21118
J. Phys. Chem. B 2005, 109, 21118-21125
Potential Energy Surface and Molecular Dynamics of MbNO: Existence of an Unsuspected FeON Minimum David R. Nutt,† Martin Karplus,*,‡,§ and Markus Meuwly*,† Department of Chemistry, UniVersity of Basel, Klingelbergstrasse 80, 4056 Basel, Switzerland, Laboratoire de Chimie Biophysique ISIS, UniVersite´ Louis Pasteur, Rue Gaspard Monge, 67000 Strasbourg, France, and Department of Chemistry and Chemical Biology, HarVard UniVersity, Cambridge, Massachusetts 02138 ReceiVed: May 9, 2005; In Final Form: August 18, 2005
Ligands such as CO, O2, or NO are involved in the biological function of myoglobin. Here we investigate the energetics and dynamics of NO interacting with the Fe(II) heme group in native myoglobin using ab initio and molecular dynamics simulations. At the global minimum of the ab initio potential energy surface (PES), the binding energy of 23.4 kcal/mol and the Fe-NO structure compare well with the experimental results. Interestingly, the PES is found to exhibit two minima: There exists a metastable, linear Fe-O-N minimum in addition to the known, bent Fe-N-O global minimum conformation. Moreover, the T-shaped configuration is found to be a saddle point, in contrast to the corresponding minimum for NO interacting with Fe(III). To use the ab initio results for finite temperature molecular dynamics simulations, an analytical function was fitted to represent the Fe-NO interaction. The simulations show that the secondary minimum is dynamically stable up to 250 K and has a lifetime of several hundred picoseconds at 300 K. The difference in the topology of the heme-NO PES from that assumed previously (one deep, single Fe-NO minimum) suggests that it is important to use the full PES for a quantitative understanding of this system. Why the metastable state has not been observed in the many spectroscopic studies of myoglobin interacting with NO is discussed, and possible approaches to finding it are outlined.
Introduction The interactions of small ligands with proteins are of practical, experimental, and theoretical interest. Due to their physiological importance, the interactions of myoglobin and its mutants with several ligands (O2, CO, NO) have been extensively studied both experimentally and theoretically.1-6 In particular, attention has recently been focused on the interaction of NO with heme proteins because of the wide range of biological functions of this ligand.7 NO is a key biological messenger which is involved in numerous physiological processes, such as inhibition of mitochondrial respiration, inhibition of the enzyme ribonucleotide reductase, and neurotransmission in the brain. In many cases, NO binding to iron atoms in both heme and non-heme proteins seems to be involved. Hence, a deeper understanding of the intermolecular interactions between NO and (por)FeHis, as in MbNO, is essential. MbXO (X ) C, N, O) is a liganded protein for which considerable experimental information is available.8,9 One important aspect concerns the conformations of the ligands when bound to the iron or trapped in the neighborhood of the heme.10 For example, it has been shown that dissociated CO can interact in two ways with the heme unit, namely, as Fe‚‚‚CO and Fe‚ ‚‚OC.10 These two structures are spectroscopically differentiated by the IR absorption of the CO molecule giving rise to the split B band.11-13 For NO, the rebinding time to the heme after photodissociation as measured by electronic spectroscopy has * To whom correspondence should be addressed. E-mail: m.meuwly@ unibas.ch. Tel: +41 61 267 3821. Fax: +41 61 267 3855. E-mail:
[email protected]. Tel: +1 617 495 4015. Fax: +1 617 496 3204. † University of Basel. ‡ Universite ´ Louis Pasteur. § Harvard University.
been found to be considerably more rapid (28 and 280 ps for a double exponential or 33 ps for a power law) compared to CO (≈100 ns) suggesting that the barrier is significantly lower for the former than for the latter;14 a very recent analysis using IR spectroscopy suggests that the rebinding time is even faster (5 and 133 ps, respectively).15 Different explanations have been suggested for the observed nonexponential rebinding of NO. They include the existence of multiple binding sites within the primary binding site16 or a time-dependent rebinding barrier.6 Another possibility, which we suggest on the basis of the present study, is that the rebinding from dissociated Mb‚‚‚NO to bound MbNO can occur via a metastable intermediate MbON which subsequently isomerizes to MbNO. Although different conformations for the ligand with respect to the heme-iron have been investigated for unbound NO, less is known about the possible structural and dynamic properties of NO bound to the hemeiron. Here, we present details of the interaction, dynamics, and spectroscopic properties of NO bound to the iron atom of the heme in its ground electronic state (2A). Myoglobin consists of 154 amino acids which makes it a comparatively small protein and is thus well suited for detailed computational investigations. Usually, computer simulations employ a parametrized force field that uses harmonic bond and valence angle terms and periodic functions for the dihedral terms.17,18 Exceptions exist but are not so widely used compared to harmonic force fields, mainly for reasons of computational efficiency. Since the experimental investigations under consideration reveal considerably more details of the structure and dynamics of heme ligands, it is of importance to extend the theoretical description beyond the harmonic approximation. In the present study, a two-dimensional (2D) potential energy surface (PES) for the interaction between heme and NO is
10.1021/jp0523975 CCC: $30.25 © 2005 American Chemical Society Published on Web 10/14/2005
