Allosteric mechanism of signal transduction in the two-component system histidine kinase PhoQ

  1. Bruk Mensa
  2. Nicholas F Polizzi
  3. Kathleen S Molnar
  4. Andrew M Natale
  5. Thomas Lemmin
  6. William F DeGrado

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    Evaluation Summary:

    This paper will be of interest to scientists who think about mechanisms of conformational signaling within transmembrane receptor proteins. It describes a model of signaling by allosteric coupling between individual domains rather than by a concerted conformational change and provides substantial experimental evidence for the model from characterization of over 30 mutational substitutions in the bacterial two-component sensor protein PhoQ. The allosteric coupling model provides a way to understand many diverse observations about signaling by two-component receptors and has the potential to be relevant to conformational signaling by many other transmembrane receptors.

    (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. The reviewers remained anonymous to the authors.)

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Abstract

Transmembrane signaling proteins couple extracytosolic sensors to cytosolic effectors. Here, we examine how binding of Mg 2+ to the sensor domain of an E. coli two component histidine kinase (HK), PhoQ, modulates its cytoplasmic kinase domain. We use cysteine-crosslinking and reporter-gene assays to simultaneously and independently probe the signaling state of PhoQ’s sensor and autokinase domains in a set of over 30 mutants. Strikingly, conservative single-site mutations distant from the sensor or catalytic site strongly influence PhoQ’s ligand-sensitivity as well as the magnitude and direction of the signal. Data from 35 mutants are explained by a semi-empirical three-domain model in which the sensor, intervening HAMP, and catalytic domains can adopt kinase-promoting or inhibiting conformations that are in allosteric communication. The catalytic and sensor domains intrinsically favor a constitutively ‘kinase-on’ conformation, while the HAMP domain favors the ‘off’ state; when coupled, they create a bistable system responsive to physiological concentrations of Mg 2+ . Mutations alter signaling by locally modulating domain intrinsic equilibrium constants and interdomain couplings. Our model suggests signals transmit via interdomain allostery rather than propagation of a single concerted conformational change, explaining the diversity of signaling structural transitions observed in individual HK domains.

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  1. Version published to 10.7554/elife.73336 on eLife
  2. eLife

    Author Response:

    Reviewer #1 (Public Review):

    Previous studies have provided crystallographic snapshots of the autokinase domains of several sensor histidine kinases (HK) involved in signal transduction in bacteria. Nevertheless, the lack of a full-length structure of these HK hampered the understanding of the molecular mechanism of signaling. Moreover, how a stimuli perceived by the membrane-bound sensor domain is transmitted to the catalytic cytoplasmic domain of an HK, to modulate its activity is poorly understood. To probe the coupling between the sensor and autokinase domains Mensa et al. used cysteine cross linking and reporter gene assay to probe the signaling state of E. coli PhoQ in a set of several point mutations. Using these data they developed a 3-domain model in which the sensor, HAMP and catalytic domain are in allosteric communication to interconvert the kinase state in an "on" or "off" conformation. The authors conclude that signals transmit to the catalytic domain through intradomain allosteric transitions, rather than through a concerted conformational change.

    This work represents an important and novel attempt to understand the mechanism of signal transduction by sensor kinases in two-component systems. This contribution challenges the concept that signal transmit via propagation of single concerted conformational changes of the sensor kinase. The authors, instead, propose that signal is transmitted by the sensor via an interdomain allosteric mechanism.

    The way in that the paper is presented appears to be directed to enzymologist working in enzyme kinetics models, rather than to a wide audience. For example, the paper starts saying that "Fully cooperative two-state models are unable to explain the gamut of activities of mutants". This affirmation seems too abrupt without defining what kind of model they are talking about. Is a molecular model, a kinetic model or a thermodynamic model? They should explain these concepts before to show the results. After we start to read it seems clear that they propose a thermodynamic model to explain the coupling of the different domains.

    We have consolidated writing on modeling to the latter half of the manuscript. The introduction to this section now clearly states that we are exploring several thermodynamic allosteric coupling models.

    For an enzymologist should be quite worrying to interpret data of activity assays with gene reporters without knowing the answers to the following: Do the mutations affect the PhoQ protein levels in cells? How accurate are the Western blots to quantify dimer formation in Y60C and establish the kinase "on" or kinase "off" states of PhoQ? The error bar of the of crosslinking experiments, shown in the different Figs, seems quite small for a Western blot quantification. Nevertheless, in Figure 8-figure supplement 2 panel, in the mutant I221F is obtained a poor fit which is not taken into account. Is it because the error is dismissed? Same for panels A and D. Is missing something the proposed model?

