Quantum chemical and molecular dynamics

PCCP PAPER

Cite this: Phys. Chem. Chem. Phys., 2017, 19, 28263

Quantum chemical and molecular dynamics modelling of hydroxylated polybrominated diphenyl ethers† Inna Ermilova, Samuel Stenberg and Alexander P. Lyubartsev

*

A series of 19 hydroxylated polybrominated diphenyl ethers (OH-PBDEs) have been studied using density functional theory (DFT) and molecular dynamics simulations with the purpose of investigating eventual correlations between their physicochemical properties and toxic action. Dissociation constants (pKa), solvation free energies and octanol–water partition coefficients (log P) have been computed. Additionally, metadynamics simulations of OH-PBDEs passing through a lipid bilayer have been carried out for four OH-PBDE species. No correlations between computed pKa values and toxicity data have been found. Received 23rd May 2017, Accepted 25th September 2017

Medium correlations were found between partition coefficients and the ability of OH-PBDEs to alter

DOI: 10.1039/c7cp03471g

parameters. It was also demonstrated that in lipid bilayers, OH-PBDE molecules differ in their orientational

membrane potential in cell cultures, which is attributed to higher uptake of molecules with larger log P distributions and can adopt different conformations which can affect the uptake of these molecules and

rsc.li/pccp

influence the pathways of their toxic action.

1 Introduction Solving environmental problems has become an important task nowadays. Noise stress, climate change and pollution have inspired many scientists around the world to do research in different areas in order to learn how to prevent or reduce the effects of these problems. Chemical methods, both experimental and theoretical, have become a good tool for studying the effects of pollution on animal and human health at the molecular level. Adverse outcomes of exposure to different chemicals can be seen as diseases, mutations, slow development, deaths and other unwanted consequences. Polybrominated diphenyl ethers (PBDEs) and hydroxylated polybrominated diphenyl ethers (Fig. 1) have been widely produced industrially since the end of the 1960s–beginning of the 1970s.1,2 Particularly, these substances are used in flame retardants for many different purposes nowadays: they are used in electronic equipment, cars, textiles, etc.3 At the same time some forms of PBDEs and OH-PBDEs are natural products of biosynthesis in the marine environment.4,5 It is worth noting Department of Materials and Environmental Chemistry, Stockholm University, SE 106 91, Stockholm, Sweden. E-mail: [email protected] † Electronic supplementary information (ESI) available: Chemical structures of OH-PBDEs with partial atom charges; energies computed in quantum-chemical calculations; additional results from Metadynamics simulations not included in the main text (pdf file). Molecular topology and force field files, molecular dynamics input files in MDynaMix and Gromacs formats (zip archive). See DOI: 10.1039/c7cp03471g

This journal is © the Owner Societies 2017

Fig. 1

General structure of OH-PBDEs.

that naturally occurring OH-PBDEs differ from synthesized substances structurally: the hydroxyl group is found to be in the ortho-position while in anthropogenic compounds this group is found in the meta- or para-position. PBDEs and OH-PBDEs were found by chemists from around the globe in water, living organisms and humans.6–11 For instance, humans can directly absorb PBDEs from their electronic devices, plastic computer parts and TV cabinets, clothes and dust due to emission3,12,13 as well as being exposed to them through their food.14–16 The negative effects of these chemical species on human health have been discussed in the literature: carcinogenesis, adverse effects on the regulation of thyroid and steroid hormones, and others.3,17–20 It was also found that OH-PBDEs are potentially more toxic than PBDEs, due to their ability to disrupt oxidative phosphorylation (OXPHOS), which is an essential process in the energy metabolism.21,22 J. Legradi and co-workers22 demonstrated that the ability of OH-PBDEs to interrupt OXPHOS in the mitochondrial matrix and in cell cultures can differ by more than two orders of magnitude for different forms of OH-PBDEs. In the same study, no cytotoxic effects of OH-PBDEs were found.

Phys. Chem. Chem. Phys., 2017, 19, 28263--28274 | 28263

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A number of experimental and computational studies have been done to investigate the molecular interactions of OH-PBDEs and PBDEs. For instance, Xinsin Li et al. have used a surface plasmon resonance technique in order to study the effect of OH-PBDEs on human estrogen receptor. Their experiments have shown that the number of bromine atoms in those species plays an important role in their effect on the human estrogen receptor.23 Computational studies based on molecular dynamics (MD) have been carried out in order to learn more about interactions of PBDEs with thyroid receptor b.24 Qing Xie et al.25 have studied the kinetics of photolysis and photooxidation reactivities of some OH-PBDEs using experimental and computational techniques. Other research studies have predicted liquid vapour pressures and n-octanol/air partition coefficients of PBDEs using QSRP analysis with DFT-based descriptors.26 A possible reason for large differences in the toxicity of OH-PBDEs can be attributed to their different ability to be adsorbed by the cellular membranes. The role of membrane–water and octanol–water partition coefficients (log P) is well established in the drug design, and the same relationship between potency and partition coefficients can be suggested for the toxicants. OH-PBDEs are known as weak acids according to their chemical structure: two phenyl rings are connected with an ether bond, and they have bromine substituents varying in number from 3 to 6 (some have chlorine substituents as well) and a hydroxyl group. Therefore they exist in solution typically as a mixture of neutral (protonated) and anionic forms, the ratio of which is defined by the specific pKa value and pH of the media. The uptake of anionic and neutral forms by biological membranes is different: while neutral hydrophobic solutes are typically absorbed by the membrane interior, charged species are absorbed (if at all) close to the interface (headgroup) region.27,28 One can thus expect that both pKa and log P values affect the way how and in what amount ionizable solvents are taken up by biological membranes. OH-PBDEs have very low solubility in water which makes experimental determination of pKa and log P difficult, and no experimental literature data for these parameters can be found. The chemical properties of OH-PBDEs and PBDEs make them interesting for computational studies which can help to determine the values of pKa and log P and study the mechanisms of interactions of these species with biological systems, particularly, with biomembranes. The methodology of determination of log P parameters in molecular dynamics simulations by computing solvation free energies is now well established29–32 though it may face the problem of accurate parametrization of the force field. There were also computational studies on determination of pKa parameters by quantum-chemical computations.33,34 In this work we have carried out computations of log P and pKa for 19 forms of OH-PBDEs studied in the work by Legradi et al.22 which are shown in Fig. S1 of the ESI.† Furthermore, for four forms of OH-PBDEs we carried out multimicrosecond metadynamics simulations in order to get insight into partitioning, conformational and orientation properties of these molecules in a lipid membrane.

