Closure of the Human TKFC Active Site: Comparison of the Apoenzyme and the Complexes Formed with Either Triokinase Or FMN Cyclase Substrates

International Journal of Molecular Sciences

Article Closure of the Human TKFC Active Site: Comparison of the Apoenzyme and the Complexes Formed with Either Triokinase or FMN Cyclase Substrates

Joaquim Rui Rodrigues 1,* , José Carlos Cameselle 2 , Alicia Cabezas 2 and João Meireles Ribeiro 2,* 1 Laboratório Associado LSRE-LCM, Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Leiria, P-2411-901 Leiria, Portugal 2 Grupo de Enzimología, Departamento de Bioquímica y Biología Molecular y Genética, Facultad de Medicina, Universidad de Extremadura, E-06006 Badajoz, Spain; [email protected] (J.C.C.); [email protected] (A.C.) * Correspondence: [email protected] (J.R.R.); [email protected] (J.M.R.); Tel.: +351-244-820-300 (J.R.R.); +34-924-289-470 (J.M.R.) Received: 18 January 2019; Accepted: 27 February 2019; Published: 4 March 2019

Abstract: Human triokinase/flavin mononucleotide (FMN) cyclase (hTKFC) catalyzes the adenosine triphosphate (ATP)-dependent phosphorylation of D-glyceraldehyde and dihydroxyacetone (DHA), and the cyclizing splitting of flavin adenine dinucleotide (FAD). hTKFC structural models are dimers of identical subunits, each with two domains, K and L, with an L2-K1-K2-L1 arrangement. Two active sites lie between L2-K1 and K2-L1, where triose binds K and ATP binds L, although the resulting ATP-to-triose distance is too large (≈14 Å) for phosphoryl transfer. A 75-ns trajectory of molecular dynamics shows considerable, but transient, ATP-to-DHA approximations in the L2-K1 site (4.83 Å or 4.16 Å). To confirm the trend towards site closure, and its relationship to kinase activity, apo-hTKFC, hTKFC:2DHA:2ATP and hTKFC:2FAD models were submitted to normal mode analysis. The trajectory of hTKFC:2DHA:2ATP was extended up to 160 ns, and 120-ns trajectories of apo-hTKFC and hTKFC:2FAD were simulated. The three systems were comparatively analyzed for equal lengths (120 ns) following the principles of essential dynamics, and by estimating site closure by distance measurements. The full trajectory of hTKFC:2DHA:2ATP was searched for in-line orientations and short distances of DHA hydroxymethyl oxygens to ATP γ-phosphorus. Full site closure was reached only in hTKFC:2DHA:2ATP, where conformations compatible with an associative phosphoryl transfer occurred in L2-K1 for significant trajectory time fractions.

Keywords: triokinase; dihydroxyacetone kinase; FMN cyclase; phosphoryl transfer mechanism; protein domain mobility; active-site closure; normal mode analysis; molecular dynamics simulation; essential dynamics

1. Introduction Human triokinase/flavin mononucleotide (FMN) cyclase (hTKFC) is a bifunctional enzyme which catalyzes the adenosine triphosphate (ATP)-dependent phosphorylation of D-glyceraldehyde (GA) and dihydroxyacetone (DHA), and also the Mn2+-dependent splitting of flavin adenine dinucleotide (FAD) by an internal cyclizing reaction that forms adenosine monophosphate (AMP) and riboflavin 40,50-phosphate or cyclic FMN [1,2]. GA kinase represents the third step of fructose metabolism [3–5] and DHA kinase is necessary for the metabolism of exogenous DHA [6–9] and the eventually generated endogenous DHA [10]. On the other hand, the biological role of the cyclase activity is unknown [2,11,12]. hTKFC is functionally and structurally similar to Citrobacter sp. DHA kinase, which displays similar activities, including GA kinase and FMN cyclase [6,10,12,13]. The Citrobacter

Int. J. Mol. Sci. 2019, 20, 1099; doi:10.3390/ijms20051099 www.mdpi.com/journal/ijms Int. J. Mol. Sci. 2019, 20, 1099 2 of 19

DHAInt. J. Mol. kinase Sci. 2018 is, also19, x FOR of biotechnologicalPEER REVIEW interest due to its efficient use for in situ production2 of of19 dihydroxyacetone phosphate (DHAP) in systems developed for C–C bond formation catalyzed by DHAP-dependentof dihydroxyacetone aldolases phosphate [14, 15(DHAP)]. in systems developed for C–C bond formation catalyzed by DHAPCitrobacter-dependentDHA aldolases kinase has [14,15 a known]. crystal structure with a unique fold [16] that defines Group 9 in theCitrobacter classification DHA of kinaseskinase has [17, a18 kn]. Thisown enzyme,crystal structure and the hTKFCwith a unique model constructedfold [16] that by defines homology Group [2], show9 in the up classification a homodimer of (inkinases agreement [17,18] with. This size enzyme, exclusion and the chromatography hTKFC model dataconstructed for hTKFC by homology [2]), each subunit[2], show with up twoa homodimer domains, K(in and agreement L, linked with by a longsize exclusion spacer (Figure chromatography1). The intertwined data for subunits hTKFC form [2]), aneach elongated subunit L2-K1-K2-L1with two domains, arrangement. K and L, Two linked kinase by a active long spacer sites lie (Figure between 1). domains The intertwined L2-K1 and subunits K2-L1, whereform an triose elongated binds L2 covalently-K1-K2-L1 to arrangement. histidine residues Two ofkinase the K active domains sites and lie between ATP binds domains to the LL2 domains-K1 and inK2 complex-L1, where with triose two binds Mg2+ covalentlyions. to histidine residues of the K domains and ATP binds to the L domains in complex with two Mg2+ ions.

Figure 1. Homology model of human triokinase/flavin mononucleotide (FMN) cyclase (hTKFC) in Figure 1. Homology model of human triokinase/flavin mononucleotide (FMN) cyclase (hTKFC) in complex with dihydroxyacetone (DHA), adenosine triphosphate (ATP) and Mg2+ (hTKFC:2DHA:2ATP). complex with dihydroxyacetone (DHA), adenosine triphosphate (ATP) and Mg2+ The ATP-to-DHA distance is indicated in the L2-K1 site. The description is in the text. The figure was (hTKFC:2DHA:2ATP). The ATP-to-DHA distance is indicated in the L2-K1 site. The description is in drawn according to the coordinates reported elsewhere [2]. the text. The figure was drawn according to the coordinates reported elsewhere [2]. In the crystal structure of Citrobacter DHA kinase and in the homology model of hTKFC (Figure1), the ATP-to-trioseIn the crystal distancestructure is of about Citrobacter 14 Å, DHA too large kinase for and phosphoryl in the homology transfer model [2,16]. of In hTKFC fact, from (Figure the structural1), the ATP data-to-triose nothing distance can be is inferred about 14 about Å , too the large mechanism, for phosphoryl and it has transfer been suggested [2,16]. In fact that, bringingfrom the ATPstructural near thedata triose nothing requires can be mobility inferred ofabout the proteinthe mechanism, domains and in solutionit has been [10 suggested,16]. In previous that bringing work, toATP study near the the flexibility triose requires of dimeric mobility hTKFC of the starting protein with domains its active in solution sites in [10,16 an open]. In conformation,previous work, we to ranstudy a 75-nsthe flexibility simulation of dimeric of the molecular hTKFC starting dynamics with of its the active structural sites in model an open of hTKFC conformation, containing we theran kinasea 75-ns substratessimulation DHA of the (actually molecular a trihydroxyprop-2-yldynamics of the structural radical model covalently of hTKFC bound containing to His221 )the and kinase ATP 221 (hTKFC:2DHA:2ATP;substrates DHA (actually Figure a1 ). trihydroxyprop The trajectory- of2-yl this radical simulation covalently shows bound the protein to His acquiring) and a ATPless open(hTKFC:2DHA:2ATP; conformation in oneFigure of the1). The active trajectory sites, with of this significant simulation decrease shows of the the protein ATP-to-DHA acquiring distance, a less whichopen conformation in the 34–37-ns in and one 47–55-ns of the active intervals sites, reaches with significant frequently decrease distances of around the ATP 5 Å,-to and-DHA include distance, very transientwhich in minimathe 34–37 of-ns 4.83 and Å at47– 34.86055-ns nsinterval and 4.16s reaches Å at 54.622 frequently ns. After distances this, the around ATP-to-DHA 5 Å , and distance include increasesvery transient up to minima around 10of Å4.83 [2]. Å at 34.860 ns and 4.16 Å at 54.622 ns. After this, the ATP-to-DHA distanceThe increases main purpose up to around of this 10 study Å [2] was. to look for further confirmation of the trend towards active-siteThe main closure purpose and to of analyze this study whether was to substrate look for bindingfurther confirmation could influence of the protein trend domain towards mobility. active- Insite particular, closure and we to wondered analyze whether if results substrate could be binding obtained could to support influence the protein movements domain required mobility. for In a directparticular, phosphoryl we wondered transfer if fromresults ATP could to thebe obtained triose as to suggested support the [10 ,movements16]. To address required these for questions, a direct differentphosphoryl studies transfer have from been ATP performed. to the triose On as thesuggested one hand, [10,16 the]. principlesTo address ofthese normal questions, mode different analysis werestudies applied have been to the performed. hTKFC:2DHA:2ATP On the one complexhand, the typical principles of the of phosphorylnormal mode transfer analysis reaction, were applied to the hTKFC:2FADto the hTKFC:2DHA: typical2ATP of FMN complex cyclase typical activity, of andthe tophosphoryl the apo form transfer of hTKFC. reaction, On to the the other hTKFC: hand,2FAD the earliertypical 75-nsof FMN trajectory cyclase ofactivity, hTKFC:2DHA:2ATP and to the apo form was extendedof hTKFC. up On to the 160 other ns, and hand, studied the ea inrlier parallel 75-ns withtrajectory new dynamic of hTKFC: simulations2DHA:2ATP of hTKFC:2FAD was extended and up apo-hTKFC to 160 ns, of and 120 studiedns. The three in parallel trajectories with were new comparativelydynamic simulations analyzed of for hTKFC: equal lengths2FAD and(120 ns apo each)-hTKFC following of 120 the ns. principles The three of essential trajectories dynamics were andcomparativel by estimatingy analyz theed degree for equal of active-site lengths (120 closure ns each) through following distance the principles measurements of essential between dynamics proper and by estimating the degree of active-site closure through distance measurements between proper reference points in the K and L domains. Finally, in search for optimal conformations for the in-line attack of DHA over ATP (phosphoryl transfer), the two active sites of the hTKFC:2DHA:2ATP dimer were analyzed along the full 160-ns trajectory, measuring the distances from each DHA hydroxyl

Int. J. Mol. Sci. 2019, 20, 1099 3 of 19 reference points in the K and L domains. Finally, in search for optimal conformations for the in-line attack of DHA over ATP (phosphoryl transfer), the two active sites of the hTKFC:2DHA:2ATP dimer were analyzed along the full 160-ns trajectory, measuring the distances from each DHA hydroxyl oxygen to the ATP γ-phosphorus, and the angles formed by these oxygen-phosphorus pairs with the scissible P–O linkage of ATP.

