by comparison of results with those obtained with a clinical colistin resistant K. pneumoniae deleted for mgrB.

RESULTS AND DISCUSSION

Eh22, a multidrug resistant strain of E. hormaechei subsp. steigerwaltii A multidrug resistant strain of ECC (named Eh22) was isolated from a patient urine sample and provided by an urban health care system (community laboratory of Djerba, Tunisia).

Analysis of the hsp60 sequence revealed that Eh22 is included in the cluster C-VIII, referred to as E. hormaechei subsp. steigerwaltii [START_REF] Hoffmann | Population genetics of the nomenspecies Enterobacter cloacae[END_REF][START_REF] Hoffmann | Enterobacter hormaechei subsp. oharae subsp. nov., E. hormaechei subsp. hormaechei comb. nov., and E. hormaechei subsp. steigerwaltii subsp. nov., three new subspecies of clinical importance[END_REF]. Furthermore, in silico multilocus sequence typing (MLST) of seven house-keeping genes (dnaA, fusA, gyrB, leuS, pyrG, rplB, and rpoB [START_REF] Miyoshi-Akiyama | Multilocus sequence typing (MLST) for characterization of Enterobacter cloacae[END_REF], in silico multilocus sequence analysis (MLSA) of four other target genes and/or other target gene regions (gyrB, rpoB, infB, and atpD) [START_REF] Brady | Taxonomic evaluation of the genus Enterobacter based on multilocus sequence analysis (MLSA): proposal to reclassify E. nimipressuralis and E. amnigenus into Lelliottia gen. nov. as Lelliottia nimipressuralis comb. nov. and Lelliottia amnigena comb. nov., respectively, E. gergoviae and E. pyrinus into Pluralibacter gen. nov. as Pluralibacter gergoviae comb. nov. and Pluralibacter pyrinus comb. nov., respectively, E. cowanii, E. radicincitans, E. oryzae and E. arachidis into Kosakonia gen. nov. as Kosakonia cowanii comb. nov., Kosakonia radicincitans comb. nov., Kosakonia oryzae comb. nov. and Kosakonia arachidis comb[END_REF], as well as the nearly complete (1,412 bp) 16S rRNA gene sequence [START_REF] Usadel | 16S/23S rRNA sequencing[END_REF], confirmed this species assignation (Tables S1 andS2, Supplementary information). MLST analysis also showed that Eh22 belongs to the sequence type, ST177 which has a single-allele different from ST93, ST294 and ST828, similarly to strains of E. hormaechei subsp. steigerwaltii for those of which the whole-genome sequencing had been performed [START_REF] Yang | Occurrence of Enterobacter hormaechei carrying blaNDM-1 and blaKPC-2 in China[END_REF][START_REF] Wu | Characterization of an Enterobacter cloacae Strain Producing both KPC and NDM Carbapenemases by Whole-Genome Sequencing[END_REF]. Enterobacter spp. are one of the most common Enterobacteriaceae resistant to third-generation cephalosporins, along with Escherichia coli and K. pneumoniae [START_REF] Lavigne | Enterobacter spp.: Update on Taxonomy, Clinical Aspects, and Emerging Antimicrobial Resistance[END_REF]. They are able to produce a low level of a chromosomal AmpC β-lactamase-type cephalosporinase that generates resistance to firstgeneration cephalosporins. Enterobacter spp. also often contain multiple resistance genes mediated by conjugative plasmids [START_REF] Lavigne | Enterobacter spp.: Update on Taxonomy, Clinical Aspects, and Emerging Antimicrobial Resistance[END_REF]. In our study, Eh22 was multidrug resistant due, in part, to the presence of a conjugative plasmid of incompatibility group IncHI2, which carried various antibiotic resistance genes, including two extended-spectrum β-lactamases and one cephalosporinase gene (blaCTX-M-3, blaSHV-12 and blaDHA-1) (data not published, whole-plasmid sequencing in progress). Eh22 remained sensitive to carbapenems (data not shown) (data not shown).. However, in recent years clinical ECC isolates resistant to carbapenems have been increasingly reported through the production of plasmid-mediated carbapenemases (1). In particular, E. hormaechei subsp. steigerwaltii strains of ST177 carrying the blaNDM-1 and blaKPC-2 carbapenemases were described [START_REF] Yang | Occurrence of Enterobacter hormaechei carrying blaNDM-1 and blaKPC-2 in China[END_REF][START_REF] Wu | Characterization of an Enterobacter cloacae Strain Producing both KPC and NDM Carbapenemases by Whole-Genome Sequencing[END_REF]. Eh22 also remained sensitive to colistin (see below) and to fosfomycin (MIC, 32 mg/liter), despite the presence of the fosA2 gene (with identical nucleotide sequence to that of GenBank accession number CP041733, except for a T393C silent mutation). FosA is widely distributed among various Gram-negative bacilli, including Enterobacter spp. [START_REF] Ito | Widespread Fosfomycin Resistance in Gram-Negative Bacteria Attributable to the Chromosomal fosA Gene[END_REF]. Thus, colistin is considered as one of the last resort treatment against these multidrug-resistant bacteria. Unfortunately, colistin resistance in ECC has been increasingly reported and the resistance molecular mechanisms are less known than in K. pneumoniae [START_REF] Guérin | Clusterdependent colistin hetero-resistance in Enterobacter cloacae complex[END_REF]. Very recently, mgrB mutations have been found in clinical strains of E. cloacae [START_REF] Dagher | Intestinal Carriage of Colistin Resistant Enterobacteriaceae at Saint Georges Hospital in Lebanon[END_REF][START_REF] Chavda | Coidentification of mcr-4.3 and blaNDM-1 in a Clinical Enterobacter cloacae Isolate from China[END_REF]. A missense mutation in MgrB (I10V) [START_REF] Olaitan | Mechanisms of polymyxin resistance: acquired and intrinsic resistance in bacteria[END_REF], as well as C39G, N42S, I45Y, W47V, W47S, *48K and *48Y changes were identified [START_REF] Cannatelli | MgrB inactivation is a common mechanism of colistin resistance in KPC-producing Klebsiella pneumoniae of clinical origin[END_REF]. Thus, it is important to confirm the role of MgrB in colistin resistance, and particularly in isolates of the C-VIII cluster, which are most frequently recovered from human clinical samples, with those of clusters C-III and C-VI [START_REF] Guérin | Clusterdependent colistin hetero-resistance in Enterobacter cloacae complex[END_REF][START_REF] Morand | Specific distribution within the Enterobacter cloacae complex of strains isolated from infected orthopedic implants. 8[END_REF].

