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Thermodynamics and kinetics of the F0F1-ATPase:
application of the probability isotherm
Brian Chapman and Denis Loiselle
Article citation details
R. Soc. open sci. 3: 150379.
http://dx.doi.org/10.1098/rsos.150379
Review timeline
Original submission:
Revised submission:
Final acceptance:
31 July 2015
11 December 2015
8 January 2016
Note: Reports are unedited and appear as
submitted by the referee. The review history
appears in chronological order.
Review History
RSOS-150379.R0 (Original submission)
Review form: Reviewer 1 (Wayne Frasch)
Is the manuscript scientifically sound in its present form?
No
Are the interpretations and conclusions justified by the results?
No
Is the language acceptable?
No
Is it clear how to access all supporting data?
Not applicable
Do you have any ethical concerns with this paper?
No
Have you any concerns about statistical analyses in this paper?
No
© 2016 The Authors. Published by the Royal Society under the terms of the Creative Commons
Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use,
provided the original author and source are credited
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2
Recommendation?
Major revision is needed (please make suggestions in comments)
Comments to the Author(s)
This manuscript investigates the mechanism of the FoF1 ATP synthase, which is comprised of
two opposed molecular motors. The authors address an apparent discrepancy in the work of
Toyabe et al. 2011 where there is a mismatch between the known chemically fruitful 120 degree
step size of rotation and their experimentally fitted value of 55 degrees. Toyabe et al. 2011
conclude that the motor operates at nearly 100 % efficiency, and explain that this disparity was
probably due to the presence of chemically fruitless jumps or trial steps.
The authors of the current manuscript present calculations that dispute the conclusion of Toyabe
et al. that FoF1 is nearly 100% efficient, and pose an alternate reason to that of chemically fruitless
rotational steps for the disparity in step size. The suggest that the discrepancy results form
molecular friction between the rotor and its housing in the F1-ATPase molecule, the work of
overcoming such friction in each 120 degree rotary step being quantised, independent of stepping
rate and direction, and equal to about half of the delta mu of ATP. The authors then provide
examples of the consequences of their alternate conclusion that include Table 1. In this regard, the
author make a significant contribution to the understanding of the mechanism of FoF1.
However, a major problem with the manuscript is one of omission. Subsequent to the publication
of Toyabe et al. 2011, a few papers have been published that have a direct impact on the current
manuscript. The authors must include and discuss their conclusions in the context of these
papers.
1. Regarding Table 1 in the manuscript, the authors will find experimental data for the
relationship between the rate of ATP synthesis, ATP hydrolysis and pmf in Steigmiller et al.
(2008) PNAS 105, 3745-3750 as well as in Petersen et al. (2012) PNAS 109 11150-11155.
The authors need to compare their calculations to examples for which experimental data exist.
2. The authors' conclusion that the rate depends on the molecular friction between the rotor and
its housing in the F1-ATPase molecule is supported by the results of Martin et al. (2014) PNAS
111, 3715-3720, and needs to be included in their discussion. Martin et al. (2014) also concluded
that the efficiency of the F1-ATPase was not 100%.
3. Any discussion concerning the efficiency of the F1-ATPase must also consider the experimental
results of Saita et al. (2015) 112, 9626-9631. The experimental results in this paper are closely
related to those of Toyabe et al. 2011. Both Martin et al. 2014 and Saita et al. 2015 provide some
insight into the 55 degrees measured by Toyabe et al. 2011.
4. The recent paper by Volkan-Kacso and Marcus (2015) PNAS (available on-line ahead of print)
should also be included in the considerations made by the authors.
The extent of the contribution made in the current manuscript can only be assessed once the
authors have considered their conclusions in light of this other recent work.
A second issue related to the manuscript is the introduction that is long on history but short on
background that are of direct relevance to the results and discussion of the manuscript. In
addition, the manuscript is written in a very "preachy" tone that can be interpreted as being
disrespectful to other groups who are attempting to understand this important motor complex.
