6420
J. Phys. Chem. B 2001, 105, 6420-6426
Proton Conduction by a Chain of Water Molecules in Carbonic Anhydrase Alexander Isaev† and Steve Scheiner* Department of Chemistry & Biochemistry, Utah State UniVersity, Logan, Utah 84322-0300 ReceiVed: March 15, 2001; In Final Form: May 1, 2001
Ab initio and density functional theory (DFT) calculations are used to investigate a (NH3)3Zn2+‚‚(OH2)n‚‚ NH3 system that models the proton conduction, via a chain of water molecules, from a Zn2+ ion to a His residue some distance removed. The optimal configuration of this chain, with n ) 3, contains a number of fairly short H-bonds separating the water molecules. The conduction of a proton from the Zn-bound water to the terminal N-acceptor is energetically favored by a concerted process wherein all protons are in flight from one molecule to the next along the chain, at approximately the same time. This optimal process also includes the shortening of each H-bond as the donor and acceptor move toward one another at the midpoint of the transfer as well as small alterations in the distance between Zn and its various ligands. The barrier for the conduction process is not adversely affected by a lengthening of the chain to include as many as five waters. However, the process is slowed considerably if additional H-bonds are formed between members of the chain and peripheral molecules. The reorientation of the chain that places the ultimate N-acceptor at an angle of greater than some 30° from the Zn- -O axis of the Zn-bound water can also slow the conduction process.
1. Introduction Carbonic anhydrase (CA), an extremely efficient catalyst of the reversible hydration of carbon dioxide, consists of more than 250 amino acids and a zinc cofactor.1 The catalytic mechanism of CA has been subject to extensive study, both experimentally2-19 and theoretically20-31 over a period of decades. Several genetically and immunologically distinct, but structurally homologous, isozymes of CA are known, each with different kinetic and ligand-binding properties. Nevertheless, the basic features of the catalytic mechanism appear to be common to all forms. Catalysis of the hydration of CO2 by CA has been useful in understanding the characteristics of proton transfer (PT) in enzymic systems. This catalysis occurs in two stages, the first of which is conversion of CO2 into HCO3- (eq 1) by direct nucleophilic attack of the zinc-bound hydroxide on CO2.12,17 The second stage comprises the series of PT steps that regenerate the zinc-bound hydroxide (eq 2).
CO2 + EZnOH- + H2O S HCO3- + EZnH2O
(1)
His64-EZnH2O + B S H+His64-EZnOH- + B S His64-EZnOH- + BH+ (2) B represents the buffer in solution, and His64 is a proton acceptor residue in CAII, which seems to fulfill the criteria for a “perfectly evolved” enzyme,32 that is, the most efficient catalyst possible for a particular reaction. Despite the general agreement about the chemical mechanism involved in the catalytic process, the details of the protontransfer mechanism remain unresolved. Extensive experimental studies by Silverman and Lindskog12 support the proposal of Steiner et al.2 of an intramolecular proton shuttle between a Zn-bound water and the His64 residue in CAII. Because the * E-mail:
[email protected]. † N. D. Zelinsky Institute of Organic Chemistry, Russian Academy of Sciences, Leninsky pr. 47, 117913 Moscow, Russia.