Selection of an mgrB mutant from E. hormaechei subsp. steigerwaltii

The colistin MIC of Eh22 was 0.125 mg/liter without any heteroresistance phenomenon as described elsewhere [START_REF] Guérin | Clusterdependent colistin hetero-resistance in Enterobacter cloacae complex[END_REF]. Using the Population Analysis Profile (PAP) analysis (ref Guérin), a colistin resistant mutant named Eh22-Mut was selected on agar medium containing 8 mg/ liter of colistin with a frequency of 1 x 10 -8 . The colistin MIC of Eh22-Mut was 32 mg/liter. Sequence analysis of pmrA, pmrB, phoP and phoQ genes did not reveal any differences between Eh22 and Eh22-Mut. In contrast, the amplified region of mgrB (353 pb) spanning from 113 pb upstream of the initiation codon to 96 pb downstream of the stop codon (Fig. 1), showed one adenine deletion in the mgrB open reading frame of Eh22-Mut, leading to a truncated protein of 6 amino acids (VKKYAG) instead of 47 for the wild type MgrB.

Detection of mgrB inactivation in a clinical strain of K. pneumoniae

The inactivation of the PhoQ/PhoP negative regulator encoded by the mgrB gene has been identified to play a prominent role in polymyxin resistance in clinical isolates of K. pneumoniae and Klebsiella oxytoca [START_REF] Olaitan | Mechanisms of polymyxin resistance: acquired and intrinsic resistance in bacteria[END_REF]. In the literature, complementation assays with mgrB genes from wild-type K. pneumoniae or K. oxytoca restored full susceptibility to colistin, and confirm that MgrB expression was the key factor for this acquired resistance to colistin [START_REF] Cannatelli | MgrB inactivation is a common mechanism of colistin resistance in KPC-producing Klebsiella pneumoniae of clinical origin[END_REF][START_REF] Poirel | The mgrB gene as a key target for acquired resistance to colistin in Klebsiella pneumoniae[END_REF][START_REF] Jayol | Modulation of mgrB gene expression as a source of colistin resistance in Klebsiella oxytoca. 1[END_REF]. These complementation assays with wild-type mgrB in K. pneumoniae were performed with recombinant plasmids as well as low or high copies, without any significant differences [START_REF] Poirel | The mgrB gene as a key target for acquired resistance to colistin in Klebsiella pneumoniae[END_REF]. However, to check our procedure of MgrB complementation in E. subsp.

steigerwaltii hormaechei with recombinant constructions using a medium copy vector (pB-mfabI), we performed in parallel and under the same conditions, the mgrB complementation of K. pneumoniae. In a previous study, we have described two carbapenem-resistant strains of K. pneumoniae, Kp5196 and Kp5241, which were respectively susceptible and resistant to colistin [START_REF] Arpin | NDM-1-producing Klebsiella pneumoniae resistant to colistin in a French community patient without history of foreign travel[END_REF]. Both strains, isolated from the same patient at a two month interval, belonged to the sequence type ST15 and were clonal as demonstrated by analysis of their pulsotype [START_REF] Arpin | NDM-1-producing Klebsiella pneumoniae resistant to colistin in a French community patient without history of foreign travel[END_REF].

At that time, molecular analysis of the colistin resistance mechanism of Kp5241 had not been studied. Thus, given the data from the literature, pmrA/pmrB and phoP/phoQ genes were amplified and sequenced as described elsewhere [START_REF] Cannatelli | MgrB inactivation is a common mechanism of colistin resistance in KPC-producing Klebsiella pneumoniae of clinical origin[END_REF][START_REF] Cannatelli | In vivo emergence of colistin resistance in Klebsiella pneumoniae producing KPC-type carbapenemases mediated by insertional inactivation of the PhoQ/PhoP mgrB regulator[END_REF][START_REF] Jayol | Resistance to colistin associated with a single amino acid change in protein PmrB among Klebsiella pneumoniae isolates of worldwide origin[END_REF]. No changes were detected in both TCRS. The mgrB locus was targeted using three pairs of primers (Table S3, supplementary material) designed to amplify the coding region and the regions flanking the mgrB gene [START_REF] Cannatelli | MgrB inactivation is a common mechanism of colistin resistance in KPC-producing Klebsiella pneumoniae of clinical origin[END_REF]. Kp5196 showed amplicons with expected sizes of 110, 250 and 1,507 bp (PCR amplifications with the primer pair mgrB_ext_F/mgrB_ext_R is depicted in Fig. S1, supplementary material). In contrast, Kp5241 yielded no amplification products with the former primers, suggesting a larger deletion of the locus carrying the mgrB gene (Fig. S1).

Such large deletions have already been showed to be responsible for colistin resistance in K. pneumoniae [START_REF] Lippa | Feedback Inhibition in the PhoQ/PhoP Signaling System by a Membrane Peptide[END_REF].

