Correct wiring is crucial for the proper functioning of the nervous system. Molecular gradients provide critical signals to guide growth cones, which are the motile tips of developing axons, to their targets. However, in vitro, growth cones trace highly stochastic trajectories, and exactly how molecular gradients bias their movement is unclear. Here, we introduce a mathematical model based on persistence, bias, and noise to describe this behaviour, constrained directly by measurements of the detailed statistics of growth cone movements in both attractive and repulsive gradients in a microfluidic device. This model provides a mathematical explanation for why average axon turning angles in gradients in vitro saturate very rapidly with time at relatively small values. This work introduces the most accurate predictive model of growth cone trajectories to date, and deepens our understanding of axon guidance events both in vitro and in vivo.DOI:http://dx.doi.org/10.7554/eLife.12248.001 For your brain to work, millions of nerve cells have to be connected together precisely. To achieve this, growing nerve fibres navigate through the developing brain by following chemical cues. One important such cue is how the concentration of a chemical varies with distance across the brain. This variation is known as a chemical gradient. However we still don't fully understand exactly how nerve fibres use such gradients to steer themselves.Nguyen et al. have built a mathematical model that accounts for the way that nerve fibres respond to chemical gradients, and showed that the model closely matched new experimental data on the growth of nerve fibres from the rat brain. The model implies that, under some conditions, nerve fibres turn surprisingly little in response to a chemical gradient.Nguyen et al.’s model can now be used to predict nerve fibre responses in many other situations, and could help researchers to understand more about how the brain becomes wired up during development. The model could also reveal more about the conditions that are needed to cause nerve fibres to turn sharply in response to chemical gradients.DOI:http://dx.doi.org/10.7554/eLife.12248.002 For the brain to function correctly, it must be wired correctly. Indeed, many neurodevelopmental disorders are likely the result of wiring defects . Axon guIn vivo, axon trajectories may potentially be influenced by many cues. In vitro assays allow individual influences, such as that from the concentration gradient of a single guidance factor, to be isolated and quantified. A substantial mystery posed by in vitro axonal chemotaxis assays is the relatively weak turning produced, even over long periods of time. The naive prediction that axons would promptly turn until they become fully aligned with the gradient turns out not to be true. In an early study of chemotactic responses of chick sensory neurons to a gradient of nerve growth factor in a diffusion chamber, only 60% of nerve tips were preferentially directed toward the gradient direction after 46 hr of growth . The groOne of the key properties of in vitro axon growth that might explain this mystery is that it is often very straight . Axons aet al. simulated trajectories by assuming the turning angle of the growth cone is in proportion to the angle between the neurite and the resultant filopodial tension  as the bearing of the growth cone at time step ϕ at time step turnψ, the total change in θ from the initial direction of growth over long periods of time. For simulations we identify each timestep as 5 min of real time. The model  in long- and finite-time regimes, and then consider the effects of noise. ξ = 0, with a fixed step size of We consider first the noiseless case (a/(a+b)) . This reb  gradient . After 2ith time . Lastly,straight .10.7554/In summary, the noiseless case generated very straight axons and growth cone angles that followed power laws with respect to time in the long time limit. Similarly, in the noisy case, the rate of change of the average turning angle was initially rapid and then slowed down even more rapidly with time. In both cases, the persistence term was a limiting factor on how much and how fast the axons could turn. Thus, this model captures, at least qualitatively, the behavior that axons turn only slightly in gradients, and even for long times do not generally become completely aligned with the gradient.Having established the basic behaviour of the model, we then asked whether it could reproduce in detail real axon trajectory statistics. We therefore analyzed the trajectories of superior cervical ganglion neurons in a new microfluidics device . This deWe measured the response to nerve growth factor (NGF) gradients of axons from dissociated P1-P3 SCG neurons. We chose this model system because almost 100% of these neurons express the NGF receptor TrkA .dK = 0.9 ± 0.3 nM , and a gradient of NGF with added KT5720, which converts attraction to repulsion by lowering levels of cAMP in the growth cone . Cells w± 0.3 nM  and show± 0.3 nM . Given t± 0.3 nM  and axon± 0.3 nM . We trac± 0.3 nM . When th± 0.3 nM   in three conditions are plotted in S = 0.72 .10.7554/π < x < π) (There was little correlation between the bearing change magnitude and step size . The dis< x < π) . That is< x < π) .p = 0.35), and were well fitted by a gamma distribution  could be well fit by the mixture von Mises distributionHaving established the key statistics of steps from the data, we now asked if the simple model in where p = 0.2, t-test)  . The mod t-test) . If succUnlike previous models, we did not assume constant steps or a uniform distribution of bearing changes but rather derived these from empirical data. The model was then able to predict the evolution of the average turning angle over time, the straightness profile and the anticorrelation in bearing changes. Most importantly, it could explain the phenomenon of slow and saturated turning, due to a weak bias term relative to the persistence term. A microscopic factor in each step led to a macroscopic phenomenon of limited, variable turning and straight paths. This often overlooked feature of axon growth turned out to be critical in our model in limiting the overall turning. We also found little difference between the attractive and repulsive case, indicating that attractive and repulsive gradients employed similar mechanisms and could not reduce the variability of axon trajectories.r. We analyzed two cases: anchoring probabilistically at each time step  radians). In both cases, more anchor points led to sharp turns in the trajectories and larger mean turning angle (ξ = 0) and regular anchoring, the growth cone angle ϕ is denoted by ime step , and ancime step . We simung angle , since tng angle . Given tnchoring . HoweverHere, we presented a model of axon trajectories in gradients and helped resolve the mystery of why axon turning angles in gradients saturate over time in vitro, revealing an important factor limiting axon turning. We found that the movement of the growth cone was strongly influenced by the axon’s tendency to maintain a straight trajectory forward, limiting the directional effect of the gradient and preventing the axon from aligning with the gradient even after a long time. Our model predicted that, averaged over a large population of axons, the initial rate of turning drops rapidly over a short period of time (20–40 min). The model shows that adding more anchor points can give the growth cone more flexibility and produce larger average turning, but also increases the variability. Thus, we predict that different substrates, producing different densities of anchor points, could result in different trajectories for the same the gradient conditions.The application of forces to axons can induce rapid elongation without axonal thinning, and thus stretch can stimulate growth . FurtherThis tension results from cytoskeletal coupling with adhesive interactions to the substrate and is critical to growth cone migration . AlthougTension is also dependent on cell type and two main properties of the substrate: stiffness and ECM components. Our data comes from peripheral nervous system (PNS) neurons growing on a laminin substrate that is hard rather than gel-like, and other cell types of different substrates might have different behaviours. Central nervous system (CNS) and PNS neurons have different sensitivities to substrate stiffness due to adaptation to their natural environments , and traOverall, our work suggests that without many anchor points, cues additional to gradients may be necessary for axons to reliably find their targets in vivo (unless the motility noise is for some reason much lower in vivo than in vitro). These could include mechanical cues and axon-axon interactions. To understand such interactions, it is important to generate assays with realistic substrates suitable for different cell types. Recent 3D culture models, in which cells are grown with a protein scaffold, can capture some aspects of the tissue environments instead of hard surfaces . It willIn conclusion, we have presented a simple mathematical model which gives accurate quantitative predictions of the properties of axonal trajectories in a microfluidics-based in vitro gradient assay. The model identifies the key importance of anchor points in controlling turning and provides an explanation for why axonal turning in gradients in vitro tend to saturate rapidly at small turning angles. This model provides a predictive framework which can be used to test whether axonal trajectories observed in vivo can be explained purely in terms of gradient guidance, or whether additional guidance mechanisms are also required.The device was designed in AutoCAD 2013 based on the pattern in . The micPDMS base elastomer  and silicon elastomer curing agent in a 10:1 (m/m) ratio were thoroughly mixed and poured on the master to a depth of about 4 mm. The mold with PDMS was degassed in a vacuum chamber for 2 hr and baked at 80°C for 2 hr. The PDMS replica was then peeled from the silicon wafer and cut into individual chambers. Holes were cored in the PDMS chambers using a 0.75 mm corer (Harris Uni-Core). To bond the PDMS chamber to a plastic tissue-culture petri dish, the