Such language that can be perceived as condescending distracts form what is otherwise a very
interesting manuscript.
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3
Review form: Reviewer 2
Is the manuscript scientifically sound in its present form?
Yes
Are the interpretations and conclusions justified by the results?
Yes
Is the language acceptable?
Yes
Is it clear how to access all supporting data?
There is no supporting data
Do you have any ethical concerns with this paper?
No
Have you any concerns about statistical analyses in this paper?
No
Recommendation?
Accept with minor revision (please list in comments)
Comments to the Author(s)
I find this manuscript very enlightening. My only concern is that some thermodynamic terms
should be defined more clearly and explicitly in order to make this manuscript better
understandable and more interesting for the general readership.
Specifically:
1)
In the manuscript the concepts of entropy creation, entropy exchange, and
thermodynamic efficiency are discussed. This is difficult to understand for a reader who is not
familiar with these aspects of thermodynamic. It would be helpful if these terms were defined
explicitly in the text.
2)
It is difficult to deduce from the text how the graphs for “contamination” in Figure 3+4
were derived. Please give the functions that were used to plot these graphs.
3)
p6, l22: “…fixing it artificially for the experimental setup.” Not all readers might be
familiar with this kind of experiments. It would be helpful if the experimental setup of Toyabe et
al. is described briefly.
Minor comments:
4)
The spelling of “F0-F1 ATP synthase” is rather unusual, most commonly it is spelled as
“FOF1 ATP synthase”. Please note that it is not F0, but FO for Oligomycin sensitive.
5)
In the text the ordinates of Figure 1 and 4 are described as the molecular free energy.
However, in the figures they are labeled as the molar free energy.
6)
p4, l43: “…unidirectional stepping rates are shown…” should read “…unidirectional
stepping rates and torque are shown…”
7)
p4, l58: “their Figure 3B” should read “their Fig.3B”
8)
Figure 4, legend, last line: “…broken black line.” should read “…black dashed line.”
9)
p8, eq. (4): the terms R, rf, rb are not defined in the text.
10)
p8, l27: “In equation (2)…” should read “In equation (4)…”
11)
p8, l47: “…310°K…” should read “…300 K…”
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4
Decision letter (RSOS-150379)
24-Nov-2015
Dear Dr Chapman,
The editors assigned to your paper ("Thermodynamics and Kinetics of the FoF1-ATPase:
Application of the Probability Isotherm") has now received comments from reviewers. We would
like you to revise your paper in accordance with the referee and Subject Editor suggestions which
can be found below (not including confidential reports to the Editor). Please note this decision
does not guarantee eventual acceptance.
Please submit a copy of your revised paper within three weeks (i.e. by the 17-Dec-2015). If we do
not hear from you within this time then it will be assumed that the paper has been withdrawn. In
exceptional circumstances, extensions may be possible if agreed with the Editorial Office in
advance.We do not allow multiple rounds of revision so we urge you to make every effort to
fully address all of the comments at this stage. If deemed necessary by the Editors, your
manuscript will be sent back to one or more of the original reviewers for assessment. If the
original reviewers are not available we may invite new reviewers.
To revise your manuscript, log into http://mc.manuscriptcentral.com/rsos and enter your
Author Centre, where you will find your manuscript title listed under "Manuscripts with
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In addition to addressing all of the reviewers' and editor's comments please also ensure that your
revised manuscript contains the following sections as appropriate before the reference list:
• Ethics statement (if applicable)
If your study uses humans or animals please include details of the ethical approval received,
including the name of the committee that granted approval. For human studies please also detail
whether informed consent was obtained. For field studies on animals please include details of all
permissions, licences and/or approvals granted to carry out the fieldwork.
