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  1. Author Response to Public Reviews

    We thank the reviewers for their careful reading of our work, and their detailed and helpful comments. Their insights have helped us in improving this manuscript. We include their comments and our replies to them below.

    Reviewer #2 (Public Review):

    Line 293, by "comparing the Apo_NE and IB_EQ simulations at equivalent points in time" and perform subtraction "from the corresponding Ca atom from one system to another at 0.05, 0.5, 1, 3, 5ns". It is not clear to me why those time points were chosen? Have authors attempted at validating whether or not the signal from the ligand-binding site has had enough time to propagate across the allosteric signaling pathway? If one considers that the ligand is a spatially localized signal, it requires time to propagate. This is in contrast with the Kubo-Onsager paper cited by authors in which the molecule is responding to a global perturbation such as an external field. However, a local perturbation on one side of the protein will need time to propagate to the other side of the protein (30 angstroms away in this case).

    The time points are chosen to highlight the propagation of signal in the short nonequilibrium simulations. We agree with the reviewer that the signal will take time to propagate; indeed, it evolves over time, as can be seen in the figures and accompanying movies. It is important to emphasise that this is averaged over many trajectories. Some conformational rearrangements will not be fully sampled, as can be seen in Figure 3–Figure supplement 3. It is important to emphasize that the short nonequilibrium simulations are used here to measure the immediate structural response towards a perturbation. The timescale of this response in the nonequilibrium simulation does not correspond to the physical timescale of conformational change induced by/associate with ligand binding. The perturbation here is nonphysical, and the response is rapid. For long simulation times, and as the correlation between the equilibrium and nonequilibrium trajectories is lost, the subtraction technique is no longer useful as the noise arising from the natural divergence of the simulations overcomes the structural response of the system to the perturbation. Thus, this method allows for the identification of the initial conformational changes associated with signal propagation. Also, the difference calculated at any given time point should not be seen in isolation. Instead, it should be compared with the other time points, as it is such a comparison that highlights the cascade of events associated with signal propagation. This is clearly illustrated in Figure 3 supplement 3 and in the movies, where the collective signal from the short nonequilibrium simulations is progressing in a trend that is comparable with the equilibrium simulations. The time evolution of the signal is striking and thought-provoking.

    A simple and naive example is to map out all the bus stops on one's route. 800 simulations between the first and second stop will not be able to provide the locations of other stops. Since authors have used this "subtraction technique" on several other proteins, it would be nice to clarify how this approach works on mapping out signaling propagation perturbed by local ligand binding/unbinding and how to choose the time points for subtraction.

    Analogies can be helpful in understanding the nonequilibrium simulations, some aspects of which are not immediately obvious. One could perhaps think of these nonequilibrium simulations as analogous to striking a bell to see how it rings. The bus stop analogy suggested by the referee is intriguing, and we develop it here.

    In this case, when ‘getting on the bus’ (beginning the simulation), we do not know where the bus is going (i.e. we only knew that we were starting at the allosteric site, so the only thing that we know is the place where we board the bus) or the route it would take to get there. The bus is not travelling on a straight road, and the destination is unknown. We could wend our way slowly by standard equilibrium MD, but we would only reach the first or second stop on the route in the time available, and we would still not know where the bus was going. We would never find out where the bus is going: it takes too long. The nonequilibrium approach is a magic bus! In this approach, as the bus meanders close to its starting point, we suddenly replace the driver. The new driver puts her or his foot on the accelerator and immediate sets off for a new destination, heading away fast from the starting point. The driver is guided by the roads available. The bus can only drive on the road network, i.e. its progress is defined by its physical environment and the available directions of travel. So, while she/he may drive at an unsafe speed, the bus should stay on the road. It’s possible that it will take a short cut or indeed take a wrong turn or enter a dead-end street. But overall, doing this ‘driver replacement’ hundreds of times, on average the bus should follow the right route and go much faster along it. So, it might be a terrifying journey,but we should get to the destination faster! It might not reach the final destination, depending how long we let it go on, but we should pass several of the bus stops along the correct route. We can test how likely the route is by averaging over hundreds of crazy new bus drivers. A well-defined route implies a well designed network. The bus can take any of the roads available to it on the network, and the route taken by the bus may be unpredictable (if it was obvious, we would not need all these crazy drivers!). In other words, the response to a perturbation is non-linear. In terms of the final destination, specifically here in TEM-1 and KPC-2,the omega loop, the 3-4 loop, the hinge region are known to be involved in substrate binding and catalysis. We observe the signal reaching these structural elements, so we can say with confidence that the perturbation is communicated to distant, catalytically important parts of the enzyme. So, in terms of the bus analogy, we show that starting in the distant hills, the crazy bus drivers actually end up in the capital city. The simulations identify the capital city as the actual destination. And the fact that the crazy drivers tend to follow the same route allows us to say that we have identified the bus route to the capital, and the important points along the route.