dish and the chamber were plasma treated at 100W at a pressure of 380 mTorr for 40 s. The plate was then covered with (3-Aminopropyl)triethoxysilane  solution (5% APTES in 70% ethanol). The plastic dish was washed thoroughly with water, air dried, and the chamber was pressed onto the dish. To avoid air bubbles forming, the dish was filled with distilled water and degassed in the vacuum chamber for 10 min before use.SCG neurons were harvested from postnatal day 1–3 Wistar rat pups. The SCGs were then cut into thirds, incubated in 0.25% trypsin (GIBCO) at 37°C for 30 min and then triturated through a flamed-polished Pasteur pipette for 5 min to dissociate individual cells. The growth solution was Opti-MEM solution (GIBCO) containing 1X penicillin/streptomycin, 10 μg/mL mouse laminin, 4% (v/v) fetal calf serum, 2% B-27 supplement (Life Technologies), and 0.3 nM NGF. The cells were suspended in the growth solution and injected in the microfluidic chamber using a 100-μL glass syringe .Two syringes were filled with either the high (10 nM) or low (0 nM) NGF solution. The high solution contained 0.1% (v/v) 40 kDa-dextran fluorescently labelled with tetramethylrhodamine to visualize the gradient. After the cells were seeded, the syringes containing the high and low solutions were connected to the chamber using polyethylene tubings. The chamber was moved to an incubated inverted microscope (Zeiss AxioObserver). The syringes were attached to a Harvard PHD pump and the flow rate was set at 10 μL/hr. After the flow had been started, fluorescent images of the chamber were taken in Zen software. Background intensity outside the chamber was subtracted from the images. The average brightness intensity and variations over time were then calculated across the chamber. A gradient of fluorescence confirmed that the NGF gradient had formed in the growth chamber. To generate a repulsive gradient, KT5720 , a specific inhibitor of protein kinase A (PKA), was added into both the high and low solutions at a concentration of 70 nM.After the onset of the gradient, the axons were imaged every 5 min for 6 hr using Zeiss Zen software. After data acquisition, axons of 30 μm length, growing in all directions, that did not branch or retract in at least 80 min, were chosen for measurements. All axons were tracked manually using customized MATLAB software (The MathWorks) for as long as possible until they branched or retracted. A 5-min time interval was chosen because, for smaller intervals, variability in identifying the centre of the growth cone was larger than the net movement between frames. The point where the axon attaches to the cell body or the main branch was considered the anchor point.S is the inverse of tortuosity, and compares the overall net displacement G of a path with the total path length T (n steps of lengths jl (j = 1...n) finishes at The straightness index length T . ConsideThis index is between 0 and 1, where 1 corresponds to movement in a straight line and 0 corresponds to a walk that returns to the origin. The closer this index is to 1, the straighter the trajectory is. Obviously, t depends on the current bearing of the growth cone Ψ and the noise ξ according to All parameters of the model are summarized in π to π. It is positive for an anticlockwise turn to get from where two parameters r, which is the inverse of the average number of steps per new anchor point.We first assume there is only one fixed anchor point where the axon initially grew out of the cell body or the main branch. We will later relax this assumption and allow the growth cone to put down new anchor points along its path. We denote the rate of anchor point deposition as Ψ = 0, and a fixed step size s every 5 min. In the idealized noiseless case (ξ = 0) as We first assume an initial direction of This gives:L to be the distance of the growth cone from its original position, and using the geometry in with ϕ(t) → Ψ = 0 as t → ∞. Using the Taylor expansion f(x0 + δx) ≈ f(x0) + δxf’(x0) and d tan−1(x)/dx = 1/(2x + 1), we invert both sides of the above equation to obtain:The approximation above is due to At Therefore, the long-term turning behaviour of axons in the model is given by the power law  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 Eve Marder (Senior Editor) and three reviewers, one of whom is a member of our Board of Reviewing Editors.Thank you for submitting your work entitled "A mathematical model explains saturating axon guidance responses to molecular gradients" 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.Summary:The authors present an interesting model to explain turning of growth cones as a function of a guidance cue gradient in vitro. At its core is a principle based on anchor points. All of the reviewers thought that this was interesting work of modeling and experimental interaction to understand why axons turn relatively weakly in response to attractant gradients. However, various aspects of the manuscript gave the reviewers pause, and need to be addressed. They are:1) To confirm the biological basis and interpretation of the essential part of the model regarding anchor points. Specifically, to address the following questions:A) Are or are not the authors’ own SCG neuron imaging data consistent with any stiffness, tension, drag or pull of the axon between an anchor point and the growth cone?B) Do anchor points exist and interact with the mechanics of the axon in specific (and testable) ways?If answers to the above cannot be definitive, then it should be made clear what experiments are motivated by the work. If not, the authors need to address whether such a model is still of use if anchors are an incorrect assumption.In essence, the questions on the behavior of their SCG neurons or the question regarding the anchor point existence more generally need to be addressed with data.2) To tone down overly strong statements. Specifically, see comments by reviewers# 2 and 3 below.3) To address technical and manuscript issues .Reviewer #1:Various aspects in the modeling were confusing/unclear.1) In the “Modeling growth cone trajectories” section, it is not clear how 2) At the end of the section “Modeling growth cone trajectories”, the power law is not clear to me – there seem to be an exponential (10^) aspect missing in the integration of the above equation?s' is used for a length – clearly there is some confusion in the presentation.3) In the second paragraph of the section “A correlated walk model of growth cone trajectories” (Results), '4) Overall, I think In essence, combine equations and figures more effectively and with a step through for one set of parameters, before showing a collection. Similarly, in I further think that it might be nice to see the full process for a set of parameters  with and without noise on the same plot i.e.,  aspects.In general, equation details need to be clarified, and the figures modified to better help the reader understand the model.r' is introduced. However, I could not find it anywhere in the equations. Please explain/show how this is included in the modeling.5) Reviewer #2:Technical questions:Growth cone angle and 'attractant gradient' are independent terms in equation 1. This sSaturation of turning is explained nicely by a persistence term in the model, which the authors relate to the axon tension and the limited number of 'anchor points'. Another explanation that crossed my mind is that the receptors in the growth cone that sense the attractants themselves saturate. Could this possibility be addressed or ruled out, even as a discussion point?Axon stiffness might also play a role in persistence. It would be nice if the authors could comment on this.Finally, how do the concentrations of NGF relate to what is known about dose-response relationships of trkA receptors, e.g. do the gradients approach a saturating concentration?Manuscript issues:There are a number of labelling issues in later figures .It certainly helps resolve this question, but it raises more questions as I have outlined in these comments. Softer language will get the message across and is less likely to put off readers with preconceived ideas.Reviewer #2 :Please clearly state unit of replication and degrees of freedom in statistical tests.Reviewer #3:1) I am not convinced that the anchor point model is a good model for growth cone turning behavior. There is no evidence that growth cones perform stepwise turning with respect to an anchor point. In the Discussion, the authors describe: "New anchor points could be established when tension is too high, or when it becomes too energetically expensive to drag the neurite." However, I am not aware of published studies that show growth cones physically 'dragging' a neurite (please direct me to such evidence if incorrect). The anchor point idea indeed predicts that the axon between the growth cone and the nearest anchor point should be 'dragged' into the direction where the growth cone moves. Of course, if the anchor point is far away (paper quote: 'the in vitro data we have presented here was well-fitted by assuming the only anchor point is where the axon emerges from the soma'), then a lot of axon would need to be dragged indeed. What would the stiffness of that axon be? The authors acknowledge that the in vivo environment will be more 'complex', but only by assuming there may be more anchor points. Not surprisingly, a closer anchor point allows sharper turns and results in more variability. This simple conclusion is actually one of the major conclusions of the paper.In summary, I think the anchor point model may be a good idea, but there is precious little evidence supporting it. I am with the authors that a simplification to an elegant in vitro system is a good approach and I would not look for further in vivo relevance, if the in vitro behavior were to fit the model. But if there is an in vivo or in vitro neurite that actually drags an axon between the growth cone and an anchor point, the reader really needs to be shown one. To my knowledge it is more likely that most axons, including in the SCG culture, lay behind the moving growth cone without experiencing any force or tensions required for provide feedback from a hypothetical anchor point. If