biomolecules

Article Calculation of the Geometries and Infrared Spectra of the Stacked Cofactor Flavin Adenine Dinucleotide (FAD) as the Prerequisite for Studies of Light-Triggered Proton and Electron Transfer

Martina Kieninger 1,*, Oscar N. Ventura 1 and Tilman Kottke 2

1 CCBG, DETEMA, Facultad de Química, Isidoro de María 1616, 11800 Montevideo, Uruguay; [email protected] 2 Department of Chemistry, Physical and Biophysical Chemistry, Bielefeld University, Universitätsstr. 25, 33615 Bielefeld, Germany; [email protected] * Correspondence: [email protected]; Tel.: +598-2-2924-8396



Received: 23 December 2019; Accepted: 27 March 2020; Published: 9 April 2020


Abstract: Flavin cofactors, like flavin adenine dinucleotide (FAD), are important electron shuttles in living systems. They catalyze a wide range of one- or two-electron redox reactions. Experimental investigations include UV-vis as well as infrared spectroscopy. FAD in aqueous solution exhibits a significantly shorter excited state lifetime than its analog, the flavin mononucleotide. This finding is explained by the presence of a “stacked” FAD conformation, in which isoalloxazine and adenine moieties form a π-complex. Stacking of the isoalloxazine and adenine rings should have an influence on the frequency of the vibrational modes. Density functional theory (DFT) studies of the closed form of FAD in microsolvation (explicit water) were used to reproduce the experimental infrared spectra, substantiating the prevalence of the stacked geometry of FAD in aqueous surroundings. It could be shown that the existence of the closed structure in FAD can be narrowed down to the presence of only a single water molecule between the third hydroxyl group (of the ribityl chain) and the N7 in the adenine ring of FAD.

Keywords: stacked flavin adenine dinucleotide (FAD) in microsolvation; vibrational spectra; supramolecular orbitals

1. Introduction Flavin cofactors, like flavin adenine dinucleotide (FAD), are important electron shuttles in living systems. As components of flavoenzymes, flavin cofactors catalyze a wide range of one- or two-electron redox reactions. In addition, flavoproteins also act as photoreceptors and photoenzymes. Photoreception involves mostly three families of flavoproteins: LOV (light, oxygen, voltage) proteins [1], cryptochromes [2] and BLUF (sensors of blue light using flavin) proteins [3]. These proteins act as blue-light-receptors in many organisms. Moreover, cryptochrome has been found to enable flies to detect magnetic fields [4] and has been discussed in connection with a putative role in the magnetoreception of migratory birds [5]. Photoenzymes with flavin cofactor are DNA photolyases, which repair UV light-damages of DNA [6], and the fatty acid decarboxylase [7]. In many flavoproteins, the cofactor is not covalently bound but in a dynamic equilibrium with the solution [8]. For FAD, different conformations have been found. In aqueous solution, predominantly a “stacked”, closed conformation of isoalloxazine and adenine rings of FAD is present and attributed to π–π interactions [9]. In most enzymes, BLUF and some LOV proteins, the FAD is bound in the extended,

Biomolecules 2020, 10, 573; doi:10.3390/biom10040573 www.mdpi.com/journal/biomolecules Biomolecules 2020, 10, 573 2 of 15 open conformation. In cryptochromes and photolyases, FAD adopts a “U-shaped” conformation in between the open and closed conformation. To gain deeper insight in the mechanisms of the electron transfer within flavoproteins and in solution, the study of FAD—experimental and computational—is an ongoing essential prerequisite. Experimental investigations done with respect to flavin cofactors include UV/vis, fluorescence and infrared spectroscopy. The excited-state behavior of FAD has been studied in aqueous solution (D2O) by employing time-resolved fluorescence up-conversion and transient absorption spectroscopy [10,11]. They found that FAD in aqueous solution exhibits significantly shorter excited state lifetime than its analog flavin mononucleotide (FMN). This result was explained by the presence of the “stacked” FAD conformation. The reason for the fast deactivation of the excited state in FAD has been explained by the existence of an intramolecular electron transfer from adenine to the isoalloxazine. In the infrared spectral range, the cofactors FAD and flavin mononucleotide (FMN) were investigated in aqueous medium (H2O) by Fourier transform infrared spectroscopy [12]. Transmission and attenuated total reflection (ATR) configuration were employed in direct comparison. Absorption 1 spectra in the range of 920–1800 cm− were determined and the carbonyl vibrations were resolved 1 at 1661 and 1712 cm− . As stated by Spexard et al. for FAD [12], the vibrational spectrum of flavin overlaps with the spectrum of adenine. Additional stacking of the isoalloxazine and adenine rings should occur, which might be visible as an influence on the vibrational modes [12]. This assumption is substantiated by the observations of Li et al. [13] using time-resolved mid-IR transient absorption spectroscopy. This study provided evidence for an electron transfer from adenine to isoalloxazine by a 1 bleach of the adenine stretch at 1623 cm− , which rises with 1.1 ps and decays with 9 ps. The addition of polar aprotic solvents such as dimethyl sulfoxide (DMSO) is altering the IR-spectra detected to resemble those of FMN, which was interpreted as a breaking of the π-stacked complex and production of a predominantly “open” conformer with a long excited-state lifetime. The model of Li et al. [13,14] has been adopted by Sengupta et al. [15] in their investigation of pH-dependent dynamic behavior of FMN and FAD on a femtosecond to nanosecond time scale. More recently the pH-depending prevalence of the stacked form of FAD proposed by Li et al. [13] has been used as a model concept in the publication of Bubniene et al. [16] about the fluorescence quenching-based evaluation of a glucose oxidase composite with a conducting polymer—polypyrrole: The stacked form of FAD is thought to be responsible for the fast quenching of the FAD fluorescence, which could not unfold freely in this specific environment as the authors stated. Despite theoretical studies which include lumiflavin, riboflavin and FMN as a model of FAD–flavoprotein interactions in proteins [17–20], theoretical studies of the stacked form of FAD as well as studies of the unfolding process from the closed to the open conformer are still missing. The present work aims to fill this gap.

