Understanding the BoronâNitrogen Interaction and Its Possible

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Understanding the Boron - Nitrogen Interaction and Its Possible Implications in Drug Design Hao Dong, Wei Li, Jianwei Sun, Shuhua Li, and Michael L. Klein J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b07783 • Publication Date (Web): 16 Oct 2015 Downloaded from http://pubs.acs.org on October 17, 2015

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The Journal of Physical Chemistry

Understanding the Boron - Nitrogen Interaction and Its Possible Implications in Drug Design Hao Dong,*,†,‡ Wei Li,‖ Jianwei Sun,§ Shuhua Li

‖

and Michael L. Klein

‡

†

Kuang Yaming Honors School, Nanjing University, P.R. China;

‡

Institute for Computational Molecular Science, Temple University, 1900 North 12th

Street, Philadelphia, Pennsylvania 19122-6078, United States; ‖

School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic

Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, P.R. China; §

Department of Physics, Temple University, 1900 North 12th Street, Philadelphia,

Pennsylvania 19122-6078, United States

1

ACS Paragon Plus Environment


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ABSTRACT 2-Aminoethoxydiphenylborate (2-APB) is a broad-spectrum modulator of various membrane proteins. Specifically, it exhibits concentration dependent modulation of calcium signaling through store-operated calcium (SOC) channels: low micro-molar concentration of 2-APB stimulates SOC entry while higher concentration induces complete inhibition. ab initio quantum chemical calculations show the relative stability of the two major isomers of 2-APB (cyclic and extended), is about 8 kcal/mol. The dual functionality of 2-APB for SOC channels is thus likely associated with its ability to switch among isomeric forms, suited to different binding sites in the SOC channels with distinct binding affinities. Importantly, the moderate relative stability of different isomers results from a delicate balance between the intramolecular boron-nitrogen coordinate bond with strength about -45 kcal/mol, and ring strain engendered by cyclic oligomerization. The synergistic effect of these two factors likely makes 2-APB an ideal dual effect drug.

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INTRODUCTION 2-Aminoethoxydiphenylborate (2-APB), shown in Figure 1, is a membrane permeable reagent that has extensive interactions with membrane proteins, including InsP3 receptors,1 transient receptor potential (TRP) channels,2 specific gap junctions (composed of connexin26 and/or connexin32),3 SERCA Ca2+ pumps,4 voltage-gated potassium channels,5 and store-operated calcium (SOC) channels.6 Especially for the study of calcium signaling through SOC channels, 2-APB has been shown to exhibit concentration dependent modulation behavior: low micromolar concentration(1~20 μM) of 2-APB can stimulate the store-operated Ca2+ entry, while higher concentration (25~100 μM) induces a complete inhibition.6-8 This bimodal effect is a characteristic of 2-APB function on SOC entry (SOCE), though its regulation mechanism is still unclear.6 Boron and nitrogen atoms in 2-APB are typical components of coordinate bonding. The boron atom, which has an open shell and is electron deficient, acts as a Lewis acid and provides a vacant coordination site, while the nitrogen contributes an electron pair as a Lewis base.9 Replacing the terminal NH2 by a NHCH3 (monomethyl-APB) or a N(CH3)2 (dimethyl-APB) does not hurt its inhibitory activity.10 However, further substituting the boron by a carbon on dimethyl-APB result in the loss of inhibition on SOCE.11 The substitute of boron-oxygen core with carbon-phosphorus core induced the loss of potentiation capacity.12 In contrast, methyl-diethylborinate (MDEB), a 2-APB analogue containing the boron-oxygen core alone is capable of potentiating the SOCE by increasing the Ca2+ influx amplitude.13 Interestingly, trimethylborate (TMB), an analog of MDEB, containing the boron-oxygen core but with the two ethyl groups being replaced by methoxyl groups, was devoid of any regulation effect on SOCE.13 Even though it was proposed that neither the boron center is the prerequisite for SOCE inhibitory activity,10 nor does the aminoethyl group being critical for SOCE inhibition,12 and some compounds are more potent than 2-APB in inhibiting SOCE, the analogues based on the mother compound 2-APB having both functional groups -- the boron center and amine group -- were reported to exhibit this dual effect.12-14 We also want to mention that, as an 3



