Subjects’ interaction is the core of most human activities. This is the reason why a lack of coordination is often the cause of missing goals, more than individual failure. While there are different subjective and objective measures to assess the level of mental effort required by subjects while facing a situation that is getting harder, that is, mental workload, to define an objective measure based on how and if team members are interacting is not so straightforward. In this study, behavioral, subjective and synchronized electroencephalographic data were collected from couples involved in a cooperative task to describe the relationship between task difficulty and team coordination, in the sense of interaction aimed at cooperatively performing the assignment. Multiple-brain connectivity analysis provided information about the whole interacting system. The results showed that averaged local properties of a brain network were affected by task difficulty. In particular, strength changed significantly with task difficulty and clustering coefficients strongly correlated with the workload itself. In particular, a higher workload corresponded to lower clustering values over the central and parietal brain areas. Such results has been interpreted as less efficient organization of the network when the subjects’ activities, due to high workload tendencies, were less coordinated. Most human activities are based on the interaction between two or more subjects, therefore the success of a task is based not only on high individual performance, but also on the ability to do effective teamwork. In this regard, during the last decade one of the aims of social neuroscience has been to define objective measures, mainly based on neurophysiological signals, of successful social and cooperative interaction ,2.During highly demanding tasks requiring cooperation among subjects, decreases in performance could be due not only to the failure of a single subject, but also to a lack of coordination within the team. In fact, it has been assessed that team coordination, defined as team members’ interaction aimed to jointly perform a key function, has positive effects on performances and affects cognitive, physiological and perceptual aspects of the involved subjects .Team coordination is usually evaluated using different subjective measures. In the aviation field, for example, subject-matter experts (SMEs) are responsible for analyzing crewmembers’ interactions by means of questionnaires during a mission preparation with the aim of predicting the success of the mission itself . Dodel eThe combination of behavioral data and brain signals ) were used to identify the presence of beta-gamma complex in coordinated activities  and a phTherefore, an objective evaluation of the mental workload under which the team is working could avoid a decrease in performance, which in cognitive psychology is known as the inverted “U-shape” relation between workload and performance , and an To investigate objectively the interaction by means of brain signals, we used the EEG hyperscanning technique , which iIn this work, we analyzed data gathered from couples of participants that shared collaborative tasks in the NASA-Multi Attribute Task Battery under different difficulty levels with the aim to investigate the relationship between workload and interaction effects. In particular, we hypothesized that (i) the density of inter-brain connections, as it has been associated with different levels of cooperation, increases when there is more cooperation between subjects , and thaThe selection of the participants was done in order to ensure the homogeneity of the experimental sample in terms of age, gender and educational background. In particular, informed consent was obtained from 10 healthy male participants (25 ± 3 years old), recruited on a voluntary basis, from the National University of Singapore (NUS), Centre for Life Sciences, after an explanation of the study. The experiment was conducted following the principles outlined in the Declaration of Helsinki of 1975, as revised in 2000. The study protocol has been approved by the local Ethical Committee. All the recruited participants accepted to participate to the study and each of them has been paid SG$200 to attend the whole experimentation. Additionally, the participants have been instructed to avoid alcohol, caffeine and heavy meals right before the experiments.The NASA-Multi Attribute Task Battery  from the center of the screen, as reported in the following formula:The indexes of the auditory monitoring task and emergency light task have been defined as a linear combination of accuracies in terms of correct answers  and the ratio between the subject’s reaction time and the maximum time for answering; then, the results have been multiplied by 100 in order to obtain a percentage, as reported in the following formulas:Finally, the index for the fuel managing task has been defined as the mean value of the fuel level in the main tanks and then multiplied by 100, as reported in the following formula:In order to get a global Performance Index, the average of the previous indexes has been calculated.The EEG was recorded by a digital monitoring system  with a sampling frequency of 256 Hz. All the 30 EEG electrodes for each subject were referred to both earlobes, grounded to the AFz channel, their impedances were kept below 10 kΩ, and the recording systems was synchronized to avoid delay between the signals recorded from two different subjects.The EEG signal was firstly band-pass filtered with a fifth-order Butterworth filter , and then it was segmented into epochs of 1 s. Each EEG epoch with amplitude higher than ±80 μV was removed in order to have an artifact-free EEG dataset from which compute the workload and estimate the parameters for connectivity analysis. All the analysis tools have been implemented in Mathworks MATLAB.From the artifact-free EEG dataset, the power spectral density (PSD) was calculated for each EEG epoch using a Hanning window of the same length of the considered epoch (1-s length means 1 Hz of frequency resolution). Then, the EEG frequency bands were defined accordingly with the individual alpha frequency (IAF) value estimated for each subject . Since tArtifacts-free epochs acquired simultaneously from each couple underwent a multiple-brain connectivity analysis. This analysis provide the information flows exchanged between scalp areas within each single subject (intra-connections) and between the couple (inter-connections), namely, scalp areas belonging to the two subjects in pair. Multiple-brain connectivity estimation is computed through the partial directed coherence (PDC) estimator adapted to the multi-subject case .PDC is a full multivariate spectral measure used to determine the directed influences among any given pairs of signals in a multivariate data set. This estimator represents a frequency version of the concept of Granger causality .t refers to time and N is the number of considered signals. Supposing that the following multivariate autoregressive (MVAR) process is an adequate description of the dataset E(t) =  is a vector of multivariate zero-mean uncorrelated white noise processes, A(1), A(2),…, A(p) are the NxN matrices of model coefficients and p is the model order, usually chosen by means of the Akaike Information Criteria (AIC) for MVAR processes [p lags considered in the estimation.Let rocesses . Equatioij coefficient of multivariate autoregressive (MVAR) model used for modeling the dataset under investigation.It is possible to define the PDC estimator as follows:In the present paper, we employed a different normalization of PDC estimator called generalized PDC (gPDC) recently introduced to circumvent the numerical problem associated with time series scaling . gPDC caained in  where thMultiple-brain connectivity patterns were estimated for each experimental condition  and each pair included in the study on 20 electrodes . The obtained gPDC values were averaged within three frequency bands .t-test between connectivity patterns related to the target experimental conditions (Easy and Hard) and those referring to the corresponding baseline. The statistical comparison was repeated for each of the three frequency bands.In order to obtain Grand Average Statistical Connectivity Maps, we performed a paired Connectivity matrices estimated for each subjects pair in Easy and Hard condition were statistically compared, at single-subject level, with threshold values extracted by applying the 95th percentile on the baseline-related gPDC distribution built among the experimental group. Such comparison made it possible to obtain for each couple, each experimental condition and each EEG band, an adjacency matrix on which graph theory indices were calculated.The density of inter-brain connections in each condition was computed as the ratio between the number of existing inter-connections, and the number of all possible connections between subjects.Furthermore, we decided to consider indices providing local information about the level of interaction between the two subjects: strength and clustering coefficients. According to  strengthN is the set of all nodes in the network; i vertex exerts influence on j vertex.The strength is defines as : (11)kiwi that belongs to set N, i.The clustering coefficient of a vertex in a network is the fraction of triangles around a node and is defined as :(12)Ci=2In this case we are interested only in evaluating the connections between subjects, therefore the strength and the clustering coefficient were computed on the between brain networks. Then the two indices were averaged across four main scalp areas: frontal ; central ; parietal , and; occipital .These indices were then statistically compared between Easy and Hard conditions in three frequency bands  for the whole population, as no significant differences in terms of workload perception were found between the Pilot and Co-Pilot groups. Moreover, their values were correlated (Pearson’s correlation) with those of the mental workload index in the considered experimental group.p = 0.014) was found (panel a in p = 0.625) and in Hard (p = 0.438) according to the Wilcoxon test. On the contrary, considering the entire experimental population, the perceived workload in the Hard condition was significantly higher (p = 0.000018) than the Easy (panel b in p = 0.059).Moving from the Easy to Hard condition, a significant decrease in the global performance index , whilst the scalp model on the right represents subjects doing tracking and lights task (Pilot). Only significant (p < 0.05) connections were reported by means of arrows whose color codifies the averaged value of the connection. The value of inter-brain density (D) for each condition is also reported. It has to be noticed the lower number of inter-connections in the Hard condition with respect to the Easy one.The inter-brain density showed an increasing trend in the Hard condition in the EEG theta and alpha band, while a decrement in EEG beta band, but none of these differences were statistically significant .R = −0.772, p = 0.008) and in the beta band . Moreover, the clustering coefficient averaged over the parietal brain area . No significant correlation was found in the Easy condition.The clustering coefficient averaged in the brain areas of interest has been correlated with the mental workload index. Significant negative correlations were found for the clustering coefficient averaged over the central brain area in the Hard condition, both in the alpha  increase in the Hard condition, coherently with the cognitive psychology literature that demonstrated an inverted relationship between mental workload and performance after exceeding an optimal threshold [Firstly, we analyzed the effects of different task difficulty on the subjects: a more demanding condition caused a significant reduction in performance with respect to the Easy condition. Subjective measures (the NASA-TLX questionnaire) reflected significant increments in the Hard condition, showing that it was actually perceived as more demanding. The neurometric  showed a marginally significant (hreshold .p < 0.05) from baseline condition, were higher in Easy than in Hard , significantly different ( in Hard  conditio in Hard . In prevHigher strength due to inter-connections during a more demanding task (Hard) in the EEG alpha band  can be explained as a higher involvement of those areas in both participants, as the strength is explanatory of brain processes . Then, wFinally, during the Hard condition the subjects who exhibited lower workload also had lower clustering coefficient in the central and parietal brain areas, as reported in the negative correlation . Since hThese results in terms of bands and areas of interest are coherent with previous knowledge both about the role of EEG alpha and beta bands , and aboThe proposed study demonstrated that different workload demands impacted differently on the individual team member both in terms of performance, and experienced workload, but also on the whole team in terms of different local network’s features, describing the brain activities that were Granger-caused to each other by the two subjects.Strength value was proven to be significantly higher for a more difficult task in the alpha band, while clustering coefficient showed negative correlation with workload index in the Hard condition in bands and areas of interest, respectively, alpha and beta EEG bands and central and parietal brain areas, as expected in coordination and interaction phenomena.To sum up, two subjects sharing a task can be seen as a system where mental resources required for each subject and some features representing the whole system are not independent: in the context of social neuroscience this relationship could be a fertile ground for the definition of a neuromarker of efficient interaction.In this study only a limited number of indexes was used with particular focus on local properties. Nevertheless, in the future studies, a more complete description of global network properties and different kind of motifs, aside from clustering, will be computed to better investigate the relationship between task difficulty and interaction. An online analysis of EEG signals will be used to follow how both neuromarkers of interaction and workload vary over time in order to predict performance decreases caused by lack of interaction and/or overload condition.As the EEG hyperscanning approach makes it possible to examine real social behavior in a real environment, by using a higher number of electrodes it could be also possible to reconstruct, using functional imaging methods based on EEG, the cortical and sub-cortical brain activations with high temporal resolution to investigate how interaction processes and behaviors are implemented by brain system.Finally, although the size of the experimental group was low, this work showed convergent findings with previous research and the possibility to correlate information of multiple-brain system with workload assessment to have a wider view of how coordinated interaction is affected by different workload demands and, in turn, how it can affect performance. Moreover, since the considered experimental task (NASA MATB) is freely available, further experiments will be run or replicated in order to enlarge the experimental group and validate the results described in the presented work.