distance between His64 and the zinc-bound water is too long for direct proton transfer, there is likely to be proton conduction along intervening water molecules; indeed, a network of hydrogen-bonded waters has been observed in the crystal structure.33,34 This proton translocation mechanism is thought to be similar to proton conductance through the gramicidin channel for which water chains form a proton wire.35,36 Studies have revealed that the Zn-bound water has about the same pKa (∼7) as a protonated His64. This similarity is rather important to the mutual proton exchange, because a large difference in pKa could lead to a large barrier in one of the proton-transfer directions. In fact, this requirement has excluded the possibility of a proton-transfer role by other functional groups or residues.28 Recent studies on isozymes CAIII (with Lys64) and CAV (with Tyr64) also support the proton-transfer mechanism outlined above.19 Site-directed mutagenesis experiments showed that, in both cases, the turnover number of the enzyme can be increased by placing a histidine at position 64. The measurements also showed an increase of the maximal velocity of catalysis when Lys64 and Tyr64 are replaced by glutamic and aspartic acids, which can serve as efficient proton shuttle residues at pH ) 6-8. According to X-ray diffraction results,37 the Zn2+ ion is located some 7.8 Å from His64, leaving room for as many as three water molecules which could form a bridge to act as a proton shuttle. The imidazole ring of His64 may function, as indicated in eq 2, to transfer a proton from the active site to buffer in solution. Solvent hydrogen isotope experiments2,4 and the release rate of 18O-labeled water into solvent at different buffer concentrations15 have shown that PT between Zn-bound water and His64 is the rate-limiting step of the maximal velocity at high buffer concentrations. At low buffer concentrations, the proton release into the medium becomes rate-limiting.18 To this point, a few theoretical works have addressed the barrier for proton conduction in the hydration direction (away from zinc).24-26,30,31 Probably the most quantitative results were obtained by Voth and Lu,31 who calculated a number of PT
10.1021/jp0109933 CCC: $20.00 © 2001 American Chemical Society Published on Web 06/08/2001
Proton Conduction by a Chain of Water Molecules
J. Phys. Chem. B, Vol. 105, No. 27, 2001 6421
potential curves with different numbers of ligand water molecules and at various R(O‚‚‚O) distances between donor and acceptor. It was found that as more water molecules are added, the PT barrier decreases and is very sensitive to the R(O‚‚‚O) distance. One may conclude that cooperative interactions of H-bonds may play a key role in the mechanism of the proton conduction process which may be dynamically related to donor and acceptor motions. Because the calculations in ref 31 were performed without geometry optimization at fixed R(O‚‚‚O) distances, better ab initio calculations taking into account motion of all the protons and oxygen atoms of the water molecules forming a proton-transfer channel are needed to quantify the proton shuttle mechanism. One of the aims of the present paper is to address the question as to whether the PT along the H-bonded chain occurs step by step, that is, from the first H2O molecule to the second, followed by others, or the PTs happen at about the same time via a concerted mechanism. The geometric and electronic structure of the transition state (TS) for the hydration reaction was calculated in order to elucidate the proton-transfer mechanism and to describe how the interaction between the H2O molecules, connecting donor and acceptor, affects the PT kinetics and charge distribution along the proton-transfer coordinate. An important issue considered here is the possible role of translational and rotational motion of the H2O molecules in the catalytic process. Another interesting question is the dependence of the PT barrier on the orientation of the proton channel in the enzyme active site as well as on the length of the H-bonded chain, connecting donor and acceptor. 2. Methods The primary question under investigation is concerned with the proton transfer from a Zn2+ ion to a His residue some distance removed, through the intermediacy of a number of water molecules. The Zn2+ ion is bound to three His residues as ligands. In terms of devising a suitable model system, and one that is small enough to be treated by accurate ab initio calculations, it was deemed adequate to replace the N-bearing histidine bases by the smaller NH3 molecules, a common substitution in such enzymatic studies.38 Of course, the reader should bear in mind that NH3 not only is smaller than the imidazole of histidine but also has different electron-donating and proton-accepting properties, so the data computed here should not be considered as a quantitative model of the His residues. The calculations were carried out using the GAUSSIAN98 set of programs.39 Various means were used to compute proton-transfer potential curves. In most cases, after having chosen a given configuration as a starting point, a given H atom was then allowed to move in uniform steps of 0.1 Å along the H-bond axis from the donor atom to the acceptor, optimizing the remainder of the geometrical parameters at each step, at the self-consistent field SCF/ 6-31G level, which does not include electron correlation. Such a profile provides an estimate of the position of the transition state and the accompanying barrier to proton transfer. A more accurate indicator of these quantities was secured by locating the transition state (TS) structure using the QST3 procedure, followed by SCF/6-31G*, SCF/6-31G**, and SCF/6-31+G**, again without electron correlation, but with progressively larger basis sets. B3LYP is a variant of density functional theory (DFT) which has shown itself to be fairly reliable for studies of hydrogen bonding. B3LYP and second-order Møller-Plesset perturbation theory (MP2) were both employed, using the 6-31G geometries and taking into account zero-point vibrational energy (ZPE).
