Introduction

Among the most important mechanisms in the epigenetic regulation of gene expression are the acetylation and deacetylation of histones. These mechanisms are controlled by two families of enzymes with opposing functions: histone acetyl transferases (HAT) and histone acetyl deacetylases (HDAC). Aberrated actions of these enzymes can alter the structure and function of chromatin and are connected to a wide range of disorders, including some types of cancers [1, 2], inflammation [3], and metabolic and neurological disorders [4, 5]. There are 18 HDACs, which are grouped into four classes. Classes I, II, and IV are metal (Zn2+ or Fe2+)-dependent hydrolases. Class III HDACs are NAD+-dependent sirtuins and do not contain a metal cation in the active site. Among the metal-dependent HDAC enzymes, HDAC8 is the most studied [6,7,8,9]. Blocking HDAC enzymatic activity using low-molecular weight inhibitors (HDACi) has been shown to reduce malignancy growth and size both in vitro and in vivo by blocking the cell cycle and inducing apoptosis [10]. Several classes of small-molecule inhibitors have been recognized and investigated [11, 12]. Most of these are hydroxamic acid derivatives with different functional groups attached to the hydroxamic moiety via a long hydrophobic hydrocarbon chain. Typical representatives of this series are suberoyl anilide hydroxamic acid (SAHA) and scriptaid (SCR) (Fig. 1). They are thought to exhibit high affinity for the metal ion in the active site of the enzyme, and thus exert their inhibitory effects by chelating that metal ion [7, 13]. Hydroxamic acids are regarded as potent inhibitors, but they generally have some issues associated with their use, such as low oral availability, poor in vivo stability, and undesirable side effects [14, 15]. Therefore, the quest for more efficient HDAC inhibitors that are tolerable to the body is ongoing.

Fig. 1
figure 1

Structures of suberoyl anilide hydroxamic acid (SAHA; left) and scriptaid (SCR; right) (Х = О)

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Sulfur- and selenium-substituted derivatives of some HDAC inhibitors have been synthesized (Fig. 2) and probed for biological activity [16,17,18]. SAHA analogs containing α-mercaptoketone and α-thioacetoxyketone have been found to exhibit high activities toward isolated histone deacetylases [16]. Derivatives of SAHA containing one or two selenium atoms were found to be two- to fourfold more selective than the unmodified SAHA for melanoma cells, and to be able to decrease melanoma tumor development by up to 87% with negligible toxicity [18, 19].

Fig. 2
figure 2

Structures of sulfur and selenium analogs of SAHA found in the literature

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Although a substantial body of information has accumulated on the structures, syntheses, and biological activities of HDAC inhibitors, a number of questions regarding their physicochemical properties and metal affinities/selectivities remain unanswered. First, how do the conformation and ionization of the hydroxamic group depend on the identity of atom X (O, S, or Se; see Fig. 1) and the dielectric properties of the medium? Second, how do these factors affect the affinities and selectivities of HDAC inhibitors for essential biogenic metal cations? Third, how does the preferred deprotonation site of the hydroxamic moiety vary with X, and what is the binding mode of this moiety to the metal cation?

In the work reported here, we endeavored to address the above questions by performing density functional theory (DFT) calculations combined with polarizable continuum model (PCM) computations. The geometry, deprotonation pattern, metal-binding mode, and metal affinity/selectivity of SAHA, a typical HDAC inhibitor, were examined, and key factors affecting its ligation properties were elucidated. Sulfur- and selenium-containing analogs of SAHA were also modeled for the first time (to our knowledge), and their potential as efficient metal-binding entities (to Mg2+, Fe2+, and Zn2+ cations) was assessed. The present calculations shed light on the thermodynamics of HDACi–metal binding and suggest additional ways to enhance their metal-ligating properties.

Methods

SAHA was explicitly modeled. The metal cations studied in this work (Fe2+, Mg2+, and Zn2+) are usually hexahydrated in aqueous solution [20, 21]. Hence, their aqua complexes were modeled as [M(H2O)6]2+ (M = Fe, Mg, Zn). In complexes with organic or protein ligands, Mg2+ and Fe2+ usually retain their six-coordinate geometry, whereas Zn2+ tends to reduce its coordination number to 4, leading to tetrahedral complexes [22,23,24,25]. Thus, octahedral complexes of SAHA with Mg2+ or Fe2+ (high spin; quintuplet) were modeled, while tetrahedral counterparts were constructed for Zn2+.

