Saccharomyces cerevisiae via topologically different ODE models, parameterized on multimodal activation data. Interestingly, our best fitting model switches between distributive and processive phosphorylation behavior regulated via a positive feedback loop composed of an affinity and a catalytic component targeting the MAP kinase-kinase Pbs2. Indeed, we show that Hog1 directly phosphorylates Pbs2 on serine 248 (S248), that cells expressing a non-phosphorylatable (S248A) or phosphomimetic (S248E) mutant show behavior that is consistent with simulations of disrupted or constitutively active affinity feedback and that Pbs2-S248E shows significantly increased affinity to Hog1 in vitro. Simulations further suggest that this mixed Hog1 activation mechanism is required for full sensitivity to stimuli and to ensure robustness to different perturbations.Cellular decision making often builds on ultrasensitive MAPK pathways. The phosphorylation mechanism of MAP kinase has so far been described as either distributive or processive, with distributive mechanisms generating ultrasensitivity in theoretical analyses. However, the in vivo mechanism of MAP kinase phosphorylation and its activation dynamics remain unclear. Here, we characterize the regulation of the MAP kinase Hog1 in  How cells shape signalling dynamics in MAPK cascades remains unclear. Here the authors combine mathematical modelling with in vivo validation to uncover a novel feedback mechanism that increases processivity and robustness of the yeast Hog1 module. Ultrasensitivity has been experimentally observed in various signaling systems and plays an important role in cellular decision-making2. Theoretical studies suggest that multi-tiered multisite phosphorylation cascades are inherently able to create ultrasensitivity3, with even single multisite phosphorylation resulting in ultrasensitivity and bistability4. In particular, the specific type of phosphorylation mechanism can alter signal response dynamics5. For dual phosphorylation, two distinct mechanisms are recognized  kinases, which regulate the cellular responses to many intra- and extracellular signals. However, investigating the impact of different phosphorylation mechanisms is challenging and normally relies on mathematical models integrating typically difficult-to-measure temporal dynamics of specific protein species. The majority of theoretical studies have reduced to a dichotomy of assumptions - either distributive or processive - with distributive mechanisms associated with ultrasensitivity and processive mechanisms with a graded, non-ultrasensitive response6. Thus, to date, theoretical studies generally suggest that ultrasensitive kinase phosphorylation events in vivo should be governed by a distributive phosphorylation mechanism7, and some experimental data from mammalian cells support this hypothesis9. However, in more complex cases of multisite phosphorylation with more than two phospho-sites, behaviors have been observed that are not well explained by either a processive or distributive mechanism10. Some of these multisite phosphorylation events involve different kinases with distinct kinetic properties, which may complicate the analysis11. Altogether, understanding phosphorylation mechanisms governing ultrasensitive responses has proven particularly challenging in cases of multisite phosphorylation and the presence of positive feedback13. Additional studies are required to understand the degree to which different mechanisms interact, as well as the theoretical potential and experimental validation of a mixed phosphorylation mechanism.Pathways integrating extracellular inputs often display an ultrasensitive response, in which beyond an input threshold, small changes in the input lead to large changes in the output. This behavior results in an essentially binary response, acting as a switch in the overall signaling cascade Fig. 1. Ultraszed Fig. . A distrHigh Osmolarity Glycerol (HOG) pathway in Saccharomyces cerevisiae, a well-studied MAP-kinase pathway which requires dual phosphorylation of the MAP kinase Hog1. Hog1 activation is needed to re-establish the balance between internal and external pressures upon osmotic shock. Upon exposure of cells to high osmolarity conditions, the two membrane-localized osmo-sensors Sho1 and Sln1 activate either the MAPKKKs Ste11 or Ssk2 and Ssk22, which converge on the MAPKK Pbs2  was used to compare and rank the results . Using autoradiography, we could indeed establish that Pbs2 is directly phosphorylated on Ser248 by activated Hog1 in vitro . In contrast to pbs2Δ controls, both strains were able to grow on plates containing 0.4 M NaCl, indicating that Hog1-dependent feedback on S248 is not essential for viability under these conditions  were varied between half to twice their original concentration, mimicking the natural fluctuations of protein expression in single cells and providing a distribution of Hog1 activation. We performed 2000 simulations of a single-step addition of 0.4 M NaCl and noted the resulting maximal Hog1 double phosphorylation. This was carried out for wild-type cells with functioning feedback loops and repeated for a model in which the affinity feedback on Pbs2 was abolished. Consistent with the experimental results, loss of affinity feedback in the Pbs2-S248A mutant showed an increase in bimodality with a higher proportion of the cell population showing intermediate Hog1 activation between 20 and 60 percent Hog1 double phosphorylation, the significance of which was again quantified and visualized using a quantile shift function Fig. .The absence of the affinity feedback reduces the processivity of the reaction making it more distributive. To generalize this behavior, we also simulated maximal Hog1 double phosphorylation upon 500 randomized perturbation schemes for the previously described best-fitting distributive, processive and mixed models. With no perturbation (0 M) or low NaCl concentrations (0.1 M), the processive mechanism resulted in slightly bimodal distributions with 2.4 times the number of perturbations generating complete activation (>70% Hog1 double phosphorylation) than the mixed mechanism, and the majority showing no activation. The distributive mechanism led to an accumulation of activation at an intermediate level (20%), while the mixed model distributed more around the unperturbed activation level Fig. . At highWe thus conclude that the mixed Hog1 activation mechanism displays a unique and favorable system’s behavior that leads to increased robustness in the input-output relations, leading to decreased sensitivity of its output to initial intracellular conditions. This behavior is at least partially distinct from positive feedback that increases the overall reaction speed.S. cerevisiae HOG pathway, Hog1 is activated by dual phosphorylation and thus the choice and kinetics of this phosphorylation mechanism can greatly affect signaling dynamics. A multitude of previous, mostly theoretical, work has focused on the extreme cases of distributive or processive mechanisms. Interestingly, however, our combined experimental and modeling analysis revealed that a mixed control mechanism regulated by positive feedback best explains the observed phosphorylation and signaling dynamics.Effective processing of external information via subsequent intracellular response is of vital importance for every cell. From a systems-engineering perspective, it is desirable for this process to be robust towards external and internal state fluctuations. Similarly, the actual input threshold to induce a cellular response should be carefully chosen to avoid unnecessary energy expenditure. In the 41. In particular, increased processivity can enhance the sensitivity to the external signal and lower ultrasensitivity. Indeed, increasing processivity diminished EC50 values, with the mixed mechanism achieving a lower value than distributive and processive mechanisms  (pGY75), was cloned into pGEX46P1 by EcoRI-XhoI. GST-Pbs2 K/MS248A (PBS2 with Ser248 to Ala mutation) (pGY77) were generated by site directed mutagenesis and verified by sanger sequencing. As a control, GST-Sic1 was also purified from E. coli as previously described56. Plasmids were incorporated into a pbs2Δ strain (yHS206) via homologous recombination.Strains for in vitro kinase assays were constructed as follows. The wild type allele of Hog1 was cloned into p426TEG1  to yield pRS426 GST-Hog1 (pEN133)S248E), YMN459 (Pbs2S248A) and YMN460 (Pbs2WT) were verified by Sanger sequencing.For strains used in western blot experiments, Pbs2 mutations were introduced with a pop-in pop-out approach from the original YMN455 (HOG1-6HA::HIS PBS2::URA), the different Pbs2 alleles were PCR amplified from . Transformants were selected by FOA counterselection. Point mutations for YMN457 (Pbs2PBS2::URA HOG1::KAN), YMN552 (BY4741 HOG1::KAN Pbs2S248E), YMN552 (BY4741 HOG1::KAN Pbs2S248A), and YMN553 (BY4741 HOG1::KAN Pbs2WT).Strains used for Pbs2 interaction experiments were derived from YMN455, 457, 459 and 460 by PCR mediate integration of KAN resistance cassette to the HOG1 locus. The resulting strains are YMN551  media with 2% glucose. Exponentially-growing cells were transferred to a microfluidic device  or 96 well plate and live cell imaging was carried out at 30 °C using a fully-automated inverted epi-fluorescence microscope  in an incubation chamber. Osmotic stress was induced with the pressure controller  or by manual pipetting by exchanging the medium with media containing NaCl at the specified concentrations. Images were taken with a high numerical aperture oil immersion objective lens , and controlled using micro-manager. Each frame was imaged with relevant fluorescent set-up . Cell segmentation, tracking and feature extraction were done using the MATLAB-based YeastQuant softwareK/M and Pbs2K/M S248A (pGY75 and pGY77 respectively) were expressed in E. coli and purified using glutathione-Sepharose beads  and STET buffer , 1 mM phenylmethylsulfonyl fluoride (PMSF), 1 mM benzamidine, 2 μg/ml leupeptin, 2 g/ml of pepstatin). Active GST-Hog1 was purified from NaCl treated (0.4 M NaCl for 10 min) wild-type cells harboring a multicopy vector .The GST fusion protein encoding Pbs2K/M or Pbs2K/M S248A in the presence of kinase buffer  and 50 μM ATP together with [γ-32P]ATP (0.1 μCi/μl) and incubated for 15 min at 30 °C. The reaction was terminated by the addition of 5 × SDS loading buffer. Labeled proteins were resolved by SDS-PAGE, stained, dried and detected by autoradiography with Fujifilm BAS-5000 phosphoimager.For kinase assays, 0.5 μg of GST-Hog1 was incubated with 0.25 μg of Pbs2Yeast cells were grown to mid-exponential log phase (OD660 = 0.7) before being subjected to osmostress (0.4 M NaCl) for the indicated times. Samples were fixed with 20% tricholoracetic acid, resolved with SDS-polyacrylamide gel electrophoresis and proteins transferred to PVDF membranes . Total or phosphorylated Hog1 was detected using either primary antibody for phospho-Hog1  or total Hog1  with a final concentration of 0.2 μg/ml and visualized by secondary antibodies for mouse (LI-COR 926-32212) and rabbit . Incubations were done in PBS-BSA 5% . Blocking and antibodies were diluted using Intercept blocking buffer  and fluorescence was detected with a LI-COR Odyssey Infrared Imaging System 9120. Western blot quantification was done using Image J and a paired t-Test .E. coli pellet, following the manufacturer’s protocol. An overnight preculture (25 ml LB + Chloramphenicol 50 µg/ml) was inoculated into 1 L of LB for 2 h at 37 °C before addition of IPTG (1 mM) for 8 