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exception, another 2-APB analog, diphenylborinic anhydride (DPBA), without the aminoethyl group, has this bimodal effect as well.12 Seemingly, the structure-function relationship analysis of these modulators leads an elusive conclusion. Yet, 2-APB was usually used as a prototype compound for designing new modulators, and a number of 2-APB analogues have been synthesized and characterized, most of which containing both B and N centers.10, 14-16 Therefore, we focused our attention to the B…N interaction in the present work. The pKa of 2-APB was determined to be 9.6,17 suggesting that the protonated form is dominant in aqua phase at neutral pH condition. However, large down shifts in the pKa value of the amine group (up to 4 pH units) in a protein interior has been observed,18-19 mainly because of the low polarizability and polarity of the low dielectric constant environment relative to the aqua phase. Therefore, the amine group, the potential Lewis base, may adopt the deprotonated form as well. For example, 2-APB in dimethyl sulfoxide (DMSO), an aprotic solvent, was detected as a cyclic form where the amine is deprotonated to serve as the Lewis base.10 In addition, the formation of dimeric 2-APB, in which the deprotonated amine group on one 2-APB interacts with the boron center on a neighboring 2-APB and thus forming a 10-member ring, was already proposed based on the mass spectral analysis.20 Presumably, the population of the deprotonated 2-APB will increase in the protein interior or in lipid bilayers. More importantly, it is likely that the different functional abilities of 2-APB for activating or blocking the SOCE is associated with its ability to switch among distinct forms, suited to different binding sites in the channel with different binding affinities (see Figure 1), in which the dynamic bonding between boron and nitrogen plays a critical role. Here we report quantum mechanics calculations designed to explore the bonding between B and N in 2-APB. The purpose of the present work is two-fold: firstly, we want to understand the nature of B…N bonding and the flexibility of the molecule, which may be helpful to better design drugs that are capable of modulating membrane proteins. Secondly, for 2-APB, we want to identify a density functional that is both reliable and more computational efficient than the accurate 4


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but expensive post-Hartree-Fock (post-HF) methods. The former in turn, could then be used to parameterize a series of compounds containing the B…N bond suitable to investigate drug-channel interactions with molecular dynamics simulations.

COMPUTATIONAL DETAILS Based on the following considerations, the medium size basis set 6-311++G(d,p) was employed: 1) one aim of the present work is to identify an appropriate and efficient density functional theory (DFT) method suitable to describe B…N bonding, and the parameterization of a force field using a large training set, 2)the energy decomposition analysis (based on localized molecular orbitals)21 we used to explore the B…N bonding is basis set insensitive, and 3)the computational cost will increase significantly with the oligomeric state (for example, the number of basis functions is 1944 for the tetrameric structure at the 6-311++G(d,p) level). We also tested the basis set effect, and found that increasing of basis set does not change the general conclusions. Benchmark calculations were carried out with generalized energy-based fragmentation (GEBF)22 method at the level of explicitly correlated coupled-cluster singles and doubles with noniterative triples corrections [CCSD(T)-F12a],23 e.g. GEBF-CCSD(T)-F12a.24 To be specific, the structures were optimized at either the M06-2X25 or the second order Møller-Plesset perturbation (MP2) theory levels with the 6-311++G(d,p) basis set. The energy difference between two representative states (A1 and A2, Figure 1) was calculated at the GEBF-CCSD(T)-F12a level with the aug-cc-pVDZ basis set, and was taken as the reference for the subsequent calculations. In the GEBF calculations, the canonical HF energies were combined with the GEBF correlation energies. Due to the fast basis set convergence, the GEBF-CCSD(T)-F12a results with the aug-cc-pVDZ basis set are comparable to the corresponding high-level CCSD(T) results with aug-cc-pVQZ basis set.24 Then, for the sake of compromised accuracy and efficiency, several density functionals were benchmarked against this standard, including the pure functional M06L,26 the hybrid functionals B3LYP,27-28 X3LYP,29 M05,30-31 M05-2X,31 M06,25 5



