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Sep 2, 2016 - Kazan National Research Technological University, K. Marx Strasse 68, 420015 Kazan, Republic of Tatarstan, Russian Federation. ‡...
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Chiral Selectivity in Inter-reactant Recognition and Electron Transfer of the Oxidation of Horse Heart Cytochrome c by Trioxalatocobaltate(III) Renat R. Nazmutdinov,*,† Michael D. Bronshtein,† Tamara T. Zinkicheva,† Niels Sthen Hansen,‡ Jingdong Zhang,‡ and Jens Ulstrup*,‡ †

Kazan National Research Technological University, K. Marx Strasse 68, 420015 Kazan, Republic of Tatarstan, Russian Federation Department of Chemistry, Building 207, Technical University of Denmark (DTU), 2800 Kongens, Lyngby, Denmark

‡

S Supporting Information *

ABSTRACT: Outer-sphere electron transfer (ET) between optically active transition-metal complexes and either other transition-metal complexes or metalloproteins is a prototype reaction for kinetic chirality. Chirality as the ratio between bimolecular rate constants of two enantiomers mostly amounts to 1.05−1.2 with either the Λ or Δ form the more reactive, but the origin of chirality in ET parameters such as work terms, electronic transmission coefficient, and nuclear reorganization free energy has not been addressed. We report a study of ET between the Λ-/Δ-[Co(Ox)3]3− pair (Ox = oxalate) and horse heart cytochrome c (cyt c). This choice is prompted by strong ion-pair formation that enables separation into inter-reactant interaction (chiral “recognition”) and ET within the ion pair (“stereoselectivity”). Chiral selectivity was first addressed experimentally. Λ-[Co(Ox)3]3− was found to be both the more strongly bound and faster reacting enantiomer expressed respectively by the ion-pair formation constant KX and ET rate constant kXET (X = Λ and Δ), with KΛ/KΔ and kΛET/kΔET both ≈1.1−1.2. rac-[Co(Ox)3]3− behavior is intermediate between those of Λ- and Δ-[Co(Ox)3]3−. Chirality was next analyzed by quantum-mechanical ET theory combined with density functional theory and statistical mechanical computations. We also modeled the ion pair K+·[Co(Ox)3]3− in order to address the influence of the solution ionic strength. The complex structure of cyt c meant that this reactant was represented solely by the heme group including the chiral axial ligands LHis and L-Met. Both singlet and triplet hemes as well as hemes with partially deprotonated propionic acid side groups were addressed. The computations showed that the most favorable inter-reactant configuration involved a narrow distance and orientation space very close to the contact distance, substantiating the notion of a reaction complex and the equivalence of the binding constant to a bimolecular reaction volume. The reaction is significantly diabatic even at these short inter-reactant distances, with electronic transmission coefficients κXel = 10−3−10−2. The computations demonstrated chirality in both KX and κXel but no chirality in the reorganization and reaction free energy (driving force). As a result of subtle features in both KX and κXel chirality, the “operational” chirality κΛETKΛ/κΔETKΔ emerges larger than unity (1.1−1.2) from the molecular modeling as in the experimental data.

I. INTRODUCTION

Chemical chirality extends further. One area is ET between chiral transition-metal complexes and redox metalloproteins.11−23 The metal centers such as the Cu centers in blue copper proteins17,19,21,22 and the Fe centers in iron−sulfur20,23 or heme proteins11−16,21,22,24 are thus chiral. In addition, by the exclusive prevalence of L-amino acids in the ligand spheres and protein matrix, chirality at several levels can be expected in both binding and elementary ET processes. Adsorption of chiral (R)and (S)-2-butanethiol on Au(111) electrode surfaces appears to follow conceptually related lines.25,26 Chirality was displayed both by the adsorbed target molecules and by ordered domains of adsorbed molecules.

Chiral selectivity in chemical processes has been known since Pasteur’s time.1 Isolation of a multitude of chiral organic molecules2,3 or transition-metal complexes4,5 and chromatographic enantiomeric separation are broad present day representatives.6,7 In recent times, sophisticated pure and applied molecular chiralities in chemical kinetics have emerged. Asymmetric molecular chemical synthesis including optically active drugs with detailed mechanistic mapping is one rapidly expanding area.8,9 Important other clues to chiral kinetics have also evolved, with the focus on outer-sphere electron-transfer (ET) processes of chiral transition-metal complexes.10−22 Following early work by Geselowitz and Taube,10 this area was developed particularly by Lappin and co-workers12−14 and by Bernauer and associates.15−17,1922 © 2016 American Chemical Society

Received: June 22, 2016 Published: September 2, 2016 9335

DOI: 10.1021/acs.inorgchem.6b01489 Inorg. Chem. 2016, 55, 9335−9345

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Inorganic Chemistry

Λ Δ recognition (KΛ/KΔ) and steroselectivity (kET /kET ) are displayed, with the Λ form both the more strongly bound and the faster ET enantiomer. The selectivity ratios are in the range 1.1−1.2 for both KΛ/KΔ and kΛET/kΔET. rac-[Co(Ox)3]3− shows an apparent kinetics intermediate between the pure enantiomers, but the formal kinetics is here more complex because of the parallel reactions of two kinetically nonequilibrated cobalt(III) species. We study next the chirality by a quantum-chemical approach. [Co(Ox)3]3−/4− was structurally optimized. cyt c(II) was represented by the heme group (structure optimized, low spin) with the chiral axial L-His and L-Met ligands. The solvent was represented as a dielectric continuum. Rather than attempting to reproduce the observed chiral recognition and selectivity, we explore the ensemble of intermolecular configurations of the pair of cyt c(II) (the heme group) and chiral [Co(Ox)3]3−. This includes a statistically averaged orientation and distance dependence as well as solvent effects and the way these are reflected in KΛ/KΔ and the ET rate constants kΛET and kΔET. The kinetic parameters are the solvent and intramolecular reorganization free energies Es and Ein, the reaction free energy or driving force ΔG0, the intermolecular interaction terms WR and WP or ion-pair formation constants, and the electronic transmission coefficient κel. The physical nature of the intermolecular interactions and the most likely binding distances and orientations are the first computational result. The second result is assignment of the chiral effects to the ET parameters, where the transmission coefficient κel and the interaction terms are chirally by far the most sensitive. The chirality is also affected by the presence of K ions (from the buffer) as counterions to [Co(Ox)3]3−.