h at 20 °C. Cells were pelleted by centrifugation (5 min 5200 g) and pellets were stored at −80 °C. Yeast extracts were obtained by growing hog1::KAN Pbs2  until mid-exponential phase before applying mild osmotic stress (0.4 M NaCl). Cell lysates were obtained by thawing cells in sonication buffer  with protease inhibitor .Hog1 ORF was cloned into pSECT vector with BamHI (pEN111) and transformed into BL21. Expressed Hog1-HIS was purified using 500 μl of Complete His-Tag purification resin  for each 500 ml of 2, ATP 50 µM). Samples were washed twice in the columns (1 min 80 g) with 500 µl of sonication buffer 100 mM NaCl and sonication buffer 200 mM. Finally, beads were resuspended in sample buffer and boiled before loading onto 10% SDS PAGE. Detection of Pbs2 was done by incubating the membranes with anti-Pbs2 antibody  with a final concentration of 2 µg/ml and total Hog1  with a final concentration of 0.2 μg/ml. Incubations were done in PBS-BSA 5% . Images from chemiluminescence were obtained using Claity ECL  and a chemiluminescence program (Odyssey Fc Imager). Image quantifications were done with Image J (Fiji).Purified bead-bound Hog1 HIS was evenly split into columns  and incubated for 2 h at 4 °C with 5 mg of total protein obtained from NaCl-stressed yeast extracts diluted in kinase buffer  the qualitative dynamics of the Hog1 response were essentially identical34. Moreover, the switch-like response resulting in full Hog1 phosphorylation for all salt concentrations above a certain, low threshold justified inclusion of these data.To determine the degree of Hog1 phosphorylation, the maximal values determined by western blot measurements were used58. For example, different antibodies are known to have different binding properties59. As a consequence, measurements of Hog1 phosphorylation in Ptp2/Ptp3 mutants in the literature revealed quite varying results60. However, despite these differences, the data largely agree that deletion of Ptp2 results in increased basal levels and prolonged Hog1 phosphorylation, while deletion of Ptp3 shows only minute differences compared to wild-type controls. To account for this variability, we utilized the data from ref. 20, but allowed the parameters for the error model of these measurements to be sufficiently big and independent from other western blot data sets. Furthermore, as the antibody used detects phosphorylated tyrosine, the corresponding output species of the model was set to be Hog1 doubly phosphorylated or mono-phosphorylated at tyrosine 176.Additional western blot measurements were utilized for different phosphatase mutants. Compared to mass spectrometry measurements, quantification of western blots is complex and these results often reveal more qualitative than quantitative results61. Volume and Hog1 relocation measurements in cells deleted for SLN1 or SHO1 were taken from ref. 62. Although the authors used sorbitol instead of NaCl for their experiments, own measurements confirmed that the response of cells to 0.6 M sorbitol is quantitatively and qualitatively nearly identical to perturbations with 0.4 M NaCl. To assess negative feedback of Hog1 on Ssk2, we used published Hog1 relocation measurements35. Due to the fact that non-phosphorylatable Ssk2 mutant exhibit reduced cell shrinkage and thus a lower maximal Hog1 nuclear to cytosolic ratio, only data from later time points were included, which correct for the increased time it takes for the Hog1 ratio to reach basal levels. Data for Gpd1 expression changes were selected from ref. 63, and information about Ptp2 and Ptp3 mRNA levels were extracted from ref. 19. Western blot measurements of total Hog1 phosphorylation upon inhibition with small-molecule inhibitors in wild type and ssk2Δ strains were taken from refs. 36 for basal activity and26 for activity upon increase of osmolarity. As most antibodies used to measure Hog1 phosphorylation bind to both the doubly and mono-phosphorylated species26, these western blot measurements were considered as total amount of phosphorylated Hog1 irrespective of phosphorylation grade.Microscopy measurements of Hog1 relocation to the nucleus report on Hog1 activity, and such data was used to quantify the response of single branch and phospho-site mutants. Similarly, microscopy-based measurements of cell size were used to fit the volume module. Information on Hog1 activation at 0.2 M NaCl stimulation with varying frequency  were extracted from ref. The observables in these data were incorporated as model variables by defining observables that correspond to the experimentally measured quantity. We defined the relative ratio between the current absolute number of a protein species and its absolute number at the very start, the phosphorylated percentage as the absolute number of phosphorylated protein divided by the total number of the protein, and the concentration ratio of Hog1 in the nucleus compared to the cytosol, for the mass spectrometry, western blot, and fluorescence ratio data sets respectively. Further details on how the observables and their corresponding data set were encoded in the model can be gathered from Supp Table 64 and computation was carried out on the Euler cluster provided by ETH Zurich accessed via BASH scripts. Parameter optimization was carried out by multistart followed by a deterministic trust region algorithm. The goodness of fit was evaluated by Goodness-of-fit = −2* log(Likelihood). For parameter optimization, parameters were considered on a log-scale. In a first step, 10,000 starting parameter vectors were created. Sampling was done uniformly between the lower and upper boundaries of each parameter. Lower and upper boundaries were first set to be minus three to three, respectively, spanning six orders of magnitude. After successful parameter estimation  the 100 best-fitting parameter vectors were taken and their correlation coefficient determined. 10,000 starting vectors for the next optimization run were generated by sampling from a multivariate normal distribution whose parameters were determined by the 100 best fitting parameter vectors of the previous run. This procedure was repeated until the best goodness of fit of the latest run turned out as good or worse than the run before.All modeling was performed using the Data2Dynamics modeling environmentTo minimize the risk of the optimization procedure redundantly reproducing solution clusters with very similar values, we included additional steps, such as optimization of crucial model topologies being redone up to eight times with different starting parameters, and ensuring that the relative ordering of the fits was consistent over various conditions, such as leaving out of data points, or changing of parameter boundaries. In general, parameter identifiability was not a major concern, as some model topologies were not able to recapitulate the data and we were primarily interested in the relative quality difference of each topology prediction. The size of the model and its complicated nature also impeded identifiability analysis by profile likelihoods. Instead, we simulated species concentration from a model with known parameters. From these simulations, we sampled data points equivalent in number and time points to the experimental dataset, and performed the parameter optimization procedure described above. All but twelve of the 82 newly fitted parameters were within one order of magnitude from the parameters used to generate the data, with a median of 0.11.67. As this was observed with all model topologies, we feel confident to compare the different topologies relative to one another even if the models do not fully capture the Sho1 sub-branch. Similarly, we did not incorporate the latest information that describes how Ste11 only phosphorylates one phospho-site on Pbs246.In all our models, certain parameters of the Sho1 sub-branch  assumed values much higher than expected (up to 10^6) after parameter optimization. We speculate that this reflects a stable complex that forms at the cell membrane which incorporates all involved species  and brings them into close proximity so that reactions occur faster than expected by simple diffusionComparison of different models was done using the AIC.k” being the number of fitted parameters and Lmax the maximal likelihood.With “Detailed information on the best fitting mixed model can be found in Supp Tables We introduced a score (2) to quantify the change in processivity of the Hog1-Pbs2 reaction over the course of the response.It is defined as the probability of a monophosphorylated Hog1 bound to activated Pbs2 undergoing a second phosphorylation step against the probability of the proteins dissociating. Feedback on Pbs2 is reflected in a higher rate of phosphorylation of Hog1 while the dissociation constant is kept constant.S. cerevisiae by NaCl stimulation occurs with a hill-coefficient of 3.3, while its mammalian counterpart p38 in HeLa cells is stimulated by anisomycin with a hill-coefficient of 345. In comparison, the highly ultrasensitive activation of p38 via sorbitol in Xenopus oocytes occurs with a hill-coefficient of 14.413, and the graded response of Erk2 in HeLa cells stimulated by EGF with a hill-coefficient of 1.245.We utilized the paradigm of Huang and Ferrell, which models the basic three-tiered MAPK cascade. We collected or generated data measuring activation of MAP kinases from both yeast and mammalian cells that display different degrees of ultrasensitivity quantified by their Hill-coefficient. We found that Hog1 activation in 68. In contrast, the graded activation of Erk2 showed a clear preference for processive phosphorylation with significantly better fitting results, consistent with experimental evidence45. Experimental measurements also corroborate the possibility that mild ultrasensitive behavior can be achieved in nature using purely processive mechanisms. Thus, a processive mechanism with the correct parameters is also able to recapitulate even highly ultrasensitive behavior and thus cannot be readily discarded.The parameters of the basic model were optimized according to our described protocol and the best overall fit determined according to log-likelihood criteria. This was done for a distributive and a processive topology of MAPK activation. For Hog1 and both p38 data sets it was not possible to distinguish between a purely distributive or purely processive mechanism. Both models were able to fit the data equally well  and the utilized parameters still range within biologically feasible boundaries (Supp Fig. 69. Multiple linear regression to determine whether a linear relationship between concentration changes of different proteins and maximal Hog1PP percentage exists was performed using built-in MATLAB functions.All data were analyzed and visualized using MATLAB software. Error bars in histograms denote the standard deviation of the proportion of measurements within specific bin limits computed from 200 resamples. A MATLAB implementation of Wilcox quantile shift function was used to quantify and plot the difference between different distributions. The implementation computes quantiles using Harrel-Davis quantile estimator, performs 200 resamples for a bootstrap estimation of 95% confidence intervals and controls for multiple testingFurther information on research design is available in the Supplementary informationReporting Summary


