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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Am Chem Soc. Author manuscript; available in PMC 2017 September 28.
Published in final edited form as:
PMCID: PMC5068489

Charge-Disproportionation Symmetry Breaking Creates a Heterodimeric Myoglobin Complex with Enhanced Affinity and Rapid Intracomplex Electron Transfer


We report rapid photo-initiated intra-complex electron transfer (ET) within a `charge-disproportionated' myoglobin (Mb) dimer with greatly enhanced affinity. Two mutually supportive Brownian Dynamics (BD) interface redesign strategies, one a new `heme-filtering' approach, were employed to `break the symmetry' of a Mb homodimer by pairing Mb constructs with complementary highly positive and highly negative net surface charges, introduced through D/E → K and K → E mutations, respectively. BD simulations using a previously developed positive mutant, Mb(+6) = Mb(D44K/D60K/E85K) led to construction of the complementary negative mutant Mb(−6) = Mb(K45E, K63E, K95E). Simulations predict the pair will form a well-defined complex comprising a tight ensemble of conformations with nearly parallel hemes, at a metal-metal distance ~ 18-19 Å. Upon expression and X-ray characterization of the partners, BD predictions were verified through ET photocycle measurements enabled by Zn-Deutoroporphyrin substitution, forming the [ZnMb(−6), Fe3+Mb(+6)] complex. Triplet ET quenching shows charge disproportionation increases the binding constant by no less than ~ 5 orders of magnitude relative to wild-type Mb values. All progress curves for charge separation (CS) and charge recombination (CR) are reproduced by a generalized kinetic model for the inter-protein ET photocycle. The intracomplex ET rate constants for both CS and CR are increased by over 5 orders of magnitude, and their viscosity independence is indicative of true inter-protein ET, rather than dynamic gating as seen in previous studies. The complex displays an unprecedented timecourse for CR of the CS intermediate I. After a laser flash, I forms through photo-induced CS, accumulates to a maximum concentration, then dies away through CR. However, before completely disappearing, I re-appears without another flash and reaches a second maximum before disappearing completely.


Myoglobin (Mb), with a net charge near zero (wild-type horse heart Mb(WT), qMb ~ −0.3e), is a convenient `workbench' for probing the electrostatic control of binding and electron transfer (ET) between hemoprotein partners. Whether Mb(WT) is partnered with the highly negatively-charged cytochrome b5 (cyt b5), the highly positively-charged cytochrome c (Cc), or another nearly neutral Mb(WT), the partners react on a `dynamic docking' (DD) energy landscape (Fig 1) where binding is uncoupled from reactivity.17 Protein partners on such a landscape exhibit multiple weakly-bound configurations in rapid exchange between the complex and its unbound components, and reactive conformers are rare. In contrast, the limiting `simple docking' (SD) behavior, has an energy landscape on which a complex exhibits one or a few well-defined reactive configurations that are in slow-exchange with their unbound partners. To shift DD-type complexes toward SD-type, we are exploring interface re-design strategies that use Brownian Dynamics (BD) docking simulations to identify surface `hot-spot' residues where charge-exchange mutations would electrostatically enhance ET-active binding.811

Figure 1
Dynamic docking (DD) and simple docking (SD) energy landscapes. ET reactive configurations represented by rainbow; ET-active geometries are red. Most stable geometries represented by wells.

The first application of this approach employed the negatively charged cyt b5 as the target for binding Mbs with increasing positive charge. Three hot-spot residues on the heme face of the Mb surface (D44, D60 and E85) were identified where introduction of positive charges through D/E → K mutations were expected to enhance binding of cyt b5 to Mb.12,13 The success of this strategy was demonstrated by preparing Zn-deuteroporphyrin (ZnD) substituted Mb variants (ZnMb) involving combinations of the hot-spot residues, along with esterification of the porphyrin propionates. Photo-induced ET measured reactive binding14, and NMR chemical-shift perturbation mapping was used to structurally characterize the re-designed complex.15,16 Increasing the positive charge near the Mb heme created a `reactive patch' defined as the area around the heme that contained the entire protein charge, and progressively transformed the weakly-bound and poorly reactive DD-type [Mb(WT), cyt b5] complex into a reactive complex whose enhanced affinity led to slow-exchange intra-complex ET on both the singlet and triplet timescales,11 with the singlet rate approaching that for the initial step in photosynthetic charge separation.14,17

Here we extend these redesign efforts, and introduce a `charge-disproportionation' approach (Fig 2) for creating a high-affinity Mb-Mb heterodimer that supports rapid intracomplex photoinduced ET. The strategy is to `break the symmetry' of a Mb homodimer by interacting a Mb construct having a highly positive surface charge with a complementary construct having a highly negative surface charge.

Figure 2
Myoglobin charge mutation dimerization strategy.

The previous redesign of the Mb surface to enhance interactions with cyt b5 led to the preparation and characterization of the positively charged Mb(D44K, D60K, E85K) triple mutant, Mb(+6): q = 5.9e, pH 7.11,13,14 Using this Mb(+6) as the partner protein, we have now performed BD X → D/E surface mutant charge-reversal scans on Mb(WT) target protein to identify residues where addition of a negative charge to the Mb surface would most enhance docking with the Mb(+6). We then constructed and expressed a Mb(−6) triple mutant protein with X → D/E charge-reversal mutations at the three most favorable residues and prepared the Zn-substituted ZnMb(−6) variant, which enables study of the laser-flash induced ET photocyle for the [ZnMb(−6), Fe3+Mb(+6)] complex. The simulations predict the [ZnMb(−6), Fe3+Mb(+6)] pair will form a well-defined, tightly-bound complex that has a structure quite different from those of known globin dimers18 and in particular Mb dimers;19,20 triplet ET quenching titrations confirm this prediction.

Most dramatically, we observe an unprecedented progress curve for the charge-separated (CS) intermediate, I, formed by photoinitiated ET. In the numerous reports of an ET photocycle with photoinitiated charge separation (CS) followed by charge recombination (CR), in both covalently-linked systems and non-covalent protein-protein complexes the timecourse for I has invariably been observed to exhibit a single maximum, in which I is formed through photoinitiated CS, reaches a maximum concentration, and then disappears through CR. Instead, the [ZnMb(−6), Fe3+Mb(+6)] complex surprisingly exhibited a well resolved biphasic progress curve. As in all previous studies of photoinduced ET studies, photoinduced CS forms the intermediate I, which accumulates to a maximum concentration then begins to decay through CR. However, before completely disappearing, I reappears without a second laser flash – here the concentration climbs to a second, comparable maximum before finally disappearing completely through CR. These observations, in conjunction with a viscosity independence of the intracomplex ET rate constants, support the conclusion that the charge-disproportionation strategy has indeed generated a tightly-bound, ET-active heterodimer well on the way to SD behavior (Fig 1).

Materials and Methods

Brownian Dynamics Simulations

In the present study, negatively charged mutants of Mb(horse) (1YMB.pdb)21 were designed using the BD docking protocol implemented in MacroDox, as previously described.13,22 In the BD simulations, the `target' partner, here uniformly chosen to be Mb(WT) or a mutant that has been given a negative charge, is fixed in space and the Mb variant with three positively charged surface mutations (D44K,D60K,E85K) is allowed to undergo Brownian motion until it either `hits' the target or `wanders' outside the cutoff threshold distance (d = 200 Å). This is repeated for 104 randomly selected starting postions and the number of trajectories resulting in a hit are tallied. To maximize electrostatic attractions between partners, a Fe3+ ion is assumed for the positively-charged Mb(+6), and a divalent metal ion (neutral porphyrin heme core) for the stationery target Mb. Ferrous-Mb is used as a surrogate for the ZnMb that is employed in photoinitiated ET measurements.