2. Materials and Methods Molecular dynamic (MD) [21] runs were performed with both, open and closed structures using AMBER [22] in water (1000 water molecules surrounding the FAD). The conditions employed were 100 ps with 500 ps runtime at a step size of 0.01 ps, the starting temperature was 0 K, the simulation temperature 298 K. In order to compare the structures of FAD in aqueous solution with structures which may be adopted by FAD in polar aprotic solvents, the MD calculations were repeated with DMSO (replacing the water molecules by DMSO molecules). The resulting structures of the MM calculations were taken as starting points of geometry optimizations with the semi-empirical PM6 method—starting with 100 explicit solvent molecules (water and DMSO, respectively). This initial step was followed by calculations which gradually reduced the number of the solvent molecules in order to build models of FAD in solution and microsolvation while keeping the geometrical properties of the solvent-FAD system intact. The resulting systems served as starting geometries of FAD in microsolvation for density functional theory (DFT) calculations [23]. Biomolecules 2020, 10, 573 3 of 15

Biomolecules 2020, 10, x FOR PEER REVIEW 3 of 15 DFT studies on FAD-solvent systems, e.g., in microsolvation with up to 15 explicit water molecules and using theDFT continuous studies on surface FAD-solvent charge systems, PCM method e.g., in followed.microsolvation The M06with potential up to 15 [explicit24] with water the 6-31G (d,p) basismolecules set and and the using ultrafine the continuous grid was surface used to charge perform PCM vibrational method followed. studies The of theM06 FAD-water potential [24] systems. with the 6-31G (d,p) basis set and the ultrafine grid was used to perform vibrational studies of the 3. ResultsFAD-water systems.

3.1. MD3. Results Calculations to Obtain Starting Geometries of FAD in the Closed Geometry

The3.1. calculationsMD Calculations were to Obtain performed Starting in Geometries order to of provide FAD in the starting Closed Geometry geometries for the calculations of FAD-water complexes with DFT methods. The focus was not on observing the course of geometry The calculations were performed in order to provide starting geometries for the calculations of changes and folding in FAD during MD. Instead the focus was on FAD in water (H O) to provide FAD-water complexes with DFT methods. The focus was not on observing the course of 2geometry starting geometries for reproducing the IR spectrum. As a starting geometry of the open conformation, changes and folding in FAD during MD. Instead the focus was on FAD in water (H2O) to provide the geometrystarting of geometries FAD as a for free reproducing ligand was chosen the IR as spectrum. it is realized As a in starting 1948 systems geometry and of listed the inopen the PDB databaseconformation, (https://www4.rcsb.org the geometry of /FADligand as /aFAD free ).ligand The was closed chosen structure as it is realized was obtained in 1948 systems by scanning and the dihedrallisted angles in the in PDB the database ribityl and (https://www4.rcsb.org/ligand/FAD). adenosine-phosphate part of theThe open closed FAD structure in search was obtained of a structure with parallelby scanning planes the of dihedral adenine angles and isoalloxazine. in the ribityl and The adenosine open as well-phosphate as the closedpart of FAD the open were FAD surrounded in by 1000search water of moleculesa structure with using parallel the features planes of of aden theine periodic and isoalloxazine. boundary conditionsThe open as insidewell as thethe closed Hyperchem FAD were surrounded by 1000 water molecules using the features of the periodic boundary Program. Both structures, the open as well as the closed FAD in water maintained their structures conditions inside the Hyperchem Program . Both structures, the open as well as the closed FAD in throughoutwater maintained the runtime their (500 structures ps) of thethroughout MD calculations the runtime (Figure (500 ps)1 ofshows the MD the calculations situation for(Figure the 1 closed FAD).shows Replacing the situation water for by the closed polar FAD). aprotic Replacing solvent water DMSO by the (i.e., polar replacing aprotic solvent the water DMSO molecules (i.e.., by DMSOreplacing molecules) the water did not molecules change by the DMSO geometry molecules) of the did open not FAD,change but the immediatelygeometry of the opened open FAD, the closed structurebut immediately (Figure2). opened the closed structure (Figure 2).

Figure 1. Result of the molecular dynamic (MD) calculation of flavin adenine dinucleotide (FAD) in BiomoleculesFigure 20 1.20 Result, 10, x FOR of the PEER molecular REVIEW dynamic (MD) calculation of flavin adenine dinucleotide (FAD) in4 of 15 waterwater using using AMBER. AMBER.

FigureFigure 2. Result 2. Result of theof the MD MD calculation calculation ofof FADFAD in dimethyl dimethyl sulfoxide sulfoxide (DMSO) (DMSO) using using AMBER. AMBER.

This first step was inspired by Visser et al. [25], who detected basically 4 different closed structures of FAD. Since each two of them are basically identical and since the “upside down” geometry (with respect to the geometry shown in Figure 1) stacks the hydrophobic part of the isoalloxazine with the amine-group of adenine, the “upside down geometry” opens during the optimization on the DFT level of theory and was therefore discarded from further investigations. In a second step water molecules in a more than 2.5 Å distance from the FAD were removed, the resulting geometries (open and closed FAD) were optimized on the semiempirical level (PM6). To obtain starting geometries for the subsequent modelling of FAD in micro solvation and the calculation of the respective IR spectra with DFT, the number of participating water molecules was even further reduced: In the end the model included water molecules at the positions N1, C2, N3, C4, and N5 of the isoalloxazine moiety, one water molecule between N7 of adenine and the ribityl chain which turned out to be very important for keeping the FAD structure in its closed geometry, two additional water molecules as a second water clip between the amine group of adenine and the isoalloxazine ring at C4 as well as a third water clip between the amine of adenine and C2 and N1, respectively. In the following the geometry and the role of each of the water molecules in the FAD-water complex will be shown and discussed.

3.2. DFT Studies on the Closed Complex FAD-Water and the Role of the Water Molecules in the FAD-Water Complex

3.2.1. The First “Water Clip” (Figure 3) Biomolecules 2020, 10, 573 4 of 15

This first step was inspired by Visser et al. [25], who detected basically 4 different closed structures of FAD. Since each two of them are basically identical and since the “upside down” geometry (with respect to the geometry shown in Figure1) stacks the hydrophobic part of the isoalloxazine with the amine-group of adenine, the “upside down geometry” opens during the optimization on the DFT level of theory and was therefore discarded from further investigations. In a second step water molecules in a more than 2.5 Å distance from the FAD were removed, the resulting geometries (open and closed FAD) were optimized on the semiempirical level (PM6). To obtain starting geometries for the subsequent modelling of FAD in micro solvation and the calculation of the respective IR spectra with DFT, the number of participating water molecules was even further reduced: In the end the model included water molecules at the positions N1, C2, N3, C4, and N5 of the isoalloxazine moiety, one water molecule between N7 of adenine and the ribityl chain which turned out to be very important for keeping the FAD structure in its closed geometry, two additional water molecules as a second water clip between the amine group of adenine and the isoalloxazine ring at C4 as well as a third water clip between the amine of adenine and C2 and N1, respectively. In the following the geometry and the role of each of the water molecules in the FAD-water complex will be shown and discussed.