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2 Computational methods 2.1

Quantum mechanical calculations of pKa

In order to compute pKa values of the molecules of interest, we have used the methodology developed in the work by Brown and Mora-Diez.33 The methodology consists of quantum-chemical calculations of the free energies of neutral and anionic forms of molecules, and determination of the dissociation constant from them. We briefly describe this approach here. The pKa of an ionizable molecule is defined as the negative logarithm of the dissociation constant, which is also the equilibrium constant of the dissociation reaction: pKa ¼ logðKa Þ ¼ log

½A ½Hþ ½AH

(1)

where [ ] denote equilibrium molar concentrations of the anionic species, hydrogen ion, and neutral (protonated) form of the molecule in the dissociation reaction: AH 2 A + H+

(2)

According to classical Physical Chemistry, the reaction constant and thus the pKa value can be calculated from the Gibbs free energy of reaction: pKa ¼

DGr RT lnð10Þ

(3)

where DGr = Gm(A) + Gm(H+) Gm(AH) and Gm stands for molar Gibbs energy. As it was shown by Braun et al.,33 the direct use of reaction (2) to compute DGr and pKa faces difficulties because the structure of water around a hydrogen ion (proton) is not well determined. Often the hydrogen ion exists as a mixture of different forms including hydronium H3O+ and H5O2+ complexes. It was shown in the same paper33 that the best results can be achieved if one computes pKa relative to a molecule with (experimentally) known pKa. Thus, one considers the reaction of acid–base equilibrium: AH + B 2 A + BH

(4)

where B is a reference molecule with (experimentally) known pKa(B). The pKa of molecule A can then be computed as pKa(A) = pKr + pKa(B)

(5)

where pKr is the equilibrium constant of reaction (4). pKr is computed from the Gibbs energy of reaction (4) which implies computations of free energies of both anionic and protonated forms of molecules A and B: pKr ¼

Gm ðA Þ þ Gm ðBHÞ Gm ðAHÞ Gm ðB Þ RT lnð10Þ

(6)

Since the free energy difference in eqn (3) includes energy of breaking a chemical bond, classical models described by force fields are not applicable to compute this difference. Quantumchemical methods can be straightforwardly used to determine the energy of reaction (2) or (4) in vacuum, but computation of the Gibbs free energy in solvent includes two principal approximations.


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First, the molecular partition function (from which the Gibbs free energy is determined) is computed in the normal mode approximation from the vibrational frequencies. Second, the effect of solvent is accounted for by some kind of polarizable continuum model. In our computations we used four different levels of quantumchemical computations: B3LYP/6-31+G(d,p), B3LYP/6-311++G(d,p), MP2/6-31+G(d,p), MP2/aug-cc-pVDZ. The molecular structures of interest were first constructed using Avogadro software35 and then optimized using the built-in GAFF force field.36 Then, the molecules were optimized within the chosen quantum theory level, and the electronic ground state energies (E0), vibrational frequencies and zero-point vibrational energies were computed to determine the molecular partition functions and Gibbs free energies using Gaussian09 software.37 The SMD solvent model38 was used when calculating Gibbs free energies as it was recommended in the manual of Gaussian09. 2.2

Partition coefficient computations

The partition coefficient is determined as the ratio of equilibrium concentrations of a solute in two non-mixing solvents. Usually a decimal logarithm of the partition coefficient is used which is referred as the ‘‘log P’’ parameter. Octanol–water partition coefficients are traditionally used as descriptors of lipophilicity of various substances which are strongly correlated with uptake of the substances by biological membranes. The octanol–water partition coefficient of a substance is determined by the difference of the Gibbs free energy of solvation of the substance in water and octanol phases:29 log P ¼

Gwater Goctanol RT lnð10Þ

(7)

Calculations of solvation free energies were carried out within classical force field models using the Expanded Ensemble (EE) methodology.30,39 According to this methodology, a reaction coordinate is introduced which describes gradual appearance or deletion of the solute molecule in the solvent. The reaction coordinate is determined by the parameter a (0 r a r 1), where a = 0 represents a pure solvent and a = 1 represents a solvent with a fully inserted molecule. This parameter is a variable in simulations which changes according to the Metropolis Monte-Carlo rules, while the motion of solute and solvent is carried out by molecular dynamics algorithm in the NPT ensemble.29,40 The partition function for the expanded ensemble is defined by Z¼

