Furthermore, spheroids are typically grown in ambient atmospheric oxygen (normoxia), whereas most in vivo tumours exist in hypoxic environments. Therefore, there are clear discrepancies between in vitro and in vivo conditions. We explore these discrepancies by combining tools from experimental biology, mathematical modelling, and statistical uncertainty quantification. Focusing on oxygen variability to develop our framework, we reveal key biological mechanisms governing tumour spheroid growth. Growing spheroids in time-dependent conditions, we identify and quantify novel biological adaptation mechanisms, including unexpected necrotic core removal, and transient reversal of the tumour spheroid growth phases.Tumours are subject to external environmental variability. However,  in vivo tumours are subject to complicated fluctuating oxygen conditions. We explore this discrepancy between experimental conditions and in vivo conditions. In experiments we grow tumour spheroids subject to time-dependent oxygen conditions and, using new mathematical models and statistical uncertainty quantification, identify and quantify novel biological adaptation mechanisms. While tumour spheroid growth has traditionally been characterised by three phases of growth, we observe transient reversal of the tumour spheroid growth phases. These experimental observations are made possible by focusing on the time evolution of spheroids overall sizes and internal structure. To reveal the biological mechanisms underlying growth and adaptation in time-dependent oxygen conditions we extend the seminal Greenspan mathematical model. Unexpectedly, in time-dependent oxygen conditions we also observe necrotic core removal.Tumour spheroid experiments have been routinely performed for more than fifty years to understand cancer progression and develop cancer therapies. Spheroids are typically grown in fixed ambient atmospheric oxygen conditions whereas most  In vivo tumours are subject to various types of environmental variability, for example due to fluctuating oxygen and nutrient availability , and radial position, r [μm]. Conservation of volume gives an equation describing the time evolution of the outer radius, Ro(t) [μm],s [day−1] is the rate at which cell volume is produced by mitosis per unit volume of living cells, and λ [day−1] is the proportionality constant describing the rate at which cell volume is lost from the necrotic core. In these experiments, Ri(t) ≥ Rn(t). This restricts our attention to two interpretations of the model that differ with respect to how Ri(t) is defined. In the following discussion, we refer to these interpretations as hypotheses and show that hypothesis 2, where oxygen mechanisms drive Rn(t) and waste mechanisms drive Ri(t), is more consistent with the spheroids considered in this study.For deeper mechanistic insight we use mathematical modelling and statistical uncertainty quantification to interpret our observations. Specifically, we use Greenspan’s mathematical model  and showk [m2 s−1], and is consumed by living cells at a constant rate, α [m3 kg−1 s−1]. The external oxygen partial pressure is p∞ [%]. Oxygen diffusion is fast relative to the growth of the spheroid, so that the oxygen partial pressure within the spheroid, p(r(t)) for 0 ≤ r ≤ Ro(t), is governed byH(⋅) is the Heaviside function and Ω [mmHg kg m−3] is a conversion constant from volume of oxygen per unit tumour mass to oxygen partial pressure  provided the oxygen partial pressure is sufficiently large (Ri(t) = 0 otherwise. Note we assume that pi [%] is a constant oxygen partial pressure independent of the external oxygen partial pressure.In hypothesis 1 , oxygen pressure . The inhly large , and Ri) [mol μm−3], is governed byRi(t), is implicitly defined through β(r(t)) = βi [mol μm−3] provided the waste concentration is sufficiently large (Ri(t) = 0 otherwise.In hypothesis 2 , diffusily large , and Ri(Rn(t) is implicitly defined by p(Rn(t)) = pn provided the oxygen partial pressure is sufficiently small, and Rn(t) = 0 otherwise. Informed by experimental results [pn = 0 [%].Both hypothesis 1 and 2 assume that  results , we set p∞, but without knowledge of additional parameters further insights are unclear.Analysis of the model provides an analytical expression for the time when the inhibited region forms . For hypRn(t). We test this assumption directly by analysing radial measurements of each spheroid at each time point independently  and Q [-] are dimensionless quantities , do not overlap and agree with observations that Ro(0) is smaller for spheroids grown in hypoxia than normoxia  of growth with proliferating cells throughout and no inhibited or necrotic region , Ri(t) and Rp(t) continue to increase but at a much slower rate (Days 4–8 of Ro(t) remains approximately constant (Days 2–8 of ξn(t), ξi(t), and ξp(t) approach values observed at late times for spheroids grown in hypoxia , specifically To interpret these deoxygenation experiments we extend Greenspan’s mathematical model . We assunditions . Immediat)>Rn(t) .α , are assumed to be constants. Hence, 2], γ(t) = λ(t)/s(t) [-] are functions of time.Before considering the region cally, α , λ = γs y, α , gives (Text C.2.1 in Rn(t) tends to s(t) and λ(t). At ts there is no immediate change in the waste concentration within the spheroid and so no immediate change to Ri(t). However, as Ri(t) evolve over time in part directly due to deoxygenation.In the region t volume . Conservith time  the wastd = (Ro(0), αn, αh, τα, sn, sh, τs, λn,λh, τλ, α(t) with mean τα = 0.23 [days] and for Ro(t), Rn(t), and Ri(t) ) ) 8.11)) 3 [days] . Furthernd Ri(t) . Therefots. These re-oxygenation experiments exhibit a range of unexpected biological adaptation mechanisms for each cell line that appear to depend on: ts; spheroid size at re-oxygenation, Ro(ts); and necrotic core fraction at re-oxygenation, ξn(ts) = Rn(ts)/Ro(ts).We also perform re-oxygenation experiments, where spheroids grown in normoxia are transferred to hypoxic conditions at time ts = 2 [days]  or phase (ii) , provided Rn(ts) > 0. In the region −1] per unit volume. We assume that a fraction, 0 ≤ ν ≤ 1, of the volume lost from the necrotic core recovers from the harsh oxygen conditions and increases the population of living cells, and the remaining volume lost from the necrotic core diffuses out of the spheroid and does not influence Ri(t). Using Bayesian inference we estimate the seventeen model parameters, Θr = (Ro(0), Rn(0), αn, αh, τα, sn, sh, τs, λn, λh, τλ, ν) and simulate the mathematical model. We observe good agreement with the experimental data suggesting our new re-oxygenation mathematical model captures key mechanisms underlying adaptation and growth . For ts = 2, confocal microscopy reveals that at ts + 1 [days] there is a necrotic region but it is not at the centre of the spheroid  and obtain hourly bright-field images after re-oxygenation. In ts = 2.5 [days], initially the necrotic core of the spheroid is visible as a dark central region. At later times the necrotic core is located closer to the edge of the spheroid and the radially symmetric internal structure is lost  and ξn(ts) here, the necrotic core is close to the edge of the spheroid but does not exit as a single object  and ξn(ts). To interpret WM164 re-oxygenation experiments we use the re-oxygenation model  exponential growth; phase (ii) reduced exponential growth; and phase (iii) saturation. However, here in re-oxygenation experiments, spheroids can transiently undergo these growth phases in reverse. Furthermore, spheroids can lose their spherically symmetric structure and necrotic core. Deoxygenation experiments also show that large changes to the internal structure of spheroids can occur while the overall size remains constant. Overall, our results suggest that oxygen and internal structure play pivotal roles in spheroid growth and should be taken into account when interpreting spheroid experiments. This is important as many studies do not provide sufficient information to replicate oxygen conditions and do not measure spheroid internal structures.Tumours grow in complicated fluctuating external environments. However, spheroid experiments used to study tumours are typically performed in constant external environments and with oxygen partial pressures that are much greater than Tumour spheroid growth is a complex process involving multiple mechanisms. However, the contribution of each mechanism to growth is unclear using experimentation alone. To quantitatively explore which mechanisms contribute to spheroid growth we use the seminal Greenspan mathematical model . The modts < t < ts + 1 [days] and long term dynamics , necrotic radius, Rn(t), and inhibited radius, Ri(t), for both hypotheses 1 and 2,Ri(t) ≥ Rn(t), consistent with our parameter choices (Rc = [6kp∞/(αΩ)]1/2; pi, and Q2 = (p∞ − pi)/p∞ so the left hand side of βi, and Q2 = βiκαΩ/(Pkp∞) so the left hand side of Here, we present the governing differential-algebraic system of equations for the outer radius, λRn(t)3,Rc2=Ro2(1Ro(t)).In thesem of Eqs .t = (3/s) log ([6k(p∞ − pi)/α]1/2/Ro(0)). For