The symmetrically stable craniofacial bony structure supports the complex functions and delicate contour of the face. Congenital craniofacial deformities are often accompanied by bony defects and have been repetitively correlated with compromised dento-maxillary stability, but neither the extent nor the pattern of cleft-related maxillary instability has been explored in detail. Furthermore, it is largely unknown if the bony defect and related instability are correlated with secondary maxillary deformity common among patients with orofacial clefts. With the aid of finite element modeling, we studied the detailed relationship between cleft-related bony defect and maxillary stability under occlusal loading. Craniofacial models were generated based on cone-beam computed tomography data and loaded with mimicked bite forces along the axial axis of each tooth. Our data showed that all cleft models exhibited more asymmetrical deformations under mastication compared with the normal. Models with palatal cleft demonstrated greater asymmetry, greater dental arch contraction, and less maxillary protrusion compared to models with alveolar cleft only. For unilateral cleft models, alveolus on non-cleft side tended to be more protruded and lifted than the cleft side. For bilateral cleft models, the most prominent feature was the seriously contracted alveolar arch and curved and pitched premaxillae. These findings indicated cleft type-specific pattern of maxillary instability, which were largely in accordance with dentoalveolar morphological features among patients. Collectively, our study elucidated the detailed relationship between cleft bony defect and the pattern of maxillary instability, and suggested a prototype for studying the abnormal maxillary and dental arch growth among patients with craniofacial deformities. In cases of congenital craniofacial deformities, which are the most common birth defects in human, craniofacial bones are often involved with compromised morphology and function4. Usually, congenital anomalies affect craniofacial bones in two ways. First, abnormal embryogenesis and development generate primary distortion and defects in the bony structure5. Second, the structural instability worsens the primary deformities and skews the growth pattern in a secondary manner6. The primary distortion and defects could be clearly defined at birth, but the secondary growth abnormalities are still difficult to predict. Although congenital craniofacial deformities have been repeatedly related to the skeletal instability9, neither the detailed instability pattern nor its correlation with specific tissue defects and growth pattern has been efficiently explored in the previous literature.Craniofacial bones constitute the most intricate part of human skeletal system. They determine the contour of the face by lending supports and attachments to the overlying soft tissues, and maintain diverse physiological functions in the craniofacial region by providing a stable structure foundation10. Besides soft tissue anomalies, facial cleft is frequently accompanied by bony defects in the alveolar and palatal regions. The cleft-related maxillary discontinuity often manifests in the form of asymmetry and disproportion11. The midfacial asymmetry coefficient among patients with cleft deformity may reach over 58%12, with the distortion most significant in the naso-dento-alverolar region13.Cleft lip and palate is the most common congenital deformity in human dento-craniofacial region, with a varying occurrence of 0.2–2.3‰ in newborns among races20. Correspondingly, maxillae stabilization has always been listed among the major aims of bone graft management for the cleft defect in the literature21. The extent and pattern of the cleft-related maxillary instability, as well as the effectiveness of bone graft in stabilizing the maxillae, however, have rarely been illuminated23.Moreover, these congenital skeletal deformities tend to become worse during the growth and development after birth. Collapse of maxillary elements adjacent to bony defect is frequently observed among patients, demonstrating narrowed and retracted dental arches, displaced premaxillae, and uneven nasal bases. Such secondary collapse and displacement are often attributed to the “instability” of the disrupted maxillary buttresses24.In cleft lip and alveolae deformity, the bony defect is limited within the primary palate. When cleft palate occurs simultaneously, the alveolar defect further extends to the posterior and results in complete disruption at the inferior surface of the maxillae. Bilateral and unilateral clefts are also different from each other in separating the maxillae into three and two elements respectively. Although it is convenient to infer that the more extensive the defect the more instable the maxillae, no concrete evidence is available to support this statement or any detailed correlation pattern between cleft severity and maxillae instability5. While it is easy to surmise that an instable maxilla tends to be susceptible to pathological influences and easily deviates from normal growth pattern, again, studies either confirming such correlation or illuminating detailed influential patterns were lacking in