• Data accessibility
It is a condition of publication that all supporting data are made available either as
supplementary information or preferably in a suitable permanent repository. The data
accessibility section should state where the article's supporting data can be accessed. This section
should also include details, where possible of where to access other relevant research materials
such as statistical tools, protocols, software etc can be accessed. If the data has been deposited in
an external repository this section should list the database, accession number and link to the DOI
for all data from the article that has been made publicly available. Data sets that have been
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manuscript and included in the reference list.
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If you wish to submit your supporting data or code to Dryad (http://datadryad.org/), or modify
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• Competing interests
Please declare any financial or non-financial competing interests, or state that you have no
competing interests.
• Authors’ contributions
All submissions, other than those with a single author, must include an Authors’ Contributions
section which individually lists the specific contribution of each author. The list of Authors
should meet all of the following criteria; 1) substantial contributions to conception and design, or
acquisition of data, or analysis and interpretation of data; 2) drafting the article or revising it
critically for important intellectual content; and 3) final approval of the version to be published.
All contributors who do not meet all of these criteria should be included in the
acknowledgements.
We suggest the following format:
AB carried out the molecular lab work, participated in data analysis, carried out sequence
alignments, participated in the design of the study and drafted the manuscript; CD carried out
the statistical analyses; EF collected field data; GH conceived of the study, designed the study,
coordinated the study and helped draft the manuscript. All authors gave final approval for
publication.
• Acknowledgements
Please acknowledge anyone who contributed to the study but did not meet the authorship
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• Funding statement
Please list the source of funding for each author.
Once again, thank you for submitting your manuscript to Royal Society Open Science and I look
forward to receiving your revision. Our sincere apology for the length of time that your
manuscript spent in review. If you have any questions at all, please do not hesitate to get in
touch.
Yours sincerely,
Matthew Allinson,
Royal Society Open Science
on behalf of Anne Donaldson
Subject Editor, Royal Society Open Science
[email protected]
Author's Response to Decision Letter for (RSOS-150379)
See Appendix A.
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6
RSOS-150379.R1 (Revision)
Review form: Reviewer 1 (Wayne Frasch)
Is the manuscript scientifically sound in its present form?
Yes
Are the interpretations and conclusions justified by the results?
Yes
Is the language acceptable?
Yes
Is it clear how to access all supporting data?
Yes
Do you have any ethical concerns with this paper?
No
Have you any concerns about statistical analyses in this paper?
No
Recommendation?
Accept as is
Comments to the Author(s)
The authors have carefully and thoroughly addressed the previous concerns of the reviewers. The
manuscript makes a significant contribution to the understanding of this important protein
complex and to that of the thermodynamics of molecular motors in general.
Review form: Reviewer 2
Is the manuscript scientifically sound in its present form?
Yes
Are the interpretations and conclusions justified by the results?
Yes
Is the language acceptable?
Yes
Is it clear how to access all supporting data?
Yes
Do you have any ethical concerns with this paper?
No
Have you any concerns about statistical analyses in this paper?
No
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7
Recommendation?
Accept with minor revision (please list in comments)
Comments to the Author(s)
In the revised manuscript “Thermodynamics and Kinetics of the FoF1-ATPase: Application of the
Probability Isothermby” by B. Chapman and D. Loiselle the authors discuss the article of Toyabe
et al., where the mismatch of experimental and theoretical step-size of the rotor is explained by
fruitless steps of the ATPase that otherwise works with nearly 100% efficiency. They argue that
this is not in accordance with the second law of thermodynamics and provide an alternative
explanation, namely some form of molecular friction. To support their interpretation the authors
provide thermodynamic arguments and calculations. The results are also discussed in light of
some recent publications that are dealing with the thermodynamic efficiency of the ATPase. In
addition they try to clarify the thermodynamic terms and laws that apply to this discussion. By
this the authors not only give a better understanding of the underlying mechanism of the ATP
synthase, but also help to better understand and interpret thermodynamic data from biochemical
reactions in general.
I find that the revised version of this manuscript covers all points previously addressed by the
reviewers and would recommend its publication in Royal Society Open Science.