Complementation of Eh22-Mut and Kp5241with the wild-type mgrB gene

Lippa and Goulian identified MgrB homologues in the genome sequences of various enterobacteria (32)(). However, regulation of TCRS, PhoP/PhoQ and PmrA/pmrB, may be different according to Enterobacteriaceae species. Indeed, examination of the available genomes of ECC revealed the absence of an homologous gene encoding for the PmrD connector, suggesting no cross-talk between both TCRS [START_REF] Guérin | Clusterdependent colistin hetero-resistance in Enterobacter cloacae complex[END_REF]. Thus, it is important to confirm the role of MgrB in ECC. In order to confirm whether the mgrB mutation found in Eh22-Mut is responsible for the colistin resistance in E. hormaechei subsp. steigerwaltii, the wild-type mgrB gene of Eh22 was inserted into pB-mfabI, giving the recombinant plasmid pB-mgrB/Eh which was used to transform Eh22-Mut. The colistin MICs of transformants showed a decreased resistance of 258-fold (0.062 mg/liter versus 16 mg/ liter without the mgrB gene or with the mutated mgrB gene) (Table 1). The decrease in MIC was comparable (290-fold, 0.11 mg/ liter vs 32 mg/ liter) for transformants from Kp5241 with the plasmid pB-mgrB/Kp (wildtype mgrB gene of Kp5196), allowing validation of our procedure (Table 1). Thus, our results show, for the first time, that MgrB is a key target for colistin resistance in Enterobacter species.

Comparison of the mgrB gene sequences

Alignment of MgrB sequences of Eh22 with 15 out of 18 ECC phylogroups (A to R) publicly available in Genbank databases (3), showed a high conservation of amino acids, in particular among the E. hormaechei meta-cluster to which Eh22 belongs (Fig. 2A)(4).

The alignment from colistin-susceptible K. pneumoniae, Kp5196 and E. hormaechei, Eh22, showed a difference of 12 amino acids with 74% identity and 93% similarity; the N-terminal sequence being the least conserved (Fig. 2B). This region with a hydrophobic stretch may function as a transmembrane domain [START_REF] Lippa | Feedback Inhibition in the PhoQ/PhoP Signaling System by a Membrane Peptide[END_REF]. Chavda et al. [START_REF] Chavda | Coidentification of mcr-4.3 and blaNDM-1 in a Clinical Enterobacter cloacae Isolate from China[END_REF] identified a missense mutation in MgrB (I10V), together with PmrA/PmrB modifications in E. cloacae, suggesting that these modifications may be responsible for colistin resistance [START_REF] Dagher | Intestinal Carriage of Colistin Resistant Enterobacteriaceae at Saint Georges Hospital in Lebanon[END_REF][START_REF] Chavda | Coidentification of mcr-4.3 and blaNDM-1 in a Clinical Enterobacter cloacae Isolate from China[END_REF]. Although a valine instead of an isoleucine is present in position 10 in the wild-type MgrB of E. coli K12 (Fig. 2B), we wanted to verify the possible consequence of such minor modifications in resistance acquisition (Fig. 2). As indicated in Table 1, the cross-complementation of mgrB wild-type genes between Eh22-Mut (with its truncated chromosomally-encoded MgrB of 6 amino acids) and Kp5241 (with its chromosomally-encoded deleted MgrB) restored similar colistin susceptibility in both species, confirming that the amino acid differences found between their respective MgrB have no impact on the structure and activity of the PhoP/PhoQ regulator system, and suggesting that the I10V change previously found in MgrB of E. cloacae is probably not the source of acquired resistance to colistin in E. cloacae.

Concluding remarks

Our data confirm for the first time the role of MgrB inactivation in colistin resistance in E. hormaechei subsp. steigerwaltii (cluster C-VIII); ECC being increasingly reported as the leading cause of resistant nosocomial infections. The knowledge of colistin resistance mechanisms is important because very few alternative therapeutic options are available for treatment of infection.