Reported kinetics of ET between redox metalloproteins and chiral transition-metal complexes of high structural sophistication include spinach plastocyanin and Pseudomonas aeruginosa azurin (blue copper proteins),17,19 spinach ferredoxin (iron− sulfur protein),20,23 and horse heart cytochrome c (cyt c, heme protein).11−16,21,22 Circular dichroism (CD) spectroscopy of the product composition, a direct comparison between the rate constants of the isolated Δ and Λ forms of the inorganic reaction partners, and binding site studies were used. The chiral selectivity is commonly expressed as the ratio kΔ/kΛ, where kΔ and kΛ are the observed bimolecular ET rate constants of the isolated Δ and Λ forms of the inorganic reaction partners. Values of this ratio mostly differ from unity by up to 10−20% with either kΔ or kΛ the larger one, but higher values are also encountered.15,17,20−22 In this work, we report the chirality in bimolecular ET between a metalloprotein and an optically active pair of transition-metal complex reaction partners in a new way. The reaction is ET between horse heart cyt c and isolated Δ and Λ forms of the cobalt(III) complex, [Co(Ox)3]3− (Ox2− = oxalate, itself achiral). The mechanism involves a strong ion pair24 cyt c(II) + [Co(Ox)3 ]3 − K

⇄ cyt c(II)·[Co(Ox)3 ]3 − kET

⎯→ ⎯ cyt c(III) + [Co(Ox)3 ]4 −

(1)

where kET is the ET rate constant within the ion pair and K the equilibrium constant for formation of the ion pair. The latter notion applies when the ion pair forms in a narrow interval of separation. The cobalt(II) product, [Co(Ox)3]4−, decomposes to [Co(OH2)6]2+ and Ox2−. Only very small, if any, chiral selectivity could be detected in the related ET processes, cyt c(III) reduction by Δ- and Λ-[Co(sep)]2+ (sep = sepulchrate)27 and cyt c(II) oxidation by Δ- and Λ-[Co(acac)3]11 (acac = acetylacetonate). Using CD product analysis and direct kinetic data for cyt c(II) oxidation by Δ- and Λ-[Co(Ox)3]3− Λ Δ separately, Lappin and associates, however, found kET /kET Λ Δ values (in fact, kET KΛ/kET KΔ; cf. below) of 1.05−1.20 depending on the ionic strength, and [cyt c(II)]/[[Co(Ox)3]3−] ratios,12−14 i.e., cyt c(II) is oxidized faster by the Λ form than by the Δ form. They did not, however, consider intermediate ion-pair formation. In the first part of the present study, we report kinetic data for the scheme in eq 1. The strong electrostatic inter-reactant interaction gives intermediate ion-pair formation reflected in saturation kinetics at high [[Co(Ox)3]3−], enabling separation of chirality in the ion-pair formation constant and the elementary ET rate constant in the ion pair. Assuming that the rate constants for ion-pair formation and dissociation are much larger than the ET rate constants (see the Supporting Information, SI) gives the rate law

II. EXPERIMENTAL SECTION Chemicals and Reactants. Λ- and Δ-[Co(Ox)3]3− (molar absorption coefficients ε425 = 230 M−1 cm−1 and ε605 = 175 M−1 cm−1) were prepared by the reported procedures.28,29 Racemic K3[Co(Ox)3]·3H2O was first prepared from CoCO3 (highest purity; BDH Chemicals, Poole, England), potassium oxalate (AnalaR, RiedelDe-Haen, Seelze, Germany), and Pb3O4. K3[Co(Ox)3]·3H2O is sensitive to light and was kept in the dark. Λ- and Δ-[Ni(phen)3]2+ (phen = 1,10-phenanthroline) were used to resolve rac-[Co(Ox)3]3− into enantiomeric forms.29 Racemic [Ni(phen)3](ClO4)2·3H2O was prepared from [Ni(OH2)6]Cl2, phen, and NaClO4 (all AnalaR, Merck, Oak Brook, IL) and separated into Λ and Δ enantiomers by selective binding to potassium antimonyl-D-tartrate (AnalaR, Merck, Oak Brook, IL). rac-[Co(Ox)3]3− was resolved into Λ- and Δ-[Co(Ox)3]3− enantiomers via binding to Λ- and Δ-[Ni(phen)3 ]2+. Their enantiomeric purity was checked by polarimetry. The water content of the product showed some variation. Concentrations refer to the observed absorbances and absorption coefficients above. Horse heart cyt c(III) (99%, Sigma, St. Louis, MO) was purified using high-performance liquid chromatography (HPLC) and a CM 52 cation-exchange column (Whatman BioSystems Ltd., Kent, England). Prior to kinetic runs, cyt c(III) was 95% reduced overnight to cyt c(II) with ascorbic acid (AnalaR, Merck, Oak Brook, IL). Concentrations of stock solutions were adjusted to 1.23 × 10−4 M for cyt c(III) (ε530 = 11.1 × 103 M−1 cm−1 (ε550 = 9.1 × 103 M−1 cm−1)30,31 and 5.26 × 10−5 M for cyt c(II) (ε550 = 27.6 × 103 M−1cm−1)30,31 with a 0.031 M phosphate buffer, pH 7.5 (KH2PO4 and K2HPO4 AnalaR grade, Laboratory Chemicals Group, British Drug House Ltd., Poole, England). Instruments. A Shimadzu UV-150-02 spectrophotometer with inhouse software and a Milton Roy diode-array spectrophotometer, both with thermostated 1 cm quartz cells, were used for recording of kinetic data and characterization of reactant samples. Temperatures were 5 and 25 °C for the kinetic runs, with 5 °C giving the best data. The

d[cyt c(II)]tot = vobs = kobs[cyt c(II)]tot dt kobs =

ion pair kET ; 1 + K[Co(III)]

ion pair kET = kETK[Co(III)]