hypothesis, 2 t = (3/s) log ([6βiκ/P]1/2/Ro(0)).Analysing the model, the inhibited region forms at t=3slog, Rn(t), and Ri(t).For 0 < al model  in normot > ts, we extend Greenspan’s mathematical model to account for adaptation to hypoxia. Rewriting Eqs (Rn(t), gives the governing differential-algebraic system of equationst → ∞, we recover Greenspan’s mathematical model for normoxia (Eqs (α(t) → αh, λ(t) → λh, s(t) → sh and t → ∞. Further, the term involving t → ∞, so t → ∞. We solve the system of Eqs  and andt > tting Eqs , and solting Eqs  for Rn+(xia (Eqs –6.3)). ). t > ts)Rn3(t),dVn(t)dtp∞α(t)Ω.Note tham of Eqs .Key details of the mathematical model to interpret re-oxygenation experiments are included in Text C.3 in Ro(t), Rn(t), and Ri(t) at each time point independently using MATLABs isoutlier function with method quartiles.Parameter estimation and identifiability analysis are performed using profile likelihood analysis , 52, 53,Parameter estimation and identifiability analysis for Greenspan’s model are first performed using profile likelihood analysis , see 1616. The Bd = (Ro(0), αn, αh, τα, sn, sh, τs, λn, λh, τλ, Rn(ts) = 0 and Ri(ts) = 0, but they could be included as additional parameters in future work.Parameter estimation for the deoxygenation model (Eqs –8.11)) ) 8.11)) sn, sh, λn and λh. Starting with experimental data from spheroids grown in normoxia, we fit a normal distribution to the initial outer radius measurements using the MATLAB fitdist function. Then for each spheroid we estimate Rc using Ro(t) and Rn(t) and fit a normal distribution using the MATLAB fitdist function. Similarly, we estimate Ro(t), Rn(t) and Ri(t) and fit a normal distribution using the MATLAB fitdist function. Next, we seek to estimate the five parameters of Greenspan’s model, MCMCstat developed by Marko Laine ; NumTrialPoints = 5000; and lowerbounds and upperbounds informed by fitted normal distributions for Ro(0), Rc, and mse we use experimental measurements as observations and simulate the deoxygenation model with the estimate of Θn from global optimisation to obtain predicted values. Next we use the MCMCstat package to generate four MCMC chains with 250,000 samples and enable automatic sampling and estimation of the error standard deviation. Next we discard the first 50,000 samples of each of the four chains as burn-in, resulting in each chain containing 200,000 samples. For other MCMCstat package options we use the default settings. To assess convergence of the MCMC chains we compute the potential scale reduction factor, h  and Rn(t). Similarly, to estimate αn, αh, τα from MCMCstat package. For estimates of α we use Eqs (Ro(t), Rn(t) and Ri(t). Note that to estimate Rc we assume that Ro(0) we fit a normal distribution using the MATLAB fitdist function to measurements of Ro(t) at the first time point.Next, we analyse the deoxygenation experimental data at each spheroid and time point independently. To estimate  use Eqs  and , αn, αh, τα, sn, sh, λn, λh to inform lowerbounds and upperbounds. To estimate Θd we use global minimisation and the MCMCstat package , Rn(0), αn, αh, τα, sn, sh, τs, λn, λh, τλ, ν), is analogous to the approach used for the deoxygenation model. Summary statistics for the MCMC chains and MCMC diagnostics are shown in Tables E and F in Parameter estimation for the re-oxygenation model formed by Eqs (S.36.1)-(S.36.11) in Text C.3 of Cell culture. The human melanoma cell lines established from primary (WM793b) and metastatic cancer sites  were provided by Prof. Meenhard Herlyn, The Wistar Institute, Philadelphia, PA,  (blue dashed line). Top set of images shows spheroids with FUCCI signal only. Bottom set of images show spheroids with FUCCI signal and pimonidazole staining. Scale bars are 400μm.Fig D: Experimental images of WM983b tumour spheroids in Experiment 6 - Re-oxygenation atts = 2.5 [days]. Scale bars are 400μm.Fig E: Experimental images of WM983b tumour spheroids in Experiment 7 - Re-oxygenation atts = 5.5 [days]. Scale bars are 400μm.Fig F: Experimental images of WM793b tumour spheroids in Experiment 1 - Normoxia. Top set of images shows spheroids with FUCCI signal only. Bottom set of images show spheroids with FUCCI signal and pimonidazole staining. Scale bars are 400μm.Fig G: Experimental images of WM793b tumour spheroids in Experiment 2 - hypoxia. Top set of images shows spheroids with FUCCI signal only. Bottom set of images show spheroids with FUCCI signal and pimonidazole staining. Scale bars are 400μm.Fig H: Experimental images of WM793b tumour spheroids in Experiment 3 - deoxygenation atts = 2 [days] (blue dashed line). Top set of images shows spheroids with FUCCI signal only. Bottom set of images show spheroids with FUCCI signal and pimonidazole staining. Scale bars are 400μm.Fig I: Experimental images of WM793b tumour spheroids in Experiment 4 - Re-oxygenation atts = 2 [days] (green dashed line). Top set of images shows spheroids with FUCCI signal only. Bottom set of images show spheroids with FUCCI signal and pimonidazole staining. Scale bars are 400μm.Fig J: Experimental images of WM793b tumour spheroids in Experiment 5 - Re-oxygenation atts = 4 [days] (green dashed line). Top set of images shows spheroids with FUCCI signal only. Bottom set of images show spheroids with FUCCI signal and pimonidazole staining. Scale bars are 400μm.Fig K: Experimental images of WM793b tumour spheroids in Experiment 6 - Re-oxygenation atts = 2.5 [days]. Scale bars are 400μm.Fig L: Experimental images of WM793b tumour spheroids in Experiment 7 - Re-oxygenation atts = 5.5 [days]. Scale bars are 400μm.Fig M: Experimental images of WM164 tumour spheroids in Experiment 1 - Normoxia. Top set of images shows spheroids with FUCCI signal only. Bottom set of images show spheroids with FUCCI signal and pimonidazole staining. Scale bars are 400μm.Fig N: Experimental images of WM164 tumour spheroids in Experiment 2 - hypoxia. Top set of images shows spheroids with FUCCI signal only. Bottom set of images show spheroids with FUCCI signal and pimonidazole staining. Scale bars are 400μm.Fig O: Experimental images of WM164 tumour spheroids in Experiment 3 - deoxygenation atts = 2 [days] (blue dashed line). Top set of images shows spheroids with FUCCI signal only. Bottom set of images show spheroids with FUCCI signal and pimonidazole staining. Scale bars are 400μm.Fig P: Experimental images of WM164 tumour spheroids in Experiment 4 - Re-oxygenation atts = 2 [days] (green dashed line). Top set of images shows spheroids with FUCCI signal only. Bottom set of images show spheroids with FUCCI signal and pimonidazole staining. Scale bars are 400μm.Fig Q: Experimental images of WM164 tumour spheroids in Experiment 5 - Re-oxygenation atts = 4 [days] (green dashed line). Top set of images shows spheroids with FUCCI signal only. Bottom set of images show spheroids with FUCCI signal and pimonidazole staining. Scale bars are 400μm.Fig R: Experimental images of WM164 tumour spheroids in Experiment 6 - Re-oxygenation atts = 2.5 [days]. Scale bars are 400μm.Fig S: Experimental images of WM164 tumour spheroids in Experiment 7 - Re-oxygenation atts = 5.5 [days]. Scale bars are 400μm.Rn(t) when the FUCCI signal in the central region of the spheroid is blurred.Fig T: Image processing to estimate  Images show one WM983b spheroid one day after deoxygenation. Scale bars are 200 μm. (a) Spheroid with FUCCI signals (green and magenta). (b) Spheroid with FUCCI signals and pimonidazole staining (cyan). (c-e) Blurred region identified using the polygon section tool in ImageJ. Spheroid with: (c) FUCCI-green signal only (green), (d) FUCCI-red signal only (magenta), and (e) pimonidazole staining only (cyan). (f-g) Images in (a) and (b) with blurred region removed.Fig U: Additional experimental measurements comparing spheroids grown in normoxia and hypoxia. (a-b) Estimates of ξn(t) = Rn(t)/Ro(t). (a-b) Estimates of ξn(t) = Rn(t)/Ro(t) with time for (a) normoxia and (b) hypoxia. (c-d) Estimates of ξi(t) = Ri(t)/Ro(t) with time for (c) normoxia and (d) hypoxia. (e-f) Estimates of ξp(t) = Rp(t)/Ro(t) with time for (e) hypoxia and (f) hypoxia. (g-h) Estimates of (g) ξn(t), (h) ξi(t), and (i) ξp(t) with against outer radius, Ro(t).Fig V: Oxygen diffusion and consumption is sufficient to describe formation and growth of necrotic core but not sufficient to describe formation and growth of inhibited region. Estimates of Rc (a) per spheroid; (b) with time; (c) against Ro(t). Estimates of α (d) per spheroid; (e) with time; (f) against Ro(t). Estimates of pi (g) per spheroid; (h) with time; (i) against Ro(t). In (a-i) each data point represents a single spheroid. Data points are only included for pi if the spheroid is in phase (ii) or phase (iii), consistent with when equations used to estimate pi are valid.Fig W: Analysing whether production and diffusion of waste describes formation and growth of inhibited region. Estimates of the outer radius when the inhibited region first forms, Ro(t). In (b-d) each data point represents a single spheroid. Data points are only included only if the spheroid is in phase (ii) or phase (iii), consistent