the literature.Moreover, along with traumatic surgical intervention and scar contracture, bony defects have been considered as one of the causes for secondary maxillary growth abnormality among patients with clefts26. In contrast, with the development of computer technology, non-invasive approaches are now available to analyze the craniofacial structure. The finite element modeling (FEM) has been widely acknowledged as an effective tool27 in the biomechanical analyses of craniofacial regions28. With accurate modeling from high-resolution CT images and elaborative definition of mechanical loading and boundary conditions, finite element analyses (FEA) could simulate complex functional activities, including the jaw mastication29. Therefore, FEM presents an opportunity to study the abovementioned cleft-related maxillary instability.One of the major obstacles to studying the craniofacial skeleton stability is the lack of reliable measuring tools. Some previous studies used artificial instruments to exert forces on cleft alveolus and measured the deformations of the lateral alveolar segments and the premaxillae, but the accuracy of measurement was severely undermined by the poor manoeuvrability of the instrument and individual variations5. The deformation characteristics of cleft alveolus under masticatory loading would help us better understand the maxillary instability among patients with CLP.The most frequent and influential oral activity is the masticationIn this study, we generated finite element models of maxillae affected by different types of cleft defects and analyze their stability and deformation under simulated mastication loadings. The FEA results were also compared with clinical data to further illustrate the potential relationship between maxillary instability and secondary skeletal deformity. Our functional stability analyses serve as a proficient prototype for the study of diverse congenital craniofacial deformities in different clinical settings.Informed consents have been acquired from all the patients (aged 7–15 years old) and their parents for CBCT scanning and analysis of the acquired CBCT images. The research protocol was approved by the ethic committee of West China Hospital of Stomatology, Sichuan University . All experiments were performed in accordance with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.EVO machine  with tube voltage of 120 kV, tube current of 80 mA and resolution of 0.5 mm. DICOM images were imported into mimics 16.0 and 3-matic 8.0  to be processed and build the normal (control) maxillary FE model. Images were segmented (Hounsfield unit between 226 and 2254), and then 3D reconstructed to build the surface rendering of the whole skull , UCAP , BCA , and BCAP ). For the UCA model, the right lateral incisor was erased together with surrounding buccal and palatal alveolar bone on CT serial images. For UCAP model, further more bone on palatal plate on the right side was removed to simulate conditions in UCAP patients  through the mesial-buccal cusp peak of right/left first molar and the mesial contact point of central incisors  was defined in the following steps: (1) The occlusal planeors Fig. . (2) Thiors Fig. . (3) Theors Fig.  were plaors Fig. . The X-aors Fig. .34 was calculated in each model as follow :To evaluate and compare the degree of deformation asymmetry of maxilla in cleft models with that in control model, the alveolar deformation asymmetry index (AI)To detect the lateral deformation of alveolae under masticatory loading, transversal contraction (TC) was calculated based on the X-axis deformation of each probe  Fig.  as folloDeformations on Y-axis direction were recorded as the forward protrusion of alveolus at each probe  images of normal person and patients with the four types of cleft deformities aged between 7 and 15 years were enrolled. All enrolled subjects were Chinese Han race. CBCT images of the 50 patients  were collected. Images were obtained using 3D Accuitomo  with radiation dose  and resolution of 0.25 mm. Dicom formatted Images were segmented with Hounsfield unit between 226–1944 in mimics and surface renderings were then transmitted to 3-matic 8.0 for morphometric analysis. Reference planes including the sagittal plane, Frankfort plane and coronal plane were constructed based on key anatomic points on the skull  point was labeled on each maxilla, and its rectangular distance to Frankfort plane was recorded as the pitch of Pmx Fig. . The shoP-value above 0.05 was adopted to determine the equal distribution patterns of samples in each two groups. The Student’s independent samples t-test was used to test the significance of difference described in this article by using the SPSS 19.0 software . P < 0.05 was considered statistically significant.Both FEA and CBCT morphometry were performed by the same investigator (X. L.). Results in each group were recorded as mean ± standard deviation. A Levene’s test was performed to assess the equality of variances for variables calculated in every two groups we compared. A The deformation simulated in each model was illustrated with a color-coded scale Fig. . DeformaThe simulated deformations under masticatory loading demonstrated some shared characteristics