We performed two separate BD simulations (104 trajectories each) for docking ferri-Mb to the respective target ferro-Mb, each using a different criterion for determining whether a trajectory results in a hit. As in previous studies1113,23, the two reaction criteria were: i) The distance between the centers of mass of the partners (COM criterion) which probes overall binding; a cutoff distance of 39 Å was used for the COM criterion. ii) The distance between any one of the carboxylate oxygen atoms of a heme proprionate of ferro-Mb and a heme carboxylate oxygen atom of its ferri-Mb partner (criterion) to probe reactive binding. As the solvent exposure of the Mb heme is less than that of the b5 heme, the cutoff distance for the O-O criterion was increased from the 4 Å used in the [Mb, cyt b5] studies to 10 Å for the [ferro-Mb, ferri-Mb] simulations.

Protein Expression, Purification, and Characterization

The design, expression, and purification of Mb(WT) and the Mb(+6) triple mutant was previously reported, along with procedures for reconstitution of their apo forms with Zn-deuteroporphyrin (ZnD).11 All Mb mutants were reconstituted with either Fe3+-Protoporphyrin IX (Fe3+) or ZnD as described previously.11 Negatively charged proteins were isolated on and recovered from anion exchange (DEAE Seapharose Fast Flow resin, GE Healthcare) columns; positively charged proteins on cation exchange columns (CM Sepharose Fast Flow resin, GE Healthcare). All proteins were further purified using size exclusion chromatography (Sephadex G-25/G-50 medium resins, GE Healthcare). Reconstituted protein concentrations were measured using an Aglient 8453 UV-Vis spectrophotometer; Soret maxima wavelengths and extinction coefficients were as follows: Fe3+-Mb, 409 nm, ε ~ 188 M−1cm−1;24 ZnD-Mb, 414 nm, ε ~ 361 M−1cm−1.2 All work with ZnD proteins was carried out in the dark to prevent photo-bleaching. Reconstituted proteins were flash frozen in liquid nitrogen, and stored at −80° C in 10mM KPi, pH 7.0 until used. Proper folding and stability of all mutants was validated by circular dichroism. Finally, all proteins' molecular weights and purity were verified by both mass spectrometry and SDS-PAGE analysis.

Crystallographic Structure Determination of Mb Variants

The light sensitivity of the proteins required carrying out crystallization procedures in the dark. All Mb crystals were obtained using the hanging drop vapor diffusion method with a 1:1 volume ratio of protein to reservoir solution at 20° C. Crystals were soaked in cryoprotectant, mounted on loops, and flash frozen in liquid N2. Native data sets were collected using synchrotron radiation at the Life Sciences Collaborative Access Team (LS-CAT) beamline (sector 21-ID-D) at the Advanced Photon Source, Argonne National Laboratory, using a Mar 300 CCD detector. The coordinates of the horse heart metMb structure (PDB ID 1YMB) were used for phasing by molecular replacement with the program Phaser.25 Descriptions of the cofactors were obtained from the CCP426 monomer library or generated with the program JLigand27 utilizing the appropriate library obtained from the Grade Web Server. Ramachandran plots were calculated with PROCHECK26,28 and validation was performed using both PHENIX29 and SFCHECK.30 Data collection and refinement statistics are shown in Table SI_3. Electron density maps were calculated using FFT26,31 and figures were prepared using PyMOL.32 The structures are described in SI and the atomic coordinates have been deposited in the PDB, Research Collaboratory for Structural Bioinformatics at Rutgers University: Fe3+Mb(D44K/D60K/E85K) structure (PDB 4NS2); ZnMb (K45E/K63E/K96E) structure (PDB 4TWV); ZnMb(D44K/D60K/E85K) structure (PDB 4TWU); and Fe3+ Mb(K45E/K63E/K96E) structure (PDB 3RJ6).

Flash Photolysis Measurements

Cuvettes containing 2 mL of working buffer were stored open to the atmosphere in a N2-filled glove box overnight. Unless noted, all measurements were made in 5 mM potassium phosphate working buffer at pH 7. Stock solutions of protein were thawed on a cold block in the glove box for several hours before the experiment. The concentration of the ZnMb in the final sample was 10 μM, as determined using ε414 = 361 mM−1cm−1.2 The concentration of the ferri-quencher was varied from 5–120 μM for experiments with Mb(WT), and 2–50 μM for all other experiments, as determined spectrophotometrically (Agilent 8453 UV-Vis) using ε409(Fe3+Mb) = 188 mM−1cm−1.24

Triplet quenching measurements were performed with an LKS.60 laser flash photolysis spectrometer (Applied Photophysics) fitted with a Xe lamp having pulsing capabilities and dual monochromators. Samples were excited with the output from a Nd:YAG Quanta-Ray INDI laser (Spectra-Physics), frequency-doubled to give excitation at 532 nm and an output power ~100 mJ. For slow triplet decays (< 1000 s−1), a setup modified from Applied Photophysics stopped-flow instrument was employed with a 9-stage photomultiplier tube for detection. Faster data collection was taken with an Agilent Infiniium 600 MHz digitizer and 5-stage photomultiplier tube for detection. The Xe lamp was pulsed to achieve the shortest timescales. Progress curves for the triplet decay were monitored at 475 nm; those for the ET intermediate were collected at 559 nm. Typically, 10 shots were averaged on the slow timescale setup and at least 20 for the fast setup data collection. All kinetic experiments were performed at 20°C.


We first describe a refined Brownian Dynamics design strategy intended to identify surface residues whose mutations will create Mb constructs with opposing high surface charges, which can then form a `charge-disproportionated' dimer that supports rapid intracomplex ET. The strategy is then implemented through the production of these highly charged Mb protein variants, and the results of ET kinetics and binding experiments are examined.

Interface Redesign

Our prior work indicated that in order to design a stable charge-disproportionated heterodimeric Mb complex that exhibits rapid ET, the two partners must have a large, negative charge product, qMb(+m)qMb(n), as would be the case for simple coulomb attraction between charged patches on the protein partners11. As the protein partners should have opposite charges, for simplicity, we employ the positive quantity,


Thus, larger values of qp correlate with complexes that exhibit greater electrostatic attraction, and in fact the previous study of [Mb, cyt b5] ET complexes showed that the binding free energy increases linearly as a function of qp. The Mb variant with three positively charged surface mutations (D44K,D60K,E85K) yielded a [Mb(+6), cyt b5] complex with qp = 29, as compared to qp = −1.7 for [Mb(WT), cyt b5], which exhibited both remarkably enhanced binding and an equally dramatic increase in ET reactivity.1114

In this study, as in previous ones, the BD interface design strategy employed two criteria for classifying a trajectory as a `hit': the O-O criterion that probes reactivity, and the center-of-mass (COM) criterion that probes binding; the definitions of this study are defined in Materials & Methods. BD hit profiles resulting from simulations that dock the ferri-Mb(WT) to the ferro-Mb(WT) target with the COM criterion exhibit many hits distributed over the entire Mb surface, while the number of hits generated using the O-O criterion is negligible (Table 1), as expected from the diminuitive charge product, qp = −0.06. The BD hit profiles for docking the ferri-Mb(+6) triple mutant to the ferro-Mb(WT) target protein are little improved (Fig 3, left). Despite the large positive charge on Mb(+6), qp remains small (qp =+1.5), so the COM hit profile for the [Fe2+Mb(WT), Fe3+Mb(+6)] complex also shows hits distributed over the ferro-Mb(WT) surface, with very few reactive hits (O-O criterion) (Table 1).