2. Results

2.1. Normal-Mode Analysis of hTKFC Models Confirms the Trend of K Domains to Approach L Domains The analysis of normal modes is a major theoretical method to predict collective movements in proteins [19–21]. Three systems were analyzed by this approach: apo-hTKFC, hTKFC:2DHA:2ATP, and hTKFC:2FAD. After the necessary thorough energy minimization, the conformations of these systems differed from the initial ones with Cα root-mean-square deviation (RMSD) values of 1.11 Å, 1.50 Å and 1.16 Å, respectively. Hessian matrices calculated from the minimized conformations were used to calculate eigenvectors (normal modes) and their associated eigenvalues. In this type of analysis, the first six normal modes (NM1–NM6) are considered trivial and disregarded. Therefore, the non-trivial normal modes NM7–NM9 obtained for the three systems are represented in Figure2 as porcupine plots. Supplemental movie 1 shows the domain movements corresponding to NM7–NM9 for the three systems, and a schematic interpretation is made in Figure3. To compare the normal modes of the systems studied, besides the possibility of direct visual comparison in Figure2 and Supplemental movie 1, quantitative comparisons can be made in terms of eigenvector inner products which would equal unity if vectors are identical or zero if orthogonal. The results of the pairwise comparison among the three systems studied are shown in Figure4. The first non-trivial modes (i.e., NM7) were very similar in the three systems. The L1(L2) domain tilted towards the K2(K1) domain in parallel to the main axis of the protein dimer that runs approximately through the mass centers of the L2-K1-K2-L1 domains (Supplemental movie 1). The similitude of the NM7 modes of the three systems was confirmed by the corresponding inner products being near to unity (Figure4). This mode is similar to the so-called hinge-bending mode defined for bilobate structures formed by two globular domains linked by a flexible hinge [22], although in hTKFC, L2-K1 (K2-L1) are not directly linked. The NM7 mode may be part of a functional movement in the case of the hTKFC:2DHA:2ATP system, as its prolongation would bring about closer contacts between the L and K domains, and therefore the needed approximation of ATP to DHA for the kinase reaction. The second non-trivial modes of apo-hTKFC and hTKFC:2DHA:2ATP (i.e., NM8) were similar to each other, and to the third non-trivial mode (NM9) of hTKFC:2FAD (Figure4). They consisted of a partial twist of the L domain around a vertical axis located between the K and L domains (similar to the twisting mode defined for bilobate structures [22]), combined with a slight tilt perpendicular to the movement in NM7 (Supplemental movie 1). The prolongation of the NM8 mode of hTKFC:2DHA:2ATP, like NM7, would also bring about some approximation between ATP and DHA. The third non-trivial modes of hTKFC and hTKFC:2DHA:2ATP (i.e., NM9) were similar to each other, and to the second non-trivial mode (NM8) of hTKFC:2FAD (Figure4). They consisted of a wobbling of the L domain about a horizontal axis approximately parallel to the main axis of the protein dimer (similar to the wobbling mode defined for bilobate structures in [22]) without bringing about any obvious approximation between L and K domains (Supplemental movie 1). Therefore, its functional character in hTKFC:2DHA:2ATP is less clear, but cannot be discarded when combined with the other modes. Int. J. Mol. Sci. 2019, 20, 1099 4 of 19 Int. J. Mol. Sci. 2018, 19, x FOR PEER REVIEW 4 of 19

Figure 2. Porcupine representation of the ﬁrst three non-trivial normal modes NM7–NM9 for the Figure 2. Porcupine representation of the first three non-trivial normal modes NM7–NM9 for the apo apo form of hTKFC and its complexes with kinase or FMN cyclase substrates. The arrows indicate form of hTKFC and its complexes with kinase or FMN cyclase substrates. The arrows indicate the the direction and extent of the motion for each Cα atom. Other atoms were omitted for simplicity. direction and extent of the motion for each Cα atom. Other atoms were omitted for simplicity. (a) (a) “Lateral” view, similar to Figure1,( b) “top” view. The ﬁrst line of each panel shows the “Lateral” view, similar to Figure 1, (b) “top” view. The first line of each panel shows the energy- energy-minimized structures used for the normal mode analysis. An animated representation can minimized structures used for the normal mode analysis. An animated representation can be seen in be seen in Supplemental movie 1. The correspondence with the three universal modes of bilobate Supplemental movie 1. The correspondence with the three universal modes of bilobate structures is structures is indicated in Figure3. indicated in Figure 3.

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Int. J. Mol. Sci. 2019, 20, 1099 5 of 19 Int. J. Mol. Sci. 2018, 19, x FOR PEER REVIEW 5 of 19

Figure 3. Schematic interpretation of the major movements contained in non-trivial normal modes shown in Figure 2. These movements can be compared to the three universal modes [22] defined for bilobate structures: (upper) hinge-bending, (middle) twisting, (lower) wobbling. Additional descriptions of the NM7–NM9 modes can be found in the text. In some cases, the normal modes of L1 and L2 differ slightly (see the text). Figure 3. Schematic interpretation of the major movements contained in non-trivial normal modes Figure 3. Schematic interpretation of the major movements contained in non-trivial normal modes shown in Figure2. These movements can be compared to the three universal modes [ 22] deﬁned shownTo compare in Figure the 2 . normalThese movements modes of can the be systems compared studied, to the three besides universal the possibility modes [22] ofdefined direct for visual for bilobate structures: (upper) hinge-bending, (middle) twisting, (lower) wobbling. Additional comparisonbilobate in structures Figure 2: and (upper) Supplemental hinge-bending, movie (middle) 1, quantitative twisting, comparisons (lower) wobbling can be. Additionalmade in terms descriptions of the NM7–NM9 modes can be found in the text. In some cases, the normal modes of L1 of eigenvectordescriptions inner of the products NM7–NM9 which modes would can be equal found unity in the iftex vectorst. In some are cases, identical the normal or zero modes if orthogonal. of L1 and L2 differ slightly (see the text). The resultsand L2 differof the slightly pairwise (see comparison the text). among the three systems studied are shown in Figure 4.

To compare the normal modes of the systems studied, besides the possibility of direct visual comparison in Figure 2 and Supplemental movie 1, quantitative comparisons can be made in terms of eigenvector inner products which would equal unity if vectors are identical or zero if orthogonal. The results of the pairwise comparison among the three systems studied are shown in Figure 4.

