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Molecular Systems Biology Peer Review Process File

Carbohydrate-active enzymes exemplify entropic principles in metabolism Oender Kartal, Sebastian Mahlow, Alexander Skupin, Oliver Ebenhoeh Corresponding author: Oliver Ebenhoeh, University of Aberdeen

Review timeline:

Submission date: Editorial Decision: Revision received: Accepted:

11 June 2011 11 August 2011 05 September 2011 09 September 2011

Transaction Report: (Note: With the exception of the correction of typographical or spelling errors that could be a source of ambiguity, letters and reports are not edited. The original formatting of letters and referee reports may not be reflected in this compilation.)

1st Editorial Decision

11 August 2011

Thank you again for submitting your work to Molecular Systems Biology. We have now heard back from two of the three referees who agreed to evaluate the study, and have decided to render a decision now to avoid further delay. As you will see, the referees were generally quite positive. The second reviewer does raise some concerns and makes suggestions for modifications, which we would ask you to carefully address in a revision of the present work. Broadly, many of the second reviewer's concerns are related to issues of clarity, and we would like to strongly emphasize that an effort should be made to ensure that this work is understandable and accessible to the broad readership of Molecular Systems Biology. Care should be taken to concisely introduce key concepts for readers that may not be familiar with plant carbohydrate metabolism or the entropy-related concepts in this work. If helpful, you may want to consider including a box that includes definitions or brief explanations of key concepts. Molecular Systems Biology provides a new functionality that allows readers to directly download the 'source data' associated with selected figure panels (e.g. ), and strongly encourages authors to provide such data for figures that directly compare experimental and theoretical results. We feel that this would be particularly appropriate for the experimental data presented in this work. Please see our Instructions of Authors for more details on preparation and formatting of figure source data (). Please resubmit your revised manuscript online, with a covering letter listing amendments and responses to each point raised by the referees. Please resubmit the paper **within one month** and ideally as soon as possible. If we do not receive the revised manuscript within this time period, the file might be closed and any subsequent resubmission would be treated as a new manuscript. Please use the Manuscript Number (above) in all correspondence. *PLEASE NOTE* As part of the EMBO Publications transparent editorial process initiative (see http://www.nature.com/msb/journal/v6/n1/full/msb201072.html), Molecular Systems Biology now © European Molecular Biology Organization

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publishes online a Review Process File with each accepted manuscript. Please be aware that in the event of acceptance, your cover letter/point-by-point document will be included as part of this file, which will be available to the scientific community. Authors may opt out of the transparent process at any stage prior to publication (contact us at [email protected]). More information about this initiative is available in our Instructions to Authors. Thank you for submitting this paper to Molecular Systems Biology. Yours sincerely, Editor - Molecular Systems Biology --------------------------------------------------------------------------Referee reports ---------------------------------------------------------------------------Reviewer #1 (Remarks to the Author): This is a novel and ingenious approach to studying factors that influence polymer metabolism. The theory makes very specific predictions about the outcomes of incubating carbohydrate polymers with different types of enzymes, and there is extremely close agreement between the predictions and the experiments designed to test the theory.. This could have a major impact on our understanding of carbohydrate metabolism, especially in plants. The manuscript is well-presented and written very clearly. Reviewer #3 (Remarks to the Author): The authors deal with the question of the product distribution, kinetics and functional role of enzymes working on carbohydrates where the change in enthalpy is negligible and entropy is the main player in governing the distribution of different products. This is an often neglected subject but of interest due to the role of such enzymes in metabolism of some of the main players inside cells. I think the analysis is interesting and illuminating and the experimental verification fits nicely the proposed theory. A major challenge is the clarity of some of the finer points in the analysis. I give detailed comments below of where I think this can be improved and where I had difficulties following the explanations and more clarifications are needed before publication. P. 4, "state variable" - explain meaning to readers. P. 5, "Two such CAZymes" - indicate which P. 6, will help to state that DPini does not have to be an integer p.6, "the total number of glucose residues, DPini," - you refer to it here as "total" but I afterwards understood that it is actually (also) the "average". This has caused me a lot of confusion and I had to read this several times. Must clarify. A concrete toy example with numbers can be extremely helpful. p. 7 because beta is always in the exponent and its value is actually a ln of some expression, this equation can also be stated without any use of beta or exponents. I would suggest at least showing it. Probably something like: 1/(Dini-1)*((Dini-1)/Dini)^D p. 7 "distribution" - it would be instrumental to take an example of DPini having some small value (say =2) and showing the theoretical distribution clearly in a schematic figure/text discussion. p. 7 "It is predicted", not clear what "it" refers to p. 7, "generalization of the mass action ratio in equilibrium", this sounds important but I couldn't fully understand it from the text itself. Maybe an example of how these are related will clarify. p. 8, "sum of glucose and maltose molecules" the natural way to state this seems to me to be only the © European Molecular Biology Organization