    We have included Figure 2-figure supplement 1, which gives examples of crosslinking western blots and quantification (also “ Figure 2-figure supplement 1 - Source data 1”). These western blots also allow for the evaluation of total protein expression. In our model fitting, each individual replicate experiment was treated separately to give data with more replicates increased statistical weight as discussed in Results and Methods. The I221F mutation was measured in a single experiment. We also have conducted the assays under conditions where the concentration is approximately linear with respect to receptor occupancy as discussed previously by Goulian et al (ref 41).

    Reviewer #2 (Public Review):

    This manuscript characterized the effects of 35 mutational substitutions in three domains the bacterial transmembrane two-component sensor protein for Mg2+, PhoQ, on the signaling state of the periplasmic sensor domain and the cytoplasmic histidine kinase domain. Signaling state was assayed by a diagnostic cysteine cross-link for the sensor domain and the expression of a coupled beta-galactosidase reporter for the kinase domain. The results of those characterizations were used to develop an allosteric coupling model of conformational signaling from sensor domain to kinase domain, with a key role played by the HAMP domain that connects sensor to kinase. Single-site mutational substitutions were at positions expected to be in the interior of the protein structure in the periplasmic, HAMP and the S-helix regions of the protein as well as at boundaries of transmembrane segments. In addition, the connections between the second transmembrane helix and the HAMP domain, and between the HAMP domain and the S-helix were disrupted by introduction of a sequence of seven glycines. Each mutant protein was assayed for the signaling states of the sensor and kinase domains at five different concentrations of Mg2+. Some of the resulting dose-response curves showed patterns much like that for the wild-type receptor in which the signaling state of the sensor and kinase domain were correlated. However, a majority of the curves exhibited a variety of altered relationships between patterns for the two domains. Importantly, the effects of the glycine insertions before and after the HAMP domain indicated that this domain reduced the native "on" signaling state of both the sensor and kinase domain to be less extreme and thus in a more balanced state between on and off. Examination of the effects of similar glycine substitutions in two related two-component sensor kinases showed a similar negative influence of HAMP domain coupling on kinase domain signaling state. A global fitting using the allosteric coupling model between the three domains was performed for all 35 pairs of dose-response curves for PhoQ, allowing variation of one or a few individual parameters relevant to the position of the particular mutational substitution. An important validation of the resulting global parameters was a reasonable fit of the wild-type dose-response curves. The global parameters fit the experimental data for most but not all mutant receptors. Overall, the allosteric coupling model performed well, providing support for its validity.

    Thus, this work provides support for concept of intra-receptor signaling via allosteric coupling between independent domains that each have their own intrinsic equilibrium between the "on" and "off" state. This allosteric coupling model introduces a third way of thinking about how ligand occupancy of a transmembrane receptor site facing the cell's exterior generates altered activity of a cytoplasmic domain inside the cell. Instead of considering that ligand binding "sends a signal" by sequential conformational changes that travel through the receptor structure or that ligand binding shifts a conformational equilibrium of the entire receptor in a concerted manner, the allosteric model suggests that signaling occurs by allosteric coupling between relatively independent domains of a multi-domain receptor protein. This constitutes an important contribution to our concepts of receptor conformational signaling.

    However, the impact of this contribution is likely to be less than it could be because of the way the manuscript is written. Specifically, the devotion of a majority of the Results section to consideration of models for signaling obscures the most compelling parts of the work, the experimental observations of the striking effects of mutational substitutions throughout PhoQ on the signaling state of the sensor and kinase domains and the explanation of those disparate effects by the allosteric coupling model of conformational signaling. For many experimental scientists interested in mechanisms of signaling, this work would be much more accessible if the experimental results were presented first, the allosteric coupling model was introduced as a way to explain the results, and much of the consideration of other models and the development and details of the allosteric model were shifted to the Materials and Methods or provided as part of supplementary materials.

    We thank the reviewer for this useful criticism. We have made several changes to bring forward and emphasize the experimental observations in our data.