Minor comments:
1)
p1, 49: “…experiment by Noji et al., … provide … proof that the mitochondrial F1ATPase…” Please note that this is technically not correct, as Noji et al. didn’t use the
mitochondrial enzyme, but the bacterial F1-ATPase from the thermophilic Bacillus PS3, which is
different in subunit and amino acid composition.
2)
Figure 4: The figure is cut off on the right side.
3)
Table 1: “-.026” should read “-0.026”
4)
There are several instances where the reference is given like “Martin et al. (2014)” only
(p6, 54), but the actual reference number is missing. Please add the reference numbers for
convenience.
5) In the excel file in the graph with the orange curve is a blue dot, which I think does not belong
there.
Decision letter (RSOS-150379.R1)
05-Jan-2016
Dear Dr Chapman:
On behalf of the Editors, I am pleased to inform you that your Manuscript RSOS-150379.R1
entitled "Thermodynamics and Kinetics of the FoF1-ATPase: Application of the Probability
Isotherm" has been accepted for publication in Royal Society Open Science subject to minor
revision in accordance with the referee suggestions. Please find the referees' comments at the end
of this email.
The reviewers and Subject Editor have recommended publication, but also suggest some minor
revisions to your manuscript. Therefore, I invite you to respond to the comments and revise your
manuscript.
• Ethics statement
If your study uses humans or animals please include details of the ethical approval received,
including the name of the committee that granted approval. For human studies please also detail
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8
whether informed consent was obtained. For field studies on animals please include details of all
permissions, licences and/or approvals granted to carry out the fieldwork.
• Data accessibility
It is a condition of publication that all supporting data are made available either as
supplementary information or preferably in a suitable permanent repository. The data
accessibility section should state where the article's supporting data can be accessed. This section
should also include details, where possible of where to access other relevant research materials
such as statistical tools, protocols, software etc can be accessed. If the data has been deposited in
an external repository this section should list the database, accession number and link to the DOI
for all data from the article that has been made publicly available. Data sets that have been
deposited in an external repository and have a DOI should also be appropriately cited in the
manuscript and included in the reference list.
If you wish to submit your supporting data or code to Dryad (http://datadryad.org/), or modify
your current submission to dryad, please use the following link:
http://datadryad.org/submit?journalID=RSOS&manu=RSOS-150379.R1
• Competing interests
Please declare any financial or non-financial competing interests, or state that you have no
competing interests.
• Authors’ contributions
All submissions, other than those with a single author, must include an Authors’ Contributions
section which individually lists the specific contribution of each author. The list of Authors
should meet all of the following criteria; 1) substantial contributions to conception and design, or
acquisition of data, or analysis and interpretation of data; 2) drafting the article or revising it
critically for important intellectual content; and 3) final approval of the version to be published.
All contributors who do not meet all of these criteria should be included in the
acknowledgements.
We suggest the following format:
AB carried out the molecular lab work, participated in data analysis, carried out sequence
alignments, participated in the design of the study and drafted the manuscript; CD carried out
the statistical analyses; EF collected field data; GH conceived of the study, designed the study,
coordinated the study and helped draft the manuscript. All authors gave final approval for
publication.
• Acknowledgements
Please acknowledge anyone who contributed to the study but did not meet the authorship
criteria.
• Funding statement
Please list the source of funding for each author.
Because the schedule for publication is very tight, it is a condition of publication that you submit
the revised version of your manuscript within 7 days (i.e. by the 14-Jan-2016). If you do not think
you will be able to meet this date please let me know immediately.
To revise your manuscript, log into https://mc.manuscriptcentral.com/rsos and enter your
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Decisions". Under "Actions," click on "Create a Revision." You will be unable to make your
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revisions on the originally submitted version of the manuscript. Instead, revise your manuscript
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Best wishes
Matthew Allinson
Senior Publishing Editor, Royal Society Open Sceince
[email protected]
Author's Response to Decision Letter for (RSOS-150379)
See Appendix B.