(2)

where Co(III) stands for [Co(Ox)3]3−. Equation 2 is based on two parallel reaction channels. One involves “freely” mobile [Co(Ox)3]3− (possibly ion paired with K+) and the other one ET via the cyt c(II)·[Co(Ox)3]3− ion pair (eq 1). Chiral 9336

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Figure 1. Observed pseudo-first-order rate constants kobs (s−1; eqs 2 and 4; with error bars) of the cyt c(II)/Co(III) reaction for Λ-, Δ-, and rac[Co(Ox)3]3− as a function of the [Co(Ox)3]3− concentration (mol L−1). Left: 25 °C. Right: 5 °C.

Table 1. Rate Constants (s−1) and Recognition (Ion-Pair) Constants (M−1) from the Data in Figure 1 temperature, °C species kXET (X = Λ and Δ), s−1 KX, M−1 kΛETKΛ + kΔETKΔ, M−1 s−1 a

25 rac (1.6 ± 0.03) × 10−1 a 250 ± 30a 44 ± 5,40 ± 15a

25 Λ form (1.1 ± 0.05) × 10−1 230 ± 10

25 Δ form (9.4 ± 0.05) × 10−2) 200 ± 10

5 Λ form (6.2 ± 0.05) × 10−2) 160 ± 10

5 Δ form (5.3 ± 0.05) × 10−2 126 ± 10

Data for rac-[Co(Ox)3]3− reported in ref 35.

reactants were mixed directly in the thermostated cells within a couple of seconds, leaving insignificant uncertainty in the starting time of the process. The enantiomeric purity of Λ- and Δ-[Co(Ox)3]3− was checked and racemization kinetics followed by a PerkinElmer model 141 polarimeter. About 2.7% of either form had racemized after 10 min, corresponding to rate constants of 2.3 × 10−5 and 2.5 × 10−5 s−1 for the Λ and Δ forms, respectively. The pseudo-first-order rate constants for the cyt c(II)/Co(III) ET processes were in the range of (0.5−5) × 10−2 s−1 for [Co(III)] in the range of (0.5−5) × 10−3 M used, i.e., much faster than racemization, which was therefore disregarded. The ET kinetics was recorded by following the absorbance at cyt c(II) 550 nm α-band maximum. Co(III) was always present in 10−100 times excess according to pseudo-first-order conditions. Absorbance changes in the Co(III) concentration from the ET process were insignificant and were disregarded. Computational Methods. The quantum-chemical calculations of the oxidized and reduced hemes of both the [Co(Ox)3]3−/4− redox couple and the [Co(Ox)3]3−/4−·K+ ion pairs were accomplished at the density functional theory (DFT) level with the hybrid functional B3LYP, as implemented in the Gaussian 09 program suite.32 A splitvalence basis set of double-ζ (DZ) quality was employed to describe the valence electrons of the Fe and Co atoms. Inner electrons were included in the relativistic core potential (LanL2) of Hay and Wadt.33 The Dunning−Huzinaga valence basis set (D95 V) was used to describe the electrons of O, N, C, S, K, and H atoms.32 As shown by us previously in modeling of the cyt c4 heme centers,34 the larger splitvalence triple-ζ basis sets with polarization functions, 6-311++g(d,p) and TZVP, lead to geometry and intermolecular reorganization energies slightly different from those at the LanL2DZ computational level. The open-shell systems were treated in terms of unrestricted formalism. The geometry of the heme complexes was fully optimized for the oxidized and reduced states without symmetry restrictions, and the stability of the Kohn−Sham orbitals was checked. Environmental effects on the electronic structure of the reactants were addressed in the framework of the polarizable continuum model.32 All calculations were run on dual-core Pentium IV workstations.

III. EXPERIMENTAL RESULTS The kinetics of the reaction in eq 1 was studied by Holwerda and associates,24 by Ficke and associates,13 and by Macyk and van Eldik.35 The Λ form was reported in ref 13 to react faster than the Δ form, with variable values of the rate constant ratio depending on the ionic strength and the concentration ratio [cyt c(II)/[Co(III)].13 Kinetic saturation and ion-pair formation (eq 2) were mapped,24,35 but separation of the chirality into “recognition” (KΛ/KΔ) and kinetic selectivity (kΛET/kΔET) has not been addressed. Pseudo-first-order rate constants (eqs 1 and 2) were calculated by fitting the following absorbance time evolution form to the data using the fitting program Enzf itter36 ∞ cyt c(II) cyt c(III) A550 − A550 = (ε550 − ε550 )S[cyt c(II)]0 exp( − kobst )

(3) A∞ 550

where A550 and are the absorbances of cyt c(II) at time t and infinity, respectively, and [cyt c(II)]0 is the initial cyt c(II) concentration. Equations 2 and 3 apply for each enantiomer, i.e. X kobs =

X kET KX[Co(III)] , 1 + KX[Co(III)]

X = Λ, Δ

(4)