Figure 3
BD hit profiles for COM simulations where Fe3+Mb(+6) is docked onto different stationary Fe2+Mb targets. Mutations shown in magenta. Charge patch shown in yellow. Conditions: COM distance cutoff = 39 Å; 10, 000 trajectories; outer boundary = 200 ...
Table 1
Charge products and hit counts for BD simulations with Mb-Mb dimers.

To identify `hot-spot' residues on the Mb(WT) surface that would create a negatively charged Mb mutant with increased affinity for and reactivity with Mb(+6), we carried out K/R/H → E charge reversal mutation scans on Mb(WT), changing each of the positively charged surface residues on Mb(WT) one-at-a-time into a negatively-charged Glu residue.33 The total number of COM hits is not significantly affected by any single surface mutation, but the number of hits using the O-O criterion varies with the mutation (Fig 4 upper), directly revealing hot-spot mutations for which the number of hits with the Fe3+Mb(+6) partner sharply increases. Three such residues (K45, K63 and K96) located near the heme (the “front” face) result in a >20-fold increase in the number of O-O hits. Two more residues (K78 and K87) are active to a lesser degree while mutations that change neutral residues along the `front face' E and F helices to Glu, corresponding to Δq = +1 (Fig 4, green symbols), did not significantly increase the number of O-O hits.

Figure 4
K/R/H → E charge reversal scans of Fe3+Mb(+6) docked to Fe2+Mb variants. A. Number of hits as a function of residue number for K/R/H → E surface mutations in Mb(wt). COM (top line) and OO (bottom line) criteria. B. Interface contacts between ...

Although the hot-spot K→E mutations on Mb(WT) found using the O-O criterion are not apparent as an increased number of COM hits, an intriguing feature of the COM scan is that K→E mutations lead to partial clustering of the COM hits in the vicinity of the mutation. as shown in Fig 3, center for the mutation at residue 63 of Mb(WT). To assess the effectiveness of a mutation in achieving `reactive clustering', that is clustering in the vicintity of the heme, we analyzed the interfaces of the hits from the COM simulations. With each charge-exchanged Fe2+Mb(WT) variant, we determined the total number of interface contacts between an atom of its heme with a surface residue on the Fe3+Mb(+6) partner, and determined the ratio of that number to the total number of hits in the simulation. This ratio is plotted in Fig 4, lower, which shows that the same three hot-spot residues found with the O-O criterion are also preeminent in enhancing interactions of the Fe3+Mb(+6) partner with Fe2+Mb(X). Examination of the corresponding contacts between the heme of Fe3+Mb(+6) and the surface of the mutants shows that the overwhelming number of hits associated with the clustering also involve the front face of the Fe3+Mb(+6); as a consequence of the large accumulation of positive charge on the Fe3+Mb(+6) front face, configurations where the backside of Fe3+Mb(+6) contacts the heme of Mb(X) are rare. Thus, this `heme-filtering' protocol successfully identifies `hot-spots' for enhancing reactive binding of Fe3+Mb(+6) with a charge-exchanged mutant.

The O-O criterion and heme-filtering protocol are not only mutually supportive, identifying the same three hot-spot residues for charge-exchange mutation, but indeed are complementary. The O-O criterion requires heme-heme contact as the criterion for binding. The heme-filtering strategy does not force this condition, rather, it is a natural outcome of the filtering protocol, thus showing that the mutations indeed generate face-to-face complexation. In addition, the heme-filtering approach requires just a single simulation (COM, which measures binding), and has the advantage of flexibility: hits can be filtered with respect to any selected location on the scanned protein, without having to re-run the simulation.

BD Simulations with Mb(−6) Multi-Mutants

To computationally test whether combining the mutations at the three hot-spot locations would create a negatively charged Mb with enhanced binding to the reactive patch surrounding the heme edge of Mb(+6), we created the Mb(K45E, K63E, K96E) multi-mutant, Mb(−6), in silico. The COM BD hit profile for [Fe2+Mb(−6), Fe3+Mb(+6)] (Fig 3, right) is strikingly different from that of the [Fe2+Mb(WT), Fe3+ Mb(+6)] reference complex (Fig 3 left): the COM hits for the moving Fe3+Mb(+6) on the fixed Fe2+Mb(WT) partner approximate to a uniform distribution on the Fe2+Mb(WT) surface, whereas the hits for the moving Fe3+Mb(+6), on the Fe2+Mb(−6) surface are highly localized in the heme vicinity (Fig 3, right).

The cluster of hits generated in the [Fe2+Mb(−6), Fe3+Mb(+6)] COM simulation (Fig 3, right) corresponds to an ensemble of `heme-heme' configurations in which the heme edges roughly face one another across the interface, with a metal-metal distance (dFe-Fe) of ~ 21 Å or less. Examination of the potential energy of protein-protein interaction for the hits shows that configurations in this cluster (~60 % of all COM hits) exhibit a strong electrostatic attraction between the partners. In contrast, the `halo' of hits outside this cluster (the remaining 40% of COM hits) involve protein configurations for which the electrostatic attraction is negligible, and where the reactive region of one or both partners is not located in the interface. These configurations thus contribute negligibly to both ET and to binding, and do not play a functional role.

To characterize the ensemble of functional configurations, we indexed each hit by its metal-metal distance (dFe-Fe) and heme-heme dihedral angle (θ), which we define in terms of the deviation from a reference structure where the heme of one partner is rotated by π relative to the other (`head-to-tail'), and generated a contour plot of the number of functional hits versus dFe-Fe and θ (Fig 5). This plot shows a major population centered around a heme-heme distance of ~ 18-19 Å, and a heme-heme dihedral angle of θ ~ 15°; the fit of a histogram of the angles for configurations in this population to a Gaussian distribution (Fig SI_1) gives a half-width of ~ 6°. The plot also suggests there may be a minor population at θ ~ 40° and possibly a third one at ~70°. The heme-heme orientations of representative configurations from the three clusters are shown along the right border of the contour plot (Fig 5, right). Notably, the secondary cluster at θ ~ 40° is centered at a slightly smaller metal-metal separation than the major form. This suggests that these minority configuations of the complex could potentially have higher ET rate constants.

Figure 5
Contour plot of dFeFe and θ for the reactive configurations (PE < −5 kcal/mol) from the hit profile for Fe2+Mb(−6), Fe3+Mb(+6)] (based on 105 trajectories) in Fig 3. This region includes 60% of the total hits. Right: Representative ...

We view this analysis as predicting that charge-disproportionation would convert the Mb-Mb homodimer from a weak DD pair to a well-defined [Fe2+Mb(−6), Fe3+Mb(+6)] complex comprising an ensemble of tightly bound and highly reactive configurations in which the heme edges face one another, in a nearly parallel geometry at an Fe-Fe distance ~ 18.5 Å, including the possibility of a minority structure of even higher ET reactivity.