    Another question is whether tracing the dynamics of Calpha alone is enough. As we have seen from the network analysis papers, Calpha sometimes missed some paths or could overemphasize others. The Center of the mass of residue has been proposed to be a better indicator of protein allostery. Authors may wish to clarify the particular choice of Calpah in this study.

    This is an interesting question. We have found in our previous analyses of nicotinic acetylcholine receptors and other systems that analysing the C-alphas allows the identification of pathways of signal transduction in nicotinic acetylcholine receptors (Oliveira et al. Structure 1171-1183. e3 (2019)) and went on to show that these pathways were common across different receptor subtypes (J. Am. Chem. Soc. 2019, 141, 51, 19953–19958 (2019)). Obviously, all residues in the protein are represented equally when analysing C-alphas. Thus, analysing the C-alphas allows direct comparison of closely related proteins with different sequences, and identification and analysis of the pathway in the framework of the protein backbone. Here, of course, we are interested in whether these C-alpha pathways identify positions of sequence variation that affect function, and the results indicate that indeed they do. There is also the practical advantage of analysing C-alpha behaviour that their motions are less subject to noise and converge more rapidly than e.g. analysing sidechains. Other features could be chosen to trace signal pathways, such as the centre of mass of residues. However, choosing more flexible parts to track signal propagation would also have an impact on speed of convergence (i.e. number of trajectories required): more simulations would be required to achieve convergence. Therefore, as in previous work on other proteins, we chose C-alpha atoms to study signal propagation here.

    The order of events associated with signal propagation is computed by directly comparing the positions of individual C-alpha atoms at equivalent points in time (namely after 0, 50, 500, 1000, 3000 and 5000 ps of simulation) for every pair of unperturbed equilibrium ligand-bound and perturbed nonequilibrium apo simulation. The C-alpha positional deviation is a simple way to directly identify the conformational changes induced by ligand annihilation and their evolution over the 5 ns of simulation. Due to statistics collected over the large number of simulations, we can be sure of the statistical significance of the structural changes identified. The conformational changes extracted from the nonequilibrium simulations reflect the (statistically significant) structural response of the system to the perturbation. These changes propagate over time from the allosteric site to the active site, demonstrating a direct connection between them. Due to the very short timescale of the nonequilibrium simulations (5 ns), the observed conformational rearrangements do not represent the complete mechanism of conformational change, but rather reflect its first steps.

    In Figure 5, the authors seem to use Pearson correlation to compute dynamic cross-correlation maps. Mutual information (M)I or linear MI have advantages over Pearson correlations, as has been discussed in the dynamical network analysis literature.

    The reviewer is indeed correct; the DCCMs were calculated based on the Pearson’s correlation. We have tested and validated this approach over the last 15 years, with results reproduced experimentally by a number of our collaborators for over 10 different enzyme systems, including cyclophilin A, dihydrofolate reductase, ribonuclease, APE1 and Rev1 DNA binding enzymes (Biochemistry 43, no. 33 (2004): 10605-10618; Nature 438, no. 7064 (2005): 117-121; Biochemistry 58, no. 37 (2019): 3861-3868; PLoS Biol 9, no. 11 (2011): e1001193; Structure 26, no. 3 (2018): 426-436; Nucleic acids research 48, no. 13 (2020): 7345-7355; Proceedings of the National Academy of Sciences 117, no. 41 (2020): 25494-25504). The reviewer’s suggestion is an interesting one, and we would be happy to investigate it in future studies. Mutual information analyses offer useful features. Based on our experience, we expect the results to be qualitatively similar and not likely to change the conclusions described in this manuscript.