N-terminal microtubule-binding domain and a C-terminal ubiquitin–binding domain. Interfering with its catalytic activity by using small synthetic molecules has been shown to be beneficial in the treatment of cancer, and neurological and immunological disorders. Thus, the development of potent and selective inhibitors of HDAC6 is an active field of medicinal chemistry. We shall here discuss the importance of monitoring the kinetics of onset and relief of inhibition to contribute important information on inhibition mechanisms during drug design/development campaigns using selected HDAC6 inhibitors as examples.Protein lysine acetylation is, with phosphorylation, the most common regulatory post-translational modification of proteins. Histone deacetylases (HDAC) catalyze the removal of acetyl groups from histone and non-histone proteins, participating in the modulation of several pathways. Histone deacetylase 6 is perhaps the most complex among histone deacetylases, comprising two catalytic domains, an N-terminal microtubule binding region and a C-terminal ubiquitin binding domain. Most of its known biological roles are related to its protein lysine deacetylase activity in the cytoplasm. The design of specific inhibitors is the focus of a large number of medicinal chemistry programs in the academy and industry because lowering HDAC6 activity has been demonstrated to be beneficial for the treatment of several diseases, including cancer, and neurological and immunological disorders. Here, we show how re-evaluation of the mechanism of action of selected HDAC6 inhibitors, by monitoring the time-dependence of the onset and relief of the inhibition, revealed instances of slow-binding/slow-release inhibition. The same approach, in conjunction with X-ray crystallography, in silico modeling and mass spectrometry, helped to propose a model of inhibition of HDAC6 by a novel difluoromethyloxadiazole-based compound that was found to be a slow-binding substrate analog of HDAC6, giving rise to a tightly bound, long-lived inhibitory derivative.Histone deacetylases (HDACs) participate with histone acetyltransferases in the modulation of the biological activity of a broad array of proteins, besides histones. Histone deacetylase 6 is unique among HDAC as it contains two catalytic domains, an  Post-translational modifications (PTMs) play important regulatory roles in cells . Among tControlling the lysine acetylation state of cellular proteins, by modulating the activities of acetyltransferases and deacetylases, has been shown to be beneficial for treating a broad array of diseases besides cancer .+ as the coenzyme  is their toxicity associated with the most effective dose ,27. Due Most inhibitors directed towards zinc-dependent HDAC have a common tripartite scaffold: a zinc-binding group targeting the catalytically essential zinc ion at the bottom of the active site cavity, a spacer and a cap group ,29. The 50) in steady-state kinetic studies is typically determined. This is very often achieved by measuring the initial velocity of the reaction at a fixed time-point in the absence (vo) and presence (vi) of a series of inhibitors’ concentrations that are pre-incubated with the enzyme for a fixed time, prior to addition of the substrate to initiate the reaction. Such experimental design implies that the equilibrium between enzyme, inhibitor and substrate is rapidly established. Thus, the residual activity measured in the presence of a fixed (sub-saturating) substrate (S) concentration and varying inhibitor (I) concentrations will reflect the rapid partitioning among free enzyme (E) and its complexes with the inhibitor (EI) and other enzyme forms  for a simple reaction and a competitive inhibitor). Any deviation from a hyperbolic dependence of residual activity (vi/vo) upon inhibitor concentration, expressed by values of the “slope factor” (s) in Equation (1), will be typically interpreted as a sign of cooperative binding of the inhibitor to the enzyme and/or the formation of complexes between the enzyme and more than one inhibitor molecule.For the assessment of the potency of inhibitors in medicinal chemistry programs, the concentration of the inhibitor causing a 50% decrease in activity of the target enzyme  well below the nM range. In such studies, the concentration of the inhibitor needs to be of the same order of magnitude of the Ki value. Thus, the velocity of formation of the enzyme–inhibitor complex may be very low.Slow binding may be related to the low concentrations of inhibitors that one may need to use in the case of dissociation constants , assuming that the process is limited by diffusion (109 M−1 s−1), is 10−9 M × 109 M−1 s−1 = 1 s−1, corresponding to a half-time of 0.693 s. Since, in steady-state assays, the time taken to mix the enzyme with substrate and inhibitor is at least 10-30 s, the equilibrium between enzyme, substrate and inhibitor is established when observation of the reaction starts. However, if the inhibition constant is in the pM (10−12 M) or fM (10−15 M) range, and the inhibitor needs to be used in those concentration ranges for activity measurements, the observed first-order rate constant for complex formation will fall in the range of 10−3 s−1 and 10−6 s−1. By taking into account transit times, it would take 103 or 106 s to form the enzyme–inhibitor complex. Thus, one would initially observe the velocity of the uninhibited reaction and a time-dependent decrease in the rate until a steady-state velocity is reached.For example, for a KIn other instances, the formation of the initial enzyme–inhibitor complex may be actually slow, or a slow conformational change needs to take place after formation of the initial enzyme–inhibitor complex in order to obtain the tight inhibited complex. Slow release of the inhibitor from such a tight complex leads to a long residence time of the inhibitor in the enzyme active site, which is a property that contributes to an actual drug’s efficacy ,36,37,38o) remains constant. Under such conditions, one is able to determine the reaction velocity at the steady-state (vs), when the inhibitor is bound to the enzyme at equilibrium, and the apparent rate constant (kobs) for the onset of inhibition through the Morrison equation (Equation (2)). The latter quantifies product formation (P) during the time-course of the reaction, by taking into account how the reaction velocity changes over time (Equation (3)) ) ,40; see ; see o ron (3))  *.The dependence of kobs and inhibitor concentration may indicate a two-step reaction with a large dissociation constant of the initial enzyme–inhibitor complex. In any case, determining the IC50, the mechanism of inhibition and the actual Ki requires the use of the vs values obtained under various conditions.The nature of the conformational change may be difficult to identify. Furthermore, observing a linear relation between kLow inhibition constants may also depend on slow release of the inhibitor from the enzyme active site, leading to a long residence time. The latter is a desired property of drugs as it guarantees that the target enzyme will remain inhibited for a significant fraction of time in the complex cell environment ,36,37,38Slow release of the inhibitor from the enzyme active site can be detected by observing the time-course of product formation (or substrate consumption) when the substrate is added to the enzyme that has been pre-incubated with the inhibitor for a time long enough to establish equilibrium. In such a case, one observes a progressive increase in the reaction velocity, as the inhibitor is released from the active site, to reach a steady-state value (see ).off of the inhibitor from the enzyme–inhibitor complex.The process is also mathematically described by Equations (2) and (3). Under high substrate concentrations (and slow binding of the inhibitor), the observed rate constant that describes the transition from the initial (inhibited) reaction to the steady-state is the kThe same concepts apply also when one wishes to measure inhibitor binding or release by biophysical methods, in order to complement kinetic studies on the effect of the inhibitor on the enzyme activity  ,34. Also50, and to observe deviations from a simple hyperbolic binding curve, as exemplified in Failure to recognize slow onset of inhibition will lead to missing the inhibitory effect of certain compounds, or to overestimate the IC1 and Compound 2) characterized by a difluoromethyl-1,3,4-oxadiazole (DFMO) zinc-binding group. The former DFMO-bearing compound was recently studied in detail  were synthetized at Italfarmaco according to published procedures  was similar to the observed rate constant for the release of Compound 1 from the enzyme in jump-dilution assays [(9.6 ± 1.1) × 10−3 min−1]  . This oba et al. , has beea et al. . Compouna et al.  shares wa et al.  only theorted in  nicely cdrolysis .Histone deacetylases are of increasing interest as therapeutic targets in several diseases . Due to 1 also highlights the importance of combining enzyme kinetics with other approaches to actually make progress in the field of inhibitor development.Here, we showed that monitoring the time-dependence of the onset and relief of the inhibition by selected compounds is a valuable approach to clarify their mode of binding to the enzyme and to rule out complex behaviors such as, for example, cooperativity effects. Our findings stress once more the importance of taking into account the kinetics of processes as part of their characterization. The example of Compound 1 of [8 of [To our knowledge, among the several classes of HDAC inhibitors that have been co-crystallized with HDAC forms, only in the case of derivatives using the DFMO moiety as the zinc-binding group , an enz1, should an enzyme-modified species be the actual tight inhibitor, one would be tempted to conclude that the observed slow rate of onset of inhibition corresponds to the enzyme-catalyzed conversion of the initial compound to generate the actual inhibitor in the enzyme active site. However, a conformational change preceding chemical modification of the ligand may be the cause of the slow onset of inhibition as demonstrated for Compound 1 [As exemplified by the case of Compound mpound 1 .Slow binding to HDAC6 has been observed with TSA, ITF2357 (Givinostat) and ITF3756, for which there is no evidence of enzyme-catalyzed chemical modification. Thus, slow onset of inhibition through a conformational change seems to be a property of the enzyme. However, with the current knowledge, whether a compound may act as a slow-binding/slow-release inhibitor cannot be predicted as the slow onset and relief of inhibition does not simply correlate with, for example, the type of zinc-binding group. Gathering information on the kinetics of binding and release of inhibitors of different structures to/from HDAC of different classes may eventually lead to shed light on this aspect that can be exploited for selective and potent drug design. As mentioned above, to our knowledge, slow inhibitor binding has been reported only for Class I HDAC members ,47,48,491 is a slow-binding inhibitor of the enzyme, due to a slow conformational change that precedes its hydration to yield a tightly bound species, characterized by a long residence time, may open new avenues for both the characterization of the mechanism of action of these compounds, and, hopefully, the development of a novel class of mechanism-based HDAC inhibitors. Indeed, slow binding has been recently observed, but not discussed, for HDAC6 in the presence of T-518 (1 to yield the ring-opened hydrazide and the final hydrazide, although at a lower rate, and at higher inhibitor concentrations than those used for HDAC6 [Several compounds based on fluoroalkyl oxadiazole zinc-binding groups are being developed as HDAC inhibitors ,50,51,52or HDAC6 .