To characterize the predicted complex in greater detail, the residues involved in the ten closest contacts for each hit in the BD ensemble interface were identified and the total contacts for each residue of the two partners for all the configurations are plotted in Fig 6, left. The most frequently contacted residues on each partner fall within oppositely-charged `reactive patches' of the two proteins that contain the heme edge and a charge equal to the net protein charge as defined by the yellow regions in Fig 6, right11. These reactive patches include the surface atoms within 10 Å of a heme atom and involve residues from helices E (residues 58–77) and F (residues 86–94).

Figure 6
Left: Number of interface contacts by residue for a COM simulation with Fe2+Mb(−6) and Fe3+Mb(+6). Coloring shows the top contacts on either side of the interface: red, acidic; blue, basic; green, neutral. The E and F helices are indicated by ...

The five most frequently contacted residues on the Fe2+Mb(−6) side of the protein-protein interface all are negatively charged: D60, a heme propionate, and the three mutation sites (K45E, K63E and K96E). Less frequently, contact is made with three charged and two uncharged residues on the periphery of the interface: E18, T70, K78, and E85, P88. Correspondingly, the most-frequently interacting residues on the positively-charged Fe3+Mb(+6) are the positively charged residues (K63, K78, K96, E85K), with less frequent interactions involving the heme and four uncharged residues (T70, A84, P88, Q91).

In short, analysis of the BD docking simulation indicates that the redesign strategy would produce a strongly-binding, ET-active charge-disproportionated hetero-Mb dimer.

Structural Characterization and Verification of Mb Mutants

To implement the surface redesign strategy, we expressed, purified and reconstituted both the ferric-heme and ZnD forms of horse heart myoglobins (D44K, D60K, E85K) (FeMb(+6)) and (K45E, K63E, K96E) (FeMb(−6)). Three dimensional structures obtained by X-ray crystallography (Figs SI_2–7, Tables SI_1–3) confirm that none of the Mb variants (the two types of triple surface mutations as well as those with heme substitution by ZnD) show significant change from the WT protein structure. Substitution of heme by ZnD preserves the overall structure of the protein, but there are two deuteroporphyrin conformations in the X-ray structure of both triple mutants, a common occurrence in Mbs.34,35

Triplet Quenching Kinetics and Binding

To measure the binding and ET-reactivity of the charge-disproportionated partners we measured the ET photocycle introduced by ZnD substitution into the Mb(−6) partner. In the absence of ferri-Mb partner, the photo-excited triplet states of the Zn-substituted Mbs decay exponentially. The presence of a ferri-Mb partner quenches the 3Zn-Mb excited state by electron transfer.

Figure 7, upper shows triplet decay traces for titrations by Fe3+Mb(+6) of ZnMb(WT) (purple), and ZnMb(−6) (green). For the titration of ZnMb(WT), the charge product (qp) is small (qp [similar, equals] 1.5, Table 2) despite the high positive charge on its partner. The decay curves remain exponential throughout the titration, and the decay constant, kobs, increases linearly with the concentration of Fe3+Mb partner (Figure 7, lower), implying the complex is in the fast exchange (FE) limit.11,12 The slope of kobs vs [Fe3+Mb] gives the bimolecular quenching rate constant, which we take to equal the association rate constant, k2 (Table 2).

Figure 7
Upper: Triplet decay traces for titrations with [ZnDMb(WT), Fe3+Mb(+6)] (purple), and [ZnD(−6), Fe3+Mb(+6)] (green). [Fe3+Mb(+6)] = 0 – 120 μM purple, 0–50 μM green. Lower: Fit parameters during [ZnDMb(X), Fe3+ ...
Table 2
Parameters describing the kinetics of decay of photoexcited 3ZnMb.

In contrast, the pairs [ZnMb(−6), Fe3+Mb(+6)] (Figure 7, green), and [ZnMb(+6), Fe3+Mb(−6)] (data not shown) have charge-products qp = 31 and 25 respectively, and these triplet decay traces become biphasic during a titration, Fig 7. This indicates that the increased electrostatic interactions have shifted both complexes to the slow exchange (SE) regime. As is characteristic of this regime, the rate constant of the fast phase kobs-fast = kD + kq ~ kq is nearly invariant with concentration (Figure 7, lower), and corresponds to that for intra-complex ET.

We note that switching the Zn substitution to the Mb(+6) partner eliminates the positive charge associated with the Fe3+P, and decreases the negative charge on the Mb(−6) partner, yielding a decreased qp for the [ZnMb(+6), Fe3+Mb(−6)] complex. As a result the intracomplex rate constant kobs-fast for the swapped pair [ZnMb(+6), Fe3+Mb(−6)] pair is smaller than for its counterpart, [ZnMb(−6), Fe3+Mb(+6)] and the small reduction in qp also causes a measureable reduction in bimolecular quenching constant, k2, Figure 7, lower.

Heterodimer Affinity

Focusing on the [ZnMb(−6), Fe3+Mb(+6)] complex, which has the larger value of qp, the complex is in SE, and an apparent value for the binding constant, Ka′, can be obtained by fitting the observed fraction of fast phase (bound complex), denoted F′, as a function of [Fe3+Mb] to a simple binding isotherm (Figure 8, blue dash). However, whereas this analysis of the biexponential slow exchange kinetics gives the correct values for the intra- and inter-complex ET rate constants, the binding constant Ka′ must be corrected for quenching in the single state. This treatment of the progress curves assumes that all ZnMb photoexcited to the 1ZnD excited state either return directly to the ground state or convert to the triplet state through inter-system crossing (ISC). However, we previously showed that singlet quenching within the pre-formed complex adds an additional decay channel for the 1ZnMb, and this decreases the early-time absorbance difference (A0) of the [3ZnMb(−6), Fe3+Mb(+6)] relative to that of free 3ZnMb(−6).14,17 As a consequence, the actual fraction of bound ZnMb(−6), denoted F, is greater than the observed fraction, F′, and as a result, Ka′ obtained from a simple fit of F′ underestimates the true binding constant, Ka.

Figure 8
Binding curves derived from [ZnDMb(−6), Fe3+Mb(+6)] titration. Data for early time absorbance drop A0 [(−6), (+6)] (red circles, solid), A0 [(WT), (+6)] (red diamonds, dashed), [(−6), (+6)] fast phase fraction (blue squares, dashed), ...

The true Ka can, however, be obtained from the 3ZnMb decay traces during a titration in two ways. The more direct is to correct the observed F′ for the effects of singlet quenching. The percent of 1ZnMb that undergo ISC is given by [empty], the ratio of the extrapolated zero-time triplet-ground absorbance difference at saturating concentrations of Fe3+Mb, divided by free ZnMb absorbance difference. It is straightforward to show that at each point in a titration, F, the actual fraction of bound complexes, is related to F′ through [empty] as follows,


The corrected fractions of bound complex, F, as obtained by applying Eq. 1 to the observed fractions F′, are also plotted in Figure 8 (blue line); their fit to a binding isotherm yields Ka = 1.1 × 105 M−1.

