Author response:
Reviewer 1:
(1) Free energy barriers appear to be very high for a substrate transport process. In Figure 3, the transitions from IF (Inward facing) to OF (Outward facing) state appear to have a barrier of 12 kcal/mol. Other systems with mutant or sodium unbound have even higher barriers. This does not seem consistent with previous studies where transport mechanisms of transporters have been explored using molecular dynamics.
First, in Figure 3, the transition from IF to OF state doesn’t have a barrier of 12 kcal/mol. The IFF to OFB transition is almost barrierless, and from OFB to OFF is ~5 kcal/mol, which is also evident in Figure 2.
If the reviewer was referring to the transition from OFB to IFB states, the barrier is 6.8 kcal/mol (Na+ bound state), and the rate-limiting barrier in the entire sugar transport process (Na+ bound state) is 8.4 kcal/mol, as indicated in Figure 2 and Table 1, which is much lower than the 12 kcal/mol barrier the reviewer mentioned. When the Na+ is unbound, the barrier can be as high as 12 kcal/mol, but it is this high barrier that leads to our conclusion that the Na+ binding is essential for sugar transport, and the 12 kcal/mol barrier indicates an energetically unfavorable sugar translocation process when the Na+ is unbound, which is unlikely to be the major translocation process in nature.
Even for the 12 kcal/mol barrier reported for the Na+ unbound state, it is still not too high considering the experimentally measured MelB sugar active transport rate, which is estimated to be on the order of 10 to 100 s-1. This range of transport rate is typical for similar MFS transporters such as the lactose permease (LacY), which has an active transport rate of 20 s-1. The free energy barrier associated with the active transport is thus on the order of ~15-16 kcal/mol based on transition state theory assuming kBT/h as the prefactor. This experimentally estimated barrier is higher than all of our calculated barriers. Our calculated barrier for the sugar translocation with Na+ bound is 8.4 kcal/mol, which means an additional ~7-8 kcal/mol barrier is contributed by the Na+ release process after sugar release in the IFF state. This is a reasonable estimation of the Na+ unbinding barrier.
Therefore, whether the calculated barrier is too high depends on the experimental kinetics measurements, which are often challenging to perform. Based on the existing experimental data, the MFS transporters are
usually relatively slow in their active transport cycle. The calculated barrier thus falls within the reasonable range considering the experimentally measured active transport rates.
(2) Figure 2b: The PMF between images 20-30 shows the conformation change from OF to IF, where the occluded (OC) state is the highest barrier for transition. However, OC state is usually a stable conformation and should be in a local minimum. There should be free energy barriers between OF and OC and in between OC and IF.
First, the occluded state (OCB) is not between images 20-30, it is between images 10 to 20. Second, there is no solid evidence that the OCB state is a stable conformation and a local minimum. Existing experimental structures of MFS transporters seldom have the fully occluded state resolved.
(3) String method pathway is usually not the only transport pathway and alternate lower energy pathways should be explored. The free energy surface looks like it has not deviated from the string pathway. Longer simulations can help in the exploration of lower free energy pathways.
We agree with the reviewer that the string method pathway is usually not the only transport pathway and alternate lower energy pathways could exist. However, we also note that even if the fully occluded state is a local minimum and our free energy pathway does visit this missing local minimum after improved sampling, the overall free energy barrier will not be lowered from our current calculated value. This is because the current rate-limiting barrier arises from the transition from the OFB state to the IFF state, and the barrier top corresponds to the sugar molecule passing through the most constricted region in the cytoplasmic region, i.e., the IFC intermediate state visited after the IFB state is reached. Therefore, the free energy difference between the OFB state and the IFC state will not be changed by another hypothetical local minimum between the OFB and IFB states, i.e., the occluded OCB state. In other words, a hypothetical local minimum corresponding to the occluded state, even if it exists, will not decrease the overall rate-limiting barrier and may even increase it further, depending on the depth of the local minimum and the additional barriers of entering and escaping from this new minimum.
(4) The conformational change in transporters from OF to IF state is a complicated multi-step process. First, only 10 images in the string pathway are used to capture the transition from OF to IF state. I am not sure is this number is enough to capture the process. Second, the authors have used geodesic interpolation algorithm to generate the intermediate images. However, looking at Figure 3B, it looks like the transition pathway has not captured the occluded (OC) conformation, where the transport tunnel is closed at both the ends. Transporters typically follow a stepwise conformational change mechanism where OF state transitions to OC and then to IF state. It appears that the interpolation algorithm has created a hourglasslike state, where IF gates are opening and OF gates are closing simultaneously thereby creating a state where the transport tunnel is open on both sides of the membrane. These states are usually associated with high energy. References 30-42 cited in the manuscript reveal a distinct OC state for different transporters.