FigureFigure 4. 4. ComparisonComparison of of normal modes NM7–NM9NM7–NM9 for the the three three systems systems studied. studied. A set of of conformationsconformations waswas generated generated for for each each system system and and mode, mode, and and the the information information about about their their Cα atoms Cα atoms was extractedwas extracted such that such the that same the number same number of atoms of was atoms considered was considered in each case. in eachThe resulting case. The trajectories resulting weretrajectories submitted were to submitted principal component to principal analysis component from where analysis eigenvectors from where and eigenvalueseigenvectors wereand derived.eigenvalues Inner were products derived. were Inner calculated products for were each calculated comparison for and each are comparison displayed and in a greyare displayed scale: from in 1.0, identity, to 0.0, orthogonality. Figurea grey scale 4. Comparison: from 1.0, identity, of normal to 0.0, modes orthogonality NM7–NM9. for the three systems studied. A set of Theconformations analysis was of normal generated modes for each showed system a and clear mode, trend and of the the information open conformation about their C ofα atoms hTKFC to wasThe first extracted non- trivial such that mode thes same(i.e., NM7) number w ere of atomsvery similar was considered in the three in systems. each case. T he The L1(L2) resulting domain progress towards a less open conformation. However, this was little dependent on the presence of tiltedtrajectories towards the were K2(K1) submitted domain to principal in parallel component to the main analysis axis from of the where protein eigenvector dimers thatand runs ligands. In fact, hinge-bending, which is the kind of movement that most clearly evokes the closure of approximatelyeigenvalues throughwere derived. the mass Inner centers products of were the calculatedL2-K1-K2 -forL1 each domains comparison (Supplemental and are displayed movie 1in). The the active site, is the one with the lowest oscillation frequency for the three systems (3.79–4.46 cm−1) similitudea grey scale of the: from NM7 1.0, identity, modes ofto 0.0, the orthogonality three systems. was confirmed by the corresponding inner withproducts barely being noticeable near to differences unity (Figure among 4). them,This mode the differences is similar consisting to the so- ofcalled slight hinge deviations-bending from mode the movementdefinedThe forfirst parallel bilobate non-trivial to structures the mode mains axis (i.e. formed, of NM7) the by protein w twoere very globular dimer similar described domains in the above.three linked systems. by a flexibleThe L1(L2) hinge domain [22], tiltedalthoughOn towards the in hTKFC, other the hand, K2(K1)L2-K1 the (K2 domain twisting-L1) are in and not parallel directly wobbling to linked. the movements main The NM7 axis of ofmode the the three may protein systems be part dimer of showed a functional that more runs accentuatedapproximatelymovement in differences, thethrough case ofthe regardless the mass hTKFC:2DHA:2ATP centers of the of rather the L2 narrow-K1 system-K2 range-L1, as domains of its the prolongation frequencies (Supplemental would associated movie bring to 1 ) about these. The −1 −1 modessimilitudecloser contacts in the of three t hebetween NM7 systems: modesthe L NM8 and of 4.74–5.51 theK domains, three cm systems and; NM9there was 5.35–5.80fore confirmed the needed cm by. approximation Despitethe corresponding the symmetry of ATP inner ofto dimericproductsDHA for hTKFC, thebeing kinase near these reaction. to movements unity (Figure were 4). notThis exactly mode equivalentis similar to for the both so-called L domains. hinge The-bending differences mode aredefined notThe easy forsecond bilobate to grasp non - structuresfromtrivial the modes observation formed of apo by-hTKFC of two Supplemental globular and hTKFC:2DHA:2ATP domains movie 1.linked The twisting by (i.e. a , flexibleNM8) modes were hinge of similar the [22] L2, domainalthoughto each other, were in hTKFC, veryand to similar L2 the-K1 third in(K2 the -nonL1) three -aretrivial systems,not modedirectly but(NM9) linked. less of so ThehTKFC:2FAD in L1, NM7 where mode the (Figure may twist be 4 of ).part They apo-hTKFC of aconsisted functional (and, of tomovementa partial a lesser twist extent, in theof the hTKFC:2DHA:2ATP) case L domain of the hTKFC:2DHA:2ATP around a was vertical mixed axis withsystem located a noticeable, as between its prolongation wobbling the K and originating wouldL domains bring from (similar about the topcloserto the of thetwistingcontacts domain. modebetween The defined wobbling the L forand bilobate modes K domains, of structures the L2and domains there[22]),fore combined of the apo-hTKFC needed with approximationa and slight hTKFC:2DHA:2ATP tilt perpendicular of ATP to differedDHAto the for movement from the kinase that of inreaction. hTKFC:2FAD NM7 (Supplemen in theirta axes,l movie while 1). those The of prolongation the L1 domains of the differed NM8 in mode that the of latterhTKFC:2DHA:2ATPThe system, second but non not,- trivial the like two NM7, modes former would of ones,apo also-hTKFC was bring mixed and about withhTKFC:2DHA:2ATP some a slight approximation hinge-bending (i.e., NM8) between movement were ATP similar and and a horizontaltoDHA. each other, axis and of rotationto the third closer non to-trivial the top mode of the (NM9) domain. of hTKFC:2FAD (Figure 4). They consisted of a partialIn summary, twist of the although L domain the normalaround modes a vertical of the axis three located systems between studied the differed K and L only domains in subtle (similar form, itto isthe possible twisting that mode these defined small differences for bilobate of structures modes can [22] explain), combined the larger with differences a slight tilt that perpendicular were seen in molecularto the movement dynamics in simulations NM7 (Supplemen (see below).tal movie 1). The prolongation of the NM8 mode of hTKFC:2DHA:2ATP, like NM7, would also bring about some approximation between ATP and DHA.

Int. J. Mol. Sci. 2018, 19, x FOR PEER REVIEW 6 of 19

The third non-trivial modes of hTKFC and hTKFC:2DHA:2ATP (i.e., NM9) were similar to each other, and to the second non-trivial mode (NM8) of hTKFC:2FAD (Figure 4). They consisted of a wobbling of the L domain about a horizontal axis approximately parallel to the main axis of the protein dimer (similar to the wobbling mode defined for bilobate structures in [22]) without bringing about any obvious approximation between L and K domains (Supplemental movie 1). Therefore, its functional character in hTKFC:2DHA:2ATP is less clear, but cannot be discarded when combined with the other modes. The analysis of normal modes showed a clear trend of the open conformation of hTKFC to progress towards a less open conformation. However, this was little dependent on the presence of ligands. In fact, hinge-bending, which is the kind of movement that most clearly evokes the closure of the active site, is the one with the lowest oscillation frequency for the three systems (3.79–4.46 cm−1) with barely noticeable differences among them, the differences consisting of slight deviations from the movement parallel to the main axis of the protein dimer described above. On the other hand, the twisting and wobbling movements of the three systems showed more accentuated differences, regardless of the rather narrow range of the frequencies associated to these modes in the three systems: NM8 4.74–5.51 cm−1; NM9 5.35–5.80 cm−1. Despite the symmetry of dimeric hTKFC, these movements were not exactly equivalent for both L domains. The differences are not easy to grasp from the observation of Supplemental movie 1. The twisting modes of the L2 domain were very similar in the three systems, but less so in L1, where the twist of apo-hTKFC (and, to a lesser extent, hTKFC:2DHA:2ATP) was mixed with a noticeable wobbling originating from the top of the domain. The wobbling modes of the L2 domains of apo-hTKFC and hTKFC:2DHA:2ATP differed from that of hTKFC:2FAD in their axes, while those of the L1 domains differed in that the latter system, but not the two former ones, was mixed with a slight hinge-bending movement and a horizontal axis of rotation closer to the top of the domain. Int. J. Mol. Sci. 20 In summary,2019, , 1099 although the normal modes of the three systems studied differed only in subtle6 of 19 form, it is possible that these small differences of modes can explain the larger differences that were 2.2.seen Comparison in molecular of hTKFC-2DHA-2ATP, dynamics simulations hTKFC-2FAD (see below). and apo-hTKFC Molecular Dynamics Trajectories

2.2.The Comparison normal of mode hTKFC analysis-2DHA of-2ATP, the systems hTKFC-2FAD apo-hTKFC, and apo-hTKFC hTKFC:2DHA:2ATP Molecular Dynamics and hTKFC:2FADTrajectories indicated that there could be subtle differences in their harmonic movements perhaps due to the The normal mode analysis of the systems apo-hTKFC, hTKFC:2DHA:2ATP and hTKFC:2FAD absence or presence of different ligands. Thus, considering that the previously published study of indicated that there could be subtle differences in their harmonic movements perhaps due to the dynamics involved only hTKFC:2DHA:2ATP [2], it was interesting to compare molecular dynamics absence or presence of different ligands. Thus, considering that the previously published study of trajectoriesdynamics ofinvolved the different only hTKFC:2DHA:2ATP systems. The comparison [2], it was was interesting performed to along compare 120-ns mo simulations.lecular dynamics In the casetrajectories of hTKFC:2DHA:2ATP, of the different systems. the previously The comparison published was 75-ns performed simulation along was 120 prolonged-ns simulations. up to In 120 the ns, whereascase of thehTKFC:2DHA:2ATP, 120-ns trajectories the of previously apo-hTKFC publish and hTKFC:2FADed 75-ns simulation were simulatedwas prolonged de novo. up to The 120 threens, 120-nswhereas trajectories the 120-ns are trajectories summarized of apo in Figure-hTKF5C byand superimposing hTKFC:2FAD were conformations simulated extractedde novo. The at regular three intervals120-ns trajectories of 2 ns and are aligned summarized with the in Figure initial 5 structures. by superimposing The three conformations simulations ext showedracted at the regular overall stabilityintervals of of the 2 complexes,ns and aligned which with conserved the initial their structures dimeric. The character, three simulations the organization showed of the the overall L and K domains,stability and of the their complexes, elongated which disposition. conserved However, their dimeric the three character, systems the showed organization signiﬁcant of the ﬂuctuations L and K thatdomains, affected and more their the L elongated domains than disposition. the centrally However, located the K domains three systems and, in general, showed affected significant more thefluctuations regions devoid that affected of secondary more structurethe L domains than thosethan the with centrally it. Upon lo visualcated K comparison domains and, of thein general three sets, ofaffected superimposed more the conformations, regions devoid the ofmost secondary remarkable structure differential than those feature with it was. Upon the closurevisual comparison of one of the activeof the sites three of hTKFC:2DHA:2ATPsets of superimposedby conformations a marked L2-to-K1, the most approximation remarkable differential not observed feature in apo-hTKFC was the orclosure hTKFC:2FAD of one of (Figure the acti5).ve sites of hTKFC:2DHA:2ATP by a marked L2-to-K1 approximation not observed in apo-hTKFC or hTKFC:2FAD (Figure 5).

Figure 5. Molecular dynamics of hTKFC and its complexes with kinase or cyclase substrates. The ﬁgure shows the superimposition of 60 snapshots extracted from 120-ns trajectories at 2-ns intervals and aligned with the initial conformations.

The divergence of the three systems with respect to the respective initial structures, after their alignment, was quantitated in terms of RMSD of the Cα positions (Figure6). The increasing deviations converged towards a plateau with RMSD about 5 Å when all the Cα atoms of hTKFC were considered. RMSD values calculated separately for each L or K domain were smaller than those for the full proteins, an indication of the occurrence of movements of one domain with respect to the other. In general, the K domains showed higher conformational stability than the L ones. Upon comparison of the three systems, there was no consistent effect of the presence of hTKFC ligands DHA, ATP or FAD. However, it must be stated that RMSD values do not give information on the vectorial aspects of the movements. As major RMSD variations are seen in the first 10 or 20 ns, the subsequent analysis of the molecular dynamics trajectory was restricted to the 20–120 ns time period. Figure7a shows the distribution of C α mobility along the two peptide chains of the three systems. In this figure, mobility is presented in terms of fluctuation relative to the mean position of each atom (RMSF). Thirteen high mobility regions were observed in each peptide chain, six of them located in the K (I–VI) and seven in the L domains (VII–XIII). They are colored in the structure of apo-hTKFC shown in Figure7b and marked by similarly colored rectangles in both parts of Figure7. In the K domains, most of the mobility was located within protein loops. This was so in mobile regions I–IV, while V and VI included significant portions of α-helices. In the L domains, the seven mobile regions corresponded each with a protein loop but included in every case significant portions of α-helices. In no case did high mobility affect β strands (present only in the K domains). With a few exceptions, the mobile regions behaved similarly in both peptide chains. Most conspicuous was the large difference in mobility of the two regions VII and, to a lesser extent, the two regions IX. In L1, Int. J. Mol. Sci. 2018, 19, x FOR PEER REVIEW 7 of 19