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M06-2X,25 M06-HF,32 the D2 version of Grimme’s dispersion corrected33 functionals B97D,34 ωB97XD,35 mPW2PLYPD,36 B2PLYPD,37 and the D3 version of dispersion corrected38 functionals TPSS-D3,39 revTPSS-D3,40 PBE-D3,41 PBE0-D3,42 BLYP-D3,27-28 B3LYP-D3,27-28 as well as the newly developed “meta-GGA made simple” and its hybrid (MGGA-MS2 and MGGA-MS2h)43-44 and the hybrid “meta-GGA made very simple” (MGGA-MVSh)45 functionals. By using each functional, the two states were optimized individually to calculate the energy difference. With the advantage of yielding quantitative agreement with high-level benchmark calculations, M06-2X is used in all of the following calculations (further described below). Due to the inherent difficulties in estimating intramolecular bonding, we built some model systems containing intermolecular B…N bonding (Figure 2) to mimic the intramolecular one in 2-APB. Some of them (for example, B1 and B2) have already been extensively studied by computation, however the results vary from different levels of theory.46-49 We further tested the performance of M06-2X by calculating the binding energy of model complexes. The interaction was characterized as follows:50 = +

(1)

where is the interaction energy, represents the distortion energy for each fragment to be promoted from isolation to the complex, and is the instantaneous interaction energy between the two fragments within the complex. In other words, and are the energies of the fragment in either fully relaxed (equation 2) or fixed in the complex structure (equation 3). In the fragmentation scheme, the molecule was separated into two neutral fragments by cutting a C-C bond (homolytic bond cleavage), so the spin multiplicity of each fragment is 2. is used for benchmark in this section, while is calculated to estimate the ring steric effect, as it is compatible with the energy decomposition analysis (EDA) we used. ( ) = ( ) − ( ) − ( )

(2)

( ) = ( ) − ( ) − ( )

(3)

With each fragment relaxed (equation 2), the calculated binding enthalpies of B1 is -28.24 kcal/mol, which is quite close to the experimental measurement of -27.5 6


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kcal/mol,51 and comparable with those computationally expensive high-level results (for

example,

-27.5

kcal/mol

obtained

by

QCISD(T)/aug-cc-pV5Z//MP2/

6-311++G(3df,2p) calculation),52 but slightly higher than Haaland’s estimation of -31.1±1.0 kcal/mol.53 Similar result can be found for B2, where the binding enthalpies is -17.92 kcal/mol (calculation, present work) vs -17.6 kcal/mol in literature (experiment).51 Therefore, the M06-2X scheme is able to describe well the systems containing either the intramolecular or intermolecular B…N interaction. However, we stress that, even though M06-2X exhibited good performance in the present study, carefully calibration of this functional is necessary, as its construction depends on a relative large number of empirical parameters, which is likely to suffer from numerical instabilities.54 Moreover, the M06-2X parameterization is not good for transition metals,55 where the increased occurrence of metal-to-boron coordinate bonding complexes have been observed.56 For different oligomeric states, the cyclic form of the monomer was taken as the reference, and the relative stability of others were calculated by using equation 4, where n represents the oligomeric state: () =

()

− (1)

(4)

Most of the present calculations were carried out with the Gaussian 09 program.57 For those functionals with empirical dispersion corrections based on Grimme’s scheme,58 GAMESS59 was used. The GEBF results were obtained with the LSQC program,60 in which the HF calculations were performed with Gaussian 0957 and the CCSD(T)-F12a calculations were carried out with the MOLPRO 2012 package.61-62 The electron localization function was generated with Multiwfn.63-64