Figure 1. Schematic diagram of two starting point configurations for proton transfer in the (NH3)3Zn2+‚‚OH2‚‚OH2‚‚OH2‚‚NH3 system. Distances between heavy atoms are indicated in units of angstroms.
3. Results and Discussion 3.1. Geometric and Electronic Structure of the System. The first set of calculations considered the situation where three water molecules separate the Zn2+ ion from the ultimate proton acceptor NH3. The first of these waters binds directly to the Zn2+ and is the original proton donor. Optimization of the geometry of this (NH3)3Zn2+‚‚OH2‚‚OH2‚‚OH2‚‚NH3 system leads to two minima on the surface, whose structures are illustrated in Figure 1. The first structure contains a nearly linear chain of water molecules between the Zn2+ and the terminal NH3, which are separated by 7.7 Å from one another. It may be noted that each water molecule is engaged in a pair of H-bonds, one as an acceptor and another as a donor. Structure 1b is basically similar, except that the chain curves around so that the third water molecule can engage one of the NH3 ligands in an additional H-bond, with a R(O‚‚N) distance of some 2.99 Å. This extra H-bond stabilizes structure 1b by 2.5 kcal/mol relative to 1a, making structure 1b the global minimum on the surface. This twist in the chain pulls the Zn2+ closer to the terminal NH3, placing them at a distance of 6.3 Å. Although structure 1b is more stable, it was rejected for further consideration for a number of reasons. In the first place, X-ray data of CAII place the imidazole ring of His64 (modeled here by NH3) within 8 Å of the zinc, close to the value found for the structure in Figure 1a. More importantly, the His ligands of Zn2+ in the enzyme would not have the pendant H atoms of the model NH3 ligands, and so they could not engage in the H-bond that makes structure 1b more stable. Further consideration of this system is hence restricted to the geometry in Figure 1a as a starting point.
6422 J. Phys. Chem. B, Vol. 105, No. 27, 2001
Isaev and Scheiner
TABLE 1: Interatomic Distances (Å) in Various Configurations of (NH3)3Zn2+‚‚OH2‚‚OH2‚‚OH2‚‚NH3 where TS Refers to Transition State and P to Product R, Å
1a
TS
P
O1‚‚‚O2 O2‚‚‚O3 O3‚‚‚N4 O1-H1 O2-H1 O2-H2 O3-H2 O3-H3 N4-H3 Zn-O1 Zn-N1 Zn-N2 Zn-N3 Zn‚‚‚N4
2.530 2.539 2.755 1.003 1.546 1.004 1.535 0.988 1.770 1.983 2.077 2.097 2.097 7.679
2.447 2.379 2.649 1.305 1.052 1.131 1.249 1.014 1.636 1.901 2.114 2.119 2.119 7.901
2.575 2.687 2.627 1.596 0.994 1.713 0.977 1.576 1.061 1.872 2.114 2.124 2.124 8.162
Focusing attention on certain specifics of the structure in Figure 1a, reported in the first column of Table 1, the two H-bonds between water molecules are 2.53 and 2.54 Å in length, respectively; the R(O‚‚N) distance of the last H-bond is equal to 2.76 Å. Although some of these H-bonds are rather short, the bridging hydrogens are very unequally shared and are clearly associated with their donating atoms. The corresponding r(OH) bond lengths of the three water molecules are 1.003, 1.004, and 0.988 Å, respectively. Finally, regarding the complex between Zn and its ligands, the R(Zn-N) bond lengths are all between 2.08 and 2.10 Å, and the R(Zn-O) bond length involving the Zn-bound water is shorter, at 1.98 Å. These distances conform with other estimates. For the protonated state of Zn-bound water, X-ray studies place the R(Zn-N) distances at 2.1-2.3 Å, while R(Zn-O) is some 1.9-2.0 Å.10,14 Molecular mechanics refinements of the solvated native CAI yielded a slightly distorted tetrahedron at the zinc, with 1.936 Å < R(Zn-N) < 1.974 Å and R(Zn-O) ) 1.923 Å.27 Molecular dynamics simulations, using ligand bonding parameters derived from ab initio studies, provide an average distance between the Zn2+ ion and the histidine residues of 2.10-2.15 Å.29 Examination of charge distributions can afford insights into the interplay between proton transfer and electronic charge shifts within the complex. Consistent with the geometrical indicators that there is little proton transfer in the structure in Figure 1a, each of the water molecules bears only a very small charge, less than 0.1, as does the NH3 molecule which is the ultimate target of the proton conduction. The positive charge of the zinc dication is distributed around to its three NH3 ligands, leaving the zinc center with an effective charge of 1.33. 