among the models, including transversal collapse of the dental arch toward the middle line Fig. , anterioThe extent of transversal dental arch collapse, as measured at the levels of canine TC1), premolar (TC2), and molar (TC3), was minimal and comparable among the normal, UCA and BCA models, but greatly increased in models with palatal cleft Fig. . In addi, premolaMasticatory loading led to protrusion in the sagittal plane in all models Fig. . Compare−3mm) under masticatory loading  Fig. . Such uping Fig. .The total deformation magnitudes of the Pmx segment were significantly higher in the BCA and BCAP models when compared with the others . The middle arch width in patients with cleft palate was significantly smaller than in the normal and patients without palatal cleft. The middle alveolar width in UCAP (41.56 ± 2.75) was narrower than those of normal  and UCA ; middle alveolar width of BCAP (41.75 ± 1.9) was also smaller than those of normal  and UCA . The arch width measurements indicated that palatal cleft tended to cause narrower dental arch at the anterior and middle third of the palate  when compared with the other three groups , which was consistent with the protrusion simulation in our FEA models (compare 5J and 4R). On the vertical dimension, the highest discrepancy was observed in the UCAP (3.65 ± 1.13) group which is significantly greater than the normal  and the UCA  and BCA  groups. Interestingly, these significant differences were all concentrated in the anterior alveolar regions, showing that alveolar segments on the non-cleft side were always more anteriorly and upwardly located than the segments on the cleft side. This is consistent with our FEA results that UCAP model showed remarkable bilateral discrepancies on AP  of the premaxillae was significantly greater among UCA  Fig. , which w67] Fig. . In gene35. These cross-linked buttresses constitute a strong mechanical grid to disperse masticatory forces from teeth to the skull32, keeping the maxillae stable36. Previous studies revealed that the palatoalveolar complex played a significant role in the maxillofacial buttressing37. On the vertical direction, all vertical buttresses begin at the alveolar process. Therefore, the integrity of alveolar process makes vertical loads distribute evenly among the media, lateral and posterior buttresses. On the horizontal direction, the palatoalveolar complex forms the major part of the middle horizontal buttress36 and its support maintains the U-shaped configuration of upper dentition. On the sagittal (AP) direction37, the hard palate articulated through the palatine bones with the pterygoid plates of the sphenoid bone, preventing AP dislocation of lateral alveolae. Thus, interruption in palatoalveolar complex from fractures37 or congenital diseases may lead to collapse of the mid-facial buttresses and result in deformations.Intact midfacial bones form the three-dimensional biomechanical buttresses21 and the palate26. Although cleft-related maxillary instability has been repeatedly mentioned in previous literature, its detailed pattern and consequences in varying types of cleft deformities has rarely been studied26.Among patients with congenital cleft deformities, the supporting matrix of the maxillae is disrupted by the bony defects at the alveolae39 proposed a device anchored onto the dentition or alveolae with studs, and measured the stability of the maxillae by reading the range of movement under certain pushing force. Beside its untested accuracy, this device could not assess multidirectional deformation of the maxillae under more complicated intraoral force loadings.One of the major obstacles to in-depth analyses of cleft-related maxillary instability used to be methodological. No capable tool is available to physically measure the stability of the maxillae. Stenstroem SJ, etc.40.Fortunately, the development of digital modeling technology lends us a tool to recapitulate the cleft maxillae and masticatory loading with more accuracy. For its low risk, high efficiency and validity, FEM has been successfully applied in approaching craniofacial problems including bone fracture reduction and rhinoplasty41. Since the material properties were assigned according to the gray values in CT images, the different modulus of bones in various mineralization extent was simulated. As all models were constructed from the same CT images, local coordinate systems for simulated bite force loading, occlusal plane placing and deformation probes locating were built following completely same protocol. All the above settings served the purpose of maintaining both the accuracy and comparability among the models.In the present study, four types of cleft FE models were generated from the CT data of a normal subject. Except the type of alveolar/palatal clefts, all procedures including CT image reconstruction, surface rendering, meshing and material assigning were kept the same to eliminate individual deviation2. Alterations on masticatory force or occlusal relationship may cause uneven distribution of biological strains or deformations, and lead to skeletal growth deformities42. For instance, unilateral mastication has been found to cause facial asymmetry43. Similarly, bony