RESULTS AND DISCUSSION Benchmark for functionals. We aim to identify a reliable and computationally efficiency functional, to accurately characterize B…N bonding in 2-APB. To do so, we choose two representative conformers of deprotonated 2-APB: the fully extended state (A1), in which the two atoms are far away from each other; and the cyclic state

7



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(A2), where B and N form close contact. Potential energy surface scan data shows that they are both local minimum (Figure S1 in Supporting Information). As shown in Figure 3, the reference data is in the range 7.65 to 8.08 kcal/mol, which is insensitive to the subtle difference of the structures optimized with different methods (MP2 or M06-2X). The corresponding data calculated with M06-2X is 8.01 kcal/mol, which is quite close to the reference. This is consistent with the results reported in literature, where by using experimental binding enthalpies as the target, the M06-2X was found to show good performance in describing substituted B…N complexes.47 Besides the M06-2X, some D3-corrected functionals including revTPSS-D3, PBE0-D3, TPSS-D3, PBE-D3 as well as M05-2X, MGGA-MS2h and MGGA-MS2, show reliable performance in the present case as well. With the advantage of yielding quantitative agreement with high-level benchmark calculations, M06-2X is used in all of the following calculations. It is worth pointing out that, the MP2 and some DFT functionals are incapable of describing well the energy difference in the present system. The stabilization energy predicted with MP2 (10.57 kcal/mol) is 2.49 kcal/mol higher than the CCSD(T) value; an overestimation error of 31%. One of the explanations is that the MP2 method overestimates the dispersion energy in some cases.65-66 Interestingly, the good performance of B3LYP in other systems does not carry over to the present system, mainly because of its difficulties to characterize pericyclic reactions.67 Even with the D3 correction, B3LYP-D3 still does not lead to a reliable prediction. In contrast, TPSS-D3 was found to have good performance to describe cyclophanes with notable strain components.68

The strength of the B…N bonding in 2-APB. The calculated B-N distance in the cyclic form of 2-APB is 1.73 Å, which is slightly longer than the x-ray structure of 1.65 Å.69-70 The packing in the crystal environment may partially account for this discrepancy. It should be noted that this bond length is significantly longer than the B-N bond of 1.57 Å71 in cubic or 1.45 Å72 in hexagonal boron nitride, but much shorter than the sum of the van der Waals radii of the two atoms (2.90 Å), indicating the 8


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characteristics of a coordinative bond. The calculated instantaneous interaction energy of B1, ( ) , with each fragment remaining at the geometry of the complex (equation 3), is -44.08 kcal/mol at the M06-2X/6-311++G(d,p) level, which is consistent with the high level CCSD(T)/aug-cc-pVQZ data of -44.16 kcal/mol reported in literature.21 Being the simplest model system containing B…N bonding, its interaction energy mainly comes from the formation of the Lewis pair. We further realized that all of the model complexes (B1~B5) have similar instantaneous interaction energies, regardless of the chemical environment of the B…N group (Figure 2). How about the B…N bonding in 2-APB? By comparing the physical descriptors of A2 and model complexes with respect to the electron localization function (ELF), molecular orbital (MO) and electrostatic potential surface (EPS), we will demonstrate that the intramolecular B…N bonding in 2-APB resembles the intermolecular one in model complexes, as further described below (Figure 4). ELF: ELF is a useful tool in interpreting bonding.73-74 According to the definition, ELF = 1 corresponds to a fully localized state and ELF = ½ represents the electron gas.73 As shown in Figure 4a, the x-axis is the coordinate of the B…N bonding with the center of the boron atom being at the origin. The location of the single attractor V(B,N) corresponding to bonding is at ~1 Å position away from the boron atom, which confirms that the bonding pair is more closely associated with the electron donor N atom. The ELF value there is ~0.943, almost the same in B1~B5 and in A2, indicating the well resembled B…N bonding in both intra- and inter-molecular systems. MO: The boron atom is approximating the idealized configuration for sp3 hybridization, that is (2s)0.51(2p)1.54 valence configuration in A2 and (2s)0.51(2p)1.55 in B5. The valance orbital hybridization of boron is consistent with its approximately tetrahedral geometry. The frontier orbital picture shows that HOMO and LUMO orbitals in B5 (Figures 4b and 4b') are quite similar to those in A2 (Figures 4c and 4c'). Specifically, HOMO is delocalized over the two phenyl rings as well as the central boron atom, the Lewis acid part. The partial overlap between the vacant p orbital of 9