3.2. Mechanism of Proton Transfer. The short H-bond lengths of 2.53-2.54 Å observed for the first two H-bonds along the chain lead one to expect a low barrier to proton transfer in each. There were several modes of proton transfer that were examined explicitly. In the first example, the proton shared by the first two waters along the chain was used as an “engine” to drive the process. That is, the r(O1‚‚H1) distance was lengthened in increments of 0.1 Å. For each step along this transfer, the positions of the other two protons that are being transferred, H2 and H3, were optimized. The energy profile traced out by this conduction process is illustrated by the solid curve in Figure 2 that is labeled W1, from which it may be seen that the barrier to the entire conduction process is between 8 and 9 kcal/mol. The details of the mechanism show that as proton H1 is moved along, the other two protons tend to move along their respective paths as well, leading to what might be termed a concerted process (although the various proton transfers are not precisely
Figure 2. Proton-transfer potentials for the (NH3)3Zn2+‚‚OH2‚‚ OH2‚‚OH2‚‚NH3 system with 1a as the starting point. The W1 label indicates the curve corresponding to use of a proton on the first water molecule as the engine for the conduction process; W2 and W3 refer to similar processes, driven by protons on the second and third waters, respectively.
synchronous with one another). It is important to note the similarity of the barrier in the W1 curve to the same property of the W2 and W3 curves in Figure 2. The latter curves were obtained by using the other two protons as transfer engines; for example, proton H2 was moved in 0.1 Å increments, optimizing the positions of H1 and H3, to trace out curve W2. This similarity indicates that the height of the transfer barrier is not sensitive to the matter of which proton is being used to drive the conduction process. (The downward shift of the left minimum in curve W2 is an artifact resulting from the assumption of the configuration in Figure 1b when r(O2‚‚H2) ) 0.95 Å.) Of course, the three potential curves in Figure 2 are not identical. It might be noted, for example, that as the identity of the proton engine for the conduction process changes from H1 to H2 to H3, the position of the barrier moves to the left. That is, H1 must stretch the r(O1‚‚H1) bond to 1.4 Å before reaching the transition state for the transfer, whereas the stretch of r(O3‚‚ H3) is only to about 1.2 Å when H3 drives the reaction. There is also what appears to be a narrowing of the transfer barrier as the engine changes from H1 to H2 to H3. Instead of allowing all three protons the freedom to transfer, it is enlightening to consider the scenario where only one proton is permitted to move at a time. The broken curve labeled W1 in Figure 3 represents the potential energy profile when H2 and H3 are held stationary while H1 transfers from O1 to O2. The barrier for this single transfer is estimated to be about 14 kcal/ mol, nearly twice that observed when all three protons are permitted to move. Likewise, the transfer of H2, with no accompanying motion of the other protons (curve W2), leads to an even higher barrier, as does the transfer of the third proton. One might conclude first that a concerted multiple transfer is energetically preferable to a single transfer. Second, the barrier for the single transfer becomes higher as the proton undergoing the motion is further removed from the Zn2+ site of formal positive charge. There are several other modes of proton transfer that provide insights into the interplay between various factors. The broken curve in Figure 4 labeled “rigid” refers to the case wherein the motion of the proton H1 occurs in isolation from any other
Proton Conduction by a Chain of Water Molecules
J. Phys. Chem. B, Vol. 105, No. 27, 2001 6423 TABLE 2: Proton-Transfer Barriers (kcal/mol) Calculated for (NH3)3Zn2+‚‚OH2‚‚OH2‚‚OH2‚‚NH3 at Various Levels of Theory level of calculations SCF SCF/6-31G SCF/6-31G*//SCF/6-31Ga SCF/6-31G**//SCF/6-31G SCF/6-31+G**//SCF/6-31G post-SCF B3LYP/6-31+G**//SCF/6-31G MP2/6-31+G**//SCF/6-31G
E†
E† + ZPVE
5.3 10.7 8.5 8.6
1.0 6.5 4.3 4.4
2.3 3.4
0.0 0.0
a SCF/6-31G*//SCF/6-31G refers to a single-point SCF/6-31G* calculation of a geometry optimized at the SCF/6-31G level. Similar definitions apply to the other calculation levels.