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  2. Reviewer #3 (Public Review):

    In the manuscript entitled "Allosteric communication in Class A 1 b-lactamases occurs via cooperative 2 coupling of loop dynamics", Galdadas et al. aim to use a combination of nonequilibrium and equilibrium molecular dynamics simulations to identify allosteric effects and communication pathways in TEM-1 and KPC-2. They claimed that their simulations revealed pathways of communication where the propagation of signal occurs through cooperative coupling of loop dynamics. This study is highly relevant to the field as allosteric regulation is believed to be a major signal transduction pathway in several drug-targeted proteins. A better understanding of these regulations could increase the efficacy and specificity of drugs.

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  3. Reviewer #2 (Public Review):

    This manuscript by Galdadas et. al. used a combination of equilibrium and non-equilibrium simulations to investigate the allosteric signaling propagation pathway in two class-A beta-lactamases, TEM-1 and KPC2, from allosteric ligand binding sites. The authors performed extensive analysis and comparison of the simulated protein allostery pathway with know mutations in the literature. The results are rigorously analyzed and neatly presented in all figures. The conclusions of this paper are mostly supported by previous mutational data, but a few aspects of simulation protocol and data analysis need to be validated or justified.

    Line 293, by "comparing the Apo_NE and IB_EQ simulations at equivalent points in time" and perform subtraction "from the corresponding Ca atom from one system to another at 0.05, 0.5, 1, 3, 5ns". It is not clear to me why those time points were chosen? Have authors attempted at validating whether or not the signal from the ligand-binding site has had enough time to propagate across the allosteric signaling pathway? If one considers that the ligand is a spatially localized signal, it requires time to propagate. This is in contrast with the Kubo-Onsager paper cited by authors in which the molecule is responding to a global perturbation such as an external field. However, a local perturbation on one side of the protein will need time to propagate to the other side of the protein (30 angstroms away in this case). A simple and naive example is to map out all the bus stops on one's route. 800 simulations between the first and second stop will not be able to provide the locations of other stops. Since authors have used this "subtraction technique" on several other proteins, it would be nice to clarify how this approach works on mapping out signaling propagation perturbed by local ligand binding/unbinding and how to choose the time points for subtraction.

    Another question is whether tracing the dynamics of Calpha alone is enough. As we have seen from the network analysis papers, Calpha sometimes missed some paths or could overemphasize others. The Center of the mass of residue has been proposed to be a better indicator of protein allostery. Authors may wish to clarify the particular choice of Calpah in this study.

    In Figure5, the authors seem to use Pearson correlation to compute dynamic cross-correlation maps. Mutual information (M)I or linear MI have advantages over Pearson correlations, as has been discussed in the dynamical network analysis literature.

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  4. Reviewer #1 (Public Review):

    Galdadas et al. applied a combinatorial approach of equilibrium and nonequilibrium molecular dynamics methods to study two important members of the Class A β-lactamase enzyme family in detail. Authors carefully chose two representative enzymes from this family, TEM-1 and KPC-2 in this study. Understanding of the nature of the communication pathways between allosteric ligand binding site and the active site has been the main focus of this study. Another very interesting finding of this study was the position of clinical variants that was precisely mapped along the allosteric communication pathway. This approach certainly has broad utility as it can be applied to study long-range communications in enzymes that are triggered by binding of a ligand (drug candidate) to an alternative/remote site, and also in cases where certain mutations occur far away from the active site but lead to drug resistance.

    Overall, the manuscript is well written, and the conclusions are mostly well supported by data.

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  5. Evaluation Summary:

    This manuscript presents a computational study aiming to understand the allosteric signaling propagation pathway in two class-A beta-lactamases. The results of this study will be of interest to the readers in the fields of beta-lactamase, antibiotic resistance, and enzyme allostery.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewers #1, #2, and #3 agreed to share their names with the authors.)

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