In our simulations, even with 10 initial images representing the OF to IF conformational transition, the occluded state is sampled in the final string pathway. There is an ensemble of snapshots where the extracellular and intracellular gates are both relatively narrower than the OF and IF states, preventing the sugar from leaking into either side of the bulk solution. In contrast to the reviewer’s guess, we never observed an hourglass-like state in our simulation where both gates are open. Figure 3B is a visual representation of the backbone structure of the OCB state without explicitly showing the actual radius of the gating region, which also depends on the side chain conformations. Thus, Figure 3B alone cannot be used to conclude that we are dominantly sampling an hourglass-like intermediate conformation instead of the occluded state, as mentioned by the reviewer.
Moreover, not all references in 30-42 have sampled the occluded state since many of them did not even simulate the substrate translocation process at all. For the ones that did sample substrate translocation processes, only two of them were studying the cation-coupled MFS family symporter (ref 38, 40) and they didn’t provide the PMF for the entire translocation process. There is no strong evidence for a stable minimum corresponding to a fully occluded state in these two studies. In fact, different types of transporters with different coupling cations may exhibit different stability of the fully occluded state. For example, the fully occluded state has been experimentally observed for some MFS transporters, such as multidrug transporter EmrD, but not for others, such as lactose permease LacY. Thus, it is not generally true that a stable, fully-occluded state exists in all transporters, and it highly depends on the specific type of transporter and the coupling ion under study.
Reviewer 2:
The manuscript by Liang and Guan provides an impressive attempt to characterize the conformational free energy landscape of a melibiose permease (MelB), a symporter member of major facilitator superfamily (MFS) of transporters. Although similar studies have been conducted previously for other members of MFS, each member or subfamily has its own unique features that make the employment of such methods quite challenging. While the methodology is indeed impressive, characterizing the coupling between large-scale conformational changes and substrate binding in membrane transporters is quite challenging and requires a sophisticated methodology. The conclusions obtained from the three sets of path-optimization and free energy calculations done by the authors are generally supported by the provided data and certainly add to our understanding of how sodium binding facilitates the transport of melibiose in MelB. However, the data is not generated reliably which questions the relevance of the conclusions as well. I particularly have some concerns regarding the implementation of the methodology that I will discuss below.
(1) In enhanced sampling techniques, often much attention is given to the sampling algorithm. Although the sampling algorithm is quite important and this manuscript has chosen an excellent pair: string method with swarms of trajectories (SMwST) and replica-exchange umbrella sampling (REUS) for this task, there are other important factors that must be taken into account. More specifically, the collective variables used and the preparation of initial conformations for sampling. I have objectives for both of these (particularly the latter) that I detail below. Overall, I am not confident that the free energy profiles generated (summarized in Figure 5) are reliable, and unfortunately, much of the data presented in this manuscript heavily relies on these free energy profiles.
Since comments (1) and (2) from this review are related, please see our response to (2) below.
(2) The authors state that they have had an advantage over other similar studies in that they had two endpoints of the string to work from experimental data. I agree that this is an advantage. However, this could lead to some dangerous flaws in the methodology if not appropriately taken into account. Proteins such as membrane transporters have many slow degrees of freedom that can be fully captured within tens of nanoseconds (90 ns was the simulation time used here for the REUS). Biased sampling allows us to overcome this challenge to some extent, but it is virtually impossible to take into account all slow degrees of freedom in the enhanced sampling protocol (e.g., the collective variables used here do not represent anything related to sidechain dynamics). Therefore, if one mixes initial conformations that form different initial structures (e.g., an OF state and an IF state from two different PDB files), it is very likely that despite all equilibration and relaxation during SMwST and REUS simulations, the conformations that come from different sources never truly mix. This is dangerous in that it is quite difficult to detect such inconsistencies and from a theoretical point of view it makes the free energy calculations impossible. Methods such as WHAM and its various offshoots all rely on overlap between neighboring windows to calculate the free energy difference between two windows and the overlap should be in all dimensions and not just the ones that we use for biasing. This is related to well-known issues such as hidden barriers and metastability. If one uses two different structures to generate the initial conformations, then the authors need to show their sampling has been long enough to allow the two sets of conformations to mix and overlap in all dimensions, which is a difficult task to do.
We partly agree with the reviewer in that it is challenging to investigate whether the structures generated from the two different initial structures are sufficiently mixed in terms of orthogonal degrees of freedom outside the CV space during our string method and REUS simulations. We acknowledge that our simulations are within 100 ns for each REUS window, and there could be some slow degrees of freedom that are not fully sampled within this timescale. However, the conjectures and concerns raised by the reviewer are somewhat subjective in that they are almost impossible to be completely disproven. In a sense, these concerns are essentially the same as the general suspicion that the biomolecular simulation results are not completely converged, which cannot be fully ruled out for relatively complex biomolecular systems in any computational study involving MD simulations. We also note that comparison among the PMFs of different cation bound/unbound states will have some error cancellation effects because of the consistent use of the same sampling methods for all three systems. Our main conclusions regarding the cooperative binding and transport of the two substrates lie in such comparison of the PMFs and additionally on the unbiased MD simulations. Thus, although there could be insufficient sampling, our key conclusions based on the relative comparison between the PMFs are more robust and less likely to suffer from insufficient sampling.