M ð Nþ1 X Y

dri expðb½HN ðri Þ þ Hint ðrNþ1 Þ þ hðam ; ri Þ þ Zm Þ

m¼0 V i¼1

(8) where b = 1/(kBT), T is the temperature, kB is the Boltzmann constant, HN represents the potential energy of N molecules of the solvent, Hint is the intramolecular potential energy of the solute, h(am,ri) is the interaction of the N + 1-th molecule representing the solute with all other solvent particles, am is a discrete set of points along the reaction coordinate, Zm represents balancing factors, or in other words, biased potential


which regulates the distribution of a, and {ri} is the set of atomistic coordinates. In this work, a soft potential path transforming solute–solvent interaction energy from h(0,ri) = 0 to the true force field interaction energy h(1,ri) was used as described in ref. 30. The result of simulation is distribution over sub-ensembles pm. Then the excess solvation free energy is calculated from the probability ratio of two extreme sub-ensembles:40 pm bGsolv ¼ ln þ Zm Z0 (9) p0 The optimal values of the balancing factors Zm were determined during the equilibration stage of the EE simulations using the Wang–Landau algorithm.30,41 All EE simulations were done using MDynaMix software v. 5.2.7.42 The EE simulations in the water phase included one solute and 512 water molecules while the octanol phase was simulated for one solute in 256 octanol molecules. In all cases the temperature was T = 298 K and pressure P = 1 bar. The time step was set to 2 fs and all the bonds were constrained by the SHAKE algorithm. The NPT ensemble was maintained using a Nose– Hoover thermostat43 and a Parrinello–Rahman barostat.44 The long-range electrostatic interactions were treated by the Ewald summation method. The number of subensembles was 26 for solutes in water and 41 for solutes in octanol. The simulations were run for 50 ns, of which optimization of the balancing factors took 10–20 ns. This simulation setup provided statistical uncertainty of the computed free energy within 1–1.5 kJ mol1. 2.3

Metadynamics simulations

Metadynamics simulations45 were carried out for a single solute molecule in a bilayer consisting of 128 lipids arranged in two leaflets and hydrated by 6400 water molecules. The simulations were done in the NVT ensemble at T = 303 K using Verlet46 as a cut-off scheme and a V-Rescale thermostat47 and lasted up to 3.5 ms. The box size was fitted to provide a tensionless bilayer at pressure 1 bar and then fixed. Other simulation parameters of importance were: time step of 2 fs; constrained bond lengths; cut-off of non-bonded interactions 1.4 nm; particle mesh Ewald summation of long-range electrostatic interactions. For metadynamics simulations we used the Gromacs v.4.6.7 package48,49 compiled with PLUMED-2.1.050,51 plug-in. A difference in the z-coordinate between the centre of mass of the solute and the membrane was chosen as a collective variable for metadynamics. The well-tempered metadynamics algorithm52 with bias factor 50 was used in which the Gaussian height was gradually decreased during the simulations providing convergence of the free energy profile53 (or potential of mean force, PMF). The computed PMF w(z) was used to determine the binding (or adsorption) free energy of the solute to the bilayer: Ð bwðzÞ ! e dz DGbind ¼ kT ln Ð B bwðzÞ (10) e dz U where U stands for the interval of z when the molecule is outside the bilayer (so-called ‘‘unbounded’’ state) and B represents


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the interval of z when the molecule is inside the bilayer (so-called ‘‘bound’’ state). Following previous works28,54 we chose the bound state up to z = 3.2 nm from the bilayer, and the size of unbound state (with w(z) = 0) equal to the bound state, thus eliminating size dependence in the definition of the binding free energy. 2.4

Force field details

The OH-PBDE molecules were modelled using the General Amber Force Field (GAFF).36 According to the GAFF recommendation, the partial charges for atoms were determined by ab initio Hartree–Fock computations for the optimized molecular geometry, with the 6-31G(d) basis set and the restricted electrostatic potential fitting (RESP) method.55 R.E.D software56 together with Gaussian0937 was used in these computations as well as for preparation of the molecular topology files. The computed partial atom charges are shown in Fig. S1 of the ESI.† As accepted in the Amber force field, the intramolecular 1–4 non-bonded electrostatic interactions were scaled by factor 0.83. Lipids in the bilayers were simulated using the Slipids force field.57,58 It was demonstrated previously that the Slipids force field is compatible with Amber-family force fields (including GAFF) to model partitioning of small molecules in the bilayer.54,57,59 The Slipids force field was also used to describe octanol molecules in the EE simulations except the polar group which was described by the GAFF parameters. Water was presented by the TIP3P model60 in all cases. Molecular topology files used in the simulations (in Gromacs and MDynaMix formats) are available in the ESI.†

3 Results 3.1

The results will be then dependent on the choice of this specific molecule. To use the whole set of experimental data, the following procedure was applied. We have computed average Gibbs energy difference between anionic and protonated forms of the reference molecules, and used this difference instead of Gm(BH) Gm(B) in eqn (5), and we used average experimental pKa value instead of pKa(B) in (6); thus all the reference molecules were included on equal footing. The results computed by this procedure are presented in Table 1, together with mean absolute deviations between experimental and computed values and Pearson coefficients. Note also that the procedure used provides zero mean deviation between experimental and computed data. A full account of quantum-mechanical energies and partition functions used in these calculations is given in Tables S1–S4 of the ESI.† Surprisingly, the computationally relatively cheap B3LYP/ 6-31+G(d,p) method showed the best results in terms of both mean absolute deviations and Pearson correlation coefficient, outperforming approaches with a larger basis set and MP2 level of theory. One can also note that all methods overestimate pKa of molecules with high pKa and underestimate for those with low pKa. Similar observations concerning comparison of computed and experimental pKa values for a series of benzimidazoles were made by Brown et al.33 The relation between computed (at the B3LYP/6-31+G(d,p) level of theory) and experimental pKa for a series of bromophenols is shown in Fig. 2. It can be fitted by the least square method to the linear dependence pKa(exp) = 0.64pKa(comp) + 2.74 3.2

