This work explored the molecular meaning of pKapp of E286 and provided a structure-based analysis of the effect of the N139D mutation on this pKa. The analysis of the apparent pKa involved a novel cycle that considers the conformational dependence of the pKa of E286 and relates it to the corresponding free energy of the conformational transition. Our analysis provides results that are simultaneously consistent with structure-based pKa calculations and with the PMF of the E286 conformational changes, both for the native and N139D mutant CcOs. Interestingly, the phenomenologically derived equilibrium constant for the conformational changes (needed to obtain the pKapp value), were found to be in a reasonable agreement with the corresponding results obtained using the PMF calculations. We are not aware of any previous study that has exploited the observed structural changes upon mutations in this way.
It is useful to note that a related pKa cycle has been considered in, however, that study did not consider the difference in PT rates for each structure, nor the relationship between the pKas of the two conformations and the pKapp. Furthermore, the treatment in Ref. involved basically hypothetical pKas rather than the pKas calculated using the structure of the given system.
The present work provides new insights into the nature of the effects of mutations in the D pathway and in particular the N139D mutant CcO. That is, our study reproduced an appreciable increase in the barrier of PT to Prd (but still not much larger than our error range) and a decrease in the barrier for PT to B−. This finding presents an interesting dilemma: one feasible, but unlikely possibility is that Prd is not the primary proton acceptor. In case the rate for PT to Prd is unchanged then the reduction in the barrier for PT to B− is the most likely reason for the inability of N139D to pump. In this case, we must also account for the fact that the overall rate for protonating B− does not increase with the mutation. In order to account for this observation and still accepting the calculated reduction in the barrier for PT from Glu286 to B−, we need to consider the possibility that the barrier for a direct transfer from Glu286 to B− is reduced in the mutant, but it required us to considerably suppress the last step in our kinetic scheme (X→X′). Still, the idea of a barrier to B− being reduced in the mutant seems to be supported by one observed fact, namely the lower free energy cost for rotating E286 in the mutant (which is established by the availability of the two observed conformations, which are absent in the wt CcO). The finding that the availability of a rotated configuration of E286 appears to help in reducing the barrier is fully consistent with our previous study, where it was found that having a water chain is not so advantageous and that (in contrast to the belief of some) the PT rate is faster when we have as little water molecules as possible between the donor and acceptor. This, of course, depends on the probability that the donor and acceptor are at a close distance.
The present analysis of the effect of the N139D mutant CcO provides a more consistent picture than that obtained in our previous studies. That is, the study of was based on the assumption that the electron transfer step is on the same time range as that of the PT, which seems now unlikely. Our subsequent electrostatic calculations have rationalized the mutational effect in terms of the change of the effective electrostatic interaction with the transferred proton in both paths. This trend is reproduced in a much more quantitative way in the present work, where the free energy of the transferred proton is modified due to the change in the local electrostatic energy, the PMF of moving the group involved and to some extent by the long range interaction with D139 (see discussion in section 6).
As clarified in our previous work it is very hard to get convergent results for the electrostatic energy of the different states by microscopic simulations. This is the reason for our use of the PDLD/S-LRA model. Although our semi-macroscopic calculations are based on many years of validations, the situation in the intirior of CcO is very complex and may involve some traps (in particular the identity of the pump site). Here, we do know the pKapp of E286 but it is harder to obtain unique results from activation barriers. In this respect, focusing on the barrier for PTR from E286 to B− in the N139D mutant (where we are confident that we are dealing with this specific barrier) offers a unique opportunity to validate the PDLD/S-LRA (EVB) calculations.
It is important to mention other attempts to rationalize the effect of mutations in the D pathway. Significant attention has been placed on the idea of delocalization of the proton (e.g.) in the D pathway. While delocalization effects are interesting and potentially important, it has been demonstrated that the activation barriers for biological PT are determined by the corresponding electrostatic profiles. In fact, even in bacteriorhodopsin, where the effort in studies of a delocalized proton has been quite successful, there is no correlation between the traps of the proton and the overall barrier for PT in the rate-limiting steps (see). In our case this is probably the situation as long as the transfer through the D pathway is not rate limiting. Interestingly, even in cases of mutant studies (e.g. Y33H) where this transfer is rate limiting, the rate is probably determined by the highest point on the energy profile and not the depth of the minima.
The work of Ref. and the much more sophisticated subsequent work of Ref. suggested that E286 serves as a valve where the rotations of the type considered here play a major role in preventing leaks and in supporting proton pumping. Although this is an appealing idea, it seems to us that as long as the barriers for rotation are small relative to the other barriers it is hard to use this element as a valve, since it is likely that the system will be able to relax to the lowest energy state of E286. In this case it may be useful to simulate the kinetics by the approach used here and to explore the resulting populations.
The considerations of the possible role of low barriers and possible conflicts with microscopic reversibility should address concerns of those who are not familiar with the power of quasi-equilibrium treatments and the ability to assess the kinetics of the system once the relaxation times are relatively clear. More specifically, if we have two states (say proton on Prd and proton on E286) we can estimate the barrier for a process that occurs at about milliseconds ignoring processes that would occur at much longer time scales (e.g. protein unfolding) and safely assume that the forward and backward rates are fully determined by the free energy barriers evaluated by considering all the configurations available in the millisecond time scale. This is related to our considerations of the time dependence of the energetics of proton transfer in bacterial reaction center, where we know the rate of change in the energy of the charge-separated state between picoseconds to nanoseconds and they would be relevant for processes that occurs as long as the back reaction is within the nanosecond range. That is, after the initial relaxation from the P* to The P+H- state (see) if we look for the competition between the forward rate (electron transfer to the quinone) and the back reaction after a nanosecond we can use the energy of the relaxed (P+H- state). Overall perhaps the best current way for handling the relaxation and quasi-equilibrium problem is to use a time dependent dielectric constant as in the approach proposed by us. Using this approach with any reasonable set of dielectric relaxation times it is very hard to construct a model that would support a time dependant gate, which does not involve a formation of another state. In other words, possible proposals of water rearrangement that would block the back reaction are likely to violate quasi-equilibrium conditions.
The above comments are also relevant to the results described in Ref., where it was assumed that the changes of the PT barrier in the D pathway can affect the pumping and explain the effect of the N139 mutation. In the case of the mutations where the reprotonation of E286 is significantly faster than the other steps (see ), the barriers in the D pathway are not relevant (this is even more true if one only considers the energetics of the unprotonated water molecules as was done in ref).
The present work places significant emphasis on quantifying the role of the rotation of E286. Related efforts have been made in Refs. (see the discussion above). Here we would like to point out that while this rotation is important, the rotational barrier obtained by current calculations is too low to provide a gate under any quasi-equilibrium considerations. Stable gates and valves probably require features of the type reproduced in and considered in).
In view of the rather long discussion above, we would like to emphasize that the main unique point of the current work is in using structural information and calculations of the relevant activation barriers to explore the effect of mutations on proton pumping by CcO. Doing so provides interesting insights and allows one to fully exploit the available structural information.