The meniscus plays an important role in the integrity of the knee joint. Therefore, meniscus tissue preserving techniques for the therapy of meniscus injuries seem to be reasonable. One of the important questions is whether meniscal repair can prevent the knee joint from early onset of osteoarthritis.According to the review of the current literature, the principles of a successful meniscal repair are explained and the functional outcome and its impact on the prevention of osteoarthritis are analyzed in this article.Current data show a positive impact of a successful meniscus repair on the functional outcome in long-term. By this a protective effect on the development of osteoarthritis via the repair of meniscus lesions to restore the meniscus integrity can be confirmed. However, higher rates of re-operations in context to meniscus suturing have to be considered.Due to the improved functional outcomes as well as preventive effect on the development of osteoarthritis within the knee joint in long-term, it is of importance to preserve as much meniscus tissue as possible in meniscus therapy. Patients previously have to be informed about the higher revision rate in context to meniscus suturing. The meniscus plays a decisive role for the integrity of the knee joint. It includes shock absorption and transmission, but also joint stabilization and proprioception as well as lubrication and nutrition of the articular cartilage pre-existing cartilage lesionspersisting ligamentary joint instabilityaxial deviation obesityage > 40 yearslow activity levelFollowing criterias are defined as risk factors for the development of degenerative changes in context to meniscus injuries (according to Mordecai)  is nourished by diffusion from the synovial fluid, the periphery in the so-called red-red zone has a vascular supply. Between the white-white zone and the vascularized portion a red-white transition zone is located.Especially the outer third and, to a lesser extent, the red-white transition zone show a regenerative potential with good preconditions for a successful meniscus suturing  meniscectomy is usually described as a short-term significant improvement of the symptoms and fast rehabilitation. However, even the meniscus suturing is described to go along with good clinical results in more than 80% of the cases in the short-term outcome  and the ones being treated between month 7 to 12 (13.7%). The cartilage lesions did not show any differences in treatment at these time points. In contrast, it was found that meniscus injuries associated with ACL reconstruction could be better reconstructed if the surgery was performed in the course of the first 6 months after trauma   general joint wear, receive an arthroscopic partial meniscectomy. In the latter case, however, conservative therapy should also be primarily discussed and considered  or mesenchymal stem cells, could provide an advantage for the regeneration of the bradytrophic meniscus tissue in terms of extension of the indication and reduction of the treatment failure rate of meniscus suturing. Results of own, preclinical studies showed meniscus lesions in the avascular region for example could be healed by the use of mesenchymal stem cells  meniscectomy. It usually goes along with a loss of symptoms and functional improvement in short-term  were found  meniscectomy meniscus preserving techniques such as meniscus suturing show a cartilage protective effect in long-term. Noyes et al. evaluated the meniscal status of 33 patients having meniscus suture after a mean follow-up of 16.8 years by MRT scan. No degenerative changes in the operated compartment or differences concerning the status of degeneration in comparison to the healthy, contralateral site were found in patients after having successful meniscus suturing (Lee et al., Regarding the development of gonarthrosis, techniques preserving a functional intact meniscus tissue are also of advantage in comparison to partial meniscectomy. Stein et al. showed no progress of radiological signs of osteoarthrosis in 81% of the evaluated patients after almost 9 years after meniscus suturing, whereas a stop of a degenerative progress was only seen in 40% of the patients after partial meniscectomy (Xu & Zhao, Meniscus preserving techniques to obtain a functional intact meniscus after meniscus injury in long-term are of great importance for the prevention of the development of osteoarthritis in the knee joint. Different significances and distributions of the studies are probably based on the heterogeneity of the evaluated patients, the different operation techniques and outcome analyses.The authors of the manuscript recommend, based on the studies cited above, to try to perform meniscus preserving techniques, such as meniscus suturing, whenever achievable, and if a partial meniscetomy is necessary, to save as much meniscus tissue as possible.Additionally, with suture treated patients always have to be informed about the failure rate, the extended period of rehabilitation and the higher rate of surgical revisions. However, further research projects, concerning for example augmented meniscus suture techniques, are necessary to reduce the failure rate and extend the indicational criterias for the meniscus preserving techniques.


An experimental test of this hypothesis revealed that affecting SM homeostasis converted flat cisternae into highly curled membranes with a concomitant dissociation of membrane curvature-generating proteins. These data lend support to our hypothesis that SM metabolism controls the structural organization of a Golgi cisterna. Together with our previously presented role of SM in controlling the location of proteins involved in glycosylation and vesicle formation, our data reveal the significance of SM metabolism in the structural organization and function of Golgi cisternae.The flat Golgi cisterna is a highly conserved feature of eukaryotic cells, but how is this morphology achieved and is it related to its function in cargo sorting and export? A physical model of cisterna morphology led us to propose that sphingomyelin (SM) metabolism at the DOI:http://dx.doi.org/10.7554/eLife.24603.001 The Golgi complex is a hub inside cells that transports many proteins to various parts of the cell. It also receives freshly made proteins and modifies them to help them mature into their final active forms. The complex is made up of a stack of disc-like membrane structures called cisternae.Are the shapes of the cisternae important for the Golgi complex to work properly? Membranes are made of mixtures of molecules known as lipids and proteins. Previous experiments show that when the mixture of lipids in the Golgi membranes changes in a specific manner, the cisternae curl into an onion-like shape and the Golgi cannot process or send out proteins anymore.Campelo et al. used mathematics and experimental approaches to investigate what causes the Golgi to change shape when the lipid mixture of the cisternae changes. A mathematical description of the shape of the Golgi predicted that some proteins keep the cisternae flat by holding the membrane rim that connects the two faces of a cisterna. To test this prediction, Campelo et al. performed experiments in human cells, which showed that when the mixture of lipids in the Golgi membranes changes, certain proteins jump from the rim, causing the cisternae to curl. These same proteins are also needed to transport cargo proteins out of the Golgi, meaning that there is a connection between the shape of the Golgi and the tasks it carries out.The shape of the Golgi complex is altered in Alzheimer’s disease and many other neurodegenerative diseases. The next challenges are to understand how these shape changes happen, how this affects cells, and if it could be possible to develop drugs that prevent these changes from occurring in patients.DOI:http://dx.doi.org/10.7554/eLife.24603.002 Interesormation  as well ormation . Based oormation . HoweverMotivated by these experimental observations, we decided to investigate the physical mechanisms by which SM metabolism controls Golgi cisternae morphology, with a general aim at understanding whether the shape and the function of the Golgi complex are two sides of the same coin and how they relate to each other. Curling of a flat Golgi cisterna has, from a physical point of view, severe consequences. A flat cisterna has a large surface area at its rim with a very high membrane curvature thereby bearing large elastic stresses . Hence, The shape of cellular organelles, such as the Golgi complex, results from the generation and stabilization of the curvature of their membranes . AccordiExperimental evidence has suggested the existence of nanoscopic SM-enriched liquid-ordered domains at the Golgi membranes, although direct visualization has remained challenging . Based oThe budding machinery, such as the COPI and clathrin coats, is responsible for generation of large membrane curvatures that are required to form transport carriers at the Golgi membranes . It is rIn order to quantify the relative effect in Golgi shaping of the two mechanisms proposed above, we developed a mathematical formulation of the free energy of a Golgi cisterna as a function of its shape and nanodomain distribution on the membrane. The major assumption of our model is that the time scale of mechanical equilibration of the cisterna shape is much smaller than that of the changes in lipid and protein composition through membrane fluxes. Non-equilibrium shapes should be considered only if the composition would change faster than the shape relaxed to the new equilibrium state . We can κ ~ 1 ms . On the κ ~ 1 ms , resultiWe consider the cisterna membrane to have a shape of a sheet bound by a rim . The shemography . Alternamography . The rimboundary . The disThe free energy responsible for the cisterna shape includes the elastic bending energy of the membrane sheet and rim and also the entropic cost of a non-homogeneous partitioning of rigid nanodomains between the sheet and the rim. The bending energy is computed based on the Helfrich model , in whic.75 nm−1 . The membudding. .The membrane nanodomains are considered to occupy a fraction membrane . The dommembrane .We determined the equilibrium shape of a Golgi cisterna by minimizing the free energy for a given set of geometric and elastic parameters see  upon speOur model predicts that, depending on the values of the two parameters,  diagram . Qualita diagram . Moreoveagram  occurs much faster than the recovery of the flat cisternae morphology and of protein colocalization. This is indicative of a hysteretic behavior of the transition from flat-to-curled cisternae and reverse, as our model predicts.The architecture of the Golgi complex in higher eukaryotes has been the subject of extensive research using numerous experimental approaches, including electron and immunofluorescence microscopy techniques , which Our model predicts the existence of shape bistability within a certain range of values of the membrane spontaneous curvature and of the membrane area fraction covered by rigid nanodomains . Within  barrier . As mentt0=ηR3/κ , where η washout . Those r washout . Accordiur model , we findnerators , the prereatment . These dLikewise, our model predicts that the Golgi cisterna shape transition is, in thermodynamic terms, a first-order transition because the transition is discontinuous in the shape parameter  . This inguration . Althougsections  to compasections .In summary, we have presented a theoretical biophysical model of Golgi cisterna