Figure 3. Proton-transfer potentials for the (NH3)3Zn2+‚‚OH2‚‚OH2‚‚ OH2‚‚NH3 system, under the restriction that the motion of each of the indicated protons is not accompanied by transfer of the other two protons.
Figure 4. Proton-transfer potentials for the (NH3)3Zn2+‚‚OH2‚‚OH2‚‚ OH2‚‚NH3 system, with varying degrees of geometry restriction. Motion of H1 with all other atoms held fixed is indicated by the “rigid” designation. “Partial opt” permits motion of other atoms, except that distances between Zn and its ligands are held constant: R(Zn-O) ) 2.0 Å, R(Zn-N) ) 2.1 Å. Relaxing the latter restriction leads to “optimized” proton-transfer curve.
motions. Not only are H2 and H3 held in place, but the heavy atoms remain stationary as well. In such a rigid mode of transfer, there is no second well in the potential, suggesting that a rigid single transfer is not a viable process. The broken curve with the label “partial opt” relaxes this restriction, permitting all atoms to move in response to the motion of H1, with the sole exception that the ligands surrounding the zinc ion are held rigidly in place. Essentially the same curve is reported earlier in Figure 2 as W1. Upon permitting the Zn-ligand distances to relax along with the proton motion, the right side of the potential is lowered (“optimized” curve in Figure 4). Not only does this effect favor the proton transfer by making it exoergic, but the barrier to proton transfer is also reduced to 5 kcal/mol or thereabouts.
In summary, these calculations suggest that the proton conduction process is facilitated by a number of cooperative interactions. There is, first of all, the ability of the protons to move in a concerted fashion. Changes in the distances separating the water molecules, accompanying the proton motions, are another major factor. In addition, the ability of the Zn complex with its ligands to “breathe” during the process further facilitates the entire process, even though these changes are on the order of only 0.1 Å. The results described above were obtained with the 6-31G basis set at the Hartree-Fock level. It is important to consider how the barrier might be affected by the enlargement of the basis set, the inclusion of electron correlation, and the consideration of zero-point vibrational energies. Some estimates of these effects may be gleaned from Table 2, where a comparison of the two entries in the first row indicates that vibrational effects would tend to lower the barrier by some 4 kcal/mol. The next row illustrates that enlargement of the basis set by the addition of polarization functions to heavy atoms would tend to raise the barrier, although this trend reverses and the barrier begins to diminish again when polarization functions are added to H atoms (**) and diffuse functions are added to heavy atoms (+). The last two rows of Table 2 indicate that electron correlation has a lowering effect on the barrier and that this effect is larger in magnitude than the barrier increases associated with basis set enlargement. As mentioned above, our system represents only a very small subset of the true enzyme, including reduction of full amino acid residues to small model molecules. According to estimates obtained in ref 31, substitution of the model NH3 ligands by the larger imidazole molecules results in an increase in the barrier height to around 15 kcal/mol. The various effects, viz. basis set enlargement, inclusion of correlation, and extension of model residues, have a certain degree of cancellation in terms of the proton-transfer barrier, leading us to anticipate that our computed values represent reasonable estimates for the enzyme itself. Nonetheless, the reader should bear in mind that the model system contains no neighboring residues or solvent molecules, nor do we have knowledge of all the geometric restrictions that the structure of the enzyme might place upon the locations or flexibility of the water molecules in the shuttle. For this reason, it is stressed that the results presented here should not be taken as a quantitative assessment of the proton-transfer barrier, but rather as a means of obtaining insights into the fundamental nature of the entire conduction process. 3.3. Structure of Transition State. The magnitude of this sort of flexibility requirement may be gleaned from Table 1, which reports the relevant geometrical parameters for the starting point of the transfer, the structure shown in Figure 1a, the
6424 J. Phys. Chem. B, Vol. 105, No. 27, 2001
Isaev and Scheiner
TABLE 3: Effect of Number of Water Molecules n in the (NH3)3Zn2+‚‚‚(H2O)n‚‚‚NH3 System upon the Geometry and Proton-Transfer Barrier n
R(Zn‚‚‚N4), Å
R(O1‚‚‚O2), Å
PT barrier, kcal/mol
1 2 3 5
4.216 6.399 8.655 13.232
2.608a 2.475 2.456 2.435
0.4 1.6 1.1 0.4
a
O2 is replaced by N4 in this case.