Molecular Dynamics of MbNO
J. Phys. Chem. B, Vol. 109, No. 44, 2005 21119
Figure 2. Optimized structures for Fe-NO and Fe-ON and the sideon structure (TS). Total energies are given relative to the Fe-NO minimum. Intermediate structures between Fe-NO and TS and TS and Fe-ON along the path are also shown. Figure 1. Structure of MbNO. The residues forming the primary binding pocket are shown in ball-and-stick. Figure produced with MOLMOL.57
calculated and then used in a parametrized form in molecular dynamics simulations. Since the metastable MbON state we find has not been observed experimentally, despite the considerable number of studies that exist, we discuss the questions raised by this apparent inconsistency in some detail. Comparisons with other heme-NO complexes, particularly those involving Fe(III) instead of Fe(II), are also given. Theoretical Methods Calculation and Parametrization of the PES. The ab initio calculations of NO-Fe(por)-Im (with low spin Fe(II)) model system were carried out using the Gaussian98 suite of programs.19 Starting from a guess wave function at the UHF/3-21G level, the final calculations were carried out using UB3LYP/VDZ/3-21G; the Fe, all N atoms (i.e., the N of NO, the pyrrole nitrogens, and the two Im-nitrogens), and the O atom were treated with the Ahlrichs VDZ basis set, while the 3-21G basis was used for the C and H atoms of the heme. For Fe, an additional uncontracted f function with exponent 0.2 was used. The wave functions were converged to better than 10-6. First, all distances and all valence angles were optimized. Next, possible stationary states for NO conformations relative to the heme were investigated. They included the Fe-NO, Fe-ON, and η2 (side-on) conformation. The first two were found to be minima (shown in Figure 2) while the latter turned out to be a transition state (TS). Both Fe-NO and Fe-ON are bent conformations, and the most relevant distances and angles are given in Table 2. To locate the TS, the QST3 method20 was used. In Figure 2, the two minimum energy structures along with the TS and selected intermediate structures are shown. To assess energetic and structural differences, we also studied the three conformations (i.e., Fe-NO, Fe-ON, and the η2 structure) for the related system with Fe(II) replaced by Fe(III). The same basis set and the B3LYP method were used as for the Fe(II)-containing system, and the electronic state is a closedshell singlet, 1A. The reason for this comparison, which is not directly related to NO ligation to normal Fe(II) Mb, is that there have been other calculations which have addressed the possibility of coordination isomers of Fe-NO. Wondimagegn and Ghosh21 investigated the NO coordination isomers of various oxidations states of Mn, Fe, Ru, Co, and Rh in model compounds using density-functional theory. The isonitrosyl (M-
ON) isomer was found to be a minimum in several cases, including Fe(II) and Fe(III). To scan the potential energy surface and obtain a simple effective energy function for use in the molecular dynamics simulations, the structure of the heme-Im was frozen at its minimum energy structure. The coordinate system for scanning the PES included the Fe-N distance (rFe-N) and the Fe-N-O angle (θFe-NO). A total of 274 points on the bound state (2A) surface were calculated. The coordinates (rFe-N,θFe-NO) were chosen because they describe the global Fe-NO minimum. They are, however, not ideal to fully describe the Fe-ON minimum. This leads to energy differences of 12.5 kcal/mol between the two minimum structures from the scan and 15.3 kcal/mol for the two stationary states on the PES from full optimizations. Contributions due to different NO bond lengths or the tilt of the NO molecule (which are all frozen in scanning the PES) contribute to this energy difference. In the Fe-ON optimized structure, the center of mass of NO lies essentially above the Fe atom with the O atom displaced from the NImFe axis (see Figure 2) while in the scan of the PES the linear Fe-ON structure has all three atoms arranged collinearly. The two coordinates (R,θ) describe the most important structural features (global and local minima with their approximate geometries and the TS around the T-shaped configuration) of the PES while their precise geometries are less well described (linear Fe-ON vs the bent local minimum energy structure). To simulate the dynamics of bound MbNO, the data points were represented with a suitable analytical form. The raw data from the 274 ab initio calculations were fitted to a potential energy function expressed in terms of R(Fe-COM) and θ(FeN-O), where COM is the NO center of mass. It is convenient to expand the potential in terms of radial strength functions, Vλ(R), and Legendre polynomials, Pλ(cosθ), where 0 e λ e 10 λ)10
V(R,θ) )
∑ Vλ(R)Pλ(cosθ)
(1)
λ)0
The radial strength functions Vλ(R) are Morse potentials with three parameters De (well depth), Re (equilibrium separation), and β (steepness of the repulsive wall). The 33 free parameters (3 for each of the 11 Legendre polynomials) were determined by least-squares fitting of the Morse parameters to the ab initio data points using the program I-NoLLS.22 The final parameters are given in Table 1, and the fitted PES is shown in Figure 3. Around both minimum energy structures the quality of the fit is good (|Eobs - Ecalc| e 2 kcal/mol) while the repulsive walls,
21120 J. Phys. Chem. B, Vol. 109, No. 44, 2005
Nutt et al.
TABLE 1: Parameters of the Fit of the Potential Energy Surfacea λ
De,λ/kcal/mol
βλ/Å-1
Re,λ/Å
0 1 2 3 4 5 6 7 8 9 10
5.13 -19.05 8.24 17.11 0.02 1.26 1.00 0.93 0.001 -0.06 0.92
2.38 2.30 2.41 1.99 2.76 2.58 2.80 1.24 2.88 2.62 2.86
2.46 2.10 2.32 1.70 3.22 2.39 2.38 2.87 3.48 2.80 1.67
a V(R,θ) ) ∑λVλ(R)Pλ(cosθ) and Vλ(R) ) De,λ(1 - exp(βλ(R - Re,λ)))2 - De,λ.