Dissociation constants of reference molecules

For reference molecules, it is instructive to choose molecules of chemical structure similar to that of the molecules of interest. We therefore selected a number of bromophenols for which experimental pKa values are available. They are listed in Table 1. We have used this set of data in order to validate the method and evaluate its accuracy. In principle, it is possible to use any of the reference molecules as a reference to determine pKa by eqn (5) and (6).

(11)

Dissociation constants of OH-PBDEs

The above described methodology was used to compute pKa of OH-PBDE molecules studied in this work. The average values of Gibbs energy and experimental pKa values from the whole set of reference bromophenol molecules were used in eqn (5) and (6). Computations were made at B3LYP/6-31+G(d,p) and B3LYP/ 6-311++G(d,p) levels of theory. Since validation computations for bromophenols showed better performance for the 6-31+G(d,p) basis set, we discuss below only results obtained for OH-PBDEs within this basis set, showing the results obtained at the

Table 1 Reference molecules, computed and experimentally determined pKa. AD is the mean absolute deviation between the computed and experimental values, and r is the Pearson correlation coefficient. Experimental values are taken from the Pubchem database (https://pubchem.ncbi.nlm.nih.gov/) accessed on 26 April 2017

Species

B3LYP 6-31+(d,p)

B3LYP 6-311++(d,p)

MP2 6-31+(d,p)

MP2 aug-cc-pVDZ

Exp.

2-Bromophenol 3-Bromophenol 4-Bromophenol 2,4-Di-bromophenol 2,6-Di-bromophenol 3,5-Di-bromophenol 2,4,6-Tri-bromophenol Penta-bromophenol

9.57 9.52 9.88 8.26 7.04 7.39 5.47 3.42

9.65 9.44 10.08 8.18 7.38 7.37 5.16 3.31

9.7 9.37 10.42 8.11 7.49 7.30 5.2 2.97

9.38 9.4 10.21 8.33 7.71 7.25 5.67 2.61

8.45 9.03 9.17 7.79 6.67 8.04 6.8 4.62

AD r

0.79 0.957

0.91 0.94

1.0 0.94


0.98 0.943

— —


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Paper Table 3 Solvation free energies (in kJ mol1) and octanol–water partition coefficients from EE simulations

Species 0

Fig. 2 Experimental pKa plotted against calculated pKa at the B3LYP/ 6-31+G(d,p) level of theory, together with linear least square fitting.

Table 2 Calculated and corrected pKa values for OH-PDBEs (B3LYP/631+G(d,p))

Species

Eqn (5) and (6)

Corr.

2-OH-BDE28 2-OH-BDE66 2-OH-BDE68 2-OH-6-Cl-BDE68 2-OH-BDE123 3-OH-BDE47 3-OH-BDE153 3-OH-BDE154 3-OH-BDE155 4-OH-BDE17 5-OH-BDE47 6-OH-BDE47 6-OH-5-Cl-BDE47 6-OH-BDE49 6-OH-BDE85 6-OH-BDE90 6-OH-BDE99 6-OH-BDE137

7.07 6.88 6.56 3.88 5.29 5.68 3.5 3.78 4.49 8.8 7.46 7.61 2.73 4.19 4.76 3.35 3.66 3.64

7.26 7.14 6.94 5.22 6.13 6.37 4.98 5.16 5.61 8.37 7.51 7.61 4.49 5.42 5.78 4.88 5.08 5.07

B3LYP/6-311++G(d,p) level in the ESI,† Table S6. A full account of the computed quantum energies is given in Tables S5 and S6 (ESI†). The computed pKa values for the set of OH-PBDEs are given in Table 2. Since the reference molecules showed some overestimation of the computed pKa dependence, a linear correction was applied adopted from ref. 33 where it showed an improvement of the results. The first order trendline function determined for the reference molecules, eqn (11), was applied to the calculated pKa values, and the corrected values are also shown in Table 2. Note that such linear correction does not affect the discussion on possible correlation between computed pKa and toxicity data later in the text. A general trend of a decrease in pKa with an increase in the number of Br atoms can be observed; a similar trend exists also for the reference bromophenol molecules. 3.3 log P parameters of OH-PBDEs from expanded ensemble calculations The results from calculations of the solvation free energies and octanol–water partition coefficients of neutral forms of the studied molecules are shown in Table 3. All the molecules demonstrate strongly hydrophobic character with partition coefficients


2 -OH-BDE28 (ortho) 2 0 -OH-BDE66 (ortho) 2 0 -OH-BDE68 (ortho) 2-OH-BDE123 (ortho) 2 0 -OH-6 0 -Cl-BDE68 (ortho) 3-OH-BDE47 (meta) 3-OH-BDE153 (meta) 3 0 -OH-BDE154 (meta) 3-OH-BDE155 (meta) 4 0 -OH-BDE17 (para) 5-OH-BDE47 (meta) 6-OH-BDE47 (ortho) 6-OH-5-Cl-BDE47 (ortho) 6 0 -OH-BDE49 (ortho) 6-OH-BDE85 (ortho) 6-OH-BDE90 (ortho) 6-OH-BDE99 (ortho) 6-OH-BDE137 (ortho) BDE-47 Uncertainty