morphology, which describes the existence of stable flat and curled Golgi cisternae for different values of the membrane spontaneous curvature. We experimentally validated some of the model's predictions. In particular, our model helps explaining the mechanisms by which a reversible flat-to-curled Golgi cisternae transition is induced upon disruption of SM homeostasis by short-chain ceramide treatment. Flat Golgi cisternae in untreated HeLa cells have stationary levels of different curvature-inducing proteins, such as components of the clathrin-coated vesicle machinery  and decrOverall, the model presented in here together with some of its experimental validation underscore the crucial role of SM metabolism in regulating the structural morphology and function of the Golgi cisternae. We foresee that future experimental work along these lines will strengthen our predictions and will help to understand better the different factors governing the shape and function of the Golgi complex.N-hexanoyl-D-erythro-sphingosine (D-cer-C6) was obtained from Matreya and dissolved in pure ethanol (Merck) to a 10 mM stock solution. Sheep anti–human TGN46 was obtained from AbD Serotec . Mouse anti-p230 was obtained from BD . Goat anti-Clathrin-HC antibody was from Santa Cruz . Alexa Fluor–labeled secondary antibodies were obtained from Invitrogen.HeLa cells, obtained from ATCC, were cultured in DMEM (Lonza) containing 10% FCS. HeLa cells stably expressing the plasmid encoding the first 100 amino acids of rat mannosidase-II in the pEGFP-N1 vector (HeLa-MannII-GFP cells) were described previously . All celFor clathrin-HC immunostaining, samples were fixed and permeabilized in methanol for 6 min at −20°C. For p230 immunostaining, samples were fixed with 4% formaldehyde in PBS for 20 min and permeabilized with 0.2% Triton X-100 in PBS for 30 min. Fixed cells were then blocked in 2% BSA in PBS for 30 min before antibody staining. Cells were then sequentially incubated for 1 hr at room temperature first with primary and then with secondary antibodies diluted in blocking buffer. Samples were analyzed with a confocal system  in confocal mode using a 100x, 1.4 NA objective and HyD detectors (Leica). Alexa Fluor 488–, 568-, 594-conjugated secondary antibodies were used. Images were acquired using the Leica software and converted to TIFF files using ImageJ . Two-channel colocalization analysis was performed using ImageJ, and the Pearson’s correlation coefficient was calculated using the Manders’ coefficients plugin developed at the Wright Cell Imaging Facility .The samples were fixed and prepared using standard methods, essentially as described previously . In brieIn this section we formulate in mathematical terms the physical model we used to describe how Golgi cisterna morphology is controlled by variations in SM homeostasis and metabolism. In the two following subsections we describe, respectively, (i) the system geometry, that is, the possible geometrical configurations of the Golgi cisterna; and (ii) the system free energy.The Golgi complex in mammalian cells and in most eukaryotes consists of multiple stacks of flattened disc-like cisternae . Our precisterna . Alternana  see . On the Thus, for the flat morphology, where which sets the constrained value of the total surface area of a Golgi cisterna. Finally, by using In the Appendix we derive simpler version of these equations by imposing a few approximations. This approximate theory will allow us to have analytical estimations of the main numerical results of this article.Our model considers that the total free energy of a Golgi cisterna, The free energy of lipid nanodomain partitioning is an entropic term associated with a possible non-homogeneous distribution of liquid-ordered nanodomains along the membrane. This free energy term is given bywhere seconds)  than theseconds) . Hence, seconds) (7)Spart=where where where The second contribution to the total membrane free energy comes from the energy of membrane bending, given by the Helfrich Hamiltonian . The memtrans-Golgi membranes  of the top, bottom, and rim bilayers (index i). Considering that the total amount of DAG is symmetrically distributed between the luminal and cytosolic monolayers of the Golgi membrane, these quantities are related to the total membrane DAG area fraction, where molecule , and ϕDA In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.eLife. Your article has been favorably evaluated by Jonathan Cooper (Senior Editor) and three reviewers, one of whom is a member of our Board of Reviewing Editors. The following individual involved in review of your submission has agreed to reveal his identity: Pierre Sens (Reviewer #2).Thank you for submitting your article "Sphingomyelin metabolism controls the shape and function of the Golgi cisternae" for consideration by The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.All three reviewers appreciated very much your effort to compare your theoretical model on Golgi shape and its bistability to experimental data. However, some concerns were raised on hypotheses that underlie your model such as an equilibrium statement or the absence of discussion about the consequence of lipid fluxes. Moreover, the referees found that your experimental data should be reinforced to convincingly support your model. You will see that there is good agreement between the reviewers. Notably they both have difficulty in reconciling the following three points (i) your model ignores the cis/trans asymmetry of the Golgi, (ii) your experimental approach seems to target only the coating of trans side, (iii) however, all cisternae similarly respond to this treatment.eLife style, we think the high quality of the feedback justifies giving it to you in largely unedited form.At the risk of burdening you with excessive feedback, we have appended a somewhat truncated version of the reviews, to help you identifying points to be clarified. While this is not the typical Reviewer #1:1) The main assumption of the model is that "The equilibrium configuration of a cisterna is assumed to correspond to the free energy minimum." The author should explain the extent to which free energy minimisation is meaningful for such non-equilibrium structure as the Golgi apparatus, which is characterised by fluxes of proteins and lipids.2) The modelling strategy and results, in particular the existence of bistability, are not particularly new for membrane systems. Nevertheless, its application to Golgi cisternae shapes is to my knowledge new. The model and the derivation of the results are well explained. I find it however very unfortunate that the results are mostly presented as numerical results, varying a handful of the many model parameters. It would be much more attractive to have analytical expression for the boundaries of the phase diagram. The full model can obviously not be analytically solved, but the main concepts can be included in a much simpler, and solvable model. The essence of the model is a bendable circular domain with edges. This is essentially the same situation as a membrane domain with a line tension, as is discussed by R. Lipowsky  and many others. This model also predicts bistability (3) The physical mechanism underlying this paper is not new, but its application to the shape of closed membranes  is new, to my knowledge. There is however a vast literature on the shape of vesicles, including stomatocyte shape not dissimilar to the curled cisternae, but driven by completely different mechanisms . This is not discussed at all in this paper, which is rather unfortunate. This paper should make clear that it proposes one possible scenario to explain the observations, but that other scenarii exists.4) Furthermore, previous work describing energetic description of Golgi cisternae, including phase separation of membrane components  317-324), should definitely be cited and the present results compared to the existing one when applicable, in particular concerning the curvature-coupled lateral segregation.5) The theory part of the Materials and methods section gives a full geometrical description of the cisterna morphology, yielding rather cumbersome expressions (for ex. Equation.5). While these expressions are probably useful, approximate expressions allowing to derive the transition boundaries in 6) Such a simplified analytical model would allow to tease apart the different contributions of the overall free energy. It is reported  that the fraction of rigid domains has little impact on the transition. This observation can mean two things: either the additional bending rigidity associated to the nanodomains is irrelevant, or it is compensated by the entropy cost of partitioning. In the absence of partitioning, one can easily understand that the bending rigidity plays no role in the transition, since it is the only energy scale in the problem, as discussed above. The effect of partitioning should be assessed by comparing entropic and elastic terms analytically (even if that means using approximate expressions).7) There is a number of simplifying assumptions in the model that do not appear justified and might well influence the results.7A) The most serious is, to my mind the fact that the radius of the rim is not optimised, but imposed arbitrarily. I can accept the fact that the luminal space h can be fixed by spacer proteins, the rim radius is probably fixed by some minimisation of elastic energy, and should highly depend upon the rim spontaneous curvature. Do the authors have argument to validate their assumption of rim radius independent of the rim spontaneous curvature? I would be looking for theoretical arguments, not experimental argument based on ultrastructural data. Since an energetic description is likely to suggest that the rim radius should depend on its spontaneous curvature, if it is observed experimentally that it doesn't, this would mean that some energetic contributions are not included in the current energy, thus casting doubt on the consistency of the theory with the data.7B) We are dealing here with a model of a mixed membrane containing at least three different types of molecule: some "neutral" lipids, rigid nanodomains, and curvature generators. It is assumed that such mixed, three component membrane can still be described by one bending rigidity one gaussian rigidity, and one spontaneous curvature. The expression of the composite bending rigidity (Equation 12) corresponds to heterogeneous curvature distribution . It is thus very likely that the total curvature energy of this mixed membrane with curvature generators will be very different from the one proposed here if the curvature generators bind preferentially to one of the two components. Apparently, SM regulates both membrane stiffness and the binding of curvature generators, so spontaneous curvature and bending rigidity are probably spatially correlated. The authors should discuss this point.8) Related to 7B): The Abstract claims to investigate the dual effect of SM, which is to affect the rigidity of membranes by forming stiff domains, and to regulates the association of curvature-generating proteins. It is not clear to me what whether SM promotes or inhibit the recruitment of curvature generators. Is this known/implemented in the model?buddingΦ and the latter to a fraction Φ, but no connection is made between these two fractions. If SM mediate both effects, should buddingΦ and Φ be connected?In the model, the former is associated to a fraction Why is the partitioning of the nano-domain partition between the rim and the mid-section