there is no such feedback, the core of the model cannot be supported.not true predictions of the model more than they are the basic data the drove the generation of the model in the first place. For example, the authors describe this 'long-standing mystery' many times, use it to justify the model, and then present the data that was used to make the model in the first place as: 'the average turning angle reached the steady state quickly and did not increase significantly with time, matching the prediction of the model (2) A key prediction of the anchor point model is the tension on the axon between the growth cone and the closest anchor. If such evidence exists for at least some instance, in vivo or in vitro, I can and should be convinced that the model is applicable. This is a true prediction of the core of the anchor point model. In contrast, the measurements provided on the turning speed and the 'saturation' of turning are he model '. This i3) I read this study as a purely hypothetical model based on previous data and some new measurements in the SCG culture using a microfluidic device. Links to biology are present only in the Discussion and as speculations , but neither integrated into the model, nor tested in experiments. As it stands, the anchor point model clearly reproduces some significant behavior or growth cone turning in vitro. However, the statements in the Abstract that ‘this model explains the long-standing mystery…’ and that ‘this work introduces the most accurate predictive model […] and deepens our understanding of axon guidance events both in vitro and in vivo’ appear to me quite dramatically overstated.4) Manuscript issues:In the section related to In the subsection "SCG neurons were guided in the microfluidic assay", the authors took into consideration only the axons that made an angle between 70° and 110° with the gradient direction since they expected impact of the gradient would be strongest on these axons. The reason behind this expectation is not well explained. Also, although Did the neurotrophin gradient majorly influence branching or retraction? Those events were discarded and not compared to the gradient control.In the section "Modelling growth cone trajectories", "s" is referred as constant speed but in the section “A correlated walk model of growth cone trajectories” it is referred as length of a step.To test whether fluid flow has any effect on statistics of the steps authors divided the axons in 4 quadrants but how this division helps understanding the effect of fluid flow is not clear.In  The authors present an interesting model to explain turning of growth cones as a function of a guidance cue gradient in vitro. At its core is a principle based on anchor points. All of the reviewers thought that this was interesting work of modeling and experimental interaction to understand why axons turn relatively weakly in response to attractant gradients. However, various aspects of the manuscript gave the reviewers pause, and need to be addressed. They are:1) To confirm the biological basis and interpretation of the essential part of the model regarding anchor points. Specifically, to address the following questions:A) Are or are not the authors’ own SCG neuron imaging data consistent with any stiffness, tension, drag or pull of the axon between an anchor point and the growth cone?We are very grateful for the prompt to add material from our study showing this directly. We have added example frames from timelapse movies , and theB) Do anchor points exist and interact with the mechanics of the axon in specific (and testable) ways?From the above movies it is clear that there are points on the axon which are attached to the substrate and do not move. Focal adhesions of axons and growth cones have been well studied in the literature . We have not definitively established that the anchor points in our assay are focal adhesions in this sense, but we venture it as a reasonable supposition.If answers to the above cannot be definitive, then it should be made clear what experiments are motivated by the work. If not, the authors need to address whether such a model is still of use if anchors are an incorrect assumption.We think the timelapse videos provide definitive evidence that anchor points exist (the red arrows point at the putative fixed anchor points). In the Discussion we now suggest experiments that could test this further.2) To tone down overly strong statements. Specifically, see comments by reviewers# 2 and 3 below.We have now done this in the Abstract, Introduction and Discussion as detailed below.3) To address technical and manuscript issues .Please see detailed responses below.Reviewer #1:Various aspects in the modeling were confusing/unclear.We apologise that various aspects of the modeling were confusing/unclear.1) In the “Modeling growth cone trajectories” section, it is not clear how(t)=a/a+b(t) equation comes about.We have now clarified this point in the section “A correlated walk model of growth cone trajectories”. In particular, in the idealized noiseless case  and 'L' (distance of the growth cone) with s<<L as they are not equivalent in terms of units. Further down it is stated s approx Lt (which does make sense in terms of units). It can't be both.s denotes a fixed step length reflecting 5 minutes of growth”.In the section “Modelling growth cone trajectories”, we have clarified that “2) At the end of the section “Modeling growth cone trajectories”, the power law is not clear to me – there seem to be an exponential (10^) aspect missing in the integration of the above equation?The equation in the section “Modelling growth cone trajectories” implies 3) In the second paragraph of the section “A correlated walk model of growth cone trajectories” (Results), 's' is used for a length – clearly there is some confusion in the presentation.s’ is the distance moved in 5 minutes, and we have now made this more explicit in the section “Modelling growth cone trajectories”.We apologise for this confusion. ‘4) a =1 and different values of b”.The caption has been changed to “with the same Overall, I think We have added the gradient direction in 1D.Perhaps there can be an additional panel that combines these in some way. Also, it would be nice to show part E for other a, b values. Maybe the authors can take the reader completely through with, say, two sets of a, b values, and then show several parameter value sets as done in parts C and D.We appreciate this suggestion. On reflection, we actually removed 1E, since it really repeated information that was already present – a problem that would be exacerbated with the extra panels.I found it confusing as set down and had difficulty visualizing/thinking about the trajectory process. For B part, symbol for turning angles could be included/introduced from equations.We have added the symbol for turning angle in In essence, combine equations and figures more effectively and with a step through for one set of parameters, before showing a collection.We hope with the clarification of the equations, Similarly, in We apologise for this inconsistency. We now show three sets of a and b in 2A with a consistent color code.I further think that it might be nice to see the full process for a set of parameters  with and without noise on the same plot i.e.,  aspects.As In general, equation details need to be clarified, and the figures modified to better help the reader understand the model.We hope the changes outlined above address these issues.5) r’ in both the Methods and the Results.We apologise for this oversight, and have now added the definition of ‘Reviewer #2:Technical questions: Growth cone angle and 'attractant gradient' are independent terms in equation 1. This s We have added the following explanation to the section “Modelling growth cone trajectories”:“As the bearing is biased by the gradient direction, the overall growth cone angle Saturation of turning is explained nicely by a persistence term in the model, which the authors relate to the axon tension and the limited number of 'anchor points'. Another explanation that crossed my mind is that the receptors in the growth cone that sense the attractants themselves saturate. Could this possibility be addressed or ruled out, even as a discussion point?We believe that we haven’t saturated the receptors since this would cause toxicity (or at least severe loss of neurite growth). According to Ohta et al., 1990, when [NGF] is high , and stiffer axons will likely have higher persistence due to their more limited ability to bend.”Finally, how do the concentrations of NGF relate to what is known about dose-response relationships of trkA receptors, e.g. do the gradients approach a saturating concentration?We used an estimate of Kd=0.6-1.2 nM for NGF as explained above, and the concentration we used was 10 nM, so 8-16 Kd. As explained above this is not a saturating concentration. We have added this clarification in the section “SCG neurons were guided in the microfluidic assay”.Manuscript issues:There are a number of labelling issues in later figures . It certainly helps resolve this question, but it raises more questions as I have outlined in these comments. Softer language will get the message across and is less likely to put off readers with preconceived ideas.We have now softened such claims throughout the paper. For instance:In the Abstract:“This model provides a mathematical explanation for why average axon turning angles in gradients in vitro saturate very rapidly with time at relatively small values.”In the Introduction:“Without such a model, it is difficult to determine if trajectories observed in vivo are in fact consistent with gradient guidance.”In the Discussion:“Here we presented a model of axon trajectories in gradients which is intended to help resolve the mystery of why axon turning angles in gradients saturate over time in vitro.”Reviewer #3:1) I am not convinced that the anchor point model is a good model for growth cone turning behavior. There is no evidence that growth cones perform stepwise turning with respect to an anchor point. In the Discussion, the authors describe: "New anchor points could be established when tension is too high, or when it becomes too