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sum of maltose. because glucose sum is also constant it is true also for both, but not as directly clear in my mind. p. 9, "three values, a rate constant reflecting maximal turnover, and two constants reflecting the different subsite affinities" maybe discuss how this compares to alternatives such as an option of characterizing using two maximal turnovers and one affinity. p. 12, "this results in a sequestration of glucoses from the DPE1-mediated transfer reactions." I did not understand this paragraph and sentence. I suggest clarifying further. p. 13 "integration of carbon fluxes coming from many chloroplasts" this seems to be a very interesting suggestion. Worth explaining further what is the challenge here. Why it is not simple to just "merge" them. p. 13, "entropy gradients." the meaning of this term should be further clarified p. 13, "to a large extent driven by entropic gradients" give in the paper text itself a few sentences to explain the meaning of this p. 14, "The downstream activity..." this whole paragraph and mechanism is very interesting and could be of high importance but I would like to see also a comparison to an alternative "simple" buffering mechanism. What if the maltose was just allowed to have a high concentration and by that achieve a buffering capacity. Alternatively, it could be that it is interconveted to some other buffer compound that does not employ entropy considerations. Are all these options equally useful (i.e. any low pass will do) or is the mechanism you find favorable? maybe it is favorable because of osmotic considerations? p. 14, "....in a robust manner" In this context the question from before arises, Are there other mechanisms to achieve these goals and is the entropy driven mechanism better than other mechanisms to achieve these goals. p. 29, Figure 2 caption and figure, I could not see an explanation in the figure or the caption what is the grey in A and similarly for B and C the yellow and cyan. This makes things very difficult. It took me a lot of time to understand these probably refer to different initial conditions. I think this is not the key point. You can have one panel showing several starting conditions but in the first panel keep things simple and clear. P. 36, Figure 3, "line width should be made larger so that colors will become clearer"

1st Revision - authors' response

05 September 2011

Reviewer #1 (Remarks to the Author): This is a novel and ingenious approach to studying factors that influence polymer metabolism. The theory makes very specific predictions about the outcomes of incubating carbohydrate polymers with different types of enzymes, and there is extremely close agreement between the predictions and the experiments designed to test the theory.. This could have a major impact on our understanding of carbohydrate metabolism, especially in plants. The manuscript is well-presented and written very clearly. We thank the reviewer for this encouraging remark.

Reviewer #3 (Remarks to the Author):