The formal rate forms are more complex for rac-[Co(Ox)3]3− because cyt c(II) here reacts in parallel with different ET rates with each nonequilibrated enantiomer. This is discussed in the SI. Figure 1 shows the pseudo-first-order rate constants as a function of [Co(III)] in the range (0.5−5.0) × 10−3 M (i.e., 1 order of magnitude concentration range) at 25 and 5 °C for Λ-, Δ-, and rac-[Co(Ox)3]3−. As noted, the process proceeds in the 10−100 s time range, i.e., significantly faster than racemization of Λ- and Δ-[Co(Ox)3]3− (minutes to half hour time range). Racemization is therefore insignificant. Saturation kinetics is clearly apparent, strongly supporting that ET is via an intermediate cyt c(II)/[Co(Ox)3]3− ion pair. The quantitative differences between the three forms are small, but Λ-[Co(Ox)3]3− clearly reacts faster than Δ-[Co(Ox)3]3−, with rac[Co(Ox)3]3− in between. Table 1 summarizes the stereoselective ET rate constants kXET and binding constants KX, where X = Λ and Δ, along with the 9337

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Inorganic Chemistry corresponding apparent values for the racemic mixture. As noted, the latter carries the notion of “apparent”, as the formal kinetics differs from that of the pure enantiomers (cf. the SI). For this reason, only the combination kΛETKΛ + kΔETKΔ can be extracted for rac-[Co(Ox)3]3−, as shown in the SI. kXET and KX, where X = Λ and Δ, are statistical averages of a large number of microscopic intermolecular binding and rate constants (cf. sections IV and V). The recognition KΛ/KΔ and stereoselectivity ratios kΛET/kΔET are given in Table 2 and discussed in section IV.

group edge. Overall, the theoretical part of our study is, however, still to be regarded as exploratory rather than being of quantitative nature. The reactant ion-pair formation constant (K) is commonly defined as

K=

25 1.2 ± 0.05 1.1 ± 0.05

(5)

where r is the distance between the reactants, δr denotes the spherical layer thickness, and NA is Avogadro’s number. Because the preexponential factor in eq 5 is largely canceled in the ratio of K for different chiral isomers, we consider only the exponential factor in eq 5, i.e., the reduced form

Table 2. Stereoselectivity and Recognition Ratios from the Data in Figure 1 and Table 1 temperature, °C kΛET/kΔET KΛ/KΔ

⎡ W (r + δr ) ⎤ 4πNAr 2δr exp⎢ − R ⎥ 1000 kBT ⎣ ⎦

5 1.2 ± 0.05 1.3 ± 0.05

K = exp(− WR /kBT )

(6)

where WR is the statistically averaged inter-reactant free energy, or “work term” in the reactants’ state (eqs 8 and 9). By far, the prevailing contribution to WR comes from a narrow layer with δr ≈ 1 Å. The ET rate constant within the ion pair is formally of first-order (s−1), while the reactant pair formation constant K is formally a reaction volume (M−1) in the bimolecular ET process, but the view of K as a reaction volume is only precise if ET proceeds through a well-defined reaction complex. Such a complex is likely to prevail because facile electronic coupling and chiral effects are feasible only for short intermolecular distances and favorable orientations. We incorporate, however, first a distribution of different intermolecular distances and relative orientations. The ET rate constant for ET in the ion pair for a given enantiomer, X (Λ and Δ), should be statistically averaged over an array of distances and orientations of the reactants38,39

The recorded kinetics at two different temperatures, in principle, offers a route to the apparent activation entropy, as reported by Tembe and co-workers.37 Interpretation of such a quantity is, however, a challenge and was not in the focus of the present study. The ET rate constants accord broadly with those reported in ref 13 and, for the racemic mixture, in refs 24 and 35, although analyses in these reports and in the present work are different. Faster ET for Λ[Co(Ox)3]3− than for Δ-[Co(Ox)3]3− was observed both in ref 13 and in the present study, but an additional outcome of the present study is that chiral selectivity in both recognition, KX, and ET kinetics, kXET (X = Λ and Δ), is found, with intermolecular binding stronger and “intramolecular” ET faster for Λ-[Co(Ox)3]3− than for Δ-[Co(Ox)3]3−. The most favorable binding site is thus also the site of strongest ET chirality. Chirality in ion-pair binding (recognition) and stereoselective intramolecular ET are both rooted in a complex statistical distribution of intermolecular chiral interactions. In the next two sections, we explore these interactions and how they are reflected in the electronic and nuclear rate parameters.

X kET =

ωeff 2π

⎡ ΔG ⧧(R⃗ , Ω) ⎤ X ⎥ dR ⃗ dΩ ⎥⎦ kBT (7)

∫ f (R⃗ , Ω) κelX(R⃗ , Ω) exp⎢⎢⎣−

where the activation free energy ΔGX⧧ includes the protein and solvent, Es, and intramolecular, Ein, reorganization free energies, the reaction free energy ΔG°, and the intermolecular interaction free energies (work terms) in the reactants’ (WR) and products’ (WP) states. κelX is the transmission coefficient and ωeff the effective vibrational frequency of all nuclear modes reorganized. The translation vector in eq 7, R⃗ , describes different positions of [Co(Ox)3]3−/4− relative to the Fe atom in the fixed heme group. The angular degrees of freedom, Ω, describes a set of [Co(Ox)3]3−/4− orientations at each R⃗ value. f(R⃗ ,Ω) is a normalized partition function; see the SI (Appendix A). The activation free energy ΔGX⧧ was found to depend much less on ⃗ R and Ω than the electronic transmission coefficient κXel. Equation 7 can therefore be recast in the simpler form