Figure 3. Fitted potential energy surface for bound NO interacting with the Fe atom of the heme group. Energies are given in kcal/mol. R is the distance between the center of mass of NO and Fe, and θ is the Fe-N-O angle. The global minimum is in the bent Fe-NO configuration with a binding energy of 21.4 kcal/mol (in the top part of the figure), and the secondary minimum is for linear Fe-ON with an interaction energy of 8.4 kcal/mol. The arrow indicates the minimum energy path from Fe-ON to Fe-NO (in the bottom part of the figure). The inset shows a comparison between the calculated and the fitted points. The index enumerates the calculated points from 1 to 274.
in particular around the T-shaped configuration, are not reproduced so well by the Morse functions (see inset in Figure 3). However, the uncertainty in the ab initio points is comparable to the inaccuracies of the fit around the minimum. Further, we represented the R dependence using Morse functions because they are very efficient compared to other functional forms (e.g., Hartree-Fock short range with electrostatic long-range expansions23). Since no accurate potential energy curve derived from experiment exists for NO, unlike CO,24 a NO potential was calculated in the following way. Starting from the optimized ab initio structure of bound heme-NO, the NO bond length was varied between 0.8 and 1.45 Å in increments of 0.05 Å. For each conformation, the total electronic energy was determined using UB3LYP/VDZ/3-21G and the resulting curve was fitted to a Morse function to give VNO(r). In this fit, the dissociation energy De of NO was set equal to the experimental value De ) 122 kcal/mol25 and the equilibrium separation re was fitted. The parameter β was determined by fitting to the experimental IR spectrum (as described below). The NO interaction VNO(r) does not depend explicitly upon R and θ, but it is taken into account in an average way (see below). The present approach includes ligand-heme interactions based on ab initio calculations. This is consistent with the strategy generally used to parametrize a molecular mechanics
(MM) force field.26 The interactions between the fragments are calculated for a model system (here NO-heme-Im) and then used within a MM framework. To ensure that the interactions between NO and the heme-Im moiety are not substantially altered by the surrounding protein framework, additional ab initio calculations for the two minimum energy structures were carried out. A QM/MM optimization was carried out using a snapshot of the MbNO structure taken from a trajectory at 300 K (see below). First, for the reference system (RS, the NOheme-His93 moiety in the geometry of the snapshot) the position of the NO ligand was optimized in the Fe-NO and Fe-ON conformations while freezing all remaining coordinates. The geometrical parameters are collected in Table 2. Only slight elongations of the NO bond length (0.01 Å) were found. Next, the entire protein was partitioned into a quantum mechanical (QM) part (identical basis set and method as above) consisting of residue His93, the NO, and the heme, while all other atoms were represented by their point charges as defined in the CHARMM22 force field.26 For His93, the CβH2 group was replaced by an H atom (replacement of His by imidazole as done for the model calculations described above). This optimization yielded a ligand N-Fe separation of 1.79 Å unchanged from the value without the protein; the N-O bond lengths are 1.17 and 1.16 Å, respectively, and the Fe-N-O angle is still 139°. Although these results refer to a particular dynamics snapshot and the heme moiety is not at its optimized geometry, they indicate that the effect of the protein is relatively small. Some of the differences in Erel may stem from this fact. In a final set of QM/MM minimizations, His64 was included in the QM region together with His93, the heme, and the NO. As above, the CβH2 group was replaced by an H atom, and all other atoms were represented by their point charges as defined in the force field. Again, only the RFeX, RNO, and θFeXY angles were optimized, where X and Y are N and O, respectively. A lengthening of the NO bond length from 1.16 to 1.20 Å and a compression of the θFeON angle from 136° to 131° is observed if the RS together with His64 are placed in the MM environment. Molecular Dynamics Simulations. Molecular dynamics (MD) simulations were carried out for native MbNO using the CHARMM program17 and the CHARMM22 force field,26 except for the treatment of the Fe-NO interaction. For this, the fitted PES (see above) was used instead of an Fe-N stretching and an Fe-N-O bending potential. The system was set up as described previously.6,12 Since only the region around the heme-NO was of interest, we used the stochastic boundary method with a 16 Å sphere of TIP3P water molecules to include solvation effects. Friction coefficients of 62 and 250 ps-1 for the Langevin dynamics were applied to the oxygen site of water and the remaining non-hydrogen atoms in the active region, respectively. Solvent molecules were constrained relative to the center by a solvent boundary potential with a radius of 16 Å. The nonbonded interactions were truncated at a distance of 9 Å, using a shift function for the electrostatic interactions and a switch algorithm for the van der Waals interactions. The time step in all MD simulations was 1 fs. To determine the parameter β in the NO potential VNO(r), a series of 250 ps MD simulations at 300 K were carried out. For each value of β, the NO frequency was determined by Fourier transforming the NO distance-distance autocorrelation function C(t). The IR spectrum was obtained from the Fourier transform of C(t), after appropriate Boltzmann weighting,27 according to
A(ω) ) ω{1 - exp[-ω/(kT)]}C(ω)
(2)
Molecular Dynamics of MbNO
J. Phys. Chem. B, Vol. 109, No. 44, 2005 21121
TABLE 2: Geometries and Relative Energies with Respect to the Minimum of Each Type of Calculation for Fe(II) and Fe(III) system Fe(II) full minimizationa RSb RS with Rest of Protein as MMc RS and His64 in QM Rest of Protein as MM
geometry
RFeN
Fe-NO η2Fe(NO)(TS) Fe-ON Fe-NO Fe-ON Fe-NO Fe-ON Fe-NO Fe-ON
1.81 3.38
Fe-NO η2Fe(NO) Fe-ON
1.65 1.94
RNO
θFeNO 139.2 70.1
1.96
1.16 1.15 1.16 1.17 1.18 1.16 1.20 1.15 1.20
2.15 1.75
1.12 1.15 1.12
179.9 83.8
RFeO
3.18 2.04
1.79 2.02 1.79 1.96 1.81
θFeON
Erel
131.0
0 20.6 15.3 0 15.5 0 18.1 0 20.0
64.0 179.9
0 26.9 33.0
88.5 135.8
139.0 135.0 139.0 132.0 137.0
Fe(III)
a For Fe(II), full minimizations were carried out for the NO-heme-His93 system. b RS is the reference system, that is, NO-heme-His93 in the geometry of the dynamics snapshot (see text). c MM is the molecular mechanics region where the atoms are placed at their positions from the dynamics snapshot with the charges from the CHARMM22 force field.