All calculations were performed with the Gaussian 09 suite of programs [26]. The B3LYP functional [27,28,29] in conjunction with the 6–311++G(d,p) [30] basis set was employed to optimize the structures of the molecules of interest and to evaluate their respective electronic energies, Eelε, in both the gas phase (ε = 1) and in solution. In the latter case, polarizable continuum model (PCM) calculations in methanol (with ε = 33, mimicking the dielectric environment at protein-binding sites) and water (ε  = 78) were performed. This combination of method and basis set was chosen based on (i) previous theoretical studies of hydroxamic acids [31] which demonstrated that this combination correctly describes the geometries and properties of these molecules and their derivatives, and (ii) our own validation of the applicability of this combination through comparison with available experimental data (Table 1). This method/basis set combination was found to be reliable as it correctly reproduced the geometries of representative Mg2+, Fe2+, and Zn2+ complexes with inorganic and organic ligands (Table 1).

Table 1 Comparison of computed with experimental mean metal−oxygen and metal–nitrogen bond distances (in Å) in Mg2+, Zn2+, and Fe2+ complexes
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All frequency calculations for optimized structures were performed at the same level of theory. No imaginary frequency was found for any of the lowest-energy configurations of the optimized structures. The vibrational frequencies were used to compute the thermal energies, Ethε, including zero-point energies, and the entropies, Sε.

The differences ΔEelε, ΔEthε, ΔPV (work term), and ΔSε between the products and reactants were used to evaluate the free energies of product formation, ΔGε, in the gas phase and condensed media at T = 298.15 K according to

$$ \Delta {G}^{\varepsilon }=\Delta {E_{\mathrm{el}}}^{\varepsilon }+\Delta {E_{\mathrm{th}}}^{\varepsilon }+\Delta PV-T\Delta {S}^{\varepsilon }. $$
(1)

A positive ∆Gε implies that product formation is thermodynamically unfavorable, whereas a negative value implies that it is favorable. The free energies of deprotonation in water solution (ε = 78) were evaluated using the thermodynamic cycle shown in Scheme 1, where the experimentally determined free energy of proton hydration (−264.0 kcal/mol [36]) was used.

$$ \Delta {G}^{\varepsilon }=\Delta {G}^1+\Delta {G_{\mathrm{solv}}}^{\varepsilon}\left(\mathrm{Products}\right)-\Delta {G_{\mathrm{solv}}}^{\varepsilon}\left(\mathrm{Reagents}\right) $$
(2)
Scheme 1
scheme 1

Thermodynamic cycle used to evaluate the free energies of reaction in condensed media

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Results and discussion

Tautomers of neutral SAHA

There are two possible tautomeric forms of each hydroxamic acid: the keto and enol tautomers (Fig. 3). Both can be stable in acidic or alkaline media [37]. Furthermore, each tautomer can adopt an E or Z conformation [38].

Fig. 3
figure 3

E and Z isomers of the keto and enol forms of hydroxamic acids

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Our calculations revealed the relative stabilities of the SAHA tautomers. The most stable form in the gas phase was found to be the 1Z-keto form (Table 2 and Fig. 4). The stabilization of the 1Z tautomer is due to the formation of an intramolecular hydrogen bond between the OH and the neighboring carbonyl group, as seen in Fig. 4. Increasing the dielectric constant of the media (methanol or water) does not change the order of conformer stability, although the energy difference between the different forms decreases with increasing polarity of the environment.

Table 2 Relative Gibbs free energies (in kcal/mol) of the keto and iminol tautomers of SAHA in the gas phase, ΔGSAHA1, in methanol, ΔGSAHA33, and in water, ΔGSAHA78
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Fig. 4
figure 4

The optimized geometry (obtained at the B3LYP/6–311++G(d,p) level of theory) of the 1Z keto tautomer of SAHA

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Tautomers of ionized SAHA

Hydroxamic acids are weak acids with two labile acidic protons in the hydroxamic moiety (O–H and N–H; see Fig. 1) which can be detached during the course of a chemical/biochemical reaction. However, the deprotonation site in the hydroxamic group is still the subject of debate in the literature [39].