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the boron center and the π orbitals of the two phenyl groups results in a pronounced Lewis acidity. When the two phenyl groups in 2-APB are substituted with two methyl group, the relative stability between the cyclic- and extended-forms drops significantly from 8.01 kcal/mol in 2-APB to 3.67 kcal/mol, indicating a weakened B…N interaction. This may explain the observations that the diphenyl moiety is important for its activity by comparing 2-APB with its structural analogs.11 Meantime, nitrogen on the amine head, the Lewis base part, is also sp3 hybridization, with the configuration of (2s)1.37(2p)4.38 in A2 and (2s)1.36(2p)4.37 in B5. The HOMO-LUMO gaps are similar in A2 and B5, which are -6.16 and -6.34 kcal/mol, respectively. Notably, the delocalization of molecular orbitals on the Lewis acid and Lewis base centers, respectively, is an indication of the non-covalent feature of the B…N bond in 2-APB. Intramolecular electron transfer (~0.1 e) takes place from N on amine head to B, confirming the formation of the adduct, and suggesting that polarization (coming from the electron transfer and charge accumulation between nuclei) could be important for the formation of the Lewis pair. EPS: The molecular electrostatic potential is a rigorously defined property, which can be characterized with quantum mechanics. The calculated EPSs of B5 (Figure 4d) and A2 (Figure 4e) resemble each other, suggesting the similar B…N bonding within the two constructs: the amine group is predominantly positive, and the boron center is almost neutral, while the neighboring oxygen atom shows strong negative distribution of electrostatic potential. Therefore, the boron center is not electrostatically complementary to the amine group even though the B…N bond is polar. However, with the presence of oxygen, the electrostatic component may still be important in such bonding, though it may not be a dominant factor. This may explain the experimental observation that replacement of boron-oxygen core with carbon-phosphorus core leads the loss of potentiation capacity.12 All of the above three independent descriptors indicate that the intramolecular B…N bonding in 2-APB resembles the intermolecular one in model complexes, among which, B5 is the best model to mimic the environment in A2. Therefore, though we do not have a direct estimation on the B…N bond strength, it is a rational speculation 10


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that the instantaneous interaction energy of B…N in A2 is -46.75 kcal/mol as well, which is much stronger than those non-bonded interactions (no stronger than -10 kcal/mol in most cases), but notable weaker than the covalent B-N single bond (-88 kcal/mol, 1.47 Å).53