where C(ω) is the Fourier transform of C(t), ω is the frequency, k is the Boltzmann constant, and T is the temperature in Kelvin. From this analysis, β ) 2.59 Å-1 was found to reproduce the experimentally observed28 NO stretching frequency (1614 cm-1) for NO bound to the heme (to be compared with 1875 cm-1 for free NO). In all subsequent calculations, this value of β was used. Since the NO molecule explores the PES V(R,θ) during the dynamics, the effect of coupling between (R,θ) and r is taken into account in an average manner. It is worth mentioning that the NO stretching frequency is sensitive to the value of β; that is, changing β by (0.1 Å-1 shifts the frequency by 60 cm-1. To investigate the stability of the secondary minimum found on the PES, a sequence of MD simulations was carried out as follows. Starting from an Fe-ON configuration near the minimum (R ) 2.5 Å and linear Fe-ON), the system was heated and equilibrated at 100 K for 250 ps. Nine structures toward the end of the equilibration, separated by 5 ps, were used as starting points for the simulations. All of these structures are in the neighborhood of the Fe-ON minimum. Thus, nine independent trajectories were calculated with the temperature of the solvent increased by 50 K at 250 ps intervals. After 10 ps the entire system reached the solvent temperature. This procedure was continued until 300 K was reached. Results PES for NO Interacting with Fe(II). The fitted 2D PES V(R,θ) for heme interacting with NO is shown in Figure 3. We note that the PES has two minima: One is a local minimum corresponding to the Fe-ON configuration, and the other is the global minimum with the well-known Fe-NO configuration. The binding energy for the global minimum (Fe-NO configuration) on the fitted 2A PES is 21.4 kcal/mol; the actual value from the ab initio calculations is 23 kcal/mol. Given that MbNO dissociates to the 4A state which is estimated to lie some 5 kcal/ mol below the 2A asymptote at large Fe-N separation (from DFT calculations on MbCO29), the approximate calculated dissociation energy in the gas phase (excluding effects of the surrounding protein) is about 18 kcal/mol. There is no measured value, but experiments (e.g., the energetics of irreversible binding of NO, in contrast to CO30) suggest that the dissociation energy is larger for NO than for CO, which is 21.4 kcal/mol.31 The calculated equilibrium geometry (R ) 1.81 Å and θ ) 139°) compares reasonably with a range of experimental values32 (between 〈R〉 ) 1.76 Å and 〈θ〉 ) 139°) and favorably with
recent calculations33 (R ) 1.79 Å and θ ) 142°). X-ray crystallography on sperm whale myoglobin with NO found an Fe-NO angle of θ ) 112 ( 5° and R ) 1.89 ( 0.04 Å; according to the authors, the extent to which crystal packing effects contribute to this rather small angle compared to most other Fe-NO motifs is not clear.34 On the other hand, the X-ray structure of Nitrophorin 4, where the Fe is also bound to a His, reveals an Fe(II)-NO angle of 159°.35 It is also of interest that a preliminary structure of the L29F mutant crystallized in a more loosely packed P6 space group has an Fe-N-O angle of θ ) 130°.34 Once more experimental observables are available, such effects could be incorporated into the PES, for example, by morphing the interaction potential.36 The secondary minimum is considerably more shallow; the Fe-ON interaction energy is 8.4 kcal/mol. However, this minimum is still deep enough to exhibit interesting dynamics. The two minima are separated by a transition state with an approximately T-shaped configuration; see Figure 2. This is discussed further below. Comparison of Fe(II) and Fe(III) Interacting with NO. To further characterize the NO-Fe(por)-Im system and to attempt to partially address the question of how the electrons are distributed in the system,37 a natural bond orbital (NBO) analysis was carried out for Fe(II) and Fe(III) for the three critical points on the PES: Fe-NO (linear for Fe(III), bent for Fe(II)), the η2 conformation (local minimum for Fe(III), saddle point for Fe(II)), and Fe-ON (linear for Fe(III), bent for Fe(II)) (structural information is given in Table 2). Interest in the Fe(III) oxidation state is increasing following the recent discovery of the Nitrophorin family of proteins.38 These are NO-binding heme proteins in which Fe is in the ferric oxidation state. In addition, NO bound to ferric Mb is also thought to be an intermediate in the oxidation of NO to NO3-, a novel function recently proposed for Mb.39 Two sets of comparisons are presented. In one of them, differences in certain observables (NBO charges and populations of the natural orbitals, respectively) for a given oxidation state but differing conformation are considered. In the other, the differences for a given conformation but differing oxidation state are reported. Differences in the populations are only given for the atoms which show the most prominent differences in the NBO charges. They include the Fe, the four porphyrin N atoms, the His93 N atom, and the NO molecule. Table 3 reports total charges (in units of e) from an NBO analysis for the Fe, Np, NHis, Nlig, and O atoms and averaged charges for the carbon and hydrogen atoms for both systems in
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TABLE 3: Charges in Units of e from a Natural Bond Orbital Analysis of the Optimized Structures of Fe(II)-NO and Fe(III)-NO for the Three Configurations Mentioned in the Texta Fe(II) atom
FeNO
Feη2(NO)
Fe Npb Np Np Np NHisb NHis Nligb O c c
25.30 7.48 7.48 7.48 7.48 7.47 7.54 6.74 8.18 6.09 0.74
25.03 7.52 7.52 7.53 7.53 7.47 7.54 6.80 8.18 6.09 0.74
Fe(III) FeON
FeNO
Feη2(NO)
FeON
25.16 7.50 7.50 7.51 7.50 7.45 7.54 6.77 8.18 6.09 0.74
25.31 7.48 7.48 7.49 7.49 7.46 7.52 6.47 8.05 6.07 0.72
25.17 7.48 7.48 7.49 7.49 7.42 7.52 6.71 8.05 6.07 0.72
25.14 7.50 7.51 7.50 7.49 7.43 7.51 6.63 7.98 6.07 0.73
a Differences between the charges for a given conformation are displayed in Figure 7. b Porphyrin N atoms are designated Np, histidine N atoms as NHis, and the ligand N atom as Nlig. c For carbon and hydrogen atoms, the averages over all atoms are given.