© European Molecular Biology Organization

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The authors deal with the question of the product distribution, kinetics and functional role of enzymes working on carbohydrates where the change in enthalpy is negligible and entropy is the main player in governing the distribution of different products. This is an often neglected subject but of interest due to the role of such enzymes in metabolism of some of the main players inside cells. I think the analysis is interesting and illuminating and the experimental verification fits nicely the proposed theory. A major challenge is the clarity of some of the finer points in the analysis. I give detailed comments below of where I think this can be improved and where I had difficulties following the explanations and more clarifications are needed before publication. P. 4, "state variable" - explain meaning to readers. We have added the following explanatory text: "The thermodynamic theory allows characterizing systems with a huge number of particles by a small number of state variables, such as temperature, pressure, internal energy or entropy. We develop an analogous description to show that the same principle holds for polydisperse reactant mixtures. In these systems, the state variable entropy plays a particularly important role." Additionally, we have outlined the basic concepts in the Box. P. 5, "Two such CAZymes" - indicate which They have now been mentioned (disporportionating enzyme 2, DPE2 and cytosolic phosphorylase, Pho). P. 6, will help to state that DPini does not have to be an integer Has been clarified in the Box where we now explicitly write: "As a consequence, the average DP maintains the constant value DPini, which is in general determined by the average DP of the initially applied mixture of glucans and can assume also non-integer values." p.6, "the total number of glucose residues, DPini," - you refer to it here as "total" but I afterwards understood that it is actually (also) the "average". This has caused me a lot of confusion and I had to read this several times. Must clarify. A concrete toy example with numbers can be extremely helpful. The reviewer is correct that ëtotalí is misleading. In the revised version, we only use the more precise term ‘average’. In the Box, we systematically explain the specific example DPini=4, for which we have also given explicit numbers, e.g. for the predicted characteristic exponent and the equilibrium entropy S. This should help to avoid confusion and make the concepts clearer to the reader. p. 7 because beta is always in the exponent and its value is actually a ln of some expression, this equation can also be stated without any use of beta or exponents. I would suggest at least showing it. Probably something like: 1/(Dini-1)*((Dini-1)/Dini)^D In fact, only assumes this simple form of a logarithm of some expression for the special case of DPE1. In general, the functional form of depends on the enzymatic constraints and for most cases a closed expression does not exist but the definition of is given in the form of an implicit equation. However, an exponential distribution is found in all examples considered in our manuscript. We therefore think an expression without or exponents is rather misleading because it does not illustrate the key meaning of the formulas. We have made it clearer in the text that the particularly simple form of (a log of something) is a special case and that for other enzymes the corresponding expression will look different. In the Box, we state: "For DPE1, the exponent assumes the particularly simple form..." and "While exponential distributions as in Eq. (1) are also found for the other examples considered in the text, the specific expressions for differ due to additional constraints on the enzymatic transitions." p. 7 "distribution" - it would be instrumental to take an example of DPini having some small value (say =2) and showing the theoretical distribution clearly in a schematic figure/text discussion. We have illustrated the example of DPini=4 in the Box. We have chosen 4 because it allows for a