(3) I also have concerns regarding the choice of collective variables. The authors have split the residues in each transmembrane helix into the cyto- and periplasmic sides. Then they have calculated the mass center distance between the cytoplasmic sides of certain pairs of helices and have also done the same for the periplasmic side. Given the shape of a helix, this does not seem to be an ideal choice since rather than the rotational motion of the helix, this captures more the translational motion of the helix. However, the transmembrane helices are more likely to undergo rotational motion than the translational one.
Our choice of CVs not only captures the translational motion but also the rotational motion of the helix. Consider a pair of helices. If there is a relative rotation in the angle between the two helices, causing the extracellular halves of the two helices to get closer and the intracellular halves to be more separated, this rotational motion can be captured as the decrease of one CV describing the extracellular distance and increase in the other CV describing the intracellular distance between the two helices. Reversely, if one of the two CVs is forced to increase and the other one forced to decrease, it can, in principle, bias the relative rotation of the two helices with respect to each other. Indeed, comparing Figure 3 with Figure S4, the reorientation of the helices with respect to the membrane normal (Fig. S4) is accompanied by the simultaneous decrease and increase in the pairwise distances between different segments of the helices. Therefore, our choice of CVs in the string method and REUS are not biased against the rotation of the helices, as the reviewer assumed.
(4) Convergence: String method convergence data does not show strong evidence for convergence (Figure S2) in my opinion. REUS convergence is also not discussed. No information is provided on the exchange rate or overlap between the windows.
The convergence of string method, REUS, the exchange rate and overlap between windows will be discussed in the reviewed manuscript.
Reviewer 3:
The paper from Liang and Guan details the calculation of the potential mean force for the transition between two key states of the melibiose (Mel) transporter MelB. The authors used the string method along with replica-exchange umbrella sampling to model the transition between the outward and inwardfacing Mel-free states, including the binding and subsequent release of Mel. They find a barrier of ~6.8 kcal/mol and an overall free-energy difference of ~6.4 kcal/mol. They also investigate the same process without the co-transported Na+, finding a higher barrier, while in the D59C mutant, the barrier is nearly eliminated.
For Na+ bound state, the rate-limiting barrier is 8.4 kcal/mol instead of 6.8 kcal/mol. The overall free energy difference is 3.7 kcal/mol instead of 6.4 kcal/mol. These numbers need to be corrected in the public review.
I found this to be an interesting and technically competent paper. I was disappointed actually to see that the authors didn't try to complete the cycle. I realize this is beyond the scope of the study as presented.
We agree with the reviewer that characterizing the complete cycle is our eventual goal. However, in order to characterize the complete cycle of the transporter, the free energy landscapes of the Na+ binding and unbinding process in the sugar-bound and unbound states, as well as the OF to IF conformational transition in the apo state. These additional calculations are expensive, and the amount of work devoted to these new calculations is estimated to be at least the same as the current study. Therefore, we prefer to carry out and analyze these new simulations in a future study.
The results are in qualitative agreement with expectations from experiments. Could the authors try to make this comparison more quantitative? For example, by determining the diffusivity along the path, the authors could estimate transition rates.
In our revised manuscript, we will determine the diffusivity along the path and estimate transition rates.
Relatedly, could the authors comment on how typical concentration gradients of Mel and Na+ would affect these numbers?
The concentration gradient of Mel and Na+ can be varied in different experimental setups. In a typical active transport essay, the Na+ has a higher concentration outside the cell, and the melibiose has a higher concentration inside the cell. In the steady state, depending on the experiment setup, the extracellular Na+ concentration is in the range of 10-20 mM, and the intracellular concentration is self-balanced in the range of 3-4 mM due to the presence of other ion channels and pumps. In addition to the Na+ concentration gradient, there is also a transmembrane voltage potential of -200 mV (the intracellular side being more negative than the extracellular side), which facilitates the Na+ release into the intracellular side. In the steady state, the extracellular concentration of melibiose is ~0.4 mM, and the intracellular concentration is at least 1000 times the extracellular concentration, greater than 0.4 M. In this scenario, the free energy change of intracellular melibiose translocation will be increased by about ~5 kcal/mol at 300K temperature, leading to a total ∆𝐺 of ~8 kcal/mol. The total barrier for the melibiose translocation is expected to be increased by less than 5 kcal/mol. However, the increase in ∆𝐺 for intracellular melibiose translocation will be compensated by a decrease in ∆𝐺 of similar magnitude ( ~5 kcal/mol) for intracellular Na+ translocation. In a typical sugar self-exchange essay, there is no net gradient in the melibiose or Na+ across the membrane, and the overall free energy changes we calculated apply to this situation.