Regular use of Thai kratom has been linked to reduced blood triglyceride levels and body mass index (BMI) in healthy individuals. We analyzed Green Thai Kratom (GTK) and Red Thai Kratom (RTK) to investigate their effects on pancreatic digestive enzymes. The ethanol extracts of GTK and RTK inhibited lipase activity more strongly than alpha-glucosidase activity, suggesting the presence of lipase inhibitors. Mitragynine, the major compound in GTK, showed potent lipase inhibition and moderate alpha-glucosidase inhibition. Quercetin, found in both extracts, strongly inhibited alpha-glucosidase but had limited effects on lipase. These findings suggest that mitragynine and quercetin may hinder triglyceride and starch digestion. Combination inhibition studies revealed synergistic effects between mitragynine and quercetin on alpha-glucosidase activity. Additionally, both GTK and RTK extracts reduced fat accumulation in 3T3-L1 adipocyte cells, with quercetin specifically inhibiting Acetyl-CoA carboxylase 1 (ACC1), a key enzyme in fatty acid biosynthesis. Thus, GTK and RTK extracts, particularly mitragynine and quercetin, exhibit potential anti-obesity effects. We report the novel finding that Thai kratom inhibits de novo fatty acid synthesis by targeting ACC1, resulting in decreased fat accumulation in adipocytes. Regular use of Thai kratom in specific populations may improve blood triglyceride levels and reduce BMI by inhibiting lipase, alpha-glucosidase, and ACC1 activity. Further clinical trials are needed to determine optimal dosage, duration, toxicity levels, and potential side effects of Kratom use. As a result, excess glucose and fatty acid lead to an increase in both the size and number of adipocytes. Inhibition of digestive enzymes is therefore one of the most important routes for managing obesity. Decreasing energy-absorbing substances such as glucose and fatty acids from food has been seen to yield promising results for weight loss and decreased hypertriglyceridemia.Obesity and obesity-related diseases including cardiovascular disease, non-alcoholic fatty liver disease (NAFLD), and type 2 diabetes are the leading causes of death worldwide . Obesityde novo lipogenesis inhibitors reached the clinical approval process for the treatment of hyperlipidemia [Studies in pharmaceutical interventions for weight management have produced results. Orlistat (anti-obesity drugs) appears to suppress digestive lipases as well as lipolysis levels, resulting in reduced fat accumulation. To treat obesity and hyperglycemia in people with type 2 diabetes, acarbose, miglitol, and voglibose have been used to block starch digestive enzyme activity in the gastrointestinal tract and limit the pace of starch digestion in order to prevent hyperglycemia . These dipidemia . In a pripidemia . It woulde novo fatty acid synthesis [Mitragyna speciosa leaves have been noted to contain trace minerals and vitamins, including calcium, potassium, and magnesium. The presence of dietary fiber in Kratom can be inferred from its leafy nature [Mitragyna speciosa), individuals have lower body mass index (BMI), serum triglyceride level, and serum LDL-C level when compared to non-users [Ki were carried out.According to WHO recommendations, plant-derived medicines consumed as part of a normal diet play an important role in promoting healthy weight management . Plant-bynthesis . Kratom ynthesis . Moreovey nature . Accordion-users , suggestpNPG)  acarbose (positive control)  orlistat .Mitragynine  was kindly obtained from Assoc. Prof. Dr. Gorawit Yusakul, School of Pharmacy, Walailak University. Quercetin , and rutin  α-Glucosidase  p-nitrophenol-α-D-glucopyranoside (M. speciosa (Kratom) were collected from Developing a Kratom Plant Control Model by using community participation in Thailand: a case study of Nam Pu Sub-district, Ban Na San district, Surat Thani province, Thailand  . Leaves of RTK and GTK were identified by Dr. Prateep Panyadee, Plant Varieties Protection, Department of Agriculture, Thailand. Voucher specimens of RTK (P. Panyadee 316) and GTK (P. Panyadee 317) were deposited at Queen Sirikit Botanic Garden (QBG), Thailand, in February 2022.Fresh leaves of The major compounds in Kratom were determined using UHPLC model Ultimate 3000 with LC-MS/MS model Altis Plus  as the previous descriptive in . After sp-nitrophenol-α-D-glucopyranoside (pNPG) as a substrate. Alpha-glucosidase hydrolyzed pNPG with Km and Vmax values of 0.18 mM and 28.24 μmol/min/mg protein is in range with the previous report [pNPG at Km (0.18 mM). The rate of alpha-glucosidase-mediated pNPG was determined by measuring the p-nitrophenol product at 405 nm ) against time (10 min). The IC50 was determined by plotting the remaining activity of alpha-glucosidase at each inhibitor concentration and test inhibitor concentration. IC50 was calculated by fitting curves to non-linear regression (GraphPad Prism version 9.3.1), and acarbose was used as the positive control. Ki and mode of inhibition were further determined for pure compounds (mitragynine and quercetin). Briefly, 0.1 U α-Glucosidase enzyme were incubated with test inhibitors ; quercetin ; acarbose ) at 37°C. After 10 min, the reactions were started with the addition of pNPG at 0.007, 0.015, 0.03, 0.06, 0.125, 0.25, and 5 mM. The mode of inhibition and inhibition constant (Ki) were determined by Lineweaver-Burk plots.Inhibition of alpha-glucosidase was performed using s report . In the p-nitrophenyl palmitate (pNPP) as a substrate. Lipase hydrolyzed pNPP with Km and Vmax values of 1.3 mM and 2.3 μmol/min/mg protein is in range with the previous report [pNPP at Km (1.3 mM). The rate of lipase-mediated pNPP was determined by measuring the p-nitrophenol product at 405 nm ) against time (10 min). The IC50 was determined by plotting the remaining activity of lipase at each inhibitor concentration and test inhibitor concentration. IC50 was calculated by fitting curves to non-linear regression (GraphPad Prism version 9.3.1.), and orlistat was used as the positive control. Ki and mode of inhibition were further determined for pure compounds (mitragynine and quercetin). Briefly, 0.1 U lipase enzyme were incubated with test inhibitors mitragynine , quercetin , orlistat  at 37°C. After 10 min, the reactions were started by the addition of pNPP at 0.02, 0.03, 0.06, 0.125, 0.25, 3.5 and 5 mM. The mode of inhibition and inhibition constant (Ki) were determined by Lineweaver-Burk plots.Inhibition of lipase was performed using s report . In the An ACC1 inhibition assay was performed using the ACC1 Assay Kit from BPS Bioscience (USA) following the manufacturer’s protocol. Mitragynine and quercetin were tested at concentrations of 0, 1, 10, and 100 μM, and incubated with 3.75 μl of Acetyl-CoA, 11.25 μl of Sodium Bicarbonate, and 15 μl of ATP in a total reaction volume of 25 μl. After a 10-minute pre-incubation period, the reaction was initiated by adding 0.1 ng/mL of ACC1 enzyme. The reactions were allowed to proceed for 40 minutes before being terminated by the addition of 100 μl of chilled acetonitrile. The samples were then centrifuged, and the supernatants were carefully transferred to new tubes for analysis. The rate of reaction was quantified by monitoring the decrease in acetyl-CoA substrate concentration using a C18 HPLC column, employing a mobile phase consisting of a linear gradient of water and methanol.The differentiation of 3T3-L1 adipocyte cells was performed according to Ngamdokmai et al., 2022. Briefly, 3T3-L1 adipocyte cells were cultured in DMEM supplemented with 10% (v/v) FBS, 0.5 mM IBMX, 1 μM DEX, and 10 μg/mL insulin (INS) for 48 hours. The effect of GTK and RTK on lipid accumulation was performed by incubation of GTK and RTG crude ethanol extract (0–10 μg/mL) with 3T3-L1 adipocyte cells. After every 24 hours (for 3 days), the media was removed and replaced with DMEM supplemented with 10% (v/v) FBS, 0.5 mM IBMX, 1 μM DEX, and 10 μg/mL insulin (INS) containing 0, 4, 6, 8 and 10 μg/ml GTK and RTK crude ethanol extract. At the end of day 3 of differentiation, the 3T3-L1 cells were washed twice with PBS and incubated with paraformaldehyde in a final volume of 1 mL for 30 min. After paraformaldehyde was removed and cells were rinsed twice with PBS, the 3T3-L1 cells were stained with filtered Oil Red O solution for 1 h. 3T3-L1 cells were then washed twice with PBS and were photographed under an inverted microscope . The resulting red-stained lipid droplets were extracted with 100% isopropanol. The absorbance was measured at a wavelength of 520 nm to quantify lipid accumulation within the adipocytes.p < 0.05 were statically significant.All data were obtained from three dependent experiments and are expressed as the mean ± standard deviation (SD). Statistical analysis was performed using GraphPad Prism 9.3.1  with one-way ANOVA. Differences with Regular use of Thai Kratom has been reported to lower blood triglyceride and BMI among healthy people when compared to non-use . We hypo50 values of 22.58 ± 1.75 μM and 42.00 ± 4.24 μM, respectively  and 128.60 μM (7.3-fold lower than acarbose (IC50 = 938.40 μM), respectively . Relative to mitragynine and quercetin, rutin showed weak inhibition of both enzymes, with IC50 more than 100 μM . According to Lineweaver Burk plots, mitragynine induced competitive and mix-typed inhibition against lipase (Ki = 13.73 μM) and alpha-glucosidase (Ki = 30.33 μM), respectively. However, quercetin was competitive for inhibition of both lipase and alpha-glycosidase, with Ki values of 40.26 and 2.37 μM, respectively. Mitragynine was a weak inhibitor when compared to orlistat , whereas mitragynine was a strong inhibitor for alpha-glucosidase (Ki = 75 μM)  .pNPG. The increasing ratio of quercetin increased the inhibition of the alpha-glycosidase enzyme. Acarbose and quercetin, in the ratio of 250 and 4.5 μM, showed stronger inhibition when compared to acarbose and quercetin at IC50 alone. Moreover, the synergistic effect of mitragynine and quercetin indicated that intakes of GTK and RTK containing mitragynine and quercetin might decrease the rate of starch digestion and absorption  has been reported to be one of the drug targets for anti-obesity.et. al., 2022 [In a previous report by La-Up l., 2022 , Thai KrpNPP with IC50 and Ki values of 22 μM and 10 μM, respectively, in the competitive mode of inhibition. The IC50 of mitragynine was comparable to mahanimbine compound isolated from Murraya koenigii leaves. Mahanimbine inhibited lipase activity with an IC50 value of 17.9 μM (50 70 μg/ml (~230 μM), resulting in blockage of triglyceride ingestion and absorption in vivo. In the quercetin-treated group, plasma triglyceride was observed to be lower than in the control group [de novo lipogenesis, resulting in excessive expansion of white adipose tissue and obesity. The control of glucose uptake might prevent the generation of fatty acid from glucose (de novo lipogenesis).Mitragynine showed effective inhibition of lipase-mediated  17.9 μM . Both miol group . It migh50 value of 5.6 μM. This is consistent with a previous report by Lim et al., 2019 which indicated that the quercetin-containing hydroxyl group at 3C of C ring showed the strongest inhibition against alpha-glucosidase enzymes when compared to lutein and eriodictyol [50 value of 128.6 μM. In the previous study O-methyl mahanine and mahanine  both displayed inhibitory activity against alpha-glucosidase, with IC50 values of 46.1 μM and 21.4 μM respectively, indicating that the hydroxy group but not O-methyl group on moiety of indole led to a decrease in IC50 : quercetin (4.5 μM)). This result is similar to that previously reported by Koh, 2022 that the combination of acarbose and quercetin produced synergistic inhibition which was stronger inhibition than either alone [According to the Lineweaver–Burk plot , Ki of mer alone . Moreovein vitro adipocyte cell model) were incubated with GTK and RTK crude ethanol extract (0–10 μg/ml). After 72 hours, fat accumulation was determined using Oil Red O staining. Herein we thus reported for the first time that GTK and RTK decreased fat accumulation in 3T3-L1 adipocytes. Our study demonstrated that quercetin effectively inhibited ACC1, which plays a crucial role as the rate-limiting enzyme in fatty acid biosynthesis  and alpha-glycosidase , respectively, resulting in a decrease of fatty acid and glucose absorption and protecting against fat accumulation. We report for the first time that Thai Kratom reduced de novo fatty acid synthesis through ACC1 inhibition, leading to a decrease in fat accumulation in 3T3-L1 adipocytes. Taken together, the regular use of Thai Kratom among certain Thai populations might lead to improved levels of blood triglyceride and lower BMI through inhibition of lipase, alpha-glucosidase, and ACC1 activity. Clinal trials are needed to determine effective dose, duration of action, lower toxic concentration, and side effects of Kratom use.GTK and RTK contain mitragynine and quercetin as their major phytochemical compounds. GTK contains levels of mitragynine higher than RTK, with values of 63 and 36 mg/g respectively, whereas quercetin levels were nearly the same in both GTK and RTK. Mitragynine and quercetin selectively inhibit lipase Click here for additional data file.S2 Fig(TIF)Click here for additional data file.S3 Fig(TIF)Click here for additional data file.