3.2. DFT Studies on the Closed Complex FAD-Water and the Role of the Water Molecules in the FAD-Water Complex

3.2.1. The First “Water Clip” The water molecule between the adenine and the isoalloxazine forms the clip which is responsible for keeping the FAD in the correctly folded structure (shown in Figure3): This water molecule is located between the third hydroxyl group (of the ribityl chain) and the N7 in the purine ring: The distance between the oxygen of the “clipping” water and the hydrogen of the hydroxyl group at position O30 in the ribityl chain of the riboflavin moiety amounts to 1.86 Å, the distance between the hydrogen of the “clipping”Biomolecules 20 water20, 10, x and FOR N7 PEER of REVIEW purine in the ADP moiety is 1.89 Å, respectively. 5 of 15

FigureFigure 3. WaterWater clip 1 is formed by a water molecule between N7 of adenine and the O3O3′0 hydroxylhydroxyl of thethe ribityl ribityl chain. chain.

TheWithout water the molecule presence of between this water the molecule adenine FAD and will the adopt isoalloxazine an open structure: forms the This clip was which tested by is responsibleremoving the for water keeping molecule the FAD located in the between correctly N7 andfolded the structure: ribityl chain This from water the FAD-water molecule is complex. located betweenPerforming the athird new geometryhydroxyl optimizationgroup (of the of ribityl the otherwise chain) and unchanged the N7 in FAD-water the purine complex ring: The shows distance that between the oxygen of the “clipping” water and the hydrogen of the hydroxyl group at position O3 ′ in the ribityl chain of the riboflavin moiety amounts to 1.86 Å , the distance between the hydrogen of the “clipping” water and N7 of purine in the ADP moiety is 1.89 Å , respectively. Without the presence of this water molecule FAD will adopt an open structure: This was tested by removing the water molecule located between N7 and the ribityl chain from the FAD-water complex. Performing a new geometry optimization of the otherwise unchanged FAD-water complex shows that the FAD will adopt a T-shaped open conformation: The vibrational spectrum of this open structure was compared with the closed structure (see “Vibrational spectra”).

3.2.2. The Second “Water Clip” A second “clip” in the FAD-water complex was detected, which is less important for keeping the FAD-water complex in a closed structure. This was verified by removing the second clip while the “first water-clip” between the adenine N7 and the ribityl was kept intact: The structure was keeping its closed geometry without the second “water clip”. This second “water-clip” consists of two water molecules and connects the adenine to the isoalloxazine in the following way: The first water molecule is bound to the amino-group of the adenine, the second water molecule spans the bridge between the water-adenine-complex and the C4O group of the isoalloxazine (Figure 4): Biomolecules 2020, 10, 573 5 of 15 the FAD will adopt a T-shaped open conformation: The vibrational spectrum of this open structure was compared with the closed structure (see “Vibrational spectra”).

3.2.2. The Second “Water Clip” A second “clip” in the FAD-water complex was detected, which is less important for keeping the FAD-water complex in a closed structure. This was verified by removing the second clip while the “first water-clip” between the adenine N7 and the ribityl was kept intact: The structure was keeping its closed geometry without the second “water clip”. This second “water-clip” consists of two water molecules and connects the adenine to the isoalloxazine in the following way: The first water molecule is bound to the amino-group of the adenine, the second water molecule spans the bridge between the water-adenine-complex and the Biomolecules 2020, 10, x FOR PEER REVIEW 6 of 15 C4O group of the isoalloxazine (Figure4):

FigureFigure 4. 4.FAD-water FAD-water complex complex formed formed by by two two water water molecules molecules bridging bridging the the C4O C4O of of isoalloxazine isoalloxazine and and thethe amino amino group group (N6A) (N6A) of of adenine. adenine. 3.2.3. Water Molecules Surrounding Isoalloxazine at the C2, N3, C4, and N5 Positions 3.2.3. Water Molecules Surrounding Isoalloxazine at the C2, N3, C4, and N5 Positions As shown in Figure5, this model was completed by adding water molecules surrounding the As shown in Figure 5, this model was completed by adding water molecules surrounding the isoalloxazine at the positions C2O, N3H, C4O, and N5. The additional water molecules at C2O and isoalloxazine at the positions C2O, N3H, C4O, and N5. The additional water molecules at C2O and C4O are important for calculating the vibrational spectrum since they may shift the bands compared to C4O are important for calculating the vibrational spectrum since they may shift the bands compared a spectrum calculated without solvation at these positions. to a spectrum calculated without solvation at these positions.

Figure 5. Microsolvation with explicit water at positions C2O, N3H, C4O, and N5 of the isoalloxazine ring.

3.2.4. The Third “Water Clip” To model a FAD complex able to perform intramolecular electron transfer suggested by Li and Glusac [13,14] the FAD-water model shown above in Figure 4 was enhanced by including an additional water molecule between the amine-group of adenine and N1 in isoalloxazine of the complex (Figure 6). This additional third water clip proved to be important since it lowers the Biomolecules 2020, 10, x FOR PEER REVIEW 6 of 15

Figure 4. FAD-water complex formed by two water molecules bridging the C4O of isoalloxazine and the amino group (N6A) of adenine.

3.2.3. Water Molecules Surrounding Isoalloxazine at the C2, N3, C4, and N5 Positions As shown in Figure 5, this model was completed by adding water molecules surrounding the isoalloxazine at the positions C2O, N3H, C4O, and N5. The additional water molecules at C2O and C4O are important for calculating the vibrational spectrum since they may shift the bands compared Biomolecules 2020, 10, 573 6 of 15 to a spectrum calculated without solvation at these positions.

FigureFigure 5.5. MicrosolvationMicrosolvation with with explicit explicit water water at positions at positions C2O, N3H, C2O, C4O, N3H, and C4O,N5 of andthe isoalloxazine N5 of the isoalloxazinering. ring.