The second method of determining Ka is to use the progressive decrease in zero-time triplet-ground absorbance as a function of Fe3+Mb concentration, ΔA[Fe]. At any given point in a titration, F is given by,


A fit of F determined in this way to a binding isotherm yields Ka = 1.2 × 105 M−1, the same value within error, as obtained by the use of Eq. 1 to calulate Fs from the F′ obtained from the decomposition of the triplet decay traces. The resultant Ka for selected Mb complexes are given in Table 2; that for [ZnMb(−6), Fe3+Mb(+6)] is no less than an ~ 5 orders of magnitude greater than that for Mb(WT) complexes.

Kinetics and Binding of the Charge Separated Intermediate, I

The optical spectra of the ZnMb variants (Fig SI_8) are identical, as are the 3ZnMb-ZnMb difference spectra. Thus, the charge-separated intermediates that form upon excitation of all the [ZnMb, Fe3+Mb] complexes, I = [D+A], could be followed equally by monitoring the transient absorbance changes at the 3ZnMb-ZnMb isosbestic point, 559 nm.

In all previous studies of photoinitiated ET between non-covalent protein partners the absorbance difference associated with a charge-separated intermediate I rose to a maximum then decayed, regardless of whether the curves were mono- or multi-phasic. In the case of related [Mb, b5] complexes, the maximum accumulation of I decreased dramatically as charge product (qp) increased, because the rate of formation of I increased more slowly than the rate of charge recombination, decreasing the extent to which I accumulated.36

The complexes of ZnMb(WT) with Fe3+Mb(WT) and Fe3+Mb(+6) partners (qp < 1.5) likewise show a single maximum in the progress curves for I, in Figure 9 (purple, green). However, in contrast to [Mb, b5] complexes, increased qp for [ZnMb(−6), Fe3+Mb(+6)] (qp ~ 31) causes an increase in the maximum accumulation of I. Most dramatically, and completely without precedent, the time-evolution of I for [ZnMb(−6), Fe3+Mb(+6)] exhibits two distinct phases, each with its own maximum (Figure 9, red). Figure 10 shows two perspectives for the changes in the progress curves of the charge-separated intermediate I during a titration of ZnMb(−6) with Fe3+Mb(+6); the upper panel of Fig 10 clearly shows the two temporal evolution of the maxima during the course of a titration, while the lower panel more clearly shows how the amplitudes evolve.

Figure 9
Progress curves for the charge separated intermediate I, for [ZnDMb(X), Fe3+Mb(X)]. [(WT), (−6)] (purple), [(WT), (+6)] (green), [(−6), (+6)] (red).
Figure 10
Upper Progress curves for I for [ZnDMb(−6), Fe3+Mb(+6)] throught a titration (red, 2μM Fe3+Mb(+6), green 4μM, blue 6μM, pink 8μM, cyan 10μM, dark red 12.5μM, dark yellow 15μM, dark green ...

Figure 10 also contains a plot of the absorption-difference maximum for the I fast phase as a function of [Fe3+Mb(+6)]:as [Fe3+Mb(+6)] increases during the titration, the early-time 'fast' phase accumulates to saturation, as expected for a simple binding isotherm.. This shows that this early-time phase corresponds to cyclic ET within the preformed 1:1 complex in slow exchange. At all points in the titration, the maximum absorbance difference of the fast phase of the I progress curve occurs at τ1 ~ 5 μs, as this phase appears and disappears with constant rise and fall times governed by intracomplex ET rate constants.

The slow I phase exhibits a second, later-time, absorbance maximum, which appears without a second laser flash. This phase has an exponential rise with the bimolecular triplet-state quenching rate, k2 ~ [Fe3+Mb(+6)]. As a result, the absorbance maximum for this phase shifts to shorter times during a titration (t > 10−5 seconds). Its amplitude initially increases as the quencher concentration increases, then decreases as the amount of free ZnMb(−6) decreases (Figure 10).

The fall of the slow phase of I is not exponential. Rather, the progress curves exhibit a “tail” indicative of a second order process after 1 equivalent of Fe3+Mb(+6) has been added, as shown by the linear dependence of the reciprocal of the absorbance difference upon time at long times (Figure SI_9). This process is even present at ratios less than 1:1 ZnMb(−6): Fe3+Mb(+6), but is hard to recognize because I must accumulate sufficiently to accurately visualize this effect. This implies I must in part dissociate to free ZnD+Mb(−6) and Fe2+Mb(+6) after ET, with the long-time behavior determined by their rebinding with charge recombination.

Overall, a description of the slow phase recovery of the ground state therefore must incorporate dissociation of I in competition with CR, recombination of the dissociated components of I, as well as association and reaction of free 3ZnMb(−6) with Fe3+Mb(+6). As a complicating feature, the dissociated ZnD+Mb(−6) is free to bind with excess Fe3+Mb(+6), preventing reaction with the liberated Fe2+Mb(+6). Thus, the Fe3+Mb(+6) free acts as an inhibitor of charge recombination.

This interpretation of the two phases as intracomplex (early-time phase) and second-order (later-time phase) is confirmed by effects of changing viscosity on the triplet quenching decay curves and the timecourse of I for the [ZnMb(−6), Fe3+Mb(+6)] complex. Figure 11 shows the response of these curves in an experiment with a fixed ratio of Fe3+Mb(+6)/ZnMb(−6) = 1. In both the progress curves for triplet-decay and I, the fast phase is invariant with increasing η, which confirms that these phases are associated with the intracomplex photocycle, ET quenching to yield I, followed by charge recombination within I, and that neither process is modulated by intra-complex dynamic processes.

Figure 11
Viscosity dependence of timecourses for I (left) and triplet quenching curves (right) for 1:1 ZnDMb(−6)/Fe3+Mb(+6). Viscosity indicated by color on the insets: 1.0 cP (red), 1.3 cP (green), 1.8 cP (cyan), 3.7 cP (pink), 10.8 cP (blue), 35.5 cP ...

In contrast, the slow phases of ET quenching and timecourses of I are strongly modulated by changes in viscosity, as expected for bimolecular quenching of unbound 3ZnMb(−6) and recombination of the dissociated partners of I. In particular, the second maximum in the progress curve of I shifts to longer time as the second-order rate constants slow, and decreases in amplitude as the triplet ET quenching decreases.

[Mb, Mb] Kinetic Scheme

Description of Kinetic Scheme

The behavior of the progress curves for I of the [ZnMb(−6), Fe3+Mb(+6)] ([D, A]) complex during a titration indicate that a complete kinetic description of the ET photocycle displayed by the (+6)/(−6) Mb pair must incorporate the features presented in Scheme 1. The scheme begins with a pre-equilibrium between bound and free ZnMb(−6) (D) and Fe3+Mb(+6) (A) (Ka as determined above), with the equilibrium reflecting formation and dissociation rate constants, (kon, koff) that are taken to describe both the ground and excited states. Free and bound ZnMb(−6) are photoexcited equally to 1ZnMb(−6) (1D). Photoexcitation of bound complex yields the singlet state complex [1ZnMb(−6), Fe3+Mb(+6)] ([1D, A]), which can undergo decay to ground, singlet ET to form 1I (1kq), or inter-system crossing to the triplet state complex [3ZnMb(−6), Fe3+Mb(+6)] ([3D, A]). Conformations of the complex that can undergo such rapid ET form a charge-separated complex that returns to ground promptly (1kb), hence on the triplet timescale this rapid photocycle merely appears as a singlet decay process that diminishes the early-time triplet-ground absorbance A0, as discussed above. Indeed, all photoinitiated processes involving 1D and [1D, A] are so rapid compared to formation and dissociation of the complex that these latter processes are not included for the singlet state in Scheme 1.