With the popularization of robot-assisted spinal surgeries, it is still uncertain whether robots with different designs could lead to different results in the accuracy of pedicle screw placement. This study aimed to compare the pedicle screw inserting accuracies among the spinal surgeries assisted by various types of robot and estimate the rank probability of each robot-assisted operative technique involved.The electronic literature database of PubMed, Web of Science, EMBASE, CNKI, WANFANG and the Cochrane Library was searched in November 2021. The primary outcome was the Gertzbein–Robbins classification of pedicle screws inserted with various operative techniques. After the data extraction and direct meta-analysis process, a network model was established in the Bayesian framework and further analyses were carried out.Among all the 15 eligible RCTs, 4 types of robot device, namely Orthbot, Renaissance, SpineAssist and TiRobot, were included in this study. In the network meta-analysis, the Orthbot group , the Renaissance group , the SpineAssist group  and the conventional surgery group  were inferior to the TiRobot group in the proportion of grade A pedicle screws. Moreover, the results of rank probabilities revealed that in terms of accuracy, the highest-ranked robot was TiRobot, followed by Renaissance and Orthbot.In general, current RCT evidence indicates that TiRobot has an advantage in the accuracy of the pedicle screw placement, while there is no significant difference among the Orthbot-assisted technique, the Renaissance-assisted technique, the conventional freehand technique, and the SpineAssist-assisted technique in accuracy.The online version contains supplementary material available at 10.1186/s13018-023-03714-8. The precise insertion of pedicle screws plays a central role in pedicle screw fixation, which provides three-column stabilization and is widely used in spine surgery. There were considerable variabilities in the anatomy of vertebral landmarks and the structure of pedicles due to specific physical or pathological variations. Even if pedicle screw insertion is the most foundational operation for spine surgeons, it is still hard to insert all pedicle screws precisely by the conventional freehand method . DeviatiWith the advance of computer-assisted navigation technology and spinal robot technology, traditional pedicle screw placement has been partially replaced. Both navigation technology and robotic technology guide screw placement according to the three-dimensional mapping of the vertebrae; the major difference being surgeon-guided vs. robot-guided execution of the screw trajectory , 4. TherIn the comparison of robot-assisted surgery and conventional spinal surgery, the accuracy of pedicle screw insertion seems controversial. Even though most previous studies support the conclusion that the use of spinal robots can increase accuracy in pedicle screw insertion , 6, therThe Bayesian network meta-analysis (NMA) approach allows for comparing methods that have never been compared directly through the common comparator. Therefore, the purpose of this NMA was to indirectly compare the pedicle screw inserting accuracies among the spinal surgeries assisted by various types of robot by evaluating data from published prospective randomized controlled trials. Furthermore, the rank probability of each particular spinal robot was estimated based on the Bayesian approach.This Bayesian network meta-analysis was reported according to the PRISMA for Network Meta-Analyses (PRISMA-NMA) statement . MoreoveUp to November 2021, a comprehensive search was performed through PubMed, Web of Science, EMBASE, CNKI, WANFANG, and the Cochrane Library using a combination of the terms “robot-assisted,” “robotic,” “robot-aided,” “spine,” ”spinal” and “pedicle screw.” Two independent authors carried out the searching process without language limitation and screened records by title and abstracts. Then, probably eligible reports were examined with the same eligibility criteria. Discrepancies were discussed in the group meeting all members reached an agreement.Inclusion criteria were as follows: (a) prospective randomized controlled trials; (b) clinical trials performed on human beings; (c) adult patients (older than 18 years old); (d) patients with degenerative or traumatic spinal diseases; (e) patients undergoing lumbar, thoracolumbar or lumbosacral spine surgery with pedicle screw implantation; (f) comparison of the robot-assisted operative method and conventional operative method or two robot-assisted operative methods; (g) Accuracy of pedicle screw placement was evaluated by Gertzbein–Robbins Scale. Exclusion criteria were as follows: (a) cadaveric studies; (b) patients with spinal scoliosis; and (c) conference articles, editorials, or letters.For each eligible report, two independent authors evaluated the quality according to the Cochrane risk of bias assessment scale, and the data were then extracted independently. The extracted items were as follows: (a) authors; (b) year of publication; (c) country; (d) study design; (e) disease; (f) the type of surgery; (g) robot devices; (h) the age of patients; (i) the gender of patients; (j) the number of patients; (k) instrumented vertebral body; (l) the number of pedicle screws; (m) pedicle screws classified by Gertzbein–Robbins Scale, etc. During the assessing and extracting process, the whole team checked and discussed all discrepancies.P < 0.05 was set as the level of significance. The Risk ratio (RR) and corresponding 95% confidence interval (CI) were used to compare dichotomous variables. The random-effects model was used regardless of the heterogeneity. Moreover, the statistical heterogeneity was assessed with the forest plot and inconsistency statistic (I-squared). The funnel plot was used to evaluate reports for publication bias. As for the Bayesian network analysis, a network consistency model was built with Markov chain Monte Carlo methods [P < 0.05 and 95% CIs beyond the null value were adopted to assess the significance.The meta-analysis and Network meta-analysis were conducted using STATA statistical software and ADDIS software.  methods . The tra methods . The RR A total of 2372 candidate records were identified through database searching. After removing duplicates, 2138 records were screened by title and abstract. Of the 153 potential studies further assessed with the full text, 138 were excluded according to the inclusion and exclusion criteria details. The final number of eligible studies involved was fifteen . In terms of the comparison to the conventional group in the proportion of grade A pedicle screws, the TiRobot subgroup  was detected with a significant difference, while the subgroups of Orthbot , Renaissance  and SpineAssist  were not significant . Further subgroup analysis by the type of robot device was carried out due to the existence of heterogeneity . According to the proportion of pedicle screws without breach of the cortical layer of the vertebral body or pedicle (Gertzbein–Robbins grade A), Fig. On the basis of the network model, the rank probability of each operative method was estimated Fig. A. Each cIn the wake of developments in science and technology, the dream of robotic spinal surgery has come into reality. Even though most current spinal robot products were mainly designed for navigation and positioning during operation, these revolutionary robot devices can provide tremendous assistance in spinal surgery. Although designed by different companies and endowed with particular characteristics, these spinal robots have some similarities in both structure and function. And the vast majority of these robots, including SpineAssist , Renaissance , Excelsius GPS , TiRobot , Orthbot , and Mazor X Stealth Edition , are shared-control robots which allow both the robot and operator to control motions simultaneously , 26.SpineAssist, the first shared-control robot approved by the FDA for use in spine surgery, mounts onto vertebral landmarks directly and aligns its arm along the designed trajectory. The location of the entry point and the direction for the guide wire are thus determined . SpineAsIn accordance with previous reports , 6, 35, Through the common comparator, the NMA approach could compare various operative techniques indirectly without direct evidence. In order to compare the accuracies of different types of spinal robot, the Bayesian framework network was established so that the indirect connection of robot-assisted techniques could be linked through the common comparator technique, and indirect evidence could be further incorporated. The NMA has been recognized as a credible approach to comparing various treatments or techniques for its high consistency with reality . The TiRThe four types of spinal robot involved in this study, namely SpineAssist (entering the market in 2004), Renaissance (entering the market in 2011), TiRobot (entering the market in 2016) and Orthbot (entering the market in 2019), represent the inheritance and development history of robot-assisted spinal surgery to some extent. Compared with SpineAssist, the second-generation counterpart Renaissance has some improvements in both software and hardware. But it is reported that these two robots face a similar problem of screw misplacement secondary to skiving , 38, whiIn this study, there were quite large differences in the number of studies and sample sizes between groups. The design of the Bayesian method represents dependencies between multiple variables as conditional probability distributions . AccordiThere are several limitations of this Bayesian network meta-analysis. Firstly, even if we have tried to select studies with relative homogeneity and high quality of evidence by setting strict criteria, some heterogeneities exist among the studies involved. Though clinical heterogeneity is inevitable, it makes little impact on the final conclusion. Secondly, accuracy is undoubtedly the most concerning outcome for robot-assisted spinal surgery, while other indexes such as radiation exposure, operative time, bleeding amount, and complication rate are also important. But currently available evidence cannot support comprehensive network meta-analyses for outcomes except for the accuracy of screw placement.Current RCT evidence indicates that TiRobot has an advantage in the accuracy of the pedicle screw placement, while there is no significant difference among the Orthbot-assisted technique, the Renaissance-assisted technique, the conventional freehand technique, and the SpineAssist-assisted technique in accuracy. With the popularization of robot-assisted spinal surgeries and the emergence of new spinal robots, more well-designed randomized controlled trials and further studies are required in future.Additional file 1. Further analyses related to the heterogeneity of the TiRobot group.