discontinuity and tooth loss of cleft maxillae would alter the distributive pattern of masticatory force and consequently the final biomechanical and growth presentation of the maxillae. Again, such complicated biomechanical situations could not be physically evaluated with ease.The most significant physiological mechanical loading to the maxillae is from mastication. Masticatory force, though of smaller magnitude than traumatic forces, is constantly transmitted via teeth and shapes the growth and remodeling of the maxillae2 transmitted via tooth roots to alveolus. In normal maxilla, bony structures and masticatory forces are quite symmetrical for functional stability. Intact maxilla also shows strong resistance to unbalanced deformation. Alveolar deformations are highly symmetrical (with AI of 0.28% shown in Fig. A structurally intact maxilla renders balanced and stable biomechanical supports, bearing masticatory forcesHowever, as observed in our results, AI varies greatly among different cleft types Fig. . In bilaAlveolar cleft and accompanied tooth loss alter the distributive pattern of bite force and the final biomechanical presentation. For the UCA deformity, reduced anterior bite force on cleft side and broken alveolar integrity lead to less protrusion on cleft side Fig.  and more44, particularly among patients with palatal cleft (Fig. 45 (Fig. As exhibited in the morphological measurement results from the normal and patients with four types of alveolar cleft, many deformity features were found in accordance with the FEA outcome. Significant arch tilting under mastication may finally lead to seriously narrowed alveolar archeseft Fig. . Unbalan 45 Fig. .46.Similar to other FEM studies, our analyses bear multiple limitations. Although the bony structure, property assignment, and masticatory loading have been simulated with supreme details, factors including soft tissue coverage, intrinsic growth, and bone remodeling were not fully recapitulated. Mechanical loading was set based on experience data, ignoring more complicated masticatory movements. In addition, the morphology of the models was generated from a normal adult, so that the maxillae ratios and occlusion may be different from those with cleft deformitiesThe stability and deformation of the maxillae bearing various types of cleft deformity was studied under masticatory loading using FEM analyses. Skeletal defects related to congenital maxillofacial deformities lead to significant instability and asymmetry in the deformation during mastication, which coincide to the deviated growth pattern observed clinically. Our study, for the first time, suggests direct relationship among structural defects, functional stability and growth pattern in the craniofacial skeleton, and proposes a reliable prototype to approach the etiology of growth abnormality of diverse congenital craniofacial deformities.Appendix Table 1; Appendix Table 2; Appendix Table 3Levene's testT test


Levees are critical in providing protection against catastrophic flood events, and thus require continuous monitoring. Current levee inspection methods rely on limited information obtained by visual inspection, resulting in infrequent, localized, mostly qualitative and subjective assessments. This hampers the timely detection of problematic locations and the assessment of levee safety in general. Satellite radar interferometry yields weekly observations of levee conditions with high precision which complement current inspection methods. Here we show that levees are susceptible to short-term swelling and shrinkage associated with meteorological conditions, and assess how deformations can be related to the geohydrological properties and the safety of the levee. Our findings allow to understand the sub-seasonal behaviour of the levee in greater detail and to predict swelling and shrinkage due to variation of the loading conditions. This will improve the detection of anomalous levee responses which contributes to the development of reliable early warning methods using continuous deformation monitoring. Earthen levees form a large part of the existing flood defence systems. Depending on the natural or man-induced driving mechanisms, levees can fail due to hydraulic failures  and/or geotechnical failures 4. Consequently, the monitoring of these levees is critical in achieving safety standards and avoiding catastrophic flooding events. Being able to identify if, where, and when a failure would suddenly occur is an important aspect to consider with respect to safety. However, current conventional levee inspection methods mostly rely on expert observers5, which result in infrequent, qualitative and labour intensive assessments8. During these inspections, the integrity of the structures is assessed using visual inspection parameters, in order to check the presence of any damage, cracks, seepage, animal burrows, or irregular vegetation on the levees9. Thus, visual inspection by expert’s judgement is not effective in detecting small (mm- to cm-level) and gradual changes in the structural behaviour of the levee10, which may be indicative of an imminent failure. Common remote sensing  and in-situ monitoring methods  are also costly and time-consuming, and are