subjected to a thermodynamic treatment , but not the curvature agents? This seems a rather arbitrary choice.s h~ Κ/2. This seems quite small compared to the overall energy scale, and does not explain the rather large shift observe Figure 1—figure supplement 2. Could the author provide an estimate for the effect of the spontaneous curvature of the flat part.9) When the entire cisterna including the mid part, has spontaneous curvature, one observes "only a general shift of the shape transitions between the flat and curled cisterna configurations towards the lower values of the membrane spontaneous curvature". It is not clear to me why this shift occurs, since if both sides of the cisterna have the same spontaneous curvature, its contribution to the global energy can only depend on the area difference between the convex and concave sides of the cisterna (which have curvatures of opposite sign). I would then expect the contribution of the spontaneous curvature of the mid part to the energy difference between flat and curled to be or order Κ J10) Related to this, the shape parametrisation is clear for flat cisternae, but a little less clear for curled one . My unde11) The effect above is discussed: "the results are highly insensitive to the amount of curvature generators present in the central part of the Golgi cisternae, basically due to the opposite curvature of the two parallel membranes composing this region." However, 12) The analysis of drug treatment and recovery is the light of the bistability discussed in this paper is quite interesting. I however do not fully understand the implication of the loss, and the recovery, of TGN46 and p230 colocalisation. These proteins appear to be TGN proteins, while this paper discusses the morphology of Golgi cisternae. Furthermore, I thought that clathrin was also mostly localised at the TGN and was responsible for transport between the TGN and the endosomes/plasma membrane. Is the curling of the Golgi cisternae accompanied with structural changes of the TGN? Should we understand the Golgi and the TGN as a single structure? The concentric stacked onion-like structure presumably involves curling of all Golgi cisternae. Where is the TGN located? In the convex or concave region of the curled stack?13) Along the same lines: the curling phenomenon is a spontaneous symmetry breaking, which predict an equal likelihood to curl one way or the other. Is curling equally likely in both direction (i.e. toward or away from the TGN) in experiments? If there is a net tendency to curl one way, that means that symmetry is broken from the start by something. This could be because the line tension effect mostly impact the TGN, which then drive the entire Golgi to curl, but in this case, the energy function should include the other Golgi cisternae. It could also be that symmetry is broken by anterograde or retrograde fluxes, in which case the entire model is problematic. More discussion on this is mandatory.14) In the mind of the authors, is the lateral segregation discussed upon D-cer-C6 treatment related to a lateral partitioning such as the one quantified in 15) The level of clathrin in the Golgi reaches its lowest level after about 30'. This suggest that the loss of the curvature generators saturates after that exposure time . HoweverReviewer #2:Theoretical part1) The authors write: 'The equilibrium configuration of a cisterna is assumed to correspond to the free energy minimum'. Given the emphasis put in local energy minima later in the text, this statement is a little bit confusing.2) The authors write: 'the results, presented in 3) In a previous study, the authors proposed an alternative mechanism for the flat to curled shift: “We suggest that these changes are a consequence of the effect of d‐ceramide‐C6 on membrane fission versus membrane fusion at the Golgi membranes. In the presence of d‐ceramide‐C6, transport carriers fuse with the Golgi membranes, however, membrane export is blocked. This increases the surface area‐to‐volume ratio of the Golgi cisternae. This is similar to morphological changes in model membranes as a result of an increase in the surface area‐to‐volume ratio.” Why is this hypothesis no longer considered here?4) A few theoretical papers on the discoïdal shape of membranes or Golgi stacks exist, notably by Derganc, Lipowski, and Svetana. Please comment, compare…5) In terms of curvature, is the curled shape so highly curved as stated in the Abstract? (…affecting SM homeostasis converted flat cisternae into highly curved membranes). Looking at the EM, the curvature of the cup shape cisternae seems rather modest.For the experimental part I have the following concerns:6) The lipid composition and the nature of protein coats associated with the cis and trans faces of the Golgi apparatus are very different. Therefore, why does the Golgi apparatus react globally by changing its shape between flat and curved geometries? Do conditions exist where the trans and cis faces react differently? If PI4P loss is the main effect promoted by short chain ceramide treatment and mostly affects clathrin adaptors recruitment, one would expect that the trans Golgi would be more affected than the cis Golgi.7) If the loss of coats is indeed at roots of the effect observed here, what does happen when BFA or other inhibitors of GEFs are added such as to prevent not only clathrin but also COPI from assembling at the rims? Along the same line: what does happen when a PI4P kinase inhibitor is added (e.g. PIK93)?8) The use of the segregation between p230 and TGN46 as an index of the curled geometry seems quite indirect. What is the relationship between this segregation and the cisternae morphology?9) Does the treatment of cells with ceramide alter the membrane bending rigidity of the Golgi or just promote the release of clathrin? In this respect, I found the Abstract and title quite misleading. The authors put a lot of emphasis there into nanodomain formation and lipid biosynthesis. Therefore, it is tempting for the reader to think that a main factor at play here would be domain formation. Instead, the authors show that the surface density of lipid domains and their size have only minor effects on the cisternae <> curled transition and that the most important factor is the coat coverage. Therefore, the tone of the Abstract should be changed. There is no indication that lipid domains play a role here. Reviewer #1:1) The main assumption of the model is that "The equilibrium configuration of a cisterna is assumed to correspond to the free energy minimum." The author should explain the extent to which free energy minimisation is meaningful for such non-equilibrium structure as the Golgi apparatus, which is characterised by fluxes of proteins and lipids.We agree that the Golgi apparatus is a highly dynamic organelle, which is continuously subject to inward and outward membrane fluxes (e.g. by means of fusion/fission of transport carriers). Remarkably, despite the extensive exchange of membranes, the characteristic stacked-cisternae morphology of the Golgi complex is maintained during interphase.The major assumption of our model is that the time scale of mechanical equilibration of the cisterna shape is much shorter than that of the changes of the membrane lipid and protein composition through the fluxes. Therefore, the cisternae shape is assumed to be mechanically equilibrated for every instant composition. Since the composition is in a steady state, the shape is in mechanical equilibrium corresponding to this steady state composition. Non-equilibrium shapes should be considered only if the composition would change faster than the shape relaxed to the new equilibrium state.We estimated, on one hand, the mechanical relaxation time as a combination of the characteristic viscosity, bending rigidity, and length scale of the cisterna, In the revised version of our manuscript we now discuss this assumption in more detail (subsection “Prediction of flat and curled cisterna configurations”).2) The modelling strategy and results, in particular the existence of bistability, are not particularly new for membrane systems. Nevertheless, its application to Golgi cisternae shapes is to my knowledge new. The model and the derivation of the results are well explained. I find it however very unfortunate that the results are mostly presented as numerical results, varying a handful of the many model parameters. It would be much more attractive to have analytical expression for the boundaries of the phase diagram. The full model can obviously not be analytically solved, but the main concepts can be included in a much simpler, and solvable model. The essence of the model is a bendable circular domain with edges. This is essentially the same situation as a membrane domain with a line tension, as is discussed by R. Lipowsky  and many others. This model also predicts bistability  can be summarized as a tug-of-war between the bending energy of the central part of the cisterna and the bending energy of the rim, the latter being effectively interpreted as an edge energy. Lipowsky applied this idea to study the budding of membrane domains associated with a line tension at their interface with the surrounding membrane, and his model predicted regions of shape bistability between flat or slowly curved membranes and buds . In our model, the "line energy" (corresponding to the bending energy of the cisterna rim) can be characterized by a line tension, which is not constant but depends on the shape of the cisterna (see e.g. Equation (A7) in the Appendix), thus preventing full closure of a highly curled cisterna due to the large negative curvature  of the Golgi rim for very small values of 3) The physical mechanism underlying this paper is not new, but its application to the shape of closed membranes  is new, to my knowledge. There is however a vast literature on the shape of vesicles, including stomatocyte shape not dissimilar to the curled cisternae, but driven by completely different mechanisms . This is not discussed at all in this paper, which is rather unfortunate. This paper should make clear that it proposes one possible scenario to explain the observations, but that other scenarii exists.We apologize for not discussing properly the papers mentioned by the reviewer in our manuscript. In the revised version, they are extensively discussed in relation to our findings .Actually, as reviewer #3 mentions, we previously thought that a reduction in the volume-to-surface ratio of the Golgi cisternae could mechanistically explain our observations . However, our observations indicate no obvious change in the volume-to-surface ratio during the flat-to-curled Golgi cisternae transition  and compelled us to reevaluate our previous hypothesis. Moreover, typical Golgi cisternae have a very low volume-to-surface ratio. We can estimate the dimensionless reduced volume (as defined in Seifert's review) for standard geometric characteristics of a Golgi cisterna to be in the order of 4) Furthermore, previous work describing energetic description of Golgi cisternae, including phase separation of membrane components  317-324), should definitely be cited and the present results compared to the existing one when applicable, in particular concerning the curvature-coupled lateral segregation.We thank the reviewer for bringing our attention to these papers. In our revised manuscript we cite, discuss and compare these papers in relation to our results  Physical description of the free energy of a Golgi cisterna”, second paragraph; Appendix