IV. COMPUTATIONAL RESULTS IV.1. Models and Basic ET Frames. In this and the following section, we address the ET process by a quantum-mechanical approach, where we combine a structural model of the reaction partners with a formal theoretical ET frame. Λ- and Δ-[Co(Ox)3]3− were represented by the fully optimized molecular and electronic structures (Figure 2a). With a view on the high buffer concentration and previously observed ionic strength effects,12−14 the role of an adjacent K ion was also addressed. The optimal position of the K+ ion was found by scanning the cation in different orientations relative to the [Co(Ox)3]3− complex with fixed geometry and projecting the cation from the most favorable orientation onto the face formed by three O atoms from the Co(III) coordination shell (Figure 2b). The hydration shell of the (weakly solvated) K+ ion was not included explicitly, and the ion pair K+·[Co(Ox)3]3− was treated as an innersphere entity, but as noted, a dielectric continuum was included. The optimized Co−K distance is 2.4 Å. Cyt c(II/III) was represented by the optimized low-spin singlet and triplet heme groups and by a deprotonated singlet form, all with axial L-histidine and L-methionine ligands34 (Figure 2c). By this model protein, the chirality is determined solely by the chiral axial ligands. The need for such simplicity is imposed by the computational complexity of the real protein. “Global” chirality of the protein structure and the strongly positively charged (S)-Lys patch around the exposed heme group in the protein thus had to be disregarded. Omission of the electrostatically charged protein part around the heme group is, however, compensated for, in part, both by the direct solvent exposure of the heme edge in “real” cyt c and by the exceedingly sensitive electronic transmission coefficient to the ET distance and mutual orientation of [Co(Ox)3]3− and the heme group. ET through longer pathways via the second protein-based coordination sphere is thus much less likely than direct ET at the solvent-exposed heme

X kET ≈

≈

⎡ ΔG ⧧ ⎤ ωeff X ⎥ exp⎢− ⎢⎣ kBT ⎥⎦ 2π

∫ f (R⃗ , Ω) κelX(R⃗ , Ω) dR⃗ dΩ

⎡ ΔG ⧧ ⎤ ωeff X ⎥κelX exp⎢− 2π ⎣⎢ kBT ⎥⎦

(8)

⧧

where ΔGX is the effective free energy barrier in the layer r + δr (see eq 5) and κXel is the electronic transmission coefficient averaged over all inter-reactant distances and orientations. Again, the prevailing contribution to κXel was found to come from a narrow spherical layer, δr ≈ 1 Å, consistent with the notion of an ion-pair formation constant, KX (eqs 5 and 6). The model cannot estimate quantitatively all of the rate parameters particularly because of the uncertainty in calculations of the reaction free energy and sensitivity of the parameters to the grid size (for this notion, see section IV.2). We therefore focus on K and the electronic transmission coefficient. To the best of our knowledge, the role of the latter (resulting from inter-reactant orbital overlap) in chiral ET processes has not been addressed before. KX(WXR) and κXel were 9338

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Figure 2. (a) Optimized structure of the heme group with the axial L-His and L-Met ligands. (b) Optimized structure of Λ- and Δ-[Co(Ox)3]3− enantiomers. (c) Optimized structure of the ion pair K+·[Co(Ox)3]3− (Δ isomer). value of 10 was taken for the dielectric constant)34,41 could also have been used. This approach is crude, especially considering that the heme complexes are nonspherical. More accurate models42,43 could instead be employed. This does not affect the quality of our model predictions because the Es values were used basically only in the electronic transmission coefficient as in eq 10. We investigated two different electronic states of reduced [Co(Ox)3]3− (oxidized ground state for a closed-shell singlet), doublet (ms = 2), and quadruplet (ms = 4). The latter (with relaxed geometry) was found to be 0.8 eV deeper in free energy than the doublet. The calculations at fixed geometry corresponding to [Co(Ox)3]3− give the smaller difference of 0.2 eV between the doublet (exited) and quadruplet (ground) states for the reduced form. The S2 values of these forms amount to 0.7553 (doublet) and 3.7637 (quadruplet) and, after annihilation, to 0.75 and 3.7501, respectively. Another notable

statistically averaged over a large number of inter-reactant distances and mutual orientations, (details are given in the SI, Appendix A). IV.2. Specific Rate Parameter Models. Computations were accomplished in two phases. The microscopic electronic transmission coefficient and intermolecular interactions at a given intermolecular distance and mutual orientation were first addressed. In the second phase, these quantities were averaged over a large number of intermolecular distances and orientations. The outer-sphere reorganization free energy Es was calculated using the model of Kharkats for two interpenetrating conducting spheres in a dielectric.34,40 The solvation (Born) radius of [Co(Ox)3] 3− was estimated to be 4.4 Å; a similar estimate for the cyt c heme gives 5.7 Å.34 A model in which the two metal centers are represented by conducting spheres, one inside and one outside a spherical protein dielectric, and the whole pair immersed in an aqueous dielectric (a 9339

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where Ψi and Ψf are the electronic wave functions of the reactants’ and products’ electronic states, respectively. The physical perturbation V̂ is taken to be essentially electrostatic (from the molecular potentials of [Co(Ox)3]3− and the heme group; see the details in ref 34). The highest occupied molecular orbital (HOMO) of reduced cyt c (with relaxed geometry) was used as Ψi. The HOMO of Co(Ox)3]4− with nonrelaxed geometry (corresponding to the oxidized state, Co(Ox)3]3−) was taken as Ψf; i.e., the crude Condon approximation was used. Statistical averaging of the rate parameters was accomplished in the second phase of the computational part of the study. The WXR and κXel values were collected as a multidimensional grid (see the technical details in the SI, Appendix D). An important feature of our computational strategy is that, because the ΔEdesolv term (eq 9) is neglected, the distance of the closest Fe− Co approach, rmin, cannot be estimated reliably. We therefore averaged KX and κXel for a set of different rmin(Fe−Co) values in a reasonable interval (8.5−11.6 Å). Part of the grid array in spheres with r < rmin(Fe−Co) was not included in the statistical averaging. IV.3. Computed Rate Constant Parameters and the Nature of the Chiral ET Process. The kinetic parameters were obtained by integration over the grid points in spherical space starting from different minimum values of the radius (rmin). The heme Fe atom was placed at the center of the sphere. We then calculated for each cobalt(III) enantiomer the binding constant (KX, where X = Λ and Δ), the electronic transmission coefficient (κXel), and the product of the two, κXelKX, which can be considered as the operational representation of the rate constants, kobs (eqs 2−4). The rate parameters of both free [Co(Ox)3]3− and the ion pair [Co(Ox)3]3−·K+ (Figure 3) were