Figure 5. Molecular dynamics of hTKFC and its complexes with kinase or cyclase substrates. The Int. J. Mol.figure Sci. shows2019, 20 the, 1099 superimposition of 60 snapshots extracted from 120-ns trajectories at 2-ns intervals 7 of 19 and aligned with the initial conformations. regionThe VII divergence was highly of mobile the three in apo-hTKFCsystems with but respect showed to the little respective ﬂuctuation initial in structures hTKFC:2DHA:2ATP, after their andalignment hTKFC:2FAD., was quantitated Similar but inless terms marked of behaviorRMSD of was the observedCα positions in L1 ( regionFigure IX. 6). RegionThe increasing VII of L2, compareddeviations to converged L1, showed towards much a lesser plateau ﬂuctuation with RMSD in about the case 5 Å of when apo-hTKFC, all the Cα and atoms higher of hTKFC mobility were in hTKFC:2DHA:2ATP.considered. RMSD values L2 region calculated IX did notseparately show differences for each L amongor K domain the three were systems. smaller The than differences those for observedthe full proteins in the mobility, an ind ofication regions of L1the VII occurrence and L1 IX, ofbetween movements apo-hTKFC of one domain and the with systems respect containing to the boundother. substrates, In general, correlate the K domains with the proximityshowed higher of bound conformational ATP or FAD stabilityto these parts than of the L1 L (see ones. Figure Upon1). Incomparison this regard, of the the different three systems, responses there of was L1 andno consistent L2 to bound effect substrates of the presence (Figure 7ofa) hTKFC are intriguing, ligands DHA, ATP or FAD. However, it must be stated that RMSD values do not give information on the and may be related to the different degree of closure of L2-K1 and K2-L1 sites during the molecular vectorial aspects of the movements. As major RMSD variations are seen in the first 10 or 20 ns, the dynamics of hTKFC:2DHA:2ATP (Figure5). subsequent analysis of the molecular dynamics trajectory was restricted to the 20–120 ns time period.

FigureFigure 6. 6.Root-mean-square Root-mean-square deviationsdeviations (RMSD)(RMSD) of CCαα atomsatoms during molecular dynamics dynamics simulation simulation ofof hTKFC hTKFC and and its its complexes complexes withwith kinasekinase oror cyclasecyclase substrates.substrates. Distances were were calculated calculated relative relative to to theirtheir initial initial positions positions inin thethe structuralstructural modelsmodels prepared.prepared. The different panels panels show, show, as as indicated, indicated, the the RMSDRMSD values values calculated calculated forfor thethe fullfull proteinprotein oror for each p proteinrotein domain separately separately.. The The colored colored traces traces correspondcorrespond to to (blue) (blue) apo-hTKFC,apo-hTKFC, (red)(red) hTKFC:2DHA:2ATPhTKFC:2DHA:2ATP and (green) hTFKC:2FAD. Each Each system system waswas ﬁrst first submitted submitted toto anan energy-minimizingenergy-minimizing andand equilibrationequilibration process, upon upon which which the the trajectory trajectory productionproduction phase phase waswas started.started. AtAt timetime zerozero the three systems differed from the the in initialitial ones ones with with Cα Cα RMSDRMSD values values of of 2.57 2.57 Å, Å , 2.392.39 ÅÅ andand 2.562.56 Å,Å , respectively.respectively.

PrincipalFigure 7a component shows the analysis distribution was of applied Cα mobility to reveal along the the most two important peptide chains movements of the in three the trajectoriessystems. In of this apo-hTKFC, figure, mobility hTKFC:2DHA:2ATP, is presented in andterms hTKFC:2FAD, of fluctuation i.e., relative their essentialto the mean dynamics, position and of alsoeach as atom an alternative (RMSF). Thirteen method high to normal mobility mode regions analysis were [ 23observed]. The magnitudes in each peptide of the chain, first 25six principalof them componentslocated in the or K eigenvectors (I–VI) and seven are shown in the inL domains Figure8. (VII In all–XIII). cases, They the are first colored component in the was structure predominant of apo- overhTKFC the shown others, in although Figure 7b the and difference marked by was similarly less marked colored in rectangles the hTKFC:2FAD in both parts system. of Figure The first7. In 3 eigenvectorsthe K domains, explain most 68% of the of themobility variance was of located the apo-hTKFC within protein and hTKFC:2DHA:2ATP loops. This was so in systems, mobile andregions 52% ofI– hTKFC:2FADIV, while V and complex. VI included Of course, significant similar portions variances of α do-helices. not mean In the similarity L domains, in termsthe seven of direction. mobile Inregions this concern, corresponded the results each of with the pairwisea protein comparison loop but included of the firstin every 3 eigenvectors case significan of thet portions three systems of α- studiedhelices. are In presentedno case did in high Figure mobility9, which affect shows β thatstrands the (present principal only components in the K ofdomains). hTKFC:2DHA:2ATP With a few andexceptions hTKFC:2FAD, the mobile differed regions from thosebehaved of apo-hTKFC, similarly inbut both also peptide that those chains. of the Most two conspicuous substrate-containing was the systemslarge difference differed in from mobility each other.of the Statictwo reg representationsions VII and, to of a thelesser first extent, eigenvector the two of regions each system IX. In L1, are shownregion inVII Figure was highly 10 in themobile form in of apo porcupine-hTKFC but plots, showed while little an animatedfluctuation representation in hTKFC:2DHA:2ATP can be seen and in SupplementalhTKFC:2FAD. movie Similar 2. but Figure less 10marked shows behavior that an importantwas observed contribution in L1 region to principal IX. Region component VII of L2, 1 wascompare maded by to theL1, movementshowed much of the lesser L2 domainfluctuation loop in labeled the case as of XIII apo in-hTKFC, Figure7 .and It is higher worth mobility noting that in thishTKFC:2DHA:2ATP. region is disordered L2 inregion the crystallized IX did not showCitrobacter differencesDHA among kinase the [16 three] used systems. as a template The differences to model hTKFCobserved [2] in (see the also mobility Section of 4.1regions). Actually, L1 VII theand large L1 IX, mobility between of apo loop-hTKFC XIII is and consistent the systems with thecontaining fact that thesebound amino substrates, acids are correlate not visible with in the the proximity electron densityof bound map ATP of or the FADCitrobacter to theseprotein. parts of As L1 displayed(see Figure in Figure1). In this10 and regard in the, the Supplemental different responses movie 2,of thisL1 and loop L2 seems to bound to play substrates an important (Figure role 7a) in are the intriguing, closure of theand L2-K1 may site.be related to the different degree of closure of L2-K1 and K2-L1 sites during the molecular dynamics of hTKFC:2DHA:2ATP (Figure 5). Int. J. Mol. Sci. 2019, 20, 1099 8 of 19 Int. J. Mol. Sci. 2018, 19, x FOR PEER REVIEW 8 of 19

Int. J. Mol. Sci. 2018, 19, x FOR PEER REVIEW 9 of 19

two substrate-containing systems differed from each other. Static representations of the first eigenvector of each system are shown in Figure 10 in the form of porcupine plots, while an animated representation can be seen in Supplemental movie 2. Figure 10 shows that an important contribution Figure 7. Distribution of mobility in the peptide chains of the hTKFC systems. (a) Root-mean square to principalFigure component 7. Distribution 1 was of mobility made byin the the peptide movement chains of of the the L2hTKFC domain systems. loop ( alabeled) Root-mean as XIII square in Figure ﬂuctuations (RMSF) of Cα atom positions relative to their mean positions during the 20–120-ns 7. It is worthfluctuations noting (RMSF) that this of Cαregion atom is positions disordered relative in the to crystallized their mean positions Citrobacter during DHA the kinase 20–120 [16]-ns used molecular dynamics simulations. Data for subunits 1 and 2 are in separate panels. (b) Location of the as a templatemolecular to dynamics model hTKFC simulations [2] .(see Data also for subunit Sections 1 4and.1). 2Actually, are in separate the largepanels mobility. (b) Location of loop of the XIII is regions with higher ﬂuctuation in the structural model of apo-hTKFC before the dynamics. The colored consistentregions with with the higher fact that fluctuation these in amino the str acidsuctural are model not visible of apo- hTKFC in the before electro then density dynamics map. The of the rectangles below the secondary structure schemes in (a) and those in (b) mark these regions in the two Citrobactercolored protein. rectangles As belowdisplayed the secondary in Figure structure 10 and schemes in the Supplementalin (a) and those inmovie (b) mark 2, this these loop regions seems to peptide chains. Only one region VI is visible in part (b). play anin important the two peptide role chainsin the. closureOnly one of region the L2 VI- Kis 1visible site. in part (b).

Principal component analysis was applied to reveal the most important movements in the trajectories of apo-hTKFC, hTKFC:2DHA:2ATP, and hTKFC:2FAD, i.e., their essential dynamics, and also as an alternative method to normal mode analysis [23]. The magnitudes of the first 25 principal components or eigenvectors are shown in Figure 8. In all cases, the first component was predominant over the others, although the difference was less marked in the hTKFC:2FAD system. The first 3 eigenvectors explain 68% of the variance of the apo-hTKFC and hTKFC:2DHA:2ATP systems, and 52% of hTKFC:2FAD complex. Of course, similar variances do not mean similarity in terms of direction.FigureFigure 8. 8.InEssential Essential this concern, dynamics dynamics the results of of hTKFC hTKFC of the and and p its airwiseits complexes complexes comparison with with kinase kinase of the or or cyclasefirst cyclase 3 eigenvectors substrates. substrates. The Theof ﬁrstthe first three 25 systemseigenvectors25 eigenvectors studie ord principal are or principalpresented components components in Figureare shown are 9 , shown inwhich decreasing in shows decreasing order that of order eigenvalue. the of principal eigenvalue. The bars components The represent bars of hTKFC:2DHA:2ATPtherepresent eigenvalues. the eigenvalues. The and lines hTKFC:2FAD represent The lines therepresent differed cumulative the from cumulative percentages those of percentages apo of eigenvalues.-hTKFC, of eigenvalues. but also that those of the

Figure 9. Comparison of principal components 1–3 for the systems studied. Inner products for each comparison are displayed in a grey scale: from 1.0, identity, to 0.0, orthogonality.