subsection “Analytical considerations of the effect of multiple stacked cisternae on the shape diagram”, first paragraph).In brief, in Derganc et al. Traffic 2006, the authors presented a model to understand the physical mechanisms setting the number of cisternae per Golgi stack, where they compared the cisternae bending energy with the adhesion energy keeping the stack together. In Derganc, Phys. Biol (2007), the author presented a model to analyse whether membrane curvature can promote lateral partitioning of membrane constituents. The author showed that, for a flat cisterna configuration, partitioning of curved lipids is, in general, relatively small (of the order of 10%), in agreement with our computations on curvature-based DAG repartitioning. Moreover, the author also showed that stiff membrane constituents hardly partition away to the flat region of the cisterna, which is in line with our results. In these studies, the authors did not considered changes in the overall shape of a cisterna, which is one of the new contributions of our model.5) The theory part of the Materials and methods section gives a full geometrical description of the cisterna morphology, yielding rather cumbersome expressions (for ex. Equation 5). While these expressions are probably useful, approximate expressions allowing to derive the transition boundaries in We thank the reviewer for this suggestion. We now include a new Appendix in our revised manuscript with an analytical approximation for our numerical results. In particular, we now present an analytical approximation describing the cisterna shape transitions, which we compare with our numerical results see – . It is n6) Such a simplified analytical model would allow to tease apart the different contributions of the overall free energy. It is reported  that the fraction of rigid domains has little impact on the transition. This observation can mean two things: either the additional bending rigidity associated to the nanodomains is irrelevant, or it is compensated by the entropy cost of partitioning. In the absence of partitioning, one can easily understand that the bending rigidity plays no role in the transition, since it is the only energy scale in the problem, as discussed above. The effect of partitioning should be assessed by comparing entropic and elastic terms analytically (even if that means using approximate expressions).Following the reviewer suggestions, we have made some assumptions to reach a relatively simple, approximate analytical expression for the relative contribution of the entropic and bending energies to the total free energy of the system. This analysis, as explained in the Appendix, shows that it is possible to define a critical nanodomain size, ns see – .7) There is a number of simplifying assumptions in the model that do not appear justified and might well influence the results.7A) The most serious is, to my mind the fact that the radius of the rim is not optimised, but imposed arbitrarily. I can accept the fact that the luminal space h can be fixed by spacer proteins, the rim radius is probably fixed by some minimisation of elastic energy, and should highly depend upon the rim spontaneous curvature. Do the authors have argument to validate their assumption of rim radius independent of the rim spontaneous curvature? I would be looking for theoretical arguments, not experimental argument based on ultrastructural data. Since an energetic description is likely to suggest that the rim radius should depend on its spontaneous curvature, if it is observed experimentally that it doesn't, this would mean that some energetic contributions are not included in the current energy, thus casting doubt on the consistency of the theory with the data.We thank the reviewer for bringing up this point, which was not explained in the text. We agree that if the size of the rim radius would not be somehow constrained, the natural tendency of the system as a response of a decrease in the rim spontaneous curvature would be to increase its radius to match the actual spontaneous curvature. In our model, the radius of the rim cross-section is set by the distance between a protein scaffold forming the flat part of a cisterna and the cisterna edge. For example, if such scaffold would extend beyond the cisterna, e.g. if the cisterna was formed by flattening of a big liposome between two infinite flat rigid plates, the edge cross-sectional radius would be simply equal to the cisterna half-thickness, independently of the spontaneous curvature of the rim. The fact that the rim is somewhat swollen as compared to the cisterna thickness reflects the distance to which the scaffold edge approached the cisterna edge. The rim would indeed tend to swell as much as possible within this constraint to match the spontaneous curvature. In this model, the membrane spontaneous curvature could influence the detailed shape of the edge cross-section profile resulting in its deviation from the circular shape. This would be the case for the shapes where The molecular identity of such protein scaffold could be the spacer proteins maintaining the luminal thickness and/or stacking factors keeping the subsequent cisternae stacked. Interestingly, it has been experimentally shown that knockdown of the stacking/tethering factors GRASP55/65 or Golgin45/GM130 in HeLa cells leads to the cisternae unstacking, and swelling of the lumen and rims of the Golgi cisternae .We explained and justified this model assumption in the revised manuscript  Geometrical description of a Golgi cisterna”).7B) We are dealing here with a model of a mixed membrane containing at least three different types of molecule: some "neutral" lipids, rigid nanodomains, and curvature generators. It is assumed that such mixed, three component membrane can still be described by one bending rigidity one gaussian rigidity, and one spontaneous curvature. The expression of the composite bending rigidity (Equation 12) corresponds to heterogeneous curvature distribution . It is thus very likely that the total curvature energy of this mixed membrane with curvature generators will be very different from the one proposed here if the curvature generators bind preferentially to one of the two components. Apparently, SM regulates both membrane stiffness and the binding of curvature generators, so spontaneous curvature and bending rigidity are probably spatially correlated. The authors should discuss this point.metabolism, since SMS-mediated conversion of ceramide to SM parallels the conversion of phosphatidylcholine to diacylglycerol (DAG). DAG recruits and activates protein kinase D (PKD), which in turn regulates the levels of PI(4)P on the cytosolic monolayer of the Golgi membranes and therefore the recruitment of PI(4)P-binding proteins, such as the clathrin adaptor AP-1. Phosphoinositides are mostly localized away from SM-rich rigid nanodomains , thus suggesting that this signaling event is spatially uncoupled from SM-rich rigid nanodomains. Moreover, SMS-mediated synthesis of SM is restricted to the luminal side of the trans-Golgi membrane , whereas recruitment of curvature generators occurs at the cytosolic side of the membrane. How luminal SM connects with the organization of the cytosolic leaflet of the Golgi membrane and the events occurring on that side is, to our knowledge, not well understood. Overall, with all the published data at hand we think it is reasonable to assume that there is no preferential binding of curvature generators to specialized membrane regions.We agree with the reviewer that if curvature generators were to be localized specifically to, say, SM-rich rigid nanodomains, the results could significantly differ from those presented in our paper. However, there are experimental arguments to consider that this might not be the case. As we mentioned in the discussion, our collaborator Giovanni d'Angelo , has recently described the metabolic pathway by which PI(4)P-binding proteins, such as the clathrin adaptor γ-adaptin, are released from the Golgi membranes upon addition of short-chain ceramide . This release is indirectly induced by sphingomyelin (SM) In the revised version of the manuscript we now stress these points both in the Discussion  and when we present the model and describe the localization of membrane curvature generators (subsection “(ii) Physical description of the free energy of a Golgi cisterna”, third paragraph). In addition, we also explicitly mention that the expression of the composite bending rigidity (Equation 12) has the meaning of an average over the rigid and soft patches .8) Related to 7B): The Abstract claims to investigate the dual effect of SM, which is to affect the rigidity of membranes by forming stiff domains, and to regulates the association of curvature-generating proteins. It is not clear to me what whether SM promotes or inhibit the recruitment of curvature generators. Is this known/implemented in the model?budding and the latter to a fraction Φ, but no connection is made between these two fractions. If SM mediate both effects, should Φbudding and Φ be connected?In the model, the former is associated to a fraction ΦThis would indeed be the case if SM directly recruited curvature generating proteins to the Golgi membranes, however, as mentioned above (see our answer to point 7B) this is not the case. It is actually SM metabolism , which controls the levels of curvature generators at the Golgi membranes. We have modified the Abstract to better explain this point.Why is the partitioning of the nano-domain partition between the rim and the mid-section subjected to a thermodynamic treatment , but not the curvature agents? This seems a rather arbitrary choice.Although we agree that a thermodynamic treatment could be implemented also for the distribution of curvature generators along the membrane, we have to take into consideration that these are cytosolic proteins, which are recruited to the membrane by specific lipids and/or adaptor proteins. Moreover, additional considerations, such as the well-known curvature-sensing properties of various curvature-generating proteins , regulate their binding affinities and subsequently affect the lateral partitioning of these proteins between the highly curved rim and the flat central part of the cisterna. Hence, for the sake of simplicity we have considered only the two extreme situations: (i) exclusive localization of curvature generators to the cisterna rim; and (ii) a homogeneous distribution of these proteins along the entire membrane of the cisternae see . We expls h~ kappa/2. This seems quite small compared to the overall energy scale, and does not explain the rather large shift observe Figure 1—figure supplement 2. Could the author provide an estimate for the effect of the spontaneous curvature of the flat part.9) When the entire cisterna including the mid part, has spontaneous curvature, one observes "only a general shift of the shape transitions between the flat and curled cisterna configurations towards the lower values of the membrane spontaneous curvature". It is not clear to me why this shift occurs, since if both sides of the cisterna have the same spontaneous curvature, its contribution to the global energy can only depend on the area difference between the convex and concave sides of the cisterna (which have curvatures of opposite sign). I would then expect the contribution of the spontaneous curvature of the mid part to the energy difference between flat and curled to be or order kappa JSee our global answer to points 9-11 below.10) Related to