    1. We have moved concerted signaling model from Figure 2 (formerly Figure 2B, 2D) to Figure 5. New Figure 2 now contains an expanded set of experimentally generated data only.
    2. We have supplemented Figure 2C with additional representatives of our diverse experimentally generated functional data.
    3. We have added Figure 2-figure supplement 1 with examples of western blots and crosslinking quantifications.
    4. We have moved the former Figure 4 forward to Figure 3.
    5. We have moved the former Figure 5 forward to Figure 4.
    6. We have added Figure 7-figure supplement 1 to further highlight and discuss rationale for choice of point mutations and Gly7 insertions.
    7. We have made several changes in the Results section that mirror the above changes.

    We have also made several changes to consolidate the discussion of the modeling work.

    1. The concerted signaling model from the former Figure 2 (Figure 2B, 2D) and the 2-domain signaling model from former Figure 3 have been moved to a new Figure 5.
    2. Former Figure 3D has been moved to Figure 5 figure supplement 1.
    3. Population fraction equations in new Figure 5 (formerly Figure 2B, 2D, 3A) have been moved to Materials and Methods
    4. Text discussing alternate allosteric models has been consolidated into one section.

    Reviewer #3 (Public Review):

    This manuscript describes a comprehensive study of kinase activation and allosteric coupling in the sensor histidine kinase (SHKs) PhoQ. Quantitative assays for sensor domain activation and kinase response are used to evaluate a large number of variant proteins that display a range of properties with respect to ligand binding, interdomain coupling and kinase activity. The data is used to construct and fit a conceptually elegant model that provides a thermodynamic explanation for domain interactions, allostery and sensing responses in SHKs. The experiments also demonstrate that sensor kinase domains intrinsically favor their "on" states and that HAMP domains act to deactivate both the sensor and the kinase units. In all it is a very impressive study that sets the bar for enzymatic approaches aimed at understanding signaling by multidomain transmembrane kinases. Generality of key principles are explored by examining several SHKs related to PhoQ. The paper is well written and the complex data and their interpretation are for the most part clearly discussed. That said, there are some issues the authors should address:

    The model applied for Mg binding should be described to a greater extent. The equations of Figs. 1, 2,3,6,7 represent a situation more complex than the accompanying schematics portray. Even the simplest equation of 1B implies sequential binding of 2 Mg ions to one PhoQ dimer (presumably 1 site per subunit). Furthermore, the binding sites are assumed to be independent and, importantly, there are no intermediate states in the model in which one subunit is "on" (in either its sensor or kinase domain) and the other is "off". Is it known experimentally that the two subunits act independently and what is the consequence of not allowing for hybrid activation states within the dimer?

    We discuss how we handle Mg2+ binding and has been elaborated based on this feedback. Given the data, we are unable to distinguish between a cooperative 2-state model versus a sequential binding model. We have 3 options: 1) 1-Mg2+/dimer creates an asymmetric signal state. This is well precedented in the review article cited (ref 17). 2) Binding occurs at both subunits in independent, unlinked events, or 3) binding occurs with negative cooperativity (first site higher affinity) or negative cooperativity (second site higher affinity). These alternatives differ only subtly in the steepness of transition from low to high signaling states. Unfortunately, our data are not sufficiently precise to distinguish between these options.

    In addition, there may be a factor of 2 missing in treating the relative dissociation constants for Mg binding to an empty PhoQ or to a singly Mg-occupied PhoQ. Because the multiplicity changes by a factor of 2 in going from both the empty to the half-occupied state and again by 2 in going from the half-occupied to the fully occupied states, the effective Kd for binding to the singly occupied state is 4x larger than for binding to the empty state. It appears that all of the models accommodate only a factor of 2. This issue affects the (1 + [Mg]/Kd)2 term, likely to a minor extent.

    Due to the difficulties in explicitly handling ligand binding in PhoQ as discussed above and in text, we report an overall ‘observed’ Kd for Mg2+. This observed Kd represents the true Kd for Mg2+ binding is implicitly scaled by the statistical factor of 2 (dimeric ligand binding), which we now state in lines 266-267. However, it is noteworthy that our purpose is to determine how mutants alter the energetic landscape, so differences such as multiplication of both the WT and mutant equilibrium by a constant factor (of 2.0) cancel out when comparing mutants.

    In a similar vein, for the final models of Fig. 6,7, why is Mg binding only considered to selected states (SenOFF/HAMP1/Akon/off, for example)? And in Fig. 6A what does AK "on/off" signify?