The nature of the B…N bonding in 2-APB It is interesting to understand the nature of B…N bonding in 2-APB, which has strength intermediate between covalent and non-covalent bonds. Among different protocols, EDA was developed as a powerful tool for the quantitative interpretation of chemical bonds.75 Here we used the localized molecular orbital based EDA protocol21 implemented in GAMESS59 to explore the B…N bonding. Besides model complexes B1~B5, HO-CH2-CH2-NH2 (B6, aiming at the C-C bond) and H2O…H2O (B7, aiming at the hydrogen bond) were used as the representatives for covalent and non-covalent bonding models. The individual contributions from the total interaction energies, including electrostatic, exchange, repulsion, and polarization terms, were normalized for direct comparison. As seen from Figure 5, the contributions of each component towards attractions are quite different among the complexes B6, B7 and B1~B5. Polarization term, accounting for the additional electrostatic stabilization due to the induced multipoles as well as the charge accumulation between nuclei, is dominant in the covalent bond (B6), which counts for ~33% of the attractive energy, but only contributes for ~10% for the non-covalent bond (B7). B…N bonding in B1~B5 has a moderate polarization component (25%) in between of the covalent and non-covalent bond. Electrostatic term is dominant in non-covalent bond (B7), and is decreasing in those B1~B5 complexes, and is further decreasing in the covalent bond (B6). Interestingly, contributions from dispersion are more important in the non-covalent bond than others. All of the three components, including polarization, electrostatic, and dispersion, vary monotonically from B6 to B1~B5, and to B7, indicating that the B…N bonding falls in between of that covalent and non-covalent bond. By calculating the localized resonance structures and the corresponding weighting factors based on the 11



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natural resonance theory, it was proposed that the B…N bond in B1 complex is 65% ionic.52

Ring strain Given the significant contribution from the instantaneous intramolecular B…N interaction (-46.75 kcal/mol), why is the cyclic form of 2-APB only 8.08 kcal/mol more stable than the extended form? When compared to the extended form, it is very likely that strain is involved in ring formation in the cyclic form and that this mainly accounts for the “extra” instability. So we propose the following energy partition protocol (protocol-I) to roughly estimate the energy of ring strain. By breaking the C-C covalent bond to divide the 2-APB into two fragments with either B or N atoms (two radical monomers), as shown in Figure 6, we get the instantaneous interaction energy between two fragments of -129.96 and -104.47 kcal/mol, respectively, for the cyclic- and extended-forms. We further propose equations (5) and (6) to partition the interaction energy into different components, including the steric of the ring, where the superscript "CS" and "ES" mean the cyclicand extended-state, respectively. Eint, EB…N, EC-C and Ering are the instantaneous interaction energy between two fragments, the B…N interaction energy, the C-C bond strength, and steric energy of the ring, respectively. The Eerror term is introduced to account for the error in the energy partition protocol we proposed here. = …" + # + +

(5)

= …" + # + +

(6)

By using (5)-(6), and assuming = , and both

and …" equal

to 0 as there is no ring steric energy and B…N bonding in the fully extended structure, we get: = ( − ) − …" − (# − # )

(7)

Eint could be calculated with EDA, and we already have an estimation on …" . So

12


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once the # is known, we are able to evaluate the ring steric. To estimate # , another model containing this covalent C-C bond is constructed, as shown in Figure 6. Taking # as an example, we built A1CC by keeping the fragment (O-CH2-CH2-NH2)

as in the original structure of A1. A hydrogen atom is added to saturate the broken bond at oxygen atom, and its position is freely optimized. We then estimate the C-C in the same way. The bond strength by breaking the bond and calculate the # calculated # and # are -107.15 kcal/mol in A1CC and -102.87 kcal/mol in

A2CC, respectively. By using this energy partition protocol, the ring strain in the cyclic form of 2-APB (A2) is estimated to be 16.98 kcal/mol. Similarly, we construct analogs (C1 and C2) to 2-APB (A1 and A2, respectively) with one more CH2 group inserted (Figure 6) to make a longer chain. After structure optimization, the C1CC and C2CC are also constructed to estimate the # in the analogs (Figure 6). The ring strain in C2 is then estimated as 12.25 kcal/mol. Therefore, increasing from 5-members A2 (2-APB) to 6-members C2 (2-APB analog) ring is estimated to gain 4.73 kcal/mol energy. To further validate the above protocol-I to estimate ring strain, we calculate the relative stability of the cyclic- and extended-forms (energy difference protocol, protocol-II). The energy difference (∆E5-members) in 2-APB is 8.01 kcal/mol, and the cyclic form of the aforementioned analog is 12.57 kcal/mol (∆E6-members) lower than its extended form, mainly because of the released ring strain. Therefore, the energy difference of ring strain (∆∆E = ∆E6-members - ∆E5-members) is 4.56 kcal/mol. The consistency of data obtained from both protocol-I and II justifies the effect of ring strain we proposed above. However, by using protocol-II, we can only estimate the relative steric energy between different ring sizes (for example, 4.56 kcal/mol between 5- and 6-members rings). In contrast, protocol-I provides an opportunity to quantitatively evaluate the ring steric effect in each specific system (for example, 16.98 kcal/mol in the 5-members ring of 2-APB, and 12.25 kcal/mol in its 6-members analog). It is clear that the ring steric effect partially counterbalance the strong attraction from the B...N bonding, and makes it more dynamic. The reversible and dissociative 13