this, the shape parametrisation is clear for flat cisternae, but a little less clear for curled one . My undeSee our global answer to points 9-11 below.11) The effect above is discussed: "the results are highly insensitive to the amount of curvature generators present in the central part of the Golgi cisternae, basically due to the opposite curvature of the two parallel membranes composing this region." However, h/R as the reviewer pointed out). However, as the reviewer also commented, given that the total surface area of the cisterna is constant during the deformation, cisterna curling leads to an increase in the surface area of the central part of the cisterna, concomitant with a decrease in the surface area of the rim. A non-zero spontaneous curvature of the central part of the cisterna therefore increases the total bending energy of this cisterna part, thereby penalizing cisterna curling and eventually shifting the flat-to-curled cisterna transition towards smaller values of the spontaneous curvature, as shown by our numerical results  The analysis of drug treatment and recovery is the light of the bistability discussed in this paper is quite interesting. I however do not fully understand the implication of the loss, and the recovery, of TGN46 and p230 colocalisation. These proteins appear to be TGN proteins, while this paper discusses the morphology of Golgi cisternae. Furthermore, I thought that clathrin was also mostly localised at the TGN and was responsible for transport between the TGN and the endosomes/plasma membrane. Is the curling of the Golgi cisternae accompanied with structural changes of the TGN? Should we understand the Golgi and the TGN as a single structure? The concentric stacked onion-like structure presumably involves curling of all Golgi cisternae. Where is the TGN located? In the convex or concave region of the curled stack?We showed in In the revised version, we have enlarged and improved the contrast of the immuno-electron microscopy images in We previously showed that short-chain ceramide treatment had several concomitant effects in the organization and shape of the membranes of the Golgi complex and the TGN . We observed by immuno-electron microscopy that the localization of the late Golgi enzyme (trans-Golgi cisternae and TGN) sialyltransferase (ST) tagged with GFP localized to the inner, concave part of the stacked onion-like structure .13) Along the same lines: the curling phenomenon is a spontaneous symmetry breaking, which predict an equal likelihood to curl one way or the other. Is curling equally likely in both direction (i.e. toward or away from the TGN) in experiments? If there is a net tendency to curl one way, that means that symmetry is broken from the start by something. This could be because the line tension effect mostly impact the TGN, which then drive the entire Golgi to curl, but in this case, the energy function should include the other Golgi cisternae. It could also be that symmetry is broken by anterograde or retrograde fluxes, in which case the entire model is problematic. More discussion on this is mandatory.cis-Golgi cisternae. In that case, the curling direction was the opposite, towards the cis-side of the stack. The reasons for this symmetry breaking can be manifold, as the reviewer already indicated, but given our experimental evidence we favor a situation where this is driven by an initial release of rim stabilizers from the trans-side of the stack.Our electron microscopy analysis shows that curling occurs towards the TGN as we explained in point 12 above. Interestingly, a previous study  showed that a morphologically similar curling of the Golgi/TGN stack occurs when HeLa cells are incubated at 15ºC, and that this shape transition is accompanied by the release of COPI proteins from the N cisternae, each of them characterized by a free energy of bending and partitioning. The different cisternae are connected along the stack by certain stacking factors, which we assume  are strong enough to impose that all cisternae curl equally. For the sake of this argument, we disregard the effects of nanodomain partitioning  as well as the analysis of the multiple cisternae scenario in the Appendix of the revised manuscript.14) In the mind of the authors, is the lateral segregation discussed upon D-cer-C6 treatment related to a lateral partitioning such as the one quantified in The mechanisms that leads to protein segregation upon short-chain ceramide treatment still remain unknown. We previously showed that such segregation  has functional consequences, such as defects in secretory cargo glycosylation . We hypothesized that changes in the physico-chemical properties of the membranes induced by the treatment (such as changes in the bilayer thickness) could induce the segregation of such proteins, but our preliminary unpublished data suggests this is not the case. Alternatively, decreased nanodomain levels and increasing partitioning could be a factor driving this segregation, as we proposed in our discussion. However, to be fair, this still remains an open question, which we intend to address in the future.In relation to the second part of the reviewer comment, we fully agree that the correlation between lateral segregation of Golgi markers and cisternae morphology is not 100%. We think that this occurs because during D-cer-C6 washout three different processes occur simultaneously albeit with different dynamics see : (i) rec15) The level of clathrin in the Golgi reaches its lowest level after about 30'. This suggest that the loss of the curvature generators saturates after that exposure time . HoweverWe understand the concerns of the reviewer regarding this apparent contradiction. Indeed, as the reviewer correctly stated before, the level of Golgi protein segregation does not perfectly correlate with the curling of the Golgi cisternae. In the case of protein co-localization, the recovery, as we proposed, would depend on the recovery of the levels and distribution of SM-rich nanodomains, which we expect would indeed depend on the duration of the short-chain ceramide treatment.In respect to Golgi morphology, as the reviewer comments, our results indicate that it mainly depends on the levels of curvature generating proteins at the membrane, and therefore, once the system has returned to the initial levels of clathrin on the membrane after short-chain ceramide washout, the recovery time for Golgi flattening should not depend on how long the treatment was. However, the total time required for the recovery of the flat morphology during the washout is the sum of the time it takes to overcome the energy barrier plus the time it takes to recover the initial clathrin levels at the Golgi membranes. To a first approximation, the former time, is indeed independent of the duration of the ceramide treatment. However, the latter time could depend on the signaling events leading to the recovery of PI(4)P and hence clathrin levels. To test this, we treated cells for 4h with D-cer-C6 treatment, and monitored the recruitment of clathrin to the Golgi membranes during the washout. We observed that this recovery time is longer (about 6h) than for a 30' treatment, therefore predicting an extra time to recover Golgi morphology in this situation new .BT). Such a subtle difference can be ascribed to different factors that might depend or change during the prolonged treatment with short-chain ceramide, such as small changes in the cisterna area.In addition, one also has to take into account that the characteristic time for stochastic transition, according to Arrhenius kinetics, grows as We included a new supplementary figure and discussion on this in the revised manuscript .Reviewer #2:Theoretical part1) The authors write: 'The equilibrium configuration of a cisterna is assumed to correspond to the free energy minimum'. Given the emphasis put in local energy minima later in the text, this statement is a little bit confusing.We changed this sentence in the revised version of the manuscript, also following the suggestion from reviewer 2 (see our response to comment 1), to be more precise in our wording.2) The authors write: 'the results, presented in We apologize for the confusion. Indeed, we mean that the energy barriers decrease when the amount of nanodomains also decreases. We have changed the wording to clarify better the text.3) In a previous study, the authors proposed an alternative mechanism for the flat to curled shift: “We suggest that these changes are a consequence of the effect of d‐ceramide‐C6 on membrane fission versus membrane fusion at the Golgi membranes. In the presence of d‐ceramide‐C6, transport carriers fuse with the Golgi membranes, however, membrane export is blocked. This increases the surface area‐to‐volume ratio of the Golgi cisternae. This is similar to morphological changes in model membranes as a result of an increase in the surface area‐to‐volume ratio.” Why is this hypothesis no longer considered here?We indeed previously thought that an increase in the surface-to-volume ratio of the Golgi cisternae could mechanistically explain our observations . However, our later observations indicated no obvious change in the volume-to-surface ratio during the flat-to-curled Golgi cisternae transition , which led us to propose new hypotheses to describe cisterna curling. Moreover, typical Golgi cisternae have a very low volume-to-surface ratio, which according to previous theoretical models cannot explain flat cisterna shapes, but likely requires rim-stabilizing agents . We discuss this point now in detail in the text .4) A few theoretical papers on the discoïdal shape of membranes or Golgi stacks exist, notably by Derganc, Lipowski, and Svetana. Please comment, compare.We thank the reviewer for bringing these papers to our attention. This comment has been brought up also by reviewer 2 . We now discuss them in the revised manuscript. Moreover, we now included an Appendix with an analytical approximation of our model, which allowed us to compare our model with the previous work the reviewer mentions.5) In terms of curvature, is the curled shape so highly curved as stated in the Abstract? (…affecting SM homeostasis converted flat cisternae into highly curved membranes). Looking at the EM, the curvature of the cup shape cisternae seems rather modest.We meant that the cup-like shape of the cisternae was highly "curled" or highly curved relative to the initial flat configuration. Indeed, this curvature is still relatively small as compared to other high curvatures in cells . Hence, we changed "highly curved" for "highly curled" in the revised Abstract.For the experimental part I have the following concerns:6) The lipid composition and the nature of protein coats associated with the cis and trans faces of the Golgi apparatus are very different. Therefore, why does the Golgi apparatus react globally by changing its shape between flat and curved geometries? Do conditions exist where the trans and cis faces react differently? If PI4P loss is the main effect promoted by short chain ceramide treatment and mostly affects clathrin adaptors recruitment, one would expect that the trans Golgi would be more affected than the cis Golgi.We thank the reviewer for this comment, which has been also raised by reviewer 2 , and it was not sufficiently clear in our original submission.We would like to emphasize that we do not claim that the entire Golgi complex/TGN morphological transition is due solely to the loss of clathrin from the TGN membranes. Indeed we now present in the Appendix new calculations