difference between the two reduced forms is the intramolecular reorganization. The electron configuration of the [Co(Ox)3]3− frontier orbitals is a21e0. The configuration of reduced doublet a21e1 induces therefore notable Jahn−Teller distortion (Table S1), giving significant intramolecular reorganization energies (both Λ and Δ forms), estimated as 0.7 eV for reduction and 1.4 eV for oxidation, with an average of 0.95 eV,44 (details are given in the SI, Appendix B). Calculations using the larger basis set for the Co and O atoms [6311+g(d)] give very similar geometries of the cobalt(III) oxalate complex for the oxidized and reduced states with an average innersphere reorganization energy of 1 eV. The configuration of the reduced quadruplet form, a11e2 leads to symmetrical reorganization of the inner sphere (Table S1) and gives notably larger Ein values of 1.89 eV (reduction), 1.36 eV (oxidation), and 1.59 eV (average) based on the 6-311+g(d) basis set. Nonlinear effects can be incorporated as warranted to accurately address the large and different values for the forward and reverse reactions.38,39 We have, however, maintained linearity because the chirality in the reorganization energies is insignificant. Formal electrochemical kinetics, in fact, favors the detachment of at least one oxalate ligand in the [Co(Ox)3]3− electroreduction.45,46 In this sense, the prevalence of the doublet [Co(Ox)3]4− state with Jahn−Teller distortions is reasonable. Further, we consider the doublet e1 frontier orbital as a probe to investigate the chirality only on the electronic transmission coefficient. Our focus is thus on the work terms and electronic transmission coefficient because only these parameters display significant chiral features. We addressed both singlet and triplet reduced cyt c hemes. These forms have nearly equal energy, and the electronic absorption spectra computed for both forms agree qualitatively with the experiment.34 The S2 values for the triplet form are 2.0376 and 2.0006 (after annealing). Intramolecular reorganization energies of 0.26−0.36 eV were calculated previously.34 The prevailing chiral rate parameters are thus the distance- and orientation-dependent interaction free energy WR (and WP) and electronic transmission coefficient κXel. WR (and WP) was represented as a combination of the partial desolvation energy ΔEdesolv, LennardJones (LJ) potential energy ULD, and electrostatic terms

WRX,(j) = ΔEdesolv (R ki) +

∑ ULD(Rki) + k ,i

1 2εeffstat

∑ k ,i

qkqi R ki

(9)

where k and i refer to atomic pair interactions in the two reactants. Rki represents the interatomic distances, while qk and qi are the interacting atomic charges. εstat eff is the effective dielectric constant (a value of 10 was used).34 The partial desolvation energy originates from distortion of the solvation shells of both reactants when they approach each other. This term depends primarily on the size of the reactants, their charge distribution, and the distance between the central atoms (Fe and Co). Reliable estimations of ΔE desolv require molecular dynamics simulations, where solvent molecules are treated explicitly, but because ΔEdesolv is chirally insensitive, we neglect this term in our further analysis (details are given in the SI, Appendix C). (see eq 7) was used in The electronic transmission coefficient κX,(j) el the Landau−Zener form38,39

κelX,(j) =

γel =

Figure 3. Structures and the distance and orientations of the two reactants, cyt c(II) (singlet heme group) and Λ-[Co(Ox)3]3− without a K+ ion (left) and Λ-[Co(Ox)3]3−·K+ with a K+ ion (brown sphere; right), giving maximum values of the exp(−WΛR /kBT)κΛR product. addressed. Technical details are given in Table S3. Both KX and κXel (X = Λ and Δ) were found to be sensitive to the number of grid points. The KX(rmin) and κXel(rmin) dependence displays some oscillation. Grids where the oscillations are minimized are the basis for the following discussion. This selection does not change the conclusions. The computational results are shown in Figures 4−9. The results shown in Figures 4−9 prompt several observations. Figure 4 shows first that the ET processes belong to the diabatic limit of weak inter-reactant interactions, with averaged electronic transmission coefficients significantly smaller than unity even at contact distance. This is probably associated with the nature of the frontier molecular orbitals of the reactants. As seen from Figure S2, the heme donor orbital is localized mostly in the plane of the porphyrin ring, while the central atom contributes most to the acceptor orbitals (AOs) of Co(III). Moreover, coupling through space prevails, not through bonds. The transmission coefficient is further slightly smaller for the ion pair [Co(Ox)3]3−·K+ than for free [Co(Ox)3]3−. The distance dependence shown in Figure 4 is an approximately exponential form, as is common for long-range ET in aqueous solution or protein media,38,39

1 − exp(− 2πγel) 1−

1 2

exp(− 2πγel)

(10)

⎞2 π 1 ⎛⎜ 1 ΔEel ⎟ ⎠ (Es + E in)kBT ℏωeff ⎝ 2

(11)

where ωeff is the effective frequency of the classical solvent polarization (1013 s−1).38 ΔEel is the resonance splitting in the crossing region of the reactants’ and products’ potential surfaces calculated from firstorder time-dependent perturbation theory 1 ΔEel ≈ 2

∫ ΨiV̂ Ψf dV − ∫ ΨiV̂ Ψi dV ∫ ΨΨ i f dV

(12) 9340

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Figure 4. Electronic transmission coefficient describing ET from cyt c heme to the Λ form of [Co(Ox)3]3− and [Co(Ox)3]3−·K+ as a function of the Fe−Co distance of closest approach. Calculated for a singlet cyt c heme. κelΛ(rmin) = κ0 exp(− βrmin)