    All species are allowed to bind Mg2+, but only 2 such species are shown for clarity. Figure 6 legend has been modified to state this explicitly.

    Line 549 - Discussion of the setpoint of the autokinase domain depends on the "reference point" given that KAK and alpha2 are correlated parameters. For example, one could view the intrinsic activity of the autokinase as being the fully uncoupled state, with KAK defined closed to 1.0 and alpha2 having a smaller value that currently modeled in the case of the Y60C (WT) protein. Could one fix KSen and KAK at the values for the Gly-decoupled systems and allow the shifts in equilibrium owing to HAMP coupling to be compensated solely for by alpha1 and alpha2? This framing might be more straightforward for understanding the HAMP coupling.

    While some HAMP coupling mutations are adequately compensated by changes in α1/ α2, we adopted a universal standard state for local parameter variation, described in lines 420-425, 866-877. Thus, coupling mutations within the HAMP primary sequence were also allowed to alter KHAMP. In cases where α1/ α2 modulation is sufficient for fitting, the KHAMP value was found to be close to the global fit parameter value (which we have highlighted in green in Table 2). HAMP mutations near the autokinase junction also necessitated floating the KAK parameter for adequate fitting; therefore, we cannot fix KAK across the board for these coupling mutants. Furthermore, Gly7 insertions do not relieve the restraints associated with PhoQ being membrane-localized, and it is hard to consider the sensor and autokinase domains as fully uncoupled.

    Although the reference position is largely arbitrary and in any given fitting scheme likely depends on the choice of constraining and fixing parameters, it does alter how one views the role of kinase-activating mutations. i.e. with the fully decoupled state as the reference, the HAMP is always deactivating, with different variants (including the WT) deactivated to varying extents. Some additional comments on this issue may help readers understand the range of kinase behavior and how it is influenced by HAMP.

    Based on this comment, we have added lines 695-698 in the Discussion.

    Related to the previous point, in Fig. 7 the alpha2 parameter seems to have a large amount of uncertainty, and appears biphasic in the fits, this behavior deserves a comment as to its impact in the model. How much would the interpretations change if alpha2 is considered to hold its extreme values?

    We have added Figure 7-figure supplement 3 to show the effect of holding α2 at one of the 2 parameter value peaks, and have made additional comments in text (lines 468-473). There is no change in fitting quality at all values of α2 < 0.1, and the biphasic behavior appears artificial in the sense that it does not appreciably change the fit so long as α2 < 0.1. The bottom line is α2 for WT is consistent with strong negative coupling between the HAMP and catalytic domain.

    p. 30 line 587 - It's unclear what is meant by the statement that the HAMP domain "serves to tune the ligand-sensitivity amplitude of the response" (p. 30 line 587). In this model, the HAMP domain does alter the sensitivity of the sensor domain by favoring the sensor OFF state (even though it does not directly modulate KdOFF), but what is meant by "sensitivity amplitude".

    We have clarified this phrase on lines 665-667.

  3. eLife

    Evaluation Summary:

    This paper will be of interest to scientists who think about mechanisms of conformational signaling within transmembrane receptor proteins. It describes a model of signaling by allosteric coupling between individual domains rather than by a concerted conformational change and provides substantial experimental evidence for the model from characterization of over 30 mutational substitutions in the bacterial two-component sensor protein PhoQ. The allosteric coupling model provides a way to understand many diverse observations about signaling by two-component receptors and has the potential to be relevant to conformational signaling by many other transmembrane receptors.

    (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. The reviewers remained anonymous to the authors.)

  4. eLife

    Reviewer #1 (Public Review):

    Previous studies have provided crystallographic snapshots of the autokinase domains of several sensor histidine kinases (HK) involved in signal transduction in bacteria. Nevertheless, the lack of a full-length structure of these HK hampered the understanding of the molecular mechanism of signaling. Moreover, how a stimuli perceived by the membrane-bound sensor domain is transmitted to the catalytic cytoplasmic domain of an HK, to modulate its activity is poorly understood. To probe the coupling between the sensor and autokinase domains Mensa et al. used cysteine cross linking and reporter gene assay to probe the signaling state of E. coli PhoQ in a set of several point mutations. Using these data they developed a 3-domain model in which the sensor, HAMP and catalytic domain are in allosteric communication to interconvert the kinase state in an "on" or "off" conformation. The authors conclude that signals transmit to the catalytic domain through intradomain allosteric transitions, rather than through a concerted conformational change.