Appendix A
Reviewer: 1
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This manuscript
investigates the mechanism of the FoF1 ATP synthase, which is comprised of two opposed
molecular motors. The authors address an apparent discrepancy in the work of Toyabe et al. 2011 where there is a
mismatch between the known chemically fruitful 120 degree step size of rotation and their experimentally fitted
value of 55 degrees. Toyabe et al. 2011 conclude that the motor operates at nearly 100 % efficiency, and explain
that this disparity was probably due to the presence of chemically fruitless jumps or trial steps.
The authors of the current manuscript present calculations that dispute the conclusion of Toyabe et al. that FoF1 is
nearly 100% efficient, and pose an alternate reason to that of chemically fruitless rotational steps for the disparity
in step size. The suggest that the discrepancy results form molecular friction between the rotor and its housing in
the F1-ATPase molecule, the work of overcoming such friction in each 120 degree rotary step being quantised,
independent of stepping rate and direction, and equal to about half of the delta mu of ATP. The authors then
provide examples of the consequences of their alternate conclusion that include Table 1. In this regard, the author
make a significant contribution to the understanding of the mechanism of FoF1.
We are grateful for this positive assessment of our contribution.
However, a major problem with the manuscript is one of omission.
Subsequent to the publication of Toyabe et al. 2011, a few papers have been published that have a direct impact on
the current manuscript. The authors must include and discuss their conclusions in the context of these papers.
We thank the Reviewer for identifying this problem and for helpfully focussing our attention on
the remedial details.
1.
Regarding Table 1 in the manuscript, the authors will find experimental data for the relationship between the rate of ATP
synthesis, ATP hydrolysis and pmf in Steigmiller et al. (2008) PNAS 105, 3745-3750 as well as in Petersen et al. (2012)
PNAS 109 11150-11155.
The authors need to compare their calculations to examples for which experimental data exist.

Steigmiller et al. (2008) have comprehensively addressed the issue of thermodynamically
determined/deduced stoichiometry - : conceptually, methodologically and analytically - but we baulk
at their invoking of ‘slippage’, as expressed in the statement:
At high rates of ATP synthesis far from equilibrium, it is conceivable that additional protons have to be
translocated through the enzyme for each synthesized ATP, e.g., slip protons, leading to what can be
called a "kinetic" H+/ATP ratio.
As we interpret their Fig. 2, as pH increases, the catalytic rate increases disproportionately (i.e.,
concave upwards to the right). This is the opposite of what one would expect if there were
stoichiometric slippage happening. However, it is not necessarily evidence that pH has a
stimulatory effect on the enzyme (as we comment in Footnote 4 on p.10).

Petersen et al. (2012): This work is four years down the track relative to that of Steigmiller et al.
(2008) and has refined some methods and arguments. However, we have issues with some of their
statements, as follows.
1. p.11152, para 1: "At high ΔH+ , coupled ATP hydrolysis is completely inhibited, because proton pumping against a high
protonmotive force is not possible, whereas uncoupled ATPhydrolysis is unaffected. " In our view, if an enzyme is "completely
inhibited" then it is inhibited in BOTH directions, synthesis and hydrolysis. Hence, we would express
their results as demonstrating that, under these conditions, the unidirectional ATPase rate is
negligible relative to the high unidirectional ATP synthase rate - it's just the thermodynamic mass
action effect.
2. p.11152, para 3: "On the basis of the thermodynamics of irreversible processes (i.e., LNET), a linear relation between the rate and
driving force (ΔpH) was expected. For CF0F1, this phenomenon has been analyzed (18): by correcting the observed nonlinear rate dependencies for
the experimentally measured ΔpH dependency of enzyme preactivation, the expected linear relation was indeed obtained."