The photo-generated triplet-state 3ZnMb(−6) in a pre-formed complex can decay to ground (kD) or undergo ET to form I = [Zn+Mb(−6), Fe2+Mb(+6)] ([D+, A], kq); once I is formed, it can undergo CR to regenerate the ground complex (kb) or dissociate into its charge separated components, Zn+Mb(−6) and Fe2+Mb(+6) (D+ + A), with rate constants *kon, and *koff. Once dissociation has occurred, it is possible for excess Fe3+Mb(+6) to bind the free Zn+Mb(−6) to form an 'inhibited' complex ([D+, A]), preventing recombination and creating an inhibitive effect.

In parallel with the transformations of the preformed complex, photoexcited free 1ZnMb(−6) rapidly undergoes ISC to 3ZnMb(−6) in competition with decay to ground. Free 3ZnMb(−6) can decay to ground (kD) or bind an Fe3+Mb(+6) (second-order rate constant, kon) to generate a photoexcited complex that undergoes the three processes described above.

The Kinetic Scheme and Progress Curves for I

The progress curves for I collected during a Fe3+Mb(+6) titration of ZnMb(−6) (Fig 10) have been fit to Scheme 1 through numerical integration of the differential rate equations implied by the scheme. Two approaches were investigated; all curves were fit individually, and the set of curves was fit globally. The two approaches yield the same values for the kinetic parameters kq, kb, kon, and koff (Table 3).

Table 3
[ZnMb(−6), Fe3+Mb(+6)]: ET rate constants from fit to Scheme 1

Intracomplex Photocycle, Fast Phase

Approximately three-quarters of the pre-formed triplet-state complexes undergo photoinduced ET to generate the CS intermediate I, the rest dissociating before ET can occur: the fraction of triplet states that undergo ET is φET=kqkoff+kq~75%. The appearance of I in the intracomplex fast phase of its progress curve is faster than the decay of the triplet state in the bound complex (triplet fast phase) in every stage of the titration, indicating that this rate is in fact the rate of ET return to the ground state, kb > kq, a relationship rarely considered. Once formed, I can either undergo CR to complete the intracomplex photocycle with rate constant kb, or dissociate. Almost all I completes the intracomplex ET photocycle; according to Scheme 1, the fraction of I that dissociates is only Fdisc=koffkoff+kb~2.5%.

Second-Order, Slow Phase

The fits to Scheme 1 further capture the systematic increase in the rate of appearance of the slow phase of the I progress curve with increasing [Fe3+Mb(+6)], which corresponds to the triplet bimolecular quenching constant of free 3ZnMb(−6) by Fe3+Mb(+6). The amplitude and decay of the slow phase is governed by second order dissociation/association of the CS intermediate I. In principle, the rate constants for dissociation/association of I should differ from those for the ground/excited-state complexes, as the ET process lowers the positive charge on the Mb(+6) partner, and increases the positive charge on the Mb(−6) partner. This has been accounted for in Scheme 1 (*kon, *koff) but in fact any differences are negligible. Note that even at very high [Fe3+Mb(+6)] concentrations, where the fraction of bound ZnMb(−6) approaches unity, the dissociation and subsequent rebinding yields a small second order contribution to charge recombination that dominates the long-time behavior of the I progress curves (Fig SI_9).

Lastly, free Fe3+Mb(+6) can bind to Zn+Mb(−6) released by dissociation of I, and by sequestering the Zn+Mb(−6) thus 'inhibit' the 2nd order recombination of Zn+Mb(−6) and Fe2+Mb(+6) and the charge recombination. As seen in Figure SI_9, the return to ground indeed slows as [Fe3+Mb(+6)] is increased, but the effect is small.

Finally, the fits to the I progress curves provide an additional method of calculating the binding affinity for the charge-disproportionated complex: Ka = kon/koff = 1.25 × 105 M−1 in agreement with the two methods associated with triplet quenching (Table 2); the three methods yield a consensus best-value binding constant, Ka = 1.0(2) × 105 M−1.37


To test which of the rate constants were controlled by 'gating' motions, progress curves for I were collected for samples at fixed ratio, [ZnMb(−6)]/[Fe3+Mb(+6)] = 1, but prepared with a range of viscosity, η, and were collected and fit (individually and globally) to Scheme 1, allowing for an inverse dependence on η: ki(η) = ki0 η−1. Visual inspection of the viscosity-dependent traces suggests that the rate constants for intramolecular CS and CR, kq and kb, are independent of η, and this was confirmed by the global fitting procedure. The rate constants for complex formation and dissociation, kon, koff and *kon, *koff (data not shown) in contrast decrease with increasing viscosity, as expected. For example, Figure 11 shows that the bimolecular quenching kon decreases in this fashion. The ki0 for the viscosity-dependent processes are given in Table 3.


In this report, we have employed a refined BD interface re-design strategy to create a `charge-disproportionated' [Mb(+6), Mb(−6)] complex in which three K → E charge reversal mutations on the Mb(WT) surface generate a Mb(−6) mutant that binds to the positively charged Mb(+6) triple mutant. These constructs were then successfully expressed, characterized and crystallized, and subjected to photoinitiated ET measurements. The ET experiments validate the expectation based on the BD simulations, that the resulting hetero-Mb dimer would form a well-defined, tight-binding complex that exhibits high ET activity. As a surprising `bonus', the CS intermediate, I, formed within this complex shows an unpredented timecourse – accumulating to a maximum concentration, disappearing, then reappearing to a second maximum before finally vanishing.

Brownian Dynamics Interface Design Strategy

Re-designing the interface of the nearly neutral Mb to create complementary Mb(+m), Mb(−n) `charge-disproportionation' partners represents a different kind of challenge than redesigning the interface of either the Mb-b5 or Mb-Cc pairs, where the b5 and Cc partner proteins are already highly charged. It is not obvious how to simultaneously introduce paired charges on a neutral protein to create partner proteins, with paired negative and positive residues, so as to optimize binding and reactivity between the two constructs. However, as we had already designed and expressed a Mb(+6) variant to interact with a negatively charged protein, b5, BD simulations/scans were conducted using this positively charged Mb as a template against which to introduce negative charges onto the surface of a neutral Mb.

An implicit assumption inherent to the BD strategy is that ET rate constants for members of an ensemble of structures vary with the heme-heme separation, orientation and/or ET pathways,22 and thus generation of a complex with enhanced ET would involve enhancement of `face-face' contacts between the heme edges. Our previously described `O-O' criterion for identifying `hot-spots' for surface charge-exchange mutations has been augmented by a new, refined “heme-filtering” design procedure, the two together enabling us to generate complementary non-covalent [Mb(−n), Mb(+6)] dimers with high homology and heme-facing-heme structures. BD simulations with both procedures led to the identification of a trio of surface hot-spot residues where introduction of negative surface charges through X → D/E mutations were predicted to cause a large proportion of BD hits by the Mb(+6) on a mutant that satisfies both the COM binding and heme-heme reactivity filter criteria (Fig 4). Notably, the O-O criterion and heme-filtering protocol are not only mutually supportive, but indeed are complementary. The O-O criterion requires heme-heme contact for a BD hit. The heme filter strategy does not force this condition; rather, it is a natural outcome of the filtering protocol, thus showing that the mutations indeed generate face-face complexation.