on a multiple cisternae model, which indicate that stack curling indeed requires the loss of curvature effectors from multiple, if not all, cisternae see – . Whether7) If the loss of coats is indeed at roots of the effect observed here, what does happen when BFA or other inhibitors of GEFs are added such as to prevent not only clathrin but also COPI from assembling at the rims? Along the same line: what does happen when a PI4P kinase inhibitor is added (e.g. PIK93)?cis side, oppositely to what we observed, which makes sense in the view that curling starts at the cisterna most affected by the treatment away from the stack, which is then followed by the remaining cisternae .Inhibition of COPI vesicle formation by adding BFA induces, within minutes, the tubulation of the Golgi membranes and their subsequent fusion to the ER, therefore preventing any slower dynamic processes such as Golgi curling. Importantly, we previously showed that short-chain ceramide-treated cells were basically insensitive to BFA in terms of aforementioned relocalization of Golgi membranes to the ER . However, Martinez-Menarguez and colleagues showed that when HeLa cells are incubated at 15ºC to block protein secretion at the level of the ERGIC, components of the COPI coat (e.g. β-COP) are released from the early Golgi membranes . Strikingly, they observed by cryo-electron microscopy that the morphology of the Golgi complex turned into a curled shape analogous to the one we observed upon short-chain ceramide treatment. Moreover, they observed that the curling of the cisternae occurred towards the Regarding the role of PI4-kinases in this process, we would like to point to the paper by D'Angelo's group , where the authors actually mapped the signaling cascade of the events leading to clathrin release upon short-chain ceramide treatment. Essentially they showed that by blocking PI4-kinases at the Golgi either by chemical inactivation (using PIK93) or by RNAi sensitized the cells against short-chain ceramide treatment, meaning that the levels of PI(4)P and their binding effectors on the Golgi membranes were unaltered. Moreover, it has been recently reported that knockdown of the two Golgi-localized PI(4) kinases in Atg5 knockout cells induces curling of the Golgi cisternae .We have now expanded these points in the revised manuscript .8) The use of the segregation between p230 and TGN46 as an index of the curled geometry seems quite indirect. What is the relationship between this segregation and the cisternae morphology?We agree with the reviewer that using the level of colocalization between p230 and TGN46 is quite an indirect readout of Golgi cisternae morphology. To avoid any confusions about this point, we now clearly state that short-chain induced protein segregation at the Golgi complex, although it correlates somehow with the changes in cisternae morphology, is driven by a yet to be identified mechanism.We stressed this in the revised version . Also, see our response to point 12 of reviewer 2.9) Does the treatment of cells with ceramide alter the membrane bending rigidity of the Golgi or just promote the release of clathrin? In this respect, I found the Abstract and title quite misleading. The authors put a lot of emphasis there into nanodomain formation and lipid biosynthesis. Therefore, it is tempting for the reader to think that a main factor at play here would be domain formation. Instead, the authors show that the surface density of lipid domains and their size have only minor effects on the cisternae <> curled transition and that the most important factor is the coat coverage. Therefore, the tone of the Abstract should be changed. There is no indication that lipid domains play a role here.We agree that the role of nanodomains in controlling the shape and shape transitions of the Golgi cisternae is minor. However, the numerical results of our model show that curling of a Golgi cisterna is accompanied by a larger degree of lateral segregation of nanodomains see . We beli


K algorithm to select backbone nodes as the nodes in the CDS, and forward the sensed data of multiple water parameters. The second part is to determine the state of each backbone node with back propagation neural network models and the sequential Bayesian analysis in the current timestamp. The third part is to establish a spatial model with Bayesian networks to estimate the state of the backbones in the next timestamp and trace the “outlier” node to its neighborhoods to detect a contamination event. The experimental results indicate that the average detection rate is more than 80% with M-STED and the false detection rate is lower than 9%, respectively. The M-STED approach can improve the rate of detection by about 40% and reduce the false alarm rate by about 45%, compared with the event detection with a single water parameter algorithm, S-STED. Moreover, the proposed M-STED can exhibit better performance in terms of detection delay and scalability.Time series data of multiple water quality parameters are obtained from the water sensor networks deployed in the agricultural water supply network. The accurate and efficient detection and warning of contamination events to prevent pollution from spreading is one of the most important issues when pollution occurs. In order to comprehensively reduce the event detection deviation, a spatial–temporal-based event detection approach with multivariate time-series data for water quality monitoring (M-STED) was proposed. The M-STED approach includes three parts. The first part is that M-STED adopts a Rule  Water is an important resource of the ecological environment in the agricultural industry. Polluted water can have directly negative impact on the agricultural irrigation and result in the low quality and output of the crops. When a large-scale water contamination event occurs, it is one of the most important issues to detect and warn contamination events and prevent pollution from spreading. One effective way is to deploy a large-scale number of water quality sensors to monitor generic water quality parameters and detect contamination events . At presK [In real application, many redundant sensor nodes are deployed in the water supply networks to improve the robustness of the monitoring systems. On the other hand, due to large-scale sensor node deployment, the amount of data from dissimilar sensors has increased tremendously. To reduce the computational cost of event detection and improve the response time, sensor node selection needs to cut down the amount of data for the spatio-temporal correlation analysis. To avoid forwarding and collecting the sensed data from all of the sensors in the WSNs, Connected Dominating Set (CDS) ,9 is intK algorithm to select backbone nodes as the nodes in the CDS, and forward the sensed data of multiple water parameters. The second part is to determine the state of each backbone node with back propagation neural network (BP) models and the sequential Bayesian analysis in the current timestamp. The third part is to establish the spatial model with Bayesian networks to estimate the state of the backbones in the next timestamp and trace the “outlier” node to its neighborhoods to detect a contamination event.Meanwhile, real-time event detection  in the WSNs should consider both spatial and temporal correlation and dynamically record the propagation path of the contamination event. This paper focuses on real-time contamination event detection with a spatio-temporal correlation model in a water supply network to achieve high accuracy and low false alarm rates. Therefore, a spatial–temporal-based event detection approach with multivariate time-series data for water quality monitoring (M-STED) was proposed. The M-STED approach includes three parts. The first part is that M-STED adopts Rule (1)A connected dominated set (CDS) approach is introduced to select backbones from a large number of sensors, which can cut down the amount of data for the spatio-temporal correlation analysis.(2)A data-driven event detection algorithm is developed, which relies on multivariate water quality time series with Bayesian sequential analysis and BP model from a WSN. Multiple parameters of water quality are fused to provide a unified decision support about a contamination event.(3)Bayesian network (BN) is used to model spatial dependency.The contributions of this work are as follows.The experimental results indicate that the proposed M-STED approach can achieve 90% accuracy with BP model and improve the rate of detection by about 40% and reduce the false alarm rate by about 45%, compared to temporal abnormal event detection of univariate spatial-temporal event detection algorithm (S-STED). Furthermore, we found that M-STED can achieve better performance in terms of response time and scalability, compared to the simple threshold algorithm and the BN-only algorithm.The rest of this paper is organized as follows. Related work is discussed in The contamination event detection approaches based on water quality measurements consist of two phases. The first phase is to set up the prediction model with the historical data as the training dataset. The second one is to determine the water quality by comparing the predicted values with the measurements. Various approaches have been proposed for addressing the problem of contamination detection, using single or multiple-type measurements which are analyzed separately or in combination, from one or more locations in the network, using model-based or model-free approaches.In the threshold-based approaches, the threshold values are set through statistical models. Simplicity is the main advantage since raw data can be directly processed. The abnormal event detection with two thresholds were adopted in . HoweverLearning-based methods can make inference of the possibility of contamination events based on the temporal and spatial correlation of water quality measurements ,13,14. IA multiple type measurement approach at a single location was proposed in , where eBased on the above analysis, most approaches for contamination event detection have been discussed via using single type water quality parameters. There are multiple components to indicate water quality in a WSN, such as free chlorine, EC, pH, temperature, TOC, and turbidity. Unfortunately, a single parameter of water quality cannot reflect the real water quality in a WSN. When a contamination event occurred, the observable values of multiple water quality parameters changed in a significant way. The contamination event detection methods based on single parameter may result in low detection accuracy and high false alarms. To improve the detection accuracy and reduce the false alarms, multiple parameters of water quality should be considered to make a decision with data fusion. Liu et al.  proposedTo clearly illustrate the event detection with spatio-temporal correlation in water sensor networks, the structure of a water supply network is shown in Before contamination event detection, the spatio-temporal correlation is modeled based on normal historical data. For a large water supply network, it is difficult to simultaneously model spatial and temporal relationships due to the complexity of the data. In this paper, spatial and temporal relationships are separately modeled. BP models and the sequential Bayesian analysis are used to detect the outlier nodes for each water quality sensor node with multivariate time series of six water quality parameters. The conditional probability of BN is used to represent the spatial