We see no
reason to expect linear flux-force relations in any enzymatic process. Indeed, it is straightforward, as
shown in the attached Excel file, to demonstrate the nonlinear force-flux relation (i.e., Net Rate vs
Gdiss) for simple first-order diffusion (Sheet 1) as well as the expected linear [A]1-flux relation and
nonlinear force-flux relation for simple second-order kinetics (Sheet 2). Given that nonlinear force-
flux relations occur in even the simplest systems, it is difficult to imagine that linear force-flux
relation are likely for any biochemical reaction of any kind, let alone a complex rotary chemi-electroosmotic enzyme such as the FoF1-ATPase/synthase.
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3. p.11152, para 3: "The dependencies of the rates on ΔpH showed different curvatures for the different Q values. Presumably, these
differences can be attributed to regulatory effects of ADP and ΔpH. In particular, it can be observed that the curvature is generally less pronounced
when, for a given ADP concentration, the ΔpH(eq) was increased owing to a higher ATP concentration. Regulatory phenomena, however, will not
shift the point of thermodynamic equilibrium."
Once again, the observation of nonlinear force-flux relations, the curvature of which can be
altered by changing some of the concentrations, all without any ‘regulatory phenomena’
whatsoever, can be readily demonstrated. These simple mass action effects may be
explored by user alteration of any GREEN cell values in the attached Excel file.
In summary, neither Steigmiller et al. (2008) nor Petersen et al. (2012) produce data which
are directly pertinent to the main import of the results contained in our Table 1. They
pertain in a general sense to the concepts of chemiosmotic reversibility which is an
essential component of our thinking and calculation and there is no incompatibility
between their findings and ours. We hope that the new paragraph and Footnote 4
inserted on our p.10 will be sufficient acknowledgment and accommodation of the work of
these authors.
2.
The authors' conclusion that the rate depends on the molecular friction between the rotor and its housing in the F1ATPase molecule is supported by the results of Martin et al. (2014) PNAS 111, 3715-3720, and needs to be included in
their discussion. Martin et al. (2014) also concluded that the efficiency of the F1-ATPase was not 100%.
This is indeed an important paper, particularly relevant to possible future investigation of the
question of friction if its ingenious methodology can be applied to the study of the intact enzyme
in chemiosmotically functional vesicles. We have duly acknowledged the relevance of this work in
the final paragraph of our p.6 and in the Conclusion and, once again, thank the Reviewer for
drawing it to our attention.
3.
Any discussion concerning the efficiency of the F1-ATPase must also consider the experimental results of Saita et al.
(2015) 112, 9626-9631. The experimental results in this paper are closely related to those of Toyabe et al. 2011. Both
Martin et al. 2014 and Saita et al. 2015 provide some insight into the 55 degrees measured by Toyabe et al. 2011.
See comment following No.4 immediately below.
4.
The recent paper by Volkan-Kacso and Marcus (2015) PNAS (available on-line ahead of print) should also be included in
the considerations made by the authors.
There is a somewhat disturbing trend in these papers cited by Reviewer #1 in points 3 and 4
above. The papers are focussed exclusively on the behaviour of the isolated F1-ATPase, its
supposed “motor” function and the thermodynamic efficiency of its chemomechanical
transduction in that supposed “motor” function.
We suggest a different perspective.
We believe that it is an unfortunate distraction to use the word “motor” in relation to an enzyme
fragment – the isolated F1-ATPase – that has a purely chemiosmotic function in its natural
physiological role as an integral component of the FoF1-ATPase. The two pertinent facts essential
to its physiology are:
1. it functions only as an ATP synthase, never as an ATPase, and
2. it doesn’t ever perform mechanical work, only chemical synthesis fuelled by a
protonmotive
force
dissipates itself throughonanJune
enzyme
Downloaded
fromthat
http://rsos.royalsocietypublishing.org/
17, 2017that happens to involve a
rotary catalytic mechanism.