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characteristics of such bonding was already observed using fs kinetic-energy resolved time-of-light mass spectrometry.76 To quantitatively show this offset, we manually change the B…N distance in B1, B5 (model compounds) and A2 (cyclic 2-APB), and calculate the relative stability by using the energy minimum of each as the reference. The former two show quite similar disassociation curves (Figure 7). The stability of the cyclic 2-APB, on the other hand, decreases slower than B1 and B5. Clearly, the release of ring strain in the cyclic 2-APB partially compensates the energy lost from B…N separation. Therefore, there is a delicate balance between ring strain and B…N bonding in the cyclic form of 2-APB, and the reversible forming and breaking of the B…N bond is possible, as disclosed by the only 8.08 kcal/mol energy difference between the cyclic- and the extended-forms. Consequently, 2-APB is free to switch among different functional forms, and may have different binding affinities in the target channels.

Oligomerization Given the ~45 kcal/mol instantaneous strength of the B…N bonding in 2-APB, it is very likely such favorable interaction can be formed either intra- or inter-molecularly. One of the potential advantages of forming a molecular complex that consists of a few monomer units is to form a more stable cluster with higher molecular volume, which may have distinct modulating behavior on the target membrane protein. Formation of higher oligomeric structures gradually releases the ring strain and therefore makes the B...N bonding more favorable, as indicated by the bond length. It is 1.73 Å in the monomer (A2), and the averaged values are 1.67 Å in the dimer (A3), 1.65 Å in the trimer (A4) and 1.63 Å in the tetramer (A5), respectively. Consequently, aggregation of the monomers increase the stability of the complex (tetramer > trimer > dimer > monomer, Figure 8). For example, the dimer is 8.8 kcal/mol per monomer lower than the monomer. However, with the increased oligomerization status, the favorable entropy changes may partly offset by the unfavorable enthalpy changes, and the steric repulsion from the bulky phenyl groups between different units is also introduced. Therefore, the relative stability of 14


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oligomers with increasing number of monomers converges rapidly.

Possible 2-APB modulation mechanism for CRAC channel gating The detailed information about 2-APB regulation is still unclear. Presumably, the stimulatory effect of 2-APB on SOCE comes from its induced pore dilation. Specially, the interaction between the extended form of 2-APB (so that the B and/or N centers are free to bind to the protein) and Orai (at the N- and/or C-terminals) facilities the opening of the central pore.77 Another plausible scenario is that the presence of 2-APB (or its analog) helps the formation of the Orai-STIM complex.16, 78-79 With regard to inhibition, an intuitive picture is that the volume-occupied cyclic 2-APB or its oligomer with larger size (which is more likely, because of the higher stability as shown in Figure 8) physically blocks the permeation pathway of ions through the channel, while other cases, including the intracellular acidification mechanism,80 are also possible. All of the above speculations are subject to further validations from both molecular modeling and experimental measurements.