    This work represents an important and novel attempt to understand the mechanism of signal transduction by sensor kinases in two-component systems. This contribution challenges the concept that signal transmit via propagation of single concerted conformational changes of the sensor kinase. The authors, instead, propose that signal is transmitted by the sensor via an interdomain allosteric mechanism.

    The way in that the paper is presented appears to be directed to enzymologist working in enzyme kinetics models, rather than to a wide audience. For example, the paper starts saying that "Fully cooperative two-state models are unable to explain the gamut of activities of mutants". This affirmation seems too abrupt without defining what kind of model they are talking about. Is a molecular model, a kinetic model or a thermodynamic model? They should explain these concepts before to show the results. After we start to read it seems clear that they propose a thermodynamic model to explain the coupling of the different domains.

    For an enzymologist should be quite worrying to interpret data of activity assays with gene reporters without knowing the answers to the following: Do the mutations affect the PhoQ protein levels in cells? How accurate are the Western blots to quantify dimer formation in Y60C and establish the kinase "on" or kinase "off" states of PhoQ? The error bar of the of crosslinking experiments, shown in the different Figs, seems quite small for a Western blot quantification. Nevertheless, in Figure 8-figure supplement 2 panel, in the mutant I221F is obtained a poor fit which is not taken into account. Is it because the error is dismissed? Same for panels A and D. Is missing something the proposed model?

  5. eLife

    Reviewer #2 (Public Review):

    This manuscript characterized the effects of 35 mutational substitutions in three domains the bacterial transmembrane two-component sensor protein for Mg2+, PhoQ, on the signaling state of the periplasmic sensor domain and the cytoplasmic histidine kinase domain. Signaling state was assayed by a diagnostic cysteine cross-link for the sensor domain and the expression of a coupled beta-galactosidase reporter for the kinase domain. The results of those characterizations were used to develop an allosteric coupling model of conformational signaling from sensor domain to kinase domain, with a key role played by the HAMP domain that connects sensor to kinase. Single-site mutational substitutions were at positions expected to be in the interior of the protein structure in the periplasmic, HAMP and the S-helix regions of the protein as well as at boundaries of transmembrane segments. In addition, the connections between the second transmembrane helix and the HAMP domain, and between the HAMP domain and the S-helix were disrupted by introduction of a sequence of seven glycines. Each mutant protein was assayed for the signaling states of the sensor and kinase domains at five different concentrations of Mg2+. Some of the resulting dose-response curves showed patterns much like that for the wild-type receptor in which the signaling state of the sensor and kinase domain were correlated. However, a majority of the curves exhibited a variety of altered relationships between patterns for the two domains. Importantly, the effects of the glycine insertions before and after the HAMP domain indicated that this domain reduced the native "on" signaling state of both the sensor and kinase domain to be less extreme and thus in a more balanced state between on and off. Examination of the effects of similar glycine substitutions in two related two-component sensor kinases showed a similar negative influence of HAMP domain coupling on kinase domain signaling state. A global fitting using the allosteric coupling model between the three domains was performed for all 35 pairs of dose-response curves for PhoQ, allowing variation of one or a few individual parameters relevant to the position of the particular mutational substitution. An important validation of the resulting global parameters was a reasonable fit of the wild-type dose-response curves. The global parameters fit the experimental data for most but not all mutant receptors. Overall, the allosteric coupling model performed well, providing support for its validity.

    Thus, this work provides support for concept of intra-receptor signaling via allosteric coupling between independent domains that each have their own intrinsic equilibrium between the "on" and "off" state. This allosteric coupling model introduces a third way of thinking about how ligand occupancy of a transmembrane receptor site facing the cell's exterior generates altered activity of a cytoplasmic domain inside the cell. Instead of considering that ligand binding "sends a signal" by sequential conformational changes that travel through the receptor structure or that ligand binding shifts a conformational equilibrium of the entire receptor in a concerted manner, the allosteric model suggests that signaling occurs by allosteric coupling between relatively independent domains of a multi-domain receptor protein. This constitutes an important contribution to our concepts of receptor conformational signaling.