Figure 4. Differences in NBO charges between the Fe(II) and Fe(III) containing NO-Fe(por)-Im systems. From top to bottom differences between Fe-NO, the η2 (side-on), and the Fe-ON conformation are shown. The aggregated difference in each graph is +1 which corresponds to the total charge difference between the Fe(III) and the Fe(II) systems. The x-axis gives the numbering of the atoms with the Fe being number one (Fe(1)), the Np(2,3,4,5), NHis(38), and N(47)O(48) as the most important atoms. This is also indicated on the top of the figure.
the three states investigated. The differences between the Fe(II)and Fe(III)-containing systems for a given configuration are shown graphically in Figure 4. It is observed that, in going from Fe(II)-NO via η2 to Fe(II)-ON, the Fe(II) atom is least positive for Fe-NO (0.70 e), then increases to 0.96 e for η2, and decreases again to 0.84 e for Fe-ON. This is counterbalanced by the four porphyrin N atoms and the NO molecule. A similar behavior is found for Fe(III), although the difference between Fe-NO and the η2 conformation is much larger than that for the N atom of NO which decreases by 0.25 e while the Fe atom gains 0.14 e. Ring atoms including the C and H atoms also participate in counterbalancing the charge redistribution. Next, changes in the charge distributions for a given conformation but differing oxidation state of the Fe atom are considered. The calculated total charge change between the Fe(II)- and Fe(III)containing systems is 1, as required. For Fe(III)-NO, most atoms are slightly more positively charged (typically ≈0.025 e) compared to those of the system containing Fe(II) except for the N and O atoms of NO. They differ by 0.30 and
0.13 e, respectively. For the η2 conformation, the Fe(III) atom is less positively charged by 0.1 e while most other atoms have increased charges by ≈0.035 e with the exception of the N and O of NO, which differ by 0.1 and 0.15 e, respectively. For Fe-ON, the situation is similar to Fe-NO with the difference that N and O of NO acquire 0.15 and 0.20 e, respectively. The most important changes in the charge redistributions concern the Fe-NO moiety (see Figure 7). Using the partial charges, the saddle point for the η2 conformation in Fe(II) vs the local minimum for Fe(III) can be rationalized as follows. For the Fe(II) system, the overall charge of NO is close to 0 e compared to 0.25 e for the Fe(III) system. Thus, there is little repulsion between NO and Fe(II) and little attraction between NO and the por-N atoms. This leads to an overall electrostatic interaction energy of close to zero. In contrast, the 0.25 e charge on the NO molecule leads to a considerable repulsion between NO and Fe(III) (0.83 e) which is counteracted by the attraction between the four por-N (each -0.49 e) at a somewhat larger distance than the Fe(III) atom. This leads to a net attraction between NO and the Fe(III)por system in the η2 conformation. This analysis can be extended by considering the changes in the populations of the molecular and atomic orbitals, as described in the Supporting Information. The direct electrostatic contribution to the fact that the η2 conformation is a saddle point in the Fe(II)-containing system is not a complete picture. A detailed analysisswhich is outside the scope of the present worksin terms of molecular orbitals would be required for that. An explanation comes from the analysis of Wondimagegn and Ghosh,21 in which they rationalize the stability of the η2 conformation of Fe(II) and Fe(III) in terms of the shape of the lowest unoccupied molecular orbital (LUMO) of the η2 conformation of the related [Fe(por)(NO)]+ complex. They describe this LUMO as having both bonding and nonbonding contributions between Fe and NO. Once an additional electron is added to this orbital, forming [Fe(por)(NO)]0, the η2 structure becomes unstable and opens up to an η1 conformation. However, to the best of our knowledge, a complete analysis of the molecular orbitals of ferrous hexacoordinate nitrosyl porphyrins as a function of the coordination mode has not been published. Other relevant work in this context has been carried out by Buchs and co-workers40 on the ferric nitroprusside ion. There, the η2 conformation is clearly found to be a minimum. Bound State Dynamics. Recent experiments have provided data for the NO and the Fe-N stretching frequencies for MbNO.33,41,42 Using the PES described above, we carried out MD simulations for bound MbNO. From these simulations the time series of the relevant coordinates (NO separation, FeNO angle, Fe-N distance) were used to determine the autocorrelation function C(t) for each coordinate. The vibrational spectrum is