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larger variety of reactions and can be used to demonstrate the diversity of possible transfers. We have also schematically shown the theoretical equilibrium distribution and stated the predicted numbers for the exponent as well as the entropy in equilibrium. p. 7 "It is predicted", not clear what "it" refers to The corresponding part has been clarified where we explain now in the Box text: "The exponent is predicted to decrease when the average initial degree of polymerization, DPini, increases." p. 7, "generalization of the mass action ratio in equilibrium", this sounds important but I couldn't fully understand it from the text itself. Maybe an example of how these are related will clarify. We are thankful for this comment because it helped us to convey this important message more convincingly. In the Box, we have devoted a paragraph to explain exactly what we mean by the ëgeneralization of the mass action ratio in equilibriumí. Summarizing, the equilibrium constants of all possible reactions can be calculated from but not vice versa. Therefore, knowledge of contains more information than knowledge of the Keq-values. This motivated us to call a generalization of the equilibrium constant. The new text in the Box is: "The equilibrium constant Keq for the single reactions can be calculated from the equilibrium concentrations (3), resulting in Keq=(xn-qxm+q)/(xnxm)=1 for every individual reaction. The functional form of , given by Eq. (4), provides additional information by revealing the dependence on the initial conditions: The exponent is predicted to decrease when the average initial degree of polymerization, DPini, increases. Apparently, _serves as an appropriate descriptor of equilibria of polydisperse mixtures and, since it entails the equilibrium constants of the individual reactions, it can be considered as a generalization of the mass action ratio in equilibrium." p. 8, "sum of glucose and maltose molecules" the natural way to state this seems to me to be only the sum of maltose. because glucose sum is also constant it is true also for both, but not as directly clear in my mind. In our original manuscript, this was indeed not clear enough. In fact, it is the sum of the concentrations of maltose and glucose that remains constant, while each single concentration may vary over time. To clarify this point, we inserted the following text: "In contrast to DPE1, DPE2 transfers single glucosyl residues only and neither utilizes maltotriose as a donor nor maltose as an acceptor (Steichen et al, 2008). This means that maltose molecules cannot be elongated and maltotriose molecules cannot be further shortened. Thus, whenever maltose donates a glucose residue a glucose molecule is released, and whenever glucose acts as acceptor a maltose molecule is formed. As a result DPE2 effectively obeys an additional constraint: the conservation of the sum of glucose and maltose molecules (x1+x2=const., see Supplementary Figure S3)." p. 9, "three values, a rate constant reflecting maximal turnover, and two constants reflecting the different subsite affinities" maybe discuss how this compares to alternatives such as an option of characterizing using two maximal turnovers and one affinity. This is an interesting suggestion and indeed, as the reviewer proposes, the characterization is equally possible with two maximal turnovers and one affinity. However, this is not supported by enzymatic studies. It is in fact different affinities of binding sites, which lead to different probabilities of the transfers of glucosyl- or maltosyl residues. For clarification, we have added the following text citing the relevant experimental evidence: "An alternative description based on two maximal turnover constants can reproduce the same kinetics but is biochemically less plausible. Glycoside hydrolase domains usually possess several binding subsites which allow for different alignments of the substrate formed with different probabilities (Thoma et al 1971). In contrast, the transfer step always acts between well-defined subsites irrespective of the actual alignment of the substrate (Barends et al 2007)." p. 12, "this results in a sequestration of glucoses from the DPE1-mediated transfer reactions." I did not understand this paragraph and sentence. I suggest clarifying further. © European Molecular Biology Organization

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We have rephrased this passage to improve clarity: "When the plastidial HK or the glucose exporter is active, glucose molecules are removed from the polydisperse pool of -1,4-glucans and are therefore no longer available as acceptor substrates for the DPE1-mediated transfer reactions. Our results (Fig. 4) suggest that under these conditions DPE1 mediates an energy-independent elongation of glucans and thereby provides substrates for the plastidic -glucan phosphorylase or even supports starch synthesis directly. The latter conjecture is consistent with the phenotype of a C. reinhardtii mutant lacking a functional DPE1 which displays aberrant starch synthesis (Colleoni et al, 1999)." p. 13 "integration of carbon fluxes coming from many chloroplasts" this seems to be a very interesting suggestion. Worth explaining further what is the challenge here. Why it is not simple to just "merge" them. We see two main challenges: First, fluctuations in concentrations (which may arise from changing export rates due to spatial inhomogeneities) have to be dampened to ensure a constant functioning of downstream pathways. Second, substrates for downstream pathways must also be temporarily provided if carbon influx stops (as is the case during sudden light-dark transitions). We have added to the text the following motivation for our thoughts: "Notably, Arabidopsis leaf cells contain around 100 chloroplasts, and starch content and degradation rate may vary considerably depending on external conditions such as light intensity or day length (Gibon et al, 2004; Graf and Smith, 2011). Maltose export occurs locally through the specific maltose exporter MEX1 (Niittyl‰ et al, 2004) leading to inhomogeneous maltose concentrations in the cytosol. A challenge for the plant is to integrate fluctuating carbon fluxes in a way which ensures stable levels of substrates for downstream processes, in particular glucose and G1P. Moreover, the supply of these substrates has to be temporarily ensured during light-dark transitions." p. 13, "entropy gradients." the meaning of this term should be further clarified We stated together with the relevant reference that an ëentropy gradientí means the change of entropy while a reaction is progressing. p. 13, "to a large extent driven by entropic gradients" give in the paper text itself a few sentences to explain the meaning of this The reviewer is right that this statement needs more comments for the broad readership. We give now more explanations in the corresponding paragraph: "While system 2 depends on a classical enzyme catalyzing one specific reaction, the enzymes of system 1 produce a polydisperse pool of metabolites. As demonstrated above, an important contribution of the driving force of these enzymes is an increase in the mixing entropy of the reactant mixture (see also Sections S2.2 and S2.3 in Supplementary Information). In this sense, system 1 is, in contrast to system 2, to a large extent driven by entropy gradients, defined as the change of entropy with reaction progress (Wicken, 1978).." p. 14, "The downstream activity..." this whole paragraph and mechanism is very interesting and could be of high importance but I would like to see also a comparison to an alternative "simple" buffering mechanism. What if the maltose was just allowed to have a high concentration and by that achieve a buffering capacity. Alternatively, it could be that it is interconveted to some other buffer compound that does not employ entropy considerations. Are all these options equally useful (i.e. any low pass will do) or is the mechanism you find favorable? maybe it is favorable because of osmotic considerations? We are thankful for this interesting suggestion and have discussed these alternative options in the main text and present some new simulation results in the Supplementary Figure S6. To summarize, high maltose concentrations are biologically infeasible due to toxicity and osmotic pressure. An alternative buffer not based on polydispersity can in fact act as a low-pass filter, but its function would require very high buffer concentrations. Thus, as the reviewer already correctly assumed, it would also imply a high osmotic pressure. Another advantage of the polydisperse buffer is its ability to autonomously adapt its buffer size. The ability to build long chains allows storage of a large