The most significant single-residue changes were associated with the Mb front face (+ → −) charge reversal mutations of residues K45, K63, and K96, which led us to introduce the K45E/K63E/K96E triplet of charge-reversal mutations, resulting in the Mb(+6) construct studied here.38 BD simulations in which this Fe3+Mb(+6) was docked to the stationary Fe2+Mb(−6) showed that the `functional' BD hits, those that contribute to binding and ET, are sharply focused near the heme on the Mb(−6) front face (Fig 3). Inspection of the structures associated with these hits showed a large increase in the number of contacts between residues in the `charged patches' that surround the heme (Fig 4). Each of these functional configurations was indexed by its metal-metal distance (dFe-Fe) and heme-heme dihedral angle (θ), which allowed the generation of a contour plot of the number of functional hits versus dFe-Fe and θ, Fig 5. This graphically shows that the hits are tightly clustered, and represent the creation of a well-defined complex comprising an ensemble of highly similar structures where the heme edges of the partners face one another at an Fe-Fe distance of ~ 18-19 Å, with nearly parallel heme planes.

Considering the absence of a defined structure for the parent, weakly interacting [Mb(WT), Mb(WT)] homodimer, or the weakly interacting [Mb(WT), Mb(+6)] heterodimer (Fig 3), the conversion to such a tight ensemble of structures through only three well-placed surface mutations (96% homology between partners), is remarkable. For completeness, we note Fig 5 suggests a possible second (or even third) minority conformation. As discussed in the next subsection, measurements of the ET photocycle for the [ZnMb(−6), Fe3+Mb(+6)] heterodimer showed tight binding and high ET reactivity, as predicted by the BD simultations.

ET Photocycle

Measurements of the ET quenching of the triplet state show that (i) the binding constant for the complex has been increased by no less than ~5 orders of magnitude through charge disproportionation, and (ii) the rate constants for both steps in the intracomplex ET photocycle are four orders of magnitude greater than those for the well-defined reference `complex' between the α1 and ß2 subunits within the mixed-metal Hb hybrid tetramer.39,40 (Table 2), where the hemes are not edge-edge.

To describe the complete ET photocycle, we employed Scheme 1. Using numerical integration of the analogous rate equations, progress curves for I were fit to Scheme 1, yielding the rate constants for charge separation (kq), charge recombination (kb), complex association (kon), and complex dissociation (koff). Note that the rate of charge recombination, kb, is larger than that of charge separation, (kq), as seen in our studies of intracomplex ET in Hb,39,40 for example, but nevertheless a kinetic phenomenon not frequently encountered in studies of protein-protein ET.

Surprisingly, the [ZnMb(−6), Fe3+Mb(+6)] progress curve for charge recombination of the CS intermediate, I, formed by photoinitiated Zn* → Fe3+ ET shows a completely unprecedented shape. Photoinduced charge separation produces the intermediate I, which accumulates to a maximum concentration, then dies away through charge recombination as seen in all previous studies of photoinduced ET. However, before completely disappearing, I reappears without a second laser flash - its concentration climbs to a second maximum before it finally disappears, to generate a timecourse for I with two well-resolved maxima (Figs 9, ,10),10), here denoted a `2H' type curve.41 This includes partners with binding affinities at both ends of the broadest range of values, 100 → 109 M−1. For example, the tightly bound α12 complex of mixed-metal hemoglobin (Hb) hybrids40,42 exhibits only intracomplex ET, and its intermediate exhibits a simple 1H progress curve with a single maximum, characterized by the appearance of the intermediate with the intracomplex CR rate constant and its disappearance with the rate constant for triplet decay, as expected for the ET photocycle of a simple docked complex. In the other extreme, intermediates for the very weakly bound [Mb(WT), b5]43 complex also exhibit a 1H curve.

The kinetic behavior of the photoexcited triplet and the unusual timecourse for the ET intermediate have been fully described by Scheme 1, as illustrated in Fig 10. In fact, Scheme 1 provides a unified kinetic scheme for ET in protein-protein complexes, and can describe the full range of behaviors seen for interprotein ET photocycles. The behavior of the scheme is determined by three critical parameters: kq, kb, and Ka. One can visualize the properties of the scheme by fixing the ET rate constants kq and kb, and varying Ka; for concreteness we choose the ET rate constants associated with [ZnMb(−6), Fe3+Mb(+6)] complexes (Table 3; kq ~ 1 × 105 s−1, kb ~ 8 × 105 s−1). As we further take complex association to be diffusion limited (kon ~109 M−1s−1), variation in Ka can also be viewed in terms of variations in the dissociation rate constant, koff. We furthermore focus on the most illuminating solution conditions, a 1:1 ratio of the ET partners, taking each at 10μM as for the 1:1 trace in the titration ZnMb(−6) by Fe3+Mb(+6).

Simulations calculated using Scheme 1 under the above specified conditions as Ka varies by ten orders of magnitude are shown in Fig 12, upper. The behavior of the scheme can be discussed in terms of three ranges for Ka.

Figure 12
Simulations of Scheme 1 with ET rates kq = 1.0 × 105 s−1 and kb = 8.0 × 105 s−1, and [ZnDMb] = [Fe3+Mb] = 10μM held constant for each simulation. Upper Ka values were varied from 100 M−1 to 109 M−1 ...

(i) When Ka > 106 M−1, the progress curves for I exhibit only a single phase (1H) at early times (t [less, similar] 10−4 s). In this range, complexes are tightly bound, and only intracomplex ET is observed. From both the point of view of triplet quenching and of I decay, this range corresponds to the slow-exchange limit. (ii) Progress curves exhibiting two maxima (2H) arise only in a rather narrow `transition' range of Ka, 106 M−1 > Ka > 104 M−1, which is explored in finer detail in Figure 12, lower. At the higher end of this range, when, 106 M−1 > Ka > 105 M−1, the amplitude of the early-time phase diminishes with decreasing Ka, and a long-time (t [greater, similar] 10−5 s) slow phase with a 2nd order decay develops. Complexes in this Ka range predominantly undergo an intracomplex ET photocycle, but the moderate binding yields a small, but measureable, amount of unbound 3ZnMb at 1:1 ratio, which reacts with free Fe3+Mb ET partner which creates the second (slow) phase. In addition, small amounts of I dissociate and recombine in a slow second order process, adding to this second phase.

At the lower end of the transition range, when 105 M−1 > Ka > 104 M−1, the amplitude of the early-time phase continues to decrease, and that of the slow phase increases (Figure 12, lower). In addition, the decay of the slow phase exhibits a more pronounced second order character as the amount of unbound 3ZnMb becomes more prevalent, and the contribution from intracomplex ET diminishes. In parallel, dissociation of I formed by intracomplex ET occurs more frequently, and CR by the free components contributes to the 2nd order `tail'.

Finally, we note that 2H progress curves for I exist only in this same overall range, 106 M−1 > Ka > 104 M−1, even when kq, kb have different values, and indeed when kq/kb > 1 (Fig SI_10), unlike the present case. What differs is only the details of the 2H curves and their change with Ka.