    However, the impact of this contribution is likely to be less than it could be because of the way the manuscript is written. Specifically, the devotion of a majority of the Results section to consideration of models for signaling obscures the most compelling parts of the work, the experimental observations of the striking effects of mutational substitutions throughout PhoQ on the signaling state of the sensor and kinase domains and the explanation of those disparate effects by the allosteric coupling model of conformational signaling. For many experimental scientists interested in mechanisms of signaling, this work would be much more accessible if the experimental results were presented first, the allosteric coupling model was introduced as a way to explain the results, and much of the consideration of other models and the development and details of the allosteric model were shifted to the Materials and Methods or provided as part of supplementary materials.

  6. eLife

    Reviewer #3 (Public Review):

    This manuscript describes a comprehensive study of kinase activation and allosteric coupling in the sensor histidine kinase (SHKs) PhoQ. Quantitative assays for sensor domain activation and kinase response are used to evaluate a large number of variant proteins that display a range of properties with respect to ligand binding, interdomain coupling and kinase activity. The data is used to construct and fit a conceptually elegant model that provides a thermodynamic explanation for domain interactions, allostery and sensing responses in SHKs. The experiments also demonstrate that sensor kinase domains intrinsically favor their "on" states and that HAMP domains act to deactivate both the sensor and the kinase units. In all it is a very impressive study that sets the bar for enzymatic approaches aimed at understanding signaling by multidomain transmembrane kinases. Generality of key principles are explored by examining several SHKs related to PhoQ. The paper is well written and the complex data and their interpretation are for the most part clearly discussed. That said, there are some issues the authors should address:

    The model applied for Mg binding should be described to a greater extent. The equations of Figs. 1, 2,3,6,7 represent a situation more complex than the accompanying schematics portray. Even the simplest equation of 1B implies sequential binding of 2 Mg ions to one PhoQ dimer (presumably 1 site per subunit). Furthermore, the binding sites are assumed to be independent and, importantly, there are no intermediate states in the model in which one subunit is "on" (in either its sensor or kinase domain) and the other is "off". Is it known experimentally that the two subunits act independently and what is the consequence of not allowing for hybrid activation states within the dimer?

    In addition, there may be a factor of 2 missing in treating the relative dissociation constants for Mg binding to an empty PhoQ or to a singly Mg-occupied PhoQ. Because the multiplicity changes by a factor of 2 in going from both the empty to the half-occupied state and again by 2 in going from the half-occupied to the fully occupied states, the effective Kd for binding to the singly occupied state is 4x larger than for binding to the empty state. It appears that all of the models accommodate only a factor of 2. This issue affects the (1 + [Mg]/Kd)2 term, likely to a minor extent.

    In a similar vein, for the final models of Fig. 6,7, why is Mg binding only considered to selected states (SenOFF/HAMP1/Akon/off, for example)? And in Fig. 6A what does AK "on/off" signify?

    Line 549 - Discussion of the setpoint of the autokinase domain depends on the "reference point" given that KAK and alpha2 are correlated parameters. For example, one could view the intrinsic activity of the autokinase as being the fully uncoupled state, with KAK defined closed to 1.0 and alpha2 having a smaller value that currently modeled in the case of the Y60C (WT) protein. Could one fix KSen and KAK at the values for the Gly-decoupled systems and allow the shifts in equilibrium owing to HAMP coupling to be compensated solely for by alpha1 and alpha2? This framing might be more straightforward for understanding the HAMP coupling. Although the reference position is largely arbitrary and in any given fitting scheme likely depends on the choice of constraining and fixing parameters, it does alter how one views the role of kinase-activating mutations. i.e. with the fully decoupled state as the reference, the HAMP is always deactivating, with different variants (including the WT) deactivated to varying extents. Some additional comments on this issue may help readers understand the range of kinase behavior and how it is influenced by HAMP.

    Related to the previous point, in Fig. 7 the alpha2 parameter seems to have a large amount of uncertainty, and appears biphasic in the fits, this behavior deserves a comment as to its impact in the model. How much would the interpretations change if alpha2 is considered to hold its extreme values?

    p. 30 line 587 - It's unclear what is meant by the statement that the HAMP domain "serves to tune the ligand-sensitivity amplitude of the response" (p. 30 line 587). In this model, the HAMP domain does alter the sensitivity of the sensor domain by favoring the sensor OFF state (even though it does not directly modulate KdOFF), but what is meant by "sensitivity amplitude".

  7. Version published to 10.1101/2021.09.03.458835v1 on bioRxiv