therefore usually only applied to locations considered to be at high risk by a visual inspection. Hence, there is a need for innovative and cost-effective complementary techniques, especially in countries with an extensive amount of flood defence infrastructure, such as the Netherlands, China, UK, and US among many others. These techniques could be most beneficial if they contribute to detecting which locations are most prone to sudden failures and estimating far in advance whether a levee would fail. This can be done by analysing the response of a levee under normal loading conditions in order to identify locations at risk of failing during extreme loading conditions, such as storm, high river discharge or drought.Failures of flood defence systems often lead to significant human, economic, social, and environmental losses, with the risk being highest in densely populated areas11, which has been studied for different soil types, such as clay13, peat16 and others19.The deformation behaviour of a levee can be divided into two main categories. Long-term, interannual deformation, such as the subsidence of the levee occurring over a period of years, mainly depends on the type and composition of the soil and can be considered irreversible. Apart from this, levees show short-term, sub-seasonal deformation, e.g. due to changing water levels, precipitation, and temperature, occurring over periods of days to weeks depending on the soil and loading conditions. The change in soil volume due to variations in soil moisture content is denoted as the swelling and shrinking behaviour of the soil4, which are not provided by current inspection methods. In recent years, satellite radar interferometry, also known as Interferometric Synthetic Aperture Radar (InSAR)21, has become an efficient tool to monitor the surface displacements, referred to as deformations in the rest of the paper. The technique provides millions of observations with meter-level spatial resolution and millimetre-level measurement precision at reasonably low costs4. SAR satellites allow day and night monitoring of the Earth’s surface in all weather conditions, with up to a sub-weekly repeat interval. Persistent Scatterer InSAR (PS-InSAR) is a processing technique to estimate deformation time-series of points in the interferometric data stack with a coherent reflection over time20. It has been successfully applied on urban areas22, railways23, dams24, highways25, landslides26, tectonic movements27, and land subsidence28. Applications on levees have been limited to interannual deformations to monitor subsidence of the levees31. However, as most geotechnical failure mechanisms are related to dynamic levee responses to changes in loading conditions happening on a time scale of days to weeks4, a better understanding of the short-term behaviour of levees is required. Understanding the levee responses in normal conditions can then help to detect or predict the levee response to more extreme conditions, which would increase our capability of detecting anomalies that could identify unsafe situations. In this study, we assess how sub-seasonal patterns due to swelling and shrinkage can be identified from continuous levee deformation observations obtained with PS-InSAR, and we analyse how these patterns are related to meteorological variations and levee safety. By determining whether the observed deformation is in line with the response predicted from loading conditions experienced by levees and relating it to geohydrological properties of levees, it would become possible to identify problematic locations and apply the appropriate countermeasures. Here we focus on earthen canal levees in Delft, located in the Netherlands, where almost 12 million people live in flood prone areas, and reliable flood defences are essential to prevent catastrophic flood events32.Understanding and monitoring levee behaviour over an extended area, however, requires the availability of frequent deformation data with high resolution33.Swelling and shrinkage result from changes in the pore water pressures inside the levee, which are due to variations in hydrological loading conditions. When the soil saturates, the pore water pressure in the soil increases, reducing effective stresses in the soil matrix and results in swelling. In turn, a reduction in pore pressures due to drying leads to shrinkage of the soil34. Changes in precipitation and temperature can lead to significant swelling and shrinkage behaviour of these types of soil. In addition, cracks can form when the levee dries and the soil shrinks. Through these cracks water can enter the levee, reducing the soil strength. Another concern is that other materials or debris may enter the crack, preventing it from closing properly when the soil returns to a wet condition again3. Hence, the resulting changes in the geohydrology of the levee, which is loaded by a fairly constant water level, can directly lead to instability and failure. Many failures of the canal levees in the Netherlands have been recorded due to the heavy rainfall, e.g. a failure close to Wilnis in 187435 or extreme warm and dry weather, such as failures in Zoetermeer in 1947, Oostzaan near Amsterdam in 1990, Bleiswijk in 199036 