with when the equations used to estimate Fig X: Bayesian inference to estimate parameters of Greenspan’s mathematical model for spheroids grown in normoxia and hypoxia. (a-e) Posterior densities for Greenspan model parameters: (a) Ro(0), (b) Rc, (c) s, (e) λ. Prediction intervals for (f) normoxia. (g) hypoxia. In (f-g) colour bands, in decreasing darkness, represent 50%, 75%, 95%, 97.5%, and 99.5% prediction intervals.Fig Y: Additional results from deoxygenation experiments for WM983b spheroids. Measurements of (a) ξn(t) = Rn(t)/Ro(t), (b) ξi(t) = Ri(t)/Ro(t), and (c) ξp(t) = Rp(t)/Ro(t).Fig Z: Prediction intervals for (a) deoxygenation experimental data and (b) deoxygenation experimental data with additional synthetic data points att = 2.5 [days]. In (a-b) colour bands, in decreasing darkness, represent 50%, 75%, 95%, 97.5%, and 99.5% prediction intervals. Additional synthetic data at t = 2.5 not shown.Fig AA: Direction of movement of necrotic core to edge of spheroid appears random in WM983b re-oxygenation experiments. (a) Schematic for re-oxygenation experiment, with ts = 2.5 [days]. (b) Exemplar experimental brightfield images of a single spheroid with image processing to detect spheroid boundary and centroid (red) and necrotic core boundary and centroid (cyan). (c) Trajectory of centroid of spheroid for spheroid imaged in (b). (d) Trajectory of centroid of necrotic core for spheroid imaged in (b). (e) Five exemplar trajectories of the centroid of the necrotic core relative to the centroid of the spheroid. In (e) the thick blue trajectory corresponds to spheroid imaged in (b).Fig BB: Additional results for WM793b spheroids. (a-d) Mechanisms governing tumour spheroid growth in normoxia and hypoxia. (a) Box chart for estimated outer radius when necrotic region forms, Rc [μm]. (b) Box chart for estimated oxygen consumption rate, α [m3 kg−1 s−1]. (c) Comparison of measured and predicted Rp(t) when pimonidazole staining is present. Note this does not include images where pimonidazole staining is present but does not surround the necrotic core, for example Day 8 of Fig G. (d) Box chart for estimated oxygen partial pressure defining inhibited region from hypothesis 1, pi [%]. (e-i) Experimental data and prediction intervals for (e) normoxia, (f) hypoxia, (g) deoxygenation, (h) re-oxygenation with ts = 2 [days], and (i) re-oxygenation with ts = 4 [days].Fig CC: Additional results for WM164 spheroids. (a-d) Mechanisms governing tumour spheroid growth in normoxia and hypoxia. (a) Box chart for estimated outer radius when necrotic region forms, Rc [μm]. (b) Box chart for estimated oxygen consumption rate, α [m3 kg−1 s−1]. (c) Comparison of measured and predicted Rp(t) when pimonidazole staining is present. (d) Box chart for estimated oxygen partial pressure defining inhibited region from hypothesis 1, pi [%]. (e-i) Experimental data and prediction intervals for (e) normoxia, (f) hypoxia, (g) deoxygenation, (h) re-oxygenation with ts = 2 [days], and (i) re-oxygenation with ts = 4 [days].Table A: Number of spheroids imaged with confocal microscopy for the WM983b, WM793b, and WM164 cell lines. For WM983b re-oxygenation experiments, denoted by *, we focus on brightfield images.Table B: Greenspan’s model parameters and MCMC diagnostics for normoxia experiments. Summary statistics of the MCMC chains include: mean; standard deviation, σ; and, 25%, 50%, and 75% quartiles, Q25%, Q50%, and Q75%, respectively. To assess convergence of the MCMC chains we compute the potential scale reduction factor, tor, R^,  where coTable C: Greenspan’s model parameters and MCMC diagnostics for hypoxia experiments. Summary statistics of the MCMC chains include: mean; standard deviation, σ; and, 25%, 50%, and 75% quartiles, Q25%, Q50%, and Q75%, respectively. To assess convergence of the MCMC chains we compute the potential scale reduction factor, tor, R^,  where coTable D: Deoxygenation model parameters and MCMC diagnostics for deoxygenation experiments. Summary statistics of the MCMC chains include: mean; standard deviation, σ; and, 25%, 50%, and 75% quartiles, Q25%, Q50%, and Q75%, respectively. To assess convergence of the MCMC chains we compute the potential scale reduction factor, tor, R^,  where cots = 2 [days].Table E: Re-oxygenation model parameters and MCMC diagnostics for re-oxygenation experiments with  Summary statistics of the MCMC chains include: mean; standard deviation, σ; and, 25%, 50%, and 75% quartiles, Q25%, Q50%, and Q75%, respectively. To assess convergence of the MCMC chains we compute the potential scale reduction factor, tor, R^,  where cots = 4 [days].Table F: Re-oxygenation model parameters and MCMC diagnostics for re-oxygenation experiments with  Summary statistics of the MCMC chains include: mean; standard deviation, σ; and, 25%, 50%, and 75% quartiles, Q25%, Q50%, and Q75%, respectively. To assess convergence of the MCMC chains we compute the potential scale reduction factor, tor, R^,  where co(PDF)Click here for additional data file.S1 Moviets = 2.5 [days]. The necrotic core of the spheroid is initially visible as a dark central region. As time progresses the necrotic core is located closer to the edge of the spheroid and the symmetric internal structure is lost. At later times the necrotic core appears to exit the spheroid as a single object.Time-lapse brightfield microscopy movie for three days following re-oxygenation at (MP4)Click here for additional data file.S2 Moviets = 5.5 [days]. The necrotic core of the spheroid is initially visible as a dark central region. At later times the necrotic core is close to the edge of the spheroid but does not exit as a single object. As the spheroid grows necrotic matter forms at the centre of the spheroid and appears to merge with the necrotic matter located closer to the periphery.Time-lapse brightfield microscopy movie for seven days following re-oxygenation at (MP4)Click here for additional data file.S3 Moviets = 2.5 [days]. The necrotic core of the spheroid is initially visible as a dark central region. As time progresses mass from the necrotic core at the centre of the spheroid moves towards the periphery and exits the spheroid. The spheroid then appears to resume growth.Time-lapse brightfield microscopy movie for three days following re-oxygenation at (MP4)Click here for additional data file. 12 Sep 2022Dear Dr Murphy,Thank you very much for submitting your manuscript "Growth and adaptation mechanisms of tumour spheroids with time-dependent oxygen availability" for consideration at PLOS Computational Biology.As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments. Your revised manuscript is also likely to be sent to reviewers for further evaluation.When you are ready to resubmit, please upload the following:[1] A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).Important additional instructions are given below your reviewer comments.Please prepare and submit your revised manuscript within 60 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email. Please note that revised manuscripts received after the 60-day due date may require evaluation and peer review similar to newly submitted manuscripts.Thank you again for your submission. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.Sincerely,Philip K MainiAcademic EditorPLOS Computational BiologyFeilim Mac GabhannEditor-in-ChiefPLOS Computational Biology***********************Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: This is a very interesting study about an area of special importance to researchers who utilise spheroids for research. Over-all, I think this is solidly put together and has interesting findings, but I worry slightly about over-interpretation of borderline results, and would like some of these aspects clarified. In no particular order, I have the following suggestions and queries:1. As a general guiding principle, I am a strong believer that Occam's razor should always be observed when constructing mathematical models and entities should not be multiplied without necessity. The reason spheroid models have been relatively simply to date is because, as the authors observe, we are typically dealing with snapshots and our existing models describe these well in terms of oxygen-limited diffusion. What the authors propose in interesting  but I would caution tempering some of the claims or providing more evidence for them.2. The authors state "In phase (ii) cells in the central region of the spheroid arrest in G1 phase while cells at the periphery continue to proliferate resulting in inhibited growth . This arrested region is thought to arise due spatial differences in nutrient availability, possibly oxygen, and/or a build up of metabolic waste from cells. In phase (iii) the spheroid is characterised by three regions: a central region composed of a necrotic core, 0 < r < Rn(t); an intermediate region of living but proliferation-inhibited cells" - this seems somewhat contradictory to what is typically observed in both spheroids and in situ tumours. One of the distinguishing features of tumour cells is their extreme hardiness and resistance to quiescence (10.1016/j.cell.2011.02.013 and many other publications). In terms of oxygen, cancer cells continue replication unimpeded up to extremely low oxygen pressure of around ~0.5mmHg before mitotic arrest (10.1093/jnci/93.4.266), which was also seen with spheroids in references the authors cite  and has also been seen in situ cancers, including glioblastoma (10.1038/s41416-020-1021-5): while a proliferation impeded region does exist for non-necrotic cells in spheroids at oxygen pressures below the necrotic region, it has a very small radial extent. My suspicion is that the authors may not be considering the image analysis of their fluorescence data and fully de-convoluting it to avoid bleed-through; this would involve analysing expression across all channels and subtracting a noise-gated version. MATLAB allows this pretty easily, but the figure in 1c looks like a tumour ellipsoid which has an entirely different oxygen profile than a spheroid (10.1098/rsif.2018.0256) so I'd like the authors to address these aspects if they could.3. Part of the problem might be the use of pimonidazole staining as a proxy for hypoxia - although it has long been used, there are problems in interpreting it 00010-0) as its binding properties fluctuate greatly with pO2, unlike EF5 which remains constant. Have the authors taken stock of this? If its possible to replicate the experiments, I'd suggest doing so with EF5 because of the problems Koch describes with the staining agent itself; if it varies with pO2, then experiments on hypoxia with it might be badly confounded.4. The necrotic core "exiting" the spheroid seems rather interesting. The video appears to be bright-field microscopy, and I have an idea of what might be happening: in the original work of Sutherland and Fryer etc, they demonstrated that spheroids eventually split apart. The necrotic cells within the core lyse, and perturbations in the suspending fluid mean unbalanced pressures occur, with the spheroid "bursting". I believe that is what the investigators are seeing, but at this point the clump of cells can not longer be said to be a spheroid. From the methods section, I don't seem to think the spheroids were made in a spinner culture or similar (10.1517/14712598.2012.707181) so it is unlikely they will maintain their approximately spherical state. The non-bursting video seems to show the spheroid becoming an ellipsoid (10.1098/rsif.2018.0256) so the figures showing no morphogenic changes from a spherical shape in figure 1 are misleading; if the shape of the spheroid departs from approximately spherical symmetry due to unbalanced pressures or irregularities in growth media, it will very quickly depart from the assumptions of perfect diffusion. The bubbles on the bright field microscopy indicate some media disturbances too.5. I do not think, based on the considerations of the above points, that the authors have proven "Oxygen diffusion alone is insufficient to describe spheroid growth" - if anything, all of the phenomena they describe in this work are consistent with pO2 limited diffusion. It would be interesting to find other factors (which presumably must exist) but as it stands I do not think the authors have overcome the threshold of proof to demonstrate this.6. Greenspan's model, it must be noted, is a very old but useful general model for spherical oxygen diffusion, but it has long since been superseded. However, following on from point 4, the primary assumption that "The model assumes each spheroid is spherically symmetric and maintained by cell-cell adhesion or surface tension" is quite clearly contradicted by the evidence the authors have provided; in this case, all spherically symmetric calculations rapidly break down, but that would be predicted by the nature of oxygen diffusion itself and basically amounts to a solution of poisson's equation is a unique geometry.doi.org/10.1371/journal.pone.0153692) - using this model or similar, you would expect these growth dynamics, but the lack of radial measures in the figure makes it difficult to directly compare and should be labelled. The general growth dynamics of spheroids are well understood including their phases : 556–560, doi not readily available) and in all cases, a sigmoid function is typically obtained (10.1111/j.1365-2184.1994.tb01407.x) - however, from what I can observe, none of the spheroids were grown to plateau stage, which unfortunately reduces ones ability to make strong generalisations from the presented data. Spheroids in this work seem very young and small, and it is difficult to see differences in properties until they grow considerably, as indeed their quasi-linear / plateau point varies by OCR and pO2 at spheroid edge.7. As I understand it, the results shown in figure 2 are consistent for the projected and measured growth dynamics in multiple cell lines shown in  and then fit the model (under various hypotheses) to experimental data where the oxygenation of the tumour spheroid is varied over time.The paper is well written and well presented. The topic is interesting to a general audience and, while I can’t vouch for the experimental component, the modelling is sound and the parameter fitting is appropriate and well explained.I would have liked to see more details on the parameter fits in the main paper but understand their position in the SI.There a few minor issues I have identified below.Figure 2 I think it should be a) and d) which show snapshotsFigure 2 What are the blue and orange lines in b and e is one a fit? Its not clear at preasent**********Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: YesReviewer #2: YesReviewer #3: Yes**********what does this mean?). If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article  digital diagnostic tool, Data Requirements:http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: Reproducibility:https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocolsTo enhance the reproducibility of your results, we recommend that you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at AttachmentMurphy_Simpson_PCB_Sept2022.pdfSubmitted filename: Click here for additional data file. 18 Oct 2022AttachmentMurphyetal2022_Cover_Letter_PLOSCB.pdfSubmitted filename: Click here for additional data file. 21 Dec 2022Dear Dr Murphy,We are pleased to inform you that your manuscript 'Growth and adaptation mechanisms of tumour spheroids with time-dependent oxygen availability' has been provisionally accepted for publication in PLOS Computational Biology.Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.Should you, your institution's press office or the journal office choose to press release your paper, you will automatically be opted out of early publication. We ask that you notify us now if you or your institution is planning to press release the article. All press must be co-ordinated with PLOS.Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology. Best regards,Philip K MainiAcademic EditorPLOS Computational BiologyFeilim Mac GabhannEditor-in-ChiefPLOS Computational Biology***********************************************************Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: I think the caveats improve the paper immensely - happy to accept now as is.**********Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: Yes**********what does this mean?). If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article  1223-442824 | ploscompbiol.org | @PLOSCompBiolPLOS Computational Biology | Carlyle House, Carlyle Road, Cambridge CB4 3DN | United Kingdom


Introduction: Neonatal intrahepatic cholestasis caused by citrin deficiency (NICCD) is a pan-ethnic complicated inborn error of metabolism but the specific mechanism is not fully understood.Methods: A total of 169 patients with NICCD who have biallelic pathogenic SLC25A13 variants detected by targeted next-generation sequencing were collected. They were divided into the “Newborn-screen Group” and “Clinical diagnosed Group” depending on the newborn screening results. Amino acid and acylcarnitine profiles were measured by MS/MS. The total bile acids, blood amino acids and acylcarnitines, general biochemistry, blood count, and coagulation parameters were monitored every 2–3 months. We compared the differences in metabolic indices and their dynamic changes between these two groups. The Mann–Whitney test and orthogonal partial least squares discrimination analysis (OPLS-DA) were used for statistical analysis.Results: At the onset of NICCD, we found that the “Clinical diagnosed Group” had higher levels of intermediate products of the urea cycle, free carnitine, and short-chain and long-chain acylcarnitines than those in the “Newborn-screen Group,” but the levels of ketogenic/glucogenic amino acids and several medium-chain acylcarnitines were lower. Furthermore, concentrations of direct bilirubin, total bile acid, lactate, prothrombin time, and several liver enzymes were significantly higher while total protein, amylase, and hemoglobin were lower in the “Clinical diagnosed Group” than in the “Newborn-screen Group.” Dynamic change analysis showed that direct