transition state for the conduction, and the final product. From the first row, it is evident that the distance between the first two O atoms contracts from 2.53 Å at the starting point to 2.45 Å at the transfer midpoint, and then stretches back to 2.58 Å at the conclusion of the process. The distance between O2 and O3 undergoes an even larger contraction, down to 2.38 Å at the midpoint. The O3‚‚‚N4 distance is slightly different in that it contracts throughout the entire transfer process. With regard to Zn and its neighboring ligands, its distance from O1 decreases throughout the process, consistent with the idea that this water ligand is converted to a hydroxide anion. The N-ligands stretch a small amount away from the Zn as the transfer proceeds. The last row of Table 1 reports the total length of the conduction chain, specifically the distance separating the Zn from the N4 atom, which is the ultimate target of the proton. There is a tendency for this chain to elongate, from 7.7 to 8.2 Å, as a result of the full conduction. In terms of the positions of the three pertinent protons in the transition state, their distances from the donor and acceptor atoms are reported in Table 1. The distances of H1, H2, and H3 from their respective donor atoms are 1.305 > 1.131 > 1.014 Å, which are consistent with a concept of the proton conduction in which all three protons move in a generally concerted fashion but the proton nearest the Zn ion “pushes” the others along and the progress of the transfer of H2 lags behind that of H1, and that of H3 lags further behind the others. This series of lags is connected with a certain amount of charge buildup along the chain. For example, if both H1 and H2 are considered to be associated with O2, because of their geometrical proximity, the resulting (H3O)+ species is computed to have a Mulliken group charge of +0.75. A transition state is traditionally defined as containing one imaginary frequency, the coordinate of which is associated with the transition from reactant to product. The imaginary frequency of our TS is some 405 cm-1; its analysis shows that the main contribution is derived from displacements of protons H1 and H2 such that both are moving along the conduction path. 3.4. Dependence of PT Barrier on the Length and Orientation of the H-Bonded Chain. The nature of the chain of water molecules that might link the Zn-bound water molecule to the ultimate His acceptor is largely a matter of inference at this point, with little precisely known about the number of water molecules in the chain, their locations, or alignment. Indeed, a recent molecular dynamics study28b reiterated the question concerning the precise number of water molecules in the putative proton-relay chain. In an attempt to establish the parameters of a chain of water molecules that could act as an effective proton conduit, a number of variations on the earlier theme were considered. The number of water molecules was not restricted to the three shown in Figure 1 but rather was allowed to vary between one and five. For each value of n water molecules, the geometry of the entire chain in (NH3)3Zn2+‚‚‚(H2O)n‚‚‚NH3 was optimized. The second column of Table 3 displays the length of the resulting chain, defined again as the distance between the Zn
TABLE 4: Effect of Removing Water Molecules from the Main Chain of (NH3)3Zn2+‚‚‚(H2O)5‚‚‚NH3 and Placing Them on the Periphery no. of “side” H-bonds R(O1‚‚‚O2), Å R(Zn‚‚‚N4), Å PT barrier, kcal/mol 0 1 2 4
2.435 2.522 2.560 2.548
13.2 12.5 11.0 4.9
0.4 3.4 9.0 no transfer
center and the N atom of the NH3 acceptor. Scanning down this column, it appears that each additional water molecule elongates this distance by some 2.2 Å or so. The next column reports the distance between the first and second water molecules (NH3 takes the place of water when n ) 1). The elongation of the chain shortens this distance, which may be taken as an indication of a strengthening of the bond. The barrier for conduction of the proton from the first water to the terminal NH3 is listed in the final column where it may be observed that the addition of a second water in the chain raises the barrier from 0.4 to 1.6 kcal/mol, but this barrier then lowers gradually as more waters are added. In any case, all of these barriers are rather low, less than 2 kcal/mol, from which it might be concluded that the barrier to the conduction process is relatively stable and is not very sensitive to the number of water molecules in the chain. Of course, water molecules do not necessarily have to participate directly in the conduction chain but might also lie adjacent to this chain, possibly forming H-bonds to it. The effect of such “side” water molecules was investigated by taking the (NH3)3Zn2+‚‚‚(H2O)5‚‚‚NH3 system as a starting point. As reported in the first row