energetically expensive to drag the neurite." However, I am not aware of published studies that show growth cones physically 'dragging' a neurite (please direct me to such evidence if incorrect).We apologise for not providing direct evidence for this from our data in the first version of the manuscript, but appreciate the opportunity now to do so. In particular we include a new figure  which shHowever, we accept that we have no evidence to support the particular sentence quoted by the reviewers, and have now removed this.The anchor point idea indeed predicts that the axon between the growth cone and the nearest anchor point should be 'dragged' into the direction where the growth cone moves. Of course, if the anchor point is far away (paper quote: 'the in vitro data we have presented here was well-fitted by assuming the only anchor point is where the axon emerges from the soma'), then a lot of axon would need to be dragged indeed. What would the stiffness of that axon be?We have not performed direct measurements of axon stiffness. However a clear implication from visual inspection of the new images and movies now included is that dragged axons must be quite stiff, since they stay fairly straight as they are being dragged.The authors acknowledge that the in vivo environment will be more 'complex', but only by assuming there may be more anchor points.only difference between the in vivo and in vitro cases: it is simply the parameter which we are focusing on in this paper. However, we have acknowledged in the Discussion that stiffness, cell-cell interactions, physical cues, ECM components are some other factors that can affect growth and might all be different in vivo.We did not mean to imply that we think an increased number of anchor points is the Not surprisingly, a closer anchor point allows sharper turns and results in more variability. This simple conclusion is actually one of the major conclusions of the paper.In summary, I think the anchor point model may be a good idea, but there is precious little evidence supporting it.While we agree do not have direct evidence, we believe that the data we have now included significantly strengthens our case in this regard.I am with the authors that a simplification to an elegant in vitro system is a good approach and I would not look for further in vivo relevance, if the in vitro behavior were to fit the model. But if there is an in vivo or in vitro neurite that actually drags an axon between the growth cone and an anchor point, the reader really needs to be shown one.As described above, we have now done this.To my knowledge it is more likely that most axons, including in the SCG culture, lay behind the moving growth cone without experiencing any force or tensions required for provide feedback from a hypothetical anchor point. If there is no such feedback, the core of the model cannot be supported.We now provide additional citations to support the claim that the axon is under tension and this tension is related to the coupling to the substrate via adhesion sites .2) A key prediction of the anchor point model is the tension on the axon between the growth cone and the closest anchor. If such evidence exists for at least some instance, in vivo or in vitro, I can and should be convinced that the model is applicable. This is a true prediction of the core of the anchor point model. In contrast, the measurements provided on the turning speed and the 'saturation' of turning are not true predictions of the model more than they are the basic data the drove the generation of the model in the first place. For example, the authors describe this 'long-standing mystery' many times, use it to justify the model, and then present the data that was used to make the model in the first place as: 'the average turning angle reached the steady state quickly and did not increase significantly with time, matching the prediction of the model '. This iWe apologise if our claims seemed too strong – we have softened them. It is certainly true that we did not formulate the model ab initio: we were initially inspired by our experimental observations that axons tend to always point back to the last anchor point. This led us to write down equation 1 as the simplest description of the balance of forces acting on the growth cone. However, the derivation from this equation of the rapid saturation of turning with time was a complete surprise to us, and was not something we tried to engineer into our model. Thus, it’s not quite fair to say that it was `the basic data that drove the generation of the model’: indeed it was primarily the model that drew our attention to this particular aspect of the experimental data.We do however agree that, for instance, some aspects of the step statistics were empirically derived, and we have therefore deleted a sentence from the Discussion, which made claims about what was predicted by the model, that we agree with the reviewer were too wide-ranging.3) I read this study as a purely hypothetical model based on previous data and some new measurements in the SCG culture using a microfluidic device. Links to biology are present only in the Discussion and as speculations , but neither integrated into the model, nor tested in experiments.We do not completely agree with this. In fact there is a strong link between our model and our microfluidics data: in particular we propose biophysical principles guiding axon growth, and show that these principles can accurately predict axon trajectories in biological experiments. Precise measurements of the nature of the focal adhesions assumed in our model are left for future work.As it stands, the anchor point model clearly reproduces some significant behavior or growth cone turning in vitro. However, the statements in the Abstract that ‘this model explains the long-standing mystery…’ and that ‘this work introduces the most accurate predictive model […] and deepens our understanding of axon guidance events both in vitro and in vivo’ appear to me quite dramatically overstated.We have softened this statement, and other statements elsewhere in the paper. For instance in the Abstract, we now say:“This model provides a mathematical explanation for why average axon turning angles in gradients in vitro saturate very rapidly with time at relatively small values.”4) Manuscript issues:In the section related to We have amplified the interpretation in the Discussion section.In the subsection "SCG neurons were guided in the microfluidic assay", the authors took into consideration only the axons that made an angle between 70° and 110° with the gradient direction since they expected impact of the gradient would be strongest on these axons. The reason behind this expectation is not well explained.We have added a clarification in the section “SCG neurons were guided in the microfluidic assay”:“An asymmetric concentration field of guidance cue across the growth cone leads to turning  and axons growing in this range experienced between 94% (i.e. sin70°) to 100% (i.e. sin90°) of the maximum possible concentration difference across the growth cone. Thus we expected the impact of the gradient would be strongest on these axons .”Also, although We have added the gradient direction in Did the neurotrophin gradient majorly influence branching or retraction? Those events were discarded and not compared to the gradient control.We are very grateful to the reviewer for raising this very interesting point. We did originally analyse our data to answer this question, but since the answer was ‘no’ we did not include this data in the original manuscript. However we now realise this negative result is still an important piece of information to include, and it is now presented in a new figure . In partIn the section "Modelling growth cone trajectories", "s" is referred as constant speed but in the section “A correlated walk model of growth cone trajectories” it is referred as length of a step.s every 5 minutes” in the section “Modelling growth cone trajectories”.We have changed “a constant speed” to “a fixed step size To test whether fluid flow has any effect on statistics of the steps authors divided the axons in 4 quadrants but how this division helps understanding the effect of fluid flow is not clear.We added the following text in the section “Flow did not affect the statistics of steps”:“To test whether fluid flow in the chamber biased the statistics of the steps, axons growing in the gradient condition with fluid flow were divided into 4 quadrants with different relative angles to the fluid flow: 2 quadrants growing perpendicular to the flow, one quadrant growing with the flow, and the other growing against the flow . CompariIn We have indicated the directions in 3D. We thought about the suggestion for panels 3E and 3F. On balance, we prefer to show them on separate graphs as they almost completely overlap, and would thus be hard to distinguish on the same graph.


We report on the temperature dependence of the electrical resistivity of solid iron at high pressure, up to and including conditions likely to be found at the centre of the Earth. We have extended some of the calculations of the resistivities of pure solid iron we recently performed at Earth’s core conditions (Pozzo et al. in Earth Planet Sci Lett 393:159–164,  The thermal and electrical conductivities of iron at Earth’s core conditions (pressures between 135 and 364 GPa and temperatures between 4000 and 6000 K) are the two key parameters needed to determine the fundamental time scales for diffusion of heat and magnetic field in the core of our planet. Traditionally, these two parameters have been obtained by extrapolations from near ambient conditions  and the high p points (about 300–365 GPa) investigated.We now come to discuss how these results compare with previous literature studies. As mentioned in the introduction, the conventional values of the resistivity of iron at high pressure and temperature are, for example, those reported by Stacey and Anderson , who estnd Royce  reportednd Royce ; Sha andnd Royce  performei et al.  performea et al. , 2015, wWe have extended our recent calculations of the resistivity of pure solid iron performed at Earth’s core conditions (Pozzo et al.