(iii) As binding decreases below the transition limit, Ka < 104M−1, the ZnMb is almost completely free in solution under the low concentration conditions employed here. ET within a preformed complex thus becomes negligible, and both CS and CR become second order, a defining characteristic of the fast-exchange limit. In progress curves where Ka < 104 M−1, only a single long-time phase is observed, with a pseudo first-order appearance associated with the reaction of free 3ZnMb with excess Fe3+Mb, and decay through bimolecular CR; the amplitude of the progress curve reaches a maximum at Ka ~ 10−3 M−1, and decreases with further decrease in Ka. These calculations provide implicit validation of estimates for the binding constant for the Mb(WT) homodimer, Ka < 5 M−1 (Table 2). Indeed, visual inspection of Fig 9 shows that the timecourses for I in Mb(WT) complexes, with their low degree of maximal accumulation and slow decay are best reproduced when Ka < 1 M−1 in Fig 12, upper.

Figure 12 computationally traverses the spectrum of affinity constants from Ka ~100 M−1 to 109 M−1, and experimenatially we have shifted the Mb-Mb affinity from Ka ~100 M−1 to > 105 M−1 through the introduction of complementary surface-charge mutations that sharply increase qp. We note that one can `backslide' these binding advances by increasing the ionic strength, which weakens electrostatic binding. Indeed, test experiments have shown that the SE [ZnMb(−6), Fe3+Mb(+6)] complex transitions to a FE complex with increasing ionic strength. This change in kinetic landscapes is accompanied by 2H → 1H progress curve transitions, as predicted in Fig 12.

Viscosity Independent Intracomplex ET Kinetics support the BD predictions

The finding that the rate constants for intramolecular charge separation and charge recombination, kq and kb are independent of viscosity (or alternatively, osmotic pressure) indicates that these rate constants truly represent ET within a well-defined complex. This behavior is unique among investigations of interprotein ET, where conformational `gating' that is modulated by viscosity/osmotic pressure has in fact been traditionally found.40,4450 The observation of such well-defined, viscosity independent intracomplex ET rate constants in turn matches with the prediction of a well-defined heterodimeric complex with a tight ensemble of structures (Fig 5). The small variations in ET rate constants that would arise in such an ensemble would be averaged to the single measured value by conformational interconversions that are fast compared to ET, even when slowed by the increase in viscosity. In short, the heterodimer behaves in a manner expected of a well defined complex that exhibits SD behavior (Fig 1).

The rate constants for photoinduced ET in the slow phase of the triplet decay and the corresponding `slow' component in the progress curve for I in [ZnMb(−6), Fe3+Mb(+6)] are instead controlled by dynamic processes, as shown by their inverse dependence on solution viscosity (Figure 11). In the present case, the ET rates are slow enough to compete with dissociation, so the viscosity dependence is consistent with kinetic control by dissociation/association.

Monomer Assembly and Configurations from Brownian Dynamics

The tight binding of the charge-disproportionated heterodimer, together with its rapid, viscosity-independent intracomplex ET photocycle, confirm that the complex has a well-defined `structure', as predicted by the tight ensemble of conformations found in the BD simulation. We now consider in more detail the likely structure of this heterodimer, as implied by the surface contacts (Fig 6) and the distances/angles between the hemes (Fig 5), and compare them to known high-affinity globin assemblies. Figure 13 displays (left) the α12 pair of Hb subunits (1DXU),51 (right) the dimeric hemoglobin from clams (Scapharca inequivalis, si-Hb, 4SDH),52,53 and (center) a representative [Mb(−6), Mb(+6)] configuration from the densest region of the BD contour plot for the heterodimer (Fig 5).

Figure 13
Globin assemblies for known high-affinity globins and a representative configuration for the [Mb(−6), Mb(+6)] complex. The E and F helices for the acidic partner (red) and the basic partner (blue) are indicated. Only the ET-active dimer is shown ...

The protein-protein interface for the [Fe2+Mb(−6), Fe3+Mb(+6)] configuration in Fig 13, center, shows that the E and F-helices of the positively-charged Fe3+Mb(+6) (Fig 13, blue) are in `anti-parallel' contact, respectively, with the F and E helices of the negatively-charged Fe2+Mb(−6) (Fig 13, red) giving facing heme edges, slightly offset, with a short metal-metal separation of dFeFe ~ 18-19 Å. This heterodimeric structure is remarkably similar to that of the homodimeric clam hemoglobin, which also has such an anti-parallel interaction between E and F helices. This globin assembly likewise has facing heme edges and short metal-metal separation (dFeFe = 17 Å), and presumably would accommodate rapid ET (Fig 13, left). These two dimeric assemblies contrast with the α12 pair of Hb subunits, where the interface does not involve the E and F helices and the heme edges are not well aligned; the closest metal-metal separation is 25Å, which leads to slow intracomplex ET rates (~ 102 s−1).39,40 Indeed, even a domain-swapped MbMb homodimer, has a structure analogous to that of the Hb α12 pair in that the heme faces (E and F helices) are not juxtaposed, and has an even longer metal-metal separation, 39.8 Å.20

NMR studies of the charge-disproportionated MbMb heterodimer will test its predicted structure (Figs 5, ,13).13). A second round of BD simulations that begin with the heterodimer structure can identify additional pairs of surface sites where complementary charge-reversals can enhance binding and reactivity. The preparation of `supercharged' green fluorescent protein, with charges of +36 and −30,54 suggests that electrostatic attractions can be further enhanced by adding even more charges to both the Mb(+6) and Mb(−6), while maintaining their structural integrity! To reach the highest affinities one may well need to incorporate shape complementarity, solvation, and hydrophic contacts.5558 However, it is not clear that higher-level approaches could take a weakly interacting Mb-Mb pair without a well-defined, known structure, and achieve the charge-disproportionated complex described here. In any case the present results showcase the exceptional utility of optimizing electrostatic interactions to enhance binding and reactivity through BD simulations.


A refined BD interface re-design strategy led to the creation of a `charge-disproportionated' [Mb(−6), Mb(+6)] complex in which three K → E charge reversal mutations on the Mb(WT) surface generated a Mb(−6) mutant that binds to the positively charged Mb(+6) triple mutant. Analysis of the BD simulations with these two constructs predicted that they would form a well-defined, tightly-bound heterodimeric complex with high intracomplex ET rate constants. In fact: (a) the binding affinity of the heterodimer is no less than 5 orders of magnitude greater than that of the Mb(WT) homodimer; (b) the intracomplex rate constants are also ~ 4 orders of magnitude greater than previously seen with mixed-metal Hb hybrids, and likely more than that for the WT Mb homodimer; (c) these rate constants are viscosity independent, suggesting they represent true inter-protein ET, rather than dynamic gating as seen in all previous studies of interprotein photocycles.

We interpret these observations to support the conclusion that the charge-disproportionation strategy has indeed generated a tightly-bound, ET-active heterodimer with high homology, which adopts a structure represented by that shown in Fig 13, and which approaches SD behavior (Fig 1). As a bonus, the CS intermediate, I, formed within this complex shows an unprecedented timecourse – accumulating to a maximum concentration, disappearing, then reappearing to a second maximum before finally vanishing. This behavior is explained by kinetic Scheme 1, which is general for protein-protein complexes.

Supplementary Material

Supporting Information


We thank Peng Xiong and Amanda Griffin for assistance in preparing the Mb(+6) crystals. We gratefully acknowledge financial support from the National Institutes of Health (HL063203, BMH; GM070473 (A.C.R.)).


Supporting Information One BD figure, 6 crystallography figures and crystallography materials and methods, 3 crystallography tables, optical spectrum, and two kinetics figures.


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