of Table 4, the distance separating the Zn and N4 atoms, spanned by this five-membered chain, is 13.2 Å. The first two O atoms along this chain are separated by 2.435 Å, and the barrier for the overall conduction process is 0.4 kcal/ mol. The next row of Table 4 refers to the configuration where one of these five water molecules has been extracted from the main chain and placed alongside the remaining four waters, H-bonded to one of them. Not surprisingly, this effective chain shortening reduces the distance between Zn and N4 to 12.5 Å. This diversion of a main chain water to a side position also raises the barrier to proton conduction to 3.4 Å and lengthens the initial O1‚‚‚O2 H-bond to 2.52 Å. As additional water molecules are removed from the main chain and placed instead in peripheral sites, the barrier to proton conduction rises quickly, reaching 9.0 kcal/mol for nside ) 2. When four waters are removed from the main chain, the conduction process ceases, that is, there is no minimum in the surface that corresponds to the fully conducted proton configuration. It is likely that this barrier increase is related to the ability of surrounding water molecules to localize the proton position by stabilizing the positive charge that accompanies the proton. That is, when a number of peripheral water molecules are able to interact with a given water molecule along the main chain, there is a tendency for the migrating proton to associate with this water and remain there rather than continue along the chain to the ultimate acceptor. For this reason, the presence of auxiliary water molecules, or indeed any other groups that might interact with the conducting chain, should be considered as an important factor in the entire process. Moreover, the ease with which H-bonds might be broken and reformed, and the ensuing dynamic conversion of one configuration to another, ought to play an important role in the enzymatic control of the process, perhaps contributing to catalytic efficiency. In the same way that there is a certain degree of uncertainty about the precise distance between the proton donor and acceptor
Proton Conduction by a Chain of Water Molecules
J. Phys. Chem. B, Vol. 105, No. 27, 2001 6425 4. Conclusions
Figure 5. Configuration of the (NH3)3Zn2+‚‚OH2‚‚OH2‚‚OH2‚‚NH3 system, wherein the terminal N atom is placed at an angle θ from the indicated Zn- -O axis.
TABLE 5: Effect of Angular Orientation upon Structural and Energetic Aspects of Proton Transfer in the System Illustrated in Figure 5 with R(Zn‚‚‚N) Fixed at 10 Å
θ optimized 0° 20° 40° 60°
PT barrier, Zn-O1, Å O1‚‚‚O2, Å O2‚‚‚O3, Å O3‚‚‚N4, Å kcal/mol 2.009 1.992 2.009 2.004 1.999
2.553 2.502 2.549 2.573 2.589
2.738 2.682 2.739 2.732 2.851
3.322 3.553 3.310 3.452 3.507
8.3 7.8 8.4 11.0 15.6
groups in the enzyme, it is important to also understand how the relative orientations of these two groups might affect the proton conduction process. For this reason, a prototype system, containing a total of three water molecules, was set up as pictured in Figure 5. The target NH3 molecule was placed at each of several deviations θ from the Zn- -O1 axis between Zn and its bound water molecule, with the restriction of a fixed separation of 10 Å between Zn and N4. For each of these locations, the proton conduction was allowed to proceed from O1 to N4, as in the earlier cases, optimizing the remainder of the geometry in each case. The sensitivity of the conduction process to this relative orientation is reported in Table 5, and it shows that the barrier climbs as the NH3 acceptor is bent away from the Zn- -O1 axis, rising from 7.8 kcal/mol for a collinear arrangement up to 15.6 kcal/mol when θ ) 60°. An examination of the internuclear distances in Table 5 provides details about the varying strengths of the bonds. The distance between Zn and O1 is rather insensitive to the overall angle of the conduction chain. The elongating O1‚‚‚O2 distance, on the other hand, suggests this H-bond is progressively weakened as θ is increased. A similar effect is observed in the next H-bond, between waters 2 and 3, although the trend is temporarily arrested between 20° and 40°. Regarding the terminal H-bond that connects the waters to the terminal nitrogen, this bond length is shortest at intermediate angles and longer and presumably weaker at the extremes of θ. It is interesting to compare these trends with the data in the first row of Table 5 where there is no restriction imposed on θ, which is allowed to fluctuate under the single restraint of a fixed R(Zn‚‚‚N) distance of 10 Å. The barrier of 8.3 kcal/mol in this case, as well as the various H-bond lengths, is similar to what is seen when θ ) 20°. This result is consistent with the finding that an angle of 20° is approximately the optimal angle for the operation of this proton channel.