The acquisition of quality clinical experience within a supportive and pedagogically adjusted clinical learning environment is a significant concern for educational institutions. The quality of clinical learning usually reflects the quality of the curriculum structure. The assessment of the clinical settings as learning environment is a significant concern within the contemporary nursing education. The nursing students’ satisfaction is considered as an important factor of such assessment, contributing to any potential reforms in order to optimize the learning activities and achievements within clinical settings.The aim of the study was to investigate nursing students’ satisfaction of the clinical settings as learning environments.A quantitative descriptive, correlational design was used. A sample of 463 undergraduate nursing students from the three universities in Cyprus were participated. Data were collected using the Clinical Learning Environment, Supervision and Nurse Teacher (CLES + T).p < 0.001). Students who had a named mentor reported more satisfied with the supervisory relationship. The frequency of meetings among the students and the mentors increased the students’ satisfaction with the clinical learning environment. It was also revealed that 1st year students were found to be more satisfied than the students in other years.Nursing students were highly satisfied with the clinical learning environment and their satisfaction has been positively related to all clinical learning environment constructs namely the pedagogical atmosphere, the Ward Manager’s leadership style, the premises of Nursing in the ward, the supervisory relationship (mentor) and the role of the Nurse Teacher (The supervisory relationship was evaluated by the students as the most influential factor in their satisfaction with the clinical learning environment. Student’s acceptance within the nursing team and a well-documented individual nursing care is also related with students’ satisfaction. The pedagogical atmosphere is considered pivotal, with reference to students’ learning activities and competent development within the clinical setting. Therefore, satisfaction could be used as an important contributing factor towards the development of clinical learning environments in order to satisfy the needs and expectations of students. The value of the development of an organized mentorship system is illustrated in the study. Mobility of health care professionals is a growing phenomenon worldwide and in the case of Europe several policies have been developed in order to harmonize nursing education in the European countries. Thus, the duration and the content of both theoretical teaching and practice in the clinical areas is explicitly regulated by the European directive2013/55/EU [The CLE is an interactive network of forces within the clinical setting that influences learning outcomes . It inclWithin this context, it is not surprising that the quality of clinical preparation of students has been systematically debated since 1980, in order to reach an optimal level of clinical learning achievements .Although the CLE has been investigated in various educational respects, there is a scarcity of studies exploring the nursing students’ point of view from the standpoint of their satisfaction with the CLE on a worldwide basis. This current study aims to explore Greek Cypriot undergraduate nursing students’ level of satisfaction with the CLE in hospital settings. Students view hospital practice areas as more meaningful and educative because they provide them with opportunities of clinical practice and linking the theoretical aspect of their studies . This wi“The attainment of certain outcomes of a clinical placement may be enhanced by modifying the CLE in ways that make it more congruent with the environment preferred by students” . For theStudents’ satisfaction is a complex and multifactorial issue . RelevanPrevious studies , 22 highEfforts at producing a high quality of CLE have recently been focused on creating a pedagogical atmosphere, and strengthening the connection between university classwork and placement experience by means of adoptive supervision models , 22. TheThese clinical learning models were also adopted by the nursing programs of all the Universities in the Republic of Cyprus. Usually they include clinical skills of about 90 ECTS (European Credit Transfer System) according to the European and National standards  and the ward’s pedagogical atmosphere includes the teamwork and the personnel’s interest in students’ learning needs. The supervisory relationship constructs that stands for the sense of trust, student/mentor equality and continual feedback. The third construct reflects the ward’s leadership style representing the relationships between the ward managers, the staff and the students. The premises of nursing on the ward refer to the organization of the nursing care and the NT’s role in clinical practice is defined as the nurse teacher’s ability to minimize the theory-practice gap.Although there is a lack of a conceptual and theoretical background describing the nursing students’ satisfaction, there is evidence that it could be conceptually clarified and measured within the context of an internationally accepted tool, specifically the Clinical Learning Environment, Supervision and Nurse Teacher (CLES + T) . In thisWhat is the level of Cypriot nursing students’ satisfaction with the CLE?If any, what is the relationship between the students’ satisfaction and some of their personal data ?If any, what is the relationship between the students’ satisfaction and the five dimensions of the clinical learning environment, as defined within the CLES + T?The study aimed to investigate nursing students’ satisfaction with the clinical learning environment. With this in mind, the following research questions were posed:The CLES + T scale was developed and validated by Saarikoski et al.  and adapFor the purpose of the current study, the CLES + T Greek version was used alongside a questionnaire on demographic data referring to the university, the gender, the age and the participants’ educational level. Demographics also included learning-teaching characteristics such as the hospital and the ward type, the clinical placement length, the frequency of the weekly meetings with the NT, the use of e-contact with the NT during clinical placement and the motivational level of the clinical setting. The satisfaction with the CLE was examined by one general question in a 5-point Likert-scale.In the Cyprus Republic there are four universities leading to a bachelor’s degree in nursing, one state and three private institutions. One private university refused to participate in the study, so only three universities were included. The total nursing student population of the 3 universities were 664 individuals. The inclusion criteria for students’ participation were: (1) the students’ informed consent and (2) practicing in hospitals and not in community settings. The questionnaires were personally administered to the students during the last nursing laboratory lesson towards the end of the academic year 2012–13. Nursing students were provided with information with regard to the purpose of the study, the anonymity of the collected data and the voluntary nature of their participation. From the total population, 463 questionnaires were returned, giving a response rate of 70.3 %. Four of the questionnaires were removed from the data analysis as they were not properly completed and so the final sample consisted of 463 nursing students.The research proposal was approved by the National Bio-Ethics Committee and permissions to access participants granted from the universities’ authorities. Permission to use the CLES + T was obtained by the authors.Descriptive statistics were used to calculate frequencies, means and standard deviations from the demographic data. The reliability of the data was estimated with Cronbach’s alpha. Taking into account the data deviation from normality, non-parametric inferential statistics were selected. The correlation analyzes between the students’ satisfaction and the five constructs of the CLE were performed with Spearman’s rho correlation coefficient. Chi-square tests were also used to examine the relationship between the nominal scales of students’ satisfaction and their demographic data as well as regarding students’ relationship with their mentors. In order to examine the relationship between the ordinal scale of students’ satisfaction with students’ demographic data and relationship with their mentors, multinomial logistic regression was used. The simultaneous entering of all the independent variables in the model has the advantage of reducing Type I errors. However, individual Chi-square tests were also performed for additional insight into the relationships.The results showed high internal consistency for the total CLES + T  and for each of the five dimensions, ranging from 0.81 (“premises of nursing care in the ward”) to 0.97 (“supervisory relationship”). Regarding the sample’s demographics, 38.7 % were males and 61.3 % females, with age ranging from 18 to 34 years, with a mean of 21.08 years and standard deviation 2.23 years. 