bilirubin, albumin, arginine, and citrulline were the earliest metabolic derangements to reach peak levels in NICCD groups, followed by acylcarnitine profiles, and finally with the elevation of liver enzymes. All abnormal characteristic metabolic indicators in the “Newborn-screen Group” came back to normal levels at earlier ages than the “Clinical diagnosed Group.” c.852_855del (41.2%), IVS16ins3kb (17.6%), c.615 + 5G>A (9.6%), 1638_1660dup (4.4%), and c.1177 + 1G>A (3.7%) accounted for 76.5% of all the mutated SLC25A13 alleles in our population.Conclusion: Argininosuccinate synthesis, gluconeogenesis, ketogenesis, fatty acid oxidation, liver function, and cholestasis were more severely affected in the “Clinical diagnosed Group.” The “Newborn-screen Group” had a better prognosis which highlighted the importance of newborn screening of NICCD. SLC25A13 gene (Citrin is an aspartate/glutamate carrier (AGC) isoform-2 of the mitochondrial inner membrane expressed in the liver, kidney, and heart . Citrin A13 gene . There aA13 gene . FTTDCD A13 gene .NICCD usually resolves spontaneously within the first year after appropriate treatment. However, very few subjects develop severe hepatic dysfunction which may require liver transplantation or die before the transplantation . The mor+ ratio in the cytosol and mitochondria, respectively, which is necessary for the synthesis of urea, proteins, and nucleotides , AGC is important for the transport of reducing the equivalent of NADH into mitochondria and the transport of aspartate to the cytosol. This function can maintain a low and high NADH/NADleotides . The defleotides .At present, tandem mass spectrometry (MS/MS) is widely used in newborn screening since it can simultaneously test 11 amino acids, 30 acylcarnitines, free carnitine, and succinylacetone . The eleIn this study, we studied the differences in metabolic indices and their dynamic changes between the “Newborn-screen Group” and the “Clinical diagnosed Group” to get a better understanding of disease progression and search for potential monitoring biomarkers.SLC25A13 gene.A total of 169 patients with NICCD were collected from Children’s Hospital, Zhejiang University School of Medicine, from January 2010 to May 2021. Among them, 51 patients were diagnosed by the newborn screening of 4.2 million Chinese neonates. They were named the “Newborn-screen Group.” The total frequency of NICCD in our cohorts is 1:82352. A total of 118 patients were admitted to the hospital with suspected neonatal hepatitis or biliary atresia and finally diagnosed with NICCD. They were named the “Clinical diagnosed Group.” Among them, 42 had negative MS/MS newborn screening results and 76 patients had not undergone newborn screening. All cases were confirmed by mutation analysis of the This study was approved by the Ethical Committee of Children’s Hospital, Zhejiang University School of Medicine (reference number: 2020-IRBAL-035). Written informed consent was obtained from the parents of all infants for the collection of samples and publication of medical data.The age of the first detection for MS/MS of the “Newborn-screen Group” and “Clinical diagnosed Group” was 0.12 ± 0.03 months and 2.68 ± 1.45 months, respectively. In newborn screening, dried blood spot (DBS) samples were collected by the heel-stick method and spotted on Whatman 903 filter paper for the neonates at 3–7 days after birth. In clinical screening, DBS samples were collected by the heel-stick method or digit for the patients with intrahepatic cholestatic. Amino acid and acylcarnitine profiles were measured by MS/MS with the NeoBase Non-derivatized MSMS Kit . In brief, a 100 μl working solution containing internal standards was added in U bottom plates. After vibrating at 700 rpm and incubating for 45 min at 45°C, 75 μl liquor was transferred into V bottom plates. After 2 h standing at room temperature, 25 μl liquor was injected into tandem mass spectrometry for metabolic analyses. Two levels of internal quality controls including low and high were used for quality control .The age of the first detection for general biochemistry, blood count, and coagulation parameters of the “Newborn-screen Group” and “Clinical diagnosed Group” was 1.53 ± 1.03 months and 2.78 ± 1.85 months, respectively. Subsequently, the biochemistry data, blood amino acids, and acylcarnitines were monitored every 2–3 months for dynamic change analysis. After the clinical manifestations and related indicators returned to normal, a follow-up was performed every 6 or 12 months.via Sanger sequencing. Long-range PCR analysis was performed to screen for the 3 kb insertion mutation in intron 16 (IVS16ins3kb) (Genomic DNA was extracted from probands and their parents. Targeted next-generation sequencing was performed with a genetic diagnosis panel of hereditary metabolic diseases covering 306 genes . The gen6ins3kb) .Treatment of NICCD patients was performed with several aspects as follows. Breast milk and ordinary formula were replaced by lactose-free milk and medium-chain triglyceride (MCT)-added milk. Ursodeoxycholic acid  was used to improve the cholestatic features and arginine was used to reduce ammonia. Dietary treatment based on low-carbohydrate and lipid and protein-rich were introduced after adding complementary foods. Fat-soluble vitamins were supplemented.The reference intervals (RIs) of metabolic indices were determined corresponding to age-matched controls. The positive rate was calculated for each indicator when the value is higher or lower than the reference intervals.p-values of less than 0.05 were considered statistically significant . The Shapiro–Wilk normality test was performed to determine whether each continuous variable is normally distributed or not. Continuous variables with normal distribution were compared by Student’s t-test, while Mann–Whitney tests were used to compare variables that were not normally distributed. nificant . The ortnificant .The dynamic change analysis of typical indicators between the “Newborn-screen Group” and “Clinical diagnosed Group” was shown further by drawing boxplots with R 4.0.5 software. GraphPad Prism 8 software was used for drawing the figure for sequential order analysis.The positive rates were used for reflecting the metabolic characteristics of the two groups. They were calculated by the reference intervals corresponding to age-matched controls. In the amino acid profiles, the “Newborn-screen Group” was featured with elevated concentrations of Cit, Met, Phe, and Tyr (positive rate >20%), while the “Clinical diagnosed Group” was characterized by elevated levels of Cit, Arg, Met, Tyr, and Orn (positive rate >40%) . In acylThe biochemical data in the two groups showed similar evidence of intrahepatic cholestasis and liver damage. In more than 50% of patients, the levels of bilirubin , total bile acid (TBA), gamma-glutamyl transpeptidase (GGT), alkaline phosphatase (ALP), alpha-fetoprotein (AFP), lactate, and ammonia were significantly elevated than the normal range, while the levels of total protein (TP), albumin globulin (ALB), globulin (GLB), cholinesterase (CHE), and amylase were significantly lower than the normal range in the two groups .We compared the metabolic indices in the two groups at first detection which reflected the metabolic status at the onset of NICCD. The “Clinical diagnosed Group” had significantly higher levels of Cit, Arg, Met, and Orn than the “Newborn-screen Group” . HoweverThe concentrations of DBil, alanine aminotransferase (ALT), aspartate amino transferase (AST), adenosine deaminase (ADA), TBA, ammonia, lactate, lactate dehydrogenase (LDH), total cholesterol (TCH), and thrombin time (TT) in the “Clinical diagnosed Group” were significantly higher than those in the “Newborn-screen Group.” However, the concentrations of TP, urea, amylase, and hemoglobin (HB) were significantly lower than in the “Newborn-screen Group” .OPLS-DA showed Cit, Arg, Met, Orn, Phe, Ala, Leu, Val, C0, C3, C16:1OH, C18:1, C18:2, ammonia, AST, and TBA representing the most contribution to the discrimination between the “Newborn-screen Group” and “Clinical diagnosed Group” .The amino acid, acylcarnitine, and biochemical profiles were detected every 2–3 months and dynamic changes of some typical indicators were analyzed during 1–12 months . The levFor Met, the peak concentrations of the “Newborn-screen Group” and “Clinical diagnosed Group” were later than Arg and Cit, at ages 2–3 months and 4–5 months, respectively. The recovery ages of the majority of patients were at 3–4 months and 6–9 months, respectively.For GGT, the “Newborn-screen Group” had peak concentrations at 1–3 months and declined to nearly normal levels during 5–6 months, while the “Clinical diagnosed Group” had peak concentrations at 2–3 months and declined to nearly normal levels during 9–12 months.The ages of the typical abnormal indicators to get back to normal were recorded and their sequential orders were analyzed. In the amino acid profiles, Phe was the earliest recovered indicator while Cit was the latest recovered indicator in both groups .In the acylcarnitine profile, C16 was