3.2.4.3.2.4. TheThe ThirdThird “Water “Water Clip” Clip” ToTo model model a a FAD FAD complex complex able able to to perform perform intramolecular intramolecular electron electron transfer transfer suggested suggested by by Li Li and and GlusacGlusac [ 13[13,14],14] the the FAD-water FAD-water model model shown shown above above in Figure in 4 Figure was enhanced 4 was enhanced by including by an including additional an wateradditional molecule water between molecule the amine-group between the of amine adenine-group and N1 of inadenine isoalloxazine and N1 of in the isoalloxazine complex (Figure of 6 the). Biomolecules 2020, 10, x FOR PEER REVIEW 7 of 15 Thiscomplex additional (Figure third 6). water This clip additional proved tothird be important water clip since proved it lowers to be the important distance between since it thelowers planes the substantially from 3.81 Å (for the model without this specific water molecule) to 3.3 Å and 3.15 Å for thedistance two structures between resulting: the planes substantially from 3.81 Å (for the model without this specific water molecule) to 3.3 Å and 3.15 Å for the two structures resulting:

Structure 1 Structure 2

FigureFigure 6. 6.Structures Structures of of stacked stacked FAD FAD with with clip clip 3, 3, a a water water molecule molecule bridging bridging the the N6A N6A amine amine group group of of adenineadenine and and N1 N1 (structure (structure 1) 1) or or C2 C2=O=O of of isoalloxazine isoalloxazine (structure (structure 2). 2).

InIn structure structure 1 the 1 water the water molecule molecule connects connects the amine the group amine of adenine group of with adenine the N1 of with isoalloxazine, the N1 of whileisoalloxazine, the water while in structure the water 2 links in structure the amine 2 links group the with amine C2O. group with C2O. OnOn both both structures structures geometry geometry optimizations optimizations have have been been performed performed in in the the singlet singlet as as well well as as in in the the triplettriplet state: state: The The total total energies energies (in (in atomic atomic units) units) of of the the triplet triplet states states are are about about 50 50 to to 30 30 kcal kcal higher higher than than thethe corresponding corresponding singlet singlet states states (Table (Table1): 1):

Table 1. Total energies of structure 1 and structure 2 in the singlet and triplet states in a.u. Energy differences between the structures as well as the multiplicities are given in kcal.

Singlet Triplet Diff (Triplet−Singlet) Structure 1 −3885.38051400 a.u. −3885.30052427 a.u. 50.19 kcal Structure 2 −3885.37366640 a.u. −3885.31405627 a.u. 37.41 kcal Diff (Struc1−Struc2) −4.29 kcal −8.49 kcal The formation of the hydrogen bond between C2O and the amine group of adenine instead of forming the hydrogen bond with N1 means a shifting of the two heterocycles of adenine and isoalloxazine in FAD towards a higher overlap of the two planes as shown in Figure 7.

Structure 1 Structure 2

Figure 7. Overlap of the pyrimidine ring of adenine (green) with the pyrazine ring (ring II) of isoalloxazine (red).

This is reflected by the distance between the isoalloxazine and the adenine which amounts to 3.3 Å for structure 1 and 3.15 Å for structure 2. Nevertheless, the third water clip in both structures improves the overlap of the two ring systems substantially (Figure 8): Biomolecules 2020, 10, x FOR PEER REVIEW 7 of 15

distance between the planes substantially from 3.81 Å (for the model without this specific water molecule) to 3.3 Å and 3.15 Å for the two structures resulting:

Structure 1 Structure 2

Figure 6. Structures of stacked FAD with clip 3, a water molecule bridging the N6A amine group of adenine and N1 (structure 1) or C2=O of isoalloxazine (structure 2).

In structure 1 the water molecule connects the amine group of adenine with the N1 of Biomoleculesisoalloxazine,2020, 10while, 573 the water in structure 2 links the amine group with C2O. 7 of 15 On both structures geometry optimizations have been performed in the singlet as well as in the triplet state: The total energies (in atomic units) of the triplet states are about 50 to 30 kcal higher than Table 1. Total energies of structure 1 and structure 2 in the singlet and triplet states in a.u. Energy the corresponding singlet states (Table 1): differences between the structures as well as the multiplicities are given in kcal.

Table 1. Total energies of structureSinglet 1 and structure 2 in Triplet the singlet and Ditripletff (Triplet states inSinglet) a.u. Energy − differencesStructure between 1 the structures3885.38051400 as well as a.u. the multiplicities3885.30052427 are a.u.given in kcal. 50.19 kcal − − Structure 2 3885.37366640Singlet a.u. 3885.31405627Triplet a.u. Diff 37.41 (Triplet kcal−Singlet) − − DiStructureff (Struc1 1Struc2) −3885.380514004.29 kcal a.u. −3885.300524278.49 kcal a.u. 50.19 kcal − − − Structure 2 −3885.37366640 a.u. −3885.31405627 a.u. 37.41 kcal TheDiff formation (Struc1−Struc2) of the hydrogen −4.29 bond kcal between C2O−8.49 and kcal the amine group of adenine instead of formingThe formation the hydrogen of the bondhydrogen with bond N1 means between a shifting C2O and of the the amine two heterocycles group of adenine of adenine instead and of isoalloxazineforming the in hydrogen FAD towards bond a with higher N1 overlap means of a the shifting two planes of the as two shown heterocycles in Figure7 . of adenine and isoalloxazine in FAD towards a higher overlap of the two planes as shown in Figure 7.

Structure 1 Structure 2

FigureFigure 7. 7. Overlap of the pyrimidine pyrimidine ring ofof adenine adenine (green) (green) with with the the pyrazine pyrazine ring ring (ring (ring II) II) of of isoalloxazineisoalloxazine (red). (red).

ThisThis isis reflectedreflected by the distance distance between between the the isoalloxazine isoalloxazine and and the the adenine adenine which which amounts amounts to 3.3 to 3.3Å for Å for structure structure 1 and 1 and 3.15 3.15 Å Å for for structure structure 2. 2. Nevertheless, Nevertheless, the the third third water clip inin both both structures structures improvesimprovesBiomolecules the the 2020 overlapoverlap, 10, x FOR of of PEER the the two twoREVIEW ring ring systems systems substantially substantially (Figure (Figure8 ):8): 8 of 15

FigureFigure 8. 8.Overlap Overlap of theof the ring ring systems systems without without the 3rd the water 3rd water clip: adenineclip: adenine (green) (green) and isoalloxazine and isoalloxazine (red). (red). More important than the interplanar distances are the changes in the distances between C4a and C10a, N1,More and important C2O as wellthan as the between interplanar C4O distances and N5 in are the the isoalloxazine changes in ring.the distances Those distances between depend C4a and onlyC10a, on N1 the, and state C2O (triplet as well or singlet)as between and C4O were and found N5 toin bethe independentisoalloxazine ofring. the Those geometry distances (structure depend 1 andonly structure on the state 2). The (triplet distances or singlet) are compared and were with found the resultsto be independent for the FAD-water of the complexgeometry without (structure the 1 clippingand structure water from2). The the distances third “clip”. are compared The values with are the given results in the for following the FAD- Tablewater2 :complex without the clipping water from the third “clip”. The values are given in the following Table 2:

Table 2. Shortening and elongation of bonds in the triplet vs. singlet state.

flavin ring: N1, C10a, C4a, flavin C4a – C10a flavin C4a – N5 flavin C10a-N1 N5

FAD triplet 1.40 Å 1.35 Å 1.32 Å FAD singlet 1.44 Å 1.30 Å 1.30 Å FAD without water clip 1.44 Å 1.31 Å 1.29 Å

3.2.5. Molecular Orbitals—HOMO/LUMO Since the geometrical properties of the FAD-water complex may be reflected by the molecular orbitals, the LUMO and HOMO as well as other molecular orbitals of interest are shown in the following graph according to their relative energies (Figure 9): Structure 1 refers to the geometry including the hydrogen bridge between the amino group of adenine towards the N1 in isoalloxazine, while structure 2 refers to the geometry featuring the hydrogen bridge between the amino group of adenine towards the C2O in isoalloxazine. BiomoleculesBiomoleculesBiomolecules 2020, 10, x2020 FOR 2020, 10 PEER, 10, x, FORx REVIEWFOR PEER PEER REVIEW REVIEW 8 of 15 8 of 8 of15 15

Biomolecules 2020, 10, x FOR PEER REVIEW 8 of 15

Figure 7.Figure FigureOverlap 7. 7. Overlap ofOverlap the pyrimidine of of the the pyrimidine pyrimidine ring of adeninering ring of of adenine (green) adenine with(green) (green) the with pyrazine with the the pyrazine ring pyrazine (ring ring ring II) (ring of (ring II) II) of of isoalloxazineisoalloxazineisoalloxazine (red). (red). (red). Figure 7. Overlap of the pyrimidine ring of adenine (green) with the pyrazine ring (ring II) of isoalloxazine (red). This is reflectedThisThis is isreflected reflectedby the distance by by the the distance betweendistance between thebetween isoalloxazine the the isoalloxazine isoalloxazine and the andadenine and the the adenine which adenine amounts which which amounts amountsto 3.3 to to 3.3 3.3 Å for structure 1 and 3.15 Å for structure 2. Nevertheless, the third water clip in both structures Å for structureÅ forThis structure is 1 reflected and 3.151 byand Å the for3.15 distance structure Å for between structure 2. Nevertheless, the 2. isoalloxazine Nevertheless, the andthird the the water adeninethird clip water which in bothclip amounts instructures both to structures3.3 improvesÅimproves forimproves the structure overlap the the 1overlap of overlapand the 3.15 two of of theÅ ring thefor two systemstwostructure ring ring systems substantially systems 2. Nevertheless, substantially substantially (Figure the (Figure8):third (Figure water 8): 8): clip in both structures improves the overlap of the two ring systems substantially (Figure 8):

Figure 8.Figure OverlapFigure 8. 8. Overlapof Overlap the ring of of thesystems the ring ring systemswithout systems withoutthe without 3rd water the the 3 rd clip:3 rdwater water adenine clip: clip: adenine(green) adenine and(green) (green) isoalloxazine and and isoalloxazine isoalloxazine Figure 8. Overlap of the ring systems without the 3rd water clip: adenine (green) and isoalloxazine (red). (red).(red). (red). More importantMoreMore important important than the than interplanar than the the interplanar interplanar distances distances distances are the changesare are the the changes in changes the distances in in the the distances distances between between C4abetween and C4a C4a and and More important than the interplanar distances are the changes in the distances between C4a and C10a, N1,C10a,C10a, and N1, C2O N1, and andas C2Owell C2O as as betweenwell well as as between C4Obetween and C4O C4ON5 andin and the N5 N5isoalloxazine in in the the isoalloxazine isoalloxazine ring. Those ring. ring. distances Those Those distances distances depend depend depend C10a, N1, and C2O as well as between C4O and N5 in the isoalloxazine ring. Those distances depend onlyonly on on the the state state (triplet (triplet or or singlet) singlet) and and were were found found to to be be independent independent of of the the geometry geometry (structure (structure 1 1 only ononly the on state the state(triplet (triplet or singlet) or singlet) and andwere were found found to beto beindependent independent of of the the geometry geometry (structure (structure 11 and structure 2). The distances are compared with the results for the FAD-water complex without the and structureandand structure structure 2). The 2). distances 2).The The distances distances are compared are arecompared compared with with the with the results results the forresults for the the FAD-waterfor FAD-water the FAD-water complex complex complex without without without the the the clippingBiomoleculesclippingclipping waterclipping2020 water from, 10water water, 573 fromthe from thirdfrom the the third the“clip”. third third “clip”. The“clip”. “clip”. Thevalues Thevalues The arevalues values aregiven given are are in given theingiven the following in following in the the following following Table Table 2: 2:Table Table 2: 2: 8 of 15

TableTable 2. TableShorteningTable 2. Shortening 2. 2.Shortening Shortening and andelongation andelongation and elongation elongation of bonds of bonds of in of bonds the inbonds the triplet in triplet in the thevs. triplet vs. singlettriplet singlet vs. vs.state. singlet state. singlet state. state. Table 2. Shortening and elongation of bonds in the triplet vs. singlet state. flavin flavinring:flavinflavin N1,ring: ring: ring:C10a, N1, N1, C10a,N1, C4a, C10a, C10a, C4a, C4a,flavin C4a, flavin C4aflavinflavin C4a – C10a C4a– C4aC10a – C10a– C10aflavin flavin C4aflavin C4aflavin – N5 – C4a N5 C4a – N5– N5 flavin flavin C10a-N1 flavinC10a-N1flavin C10a-N1 C10a-N1 N5flavin N5 ring:N5 N5 N1, C10a, C4a, N5 flavin C4a – C10a flavin C4a – N5 flavin C10a-N1

FAD triplet 1.40 Å 1.35 Å 1.32 Å FAD tripletFADFAD triplet triplet 1.40 Å 1.40 1.40 Å Å 1.35 Å 1.35 1.35 Å Å 1.32 Å 1.32 1.32 Å Å FAD tripletFAD singlet 1.40 1.44 Å 1.30 1.35Å Å 1.30 Å 1.32 Å FAD singletFADFAD singlet singlet 1.44 Å 1.44 1.44 Å Å 1.30 Å 1.30 1.30 Å Å 1.30 Å 1.30 1.30 Å Å FAD singletFAD without water clip 1.44 Å 1.31 Å 1.30 Å 1.29 Å 1.30 Å FADFAD without withoutFADFAD without water waterwithout clip clipwater water clip clip 1.44 1.44Å 1.44 Å 1.44 Å Å 1.31 Å 1.31 1.31 1.31 ÅÅ Å 1.29 Å 1.29 1.29 1.29 Å Å Å 3.2.5. Molecular Orbitals—HOMO/LUMO 3.2.5. Molecular3.2.5.3.2.5. Molecular Molecular Orbitals—HOMO/LUMO Orbitals—HOMO/LUMO Orbitals—HOMO/LUMO 3.2.5. Molecular Orbitals—HOMO/LUMO