149 participants studied in private universities and 318 at the public university (Table p < 0.001) (Table p < 0.001)  Table . Similar1) Table Table 2Bip = 0.01), the frequency of meetings with NT (p = 0.02), the frequency of supervision with mentor (p = 0.05), the method of supervision (p = 0.01), mentor or NT (p < 0.001) and the motivation (p < 0.001). Specifically, the first year students had the highest satisfaction level compared to the other years (2nd to 4th). Those students who reported that they met with their NT at least three times per week had a higher level of satisfaction in comparison to those that met only once or twice a week. The highest satisfaction was found among those students who had a named mentor with whom their relationship was effective, while the lowest was reported by those who did not have a named supervisor. Students who had frequent meetings with their mentor had a higher level of satisfaction compared to those who did not have any meetings at all, or had very rare meetings . Those who answered that the most important person was the NT had the lowest satisfaction, compared to those who placed emphasis for their supervision on “mentors” or “both” the NT and a mentor. Students who had no motivation had the lowest satisfaction, followed by those who had some motivation. The most satisfied nursing students were those who had high levels of perceived motivation by the CLE. It should be noted that individual Chi-square tests showed the same significant relations, , while two additional variables were found to be significant, namely University (p = 0.04) and type of nursing ward (p = 0.02), where the results revealed that nursing students from the private universities were found to be less satisfied than those from the state university, and students practicing in paediatrics units had the lowest satisfaction compared to other nursing wards.Multinomial logistic regression showed significant relations between students’ satisfaction and demographics, as well as with the student’s relationships with their mentors Table . The resp-value smaller than 0.001, significant differences were revealed across the satisfaction level and the supervision method. Further examination of data showed that the highest satisfaction level was found for those with successful supervision (mean satisfaction = 4.11), followed by those with group supervision (mean satisfaction = 3.86), and the least satisfied were students with unsuccessful supervision (mean satisfaction = 2.61).In the examination of the relationship between the method of supervision and the satisfaction, the six method levels were grouped into three subcategories to facilitate presentation and interpretation. The first subcategory  included the following characteristics: the student did not have a named supervisor, a personal supervisor was named, but the relationship did not work or the named supervisor changed during the course of training. The second subcategory  referred to cases where the supervisor had several students and satisfaction varied according to shift or location. The third subcategory  included students who had a named mentor and their relationship was effective. Taking eight degrees of freedom and p < 0.001). The students’ satisfaction was also found to be positively related to all the individual items of the factors comprising the learning environment in clinical settings. Although the evidence on student satisfaction from learning in the practice environment is limited, efforts have been made to improve the quality of clinical placements in Cyprus and elsewhere [The positive learning experiences revealed in the current study correspond to the supervisory relationship in combination with the frequency of individual meetings, the presence and support of the NT and the sense of “team spirit” in a well-organized nursing care environment. These findings are in agreement with previous findings of the Cypriot studies , 17, 20 lsewhere . TherefoThe mentorship relationship was evaluated by the students as the most influential factor for their satisfaction, a similarity that was echoed across earlier studies using the CLES + T , 20, 22.In addition to this concern, it was also argued that a successful mentorship might be depended on student preparedness, readiness and willingness to learn . FinallyRegarding the academic year, the first year students reported the highest satisfaction compared to other, later years. This was reported likewise within other relevant studies , which sThe common meetings between myself mentor and NT were a comfortable experience”, suggesting that NT presence in clinical area, as a member of academic staff, is useful in order to monitor and guide through the medium of the mentor–student relationship and to act as a learning advocator [r = 0.381 p < 0.001) between students’ satisfaction and both of the CLE dimensions Role of the NT and leadership style of the ward manager, showed that the supervision models of ward placements may have led ward managers not to place students’ education within the priorities of the ward [Also, the frequency of meetings with the NT and mentor in relation to the satisfaction level was demonstrated. Even though the two models of supervision had different perspectives, the nursing students expressed their satisfaction from the meetings with both the NT and the mentor. Students’ satisfaction is also shown in the statement declaring that “dvocator . The NT dvocator , 37. In dvocator . Besidesdvocator . Howeverthe ward . This maAnother finding that is congruent with previous studies  is the lpedagogical atmosphere and premises of nursing care indicated that students’ satisfaction is higher when they are actively involved in individual patient care with clear information flow and clear documentation of nursing care within a welcoming and educationally structured environment. This is in line with the findings of previous studies [The staff learned to know the students by their personal names”, which compromised the students dignity as adult learners and implied their status to be “just a pair of hands” [Finally, the strong and significant correlation found between the  studies , 34, con studies . It is a studies . In the  studies  study, s studies  is that f hands” . Accordif hands” , the conf hands”  and the f hands” .Conclusively, the CLES + T scale could be considered useful in exploring nursing students’ satisfaction with their clinical experiences and the supervision with which they are provided. In future studies, satisfaction level could be used as an important contributing factor towards the development and/or reforms of clinical learning environments in order to satisfy the needs and expectations of students.Some limitations should be noted when drawing firm inferences from the findings of this study due to the relatively short periods of time spent in specific ward environments, specifically from two to three days per week during a period of seven to eight weeks as “short clinical rotations”. These may not provide sufficient time to build mutual understanding and familiarity within the specific CLE. A longitudinal approach will be very helpful in assessing students’ satisfaction with the CLE from the standpoint of the novice as younger students to experience as older students. Of course a mix methodology similar to other relevant studies , 22 coulThe need for evaluating students’ satisfaction with their practice environment is associated with two important issues of nursing workforce: the competency of graduates and students’ retention. In the context of the current study, Cypriot nursing students were found to be highly satisfied with the CLE and this was related to the level of motivation and the nursing care delivery, the supervisory relationship with the mentor and NT’s role in clinical practice. However, students’ satisfaction was found to change according to the level of study, indicating that learning needs and expectations differentiate as student coming up the“ladder of competence” indicating that clinical supervision and support need to be tailored according to the their individual needs.The current study illustrated the value of the development of an organized mentorship system. This was viewed by the participant nursing students as one of the most important variables in their clinical learning and their satisfaction with the CLE. Student’s acceptance within the nursing team and the organization of nursing care impact students’ satisfaction.Under current economic distress, there is a need to re-clarify the potential roles of all parties involved in students’ clinical learning so that adequate preparation will be made to meet educational objectives. Also, findings support the need to encourage both the nursing staff and the mentors in order for theoretical knowledge to be effectively transferred into clinical practice, thus minimizing the gap between the theoretical ideal and the reality of the clinical world. However, the findings across relevant studies presented an ensemble of factors that impact nursing students’ satisfaction of the CLE. Further investigation of the field is therefore recommended.NT, Nurse TeacherCLE, Clinical Learning Environment; CLES + T, Clinical Learning Environment, Supervision and Nurse Teacher;


We construct a rich dataset covering 47 developing countries over the years 1990–2007, combining several micro and macro level data sources to explore the link between political factors and body mass index (BMI). We implement a heteroskedastic generalized ordered logit model allowing for different covariate effects across the BMI distribution and accounting for the unequal BMI dispersion by geographical area. We find that systems with democratic qualities are more likely to reduce under-weight, but increase overweight/obesity, whereas effective political competition does entail double-benefits in the form of reducing both under-weight and obesity. Our results are robust to the introduction of country fixed effects. We use a categorical version of the BMI variable , and analyze the entire BMI distribution not restricting our analysis to obese e.g.  or underSince several of the countries in our sample are facing a double burden of both over- and under-weight . The heteroskedastic specification suggests a significant difference in the variance of BMI across geographical areas, with Asian countries showing the lowest variability.The paper is structured as follows. In Section 2Ecological studies have shown that political freedom  and demoWhile the above-described body of evidence does not focus on BMI outcomes, potentially relevant insights may still be inferred for the present paper. There are multiple channels through which political characteristics might in principle affect health. First, democratic governments may be more efficient  and poliThe above theoretical mechanisms should lead us to expect that democracy aids in reducing at least under-nutrition, while the expected effect of democracy or other political factors on obesity in countries that have exceeded a minimum level of food availability is ambiguous. To the extent that obesity reflects the rational, free choice of individuals , autocraOnly While evidence on the impact of political settings on obesity in developing countries is scarce, important work on the more “standard” determinants informs our choice of covariates. 