CONCLUSIONS In this work, we propose that the B…N interaction, a reversible coordinate bonding in 2-APB, is critical for its known dual pharmaceutical effect. Importantly, the character of the intramolecular B…N bonding, with respective to the electron localization function, molecular orbitals and electrostatic potential surface, resembles that found in complexes containing intermolecular B…N bonding. The instantaneous strength of the B…N bond is 45 kcal/mol, which lies between a covalent and a non-covalent bond. The delicate balance between B…N bonding and ring steric strain makes 2-APB in principle an ideal drug to present distinct forms and/or binding affinities at different binding sites. Seemingly facile formation and easy dissociation of oligomers is the key factor enabling 2-APB to exhibit broad-spectrum activity on membrane proteins. Understanding the subtlety of oligomer formation and stability obtained herein should provide new insights for generating novel, improved clinical candidates for the CRAC channel. 15



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Supporting Information 2D potential energy surfaces of the cyclic- and extended-forms of 2-APB (A1 and A2). This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This work was supported by the National Natural Science Foundation of China (Grant No. 21503107) and the "Fundamental Research Funds for the Central Universities". Part of the calculations were performed using resources on IBM Blade cluster system from the High Performance Computing Center (HPCC) of Nanjing University.

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Figure 1. Different oligomeric states of 2-APB (left) and its potential binding sites (right) in the SOC channel.

Figure 2. Shown are selected model complexes exhibiting intermolecular B…N bonding. The calculated interaction energies between pairs of fragments are quite similar for each of these dimeric systems. Energy is shown in kcal/mol.

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Figure 3. Shown are the estimated energy differences between the cyclic- and extended- forms of 2-APB. Using GEBF-CCSD(T)-F12a/aug-cc-pVDZ data as the benchmark, different functional as well as MP2 are tested at the 6-311++G(d,p) level. M06-2X gives the most accurate result in this case, and some other functionals highlighted in the red frame also show good performance. Ref[MP2] and Ref[M06-2X] are benchmark calculations based on the MP2 and M06-2X optimized structures, respectively. Energy is shown in kcal/mol.

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Figure 4. Physical descriptors show high similarity between the inter- and intra-molecular B…N bonding, indicating the medium strength of the B…N interaction in 2-APB. (a) 1-D electron localization function along the B…N bond in model complexes B1~B5 (black, yellow, green, blue and red lines) and 2-APB (pink line). The HOMO (b) and LUMO (b') orbitals in B5, which mimics the 2-APB (A2). The molecular orbitals (c for HOMO and c' for LUMO) of A2 are quite similar to those of B5. Electrostatic potential surfaces of B5 (d) and A2 (e) resemble each other as well.

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Figure 5. Shown is the energy decomposition analysis of B…N bonding. Data from both covalent and non-covalent bonds is presented for comparison. The contributions to attraction from each component are normalized for comparison. Polarization, electrostatic, and dispersion terms vary monotonically from B6 (covalent bond) to B1~B5, A2 and to B7 (non-covalent bond), indicating that the B…N bonding in A2 (as well as in B1~B5) falls in between a covalent and non-covalent bond.

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Figure 6. Shown is the energy partition protocol to estimate the ring steric effect and the instantaneous energy of the C-C bond. C1 and C2 are analogs to A1 and A2, respectively, with one more CH2 group inserted. In the energy partition protocol, each molecule was separated into two neutral pieces by cutting the C-C bond (as indicated by the red arrowhead). The Eint between the two fragments was then calculated with the energy decomposition analysis. Model compound XCC was constructed to estimate EC-C, where its geometry is kept in the original position as in the primary compound X. With known Eint and EC-C, the effect of ring strain (Ering) could be estimated using equation 7.

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Figure 7. Shown are the relative stabilities of the compounds (B1, B5 and A2) at different B…N distances. For A2 (blue curve), the release of ring strain partially offset the energy lost when the B…N distance is increasing, showing the delicate balance between B…N bonding and ring strain in the cyclic form of 2-APB.

Figure 8. The computed stability of different oligomers indicates that aggregation increases the stability of the complex.

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Understanding the BoronâNitrogen Interaction and Its Possible

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Understanding the BoronâNitrogen Interaction and Its Possible