In our paper we say, "It is a necessity of the Second Law that free energy must be dissipated if there is to
be any net chemiosmotic reaction. Free energy dissipation as heat for the FoF1-ATPase (or ATP synthase)
comprises the internal work of overcoming the internal viscosity and resistance of the rotary mechanism
and its associated proton channel. In no sense whatsoever is there free energy transduction (conservation)
as useful mechanical work under physiological conditions. ..."
In short, we contend that all the external work measured by Toyabe et al.,
Saita et al., and Volkan-Kacso
et al., and perhaps much of the internal work deduced by the latter two groups, may be peculiar
to their ingeniously designed measuring protocol for the isolated F1-ATPase, and which may not
obtain to the same extent for the intact FoF1-ATPase in vivo.
This brings us to one of the central points of our paper, our difference in interpretation from that
of Toyabe et al., based on the possibility that the isolated F1-ATPase might display more internal
friction for gamma shaft rotation than the intact FoF1-ATP synthase. If this possibility does not
obtain, then the inescapable 'overhead' cost of rotating the gamma shaft in either direction is
around half the magnitude of the GATP associated with either ATP synthesis or ATP hydrolysis.
This has profound implications for assumptions about the H/ATP ratio and the thermodynamic
efficiency of oxidative phosphorylation in vivo.
The extent of the contribution made in the current manuscript can only be assessed once the authors have
considered their conclusions in light of this other recent work.
We would argue that the additional research that Reviewer #1 has required us to consider serves
to increase the timeliness and importance of the alternative explanations and viewpoint that we
bring to this discussion.
A second issue related to the manuscript is the introduction that is long on history but short on background that are
of direct relevance to the results and discussion of the manuscript.
We accept this criticism and have altered the Introduction accordingly. This has increased its
length significantly, but we feel this is warranted in view of the importance of the additional
research that Reviewer #1 has asked us to bring to account.
In addition, the manuscript is written in a very "preachy" tone that can be interpreted as being disrespectful to
other groups who are attempting to understand this important motor complex. Such language that can be
perceived as condescending distracts form what is otherwise a very interesting manuscript.
We deeply regret any offence that may have been caused by the tone of our first draft. It was
certainly not our intention to express disrespect or condescension to scientists whose creativity of
experimental design and technical wizardry can only inspire awe. We do, however, confess to a
measure of frustration with the LNET school, the continuing presence of which – even if only in
trace amounts – constitutes, in our opinion, a wasteful distraction from productive progress in
what promises to be a golden age of nano-discovery, thanks to the stunning technological miracles
taking place in ever increasing quantities in the world’s experimental laboratories. This frustration
may well have coloured some of our language and modes of expression in an unhelpful manner.
Having looked critically at our draft in the light of Reviewer #1’s specific complaint, we have
eliminated or altered what we judge to have been perceived as potentially abrasive passages.
Reviewer: 2
I find this manuscript very enlightening.
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We are grateful for this positive assessment of our contribution.
My only concern is that some thermodynamic terms should be defined more clearly and explicitly in order to make
this manuscript better understandable and more interesting for the general readership.
Specifically:
1) In the manuscript the concepts of entropy creation, entropy exchange, and thermodynamic efficiency are discussed. This is
difficult to understand for a reader who is not familiar with these aspects of thermodynamic. It would be helpful if these terms
were defined explicitly in the text.
We have included a section headed “Entropy exchange, entropy creation and thermodynamic
efficiency”. This is fairly lengthy and we hope that it will be satisfactory.
2) It is difficult to deduce from the text how the graphs for “contamination” in Figure 3+4 were derived. Please give the functions
that were used to plot these graphs.
We have included a section headed “Calculation details for the plotted curves of Figures 3 and 4” in the
Supplementary Information. This gives the essential code used for the calculations with explanatory
‘comments’. We do not think it’s necessary to mention that the code is written in ToolBook’s OpenScript,
but will do so if requested.
3) p6, l22: “…fixing it artificially for the experimental setup.” Not all readers might be familiar with this kind of experiments. It
would be helpful if the experimental setup of Toyabe et al. is described briefly.