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number of glucose residues per buffer molecule without causing exceeding osmotic pressure while at the same time the buffer capacity can simply be increased by increasing the average DP. This is now explained in detail in the corresponding Supplementary Text Section S3.2 and in the main text: "For two reasons, a simple buffering by high maltose levels is biologically not feasible (Sharkey et al, 2004): first, high maltose levels are toxic to the plant and second, it would imply a high osmotic pressure on leaf cells because the plasma membrane is impermeable for maltose. A low-pass filter could in principle also be achieved by a monodisperse maltose buffer, in which maltose is bound to a hypothetical buffer molecule with a higher capture rate compared to its release rate (see Section S3.2 and Supplementary Figure S6). However, this would again lead to a high osmotic pressure since the buffer concentration has to be large in order to compensate fluctuations. Furthermore, cells would need to regulate the buffer concentration in dependence on the ratio of maltose influx to glycolytic activity. In case of high maltose influx, the buffer becomes saturated, leading to a reduced capability to dampen fluctuations. This can only be compensated by further buffer production. The SHG buffer mechanism circumvents these problems. First, high osmotic pressure is avoided because of its polydispersity. Second, the buffer size is intrinsically regulated because accumulation of maltose will simply lead to the production of glucans with a longer DP without the need to increase the concentration of buffering molecules." p. 14, "....in a robust manner" In this context the question from before arises, Are there other mechanisms to achieve these goals and is the entropy driven mechanism better than other mechanisms to achieve these goals. The main advantage of the SHG pool mechanism is that it acts similar to an adaptive filter while a classical (monodisperse) buffer system would need some external control mechanism (see above). This is now also mentioned in the Supplementary Text Section S3.2. p. 29, Figure 2 caption and figure, I could not see an explanation in the figure or the caption what is the grey in A and similarly for B and C the yellow and cyan. This makes things very difficult. It took me a lot of time to understand these probably refer to different initial conditions. I think this is not the key point. You can have one panel showing several starting conditions but in the first panel keep things simple and clear. We really wish to express our thanks to the reviewer for pointing out this unclearness. We have now a schematic Figure in the Box where we show an illustrative example with only one (pure) starting condition and the resulting equilibrium distribution. Here we also introduce the relevant time and entropy definitions and believe that the following Figures are much better understandable now. Furthermore, we have improved the corresponding Figure legend according to the suggestions. P. 36, Figure 3, "line width should be made larger so that colors will become clearer" Done.


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