Goct

Gwater

log P

65.1 65.9 64.9 70.6 66.6 63.8 74.1 70.4 65.4 79.2 62.9 63.6 73.0 62.0 71.6 72.9 77.2 80.2 55.8

23.9 16.2 17.9 14.3 14.7 21.7 17.2 14.4 11.8 39.9 16.8 17.0 23.1 16.4 17.8 20.9 22.3 22.0 7.6

7.22 8.56 8.25 9.87 9.09 7.38 9.83 9.83 9.4 6.89 8.08 8.17 8.73 7.99 9.43 9.12 9.63 10.20 8.45

1

0.3

1.5

mostly in the range between 7 and 10. It might therefore be expected that these molecules show substantial uptake by the biomembranes of living organisms if they are present in nanomolar concentrations in the surrounding aqueous media. 3.4

Free energy profiles from metadynamics simulations

We have carried out calculations of the potential of mean force (PMF) for several selected OH-PBDEs to penetrate a lipid membrane bilayer using the Metadynamics45 approach, which according to recent comparative studies is a more efficient approach than umbrella sampling which is routinely used for the same purpose.61 Due to limitations on available hardware resources metadynamics simulations of other OH-PBDEs were not feasible. Particularly, we simulated 2 0 -OH-BDE68, 6-OH-BDE47, 6-OHBDE85 and 3-OH-BDE155 in the DMPC (which is known as 14 : 0/14 : 0 PC, 1,2-dimyristoyl-sn-glycero-3-phosphocholine) bilayer. These molecules are shown in Fig. 3, together with information on atom names and torsion angles referred further in the text. Additionally, 2 0 -OH-BDE68 was simulated in the POPC (which is known as 16 : 0–18 : 1 PC, 1-palmitoyl-2-oleoyl-sn-glycero-3phosphocholine) bilayer in order to investigate the effect of a lipid type on the partitioning of solute in the bilayer. This choice of OH-PBDEs was related to specific features of their toxic action as observed in the study by Legradi et al.22 Thus, 6-OH-BDE47 was found to be one of the most potent disrupters of OXPHOS via inhibition of the electron transporting complex; 6-OH-BDE85 was almost of the same potency as 6-OH-BDE47 but it acted via uncoupling of the protonophoric process. 3-OH-BDE155 and 2 0 -OH-BDE68 are examples of molecules that do not disrupt OXPHOS in zebrafish embryos; however 2 0 -OH-BDE68 is a rather strong disruptor of OXPHOS in the mitochondria matrix. The center-of-mass motion of OH-PBDEs relative to the membrane middle plane during metadynamics simulations is shown in Fig. S2 of the ESI.† One can see that the molecules


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Fig. 3 The molecules used in metadynamics simulations. The molecular vectors and various dihedrals referred further in the text are defined as in the image above.

repeatedly cross the membrane in both directions and sample the whole range of distances. The free energy profiles symmetrized relative to the membrane mid-plane are shown in Fig. 4. They were obtained by averaging the profiles generated after 1 ms of simulation with 0.5 ms intervals; this procedure was discussed in a recent publication.61 From the variance of the free energy profiles observed during metadynamics simulations we evaluate precision of PMF calculations as within 5 kJ mol1. The PMFs have a similar shape reaching a minimum of 40 to 60 kJ mol1 in the membrane interior but differing in details. Particularly, the PMF of 6-OH-BDE85 begins to decrease already at the bilayer surface and reaches a minimum in the bilayer centre. The PMF of 6-OHBDE47 is also negative at the membrane surface, but it has a weak maximum in the membrane centre. The least negative is the PMF of 2 0 -OH-BDE68 in the POPC bilayer which can be an indication that uptake of this molecule is lower in unsaturated lipid bilayers compared to saturated ones.

Fig. 4 The free energy profile (potential of mean force) for the metadynamics simulations with four OH-PBDEs in the membranes. The Z-coordinate (X axis) shows the distance between the centres of masses of molecules and the membrane middle plane.


Table 4 Adsorption free energies of OH-PBDEs to a lipid bilayer (DGbind), and the difference of solvation free energies in the octanol and water phase. All values are given in kJ mol1