3This study employs a rich set of data  country level political characteristics are taken from the Polity IV Project database, which covers all major independent states world-wide,5Using the WHO BMI classification, individual BMI is transformed into a categorical measure taking four values: underweight (<18.5), normal weight (18.5–24.99), overweight (25.00–29.99) and obese (>30). Out of our set of explanatory variables, the definitions of the political variables, which are the primary interest of our study, warrant further discussion. Since the literature has focused both on the effect of the type of government and on the way political competition takes place, we chose two variables to capture the political characteristics of a country. Following To control for confounding and to isolate the effect of political characteristics on BMI, a number of covariates are introduced in the estimation see , both atFurthermore, changes in individual BMI are likely to respond to country level changes of the past – a feature we account for by introducing three-year moving averages  for all country level covariates. Therefore country level binary covariates are transformed into the proportion of, for example, democratic years over the three years (i.e. the current one plus the past two).Finally, we restrict our sample to individuals of 18 years old and over, to avoid the idiosyncratic patterns exhibited by students and adolescents. 4j = 1, …, J is the number of BMI categories  and i = 1,…,n is the individuals in the sample. The vector Xi indicates the covariates used in the estimation, while aj are the cut-off points to be estimated along with the rest of the parameters.Using the ordinal nature of the BMI variable and assuming BMI to be a linear function of the covariates that is logistically distributed, the ordered response logit models can be written asj − 1 binary regressions, assuming that the slope coefficient for each covariate is constant across regressions .Such specification constrains all parameters  to be equal across all BMI categories. This assumption is referred to as single crossing property and requires that as one moves from the probability of the smallest outcome to the probability of the largest outcome, the marginal probability effects are allowed to change their sign (effect) onceaij = kj + Xiγj in Eq. βj = γj − β.Relaxation of this assumption can be carried out by making the cut-off points linear functions of the covariates, and as such introduce heterogeneity in the coefficients . Substitσ) and making it a function of observable characteristics. As past literature argues (σi = exp(z1 · Asia + z2America + z3MiddleEast), where Africa is the reference category with σi = exp(0) = 1 and the rest of the scales (i.e. z) are estimated.A further common assumption of the model is its assumed homoskedasticity, which we relax by parameterizing the variance  have been spent under democratic regimes, and about the same length of time have been spent in regimes with a competitive executive nominating process. In term of economic characteristics, the reported mean three-year moving average GDP per capita is $2738, with imports of goods and services covering 34% of the GDP. The average proportion of fat in the diet (over three years) is at about 18%.5.2The other covariates also offer interesting insights: As expected, individuals in countries with higher per capita GDP face a significantly reduced risk of being underweight and an increased probability of being overweight  with a percentage increase in GDP increasing the odds of being overweight by 0.2 p.p., while reducing underweight probability by approximately 0.06 p.p. By contrast, a percentage increase in annual per capita GDP growth reduces the probability of being overweight or obese by 0.2 and 0.25, respectively, while it increases the probability for individual normal BMI by 0.4 p.p. and appears to have no significant impact on underweight. Finally, looking at an indicator of the level of globalization and openness of the economy, devoting an extra 10% of GDP toward imports of goods and services, will decrease the probability for normal BMI by 1.2 p.p.The number of physicians, that we include as a proxy of the quality of the health system and as a proxy of the level of investment in health, to capture the fact that democracies tend to spend more on healthcare , has no All educational levels (compared to no education) tend to increase the likelihood of being overweight or obese and decrease the likelihood of being underweight and normal weight. Education seems to have a linear effect, with the absolute effect magnitude increasing in size as we go from lower to higher levels of education. As expected from the literature on obesity e.g.  age dispThe nutritional pattern, proxied by the  percentage of fat in the diet, is significantly associated with the individual probability of being normal or overweight/obese, but not with underweight: a 10% increase in the percentage of fat in the diet increases the likelihood of normal BMI by 7.6 p.p., while it reduces the probability of being overweight and obese by almost 6 p.p. and 2 p.p., respectively.Finally, the parameterization of the variance was significant, indicating non-negligible variability in the estimates by geographical location and underlining the importance of our correction for heteroskedasticity. As expected, compared to Africa, Asian populations seem to have significantly less variability in the BMI outcomes, while the variability is higher than the reference group, when considering individuals living in American and Middle Eastern countries.6Using a global perspective and employing a large dataset covering 47 developing countries, this paper is the first to use such a rich and extensive dataset to examine the impact of political factors on nutritional status (proxied by BMI) at the individual level. With obesity and malnutrition rapidly becoming global problems affecting the developing world, this paper adds to the general literature on the role of political characteristics in determining health. Owing to our flexible econometric specification, the links between the entire distribution of BMI (i.e. underweight to obese) and the quality of the government could be examined.Even after controlling for a large set of individual and country specific covariates and country fixed effects, our analysis shows that political factors at the country level do explain a significant part of the variation in the BMI status. The influence of the “quality” of the political system (i.e. our executive competition variable) in a country confirms the idea that it may not only be the type of government that determines health, but also the way political competition works. Our findings are in line with the broadly related literature suggesting that democratic countries seem to be able to increase the amount of calories consumed, as argued by By contrast, our results regarding the variable measuring the efficiency and freedom in the choice of politicians and policy makers support the idea that competition between politicians ultimately promotes the implementation of better  policies, at least as far as the health proxies considered here are concerned. We specifically find that improvements in the quality of the political competition are beneficial in curtailing the tails of the BMI distribution. Countries whose electoral mechanisms work effectively are characterized by a lower prevalence of both malnutrition and obesity. Our estimated drop in obesity by 1.5 percentage points is close in magnitude to the effect obtained by One basic motivation for our analysis was to ideally identify factors that either could help tackle both under- and overweight at the same time, or at least one of them without harming the other. If this was the case, and if those factors were amenable to policy intervention, then this would lead to fairly straightforward policy implications, even in countries facing a double burden of under- and overweight. Unfortunately, our results suggest that this ideal scenario is the exception rather than the rule. For a number of factors we find a beneficial effect on one type of malnutrition coupled with an adverse effect on the other. This holds for our indicator of democracy and for other controls such as the level of education, urbanization, GDP per capita and the number of physicians per capita.The estimated effect for education in terms of decreasing the probability of being underweight is in line with previous results , while tThe increased probability of being overweight and obese for people living in urban areas and in more open economies confirms the hypothesis that people more exposed to western culture are more likely to be obese. This is akin to the idea that globalization tends to stimulate an obesogenic environment in developing countries , fueled Looking at the number of physicians, used as a proxy for health care quality, we find a reduction in the likelihood of underweight and an increase for overweight. In some cultures being overweight does not carry negative connotations, but is instead seen as a sign of being wealthy that may not require immediate medical intervention , in contInterestingly, the rate of economic growth, controlling for the level of per capita GDP, and labor force participation improve the entire BMI distribution, i.e. shortening the tails. This is in some contrast to A number of limitations for our analysis need to be acknowledged. First of all, even if robust, our results do not necessarily imply a causal link between political factors and BMI. And even if causal inference was allowed, it is important to bear in mind that the changes in the political system that would be required to achieve a notable reduction in malnutrition would be quite substantial . Nevertheless, our findings confirm, strengthen and add some nuance to the correlation found by Further, due to data constraints, we only employ an aggregate measure of economic status (GDP per capita), without being able to include an individual income measure in the analysis. In fact, in developing countries it is very difficult to correctly identify rich and poor individuals given that wage income fails to capture the true material wealth of a household, as many households rely on self production. A more widely used and likely more meaningful measure of households’ economic wealth is an asset-based wealth index , construDespite the lack of available data to address such caveats, the global perspective adopted in this paper and the rich econometric specification allow for the study of the effect of political factors on the full range of the BMI distribution, while accounting for a wide range of influencing factors, country fixed effects and potential regional heterogeneity of BMI. It constitutes the first study of its kind and prepares the ground for more in-depth exploration of the issue.