The phase transition between water and ice is ubiquitous and one of the most important phenomena in nature. Here, we performed time-resolved x-ray scattering experiments capturing the melting and recrystallization dynamics of ice. The ultrafast heating of ice I is induced by an IR laser pulse and probed with an intense x-ray pulse which provided us with direct structural information on different length scales. From the wide-angle x-ray scattering (WAXS) patterns, the molten fraction, as well as the corresponding temperature at each delay, were determined. The small-angle x-ray scattering (SAXS) patterns, together with the information extracted from the WAXS analysis, provided the time-dependent change of the size and the number of liquid domains. The results show partial melting (~13%) and superheating of ice occurring at around 20 ns. After 100 ns, the average size of the liquid domains grows from about 2.5 nm to 4.5 nm by the coalescence of approximately six adjacent domains. Subsequently, we capture the recrystallization of the liquid domains, which occurs on microsecond timescales due to the cooling by heat dissipation and results to a decrease of the average liquid domain size. The phase transition between water and ice is a ubiquitous phenomenon in nature. Here, the authors conduct a time-resolved x-ray scattering experiment using X-ray Free Electron Lasers to elucidate a comprehensive picture of the melting and recrystallization dynamics of crystalline ice, based on direct structural information. Thus, it is crucial to understand the fundamental mechanisms of the phase transition between ice and water. The melting of ice has been investigated intensively by using time-resolved optical spectroscopies16 and computer simulations23. However, the detailed mechanisms of the melting and recrystallization of ice in terms of the structural dynamics are not fully elucidated due to the lack of direct length scale sensitivity of the spectroscopic methods, and the limited size of the system in computer simulations.The melting of ice and the crystallization of liquid water are amongst the most common and important phenomena in nature and everyday life12. More recently, using a similar approach with a wider time window, it was observed that the superheating and homogeneous melting of ice are temporally overlapped and only a partial melting of ice occurs within the first 25 ns, even when excess energy is provided15. Even though these spectroscopic studies have provided insight on the dynamics of melting and superheating of ice, more direct structural information, such as the number and size of the molten domains and how they change over time, is necessary to fully understand the mechanism of the phase transition between ice and liquid water. Moreover, previous studies have not elucidated the recrystallization process . An experiment utilizing time-resolved Mie scattering spectroscopy, with a millisecond (ms) time window, probed the time-dependent size of the molten domain and suggested a model for the melting and recrystallization dynamics. However, the direct estimation of the size was only possible at very late delays (after 0.3 ms)16.In a study using time-resolved IR spectroscopy, a rapid temperature increase (T-jump), induced by an intense IR pump pulse, was previously utilized to investigate the homogeneous melting of bulk ice. In this study, experimental evidence of the superheating of ice on sub-ps to hundreds of ps timescales was observed27. By combining a rapid T-jump, induced by an IR laser pulse, with an intense x-ray pulse from free-electron lasers (FELs) as a probe (x-ray scattering), the detailed structural dynamics of the melting and recrystallization of ice can be elucidated. Furthermore, in x-ray scattering experiments, structural information with different length scales can be obtained depending on the observed scattering angle. While the wide-angle x-ray scattering (WAXS) is sensitive to the molecular structure and the local structure between adjacent molecules, small-angle x-ray scattering (SAXS) is sensitive to the size and shape of much larger domains. By combining the results extracted from SAXS and WAXS after the T-jump, a more comprehensive picture on the melting and recrystallization dynamics of ice with direct structural information can be elucidated.An x-ray probe can be the optimal tool for providing structural informationIn this work, we investigate the melting and recrystallization dynamics of ice by conducting the time-resolved x-ray scattering experiments with rapid T-jump. Through the analysis of the WAXS patterns, the molten fraction and the corresponding temperature at each delay are determined. The SAXS patterns, together with the information extracted from the WAXS analysis, provide the time-dependent change of the size and the number of the liquid domains.29. The experimental setup is shown schematically in Fig. 26 and in the Method section. Briefly, an ice I sample with a thickness of ~84 μm was prepared on a Cu-grid and loaded on custom-made sample holder connected to a cryostat. The sample was then placed inside a vacuum chamber with a pressure of less than 0.1 Pa. Femtosecond IR laser pulses at 2 μm wavelength with a pulse energy of 250 μJ/pulse were focused to a spot size of 70 μm (FWHM) and were used to induce the ultrafast T-jump of the ice sample. Femtosecond x-ray pulses generated by PAL-XFEL were used to measure scattering patterns of the sample before and after the T-jump. The momentum transfer q-range of 0.1–3.0 Å−1 was covered by a large area CCD detector . To probe a fresh spot for each measurement, the sample holder was moved to an unexposed position prior to each pump-probe measurement. We note that our ice sample is mounted without using any windows and thus is directly exposed to the pump and probe pulses. Our setup provides the following advantages: (1) There is no background scattering from any window materials, (2) there is no extra cooling process that can be induced by the heat conduction between the sample and the windows, and (3) the total volume of the sample is not constrained, and it allows the sample to change in volume.We measured the time-resolved wide and small angle x-ray scattering pattern of ice I at various time delays before and after the T-jump to follow melting and recrystallization dynamics of ice at the XSS beamline of PAL-XFEL30), clearly indicating that the ultrafast T-jump causes the melting of ice I. We note that for clarity, the q range that is affected by the Bragg peak of ice I is omitted in the difference pattern.The experimental results of the IR laser-induced melting of ice I are summarized in Fig. The difference scattering intensities in the SAXS and WAXS regions at various time delays from −8.4 ns to 10 μs are shown in Fig. 30, we can directly estimate the total thickness of the liquid water in the probed volume at each delay. We performed the fitting analysis by using the liquid water scattering patterns at various temperatures and adjusting the scaling factor. The temperature that gives the best match was chosen as the temperature of the molten domain at each time delay. By using this scaling factor, we converted the integrated WAXS intensity of the experimental data into the thickness of the liquid water. The time-dependent change of the thickness of the molten fraction is shown in Fig. Given that WAXS is only sensitive to the local structures at short distances, the difference intensity of the diffuse scattering at the WAXS region is directly proportional to the total amount of liquid water in the probed volume at a specific time delay. Thus, by comparing the integrated intensity of the diffuse scattering in the WAXS region with that measured from a sample with a known thickness at various temperatures, ranging from 254 to 366 K15. In that study, the time-dependent change of ν2 + L2 absorption bands of liquid water reached its maximum at around 25 ns, and a melting time constant of 4.1 ns was reported. However, the timescale of recrystallization (~1 μs) in our present study is faster than those previously reported using time-resolved Mie scattering spectroscopy (within a few ms)16. Since the crystallization is limited by the timescale of the heat dissipation to the surrounding in this case, we consider the discrepancy to originate in the current study from using a much lower base temperature (170 K vs. 270 K).The timescale of the melting process is consistent with a previous study using time-resolved IR spectroscopy15. We determined the molten fraction of the sample within the probed volume to be of about 13% , which is lower than that reported of a previous study using time-resolved IR spectroscopy (32.4%)15. Once more, we consider this discrepancy to be caused by our lower base temperature (170 K vs. 270 K). This is also consistent with the results from our measurement at the base temperature of 117 K (see Supplementary Information for details). For example, only about 8% of the molten fraction was found at this condition.We clearly observe partial melting, which is qualitatively consistent with the results reported as superheating in the previous spectroscopic studies31 and is qualitatively in good agreement with the value estimated from the experiment as shown in Fig. It is well known that the shape of the scattering pattern of liquid water at WAXS region varies depending on the temperature. Thus, as explained above, by comparing the shape of the diffuse scattering generated by the ultrafast melting with that of liquid water measured at various temperatures, the temperature of the molten fraction can be estimated. The comparisons are shown in Fig. r3), the SAXS intensity within our q range decreases with increasing the size of the molten domain as shown in Fig. As shown in Fig. c is a scaling factor between the theory and the experiment, Np is the number of molten domains, Δρelectron is the difference in the number density of the electrons between the liquid and ice phases of water, r is the radius of the liquid domain, and q is the momentum transfer. To minimize the risk of overfitting, we used only one free parameter  which was adjusted during the fitting analysis, while the other parameters are fixed to values estimated from the WAXS analysis. The number of the molten domain, Np is dependent on the radius (r) and calculated by the following equation.By analyzing the SAXS patterns, taking into account the total amount of liquid water as estimated from the WAXS data, the size and the number of liquid domains at each delay can be determined. If we assume molten domains as homogeneously distributed spherical particles in the ice medium, we can fit the experimental SAXS patterns at each time delay with the theoretical SAXS pattern calculated by using the form factor of a sphere (See Method section for details):Vwater is the total volume of liquid water within the probed volume generated by the ultrafast melting of ice which was estimated from the WAXS analysis .sis Fig. . Vp is tr) and the calculated number (Np) of the molten domains as a function of time delays are summarized in Fig. ca. 4.5 nm and the number of domains decreases by a factor of 6. The previous is consistent with our proposed coalescence scenario, inferred from the integrated SAXS intensity and the difference in decay times between SAXS and WAXS.The theoretical SAXS patterns obtained from the fitting analysis are shown together with the experimental data in Fig. After about 1 μs, the radius decreases again to less than 2 nm, while the number of domains stays the same, corresponding to the recrystallization of the molten fraction. We note that the timescale of the recrystallization is consistent with the cooling process estimated from the WAXS analysis, as shown in Fig. 16, but it is consistent with the recrystallization rate increasing at lower base temperatures.In Fig. In summary, we have performed a time-resolved x-ray scattering experiment on the effects of IR-irradiation-induced ultrafast heating of crystalline ice and have elucidated the melting and recrystallization dynamics of crystalline ice with direct structural information. Our study demonstrates that by combining the structural sensitivity of x-ray scattering experiments on different length scales with ultrafast temporal resolution, a comprehensive picture on the complicated processes such as ultrafast melting and recrystallization of ice can be elucidated. Finally, we note that by utilizing the experimental and analysis protocol established here, future experiments focusing on the femtosecond time regime and/or using the various pump fluences can reveal important structural details in the ice phase of the initial melting process, such as the mechanism of the formation of superheated water or the energy dissipation through the ice lattice.Ice I samples were prepared in a 0.1-mm-thick Cu-grid that has a total diameter of 10 mm and contains holes of 0.8 mm or 1.5 mm in diameter. The Cu-grid was first filled with ultra-pure deionized water and then dipped into liquid nitrogen to form ice I.29. Ice I samples on a Cu-grid were loaded on a custom-made sample holder connected to a cryostat . The temperature of the cryostat was controlled