Figure 10. Porcupine representation of principal component 1 for the systems studied. The first line shows the more open of the two extreme conformations defined by the first principal component. The central and lower lines show, respectively, “lateral” and “top” views of the arrow sets indicating the direction and extent of the motion for each Cα atom. An animated representation can be seen in Supplemental movie 2.

Int. J. Mol. Sci. 2018, 19, x FOR PEER REVIEW 9 of 19 Int. J. Mol. Sci. 2018, 19, x FOR PEER REVIEW 9 of 19 two substrate-containing systems differed from each other. Static representations of the first eigenvectortwo substrate of each-containing system are systems shown differed in Figure from 10 in each the form other of. Staticporcupine representations plots, while of an theanimated first representationeigenvector of ca eachn be systemseen in are Supplemental shown in Figure movie 10 2in. Figurethe form 10 of shows porcupine that an plots important, while an contribution animated to principalrepresentation component can be seen1 was in made Supplemental by the movement movie 2. Figure of the 10L2 shows domain that loop an importantlabeled as contributionXIII in Figure to principal component 1 was made by the movement of the L2 domain loop labeled as XIII in Figure 7. It is worth noting that this region is disordered in the crystallized Citrobacter DHA kinase [16] used 7. It is worth noting that this region is disordered in the crystallized Citrobacter DHA kinase [16] used as a template to model hTKFC [2] (see also Section 4.1). Actually, the large mobility of loop XIII is as a template to model hTKFC [2] (see also Section 4.1). Actually, the large mobility of loop XIII is consistent with the fact that these amino acids are not visible in the electron density map of the consistent with the fact that these amino acids are not visible in the electron density map of the Citrobacter protein. As displayed in Figure 10 and in the Supplemental movie 2, this loop seems to Citrobacter protein. As displayed in Figure 10 and in the Supplemental movie 2, this loop seems to play an important role in the closure of the L2-K1 site. play an important role in the closure of the L2-K1 site.

FigureFigure 8. 8.Essential Essential dynamics dynamics of of hTKFC hTKFC and and its its complexescomplexes with kinase oror cyclasecyclase substrates. substrates. The The first first

25Int. 25 eigenvectors J. eigenvectors Mol. Sci. 2019 , or20 or, 1099principal principal components components areare shown shown inin decreasing order order of of eigenvalue. eigenvalue. The The9 of bars bars19 representrepresent the the eigenvalues. eigenvalues. The The lines lines represent represent the the cumulativecumulative percentages of of eigenvalues. eigenvalues.

Figure 9. Comparison of principal components 1–3 for the systems studied. Inner products for each FigureFigure 9. Comparison 9. Comparison of principal of principal components components 1–31–3 forfor the the systems systems studied. studied Inner. Inner products products for each for each comparison are displayed in a grey scale: from 1.0, identity, to 0.0, orthogonality. comparisoncomparison are displayed are displayed in ina grey a grey scale: scale: from from 1.0,1.0, identity, identity, to to 0.0, 0.0, orthogonality. orthogonality.

Figure 10. Porcupine representation of principal component 1 for the systems studied. The first line Figureshows 10. thePorcu morepine open representation of the two extreme of principal conformations component defined 1 for by the the systems first principal studied component.. The first line shows the more open of the two extreme conformations defined by the first principal component. The FigureThe 10. central Porcu andpine lower representation lines show, respectively, of principal “lateral” component and “top” 1 for views the ofsystems the arrow studied sets indicating. The first line centralthe directionand lower and lines extent show, of the respectively, motion for each “lateral” Cα atom. and An “top” animated views representation of the arrow cansets be indicating seen in the shows the more open of the two extreme conformations defined by the first principal component. The directionSupplemental and extent movie of 2. the motion for each Cα atom. An animated representation can be seen in central and lower lines show, respectively, “lateral” and “top” views of the arrow sets indicating the Supplemental movie 2. direction2.3. Active-Site and extent Closure of in the the motion hTKFC-2DHA-2ATP for each Cα Complex: atom. An Conformations animated representation for In-Line Nucleophilic can be Attack seen in and Phosphoryl Transfer from ATP to DHA Supplemental movie 2. The major reason to undertake this molecular dynamics study was to investigate the closure of hTKFC active site as the possible way for ATP and triose, which in the initial structure bind quite apart from each other (Figure1), to reach an optimal conformation for an in-line phosphoryl transfer. For a hypothetical attack operating through an associative mechanism [24], such conformation should display both the proper distance (e.g., <3.5 Å) between the γ-phosphorus atom of ATP and one of the primary hydroxyl oxygens of the trihydroxyprop-2-yl radical covalently bound to His221, and an adequate angle (e.g., >155◦) formed by this oxygen-phosphorus pair with the scissible P–O linkage of ATP. Int. J. Mol. Sci. 2018, 19, x FOR PEER REVIEW 10 of 19

2.3. Active-Site Closure in the hTKFC-2DHA-2ATP Complex: Conformations for In-Line Nucleophilic Attack and Phosphoryl Transfer From ATP to DHA The major reason to undertake this molecular dynamics study was to investigate the closure of hTKFC active site as the possible way for ATP and triose, which in the initial structure bind quite apart from each other (Figure 1), to reach an optimal conformation for an in-line phosphoryl transfer. For a hypothetical attack operating through an associative mechanism [24], such conformation should display both the proper distance (e.g., <3.5 Å ) between the γ-phosphorus atom of ATP and one of the primary hydroxyl oxygens of the trihydroxyprop-2-yl radical covalently bound to His221, and an adequate angle (e.g., >155°) formed by this oxygen-phosphorus pair with the scissible P–O linkage of ATP.

OneInt. important J. Mol. Sci. 2019 aspect, 20, 1099 of this question was to evaluate the influence of substrates10 of 19 bound to hTKFC on the trend towards active-site closure. As stated above, the direct visual inspection of the trajectories summarized in Figure 5 makes clear the marked closure of the L2-K1 site in the presence One important aspect of this question was to evaluate the inﬂuence of substrates bound to hTKFC of DHAon and the trend ATP, towards not in active-site the other closure. systems As stated. To above, make the this direct a visual quantitative inspection comparison of the trajectories, distances betweensummarized marker atoms in Figure in the5 makes L domain clear the and marked the closureK domai of then of L2-K1 the sitesame in thesite presence (i.e., L2 of-K1 DHA or K2-L1), irrespectivelyand ATP, ofnot the in presence the other systems. or absence To make of thisligands, a quantitative were taken comparison, from distances the 120 between-ns trajectories marker of the three systems.atoms in The the L marker domain and atoms the K were domain chosen of the same by their site (i.e., involvement L2-K1 or K2-L1), in irrespectivelythe hTKFC:2DHA:2ATP of the presence or absence of ligands, were taken from the 120-ns trajectories of the three systems. The marker complex in the binding of ATP or DHA. The atoms selected were Mg2, which is coordinated with the atoms were chosen by their involvement in the hTKFC:2DHA:2ATP complex in the binding of ATP or L domainDHA. and The interacts atoms selected with the were γ Mg2,-phosphoryl which is coordinated group of withATP the when L domain present, and interacts and the with Nε2 the atom of His221, toγ -phosphorylwhich triose group is covalently of ATP when bound present, when and the present. Nε2 atom The of Hisshortening221, to which of triosethe Mg2 is covalently···Nε2 distance was usedbound as an when indication present. of The active shortening-site ofclosure, the Mg2 and···Nε 2its distance evolution was used during as an the indication 120-ns of trajectories active-site in the two activeclosure, sites and of itsthe evolution three systems during the is 120-nsshown trajectories in Figure in the11. two In activeagreement sites of with the three the systems observations is of shown in Figure 11. In agreement with the observations of Figure5, active-site closure was clearly Figure 5, active-site closure was clearly favored by the presence of bound ATP and DHA, although favored by the presence of bound ATP and DHA, although only in the L2-K1 site, not in the K2-L1 one. only in the L2-K1 site, not in the K2-L1 one.