We report wide range and reversible tuning of the selective reflection band of a single crystal cholesteric liquid crystal elastomer (CLCE). The tuning is the result of mechanical shortening of the helical pitch achieved by imposing a uniform uniaxial strain along the helical axis. On doping the CLCE sample with a laser dye, we observe lasing from the CLCE in both glassy and rubbery states. By changing the cholesteric pitch, mechanical compression provides tuning of the laser emission from the dye doped CLCE over a significant part of the fluorescence band of the laser dye. In this work we demonstrate for the first time that both the CLCE pitch and the lasing wavelength are linearly dependent on the strain imposed on the CLCE film. Liquid crystals (LC) self-assemble into variety of mesophases with spatially periodic molecular arrangements. These are characterized by orientational order, and varying amounts of positional order. The orientational order can often be characterized by a scalar order parameter, which gives a measure of the degree of oreintational order, and a unit vector, called the director, which indicates the direction of alignment. Supramolecular periodicity together with the anisotropic properties of LC molecules results in spontaneously formed photonic crystal with a band-gap where the propagation of electromagnetic waves with wavelengths comparable to the period of these structures is forbiddenCLCs with a selective reflection band were predicted to serve as a distributed feedback cavity45264511131617192CLCEs are soft solids formed by mesogenic molecules incorporated into a polymer network with helical structure similar to low molecular weight CLCs. The interaction between the polymer chains and mesogens couples orientational order to mechanical strain. Such a coupling allows a variety of electro-mechanical and opto-mechanical effects with a great potential for applicationsAn alternative method of mechanical tuning of the lasing wavelength from single192223241926In this work, we use an improved CLCE material and a new geometry for its deformation, different from that reported in our earlier paperThe CLCE film was fabricated using the method described in detail elsewhereWe used the laser dye 4-(dicyanomethylene)-2-methyl-6-(4-dimethylamino styryl)-4-H-pyran (DCM)  to achieve lasing, The CLCE film produced is initially in the ordered state with helical axis perpendicular to the surface of the film with a clear selective reflection band, as shown on Tg ~70 °C. Upon transition from the glassy to the rubbery state, the selective reflection band of the CLCE film narrows in width and its position red-shifts indicating the considerable temperature dependence of the refractive indices and of the helical pitch of the CLCE film. Reflectance spectra from an undeformed CLCE film in the glassy state near room temperature (22.8 °C) and from an undeformed CLCE film in the rubbery state at the high temperature of the experiment (74.4 °C) are shown on g.Close to room temperature, at ~23 °C, the CLCE film is in a brittle glassy state. Appreciable mechanical deformation of the CLCE film is possible only in its rubbery state, above the glass transition temperature of In order to achieve lasing, the sample was optically pumped using a frequency doubled Coherent Nd:YAG laser, with 7.5 ns pulses and rep. rate of 2 Hz at λ = 532 nm. The intensity of the pump beam was controlled with a polarizer and an analyzer. The pump beam was divided in two to allow simultaneous measurements of the pump energy and emission wavelength. The pump beam with 9 mm diameter was focused on the CLC film using a 12 cm focal length lens to a beam waist of ~50 μm. The angle of incidence of the pump beam on the sample was ~45°. The pump energy was measured using a Molectron Optimum 4001 energy meter and the emission spectrum from the sample was measured using a Jobin Yvon-Spex TRIAX 550 spectrometer. The optical setup for lasing is shown on Initially, we verified that the CLCE film can lase, and we measured the lasing threshold at room temperature in the glassy state of the CLCE sample. Subsequently, we performed lasing experiments and demonstrated mechanical tuning of the wavelength of the laser emission from the sample in the high temperature (~75 °C) rubbery phase.2/s. Lasing in the glassy state was observed closer to the high energy edge of the selective reflection band, as shown on When in the glassy state at room temperature 22.8 °C) the sample was supported by a single microscope glass slide. In order to create a weak adhesion to the CLCE film, the surface of microscope glass slide was coated with a thin film of silicone oil with viscosity of 1 m2.8 °C thPumping at high energies can cause thermal degradation of the distributed feedback cavity2/s. The compression cell with the enclosed CLCE film was located inside a plexiglass chamber with hot silicone oil of low viscosity (2 × 10-3 m2/s) pumped through it. The oil temperature and flow rate of were controlled by a Haake FE2 Heated Bath Circulator and adjusted to maintain the desired temperature of the compression cell. The temperature of the compression cell with the sample was measured using a calibrated thermistor next to the cell in the heating chamber. During all experiments with the CLCE in rubbery state, the sample temperature was maintained at 75 °C. The fluctuations of the temperature from uncontrolled heat losses were not more than +/–3 °C. Temperature fluctuations on this scale are not expected to affect significantly the optical and mechanical properties of the CLCE film.In the rubbery state above the glass transition temperature, the CLCE film is elastic and can support mechanical deformations such as stretching or compression. In our experiments, we uniformly compressed the CLCE film confined between two parallel glass plates. Such mechanical deformations were performed using a custom built device able to accurately control the separation of the glass plates using three screws with a fine (80 threads/inch) thread. Glass plates of 0.25 inch thickness were used to minimize bending. In order to prevent strong adhesion of the CLCE samples to the glass and possible damage to the film, again the glass plates were coated with a thin layer of silicone oil with viscosity of 1 mp of the CLC can be calculated from the known ordinary no and extraordinary ne refractive indices and the measured position of the selective reflection band as follows:Compression of the CLCE film in its rubbery state between parallel plates creates a uniaxial strain enlarging the area of compressed film. Since the strain is applied along the helical axis, due to the strong coupling between the CLCE director and polymer network the CLC pitch shortens with the macroscopic compression of the CLCE film. The pitch λL and λR are the short and long wavelength edges and λc is the central wavelength of the selective reflection band. Based on the measured width of the selective reflection band, the refractive indices are taken to be no = 1.50, ne = 1.65 at room temperature and no = 1.53, ne = 1.59 at the high temperature of the experiment.where c = 705 nm to λc = 370 nm, as shown on 2.Using the compressing device, we were able to uniformly compress the CLCE film and dramatically shift the selective reflection band. The largest observed blue-shift of the selective reflection band was from λc = 635 nm) to 584.8 nm (λc = 584 nm), as shown on Lasing emission from the CLCE film in a rubbery state at 75 °C was always observed at the low energy edge of the selective reflection band, as shown on 2. Regardless of the nontrivial deformation of the shape of the film, the average reflection band remained essentially uniform over the entire film, indicating that the change of shape only shortened the CLC pitch but left the cholesteric helical structure unchanged. In all of the compressed and uncompressed states, the CLCE film was uniformly colored in reflection with local deviation of the CLC pitch in different spots of the film less than 2.4%.A complex deformation of the shape of the CLCE film was observed as result of the applied strain. We measured the reflectance and area of the CLCE film in a rubbery state and calculated the change of the helical pitch as a function of applied strain. Assuming volume conservation, the thickness of the CLCE film in states of different strain was calculated with reference to the glassy state, where the thickness of the CLCE film is known to be 25 μm. The cholesteric pitch and the area of the CLCE film were found to be linearly dependent on the strain created by the uniaxial compression. c = ~450 nm to λc = ~700 nm is shown on 2/s). The glass slide was placed on the surface of a hot stage which is visible on images as a black background. The temperature of the surface of the hot stage was set to 75 °C. The free recovery of the shape and reflectance of the compressed CLCE sample with area of ~15 mm2 was completed in ~15 minutes. Films with ~3 times smaller area were able to recover under identical conditions and from similar compression in ~2 minutes, with significantly smaller visible wrinkling.When the applied force causing compression is removed, the CLCE spontaneously returns to its original equilibrium state with film area and selective reflection band matching their original values before the deformation. A sequence of photographs in reflected light of a previously compressed CLCE film during a free recovery process corresponding to a relaxation of the selective reflection band from λWe have demonstrated lasing from CLCE films both in glassy and rubbery states. A dramatic reversible blue-shift of the selective reflection band from near IR to near UV ranges of the spectrum was achieved by a novel mechanical compression of the CLCE film using uniaxial strain along the helical axis. Using an accurate measurement scheme based on volume conservation of the CLCE film, we have shown here, for the first time, that both the helical pitch and the wavelength of laser emission from the CLCE film in the rubbery state are linearly dependent on the mechanical strain applied to the film.How to cite this article: Varanytsia, A. et al. Tunable lasing in cholesteric liquid crystal elastomers with accurate measurements of strain. Sci. Rep.5, 17739; doi: 10.1038/srep17739 (2015).