In order to shed light on this issue, we modeled the two deprotonation pathways in SAHA (OH and NH deprotonation) and evaluated their thermodynamic efficiencies (Table 3). The most stable deprotonated form in the gas phase was found to be the N-deprotonated 1Z form (Fig. 5b), which is 13.7 kcal/mol more stable than the O-deprotonated 1Z form (Fig. 5a). The stabilization of the N-deprotonated 1Z form is mainly due to the intramolecular hydrogen bond that is preserved from the neutral parent structure (Fig. 4). Note that our calculated gas-phase free energy of deprotonation (334.2 kcal/mol; Table 3) is in very good agreement with the experimentally measured value (obtained via Fourier transform ion cyclotron resonance) of 339.1 kcal/mol, revealing that the acetohydroxamic acid CH3CONHOH behaves essentially as a NH acid in the gas phase [40]. As the calculations imply, the N-deprotonated 1Z form is the most stable of the conformers examined (it has the lowest free energy of deprotonation in Table 3). It remains the lowest-energy conformer in a water environment as well (Table 3). The opposite tendency is found for the 1E conformers: the O-deprotonated forms, characterized by lower ΔG values, appear to be more stable than their N-deprotonated 1E counterparts.

Table 3 Change in the Gibbs free energies (in kcal/mol) in the gas phase and in water for the deprotonation of SAHA (AH → A− + H+)
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Fig. 5a–b
figure 5

The B3LYP/6–311++G(d,p)-optimized structures of SAHA deprotonated at the a OH site and b NH site of the hydroxamic moiety. Bond lengths are given in Å

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It is of particular interest to examine the stabilities of the respective deprotonated tautomers upon metal complexation. Therefore, we evaluated the OH and NH proton dissociation energies of zinc-coordinated SAHA. When SAHA is complexed with Zn2+, it exhibits different trends to those seen for the metal-free ligand (see above): the complex of the O-deprotonated form with Zn2+ (Fig. 6b) becomes more stable (by 16.8 kcal/mol in the gas phase) than the corresponding complex with the N-deprotonated ligand (Fig. 6a), in agreement with experimental crystallographic observations [7, 13]. This is because O–H ionization increases the negative charge density on the oxygen atom, which then directly participates in metal ligation (Fig. 6b), leading to more energetically favorable metal chelation than in the case of N–H ionization, where the negatively charged N atom does not coordinate to the metal cation (Fig. 6a).

Fig. 6a–b
figure 6

The B3LYP/6–311++G(d,p)-optimized geometries of a N-deprotonated and b O-deprotonated complexes of SAHA

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Tautomers of sulfur and selenium derivatives of SAHA

Could replacing the oxygen atom in the hydroxamic hydroxyl moiety with an analog from the same group of the periodic table (i.e., X = S or Se in Fig. 1) alter the tautomeric equilibrium of SAHA? To answer this question, we modeled and thermodynamically characterized the S and Se derivatives of this molecule. The calculations revealed that the most stable conformer is the 1Z-keto form (Table 4), just as for the unmodified molecule (Table 2). The energy difference between the 1Z- and 1E-keto forms in the sulfur and selenium derivatives of SAHA (i.e., SAHA-Se, SAHA-S) is, however, much smaller than for the respective oxygen-containing analogs (Table 4 and Table 2). This can be attributed to the absence of hydrogen bonding in the selenium- and sulfur-containing compounds, in contrast to the unmodified molecule (Fig. 7).

Table 4 The relative stabilities of the keto and enol tautomers of SAHA-S and SAHA-Se
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Fig. 7a–c
figure 7

The B3LYP/6–311++G(d,p)-optimized geometries of a SAHA, b SAHA-S, and c SAHA-Se

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Unlike the original SAHA, SAHA-S and SAHA-Se preferentially deprotonate at the 1Z-SH/SeH site rather than the 1Z-NH site (Table 5). This is due to the lack of a stabilizing intramolecular hydrogen bond in the S/Se analogs and to the greater acidity of the thiol and selenol groups compared to their hydroxyl counterpart. Data collected in Table 5 imply that the heavier the heteroatom in the OH/SH/SeH group, the more favorable the proton dissociation at this location. Thus, even for the metal-free ligands, the S− and Se− forms are the thermodynamically preferred deprotonated structures.