SinceBiomolecules the geometrical 2020, 10, x FOR propertiesPEER REVIEW of the FAD-water complex may be reflected by9 theof 15 molecular orbitals, the LUMO and HOMO as well as other molecular orbitals of interest are shown in the following graph accordingSince to the their geometrical relative properties energies of (Figurethe FAD-water9): Structure complex may 1 refers be reflected to the by geometry the molecular including the orbitals, the LUMO and HOMO as well as other molecular orbitals of interest are shown in the hydrogenfollowing bridge between graph according the amino to their group relative of energies adenine (Figure towards 9): Structure the N1 in1 refers isoalloxazine, to the geometry while structure 2 refers toincluding the geometry the hydrogen featuring bridge thebetween hydrogen the amino bridge group betweenof adenine thetowards amino the N1 group in isoalloxazine, of adenine towards the C2O inwhile isoalloxazine. structure 2 refers to the geometry featuring the hydrogen bridge between the amino group of adenine towards the C2O in isoalloxazine.

9

8

Figure 9. MOs 238–241 of the singlet/triplet in structure 1 and 2. Figure 9. MOs 238–241 of the singlet/triplet in structure 1 and 2. The corresponding energies (in atomic units a.u.) are shown in the following Table 3.

Table 3. Energies of MOs 238–241 of the singlet/triplet in structure 1 and 2.

Structure 1 Structure 2 MO Singlet [a.u.] Triplet [a.u.] Singlet [a.u.] Triplet [a.u.] −0.2511 238 −0.2473 −0.2383 Biomolecules 2020, 10, 573 9 of 15

The corresponding energies (in atomic units a.u.) are shown in the following Table3.

Table 3. Energies of MOs 238–241 of the singlet/triplet in structure 1 and 2.

Structure 1 Structure 2 MO Singlet [a.u.] Triplet [a.u.] Singlet [a.u.] Triplet [a.u.] 0.2511 238 0.2473 − − 0.2383 − 0.2399 0.2398 239 0.2360 HOMO − 0.2356 HOMO − − 0.1785 HOMO − 0.1785 − − 0.1722 LUMO 0.1722 240 0.1059 LUMO − 0.1188 LUMO − − 0.0854 − 0.0852 HOMO − − 0.0454 LUMO 241 0.0417 − − 0.0329 − Biomolecules 2020, 10, x FOR PEER REVIEW 10 of 15 Biomolecules 2020, 10, x FOR PEER REVIEW 10 of 15 3.2.6. Supramolecular Orbitals 3.2.6. Supramolecular Orbitals 3.2.6. Supramolecular Orbitals Only FAD-water complexes with the 3rd water clip between the amine group of adenine and N1 Only FAD-water complexes with the 3rd water clip between the amine group of adenine and or C2OOnly show FAD the-water two supramolecular complexes with orbitals the 3rd found water in thoseclip between structures the (Figure amine 10 group). While of adenine MO 241 hasand N1 or C2O show the two supramolecular orbitals found in those structures (Figure 10). While MO beenN1 or identified C2O show as thethe LUMOtwo supramolecular in one of the triplet orbitals states, found the in supramolecular those structures MO (Figure 238 plays 10). notWhile such MO a 241 has been identified as the LUMO in one of the triplet states, the supramolecular MO 238 plays role241 ashas HOMO. been identified Nevertheless, as the MO LUMO 238 encompasses in one of the MO triplet 239 states, in the tripletthe supramolecular of structure 1, MO the energy238 plays of not such a role as HOMO. Nevertheless, MO 238 encompasses MO 239 in the triplet of structure 1, not0.2399 such a.u. a role for MOas HOMO. 239 compares Nevertheless, with 0.2383 MO 238 a.u. encompasses for MO 238 (orMO 0.8 239 kcal). in the triplet of structure 1, − the energy of −0.2399 a.u. for MO 239− compares with −0.2383 a.u. for MO 238 (or 0.8 kcal). the energy of −0.2399 a.u. for MO 239 compares with −0.2383 a.u. for MO 238 (or 0.8 kcal).

MO 238 structure 1 (singlet and triplet) MO 241 LUMO structure 2 (triplet) MO 238 structure 1 (singlet and triplet) MO 241 LUMO structure 2 (triplet) FigureFigure 10. 10.Supramolecular Supramolecular orbitals orbitals in closedin closed FAD-water FAD-water complexes. complexes. Figure 10. Supramolecular orbitals in closed FAD-water complexes. NeitherNeither the the open open FAD FAD nor nor the the closed closed structure structure without without the the third third water water clip clip show show this this behavior: behavior: Neither the open FAD nor the closed structure without the third water clip show this behavior: InsteadInstead the HOMO the HOMO is confined is confined to the adenine to the moiety adenine while moiety the LUMO while occupies the LUMO solely occupies the isoalloxazine solely the Instead the HOMO is confined to the adenine moiety while the LUMO occupies solely the ringisoalloxazine system (Figure ring 11 system). (Figure 11). isoalloxazine ring system (Figure 11).

HOMO of the open FAD structure LUMO of the open FAD structure HOMO of the open FAD structure LUMO of the open FAD structure Figure 11. HOMO/LUMO of open FAD-water complexes. FigureFigure 11.11. HOMOHOMO/LUMO/LUMO ofof openopen FAD-waterFAD-water complexes. complexes. 3.2.7. Vibrational Spectra 3.2.7. Vibrational Spectra The comparison of the experimental IR-spectrum with the calculated vibrational spectrum is The comparison of the experimental IR-spectrum with the calculated vibrational spectrum is given in the following graph (Figure 12): given in the following graph (Figure 12): Biomolecules 2020, 10, 573 10 of 15

3.2.7. Vibrational Spectra The comparison of the experimental IR-spectrum with the calculated vibrational spectrum is given in the following graph (Figure 12): Biomolecules 2020, 10, x FOR PEER REVIEW 11 of 15

Figure 12.12. Comparison ofof thethe calculatedcalculated spectrum spectrum of of FAD FAD with with the the experimental experimental spectrum spectrum recorded recorded in Hin2 HO.2O. The The peak peak signed signed with with * contains * contains contributions contributions from from water water clip clip 1. 1.