MATERIALS AND METHODS

Bacterial strains and plasmids

The ECC strain, Eh22 was identified by using the commercialized system Api20E gallery (bioMerieux), analysis by rDNA16S sequencing with the universal primers 27F/1492R (sequence overlapping the region from bases 71 to 1,482 of the complete sequence of 1,552 bp) [START_REF] Usadel | 16S/23S rRNA sequencing[END_REF], and the matrix-assisted laser desorption ionization-time of flight mass spectrometry identification (MALDI-TOF MS, Bruker Daltonics). Cluster Enterobacter membership was determined by partial sequencing of the hsp60 gene [START_REF] Hoffmann | Population genetics of the nomenspecies Enterobacter cloacae[END_REF][START_REF] Hoffmann | Enterobacter hormaechei subsp. oharae subsp. nov., E. hormaechei subsp. hormaechei comb. nov., and E. hormaechei subsp. steigerwaltii subsp. nov., three new subspecies of clinical importance[END_REF]. The ST was determined using the genomic sequence to query the MLST database of E. cloacae (http://pubmlst.org/ecloacae/) [START_REF] Miyoshi-Akiyama | Multilocus sequence typing (MLST) for characterization of Enterobacter cloacae[END_REF], and MLSA was performed using the primers and conditions as described previously [START_REF] Brady | Taxonomic evaluation of the genus Enterobacter based on multilocus sequence analysis (MLSA): proposal to reclassify E. nimipressuralis and E. amnigenus into Lelliottia gen. nov. as Lelliottia nimipressuralis comb. nov. and Lelliottia amnigena comb. nov., respectively, E. gergoviae and E. pyrinus into Pluralibacter gen. nov. as Pluralibacter gergoviae comb. nov. and Pluralibacter pyrinus comb. nov., respectively, E. cowanii, E. radicincitans, E. oryzae and E. arachidis into Kosakonia gen. nov. as Kosakonia cowanii comb. nov., Kosakonia radicincitans comb. nov., Kosakonia oryzae comb. nov. and Kosakonia arachidis comb[END_REF]. Two previously described K. pneumoniae, Kp5196 and Kp5241, respectively susceptible and resistant to colistin, were included in our study [START_REF] Arpin | NDM-1-producing Klebsiella pneumoniae resistant to colistin in a French community patient without history of foreign travel[END_REF]. E. coli DH5α was used for cloning and sub-cloning experiments of mgrB genes. pB-mfabI is a pBR322 vector (4.4 kb, New England Biolabs), which carries the mfabI gene (mutant fabI) affecting the binding of triclosan to FabI allow the bacteria (E. coli or E. cloacae complex) to grow in the presence of 4 mg/liter of triclosan [START_REF] Jang | A novel selection marker for efficient DNA cloning and recombineering in E. coli[END_REF]. The mfabI gene was inserted between the ScaI and PvuI restriction sites of the pBR322 vector, inactivating the ß-lactamase gene, blaTEM-1. pBR322 is described in the literature as a medium copy vector (~ 15-20 copies by cell). The pGEM-T Easy TM vector (Promega) was used for PCR product cloning.

Antimicrobial susceptibility testing

Minimum inhibitory concentrations (MICs) of colistin (Sigma Chemical co.) were determined by the microdilution reference method using Mueller-Hinton broth adjusted for divalent cations (CA-MHB, BioRad) in accordance with the European Committee on Antimicrobial Susceptibility Testing (EUCAST) guidelines (http://www.eucast.org/). Fosfomycin MIC was determined by the E-test method (BioMérieux). Fosfomycin and colistin MICs were interpreted as indicated by the EUCAST breakpoint tables; For colistin MICs, isolates with MICs of ≤2 mg/liter were categorized as susceptible, whereas those with MICs of >2 mg/liter were categorized as resistant.

Selection of in vitro colistin mutants

Selection of mutants from Eh22 were carried out by plating a high inoculum (~ 10 10 colony forming units, CFU) on Luria-Bertani (LB) agar plates containing 2 to 32 mg/liter of colistin, as previously described for the analysis of PAP, analysis, as described elsewhere [START_REF] Guérin | Clusterdependent colistin hetero-resistance in Enterobacter cloacae complex[END_REF].