Figure 11. Estimation of the closure of the active sites of hTKFC and its complexes with kinase or Figure 11. Estimation of the closure of the active sites of hTKFC and its complexes with kinase or cyclase substrates during the simulated trajectories. Distances were measured between Mg2 in the L cyclase substratesdomain and dur the Ningε2 ofthe His simulated221 in the K trajectories. domain of the D sameistance site,s i.e., were L2-K1 measured or K2-L1. between Mg2 in the L domain and the Nε2 of His221 in the K domain of the same site, i.e., L2-K1 or K2-L1. Once it was established that ATP and DHA bound to hTKFC favored at least the closure of one Onceof theit was active established sites, we scanned that ATP the 160-ns and DHA trajectory bound of hTKFC:2DHA:2ATP to hTKFC favored for at the least two parametersthe closure of one which delimit the possibility of in-line nucleophilic attack of DHA (the trihydroxyprop-2-yl radical of the activecovalently sites, bound we scanned to His221 )the over 160 the-γns-phosphorus trajectory of of ATP: hTKFC:2DHA:2ATP O···P distance and O··· forP–O the angle. two Since parameters which delimitthe two the hydroxyl possibility groups of DHAin-line (and nucleophilic of the trihydroxyprop-2-yl attack of DHA radical) (the are trihydroxyprop equivalent, two O-2···-Pyl radical covalentlypairs bound were considered to His221) in over each the active γ- site.phosphorus of ATP: O···P distance and O···P–O angle. Since the two hydroxylFigure groups12 shows of the DHA scan of(and O··· Pof distance the trihydroxyprop in the two active-2 sites.-yl radical) Distances are <3.5 equivalent, Å were found two O···P pairs werein theconsidered L2-K1 site (notin each in K2-L1) active for site. signiﬁcant time fractions of the trajectory, either with one or the other DHA hydroxyl oxygen atom. This occurred, with DHA O1, at times 91–92 ns, 111–115 ns and Figure 12 shows the scan of O···P distance in the two active sites. Distances <3.5 Å were found in 130–160 ns, and with DHA O3, at 105–112 ns. Therefore, the O···P–O angle was scanned only in the the L2-K1L2-K1 site site(not from in K2 90- nsL1 to) for 160 ns,significant to search fortime the fractions coincidence of of the adequate trajectory, distances either (<3.5 with Å) with one good or the other DHA hydroxylangles (>155 oxygen◦). These atom. coincidences This occurred, were found with only DHA for DHA O1, O3 at within times the 91 105–112–92 ns, ns range.111–115 The ns data and 130– 160 ns, andfor thewith 7000 DHA snapshots O3, at of this105 range–112 arens. presented Therefore, in Figure the O 13···a.P The–O lower-rightangle was part scanned of the distribution only in the L2-K1 site fromcorresponds 90 ns to 160 to ns the, to snapshots search displayingfor the coinc theidence shorter Oof··· adequateP distances distances and the larger (<3.5 O Å)···P–O with angles. good angles The data for the 395 snapshots with O···P distances <3.5 Å and O···P–O angles >155◦ are shown in (>155°). These coincidences were found only for DHA O3 within the 105–112 ns range. The data for Figure 13b. Any of them is a plausible conformation for an in-line phosphoryl transfer. Two of these the 7000 snapshotssnapshots are of shown this range as examples are presented in Figure 14 in, oneFigure selected 13a. because The lower it displays-right thepart shortest of the O distribution···P correspondsdistance to (3.16the snapshots Å), the other displaying because it displays the shorter the largest O··· OP··· distancesP–O angle (178.45and the◦). larger O···P–O angles. The data for the 395 snapshots with O···P distances <3.5 Å and O···P–O angles >155° are shown in

Int. J. Mol. Sci. 2018, 19, x FOR PEER REVIEW 11 of 19

Int. J. Mol. Sci. 2018, 19, x FOR PEER REVIEW 11 of 19 Figure 13b. Any of them is a plausible conformation for an in-line phosphoryl transfer. Two of these snapshotsFigure 13 areb. Anyshown of them as examples is a plausible in Figure conformation 14, one for selected an in-line because phosphoryl it displays transfer. the Two shortest of these O··· P Int. J. Mol. Sci. 2019, 20, 1099 11 of 19 distancesnapshots (3.16 are Å ),shown the other as examples because itin displays Figure 14, the one largest selected O···P because–O angle it (displays178.45°). the shortest O···P distance (3.16 Å ), the other because it displays the largest O···P–O angle (178.45°).

FigureFigureFigure 12. 12.Evolution 12. Evolution Evolution of of theof the the DHA-to-ATP DHA DHA-to-to-ATP-ATP distance distancedistance inin the hTKFC:2DHA:2ATP trajectory. trajectory. trajectory. Distances Distances Distances werewerewere measured measured measured in in the in the the full full full 160-ns 160 160-ns-ns trajectory trajectory trajectory between between between each ofof of the the the hydroxylhydroxyl hydroxyl oxygens oxygens oxygens of of DHA of DHA DHA (the (the (the trihydroxyprop-2-yltrihydroxyproptrihydroxyprop-2-yl2 radical-yl radical radical covalently covalently covalently bound bound bound to toto His HisHis221221)) and and thethe the γ γ-γ-phosphorusphosphorus-phosphorus of of A of ATP ATPTP in in the in the same the same same site site site (i.e.,(i.e. L2-K1(i.e., L2, -L2K1 and-K1 and and K2-L1). K2 K2-L1-L1) The. )The. The pink pink pink line line linemarks marks marks the thethe 3.53.5 Å distance. TheThe The first first ﬁrst 75 75 75-ns-ns-ns of of this of this this trajectory trajectory trajectory have have have beenbeen reportedbeen reported reported in in earlier inearlier earlier work work work [ 2[2]]. [2]. .

Figure 13. Combination of O···P distances and O···P–O angles in the L2-K1 site during the Figure 13. Combination of O···P distances and O···P–O angles in the L2-K1 site during the FigurehTKFC:2DHA:2ATP 13. Combination trajectory of O··· inP thedistances 105–112 and-ns timeO··· P range–O angles. The points in the correspond L2-K1 site to snapshot during s the hTKFC:2DHA:2ATPhTKFC:2DHA:2ATPextracted at 1-ps intervals trajectory trajectory andin inindicate the the 105–112-ns 105 O–···112P distance-ns timetime from range. range the. TheDHA The points pointsO3 oxygen correspond correspond to the P to atom,to snapshot snapshots and s extractedextractedthe corresponding at 1-psat 1-ps intervals intervals O··· andP –andO indicate angle. indicate (a O) ···O D···PataP distance distance for the from7000 from the snapshots. the DHA DHA O3 (O3b) oxygen Magnificationoxygen to to the theP ofP atom, atom, the red and and the correspondingtherectangle corresponding of O ···panelP–O O a···, angle. includingP–O angle.(a) Data395 ( asnapshots for) D theata 7000 for. The the snapshots. conformations 7000 snapshots. (b) Magniﬁcationmarked (b) inMagnification red in of the the close red of rectangle- up the are red of panelrectangleidentified a, including of panelby its 395 timea, snapshots.including in picosecond 395 The snapshotss conformations (shown in. The Figure conformations marked 14). in red marked in the close-up in red in are the identiﬁed close-up are by its Int.time J. Mol.identified in Sci. picoseconds 2018 by, 19 its, x time FOR (shown inPEER picosecond inREVIEW Figures (14shown). in Figure 14). 12 of 19 3. Discussion 3. Discussion hTKFC catalyzes the ATP-dependent phosphorylation of DHA and GA, and the splitting of FAD to hTKFCform cyclic catalyzes FMN. Inthe previous ATP-dependent work a detailed phosphorylation enzymatic stud of DHAy of the and protein GA, and was the undertaken. splitting of This FAD to formincluded cyclic probing FMN. the In previousrole of several work amino a detailed acids enzymatic by mutagenesis study and of the the proteinindividual was exp undertaken.ression of the This includedK and Lprobing protein the domains role of [2] several. The main amino objective acids by of mutagenesis the current paper and the was individual to get further exp ressioninsights of on the K andthe roleL protein of protein domains domain [2] mobility. The main into objective the mechanism of the ofcurrent the DHA paper kinase was activity to get furtherof hTKFC. insights on the role of protein domain mobility into the mechanism of the DHA kinase activity of hTKFC.

FigureFigure 14. 14.Selected Selected near near attack attack conformations conformations of hTKFC:2DHA:2ATP detected detected during during the the molecular molecular dynamicsdynamics trajectory trajectory in in the the L2–K1 L2–K1 site. site. LightLight gray, L2 domain; dark dark gray, gray, K1 K1 domain. domain. The The images images correspondcorrespond to to snapshots snapshots 107633 107633 (left) (left) and and 108032108032 (right-hand(right-hand side).

Two enzymatic systems are known that phosphorylate DHA [10]. On the one hand, in eukaryotes and some bacteria, including Citrobacter, this reaction is catalyzed by enzymes which require ATP as cosubstrate, and are commonly known as ATP-dependent DHA kinases. It is not known whether all these enzymes are also able to convert FAD in cyclic FMN, but this is true at least for the Citrobacter enzyme [12]. The crystal structure of Citrobacter DHA kinase is available [16] and it was used by us as template to model hTKFC [2]. Both the bacterial enzyme and the model of the human one are homodimeric proteins formed by chains (1 and 2) having each two domains, K and L, connected by an extended, 20-amino acids linker. ATP, in complex with two Mg2+ ions, binds to domain L, whereas DHA binds covalently to domain-K His221 (hTKFC; His220 in Citrobacter). As described (see Figure 1), these proteins display an elongated intertwined structure L2-K1-K2-L1, with two active sites per dimer, located in the interfaces between, respectively, K1 and L2, and K2 and L1 domains. It may be assumed that putative ATP-dependent DHA kinases sharing high homology with hTKFC, will have a similar general structure. On the other hand, in most bacteria the DHA kinase system is composed of three randomly interacting proteins DhaK, DhaL and DhaM, which have been enzymatically and structurally studied in e.g., Escherichia coli [25–27] and Lactococcus lactis [28]. Rather than using ATP as a cosubstrate, this system depends on ADP tightly bound to DhaL as a prosthetic group, which in each enzyme cycle is alternatively phosphorylated to ATP by DhaM, a phosphoprotein of the phosphoenolpyruvate:sugar phosphotransferase system (PTS), and dephosphorylated when the phosphoryl group of ATP is transferred to DHA covalently bound to DhaK [29]. However, important similarities exist between the ATP-dependent and the PTS- dependent kinases. First, the DhaK and DhaL subunits of PTS-dependent DHA kinases are homologous to the K and L domains of the ATP-dependent DHA kinases, both in sequence and function. Second, the E. coli DhaK-DhaL complex crystallizes as a heterotetramer formed by two DhaK and two DhaL monomers, in which the overall disposition DhaL-DhaK-DhaK-DhaL resembles the L2-K1-K2-L1 structure of the hTKFC homodimer. Third, in both groups of enzymes, DHA is bound to a His residue by a hemiaminal linkage. The crystal structure of the E. coli DhaK–DhaL complex contains ADP and DHA [27]. When ADP is replaced by ATP (i.e., the phosphorylated form of the cofactor), the γ-phosphoryl atom of ATP appears located 3.9 Å away from the 1(3)-OH group of DHA, and the orientation of DhaL relative to DhaK is consistent with a direct transfer of the γ-phosphoryl moiety from ATP to a terminal hydroxyl group of DHA. Taking into account the structures obtained, a general three-step mechanism has been proposed for PTS-dependent DHA kinases: formation of the hemiaminal linkage, direct phosphoryl transfer from ATP to DHA, and release of DHAP [27]. Recently, a theoretical study of this mechanism has been performed using quantum mechanics/molecular mechanics methods [30]. Contrary to what is seen in the E. coli enzyme, in the crystal structure of the Citrobacter DHA kinase the ATP molecule and the DHA moiety lie too far apart (≈14 Å ) for an in-line phosphoryl