Lipid

Molecule

DGbind

Goct Gwater

POPC DMPC DMPC DMPC DMPC

2 0 -OH-BDE68 2 0 -OH-BDE68 6-OH-BDE47 6-OH-BDE85 3-OH-BDE155

40.6 47.1 50.5 60.2 46.7

47.0 46.6 53.8 53.6

The adsorption free energies computed by integration of the potential of mean force using eqn (10) are given in Table 4. Also given in Table 4 are differences of solvation free energies in the octanol and water phase computed in expanded ensemble simulations. One can see that these free energies are similar but do not necessarily follow the same order: for 6-OH-BDE85 the membrane adsorption energy is lower than the difference of solvation free energies in octanol and water, while the relationship is opposite for 3-OH-BDE155. One can also see that the adsorption free energy for the same substance (2 0 -OH-BDE68) is different in the DMPC and POPC membrane. We can further note that in a recent paper on the behaviour of anesthetic molecules in a lipid bilayer28 it was also demonstrated that while the octanol– water partition coefficients follow the same trend as adsorption free energies in a bilayer, these two properties do not necessarily have point-to-point correspondence. In order to get insight into the behaviour of OH-PBDEs in lipid bilayers which can modulate the adsorption behaviour and affect the toxicity pathways, we have investigated in more detail orientational and conformational properties of the molecules in different parts of the bilayer system, as well as their interactions with lipids and water. Panels (a) of Fig. 5 and 6 show orientation of 2 0 -OH-BDE68 and 6-OH-BDE47 in the DMPC bilayer. Orientation of the molecule is determined by the angle between the long molecular axis and the bilayer normal. For exact definition of molecular axes, as well as torsion angles, see Fig. 3 and its caption. The distributions were calculated in the bilayer centre (for molecules with Z-coordinate 0.5 nm around the bilayer centre) and at the surface (for molecules with Z-coordinate 0.5 nm around the plane defined by the carbon atoms of the lipid choline groups). Panels (c) show distribution of the


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Fig. 5 Distributions of dihedrals in 2 0 -OH-BDE68 (ortho) and angles between the selected vector and a normal to the membrane consisting of DMPC lipids. (a) Probability distribution of cosine of angle (a) between the normal to the membrane and the molecular vector. (c) Probability distribution of dihedral d. (b and d) Distribution map of cosines for two dihedrals (b1 and b2). Each point corresponds to a trajectory frame and is coloured according to the absolute value of cosine of the angle a between the molecular vector and the normal to the membrane. (b) For molecules located in the centre of the membrane, (d) for molecules located at the bilayer surface. For definition of angles, see Fig. 3.

angle d (which is related to the angle between the rings) when the molecule is located in the center and on the surface of the membrane as well as in the water phase (0.5 nm from the middle of the water layer). Panels (b and d) of these figures show distribution maps of torsional angles in the ether linkage b1 and b2 (Ramachandran plot) as well as orientation of the molecule relative to the bilayer normal. Each point on these graphs corresponds to a simulation frame when the molecule is in the center (panels b) or at the surface (panels d) of the bilayer. The location of each point on the graph gives b1 and b2 torsion angles of the molecule in this frame while the colour shows the orientation (a angle between the molecular axis and the bilayer normal) according to the colour scale displayed on the right of the graphs. For other molecules, as well as for 2 0 -OH-BDE68 in the POPC bilayer, these distributions are shown in Fig. S2–S4 of the ESI.† Our data show that distributions of the orientational angle and dihedrals vary from molecule to molecule. One can see that for 2 0 -OH-BDE68 the preferable angle with membrane normal is around 901 for molecules both in the membrane centre and at the surface, which means that the molecule prefers to orient itself parallel to the bilayer plane. However 6-OH-BDE47 does not show preferential orientation in the middle of the bilayer (red line in Fig. 6(a)). Distributions of the torsion angles at the ether linkage (b1 and b2) are also different. For 2 0 -OH-BDE68 both angles show most dense distribution when one of the


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Fig. 6 Distributions of dihedrals in 6-OH-BDE47 (ortho) and angles between the selected vector and a normal to the membrane consisting of DMPC lipids. (a) Probability distribution of cosine of angle (a) between the normal to the membrane and the molecular vector. (c) Probability distribution of dihedral d. (b and d) Distribution map of cosines for two dihedrals (b1 and b2). Each point corresponds to a trajectory frame and is coloured according to the absolute value of cosine of the angle a between the molecular vector and the normal to the membrane. (b) For molecules located in the centre of the membrane, (d) for molecules located at the bilayer surface. For definition of angles, see Fig. 3.

angles is close to 1801 (cosine values 1). For 6-OH-BDE47, the maximum of b1 angle distribution is also around 1801 while the distribution of the b2 angle is concentrated in the range around and below 901. A similar effect is observed for 6-OH-BDE85 (Fig. S3 of the ESI†). This conformational behaviour can be related to the presence of the Br atom in the 6-position of the ring. Interestingly however combined dihedral angle d which involves bonds from both rings of the molecule has a rather similar distribution for all the molecules, with the maximum at around 60–70 degrees. Visual analysis of the trajectories confirms also that this is the most typical value for the angle between the two rings. Another important internal degree of freedom for the considered molecules is orientation of the hydroxyl group relative to the oxygen of the ether linkage. To analyse its behaviour, we computed distribution of distances between hydrogen of the hydroxyl group and oxygen of the ether link, and distribution of the torsion angle t describing orientation of the hydroxyl group. These results, collected separately for the solute molecules located in the centre and on the surface of the bilayer, as well as in the water phase, are shown in Fig. 7 and 8 for 2 0 -OH-BDE68 and 6-OH-BDE47, and for other molecules in Fig. S6 and S7 of the ESI.† Clearly, the behaviour of the OH-group is different: while for 2 0 -OH-BDE68 in the DMPC bilayer the OH bond is directed towards the ether oxygen atom forming a configuration corresponding to a weak intramolecular hydrogen bond, in 6-OHBDE47 and 6-OH-BDE85 the OH bond is directed preferentially


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Fig. 7 Distribution of distances between hydrogen of the hydroxyl group and oxygen of the ether link for 2 0 -OH-BDE68 (ortho) and 6-OH-BDE47 (ortho) in the membrane interior, at the surface and in the water phase.