the earliest recovered indicator while C18:1 was the latest recovered indicator in the “Newborn-screen Group.” C18:2 was the earliest recovered indicator while C0 was the latest recovered indicator in the “Clinical diagnosed Group.”As for the biochemical data, coagulogram  was the early recovered indicator while AFP and GLB were the late recovered indicators in both groups. The lactate was recovered early in the “Newborn-screen Group” while lately recovered in the “Clinical diagnosed Group.”SLC25A13 alleles in our population (c.852_855del (p.Met285Profs*2), IVS16ins3kb, c.615 + 5G>A, 1638_1660dup (p.Ala554Glyfs*17), and c.1177 + 1G>A were the most common mutations with a frequency of 41.2%, 17.6%, 9.6%, 4.4% and 3.7%, respectively. They accounted for 76.5% of all the mutated pulation .SLC25A13 variants  than the “Newborn-screen Group.” The increased long-chain acylcarnitines had been reported in patients with NICCD during infancy and indicated suppressive β-oxidation of fatty acids (FAO) in the mitochondria . In the OPLS-DA showed that Cit, Arg, Met, Orn, Phe, Ala, Leu, Val, C0, C3, C16:1OH, C18:1, and C18:2 contributed most to the discrimination between the “Newborn-screen Group” and “Clinical diagnosed Group.” In a previous study, Ala/Cit used as a secondary indicator can diagnose more confirmed cases and increase positive predictive values . We suggAs for biochemical indices, the “Clinical diagnosed Group” has higher levels of bilirubin (DBil), TBA, liver enzymes , ammonia, lactate, TCH, and prothrombin time (TT) than the “Newborn-screen Group.” Bilirubin and TBA were the major elevated indicators of cholestasis. TBA was also one of the most contributed discriminations with the “Newborn-screen Group” showed by OPLS-DA. Dynamic change analysis showed that the age of peak concentration of TBA in the “Clinical diagnosed Group” was 2 months later and the concentration was much higher than that in the “Newborn-screen Group.” It was thought that the severely affected excretion of TBA was the main mechanism of cholestasis in NICCD . CoaguloDynamic change analysis showed that DBil, ALB, Arg, and Cit were the earliest metabolic derangements to reach peak levels in NICCD groups, followed by acylcarnitine profiles, and finally with the elevation of liver enzymes. This seemed to be accordant with previous findings . Met reaAll characteristic metabolic indicators in the “Newborn-screen Group” came back to normal levels at earlier ages than in the “Clinical diagnosed Group.” We found that in the amino acid profiles, Phe and Tyr (data not shown) were the earliest abnormal indicators in the “Clinical diagnosed Group.” In our previous case, we found an NICCD patient with a suspected diagnosis of phenylketonuria initially (data not shown). Two NICCD screen-negative patients were reported to be misdiagnosed with tyrosinaemia type I . These cALB was the earliest abnormal biochemical indicator in both groups. Coagulogram  was recovered early while AFP and GLB were the late recovered indicators in both groups. Protein synthesis may be affected by liver dysfunction in NICCD and the immature liver delays the conversion of AFP to ALB . We suggSLC25A13 alleles. It is consistent with other reports in Chinese cohorts , IVS16ins3kb (17.6%), c.615 + 5G>A (9.6%), 1638_1660dup (4.4%), and c.1177 + 1G>A (3.7%) accounted for 76.5% of all the mutated  cohorts . However cohorts , while i cohorts . It seem


Candidatus Carsonella ruddii , the obligate symbiont of the hackberry petiole gall psyllid, Pachypsylla venusta . The genome of this symbiont is one of the smallest known for cellular organisms, at 160 kb. The analysis revealed that Carsonella within a single bacteriocyte has ∼6 × 104 copies of the genome, indicating that some Carsonella cells can contain thousands or even tens of thousands of genomic copies per cell. The basis of polyploidy of Carsonella is unknown, but it potentially plays a role in the repair of DNA damage through homologous recombination.Polyploidy is the state of having multiple copies of the genome within a nucleus or a cell, which has repeatedly evolved across the domains of life. Whereas most bacteria are monoploid, some bacterial species and endosymbiotic organelles that are derived from bacteria are stably polyploid. In the present study, using absolute quantitative PCR, we assessed the ploidy of IMPORTANCE Mitochondria and plastids are endosymbiotic organelles in eukaryotic cells and are derived from free-living bacteria. They have many highly reduced genomes from which numerous genes have been transferred to the host nucleus. Similar, but more recently established, symbiotic systems are observed in some insect lineages. Although the genomic sequence data of such bacterial symbionts are rapidly accumulating, little is known about their ploidy. The present study revealed that a bacterium with a drastically reduced genome is an extreme polyploid, which is reminiscent of the case of organelles. Buchnera aphidicola  , had 10 to 600 genomic copies per cell depending on developmental stages and morphs of the host insect  of the green sharpshooter Draeculacephala minerva  had 200 to 900 genomic copies per cell   of the pt insect . DigitalCandidatus Carsonella ruddii  , has a genome of 160 kb, one of the smallest genomes known for cellular organisms  for females and 3571 ± 575 (n = 6) for male insects. When calibrated with the RpL32 gene, the values were 3942 ± 518 (n = 6) for females and 4040 ± 769 (n = 6) for male specimens (P. venusta are 16-ploid (Carsonella within a single bacteriocyte has ∼6 × 104 copies (16 × ca. 4 × 103 copies) of the genome, assuming that all bacteriocytes are uninucleate. Because Carsonella is pleomorphic and usually tubular, the cell number within a single bacteriocyte varies (Carsonella can be extremely long (greater than hundreds of micrometers), and only a few Carsonella cells are observed within a single bacteriocyte (Carsonella cell can contain thousands or even tens of thousands of genomic copies. This is much more than observed in Buchnera or Sulcia (8–Epulopiscium sp. (Firmicutes), a giant bacterium observed in the fish gut, which contains tens of thousands of genomic copies per cell  , the oblrganisms . To measriocytes –15. Wheriocytes –, 16–18, imentary , 15, 19.a genome , was ampa genome . For cala genome , were alpecimens . Becausee varies , 14, 18.eriocyte . Thus, aper cell . There ae genome .Carsonella is mutational degradation of ancestral genes linking chromosome replication to cell division, resulting in extremely large cell sizes and polyploidy. However, a presumed benefit of polyploidy is to facilitate the mutualistic role of synthesizing essential amino acids that are required by the host psyllid . The quality of extracted DNA was assessed using a NanoDrop 2000c spectrophotometer (Thermo Fisher Scientific) and the quantity was assessed using a Qubit 2.0 Fluorometer with a Qubit dsDNA HS assay kit (Thermo Fisher Scientific). Reference standards for quantification were constructed by PCR followed by TA-cloning as described previously (P. venusta and gene-specific primers (Escherichia coli JM109. Inserts were sequenced following colony PCR using M13-F (5′-GTAAAACGACGGCCAG-3′) and M13-R (5′-CAGGAAACAGCTATGAC-3′) primers annealing to the vector. Plasmids with appropriate inserts were amplified in E. coli and purified using a Fast Plasmid Minikit (Eppendorf). PCRs were performed again using purified plasmids and M13-F and M13-R primers. Subsequently, PCR products were purified with a QIAquick PCR purification kit (Qiagen) and quantified with a Qubit 2.0 Fluorometer and Qubit dsDNA BR assay kit (Thermo Fisher Scientific). Copy numbers of the PCR products were calculated based on their concentration and molecular weights. For each target gene, 108, 107, 106, 105, 104, and 103 copies/μL of PCR product solutions were freshly prepared in LoBind tubes (Eppendorf) for use as reference standards. Real-time quantitative PCR was performed using the LightCycler instrument and FastStart DNA Master SYBR green I kit (Roche). Running parameters were 95°C for 10 min, followed by 40 cycles of 95°C for 10 s, 58°C for 3 s, and 72°C for 6 s. Signal intensity was measured at the end of each elongation phase. The absence of nonspecific products was confirmed by melting curve and electrophoretic analyses. Copy numbers of target genes in specimens were calculated based on standard curves generated with reference standards using the LightCycler software . The copy number of the Carsonella 16S rRNA gene was normalized to the copy numbers of the P. venusta genes for RpL18 and RpL32. Analyses were performed with six biological replicates for each sex and three technical replicates.Absolute quantification was performed by real-time quantitative PCR targeting the eviously . Briefly primers . The PCRBacteriomes were dissected from 5th instar nymphs, fixed with fixation buffer , and stained with 4′,6-diamidino-2-phenylindole (DAPI). After repetitive pipetting, specimens were put on a glass slide and covered with a coverslip. The slides were examined by fluorescence microscopy .