Figure 6. Chiral recognition of the reactant pair binding constants KΛ/ KΔ for [Co(Ox)3]3− and [Co(Ox)3]3−·K+ as a function of the Fe−Co distance. Calculated for a singlet heme. coefficient, KΛ/KΔ of free [Co(Ox)3]3− is larger than for that the ion pair but drops rapidly with increasing distance, i.e., within less than 1 Å to values close to unity. This behavior can be compared with the strong decay of the individual KX values over the whole distance range of 8.5−11.5 Å (Figures S3 and S4). Because the desolvation term dEdesolv had to be neglected, the individual values are somewhat overestimated, but the overestimation is largely canceled in the ratio KΛ/KΔ. Figure 7 finally shows the distance dependence of the

(13)

where rmin is the Fe−Co distance (rmin ≥ 7 Å). κ0 = 72.089 and β = 1.057 Å−1 for [Co(Ox)3]3− and κ0 = 33.6055, and β = 0.982 Å−1for [Co(Ox)3]3−·K+, close to values commonly encountered. Figure 5 shows that the transmission coefficient ratio, or kinetic stereoselectivity, κΛel /κΔel , gathers closely around unity but drops rapidly

Figure 5. Chiral selectivity ratios of the electronic transmission coefficients κΛel /κΔel for [Co(Ox)3]3− and [Co(Ox)3]3−·K+ as a function of the Fe−Co distance of closest approach. Calculated for a singlet cyt c heme.

Figure 7. Chirality of the products of the electronic transmission coefficients and the binding constants κΛel KΔ/κΔel KΔ for [Co(Ox)3]3− and [Co(Ox)3]3−·K+ as a function of the Fe−Co distance. Calculated for a singlet heme.

for [Co(Ox)3]3−·K+ to significantly smaller values, 0.53 or so at the smallest inter-reactant distances. The observed overall chiral ratios are 1.1−1.2, suggesting then that the chirality is dominated by the binding constants, as substantiated by computation of the ratio KΛ/KΔ and the transmission coefficient of free [Co(Ox)3]3−. The latter chirality originates from differences in the structure of the AOs with equal energies for the Δ and Λ isomers. It is thus shown in Figure S4 that the main contribution to the AO of the Λ isomer comes from the 3dz2 orbital of the Co atom, while the 3dx2−y2 orbital is the most important for the Δ isomer (see the Cartesian coordinate system in Figure S5). Figure 6 shows that the computed chiral recognition ratio KΛ/KΔ is large, i.e., 5−9, at very short distances, with a conspicuous difference between [Co(Ox)3]3− and [Co(Ox)3]3−·K+. As for the transmission

“operational” observable rate constant ratio kΛobs/kΔobs = κΛel KΛ/κΔel KΔ, where X = Λ and Δ. This ratio is significant and dominated by the constants, KX, where X = Λ and Δ, but only at very short contact distances. Notably, accordance with the observed values of 1.1−1.2 is only found in the narrow distance range of 8.8−9.2 Å. Chiral recognition and ET stereoselectivity of the free and K-ionpaired cobalt(III) complex with triplet and partially deprotonated cyt c were also addressed. The importance of these forms was discussed in ref 34. It is seen from Figure 8 that the chiral effect is notably smaller for a heme triplet than a heme singlet (Figure 7). The triplet distance behavior differs, however, from that of a singlet heme. The chiral effect 9341

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reactant binding and electronic transmission coefficients. We have completed test calculations for a singlet cyt c to estimate the chirality in the averaged activation (Franck−Condon) barrier ΔG⧧ (eq 8). The reaction Gibbs energy of the elementary act was estimated from the standard potentials of the redox pairs, E0 = +0.6 V ([Co(Ox)3] 3−/4− 45 ) and E0 = +0.27 V (cyt c)47). The WP − WR work term was addressed too. These results show that the ΔGΛ⧧/ΔGΔ⧧ ratio is very close to unity and contributes insignificantly to the kinetic chirality.

V. PHYSICAL ORIGIN OF OBSERVED RECOGNITION AND STEREOSELECTIVITY Chiral recognition and stereoselectivity could be obtained from the computations in section IV for the four bimolecular ET processes, cyt c(II)/Λ-[Co(Ox)3]3−, Λ-K+·[Co(Ox)3]3−, and their Δ-Co(III) analogues. Figures 5 and 6 show the distancedependent stereoselectivity of the transmission coefficient ratio κΛel /κΔel and the recognition factor KΛ/KΔ, both statistically averaged over a range of mutual orientations and distances. Figure 7 shows the chirality of the statistically averaged overall rate constant, kΛobs/kΔobs ≈ κΛel KΛ/κΔel KΔ. Figures 5−7 refer to a fully protonated singlet heme. In comparison, Figure 8 shows the distance-dependent kΛobs/kΔobs = κΛel KΛ/κΔel KΔ ratio for a triplet heme and Figure 9 that for for the partially deprotonated singlet form. We discuss details of the chirality patterns in section VI but note presently, first, that strong but opposite chirality in the transmission coefficient (stereoselectivity) and ion-pair binding constant (recognition) emerges from the computations for the dominating singlet form at a short distance, perhaps corresponding to intercalation of the heme group between the chirally oriented chelate Ox2− ligands. The rate constant and binding constant ratios stabilize within a fraction of an angstrom around unity for distances larger than about 9 Å. Formal accordance with the data, i.e., kΛobs/kΔobs = κΛel KΛ/κΔel KΔ > 1, requires that the chirality is dominated by recognition, i.e., by subtle desolvation and electrostatic interactions that overcome the short distance opposite chirality from the electronic transmission coefficient. Second, accordance is achieved only in a narrow distance range of about 0.5 Å around the contact distance, pointing to a well-defined relative distance and mutual orientation of the reaction partners and the validity of the concept of a reaction volume. This view is supported by the negative activation volume reported,35 indicative of a small separation between the reactants in the precursor complex. Finally, the chirality was found to be stronger for free [Co(Ox)3]3− than for the ion pair [Co(Ox)3]3−·K+. Very similar observations apply to the deprotonated heme group, but the absolute values of the recognition factors are here much smaller because of the added Coulomb repulsion. A triplet heme shows some intriguing differences from a singlet heme. The ion pair now shows larger chirality, kΛobs/kΔobs = κΛel KΛ/κΔel KΔ than free Co(III), and the two chiral factors κΛel / κΔel and KΛ/KΔ are much closer to each other. There is also a maximum in kΛobs/kΔobs = κΛel KΛ/κΔel KΔ for the ion pair of around 9 Å and a shallower maximum of around 10 Å for [Co(Ox)3]3−. The physical origin of this feature is perhaps caused by a spatial electronic charge redistribution in the excited triplet state compared to the singlet ground state.