and near Wilnis in 2003. Hence, extreme conditions, i.e. too dry (high temperature and low precipitation) or highly saturated soil (mainly heavy precipitation with low temperatures) cause a reduction in the soil strength of the levee, which can lead to a failure.The swelling and shrinkage behaviour of the soil is especially relevant for the safety of the canal levees. Water levels in these canals are fairly constant and typically exceed surface levels of adjacent polders, posing a continuous flooding threat to the hinterland, even under normal conditions. These canal levees were often built centuries ago and strengthened several times using local peat and clay, amply available materials in the Netherlands37 with an approach based on geodetic estimation theory38. Deformation time-series are created spanning a period of 6 years (2009–2015) . We first estimate the deformation time-series of each measurement point  on the canal levees of Delft using the PS-InSAR technique15) Fig. . AlthougvPT-model (see Methods for the details), considering the meteorological loading conditions  as indirect indicators of the water content inside the levee. The model is used to analyse the swelling and shrinkage behaviour, and to assess whether these sub-seasonal patterns can be identified in the deformation time-series. Figure d(t) and the deformation vPT-model, is given in Fig. vPT-model, which uses the meteorological data shown in Fig. To examine the swelling and shrinkage behaviour of the levees, we developed a predictive deformation model, called vPT-model occur, e.g., in December 2010 and in summer 2011, see Fig. Nevertheless, deviations from the vPT-model has been applied on each PS point along the canal levees in Delft, comprising of 1184 PS points. To assess how well the vPT-model describes the deformation compared to the steady-state model, we apply hypothesis testing to both models independently. Firstly, the significance of the vPT-model is tested using an Overall Model Test (OMT)  and compared with the steady-state model for different values of the assumed variance of the observations, H0, is rejected. The results are given in Fig. H0 is sustained. It can be seen that, already for vPT-model is providing a higher number of PS time-series that can be well modelled compared to the steady-state model. By decreasing the value of vPT-model, which results in better estimates of the observed deformation time-series.The developed entclass1pt{minimavPT-model. The reduction in the MSE for the vPT-model compared to the steady-state model can be clearly observed on the two maps, with green points representing the PS time-series showing a low MSE, and red points representing PS time-series giving high MSE. The MSE values are also given in the histograms, which illustrates the error distribution for the PS points considered. The comparison between the two distributions highlights a clear shift of the MSE towards lower values.In order to quantify this improved modelling capability, we then evaluate the quality of the estimations by calculating the mean square error (MSE) for each PS time-series. In Fig. 2, the vPT-model gives 79% of the PS points with vPT-model with higher quality of the estimations. Thus, for those points that have low MSE, the vPT-model can also provide better indications of the swelling and shrinkage patterns.The reduction in the MSE also allows to assume a lower variance 2) are still included in the results. In general, a high MSE could be related to several factors, such as radar signal decorrelation38 , or unmodelled deformation behaviour due for instance to problematic locations or soil compositions responding differently to meteorological changes4.However, deformation estimations with low precision , and heterogeneity of the soil profiles in between two boring measurement locations and other factors. More quantitative results and a better validation of the vPT-model lies in the ability of describing not only the interannual subsidence phenomenon, but also the sub-seasonal deformation behaviour using meteorological data, i.e., precipitation and temperature, as indirect indicators of the water content inside the levee. This also allows analysing the influence of the meteorological conditions on the swelling and shrinkage behaviour on a weekly basis, thus enabling predictions of the expected behaviour of the levee due to variations in the loading conditions. Being able to model and predict the sub-seasonal behaviour of a levee based on recorded extreme meteorological events would thus increase our ability of identifying critical situations.The strength of the proposed 39. Using the documented information by Van Baars39 on the weight changes from saturated to unsaturated conditions of the levee and assuming isotropic deformation, we roughly estimate 2 to 10% of shrinkage on the crest before the actual failure. In case of a deformation mostly on the vertical direction, this range can increase up to 20% during a dry period of 100 days (see Methods for the details). Expected deformations in the first phases of the drying process are estimated to be already in the range of few centimetres. While no SAR satellite data were available in the period of failure, this