In order to determine whether GABA is truly effective in promoting rice resistance under a certain level of salt stress or not and to evaluate its effect on the growth and some physiological responses of two Japonica rice varieties under salt stress. 3-leaf rice seedlings germinated from seeds were cultivated in a separate hydroponic cup with a nutrient solution that was salinized with 0, 25, 50, or 75 mmol K+ of NaCl. A 4 mmol L−1 GABA solution or water were sprayed onto leaves once a day for 8 days prior to an assessment of the seedling growth, the growth indices, root activities and three antioxidant enzyme activities in leaves were measured. Data analyses indicated that as the salt concentration increased, the plant height and the leaf area of both rice varieties decreased, while the dead leaf rate, weight ratio of the dry- and fresh-roots, superoxide dismutase (SOD) and peroxidase (POD) activities increased. Under the same saline conditions, the root activities and the leaf ascorbate peroxidase (APX) activity were enhanced at a low NaCl concentration but reduced when the salt concentration was high. A foliar application of GABA daily on both rice varieties for over a week under 3 different salinized treatments as compared with the corresponding treatments sprayed with water resulted in an enhanced effect on plant height increment by 1.7-32.4%, a reduction of dead leaf rate by 1.6-36.4%, a decline of root dry weight by 9.3-30.9% respectively, and an increment in root activities by 8.1-114.5%, and POD, SOD and APX enzyme activities increased by 5.0-33.3%, 4.1-18.5%, and 7.2-64.4% respectively. However, two rice varieties showed a significant difference in response to various salinized levels. Overall results of this study demonstrate that the application of exogenous GABA on the leaves of rice seedlings under salt stress has improved rice salt tolerance, which should provide a sufficient information for ultimately making it possible to grow rice in salinized soil.Exogenous  Saltl−) ions , 4, affel−) ions –7. Rice dy crops , 9. Becady crops , but it ops [m−1 . The excops [m−1 , 12. Morops [m−1 . During γ-aminobutyric acid (GABA) is a non-protein four-carbon amino acid that is associated with various physiological responses such as the regulation of cytosolic pH, carbon fluxes in the tricarboxylic acid cycle, and nitrogen metabolism [−1 exogenous GABA solution under a 150 or 300 mmol L−1 NaCl stress, likely through increase of photosynthesis, osmo-protectants and antioxidants [−1 GABA solution was used to soak seeds under a 100 mmol L−1 NaCl stress, resulting in a significant increase of the Na+/K+ content and transcript levels of genes encoding Na+/K+ transportation, e.g. HKT1, HKT8, HAL2, H+-ATPase and SOS1 [−1 exogenous GABA in the hydroponics solution with less than 300 mmol L−1 NaCl in it to grow wheat seedlings could improve photosynthesis and chlorophyll fluorescence parameters, increase antioxidant enzyme activities, and reduce a malondialdehyde accumulation in leaves [−1 exogenous GABA hydroponics plus 175 mmol L−1 NaCl significantly reduced Na+ accumulation in tomato leaves and roots by preventing a Na+ influx into roots and the Na+ movement further from roots to leaves. Kalhor et al indicated that 25 μ mol L−1 of GABA hydroponics plus 40 or 80 mmol L−1 NaCl significantly reduced the negative effects of salinity on lettuce growth by improving the photosystem II and reducing electrolyte leakage [−1 exogenous GABA on rice leaves at the tillering had the most effectiveness in improving the antioxidant metabolisms and increasing the rice yield [Up to the present, more than 58 ESs have been reported to play a role in alleviating plant salt stress . Among ttabolism . Many retabolism . Wang etoxidants . A same and SOS1 . Li et an leaves . Similarn leaves  who also leakage . Zhao etce yield . As summIn a large scale, rice is generally grown through transplanting , so the −1, available phosphorus 338.9 mg kg−1, and available potassium 2,334 mg kg−1. Half-strength Kimura B nutrient solution formula [This experiment was carried out from July to September 2021 at the National Japonica Rice Engineering Technology Research Center . Two japonica rice varieties, ‘Tianlongyou 619’ and ‘Dajueyipin’, were provided by Tianjin Tianlong Technology Co., Ltd. GABA is provided by Shandong Shengyuan Biotechnology Co., Ltd. The seedling cultivation substrate was prepared by mixing soddy soil, perlite and vermiculite in proportion of 3:1:1 . The nutrient components were: organic mass 35.3%, hydrolysis nitrogen 2,531 mg kg formula  was usedHealthy rice seeds were disinfected with 70% alcohol for 1 min, washed with distilled water, soaked for 36 h in a dark container, and then sowed in a 72-holes tray. Seedlings in the tray were grown outdoors and watered daily without fertilization before being transplanted for the experiment.−1) were prepared in hydroponic cups (10 cm high and 8 cm in diameter) with a nutrient solution to generate a series of artificial salt stress since it contributes approximately 50% of salinity to irrigated soils [−1) were tested in a pilot trial for the most significant mitigating effect on alleviating salt stress, from which the 4 mmol L−1 GABA solution described by Sha et al. [−1) that were designated as S0, S25, S50, S75 and SG0, SG25, SG50, SG75, respectively.The indoor hydroponic experiment started when rice seedlings reached the 3-leaf-1-heart stage prior to tillering. Four NaCl concentrations .There were 16 treatments in total with the experiment, 4 replications (cups) for each treatment, and 6 seedlings per cup. A nutrient solution was used to grow seedling growth and different amount of NaCl was added to prepare to generate a certain level of salt stress in the hydroponic cultivation. The hydroponic rice solutions were replaced or replenished once in two days. Indoor supplementary lighting was timed to switch on and off for 14 h per day at a full spectrum. The average temperature of the plant growth environment was 25°Seedling morphological indexes. The plant height of all rice seedlings was measured using a ruler before and on the 8th DAHE, yellowing leaves counted on the 8th DAHE, and the dead leaf rate calculated. With each treatment, five uniform seedlings were measured for the length and width of expanded leaves using a ruler, and the leaf area was calculated using the formula proposed using Eqs C to a constant dried weight for a ratio of dry and fresh weight. Fresh roots were obtained from the cultivated seedlings and their root activity was determined using an assay kit . Salt tolerance index was calculated using i is the growth indicators under salt stress, G0 is the growth indicators under zero salt stress.1) Antioxidant enzyme activity in seedling leaves. Fully expanded true leaves (3rd leaf from the top) of the rest seedlings were cut and mixed to determine the antioxidant enzyme activity. Superoxide dismutase (SOD), peroxidase (POD) and ascorbate peroxidase (APX) activities that have been proven to be the most indicative and meaningful enzymes actively involved in responses against salt stress were measured using an assay kit , and each measurement was repeated three times.2) The data was routinely processed and plotted in Office Excel 2019 software, and SPSS 17.0  was used for the analysis of significant differences and variance of multiple factors.P > 0.05) in terms of the plant height alone due to the measurements were greatly affected by the variation of the initial seedling heights. The percentage of dead leaves with all salt stressed treatments increased significantly (P < 0.05) in comparison with the NaCl-free treatment. As shown in −1 NaCl concentration, but was affected less than ‘Dajueyipin’ under the 50 or 75 mmol L−1 NaCl stress.The plant height increment and the leaf area of seedlings with two rice varieties showed a downward trend while salt stress intensified Figs  and 2 an−1 NaCl concentration increased by -12.9%, 1.7%, 2.3% and 32.4%, the leaf area increased by -6.2%, 4.9%, 4.3% and 9.1%, and the percentage of dead leaves decreased by 63.6%, 23.3%, 4.8% and 1.6%, respectively; while the plant height increment of ‘Dajueyipin’ at four different salt stresses showed a 27.2%, 5.7%, 23.4% and 19.4% increase with the plant height increment, a -0.2%, 0.1%, 23.9% and 0.9% rise with the leaf area, and a 57.1%, 36.4%, 21.1% and 11.4% decrease with the percentage of dead leaves, respectively. It could be seen that spraying GABA alleviated salt stress and improved the growth of rice seedlings, which was also correlated to salt tolerance of different rice varieties/varieties and the salt stress intensity. In addition, spraying GABA had a greater effect on promoting plant height growth of ‘Dajueyipin’ cultivated in the nutrient solution with less than 50 mmol L−1 of NaCl.Compared with the treatment without GABA spraying, the plant height increment of ‘Tianlongyou 619’ at the 0, 25, 50 or 75 mmol LP < 0.05. Error bars represent standard deviation (± SD). S0, S25, S50, and S75 indicate that rice seedlings were cultivated in 0, 25, 50, 75 mmol L−1 NaCl solution, respectively, while GS0, GS25, GS50, and GS75 indicate that rice seedlings were cultured in 0, 25, 50, 75 mmol L−1 NaCl solution and sprayed with 4 mmol L−1 GABA. Same notations are used in the figures bellow.Values followed by different letters are significantly different at −1 NaCl solutions, respectively. On the other hand, with the treatments with a GABA foliar application, the root fresh weight of ‘Dajueyipin’ decreased