The theoretical theoretical values values show show overall overall good good agreement agreement with with the the experiment. experiment. The peak in both spectraspectra (experimental(experimental andand theoretical)theoretical) atat 16001600 (signed(signed withwith *)*) hashas to be attributed to vibrations caused by water clip 1 (between(between N7 of adenine and the ribityl chain) and the adenine (amine group and the imidazoleimidazole moiety):moiety): The calculation overestimates the contribution of this vibration due to some bulk eeffectffect ofof thethe surroundingsurrounding waterwater molecules.molecules. The vibrational spectrum of the open FAD has been calculated in order to compare it with the spectrumspectrum of the closedclosed form,form, thethe comparisoncomparison between both forms are shown in thethe followingfollowing graph (Figure(Figure 1313):):

Figure 13. Calculated spectra of FAD in the open and closedclosed forms.

The values of the most prominent vibrations (closed versus open FAD) are listed in the Table 4, the values have been scaled by a factor of 0.96. The open geometry was obtained by removing all water clips of the closed form: Optimizing this geometry resulted in an open, T-shaped conformation. In order to compare this open structure with the closed FAD-water complex in microsolvation, water molecules have been added to the “gas phase” open FAD at the positions C2, N3, C4, and N5 of the isoalloxazine and the amine group of adenine, geometry optimization was performed on this Biomolecules 2020, 10, 573 11 of 15

The values of the most prominent vibrations (closed versus open FAD) are listed in the Table4, the values have been scaled by a factor of 0.96. The open geometry was obtained by removing all water clips of the closed form: Optimizing this geometry resulted in an open, T-shaped conformation. In order to compare this open structure with the closed FAD-water complex in microsolvation, water molecules have been added to the “gas phase” open FAD at the positions C2, N3, C4, and N5 of the isoalloxazine and the amine group of adenine, geometry optimization was performed on this structure. The corresponding geometries of the open and closed FAD in gas phase and in microsolvation are shown in Figure 14.

Table 4. Selected calculated frequencies of vibrations of FAD.

Open FAD Open FAD FAD in Biomolecules 2020[scaled], 10, x FOR PEER REVIEW [scaled] [scaled] Experiment12 of 15 (gas phase) (Microsolvation) Structure 1

C4=Ostructure. The1830 corresponding [1757] C4=O, geometrieswater 1835 of the[1762] openC 4= andO, water closed FAD1804 in[1732] gas phaseC4=O and in 1712 C2=Omicrosolvation and are shown in Figure 14. H-bridge amine 1774 [1703] C2=O, water 1783 [1712] C2=O, water 1758 [1687] C2=O 1657 (adenine) Table 4. Selected calculated frequencies of vibrations of FAD. adenine, water Adenine 1668 [1600] Adenine 1700 [1632] 1680 [1612] Adenosine 1657 open FAD [scaled] open FAD [scaled] FADclip in 1 structure 1 [scaled] Experiment (gas phase) (microsolvation) ring I, II, III, C4ring=O I, II, III, 1830 [1757] ringC4=O, I, water II, III, 1835 [1762] C4=O, water 1804 [1732] C4=O 1712 1638 [1572] 1640 [1574] water clip 1 & 2, 1640 [1574] band I 1626 C2amine=O and (adenine)H-bridge 1774 [1703] amineC2=O, water (adenine) 1783 [1712] C2=O, water 1758 [1687] C2=O 1657 amine (adenine) solvating water Adenine 1668 [1600] Adenine 1700 [1632] adenine, water clip 1 1680 [1612] AdenosineAdenosine 16051657 ring I,II,III, amine 1638 [1572] ring I,II, III, 1640 [1574] ring I, II, III, water clip 1640 [1574] band I 1626 ring I, II, III, band II 1580 (adenine)ring I, II, III, 1ring & 2, I,solvating II, III, water 1591 [1527] amine (adenine), 1594 [1530] 1594 [1530] amine (adenine) water clip 3 band III 1547 solvating water band IV 1506

closed FAD structure1 open FAD gas phase open FAD microsolvation microsolvation

FigureFigure 14. 14.Geometries Geometries correspondingcorresponding to to the the structures structures of Table of Table 4. 4.

The followingThe following graph graph provides provides a compilation a compilation of of all all the the spectra spectra whichwhich havehave been calculated, calculated, e.g., e.g., the openthe structures open structures with and with without and without solvating solvating water moleculeswater molecules as well as aswell the as closed the closed FAD-water FAD-water complex complex in its singlet and triplet state (Figure 15). The most prominent band for the triplet at 14901 in its singlet and triplet state (Figure 15). The most prominent band for the triplet at 1490 cm− has cm−1 has to be attributed to concerted vibrations of the isoalloxazine system together with vibrations to be attributed to concerted vibrations of the isoalloxazine system together with vibrations in the in the adenine moiety: This type of coupled movement has not been detected when calculating the adeninespectra moiety: related This to all type the ofother coupled geometries movement of FAD hasor FAD-water not been detectedcomplexes. when calculating the spectra related to all the other geometries of FAD or FAD-water complexes.

Figure 15. Comparison of calculated spectra of FAD including the triplet state.

4. Discussion Biomolecules 2020, 10, x FOR PEER REVIEW 12 of 15

structure. The corresponding geometries of the open and closed FAD in gas phase and in microsolvation are shown in Figure 14.

Table 4. Selected calculated frequencies of vibrations of FAD. open FAD [scaled] open FAD [scaled] FAD in structure 1 [scaled] Experiment (gas phase) (microsolvation) C4=O 1830 [1757] C4=O, water 1835 [1762] C4=O, water 1804 [1732] C4=O 1712 C2=O and H-bridge 1774 [1703] C2=O, water 1783 [1712] C2=O, water 1758 [1687] C2=O 1657 amine (adenine) Adenine 1668 [1600] Adenine 1700 [1632] adenine, water clip 1 1680 [1612] Adenosine 1657 ring I,II,III, amine 1638 [1572] ring I,II, III, 1640 [1574] ring I, II, III, water clip 1640 [1574] band I 1626 (adenine) amine (adenine) 1 & 2, solvating water Adenosine 1605 ring I, II, III, amine ring I, II, III, ring I, II, III, band II 1580 (adenine) 1591 [1527] amine (adenine), 1594 [1530] water clip 3 1594 [1530] band III 1547 solvating water band IV 1506

closed FAD structure1 open FAD gas phase open FAD microsolvation microsolvation

Figure 14. Geometries corresponding to the structures of Table 4.