related to the Boltzmann-averaged Fourier transform of C(t); see Theoretical Methods. Figure 5 shows the spectra obtained by averaging over five independent trajectories, each 250 ps in length, calculated at 300 K. The blue line shows the calculated Fe-N stretch while the green curve shows the calculated Fe-N-O bend. These spectra are not “pure” spectra since the two coordinates are coupled.33 In fact, the three spectra (Fe-N, N-O, and Fe-N-O) are strongly coupled. For example, the N-O stretching frequency at 1614 cm-1 appears in the spectrum from the Fe-N time series showing that the N-O and the Fe-N motions are coupled. The same position for the NO stretch is calculated from the pure N-O time series (red curve, amplitude decreased by a factor of 100). Comparison of the two spectra shows which lines are dominated by a givencoordinate. The Fe-N vibrational frequency is most likely
Molecular Dynamics of MbNO
Figure 5. Spectra for the Fe-N stretching, Fe-N-O bending, and the N-O stretching coordinates (NO, red; Fe-NO, blue; Fe-ON, green) from time-correlation functions of the respective time series. Spectra are averaged over five independent runs and smoothed over five neighboring points. Frequencies are in cm-1 and intensities are in arbitrary units. The line marked with a star is the only prominent feature occurring exclusively in the Fe-N stretching coordinate. The maximum of the expected IR spectrum for NO in the Fe-NO configuration (blue) is at 1614 cm-1, essentially unshifted from the band for free NO (red), while the expected line for NO in the Fe-ON conformation (green) peaks at around 1635 cm-1 and is considerably broadened.
to be associated with the feature at 504 cm-1 that only occurs in the blue (Fe-N) spectrum. This value is in the region also found by experiment (between 520 and 550 cm-1), based on the difference spectrum between Fe14NO and Fe15NO. All other features arise from correlated motions along coupled degrees of freedom and appear to involve Fe-N stretching, N-O stretching, and Fe-N-O bending. Simulations with 15NO give a red-shifted N-O stretching frequency between 1580 and 1585 cm-1, which is in good agreement with experiment; the experimental value is 1586 cm-1.33 It is possible that the position of the NO band depends not only on β (see Theoretical Methods) but also on the atomic charges of the NO, since they interact with nearby polar residues and some of the heme atoms. To test whether different charge assignments alter the NO IR spectrum, atom-centered charges from a NBO analysis were calculated at the minimum energy structure of heme-NO; the NBO charges on the N and O atom are -0.25 and 0.20 e, respectively, while the Fe value is 0.78 e. To maintain the heme group at its formal total charge of -2 (as defined in the CHARMM22 force field26), the difference of 0.54 e between the original and the modified charge set was equally distributed over the porphyrin Np atoms. MD simulations at 300 K with β ) 2.59 Å-1 gave an absorption band at 1614 cm-1; that is, it is not shifted with respect to the result from the original charge set. This indicates that β is the dominant parameter responsible for determining the position of the absorption band. The Alternative Minimum. Since the fitted Fe-NO PES exhibits two minima (a local minimum at collinear Fe-ON and the global minimum at the bent Fe-NO configuration), the dynamical stability of the local minimum was investigated. Nine simulations were carried out as described in the Theoretical Methods. Starting from linear Fe-ON near the minimum at 100 K and increasing the temperature in increments of 50 K, no crossing to the Fe-NO minimum was found up to 250 K in 250 ps. The nine different trajectories were continued for further intervals of 250 ps at 300 K until isomerization to Fe-NO occurred. Four trajectories made the transition during the first 250 ps, three more trajectories were found in the Fe-NO conformation after 500 ps, while after 750 ps eight out of the
J. Phys. Chem. B, Vol. 109, No. 44, 2005 21123
Figure 6. Projections of the trajectories (at 300 K) which make the transition from Fe-ON to Fe-NO. Eight trajectories are continuations of the equilibrated trajectory at 250 K. R is the distance between the center of mass of NO and Fe, and θ is the Fe-N-O angle. To better follow the traces, the density of points around the transition state (40° e θ e 120°) is 50 times higher than that for the remaining part of the trajectories. Note the considerable width of the transition seam. The three black trajectories are not equilibrated with initial assignment of velocities at 300 K, while all other trajectories start from equilibrated trajectories (see text).