Int. J. Mol. Sci. 2019, 20, 1099 12 of 19

3. Discussion hTKFC catalyzes the ATP-dependent phosphorylation of DHA and GA, and the splitting of FAD to form cyclic FMN. In previous work a detailed enzymatic study of the protein was undertaken. This included probing the role of several amino acids by mutagenesis and the individual expression of the K and L protein domains [2]. The main objective of the current paper was to get further insights on the role of protein domain mobility into the mechanism of the DHA kinase activity of hTKFC. Two enzymatic systems are known that phosphorylate DHA [10]. On the one hand, in eukaryotes and some bacteria, including Citrobacter, this reaction is catalyzed by enzymes which require ATP as cosubstrate, and are commonly known as ATP-dependent DHA kinases. It is not known whether all these enzymes are also able to convert FAD in cyclic FMN, but this is true at least for the Citrobacter enzyme [12]. The crystal structure of Citrobacter DHA kinase is available [16] and it was used by us as template to model hTKFC [2]. Both the bacterial enzyme and the model of the human one are homodimeric proteins formed by chains (1 and 2) having each two domains, K and L, connected by an extended, 20-amino acids linker. ATP, in complex with two Mg2+ ions, binds to domain L, whereas DHA binds covalently to domain-K His221 (hTKFC; His220 in Citrobacter). As described (see Figure1), these proteins display an elongated intertwined structure L2-K1-K2-L1, with two active sites per dimer, located in the interfaces between, respectively, K1 and L2, and K2 and L1 domains. It may be assumed that putative ATP-dependent DHA kinases sharing high homology with hTKFC, will have a similar general structure. On the other hand, in most bacteria the DHA kinase system is composed of three randomly interacting proteins DhaK, DhaL and DhaM, which have been enzymatically and structurally studied in e.g., Escherichia coli [25–27] and Lactococcus lactis [28]. Rather than using ATP as a cosubstrate, this system depends on ADP tightly bound to DhaL as a prosthetic group, which in each enzyme cycle is alternatively phosphorylated to ATP by DhaM, a phosphoprotein of the phosphoenolpyruvate:sugar phosphotransferase system (PTS), and dephosphorylated when the phosphoryl group of ATP is transferred to DHA covalently bound to DhaK [29]. However, important similarities exist between the ATP-dependent and the PTS-dependent kinases. First, the DhaK and DhaL subunits of PTS-dependent DHA kinases are homologous to the K and L domains of the ATP-dependent DHA kinases, both in sequence and function. Second, the E. coli DhaK-DhaL complex crystallizes as a heterotetramer formed by two DhaK and two DhaL monomers, in which the overall disposition DhaL-DhaK-DhaK-DhaL resembles the L2-K1-K2-L1 structure of the hTKFC homodimer. Third, in both groups of enzymes, DHA is bound to a His residue by a hemiaminal linkage. The crystal structure of the E. coli DhaK–DhaL complex contains ADP and DHA [27]. When ADP is replaced by ATP (i.e., the phosphorylated form of the cofactor), the γ-phosphoryl atom of ATP appears located 3.9 Å away from the 1(3)-OH group of DHA, and the orientation of DhaL relative to DhaK is consistent with a direct transfer of the γ-phosphoryl moiety from ATP to a terminal hydroxyl group of DHA. Taking into account the structures obtained, a general three-step mechanism has been proposed for PTS-dependent DHA kinases: formation of the hemiaminal linkage, direct phosphoryl transfer from ATP to DHA, and release of DHAP [27]. Recently, a theoretical study of this mechanism has been performed using quantum mechanics/molecular mechanics methods [30]. Contrary to what is seen in the E. coli enzyme, in the crystal structure of the Citrobacter DHA kinase the ATP molecule and the DHA moiety lie too far apart (≈14 Å) for an in-line phosphoryl transfer to take place, and attempts to crystallize alternative more closed conformations have been unsuccessful. It has been suggested that K- and L-domains, connected just by a long spacer, could move with respect to each other, and that domain mobility would be required for kinase activity [10,16]. The relative mobility of both domains has been actually shown by us in a previous work with the homology model of hTKFC, where, in the course of a 75-ns trajectory of molecular dynamics, transient ATP-to-DHA approximations are seen in the L2-K1 site, displaying apparent near-attack conformations that, however, last very shortly [2]. In the current work, we have followed different approaches that conﬁrm the trend towards closure of at least one of the hTKFC active sites. On the one hand, normal mode analysis indicated that the Int. J. Mol. Sci. 2019, 20, 1099 13 of 19

first non-trivial mode of the protein displayed precisely this trend, although this was independent of the presence or absence of substrates in the protein complex (Figure2, NM7 mode). On the other hand, when the simulation of molecular dynamics was extended beyond the original 75 ns, the L2-K1 site resumed its closure movements and reached closer ATP-to-DHA approximations, including O···P distances <3.5 Å measured between the entering hydroxyl oxygen and the attacked phosphorus atom, which lasted for several nanoseconds (Figure 12). These approximations to <3.5 Å distances included many snapshots in which the O···P–O angle was near 180◦, pointing to an almost perfect in-line attack conformation (Figure 13). The molecular dynamics of apo-hTKFC and hTKFC:2FAD showed a much less marked trend towards active-site closure (Figure 11). In fact, such movement is unlikely to have any significance for the FMN cyclase activity of hTKFC, as it has been shown that the isolated L domain is almost as efficient cyclase as the dimeric protein [2]. Regarding the fact that during the 160-ns molecular dynamics trajectory only one of the two active sites reaches a closed state, several arguments may be made. One possibility is that both centers could not close simultaneously. However, from our kinetic studies it seems that the enzyme follows a standard hyperbolic kinetics, with no signs of substrate cooperativity, either positive or negative [2]. So, it seems that the behavior of one active site would not affect the other. Furthermore, normal mode analysis suggested that both sites could actually move towards a closed conformation (Figure2). More likely, it could be that a longer molecular dynamics trajectory could be needed to obtain a fully closed enzyme. Actually, from our former kinetic studies [2] it is known that the DHA kinase activity of −1 hTKFC has a kcat of 5 s , i.e., one catalytic event each 200 ms. Therefore, the 160 ns simulation is far from covering the time length required for a full catalytic event. From the results discussed above, it may be assumed that, despite the large difference of relative positioning of ATP and DHA in PTS-dependent and ATP-dependent DHA kinases, inferred from structural data, the phosphoryl group is transferred directly from ATP to enzyme-bound DHA in both enzyme kinds, without any enzyme intermediary phosphorylation step. The general chemical mechanisms of phosphoryl transfer have been reviewed by several authors [24,31–34]. In principle, these transfer reactions may be described as following either a stepwise (associative or dissociative) or a concerted mechanism. A stepwise, fully associative addition-elimination mechanism proceeds via a bipyramidal intermediate in which the phosphorus atom of a phosphorane intermediate is simultaneously bound to the entering and leaving oxygen. At a near-attack conformation, the entering oxygen should be at a distance of ≈3.3 Å of the phosphorus, i.e., the van der Waals sum of both atoms (P, 1.9 Å; O, 1.4 Å). Remarkably, in our simulation of the molecular dynamics of hTKFC:2DHA:2ATP, starting from a distance ≈14 Å, conformations easily compatible with a fully associative mechanism were reached (Figures 13b and 14). A stepwise, fully dissociative elimination-addition mechanism proceeds via the separation of the phosphoryl group from the donor to form a metaphosphate intermediate that then reacts with the acceptor. At the intermediate step, when the metaphosphate intermediate exists, there could be contact between the P atom and both oxygens, but not bonding. At this time, both P–O distances would be ≥3.3 Å. If one assumes that, once the attack conformation is reached, the relative positions of the entering and leaving oxygens do not change significantly, in the near-attack conformations of Figures 13b and 14 there would be no room for a fully dissociative reaction. The two kinds of stepwise mechanisms may better represent two extreme situations, while many enzymes would follow an alternative one-step concerted mechanism, in which breaking and forming of the phosphorus bonds with the leaving and entering oxygen atoms occurs more or less simultaneously. As these processes do not necessarily occur synchronously, a concerted reaction can proceed through different types of transition states, ranging from more loose (or dissociative-like) to more tight (or associative-like) ones. The near-attack conformations of Figures 13b and 14 are compatible also with this kind of mechanism. Int. J. Mol. Sci. 2019, 20, 1099 14 of 19

In summary, as during the molecular dynamics trajectory, very short distances were reached between the ATP γ-phosphoryl group and the DHA moiety (Figures 13b and 14), it seems unlikely that the phosphoryl transfer between both substrates could follow a fully dissociative reaction. So, the results presented here for the DHA kinase activity of hTKFC would more likely point to either an associative mechanism or a concerted mechanism with a (more or less) tight transition state.

4. Materials and Methods

4.1. Structural Models of hTKFC The coordinates for hTKFC:2DHA:2ATP were those of a homology model constructed with Modeller [2] using two crystal structures of Citrobacter sp DHA kinase proteins as templates, one in apo form and the other containing bound ATP-Mg and DHA covalently bound to histidine [16]. The model of apo-hTKFC was obtained by manual removal of ATP and DHA (actually the trihydroxyprop-2-yl radical covalently bound to His221) from hTKFC:2DHA:2ATP also as described [2]. The structural model of hTKFC:2FAD was obtained by modiﬁcation of the published model of hTKFC:FAD which contains only one FAD bound to the L domain of subunit 1 [2]. Starting from this hTKFC:FAD model, the second FAD molecule was added to the L domain of subunit 2 using a transformation matrix, calculated with the VMD program version 1.9.1, that allowed to align subunit 1 with subunit 2. Slight atomic overlaps appearing in the binding of FAD to the second site were removed by energy minimization of the complex. The use of a homology model to study molecular dynamics adds a degree of uncertainty to the simulations as compared with the study of molecular dynamics based on crystal structures. This could be seen as an important limitation of the study. However, the models seem quite reliable, as hTKFC shares with the templates a 40% identity evenly distributed along the 575 amino acid sequence, while model and template display an overall RMSD of 0.7 Å. Actually, 40% identity is well within the safe homology modeling zone for protein alignments of this length [35,36]. The major concern deals with the completeness of the templates themselves. In the published structures of the Citrobacter DHA kinase, the amino acids aligning with residues 541–548 of hTKFC are missing, indicating that they are rather disordered [16]. Therefore, to be able to run the molecular dynamics simulation those residues were modeled de novo [2]. This part of the protein corresponds to the loop labeled XIII in Figure7. The composition of the three systems used for molecular simulations is summarized in Table1.