The techniques and methodologies allowing attachment of an indicator (in the original
experiment, Noji et al used an actin filament) are very complex but essentially unimportant. The
central importance of applying some external connection, thereby slowing rotation and allowing
visualisation has now been parsimoniously stated in the Introduction: “ In the same year, a stunningly
conceived and executed experiment by Noji et al. (4), involving attachment of a single, fluorescentlytagged, 2.6 m actin filament to the -subunit, provided direct visual proof that the mitochondrial F1ATPase indeed operates with a rotary mechanism - its central -shaft spinning in a stationary stator barrel
comprising three  and three  subunits .”
Minor comments:
4)
The spelling of “F0-F1 ATP synthase” is rather unusual, most commonly it is spelled as “FOF1 ATP synthase”. Please note that
it is not F0, but FO for Oligomycin sensitive.
5)
In the text the ordinates of Figure 1 and 4 are described as the molecular free energy. However, in the figures they are labeled
as the molar free energy.
6)
Done.
Done.
p4, l43: “…unidirectional stepping rates are shown…” should read “…unidirectional stepping rates and torque are shown…”
Done.
Done.
7)
p4, l58: “their Figure 3B” should read “their Fig.3B”
8)
Figure 4, legend, last line: “…broken black line.” should read “…black dashed line.”
9)
p8, eq. (4): the terms R, rf, rb are not defined in the text.
10)
p8, l27: “In equation (2)…” should read “In equation (4)…”
11)
p8, l47: “…310°K…” should read “…300 K…”
Done.
Done.
Done.
Done – but note that it really is 310 K, not 300 K.
Appendix B
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Reviewer 2:
In the revised manuscript “Thermodynamics and Kinetics of the FoF1-ATPase: Application of the Probability Isotherm” by B.
Chapman and D. Loiselle the authors discuss the article of Toyabe et al., where the mismatch of experimental and
theoretical step-size of the rotor is explained by fruitless steps of the ATPase that otherwise works with nearly 100%
efficiency. They argue that this is not in accordance with the second law of thermodynamics and provide an alternative
explanation, namely some form of molecular friction. To support their interpretation the authors provide thermodynamic
arguments and calculations. The results are also discussed in light of some recent publications that are dealing with the
thermodynamic efficiency of the ATPase. In addition they try to clarify the thermodynamic terms and laws that apply to
this discussion. By this the authors not only give a better understanding of the underlying mechanism of the ATP synthase,
but also help to better understand and interpret thermodynamic data from biochemical reactions in general.
We are grateful for this assessment of our specific and general contributions to this field.
I find that the revised version of this manuscript covers all points previously addressed by the reviewers and would
recommend its publication in Royal Society Open Science.
We are grateful for this favourable recommendation.
Minor comments:
1) p1, 49: “…experiment by Noji et al., … provide … proof that the mitochondrial F1-ATPase…” Please note that this is
technically not correct, as Noji et al. didn’t use the mitochondrial enzyme, but the bacterial F1-ATPase from the
thermophilic Bacillus PS3, which is different in subunit and amino acid composition.
Corrected.
2)
Figure 4: The figure is cut off on the right side.
Corrected.
3)
Table 1: “-.026” should read “-0.026”
Corrected.
4) There are several instances where the reference is given like “Martin et al. (2014)” only (p6, 54), but the actual
reference number is missing. Please add the reference numbers for convenience.
All corrected, along with inclusion of the reference to Jiang et al. (2001) previously omitted
from the References.
5) In the excel file in the graph with the orange curve is a blue dot, which I think does not belong there.
Corrected.
Reviewer 1:
Comments to the Author(s)
The authors have carefully and thoroughly addressed the previous concerns of the reviewers. The manuscript makes a
significant contribution to the understanding of this important protein complex and to that of the thermodynamics of
molecular motors in general.
We are grateful for this assessment of our specific and general contributions to this field.