The following graph provides a compilation of all the spectra which have been calculated, e.g., the open structures with and without solvating water molecules as well as the closed FAD-water complex in its singlet and triplet state (Figure 15). The most prominent band for the triplet at 1490 cm−1 has to be attributed to concerted vibrations of the isoalloxazine system together with vibrations Biomoleculesin the adenine2020, 10 moiety:, 573 This type of coupled movement has not been detected when calculating12 of the 15 spectra related to all the other geometries of FAD or FAD-water complexes.

FigureFigure 15.15. ComparisonComparison ofof calculatedcalculated spectraspectra ofof FADFAD includingincluding thethe triplettriplet state.state. 4. Discussion The main purpose of this study was the determination of the geometry of FAD in aqueous environment to explain the experimental spectroscopical data of Spexard et al. [12]. Our model of the closed FAD structure in microsolvation is able to reproduce the prominent bands of the infrared spectrum, the C2=O and the C4=O stretches as well as the bands due to the stretches in the isoalloxazine moiety. The vibrational spectrum of the triplet shows the typical shift with respect to the singlet, e.g., 1 1 1490 cm− compared to 1594 cm− . While the singlet includes only the vibrations in the isoalloxazine, 1 the peak at 1490 cm− (triplet) shows an involvement of both moieties, the adenine and the isoalloxazine. The majority of computational studies on FAD in the past have been dedicated to flavoproteins with FAD adopting T-shaped and other “open“ geometries, the “stacked“ geometry of FAD has not yet been the subject of those studies. The recent publication of Bubniene et al. [16] reflects this gap. According to Bubniene et al. differences in the FAD and polypyrrole average fluorescence relaxation time showed that the FAD composite with polypyrrole effectively quenched the FAD fluorescence since FAD could not freely unfold in this environment. Moreover they state that the intramolecular electron transfer took place between adenine and isoalloxazine moieties over the first 5 ps after the excitation. However, the FAD models of Bubniene et al. remain schematic and rely on the qualitative reasonings of Li et al. [13]. The same holds true for the study of Kao et al. [10]: Their “stacked” FAD geometry resembles more to an open or T-shaped geometry than to a closed structure. Although being interested mainly in reproducing the experimental data of Spexard et al. [12], our attention was turned to the possibilities for obtaining the π-stacked complex suggested by Li et al. in 2008 [13]. In general the π-stacked complex shows the following properties: It depends indeed on the presence of the aqueous environment, featuring three important hydrogen-bonds. The most important “water clip” consists of the water between N7 of adenine and the ribityl moiety which fixes the position of the isoalloxazine with respect to the ADP backbone and keeping the two aromatic ring systems parallel in an adequate distance for a possible charge transfer. The second “water clip” consists of two water molecules and spans the distance between the amine group of adenine and the C4O of the isoalloxazine. These two water molecules are part of the whole microsolvation “water network” around the isoalloxazine moiety at C2O, N3 and C4O and are one of the reasons for the overall good agreement of the calculated vibrational bands with the experimental data. The third “water clip” may play a role in the fast quenching of FAD. As Wu et al. [26] stated in their studies about mechanisms of photoreactivity in hydrogen-bonded adenine–H2O complexes, the amine group of adenine acts as an H donor. Our studies involved the singlet and triplet state of FAD: While the singlet state remains in the geometry of the oxidized FAD, the results for the triplet state show a shortening of the C4a-C10a bond Biomolecules 2020, 10, 573 13 of 15 while elongating the C4a-N5 and C10a-N1 bonds in the FAD-water complex, these properties tend to the geometry of the reduced FAD. The most interesting result of studying the closed FAD-water complex consists in finding the supramolecular orbitals 238 and 241 in the triplet: Energetically MO 238 overlaps with MO 239 (HOMO), while the charge transfer involves MO 241 (LUMO). As stated before, the supramolecular orbitals originate from the closed FAD-water complexes specifically including the water molecule between adenine and isoalloxazine (e.g., water clip 3)—without the third water clip the supramolecular orbitals are not found. Moreover, the triplet shows reduced HOMO-LUMO gaps with respect to the singlet: While the energy difference between the orbitals 239 (HOMO) and 240 (LUMO) in the singlet amounts to 81 kcal in structure 1 and 73 kcal in structure 2, respectively, the gap between HOMO (239) and LUMO (240) is reduced to 4 kcal for the triplet in structure 1. In both cases (in the triplet as well as in the singlet) the HOMO (MO 239) involved is extended over both planes of the FAD, namely the isoalloxazine and the adenine. Most interestingly the triplet in structure 2 shows an involvement of the supramolecular orbital 241 which becomes the new LUMO with an energy difference to MO 240 (the “new” HOMO) of 24 kcal. Since the supramolecular orbital 241 (Figure 10) extends over the isoalloxazine and the adenine, while MO 240 remains located in the isoalloxazine moiety, the process of the charge transfer towards the isoalloxazine seems to be turned upside down by describing MO 240 as the “new” HOMO: This “reordering” of the molecular orbitals involved in the charge transfer may be due to the relatively modest basis set combined with the exchange correlation functional chosen and should be checked including larger basis sets and the global hybrid functional with 54% HF exchange.

5. Conclusions Our calculations of the vibrational spectra of FAD water complexes show that the vibrational bands in the IR spectrum can be attributed to the closed and “π-stacked” structure of the FAD-water complex. The existence of the closed structure depends on the water between N7 of adenine and the ribityl backbone of FAD which fixes the planes of the adenine and the isoalloxazine in the adequate distance for a possible charge transfer.

Author Contributions: M.K. and T.K. designed this study, T.K. presented the experimental data, M.K. performed the calculations and analyzed the data. O.N.V. collaborated on the technical aspects of the calculations and technical aspects of the publication. M.K. wrote the manuscript under participation of T.K. and O.N.V. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Deutsche Forschungsgemeinschaft via a Heisenberg fellowship (TK3580/4-2) to T.K. Acknowledgments: M.K. and O.N.V. gratefully acknowledge current support for this research by ANII, CSIC, and Pedeciba in Uruguay. The Alexander von Humboldt-Stiftung is also gratefully acknowledged for the economic support of a stay at the University of Bielefeld (M.K.). Part of the calculations presented in this paper was carried on the Cluster.uy (National Center for Supercomputing of Uruguay). Conflicts of Interest: The authors declare no conflict of interest.

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