nine trajectories were in the Fe-NO state. Thus, even at 300 K the Fe-ON configuration has short time (>100 ps) dynamical stability. Figure 6 shows the PES together with the trajectories for the 250 ps interval in which they crossed from Fe-ON to Fe-NO. The transition seam (the region in which crossings occur) is extended (width of more than 1 Å; from R ≈ 3.0 to 4.4 Å where R is the distance between the center of mass of NO and Fe and θ is the Fe-N-O angle). Around the transition state (40° e θ e 120°) every point along the trajectory is shown, while otherwise only every 50th point is included. To determine whether previous equilibration of the system is required for dynamical stability of the Fe-ON configuration, three additional trajectories were started from a random Fe-ON position and velocity assignment at 300 K. They are the black traces in Figure 6. Two trajectories make a rapid transition while the third one diffuses around the transition state before it crosses. This shows that thermalization is not required in the simulations to dynamically stabilize the Mb-ON configurations. In Figure 7 the time dependence of the isomerization from the nine equilibrated trajectories is shown. The transition always occurs in one sweep (without recrossing) and is intimately connected with excursions of NO to large distances from the Fe atom as seen from Figure 6. From the MD trajectories, the expected IR spectrum for NO can be calculated separately for the two wells (Fe-NO and FeON). As described above, the spectrum associated with FeNO has one well-defined peak at 1614 cm-1. For Fe-ON, the NO spectrum is shifted to the blue by approximately 20 cm-1 to 1635 cm-1. This suggests that it may be possible to differentiate the two species in time-resolved low-temperature experiments. For comparison, in the model compound Fe(OEP)(NO) a shift of 34 cm-1 was found.43
21124 J. Phys. Chem. B, Vol. 109, No. 44, 2005
Figure 7. Time evolution of the Fe-N-O angular coordinate for the transition from Fe-ON to Fe-NO for the trajectories at 300 K. For Fe-ON, the minimum on the potential is at θ ) 0 while for Fe-NO it is at 140°. The fluctuation of θ in the Fe-NO conformation is about (10°. No recrossing is observed. One of the nine trajectories (black) does not cross on a time scale of 750 ps. Trajectories that crossed after 250 and 500 ps, respectively, are not continued (e.g., green and yellow (stopped after 250 ps) or magenta (stopped after 500 ps)).
Discussion and Conclusions The potential energy surface of NO interacting with the heme in ferrous myoglobin has been calculated and is shown to be bistable with an energetically preferred, bent Fe-NO configuration and a locally metastable, linear Fe-ON structure. The forward barrier Fe-NO f Fe-ON is 23.4 kcal/mol while the reverse barrier is 8.4 kcal/mol. The existence of the calculated secondary minimum is confirmed by both structural minimizations and the scan of the PES along the two progression coordinates R (Fe-NO center of mass distance) and θ (FeN-O angle). In synthetic work, an Fe-ON binding mode has been previously found for five-coordinate Fe(TPP)(ON)43 and more recently a six-coordinate Fe(TPP)(ON)(NO2) was found.44 However, their relevance to the present analysis of myoglobin is unclear, in particular for the latter compound, because the sixth ligand (NO2) strongly influences the electronic structure of the porphyrin.45 The calculated binding energy of Fe-NO is larger than that of CO31 (≈25 vs 21.4 kcal/mol) but smaller by about 10 kcal/mol than a previous calculation.46 Although no experimental value for MbNO is available, we note that measurements exist for [hemeNO]+ which give a dissociation energy of 24.8 kcal/mol.47 However, there is no simple relation between our calculated value for Fe(II) and this measurement for Fe(III). Also, the measured value43 of the NO vibrational frequency in five-coordinated Fe(TPP)NO is 1532 cm-1, while the harmonic ab initio calculated values for Fe(II)-NO and Fe(II)-ON are 1789 and 1845 cm-1, respectively. This compares with 1614 and 1635 cm-1 from the MD simulations. We suggest that the existence of a secondary minimum could give rise to observable effects in the rebinding dynamics of free NO to Mb. Since the initial rebinding from a separated Mb‚‚‚NO system6,14 could involve the Fe-ON configuration as well as the Fe-NO configuration, the transition to the minimum energy state (Fe-NO) from Fe-ON could be considerably delayed due to the stability of Fe-ON, particularly at low temperatures. It would be interesting, therefore, to extend the experimental study of Petrich et al.14 into the lowtemperature range to determine whether the alternative binding mode has an effect on the rebinding dynamics. Even at 300 K, where the photolysis/rebinding studies were carried out, the alternative binding mode could contribute to the observed nonexponential behavior.
Nutt et al. Very recently, Kim et al. have published time-resolved femtosecond IR spectra which probe the dynamics of rebinding of NO to myoglobin.15 They confirm the finding that the rebinding process is nonexponential and obtain time constants of 5.3 and 133 ps, significantly faster than those previously obtained by Petrich et al. (28 and 280 ps).14 Comparison with data obtained from rebinding to a microperoxidase (a partially digested cytochrome) led to the suggestion that the slower phase of rebinding is due to protein relaxation.15 On the other hand, Shreve et al. proposed that the two time scales are due to rebinding from two different photodissociated states, B1 and B2.48 Kim et al. found no evidence to support a metastable FeO-N intermediate, but they were not looking for such a species. There is no experimental evidence for the existence of a local minimum Fe-ON conformation in Mb. Experimental and theoretical data from model compounds, however, suggest that such a conformer exists.21,43,49 The spectroscopic and computational work on ferrous FeP(NO) (with P ) porphine dianion) indicate that the FeP(NO) structure is more stable by about 35 kcal/mol than the FeP(ON) isomer.21,43 This energy difference includes