This work has focused on a chain of water molecules which might serve as a proton-conducting conduit connecting an NH3 molecule and a Zn2+ cation; the latter is surrounded by three NH3 molecules as model ligands. The calculations first addressed the case where the chain is three water molecules in length. The optimal configuration of this chain contains a number of fairly short interwater H-bond lengths, with R(O‚‚ O) on the order of 2.53 Å. The protons that act as bridges between these water molecules are clearly associated with one oxygen atom or the other, although the r(OH) bonds are significantly stretched when compared to those of an isolated water molecule. There are of course a host of different mechanisms by which the proton from the Zn-bound water molecule can move through the water chain and reach the ultimate proton-acceptor molecule. Some of these mechanisms would require the surmounting of a higher energy barrier than others. The most energetically accessible pathway is a concerted one of sorts, in that all three protons are simultaneously in flight from one molecule to the next. There is a proclivity for the entire process to be “driven” by the motion of the first proton from the Zn-bound water to the next in the chain, but the energetic cost of another proton initiating the process is a small one. The relaxation of the positions of all three water molecules that accompany the motion of the protons is an essential ingredient in that the energy barrier for this process is much higher when the water molecules are held stationary. The water molecules have a tendency to move toward one another, shortening the H-bond lengths, as the protons are being transferred. Another component in reducing the barrier is the freedom of the Zn ligands to change their distance from the central metal atom by a small amount during the process. On the question of the influence on this process of the precise number of water molecules in the chain, the calculations suggest that there is not a great sensitivity here and that the chain can easily contain as many as five water molecules, with no negative energetic implications for the process. Also investigated was the matter of peripheral H-bonds, between the waters of the chain and molecules that are not themselves part of the chain. Adding such extraneous H-bonds does seem to have a substantial effect upon the proton conduction process, raising the energy barrier and eventually quenching the process entirely. This inhibitory effect is likely due to the ability of these peripheral H-bonds to preferentially stabilize the configuration in which the excess proton has arrived at one particular water molecule and to prevent any further migration along the chain. In addition to considering the length of the chain of water molecules, calculations also addressed the angular aspects of such a chain. It was learned that the barrier to proton conduction climbs as the proton acceptor molecule is oriented further and further from the Zn- -O axis of the Zn-bound water. An optimal chain places the ultimate N-acceptor within about 0-30° of the latter axis. Acknowledgment. This work was supported by a grant from the COBASE program of the National Research Council. References and Notes (1) Notstrand, B.; Vaara, I.; Kannan, K. K. In The Isozymes; Markers, C. L., Ed.; Academic Press: New York, 1975; pp 575-599. (2) Steiner, H.; Jonsson, B. H.; Lindskog, S. Eur. J. Biochem. 1975, 59, 253. (3) Kumar, K.; King, R. W.; Carey, P. R. Biochemistry 1976, 15, 2195. (4) Poker, Y.; Bjorkquist, D. W. Biochemistry 1977, 16, 5698.
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