by a silicon diode and a cryogenic temperature controller . The sample was placed inside a vacuum chamber with a pressure of less than 0.1 Pa and cooled with liquid nitrogen. The base temperature of the sample during the measurement was maintained at 170 K. Femtosecond optical laser pulses at 2 μm wavelength with an energy of 250 μJ/pulse were generated from an optical parametric amplifier, which was pumped by pulses at 800 nm center wavelength of a Ti:sapphire regenerative amplifier. The laser beam was focused to a spot of 70 μm (FWHM) diameter. Femtosecond x-ray pulses were generated from the x-ray free-electron laser (XFEL) at PAL-XFEL by self-amplified spontaneous emission (SASE). The x-ray beam has a mean energy of 9.7 keV and an energy bandwidth of 0.3% (ΔE/E) and was focused to a spot of 19 μm × 32 μm. An optical laser pulse was spatially overlapped with an x-ray pulse with an angle of 20°. The q range of 0.1–3.2 Å−1 was covered by a large area CCD detector  at a distance of 250 mm. An ultrafast temperature jump (T-jump) within the sample was induced by an optical laser pulse (pump) and the time-dependent change of the sample was probed by an x-ray pulse (probe). To probe a fresh sample for each measurement, the sample holder was moved to a fresh position prior to each pump-probe measurement. Laser-off images (probe-only) prior to the pump-probe measurement were acquired as references for each position and used for obtaining the difference x-ray scattering pattern at each time delay. The scattering images were acquired at the following time delays: −8.4 ns, 8.4 ns, 16.8 ns, 33.6 ns, 42 ns, 50.4 ns, 58.8 ns, 84 ns, 100 ns, 150 ns, 200 ns, 300 ns, 1 μs, 3 μs, and 10 μs.An x-ray scattering experiment with a pump-probe scheme was performed at XSS-FXS beamline of PAL-XFELq range from 0.10 Å−1 to 0.30 Å−1 was used for the SAXS region and from 1.00 Å−1 to 2.73 Å−1 was used for the WAXS region. The q range where the Bragg peaks of ice I appear was excluded. The integrated intensities are shown in Fig. As a measure of time-dependent changes of the difference scattering pattern associated with the melting and recrystallization dynamics of ice, the integrated intensities at SAXS and WAXS regions were used. The 30. We performed the fitting anlysis by adjusting the scaling factor, and the temperature that gives the best match was chosen as the temperature of the molten domain at each time delay. The comparisons at all time delays are shown in Supplementary Fig. 30. By using this scaling factor, we converted the integrated WAXS intensity of our experimental data into the thickness of the liquid water. The time-dependent change of the estimated thicknesses of the molten domain is shown in Fig. We estimated the temperature of the molten domain by comparing the shape of the diffuse scattering at WAXS region with that of liquid water measured at various temperatures, ranging from 254 K to 366 Kr32.By analyzing the difference SAXS intensities, the size and the number of the liquid water domains at each time delay were determined. Equation  describec is a scaling factor between the theory and the experiment, Np is the number of the molten domain, Δρelectron is the difference in the number density of the electron between the liquid and ice phases of water, r is the radius of the liquid domain, and q is the momentum transfer. The free fitting parameter that was adjusted during the fitting analysis is the radius of the liquid domain, r. The electron densities of liquid water and ice are calculated from the mass densities of liquid water and ice, and they are 0.98 and 0.93 g/cm3, respectively. Since the mass density varies slightly depending on the temperature, the average value was used. A scaling factor between the theory and the experiment, c, was determined from the WAXS analysis by comparing our experimental diffuse scattering with the normalized scattering pattern of liquid water30 (See Temperature and thickness estimation of the molten domain section for details). The number of the molten domains, Np, was calculated by Eq.  for calculating the theoretical SAXS patterns instead of using a single value of r.σr is the variance and rmean is the mean value of the radius. For the representative fitting results, the ratio between the variance and the mean value of the radius, (σr/rmean), was set to be 0.2. We note that the distribution of radius effectively reduce the oscillatory features in the theoretical SAXS pattern by averaging trigonometric functions with different period and the choice of the degree of the distribution does not affect our conclusion. The theoretical SAXS patterns obtained from the fitting analysis are shown together with the experimental data in Supplementary Fig. r) and the calculated number (Np) of the molten domains as a function of time delays are shown in Fig. In a more realistic picture, the molten domains with slightly different sizes can exist at the same time with a certain distribution. In order to take this into account, we used a normal distribution of the radius entclass1pt{minima−6 m2/s at 170 K to 1.17 × 10−6 m2/s at 273 K31. The time-depenent changes of the temperature near the center (red) and the edge (green) of the irradiated area were calculated and are shown in Supplementary Fig. After the ultrafast T-jump, the cooling process occurs due the the heat dissipation. The timescale of the cooling process is estimated by using the thermal diffusivity. The initial temperature of the irradiated area right after the ultrafast T-jump was estimated to be ~350 K based on the WAXS analysis as shown in Fig. Supplementary Information


Numerical modelling combined with laboratory measurements demonstrates that internal deformation within a cave ice body cannot fracture stalagmites, even on a steep slope. Instead, temperature changes lead to thermoelastic stresses within an ice body that reach values equaling to and exceeding the tensile strength of even large stalagmites. Differences in thermal expansion coefficients cause a sharp vertical jump in stress between the stalagmite and the surrounding ice body, and the ice lifts the stalagmite as it expands with increasing temperature. This study refutes the previously accepted model that flow of ice breaks stalagmites, and suggests a link between glacial climate variability and corresponding cooling and warming cycles in the subsurface that weaken and eventually fracture stalagmites due to the opposing thermoelastic properties of calcite and ice.Damage to speleothems is a common phenomenon in mid-latitude caves, and multiple causes have been proposed. Here we report on one of such type of damage, namely stalagmites that are broken and partially sheared near their base but are still in upright position. Such stalagmites occur in the Obir Caves (Austria) associated with cryogenic cave carbonates, demonstrating the former presence of cave ice.  Radiometric techniques, particularly 230Th dating2, allow speleothems to be used as accurate chronometers for the past of approximately 600 ka .Speleothems are secondary mineral deposits in caves, usually composed of calcium carbonate. They come in a variety of shapes and dimensions, with stalactites (growing from the ceiling), stalagmites (growing upward from the floor), and flowstones (sheet-like formations) being the most common types. In addition to their aesthetic aspect (e.g. in show caves), speleothems are also of high scientific value as archives of past environmental and climate changes8. Dating the youngest calcite of a seismically fractured speleothem provides a maximum age constraint for the seismic event. Combining this with a date for calcite healing these fractures and/or growing on top of such a fallen formation offers a way to bracket the age of the suggested earthquake in the past9.In addition to paleoclimate research, speleothems from caves in seismically active regions have also been used as recorders of strong earthquakes in the past. In several studies, intensities and ground accelerations of paleoseismic events were derived from damaged stalagmites, partly calibrated by measurements of petrophysical properties of speleothems11.Damage of speleothems, however, can have other causes as well, such as severe cave flooding, mechanical instabilities  or destruction by humans16. These observations were primarily made in mid-European and some British caves where other processes such as strong earthquakes were regarded as unlikely given their stable tectonic setting. In several of these caves, there is independent evidence for the presence of ice deposits provided by the close association of damaged speleothems and accumulations of coarse grained cryogenic cave carbonates (CCC17). The stable isotopic composition of these CCC indicates crystallization in very slowly freezing pools of water in cave ice18.A final process that can cause damage to speleothems is deformation by ice that has accumulated in caves during cold climate periods. Although not previously reported from modern ice-bearing caves, there are a number of observations in studies from currently ice-free caves that strongly suggest that ice damage to speleothems is a widespread phenomenon in mid-latitude caves. These include (a) stalagmites sheared from the base, some still upright, some titled or overturned, or lying on the floor, (b) stalactites broken at some level across a cave chamber, (c) precariously placed fragments of speleothems or bedrock attached (cemented) to steep cave walls, (d) cracked conical stalagmites, (e) fractured flowstones, and (f) shattered stalagmites21, systematic studies investigating the deformation of speleothems by ice are lacking. Furthermore, to our knowledge, no attempt has been made to numerically model this type of mechanical deformation, with the exception of a short report suggesting that thermal expansion of ice due to warming could exert sufficient mechanical force to shear stalagmites from their base14.While these empirical observations are important and generally consistent with independent paleoclimatic interpretations suggesting wide-spread permafrost in regions such as Central Europe during very cold climate epochs of the last glacial periodThe aim of this study was to combine field observations from a cave showing damaged speleothems with numerical simulations calibrated with rock-mechanical parameters obtained from speleothems of the same cave to investigate the process of speleothem deformation by ice. We selected a cave system where deformed speleothems are spatially associated with CCCs formed during the Last Glacial Maximum, and focused on stalagmites because of their well-defined geometry.22. Because of their hypogene origin, these caves had no natural entrances and where only discovered during ore mining in the nineteenth century. Modern air temperature in the Obir Caves is close to 6 °C, which corresponds to the mean annual air temperature outside at the elevation of the caves (approximately 1000–1100 m a.s.l.).The Obir Caves comprise a set of caves in the Northern Karawank Mountains of southern Austria, near the border with Slovenia .Many parts of Obir Caves are decorated with stalactites, flowstones and stalagmites and parts of these caves are a show cave. 24. Thus, during this interval, which corresponds to the first part of the Last Glacial Maximum, perennial ice deposits occupied parts of these caves that where close to the 0 °C isotherm and allowed precipitation of CCC. In this study, we focus on the Banane system of Obir Caves, a fairly pristine part of these caves where CCC are spatially associated with deformed stalagmites. The caves of the Banane system are between about 49 and 67 m below the surface.In parts of these labyrinthic caves, CCC are present that formed between 26.6 and 23.5 ka BP8, providing a unique opportunity of compare these deformation features with those associated with the past presence of ice.Other parts of Obir Caves have recently been studied in the context of paleoseismicity because the cave is located near the Periadriatic Lineament, a major seismically active strike-slip fault. These studies provided evidence for speleothem fracturing associated with movement along faultsStalagmites are found in several places in the Banane system and are mostly slightly conical in shape and less than half a meter high. Slim equal-diameter (candle-stick type) stalagmites with height/width ratios > 10 are not present in Banane system and are also rare in other parts of the Obir Caves. The pre-Holocene speleothem generations in the Obir Caves are relatively easy to distinguish from the Holocene ones by their color (yellowish vs. white). Deformation features were observed only in Pleistocene stalagmites, i.e. yellowish stalagmites, that are inactive and locally overgrown by young whitish calcite . Few examples of oblique fractures were found, probably due to the angle of the inclined substrate. One stalagmite shows two fractures at different heights Fig. B. RoughlBesides fractured stalagmites, we also observed stalagmites and fragments of them scattered on the ground. Broken stalactites are even more common in some parts of the Banana system, while fractured flowstones have been observed in only a few