Table 1. Composition of the systems submitted to normal-mode analysis and molecular dynamics.

apo-hTKFC hTKFC:2DHA:2ATP hTKFC:2FAD Components used for both procedures hTKFC chains 2 2 2 Mg2+ 4 4 4 DHA 0 2 0 ATP 0 2 0 FAD 0 0 2 Components used only for molecular dynamics Na+ 84 84 84 Cl− 94 86 90 H2O 87,364 87,570 87,304 Total number of atoms In normal mode analysis 16,814 16,924 16,982 In molecular dynamics 279,084 279,804 279,068

4.2. Normal-Mode Analyses These simulations were run with GROMACS 4.0.7 [37] using the AMBER03 force ﬁeld [38]. τ The topologies and parameters of N -(1,2,3-trihydroxyprop-2-yl)-L–histidine, ATP and FAD are Int. J. Mol. Sci. 2019, 20, 1099 15 of 19 available under access codes F-86 and F-91 in the R.E.DD.B. database [39]. For the normal mode analyses, the three structural models of hTKFC obtained as described above were used in vacuo: apo-hTKFC, hTKFC:2DHA:2ATP, and hTKFC:2FAD. Prior to the analyses, the models were optimized with the GROMACS MD engine mdrun by running 5000 energy-minimization iterations by the steepest descent method, followed by 10,000–15,000 iterations with the low memory Broyden–Fletcher–Goldfarb–Shanno algorithm, such that the maximal force in any atom of the minimized structures was below 10−6 kJ mol−1 nm−1. For the energy minimizations, van der Waals and electrostatic interactions up to a distance of 10 Å were taken into account, although above 8 Å a corrective function was applied to make null the resulting energies of interactions at 10 Å. The atomic coordinates of the minimized conformations were used to calculate, also using mdrun, their hessian matrices (H), which are composed by the elements of Equation (1)

∂2V Hij = (1) ∂xi∂xj xi and xj being the cartesian coordinates of i and j atoms, and V the potential energy for their interaction. Eigenvectors and eigenvalues were determined from the hessian matrices with the program g_nmeig according to Equation (2)

−1/2 −1/2 T Λ = diag(λ1 ··· λ3N) = RM HM R (2)

T where Λ is a diagonal matrix with 3N eigenvalues λi, R is a matrix with eigenvectors in columns, R is the transpose of R, and M is a matrix containing the masses of the N atoms considered (Table1). The eigenvectors or normal modes are 3N-dimensional unitary vectors that describe the direction of collective atom movement, whereas the eigenvalues λi yield the frequencies of the normal modes through Equation (3) √ λ υ = i (3) i 2π After ordering the normal modes by increasing frequencies and disregarding the six trivial ones (NM1–NM6), which display the lowest frequencies, the next three modes, i.e., NM7, NM8 and NM9, were analyzed. Starting with the minimized conformations and the eigenvectors, the program g_nmtraj was used to generate trajectories that allowed visualization of the harmonic oscillations of each mode. Porcupine plots, drawn with the Normal Mode Wizard tool of VMD [40], were used as static representations of the normal modes. Quantitative comparisons between the normal modes of molecular systems with different numbers of atoms needs their reduction to sets of atoms shared in common. Therefore, to allow for the comparison of the normal modes of apo-hTKFC, hTKFC:2DHA:2ATP, and hTKFC:2FAD, the following approach was used. For each system and normal mode, a set of 5000 conformations was generated at 300 K with the g_nmens program included in GROMACS. From these conformations, the Cα, C, O and N atoms of the protein main chain were extracted, what gave the same atom number (4600) in every case. Principal component analyses of these sets of conformations, run as described in Section 4.4, allowed the eigenvalues and eigenvectors characteristic of each normal mode to be obtained. For the conformations for a single normal mode, only the ﬁrst eigenvalue is signiﬁcant while the rest are near null. To evaluate the similitude between normal modes of different systems, the inner products of their protein main chain eigenvectors were calculated, which adopted values between 1, indicative of identity, and 0, indicative of orthogonality.

4.3. Molecular Dynamics The trajectories of molecular dynamics of apo-hTKFC, hTKFC:2DHA:2ATP, and hTKFC:2FAD were simulated in the presence of explicit solvent (water and NaCl) using GROMACS 4.0.4 [37] and the AMBER03 force ﬁeld [38] supplemented like for the normal mode analysis. The conditions of the Int. J. Mol. Sci. 2019, 20, 1099 16 of 19 simulations, including the preliminary energy-minimizing process and equilibration steps, were as previously reported for a 75-ns trajectory recorded for hTKFC:2DHA:2ATP [2]. This was prolonged up to 160 ns under the same conditions, which were used also to record the 120-ns trajectories of apo-hTKFC and hTKFC:2FAD.

4.4. Essential Dynamics Principal component analysis was applied to the last 100 ns of the 120-ns trajectories recorded for the molecular dynamics of apo-hTKFC, hTKFC:2DHA:2ATP, and hTKFC:2FAD. To simplify the calculations, the procedure was applied only to the 1150 Cα atoms of each dimeric system (i.e., 575 per subunit). The g_covar program, included in GROMACS, was used to align 100,001 conformations of each system with the initial conformation to remove translation and rotation motions, thus generating x(t) trajectories (that can be viewed as matrices of size 3 × 1150 coordinates × 100,001 conformations), from which symmetric covariance matrices (C) of size 3450 × 3450 were calculated. The elements of C are given by Equation (4) Cij = h(xi − hxii) (xj − hxji)i (4) where hi represent time-averaged values. The same program was used to diagonalize C and to obtain Λ and R matrices T Λ = diag(λ1 ··· λ3450) = RCR (5) where Λ is a diagonal matrix with 3450 eigenvalues λi in decreasing order, R is a 3450 x 3450 matrix with eigenvectors in its columns, and RT is the transpose of R. The i column of R is the eigenvector associated to the λi eigenvalue of Λ. Each eigenvector describes a collective movement of atoms and the associated eigenvalue is the variance of its ﬂuctuations and represents the magnitude of the collective movement. The analysis of eigenvectors and eigenvalues was made with the g_anaeig program, also part of GROMACS.

5. Conclusions Computational evidence supports a marked trend of hTKFC:2DHA:2ATP, i.e., the complex typical of the DHA kinase activity of hTKFC, towards active-site closure in one of the two sites displayed by the dimeric enzyme. Normal mode analysis indicates a clear trend of both active sites towards closure in the first non-trivial normal mode. However, by this approach, no major, but only subtle differences are observed with respect to the normal modes of hTKFC:2FAD, the complex typical of the FMN cyclase activity of hTKFC, or of apo-hTKFC, the substrate-free enzyme. By contrast, molecular dynamics simulations run up to 120 ns with the three hTKFC systems indicate that one of the hTKFC:2DHA:2ATP active sites undergoes a full closure, with a very strong approximation of ATP to DHA, from about 14 Å in the initial state to below 3.5 Å. No such degree of active-site closure is observed in hTKFC:2FAD or apo-hTKFC, indicating that this marked movement is specific to the enzyme complex ready to catalyze phosphoryl transfer. Principal component analysis of the three trajectories supports also this specificity. In the course of the molecular dynamics trajectory of hTKFC:2DHA:2ATP, after 100 ns, many conformations are reached with the geometry needed for a direct in-line attack of one of the primary hydroxyl oxygens of DHA over the γ-phosphate of ATP. This includes O···P distances below 3.5 Å (some around 3.3 Å, the theoretical contact distance between oxygen and phosphorus) and O···P–O angles larger than 155◦ (some very near to 180◦). According to theory, this is compatible with an associative mechanism or with a concerted mechanism with a rather tight transition state. Despite the reported inability to find crystal structures of the Citrobacter DHA kinase (an ortholog of hTKFC) showing ATP-to-DHA distances below 14 Å, there is no need to invoke an indirect phosphoryl transfer to explain the kinase activity of these enzymes. Such activity can be accounted Int. J. Mol. Sci. 2019, 20, 1099 17 of 19 for by the marked flexibility of their dimeric structure with active sites formed between domains of different subunits.

Supplementary Materials: Supplementary materials can be found at http://www.mdpi.com/1422-0067/20/5/ 1099/s1. Author Contributions: Conceptualization, J.R.R. and J.C.C.; Formal analysis, J.R.R., A.C. and J.M.R.; Investigation, J.R.R.; Supervision, J.C.C. and A.C.; Writing—original draft, J.R.R., J.C.C. and J.M.R.; Writing—review and editing, J.R.R., J.C.C., A.C. and J.M.R. Funding: Financed in Leiria by project POCI-01-0145-FEDER-006984 funded by European Regional Development Fund through COMPETE2020–POCI and national funds through Fundação para a Ciência e a Tecnologia, Portugal. Research in the Grupo de Enzimología in Badajoz is funded by Consejería de Economía e Infraestructuras, Junta de Extremadura, Spain, grant numbers IB16066, GR15143 and GR18127, cofinanced by European Regional Development Fund. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

Abbreviations

ATP Adenosine 50-triphosphate DHA Dihydroxyacetone DHAP Dihydroxyacetone phosphate FAD Flavin adenine dinucleotide FMN Flavin mononucleotide GA D-Glyceraldehyde hTKFC Human triokinase/FMN cyclase RMSD Root-mean-square deviation PTS Phosphoenolpyruvate:sugar phosphotransferase system

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