relationship. In this paper, the proposed M-STED approach keeps monitoring streams from the backbone nodes at every timestamp and traces from one outlier to its neighborhood to find a contamination event. First, the water supply network keeps monitoring data from the sensor nodes in the CDS at every timestamp, and then the selected nodes analyze whether a temporal outlier appears with BP models and sequential Bayesian analysis for each node in the CDS. If it does not, the system waits to monitor the data streams from the backbone nodes in the next timestamp. Otherwise, a candidate CDS set is generated for each “outlier” node and its children nodes of each “outlier”. Then, in the next timestamp, the monitoring scope will be expanded, including the backbone nodes and the nodes in the candidate sets. Once a node in a candidate set is detected as a spatio-temporal outlier node, the children nodes of the outlier node will be added to the candidate set. When the number of spatio-temporal outliers is equal to or greater than the threshold Thousands of water quality sensors are deployed in a water supply network to sense, transmit, and forward the massive sensed data, which brings heavy burdens to further contamination event detection in the context of real-time analysis. To avoid forwarding and collecting all of the sensed data from all sensors in the WSNs, optimal sensor node selection is needed to reduce the amount of transmitted data and improve the response time for event detection. CDS is one of the optimal node selection strategies from Graph Theory .K algorithm was proposed in our previous work [K algorithm [A dominating set (DS) of an undirected graph ous work , which ilgorithm  is adoptK algorithm consists of two parts: marking process and pruning rule.Rule In the marking process, all of the water quality sensor nodes are non-dominated nodes. Each node In the pruning process, it should reduce the size of dominant node set because the number of candidate dominant node selected via marking process is excessive. The basic idea of pruning rules is that if the The temporal outlier detection approach consists of two phases: an off-line phase and an on-line phase. At first, the system is in the off-line phase. During the off-line phase, one data-driven model—BP neural network is established. The historical data is trained for temporary analysis of multivariate water quality time series. If the obtained model has low residuals, the system enters into the on-line phase manually. In the on-line phase, Bayesian sequential analysis and BP model are adopted to compute the new measured parameter’s value of each water parameter. Six parameters of water quality are fused to provide a unified decision support about a contamination event. After a period of time, with the increase of the measured values, it needs to retrain the historical data to refine the assessment model. A summary of the overall temporal outlier detection framework is presented in Off-line phase: First, six BP neural networks were established and trained to simulate the six water quality parameters , respectively. Then, the residuals are calculated for each new measured value of each quality parameter as the total error. The possible outliers can be identified based on the residuals. The next step is to evaluate the sensitivity of the BP model and assess its accuracy.The on-line phase includes four main steps for each incoming measured value: (1) data-driven model training—the relationships between water quality parameters are examined using BP models; (2) error threshold setting—calculated residuals are classified as normal or abnormal values using thresholds for each water quality parameter; (3) identification of events—the probability of an event is updated using sequential Bayesian analysis based on the residual classification; and (4) information fusion—univariate event probabilities are fused to provide a unified multivariate event probability reflecting the likelihood of an event based on all water quality parameters. Each water quality parameter is assigned a weight reflecting its influence on the fusion decision. Steps (1) and (2) are initially trained using available data collected from the WSN. Steps (1) to (4) are then repeatedly executed in real-time for each new incoming measured value.BP model is adopted to estimate the relationships between six water quality parameters through nonlinear, weighted functions during normal operation. The development of BP model does not require any knowledge of the physical and chemical laws affecting water quality parameters. Thus, BP model can be available to model the multivariate reactions in the WSN.In the water supply networks, contamination events heavily rely on multiple water quality factors, which results in the difficulties to pre-specify the events. In the case of free chlorine, BP model is just established with the historical data from single water parameter—free chlorine to estimate the predicted value. When there is a small difference between the measured and estimated free chlorine values, it has obvious great deviations between the measured values of other water parameters and their normal states. The reason is that the measured values of free chlorine exhibit great deviations from the normal operation conditions due to the interplay among some of water quality parameters. The prediction model based on a single water quality parameter would obtain a lower accuracy of estimated values. To improve the accuracy of the prediction model, BP neural networks are adopted and trained for modeling the relationships between multiple variate water quality parameters in WSNs. One of the most important components in the BP model are multi-layer perceptrons (MLPs). MLPs are represented by an input layer, a hidden layer, and an output layer and correlate input variables to output variables depending on the nonlinear, weighted, parameterized functions. The BP model is shown in Equation (1):To avoid the interplay among multiple water quality parameters, for each target water quality parameter, the corresponding BP model is established with the input measured time series of all predictive parameters and lagged target parameter, as formulated in Equation (2).Water quality parameters include free chlorine, electrical conductivity (EC), pH, temperature, total organic carbon (TOC), and turbidity. Six BP models can be created and trained. One of each water quality parameter The accuracy of BP model can be evaluated through mean error, standard deviation , represented as time series.To distinguish the normal operation of a water supply network from the contamination events, the estimated residuals TP), the residual is classified as an outlier during an actual event; false oositive (FP), the residual is classified as an outlier during normal operation condition; true negative (TN), the residual is classified as reasonable model error during normal operation; false negative (FN), the residual is classified as a reasonable model error during a contamination event, as shown in In this stage, the probability of a contamination event is updated using sequential Bayesian analysis for each incoming value. In the sequential Bayesian analysis, the number of incoming values is unknown in advance. In fact, the measured values come in sequence and a decision is required to be made about the current state. The performance of the BP model is measured through a confusion matrix during the training . The conAdditional common metrics, two others can be derived from the confusion matrix as described in Equation (5).To determine the possibility of a contamination event occurrence from previously classified states , the probability of a contamination event is updated based on the classification of the residuals. The state of an event has two states: normal and outlier, as shown in Equation (6). In the sequential Bayesian analysis for each new incoming data, the number of measured values is not known in advance. The measured values come in sequence, and a decision is made based on the current state.At first, the probability of a contamination event is assumed to be rare. With each new incoming measured value, the probability of an event is updated with sequential Bayesian rule, as shown in Equation (7).From Equation (7), each event probability is updated through the sequential Bayesian rule depending on the new measured value and on the −5, and the default threshold probability for a contaminating event is set to −1 indicates an event. Alarm (1) represents at least one water quality parameter raised an alarm. Alarm (2) shows that an alarm is raised if at least two water quality parameters or more are fused. In this case, only one event is undetected with one false alarm. As shown in In the application of contamination event detection, the initial probability of an event is set to 10To improve the model’s estimation of a temporal event and to lower the number of false alarms, a process of multivariate fusion decision is invoked. This process ensures that only when a predetermined number of parameters indicates an event, an alarm is raised. This process reduces the number of false alarms and improves the alarms’ reliability. The univariate event probabilities are fused to compute the multivariate event probability reflecting the likelihood of a contamination event based on all measured water parameters.Since water quality parameters differ in their predictive ability of contamination events, weights reflecting their influence on the synchronized decision should be allocated. In this paper, uniform weights were given to reflect no prior information. In .Assume that there are three sensor nodes After the training phase, the conditional probability table of each sensor can be learned. The temporal event probabilities of sensor (1)The nodes in the CDS collect the sensed data. If temporal abnormal events occur, the nodes individually go through the BP model and sequential Bayesian updating with multivaries time series of six water quality parameters for a period of time (2)If the temporal event occurs in one of the backbone nodes, a candidate set is constructed with each backbone node in the “outlier” state, and its corresponding children nodes. If there is no temporal event in these backbone nodes, these nodes just wait for sensing and will be checked in the next time period.(3)The reasoning ability of BN can be used to estimate the expected state of the backbone nodes (4)If the observed value (5)In the following timestamp, the scope of monitoring is expanded, including the backbone nodes and their candidate nodes. They continue to detect whether there is a temporal and spatial deviation.(6)If the number of nodes in the “outlier” state in the CDS is equal to or greater than the threshold The contamination event detection approach, M-STED, based on the spatio-temporal correlation model is as follows:The methodology is tested on real data from CANARY . The datEvent Simulation: Contamination events in the water supply networks heavily depend on environmental factors, which makes it harder to detect contamination events. To cope with the above difficulty, contamination events are superimposed on normal patterns, characterized by the magnitude, direction, and duration [duration , which cduration . Figure duration .The experiments include three parts: (1) BP model assessment. The historical training subset of each water parameter was exploited to establish, train, and evaluate the BP model through mean square error  was proposed. M-STED adopts Rule