range of deformation is well within the observability capabilities of current SAR sensors and PS-InSAR algorithms. The monitoring and modelling of this kind of deformation behaviour, which normally takes place over a period of several weeks to months and eventually leads to a failure, could help to flag the extreme shrinkage of the levee. This would allow levee managers to apply timely countermeasures, such as watering or installing stability berms, to prevent instability.In addition, the observed deformation can also be related to changes in geohydrological properties of a levee, such as the moisture content, weight and phreatic line (i.e. groundwater table in an unconfined aquifer). An instability or sliding of the landside slope can in fact occur when the levee loses weight due to drying and/or due to changes in effective stress in the soil. In order to illustrate the potential of satellite monitoring to detect stability problems, we consider the canal levee failure that occurred near Wilnis, the Netherlands, in 2003, as an example. Extreme drying out of this peat levee during the hot summer led to its loss of weight, triggering levee instability which consequently lead to flooding of the neighbourhood behind itvPT-model is the detection of deformation anomalies in the framework of an early warning system. For example, when the soil has dried, the shrinkage and the volume change may result in cracks in the soil. In this case, the deformation behaviour of the levee will deviate from the expected deformation. This particular event would then be regarded as an anomaly with respect to the normal behaviour of the levee, which should be an indication for a potential weakness and a call for more in-depth analysis of the situation.A related possible future application of the proposed It is noted that levee deformation and its effect on safety will be highly dependent on local soil and geohydrological conditions of the levee. Further research on these aspects would need to address the relationship between deformation and geohydrological levee properties and the effects on levee stability for a number of representative situations.In conclusion, this study shows that (a) sub-seasonal deformations obtained from monitoring a levee with the PS-InSAR technique can be observed on the time scale of weeks, that (b) these deformations are strongly correlated with the changes in meteorological conditions, that (c) deformation changes in time can be estimated using a relatively simple regression model, and that (d) deformations can be directly related to geohydrological properties and the safety of the levee. Even though the examples are given for the Netherlands, this technology is applicable to other parts of the world, thus supporting levee management especially in countries with extensive flood defence systems. Findings of this study will assist the future development of reliable early warning methods using continuous deformation monitoring, thus enhancing flood protection.This paper focuses on a 10 × 10 km area south of Delft, the Netherlands. The levees used in this study are regional flood defences, as they are situated along regional rivers and canals. The canals are used to drain excess water from the lower-lying polders to the main rivers and the sea.Precipitation [mm/day] and temperature [°C] data are obtained from meteorological station 344 from the Royal Dutch Meteorological Institute near Rotterdam. Both precipitation and temperature are measured hourly with electronic sensors with a precision of 0.1 mm and 0.1 °C, respectively. The distance from the meteorological station to the study area is approximately 4 km. Hence, the measured data are expected to differ slightly from the meteorological conditions at the study area. However, since cumulative and average meteorological values are used in our model, the effect is assumed to be negligible.Soil profiles were obtained from borings performed in 2011 by Water Board Delfland at 17 different locations along the levee. Taking into account the non-uniformity of the soil compositions and the changes in soil moisture content of unsaturated zone, the dominant soil type from 0 to 2 meters below the surface level is being considered.The case study area has been monitored using data from TerraSAR-X to estimate the deformation time-series of each PS point between 8 April 2009 and 8 January 2015. This satellite provides X-band high resolution data with a wavelength of 31 mm, 3 × 3 m pixel size and a repeat cycle of 11 days.