by 0.5%, 0.2%, 21.4%, 4.2%, its root dry weight reduced by 10.7%, 9.7%, 30.9%, 16.0%, and its root activity of the variety increased by 45.0%, 114.5%, 73.2%, 8.1%, respectively. Therefore, the foliar GABA application reduces the dry and fresh weight of rice roots and improved the root activity.While salt stress intensified, the ratio of dry and fresh roots of seedlings with both rice varieties had an upward trend, but the root activity increased under less salt stress and then decreased with a higher salinity . However−1 NaCl treatment. With each of different salt stress treatments, the POD activity in ‘Tianlongyou 619’ leaves increased by 25.0%, 20.8%, 5.0% and 7.1%, the SOD activity increased by -6.5%, 17.3%, 15.8% and 9.8%, and the APX activity increased by 4.6%, 7.2%, 54.8% and 64.4%, respectively at four different salt stress levels with the GABA treatment. The POD activity of ‘Dajueyipin’ in leaves increased by 33.3%, 33.3%, 22.2% and 25.9%, the SOD activity increased by -13.2%, 4.1%, 18.0% and 18.5%, and the APX activity increased by 25.9%, 28.0%, 9.6% and 20.6%, respectively under the same salt stress level and the GABA treatment. So, it is obvious that foliar GABA applications against salt stress facilitated the activities of a group of antioxidant enzymes in rice seedling leaves.The activity of antioxidant enzymes such as POD and SOD in leaves of rice seedling increased with all different levels of salt stress except APX that increased first at lower NaCl concentration and then decreased under high salt stress . In compP < 0.01), while the main effect of ‘varieties’ and ‘spraying GABA or not’ was least significant (P > 0.05), with which the P value of ‘spraying GABA or not’ was 0.055. With the two-dimensional interaction, the main effect of ‘varieties’ × ‘spray GABA’ and ‘varieties’ × ‘salt stress degrees’ were significant (P < 0.05), but the main effect of ‘spray GABA’ × ‘salt stress degrees’ was not significant (P > 0.05). With the three-dimensional interaction, the main effect of ‘varieties’ × ‘spraying GABA or not’ × ‘salt stress degrees’ was significant (P ≤ 0.05). Partial Eta squared (η2) value indicated the magnitude of the main or interaction effect. Therefore, from the analyses described above, the ranking of the significance of those main and interaction effect on the plant height increment should be: ‘salt stress degrees’, ‘varieties’× ‘salt stress degrees’, ‘varieties’ × ‘spraying GABA or not’ × ‘Salt stress degrees’, ‘varieties’ × ‘spraying GABA or not’.Plant height increments throughout the whole growing period and the root dry mass at the end of the experiment were used to evaluate salt stress and its alleviation through GABA applications and their interactive effect on the growth of rice seedlings. Tables P < 0.01) affected the root dry weight, while two-dimensional interactions, such as ‘varieties’ ×’spray GABA’, ‘varieties’ × ‘salt stress degrees’ and ‘spraying GABA or not’ × ‘salt stress degrees’ were significant (P < 0.05). With the three-dimensional interactions, the main effect of ‘varieties’ × ‘spraying GABA or not’ × ‘salt stress degrees’ was not significant (P > 0.05). The order of the effect of those factors and their interactions on root dry weight was ‘varieties’, ‘salt stress degrees’, ‘varieties’ × ‘salt stress degrees’, ‘spraying GABA or not’, ‘spraying GABA or not’ × ‘salt stress degrees’, and ‘varieties’ × ‘spraying GABA or not’.The results demonstrated that variety had the greatest effect on the growth indexes of rice seedlings that was represented by root dry mass, followed by the degree of salt stress, the interaction between ‘varieties’ and ‘salt stress degrees’, and last ‘spraying GABA or not’. The least effect of those interactions belonged to the ‘varieties’, ‘salt stress degrees’ and their interactions with the ‘spraying GABA or not”. Salt stress played the most significant role in the growth of rice seedlings that was represented by the plant height increment, followed by the interaction of ‘varieties’ × ‘salt stress degrees’, the three-dimensional interaction of ‘varieties’ × ‘spraying GABA or not’ × ‘salt stress degrees’, and the interaction of ‘varieties’ × ‘spraying GABA or not’. It was obvious that foliar-applied GABA affected the growth of rice seedlings, and there were differences with the ‘varieties’ and various plant growth factors.+ and Cl− [In this study, salt stress was simulated at different levels post transplanting of rice seedlings and the results derived from data analyses were consistent with previous research findings in general, suggesting that with the increase of salinity, the plant height increment, leaf area, root dry and fresh weight of the two tested rice varieties showed a downward trend. The possible underline impact of the salt impairment was likely due to inhibition of photosynthesis in rice , 19, 27  and Cl− , 28. Mor−1 NaCl solution) instead of a higher one (80 mmol L−1 NaCl solution) was used in a previous report [Rice root activities and their changes are regarded as reliable estimators for the healthy root growth and plant salt resilience at the end of the Es treatment under salt stress. Our data analysis also indicated that rice root activities were slightly boosted first at the least salt stress and then reduced when salt concentration was higher, which was different from the findings previous reported under salt stress because a lower salt concentration (75 mmol Ls report . A low ls report , 29. Ours report , 20, 22.Two aboveground plant growth indexes, the plant height increment and the leaf area were measured to present salt tolerance of two rice varieties, the smaller the value of salt tolerance index is, the greater the degree of salt damage would be, and vice versa. The evidence provided through this study indicates that both aboveground plant growth indexes well reflect the responses of rice seedings to different levels of salt stress even if a significant difference between two rice varieties exists in terms of their salt tolerance. However, we were unable to see the difference of plant heights among or between different salt-stressed treatments possibly due to the fact that the height of initial rice seedlings varied or/and that the duration of the experiment was not long enough so as to generate a significant difference among each individual seedlings, which might have concealed the true effect of GABA among the treatments on promoting plant growth indexed as the plant height.−1 NaCl increased to a various extent, which was consistent with the previous reports on maize [−1 NaCl treatments and in the GABA treated seedlings, the plant height increment and leaf area increased, the percentage of dead leaves decreased, the fresh and dry weight of roots decreased, and the root activity increased in general. Therefore, it is concluded that foliage-sprayed GABA can promote the growth of the aboveground parts of rice seedlings in response to salt stress, reduce the allocation of photosynthetic products to roots, and improve the root activity. There were many reports of exogenous GABA on improving the growth of aboveground plant parts [μ mol L−1 under a 100 mg L−1 NaCl salt stress [−1 of a saline-alkali stress and found that the dry weight of aboveground plant parts and root of rice seedlings increased in day 5 after those seedlings were treated with 1.5 mmol L−1 GABA [Leaves are the most important vegetative tissues of plants other than roots. Once being applied on leaves, exogenous substances enter the leaf surface first by diffusing through the wax and cuticle layers and then are absorbed and utilized by mesophyll cells. This direct foliar application of GABA or other exogenous substances enables plants to absorb these potentially foreign alleviators substances more quickly, allowing them to initiate possible defensive mechanisms, to regulate the ion balance in leaf tissues, and to stabilize enzyme activities against salt stress or subsequent damages . Our stuon maize , wheat [on maize , tomato on maize , rice [2on maize , 25,and nt parts , 20, 25,t stress . In a peL−1 GABA . The difL−1 GABA  used seeL−1 GABA . Althoug−1 exogenous GABA solution was sprayed on foliage of rice seedlings daily for 8 days. Our results derived from assessments of plant growth indexes, root activities, and antioxidant enzymes show that both salt stress and rice variety have primarily affected the growth of rice seedlings and the foliar-applied GABA has improved the activity of antioxidant enzymes and the root function of both tested rice varieties, thereby has enhanced salt tolerance. However, different rice varieties may response to salt stress differently and the effect of foliar-applied GABA may vary accordingly in mitigating the damages caused by excessive salinity. This study also confirms that GABA application on leaves of rice seedlings has enhance the movement of photosynthetic products within the aboveground plant tissue. Finally, the concentration and foliage delivery method of exogenous GABA are adequate to be used in cultivation of rice seedings in nursery to develop a potential tolerance against salt stress, especially at a mild or a mild-to-severe level. A further field trial or prolonged duration of rice growing would be useful to evaluate the effect of exogenous GABA on salt stress alleviation and to determine if the alleviating effect lasts throughout the whole rice growing season or is just temporary.Rice seedlings with 3 leaves and 1 heart was cultivated in a hydroponic setting under four levels of salt stress and a 4 mmol L