Figure 8. Computed chirality of the products of the electronic transmission coefficients and the binding constants κΛel KΔ/κΔel KΔ for [Co(Ox)3]3− and [Co(Ox)3]3−·K+ as a function of the Fe−Co distance. Computed for a triplet heme. of a triplet heme is larger for the [Co(Ox)3]3−/4−·K+ ion pair than for free [Co(Ox)3]3−/4− in the interval 8.5 < rmin < 9.5 Å. The distance dependence of kΛobs/kΔobs = κΛel KΛ/κΔel KΔ for the ion pair also shows a maximum at rmin(Fe−Co) = 9.0 Å. The ratio KΛ/KΔ is, furthermore, comparable with the ratio κΛel /κΔel for both the free complex and ion pair. Figure 9 shows finally the κΛel /κΔel ratios computed for the

Figure 9. Chirality of the products of the electronic transmission coefficient and the binding constant κΛel KΔ/κΔel KΔ for [Co(Ox)3]3− and [Co(Ox)3]3−·K+ as a function of the Fe−Co distance. Calculated for a deprotonated singlet heme. oxidation of a partially deprotonated singlet heme by [Co(Ox)3]3−/4− and [Co(Ox)3]3−/4−·K+. The dependence looks very similar to the ratios for the protonated form shown in Figure 7. KΛ/KΔ clearly dominates over the chiral ratio of the electronic transmission coefficients, but the absolute KX values for a deprotonated heme are significantly smaller than those for a protonated heme because of the strong Coulombic repulsion from the cobalt(III) complexes. Major conclusions from the computational part of our study are thus, first, that a rationale for the observed chirality is achieved and accords with optimized molecular structures and orientations of the reaction partners. Second, accordance is only in a very narrow distance range of less than 0.5 Å or so, close to contact inter-reactant distances of 8.8−9.2 Å. The accordance could finally be ascribed to inter-

VI. DISCUSSION We have explored chiral recognition and kinetic stereoselectivity of a prototype bimolecular outer-sphere ET process, where a redox metalloprotein (cyt c) is oxidized by a pair of 9342

DOI: 10.1021/acs.inorgchem.6b01489 Inorg. Chem. 2016, 55, 9335−9345

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Inorganic Chemistry chelate transition-metal complex enantiomers, Λ- and Δ[Co(Ox)3]3−. The ligands themselves are simple and achiral, and the intermolecular interaction is strong and largely electrostatic because of the high reactant charges. The data show that ET proceeds via a strongly bound ion pair, as noted in previous reports,24,35 with a binding constant of about 200 M−1 and a relatively slow ET process in the ion pair, ≈10−2 s−1 at 25 °C. The latter is due to substantial intramolecular reorganization of ≈0.7−0.9 eV in the [Co(Ox)3]3−/4− couple and a small electronic transmission coefficient of 10−3−10−2. Chirality in both the binding constant and ET rates is observed, with the Λ form both the more strongly bound and with faster ET. The recognition factor KΛ/KΔ and stereoselectivity κΛel /κΔel are both unity at a large distance but clearly different at short Fe−Co separations. The most favorable binding site thus appears also to be the site for the fastest ET. The experimental data for the recognition factor, ET rate constants, and their chirality are coarse-grained quantities averaged over all inter-reactant distances and mutual orientations. We have explored details regarding the interaction (free) energies and ET parameters by quantum-chemical methods, together with molecular ET theory and a statistical mechanical approach, with a view on identifying the physical origin of the chirality. The computations addressed all of the core ET parameters, i.e., solvent and intramolecular reorganization (free) energies, the reaction free energy, and particularly the inter-reactant interaction free energy (ion-pair binding constants or work terms) and electronic transmission coefficient. The heme group with the axial L-His and L-Met ligands was taken as a model for cyt c. Reasons for this simplication were noted. The heme group with axial ligands is, however, still chiral. As an illustration, the AOs of the heme group (cyt c) with axial R-His and R-Met ligands were also computed (data not shown) and found to be practically completely identical with those for L-His and L-Met. The chirality in other more remote amino acid residues in the protein matrix outside the first coordination sphere is therefore also expected to affect the electronic structure of the heme center and the electronic transmission coefficient insignificantly. These amino acids might, however, still affect the recognition factor KΛ/KΔ. Work on such chirality is in progress. With these reservations, most focus was on the dominating fully protonated singlet heme group, but attention was also given to the triplet state and the partially deprotonated singlet form. As expected, the reorganization free energies were found to be significant but with quite insignificant chirality. The chirality is instead entirely dominated by the inter-reactant interaction free energy and the electronic transmission coefficients of the reaction, which appears to be notably diabatic. The computational results are presented in Figures 4−9 in the form of the distance dependence of the two parameters, statistically averaged over all mutual orientations at each given distance. KX and κXel, statistically averaged over all mutual orientations at each Fe−Co distance, show opposite chirality. Chirality significantly different from unity begins within a very narrow range (