PCR amplification, sequencing and plasmid purification

Plasmids were purified by using the Macherey-Nagel Nucleospin plasmid kit according to the supplier recommendations. PCR experiments of pmrA, pmrB, phoP, phoQ and mgrB genes using specific primers (Table S3, Supplementary information), and amplicons were verified by Sanger's sequencing (MWG operon society, https://www.eurofinsgenomics.eu). The nucleotide and deduced protein sequences were analyzed at the NCBI website (http://www.ncbi.nlm.nih.gov) using the Basic Local Alignment Search Tool (BLAST) program.

TABLE and FOOTNOTES

Table 1. Colistin MIC of strains and transformants of E. hormaechei and K. pneumoniae. (a) Mean of at least three independent experiments. In E. hormaechei meta-cluster, three groups have unavailable MgrB sequences: F (E. mori), O and R (E. cloacae complex).

  (b) SD, standard deviation indicated in parenthesis.

( c )

 c Values obtained without triclosan. For the other experiments, the values are obtained with a final concentration of 0.5 mg/liter of triclosan used for plasmid maintenance.

( d )

 d Values in accordance with Arpin et al.[START_REF] Arpin | NDM-1-producing Klebsiella pneumoniae resistant to colistin in a French community patient without history of foreign travel[END_REF].

( e )

 e Plasmid without or with mutated mgrB.(f) Non-significant differences (P-value of 0.2) by using a Student unpaired bilateral t-test.-= without plasmid. Nd = not determined.PlasmidMean of colistin MIC (mg/liter)(SD)(a, b)

FIG 1 .

 1 FIG 1. Sequences of the Eh22 mgrB open reading frame and upstream/downstream

FIG 2 .

 2 FIG 2. MgrB alignment comparison of Eh22.

ACKNOWLEDGMENTS

We warmly thank Sabine Aillerie and Nathalie Peyron for their technical assistance. We thank Véronique Dubois for allowing us access to the device (MALDI-TOF) of the Bacteriology Laboratory of University Hospital of Bordeaux. We thank Christine Reix for the English correction.

.

mgrB gene cloning and complementation experiments

After ligation into the pGEM-T Easy TM vector, PCR products of mgrB obtained after amplification with primer pairs: EhmgrB_F113 and EhmgrB_R96 (for Eh22) and KpmgrB_F112 and KpmgrB_R88 (for Kp5196) (Table S3), were used to transform E. coli DH5α chemically competent cells. The selection of recombinant clones was carried out on LB agar medium supplemented with 100 mg/liter of ampicillin (Sigma Chemical Co.), 0.5 mM of isopropyl-β-D-thiogalactopyranoside (IPTG, Eurobio) and 80 g/mL of 5-bromo-4-chloro-3indolyl-β-D-galactopyranoside (X-Gal, MP Biomedical). After plasmid extraction and EcoRI digestion (Promega), fragments containing mgrB gene were purified on agarose gel and extracted using the "Gel and PCR clean-up" kit (Macherey-Nagel). The insert was cloned into the EcoRI site of the linearized and dephosphorylated plasmid pB-mfabI using T4 DNA ligase (Promega). After E. coli DH5 transformation, bacteria were selected on LB agar medium with tetracycline (15 mg/liter). Recombinant plasmids, with mgrB inserted in the same orientation, were verified by sequencing analysis using the primers Tetra-161_F and Tetra+95_R (Table S3). Eh22-Mut (colistin resistant mutant of Eh22) and Kp5241 were transformed with mgrB constructs using chemically competent cells prepared by CaCl2 treatment, followed by heat shock. Transformants were selected on MH agar plates containing 4 mg/liter of triclosan. We have no relevant financial disclosures or funding to declare.

(B) MgrB alignments of E. coli K12, Eh22 and K. pneumoniae Kp5196.

. The putative transmembrane domain of E. coli MgrB is underlined according to Lippa et Goulian [START_REF] Lippa | Feedback Inhibition in the PhoQ/PhoP Signaling System by a Membrane Peptide[END_REF], and the amino acid at position 10 is indicated in bold.

The MgrB sequences of Eh22 (A) and E. coli K12 (B) are given and only different residues are shown for the other alignments.