places. These damaged speleothems have not been studied in detail, as their origin can be less reliably associated with the past presence of ice. In a few places, fragments of speleothems attached (cemented) precariously to fractured stalagmites are also present Fig. A.Three stalagmites showing post-fracture calcite were sampled using small-diameter drilling; results are shown in Fig. 26. The same type of calcite was also observed in the small-diameter drill cores obtained from damaged stalagmites in Banane cave.The broken stalagmites collected for laboratory testing are composed of dense calcite with a compact, columnar fabric. This is consistent with stalagmite samples obtained from other parts of the Obir Caves that show the same type of calcite crystal fabric regardless of ageThe tensile and compressive strengths exhibit high standard deviations of 35% and 54%, respectively, indicating a large variability in the strength properties of the measured stalagmite samples. The differences are most likely due to inhomogeneities of the stalagmites reflecting the uneven growth structure and/or the possible presence of microcracks as these specimens were detached from their substrate (unknown fracture process). Varying densities and associated porosities, as shown by the measured density variation of the samples, significantly affect strength performance, especially when small sample geometries are examined.The Young’s modulus in tension is about 9% lower than in compression Table . The staThe mean value of the tensile strength of the investigated stalagmite material is 4.3  ±  1.5 MPa. This value compares well with literature values for speleothems and limestone Fig. .Figure 2Although the results of the stalagmite parts studied show considerable variation in mechanical properties, it can be assumed that the entire stalagmites have mechanical properties that correspond to the mean values determined by these measurements.hice and slope angle βice were varied, while the stalagmite diameter ds was fixed at 0.4 m, as were the overall X and Y dimensions (− 7 ≤ X ≤ 14 m and − 3.5 ≤ Y ≤ 3.5 m). No-slip boundary conditions we applied to the side walls of the domain  and to the stalagmite. At the lower boundary, we allowed free sliding along the bed to simulate the end-member case of a fully lubricated bed, which will result in the highest stresses at the stalagmite. At the upper boundary, we defined a stress-free surface boundary to allow free movement of the ice surface.First, we explored the potential of ice flow to shear off stalagmites. To do this, we created a rectangular geometry with the coordinate system centered on the stalagmite Fig. . Ice thiw = σ∙n) around the stalagmite  to estimate the effect of flowing ice on the structural integrity of the stalagmite. As shown in Table We investigated the wall shear stress (τT–T0), its linear contribution to the overall stress regime is obvious. Therefore, we simulated only T–T0 = 1 K, since the computed results can be easily multiplied by any T–T0 value to obtain the effect of a given temperature increase or decrease on the stress regime.To compare the thermoelastic stresses with the wall shear stresses caused by ice deformation, we performed a series of numerical experiments that solve Eq.  for diffds =  m) and the ice thickness  for stalagmite location and side wall configurations as described in Table We varied the stalagmite diameter  for szz), as shown in Fig. The highest stresses at the stalagmite base occur in the principal stress components, especially in the z-direction  and younger than 44 ka . The determined age range of 12.5 < X < 44 ka is also consistent with data from CCC collected in the same parts of the cave, demonstrating the presence of cave ice from at least 26.6  ±  0.2 to 23.5  ±  0.1 ka BP24. The spatial association of broken speleothems and CCC, as well as their age distribution, suggest damage during the Last Glacial Maximum.The observations made in the Banane system show that in-situ stalagmites were subjected to stresses that exceeded their strength, causing one or even more cracks to form, sometimes associated with a small lateral displacement. The number of identified fractured stalagmites is a minimum estimate because stalagmites that may have fallen and are no longer in place were not considered, and some fractures of in-situ stalagmites may be obscured by younger calcite. No Holocene stalagmite exhibited this type of mechanical damage. Although the exact timing of the fracture and partial shearing cannot be determined directly by 27).That these deformation features are due to ice rather than earthquakes is consistent with the absence of neotectonic features such as fault planes in those parts of the Banane cave where the fractured stalagmites occur. Furthermore, experimental and numerical studies have shown that extremely high ground accelerations would be required to fracture such rather short (< 1 m high) and thick stalagmites . We suspect that multiple cooling and warming cycles below 0 °C weaken the stalagmites, eventually causing them to break. As a result, the stalagmites are locally slightly displaced laterally by ice flow, sometimes falling to the ground, or are cemented in an upright position by calcite.Fractured stalagmites that are still in situ are not only a diagnostic indicator of the past presence of cave ice, but also indirectly witness significant paleotemperature fluctuations below the freezing point in karst rocks resulting in fracturing of even large and thick stalagmites.The simultaneous occurrence of damaged stalagmites and CCC in now ice-free caves reflects a specific temperature history: (1) cooling of the cave below 0 °C, (2) accumulation of floor ice by freezing of water entering the cave, (3) warming of the cave and its ice deposit by up to a few degrees, but still below 0 °C, leading to breakage of stalagmites encased in the ice, locally accompanied by small a lateral displacement and/or rotation, (4) further slow warming under fairly stable thermal conditions just below 0 °C, infiltration of drip water and the local precipitation of CCC in pools of water in the floor ice, (5) major warming beyond 0 °C, deglaciation of the cave and overturning of some fractured stalagmites. Critical to effective fracturing of stalagmites are (a) severe initial cooling (and subsequent warming in the subzero temperature range causing ice expansion), (b) sufficiently thick floor ice , and (c) multiple cooling and warming cycles at subzero temperatures that weaken even large stalagmites.29) and by a high degree or climate variability, including Heinrich stadials and minor events of iceberg discharge into the North Atlantic, which influenced the climate in Europe32. Permafrost was widespread in the Central Europe between the southern margin of the Scandinavian ice sheet and the Alpine ice sheet, including the southern part of England20. It is therefore not surprising that most reports of presumably ice-damaged speleothems are from caves extending from Slovakia16 and the Czech Republic17 to Germany35, Belgium36 and southern England15. No systematic dating of damaged stalagmites at these sites has been performed, but the 230Th ages of the associated CCC range mostly from about 40 to 15 ka40, demonstrating the presence of ice in these (currently ice-free) caves.This temperature evolution of the shallow subsurface argues for a paleoclimate characterized not only by strong cooling to temperatures below 0 °C , but also by temperature fluctuations that resulted in cycles of ice contraction and expansion of cave ice. This is consistent with the magnitude and pattern of climate change during glacial periods and especially during glacial maxima. These periods were characterized by severe cooling  due to changes in the thermal regime has the potential to break off stalagmites. Depending on the ice thickness and the diameter of the stalagmite, a temperature increase of as little as 2 K can cause vertical shear stresses strong enough to vertically shear off a stalagmite near its base. If the cave ice body is not confined by surrounding walls, i.e. the cave chamber is only partially filled with ice, vertical shear stress gradients can form at the stalagmite base, resulting in effective rotational stresses.230Th dating.Vertical uplift of stalagmites by expanding ice – rather than breakage by lateral ice flow as previously assumed – provides a physical explanation for the wide-spread damage to speleothems in mid-latitude caves during cold climate periods of the Pleistocene. The observed characteristics of ice-damaged stalagmites, which exhibit fractures, some of which are associated with minor lateral displacement but are still in-situ, i.e. in growth position, differ from the damage caused by strong earthquakes on speleothems growing on active fault zones in other parts of this cave system. In this respect, the Obir Caves represent a rare example where both types of speleothem deformation can be studied and chronologically constrained by 24. We documented the deformation features and drilled short cores (7 mm diameter) to sample the pre- and post-deformation calcite for 230Th dating.We examined fractured stalagmites in the same chambers of the Banane system where samples of CCC from the Last Glacial Maximum were recoveredWe also extracted a few larger broken stalagmites for laboratory tests of the mechanical properties of speleothem calcite. Samples for these tests were cut from the interior of these stalagmites as prismatic blocks with edge lengths of 20 to 40 mm and heights from 50 to 75 mm.230Th dated at the Isotope Laboratory of Xi’an Jiaotong University, using standard chemistry procedures41 to separate U and Th. U and Th isotopes were measured using a multi-collector inductively coupled plasma mass spectrometer (ThermoFinnigan Neptune Plus) equipped with a MasCom multiplier behind the retarding potential quadrupole in peak-jumping mode. Instrumentation and standardization are described in Cheng et al.2. 230Th ages were calculated using decay constants of Jaffey et al.42 and Cheng et al.2.The drill cores were examined macroscopically and samples for dating were obtained from these cores using a hand-held dental drill, operated in a laminar-flow hood. The samples were prepared and Measurements of mechanical properties, i.e. tensile and compressive strength – the Young’s modulus and Poisson ratio in tension and compression, respectively – were performed on prismatic samples were cut from large broken stalagmites. For the measurements in tension aluminum posts with a thread in the center were glued to the face sides (using X60 glue from HBK company) and mounted in the testing machine. For the compression measurements, the samples were placed between two steel plates in the testing machine .To measure the Young’s modulus and Poisson ratio, specimens were subjected to three loading cycles. The loading rate was adjusted so that both the maximum and minimum loading of each cycle were achieved within 12 to 15 s. After loading and unloading, the corresponding load was held constant for 30 s. Data were recorded using a Spider8 data acquisition system (HBK company) at a frequency of 5 Hz.The change in length was measured with two DD1 displacement transducers (HBK company) attached directly to the specimen. In addition, a T-Rosette  was glued to the specimen at half height to determine the linear and lateral strain. The Young’s modulus was determined from the recorded data of three loading cycles. This parameter was calculated for each loading and unloading step and an average value was determined for the specimen. The Poisson ratio was calculated from the average values of the longitudinal and lateral strain of each loading and unloading period and a mean value was determined.We investigated two possible mechanisms associated with ice formation in a cave: (a) ice deformation under gravity, and (b) expansion/contraction of ice due to temperature changes. We used finite-element models for thermoelasticity and full-Stokes ice flow to determine the relative contributions of these two processes to basal stresses around stalagmites.https://fenicsproject.org44) framework, were used. This framework allows for an easy definition of the model physics equations in variational form and subsequently derives a functional FEM model code (including boundary condition treatments), which can be used for computations. Symbols used in both models and values of standard parameters are listed in Table Two finite element models (detailed below), implemented in the FEniCS  using a linearized thermoelastic constitutive equation:σ is the stress tensor, C the stiffness tensor and ε the strain tensor. Rewriting Eq. (x) leads toλ and µ being the Lamé parameters and α the thermal expansion coefficient48. The relative temperature change of ice and speleothem calcite is now expressed with respect to a reference temperature (T0) and δij is the Kronecker delta. Both Lamé parameters can be related to the Young’s modulus (E) and the Poisson ratio (ν):We describe the volumetric changes and resulting stresses within the ice and the stalagmite caused by ambient temperature changes (ΔWe implemented Eq.  in FEniCSupplementary Information.