Fig. 8 Distribution of the hydroxyl group torsion angle (see definition in the caption of Fig. 3) in the membrane interior, at the surface and in the water phase.

away from the ether oxygen, with the population of the two conformations changing from the bilayer centre to the water phase. Interestingly for 20 -OH-BDE68 in the middle POPC bilayer (Fig. S6, ESI†) there is also a substantial fraction of conformation with the OH bond directed away from the ether oxygen, which illustrates the influence of the bilayer type on the conformations of the solute molecules. Note further that the energy barrier of the torsional rotation of the OH group in OH-PBDE molecules is below 8 kJ mol1 (according to the force field) which provides a good sampling of possible conformations. In order to make comparative analysis of interactions of OH-PBDEs with lipids and water and investigate possible hydrogen bond formation, we have also computed radial distribution functions (RDF) between some polar atoms of OH-PBDEs, lipids and water, which are shown in Fig. 9 and Fig. S8 of the ESI.† The RDFs were computed from the Metadynamics trajectories excluding the first ms of the simulations. Since in Metadynamics simulations the solute molecule is moved in a biased potential, the shown distributions are not RDFs of the canonical ensemble. Still, keeping in mind that during the equilibrated part of metadynamics simulations the distribution of the solute molecule over the Z coordinate becomes nearly flat, the computed distributions can be used for evaluation and comparison of affinity of the solute atoms to different atomic groups of the solvent and membrane. Fig. 9(a) shows RDFs between hydrogen of the hydroxyl group of OH-PBDEs and phosphate oxygens of lipids. The first peak of RDF is very strong for 6-OH-BDE47 and 6-OH-BDE85 indicating a strong hydrogen bond formed between these molecules and the phosphate group of lipids. This strong binding can


Fig. 9 Radial distribution functions between hydrogen of the hydroxyl group of OH-PBDEs and (a) lipid phosphate oxygen and (b) water oxygen.

explain the decrease of PMFs already in the membrane interface region at distances 2–2.5 nm from the membrane centre which corresponds to positioning of the phosphate groups (Fig. 4). These two molecules also have stronger hydrogen binding to water (Fig. 9(b)), and they have preferential orientation of the hydroxyl group away from the oxygen of the ether link. Two other molecules, 2 0 -OH-BDE68 and 3-OH-BDE155, show stronger hydrogen bonding to the oxygens of the carbonyl group of lipids, Fig. S8(a) (ESI†). Other possible sites for hydrogen bonding show only weak (to oxygens of ester groups, Fig. S8(b), and between oxygen of the OH-PBDE hydroxyl group and water hydrogen, Fig. S8(c), ESI†) or no association (to oxygen of the ether link, Fig. S8(d), ESI†).


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The discussed differences in the conformational properties of OH-PBDE molecules and their interaction with lipids and water can modulate the behaviour of the potential of mean force curve revealing the differences in the behaviour of OH-PBDEs which cannot be captured by pKa and log P coefficients determined in an isotropic environment.

4 Discussion While the considered molecules have similar chemical structures and show qualitatively similar properties being strongly hydrophobic weak acids which are strongly adsorbed by biological membranes, the computed values of pKa and log P parameters differ by up to 3–4 units, which indicates potentially large, by 3–4 orders of magnitude, quantitative differences in the balance of equilibrium concentrations of dissociated and neutral forms and in the degree of uptake by biomembranes. This in principle can be the reason for the different toxic response of these molecules. We therefore have analysed possible correlations between pKa and log P values on the one hand, and toxicity responses determined in the study by Legradi et al.22 on the other hand. In that work, two mechanisms of interruption of OXPHOS in mitochondrial membranes (trophenylphosphonium, or TPP assays) were investigated: by protonophoric uncoupling disrupting the electrochemical gradient across membranes by proton transfer, and by inhibition of the electron transporting complexes. Additionally, altered membrane potential was measured in zebrafish embryo cells. The lowest observed effect concentrations (LOEC) were measured for these three types of studies; and for altered membrane potential EC50 concentrations (showing half of the effect) were also determined. Plotting the computed pKa and log P values against logarithm of LOEC and EC50 concentrations (also called toxicity endpoints) provides a basis from which correlations can be derived. These graphs are shown in Fig. 10 and 11, with nominal concentrations given in mM. It is difficult by eyes to see any correlation between computed pKa and toxicity endpoints, while some trend can be seen for log P coefficients. A quantitative evaluation of possible linear correlations between two data sets is given by Pearson coefficients, which are listed in Table 5. The Pearson coefficients between computed pKa values and all toxicity endpoints are below 0.25, which is generally accepted as no correlation observed. No correlations are either observed between log P values and endpoints related to uncoupling and inhibition mechanisms when the whole set of molecules is considered. However, a weak to medium correlation is observed between log P values and altered membrane potential endpoints (LOEC and EC50), with Pearson coefficients 0.45 and 0.37 respectively. We can note in this connection that measurements of inhibition and uncoupling were done in isolated mitochondria;19,22 thus the OH-PBDEs had no cellular membrane to traverse in order to disrupt OXPHOS. In the altered membrane potential measurements PAC2 cells from zebrafish were used and the OH-PBDEs had to diffuse through the cellular membrane to enter the cell, and this process can be affected by the log P value of the molecule.


Fig. 10 Experimental toxicity endpoints from ref. 22 vs. pKa of OH-PBDEs and least square linear fitting. (a) Uncoupling, LOEC; (b) inhibition, LOEC, (c) altered membrane potential, LoEC; (d) altered membrane potential, EC50. Points in blue correspond to ortho structures without Cl atoms.