Table 5 Changes in the Gibbs free energy (in kcal/mol) in water for the deprotonation of SAHA, SAHA-S, and SAHA-Se
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Metal selectivity of SAHA

The nature of the metal cofactor at the active center of the enzyme greatly affects the thermodynamics and kinetics of the interactions of the enzyme with substrates and enzyme inhibitors. In proteins, metal cations such as Mg2+, Zn2+, and Fe2+ very often compete for the same binding site [21, 41,42,43,44], and the appropriate metal cofactor is selected either by the protein itself or by the cell machinery, which strictly regulates the free metal concentration in the intracellular compartments [45]. Note that the identity of the native metal cofactor at the active site of HDACs is still an enigma. Transition metal dications such as Zn2+, Co2+, and Fe2+ have been implicated in the activation of the enzyme. Note that there are metal-dependent enzymes (including HDAC) that have been reclassified from Zn2+-dependent to Fe2+-dependent enzymes [46,47,48,49]. Thus, it is of particular interest to study the metal-binding properties of HDAC inhibitors to different biogenic metal cations and to elucidate the major factors that control their metal affinities and selectivities.

The selectivity of SAHA for metal ions can be expressed in terms of the free energy, ΔGε, for the substitution of inhibitor-bound Zn2+ by a rival cation M2+ (M = Mg, Fe):

$$ {\left[\mathrm{Mg}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{2+}+{\left[\mathrm{SAHA}-\mathrm{Zn}{\left({\mathrm{H}}_2\mathrm{O}\right)}_2\right]}^{+}+2{\mathrm{H}}_2\mathrm{O}\to {\left[\mathrm{Zn}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{2+}+{\left[\mathrm{SAHA}-\mathrm{Mg}{\left({\mathrm{H}}_2\mathrm{O}\right)}_4\right]}^{+} $$
(3)
$$ {\left[\mathrm{Fe}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{2+}+{\left[\mathrm{SAHA}-\mathrm{Zn}{\left({\mathrm{H}}_2\mathrm{O}\right)}_2\right]}^{+}+2{\mathrm{H}}_2\mathrm{O}\to {\left[\mathrm{Zn}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{2+}+{\left[\mathrm{SAHA}-\mathrm{Fe}{\left({\mathrm{H}}_2\mathrm{O}\right)}_4\right]}^{+} $$
(4)

A positive ΔGε implies a Zn2+-selective ligand, whereas a negative value implies a Mg2+/Fe2+-selective one. The thermodynamic parameters evaluated for SAHA and its derivatives in the gas phase and in condensed media are summarized in Tables 6 and 7. Optimized structures of the metal complexes are shown in Fig. 8. The energy changes show that the substitution reaction for the unmodified SAHA is exothermic for both metal ions, Fe2+ and Mg2+, in the gas phase. In condensed media, however, this substitution becomes unfavorable, as demonstrated by positive free energies of metal exchange. This implies that it will be difficult for both metal cations to replace Zn2+ in these complexes. The S- and Se-containing SAHA derivatives, on the other hand, exhibit high Zn2+ selectivities in both the gas phase and condensed media (higher free energies of metal exchange in Tables 6 and 7). This finding is not surprising in view of the “softer” character of the Zn2+ cation relative to the Fe2+ and Mg2+ cations, which favors interactions between Zn2+ and the soft S- and Se-containing ligands rather than those between Fe2+ and Mg2+ and SAHA-S/SAHA-Se.

Table 6 Changes in the Gibbs free energy (in kcal/mol) for the Mg2+ → Zn2+ exchange reaction in the SAHA, SAHA-S, and SAHA-Se complexes
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Table 7 Changes in the Gibbs free energy (in kcal/mol) for the Fe2+ → Zn2+ exchange reaction in the SAHA, SAHA-S, and SAHA-Se complexes
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Fig. 8a–c
figure 8

B3LYP/6–311++G(d,p)-optimized structures for the complexes of SAHA with a Zn2+, b Fe2+, and c Mg2+. Green Zn2+, purple Fe2+, yellow Mg2+

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Conclusions

A systematic theoretical study of a representative HDAC inhibitor, SAHA, as well as its sulfur and selenium analogs, has been performed using density functional theory combined with polarizable continuum model calculations. The relative stabilities of different conformers of the studied molecules were determined. In all cases, the most stable form was found to be the 1Z-keto form. The deprotonation energies for the two ionizable groups, OH and NH, were also determined. It was found that for the metal-free molecule, deprotonation of the NH group is thermodynamically more favorable than deprotonation of the OH group. However, in metal complexes, metal coordination to the O-deprotonated hydroxamic moiety is more advantageous. Sulfur- and selenium-containing analogs are deprotonated more easily than the parent SAHA molecule. Deprotonation at the SH and SeH sites is more favorable for both compounds. In condensed media, SAHA and its sulfur and selenium analogs exhibit greater affinity/selectivity for Zn2+ cations, with the affinity noticeably increasing in the order O < S < Se.