contributions from the porphine distortions and is due not only to the different binding energies of NO to FeP. Further calculations21 established the minima for the Fe-NO and FeON; the latter is ≈40 kcal/mol above Fe-NO conformation in [Fe(III)(P)(NO)]+. For this system, the η2 side-on conformer was found to be stable and to lie 33.6 kcal/mol above the minimum Fe-NO structure.21 Previous experimental work to characterize MbNO includes ESI-MS together with UV-vis spectroscopy,50 electronic spectroscopy,51 EPR spectroscopy,52 and IR and Raman spectroscopy.28 In all these studies, an Fe-NO conformer was found or tacitly assumed. Consequently, additional studies that specifically search for the Fe-ON isomer are needed. In model compound studies43,49 based on IR spectroscopy, it has been shown that NO isomers can be generated by low-temperature irradiation in the 25 to 77 K range. Alternatively, the Fe-ON isomer could be produced via rebinding from a photodissociated state (Mb‚‚‚NO) into the Fe-ON metastable state. One difficulty in finding the Fe-ON conformation, in Mb, relative to the model compound studies is the possible overlap with protein IR bands, for example, the NO IR spectrum (1614 cm-1 in wildtype Mb) and the amide I band (1655 cm-1). Furthermore, a band corresponding to Fe-ON can be expected to be significantly weaker than the corresponding Fe-NO signal. In the recent IR study of Kim et al.,15 such a signal was likely not to be found, if it was not looked for; for example, small features in the wings of the NO stretching bands (where a potential FeON conformer would absorb) were assigned to conformational relaxation of photodissociated Mb15,53 and were subtracted as part of the background spectrum. Experimentally, the situation is further complicated by the photodissociation quantum yield of around 50%54 (although Zemojtel et al. suggest that it is between 80 and 100%55). If 50% of the photons lead to dissociation while the remaining 50% go into heating the protein, then it is possible that FeON is formed. The data analysis would need to take such effects into account to detect a signal due to Fe-ON. In a difference FTIR spectroscopy study of MbNO, Miller et al. present IR spectra of bound and photolyzed MbNO.56 However, to calculate the difference spectra, the spectrum obtained after photodissociation at 7 K was divided by the partially rebound spectrum after warming to between 10 and 30 K. If some fraction of the undissociated proteins is converted to the Fe-ON conformation, then it will contribute to the signal following photolysis but
Molecular Dynamics of MbNO give equal contributions at both 7 and 30 K. As a result, any signal due to a potential Fe-ON conformation would not have been observed in this experiment. Experimental observation of the Fe-ON conformation in myoglobin would be assisted by a better signal/noise ratio and improved background correction and possibly modified data analysis tools. In conclusion, the present investigation supports the existence of an Fe-ON conformation in model compounds and in MbNO. This result is in accord with recent experiments on different model compounds and previous calculations. The PES for the Fe-NO interaction captures the essential difference in the energetics of the Fe-NO and Fe-ON minimum configurations. The 2D coordinate system used for parametrizing the dynamics provides a satisfactory characterization of the global FeNO minimum but is not as good for the metastable FeON conformation. The dynamics of bound MbNO exhibits interesting effects (extended stabilization of the metastable FeON conformation, correct IR absorptions also upon isotopic substitution, coupling of the vibrational frequencies) due to the existence of the metastable Fe-ON conformation and suggests that experiments may be able to detect this species. This would lead to a deeper understanding of the photodissociation dynamics of NO in Mb. Acknowledgment. We gratefully acknowledge financial support from the Schweizerischer Nationalfonds. M.M. is a Fo¨rderungsprofessor of the Schweizerischer Nationalfonds. The research of M.K. at Harvard University is supported by the National Institutes of Health. Generous allocation of computing time at the CSCS in Manno, Switzerland, and the CINES, Montpellier, France, is acknowledged. Supporting Information Available: Further analysis of the differences between Fe(II) and Fe(III) in terms of orbital occupations (PDF) with accompanying figures in PostScript format. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Austin, R.; Beeson, K.; Eisenstein, L.; Frauenfelder, H.; Gunsalus, I. Biochemistry 1975, 14, 5355. (2) McCammon, J. A.; Harvey, S. C. Dynamics of Proteins and Nucleic Acids; Cambridge University Press: Cambridge, U.K., 1987. (3) Brunori, M.; Gibson, Q. H. EMBO Rep. 2001, 2, 674. (4) Henry, E. R.; Levitt, M.; Eaton, W. A. Proc. Natl. Acad. Sci. 1985, 82, 2034. (5) Elber, R.; Karplus, M. Science 1987, 235, 318. (6) Meuwly, M.; Becker, O. M.; Stote, R.; Karplus, M. Biophys. Chem. 2002, 98, 183. (7) Richter-Addo, G. B.; Legzdins, P.; Burstyn, J. Chem. ReV. 2002, 102, 857. (8) Brunori, M. Biochemistry 2000, 30, 221. (9) Frauenfelder, H.; McMahon, B. H.; Fenimore, P. W. Proc. Natl. Acad. Sci. 2003, 100, 8615. (10) Vitkup, D.; Petsko, G. A.; Karplus, M. Nat. Struct. Biol. 1997, 4, 202. (11) Lim, M.; Jackson, T. A.; Anfinrud, P. A. J. Chem. Phys. 1995, 102, 4355. (12) Nutt, D. R.; Meuwly, M. Biophys. J. 2003, 85, 3612. (13) Nutt, D. R.; Meuwly, M. Proc. Natl. Acad. Sci. 2004, 101, 5998. (14) Petrich, J. W.; Lambry, J.-C.; Kuczera, K.; Karplus, M.; Poyart, C.; Martin, J.-L. Biochemistry 1991, 30, 3975. (15) Kim, S.; Jin, G.; Lim, M. J. Phys. Chem. B 2004, 108, 20366. (16) Li, H.; Elber, R.; Straub, J. J. Biol. Chem. 1993, 268, 17908. (17) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. J. Comput. Chem. 1983, 4, 187. (18) Weiner, S. J.; Kollman, P. A.; Case, D. A.; Singh, U.; Ghio, C.; Alagona, G.; Profeta, S., Jr.; Weiner, P. J. Am. Chem. Soc. 1984, 106, 765. (19) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.;
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