Fig. 11 Experimental toxicity endpoints from ref. 22 vs. log P of OH-PBDEs and least square linear fitting. (a) Uncoupling, LOEC; (b) inhibition, LOEC, (c) altered membrane potential, LoEC; (d) altered membrane potential, EC50. Points in blue correspond to ortho structures without Cl atoms.

Table 5 Pearson correlation coefficients describing the relation between calculated log P and pKa values and toxicity endpoints. ‘‘all’’: computed for the whole set of molecules; ‘‘ortho’’: computed only over ortho-types of molecules without Cl atoms

log P

pKa

Endpoint

all

ortho

all

ortho

Uncoupling, LOEC Inhibition, LOEC Alt. mem. potential, LOEC Alt. mem. potential, EC50

0.03 0.14 0.45 0.37

0.63 0.77 0.6 0.56

0.02 0.04 0.23 0.23

0.18 0.11 0.09 0.05


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No or low correlations between pKa and log P values and toxicity endpoints can be a consequence of other factors related to a specific molecular structure affecting the action mechanisms. We therefore selected a subset of 10 molecules having ortho structures (with the hydroxyl group next to the ether linkage, which makes it possible to form an internal hydrogen bond) and not containing Cl atoms. In Fig. 10 and 11 points corresponding to these molecules are given in blue. The Pearson coefficients corresponding to this subset of molecules are also given in Table 5. One can see higher (but still not strong) correlations between log P values and all four toxicity endpoints with Pearson coefficients of order 0.6 to 0.7, but still no correlations between the toxicity endpoints and pKa values are observed. A negative correlation between toxicity endpoints expressed in terms of LOEC and EC50 concentrations and log P parameters can be expected, since log P parameters are related to uptake of the substances by biological membranes. For more than 100 years ago Meyer and Overton discovered correlations between potency of anesthetic drugs and their lipid solubility,62 and nowadays the log P value is one of the most important parameters in drug design. It can be expected that similar correlation exists for the toxic action. The absence of correlations between computed pKa values and the toxicity endpoints, even for a smaller, more homogeneous set of ortho-molecules, is another result of this study. In principle one can hypothesize that pKa values may affect the protophoric uncoupling which is caused by proton transfer across the membrane assisted by ionizable OH-PBDE molecules. One of the reasons for the absence of such correlations may be insufficient precision of pKa computations which we cannot validate by experimental measurements for OH-PBDE molecules. This reason seems to be less likely since we obtained good correlation between computed and experimental pKa values for structurally similar bromophenol molecules. It is more probable that the protophoric process is determined by other factors than pKa, such as rate of the dissociation reaction which in turn depends on the transition state energy, or preferable localization of the neutral and anionic forms of the molecules in lipid membranes. Our metadynamics results for four selected OH-PBDE molecules show that they can differ with respect to conformational properties, formation of hydrogen bonds with water and various sites of lipids, and their partitioning and orientation in lipid bilayers. Particularly, 6-OH-BDE47 and 6-OH-BDE85 show conformational and hydrogen bonding behaviour noticeably different from two other selected species. Noteworthily, LOEC and EC50 concentrations for altered membrane potential of 6-OH-BDE47 and 6-OH-BDE85 are substantially lower compared to the other two species (5.6–8 mM vs. 4100 mM or non-detected22), though it is not appropriate to make a definite conclusion from considering only four cases. Detailed investigation of a possible role of each of these factors and linking them to toxicity require further extensive studies, and investigation along these lines will be the matter of our forthcoming research.

5 Conclusion We have carried out extensive computational studies of hydroxylated polybrominated diphenyl ethers with the purpose of


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getting insight into possible molecular mechanisms of their toxic action. For all the considered molecules, dissociation constants pKa were determined by DFT computations using normal mode approximation and a polarisable continuum model, and octanol– water partition coefficients log P have been calculated by the expanded ensemble molecular dynamics calculations within classical force field models. Additionally, metadynamics simulations have been carried out for four OH-PBDE molecules in DMPC and POPC bilayers with the purpose of determining the free energy profile for the molecules crossing the lipid bilayer, and investigating orientational and conformational properties of the molecules in different parts of the bilayer. Our calculations showed no correlation between computed pKa values of the considered molecules and experimental toxicity data. A weak correlation, which becomes stronger if only ortho-type of molecules are considered, was found between log P values and concentrations inducing certain toxicity mechanisms. These correlations can be ascribed to higher uptake by the biomembranes of the molecules having higher log P values. The interconnection between octanol–water partition coefficients and membrane binding is however not straightforward, as demonstrated by metadynamics simulations. Different conformational properties of the molecules, their interaction with water and lipids, and their different preferential orientation in the membrane can modulate their partitioning across the membrane and initiate different toxicity responses. Computational toxicology is an emerging area of research, and this study is, to our knowledge, the first attempt to use molecular modelling to investigate a specific class of compounds linking their computed physical–chemical properties to their toxic action. It demonstrates the potency of molecular modelling to discriminate between thinkable toxicity pathways and provides information important for our understanding of the molecular phenomena behind the toxic action.

Conflicts of interest There are no conflicts to declare.

Acknowledgements We thank Anna-Karin Dahlberg and Lillemor Asplund for bringing our attention to this subject and useful discussions, and Erik Brandt for help with the PLUMED software. This work has been supported by the Swedish Research Council (Vetenskapsrådet). The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at PDC ¨ping (Royal Institute of Technology, Stockholm) and NSC (Linko University) computational centres.

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