αh, and the incidence angle of the radar, θinc.The main principle of satellite radar imaging can be described as follows. Radar sensors transmit pulses of high-frequency electromagnetic waves from space to Earth and record the strength and the fractional phase of the back-scattered signals that are reflected from the surface to construct SAR images. By interfering at least two radar images acquired at different times over the same location, the combined effect of surface deformation, topography and atmospheric signal delay is obtained. In order to estimate and isolate the surface deformation from the other phase contributions, a large stack of SAR images acquired by the same satellite is analysed by interferometric time-series methods. All deformations are projections of the real deformation [mm] onto the Line-of-Sight (LOS) direction. This direction from satellite to object is determined by the heading angle of the satellite, 20) and 3) quality assessment: evaluating the quality of the results38. In this study, the interferometric stack processing of the radar data has been performed using the Delft Object-oriented Radar Interferometric Software (DORIS)40. The Delft implementation of Persistent Scatterer InSAR (DePSI)38 has been applied on 168 TerraSAR-X strip-map images in order to estimate the Line-of-Sight (LOS) deformation time-series. The main principles of PS-InSAR and a general overview of the past studies can be found in a review41, whereas another study4 discusses the applicability of the technique to continuous levee monitoring.Various time-series processing techniques can be applied to estimate the deformations from the satellite data. The most suitable approach depends on a number of factors, such as the number of available radar images, satellite characteristics, the area of interest , and the expected deformation signal. Regardless of the specific approach used, PS-InSAR analysis typically includes three main steps; 1) stack processing: creating the multiple interferograms from complex data, 2) PSI analysis: detecting Persistent Scatterers (PS) and separating deformation phase from other contributions  in [mm] for deformation, P(t) for the cumulative precipitation, in [mm], over a time interval ΔtP, starting at t − ΔtP and ending at t, and T(t) for the average temperature, in [°C], over a time interval ΔtT, starting at t − ΔtT and ending at t. The offsets for precipitation and temperature time-series are represented by δP in [mm] and δT in [°C], respectively, while the time delay parameters for P(t) and T(t) with respect to d(t) are denoted as τP and τT, with their units in [day]. Lastly, cP in [mm/mm] and cT in [mm/°C] are the scaling coefficients of the linear combination, between d(t) and P(t) and between d(t) and T(t), respectively.In order to describe this deformation behaviour of earth-filled levees, we consider its relation with respect to those meteorological data, i.e. precipitation and temperature, which are expected to give an indication of soil moisture changes. For this reason, the steady-state model, which considers the interannual trend, due to the long-term irreversible behaviour of the levee (e.g. subsidence), is extended with the introduction of precipitation, tT = 10 days and ΔtP = 30 days are considered, respectively. The time period for the cumulative precipitation was chosen to be longer than the time resolution of the deformation data to take into account for the long-term effect of precipitation.Soil deformation is expected to result from cumulative and smooth variations in precipitation and temperature. For this reason, the mean temperature and the cumulative precipitation data over time periods ΔvPT-model in equation (d(t), P(t) and T(t) are the deformation and meteorological data preprocessed as described above, and the global offset coefficient is defined as δ = (cPδP + cTδT − b). This model is non-linear due to the products cPτP and cTτT. For this reason, we use the cross-correlation method42 to estimate the τP and τT parameters. This approach is used to shift P(t) and T(t) with respect to d(t) (after removing the steady-state trend v⋅t) and to compare the two records at each possible time delay, where The equation  can be svPT-model is simplified asAfter the time alignment, the vPT-model are estimated by minimizing the mean square error between the deformation data and the model estimated is the m × 1 vector containing the LOS deformation observations, A is the m × n design matrix whose columns are the time vector t, the vectors 1 is a vector containing only ones, and x is the n × 1 vector of the model parameters (the symbol ′ indicates the transpose). The estimated optimal values of x are then given by the least squares solution43 asQd specifies the dispersion of the measured deformation data. The observations in the time-series are assumed to be uncorrelated, each having a fixed variance of unit weight Im an m × m identity matrix.The optimal values for the linear parameters of the vPT-model of equation H0 indicates that the deformation behaviour is not significantly well described by the chosen model, given the assumed level of significance. For InSAR time-series, α is typically defined in the range of 0.2% < α < 2%, as we prefer to stick to a relatively simple null hypothesis if possible45. In this study, we assumed an α value of 1%, but in practice this is a decision to be taken by the local authorities. The variance of unit weight for TerraSAR-X with a 31 mm wavelength is conservatively assumed to be 45.Rejection of 39, two scenarios for changes of the phreatic line in the peat levee are considered: (a) fully saturated (phreatic line is at the crest), and (b) unsaturated (phreatic line drops 1 m below the crest level). Relevant information and the cross section of the levee can be found in the original study39. Here we estimate the expected deformation of the crest in case the phreatic line drops from scenario (a) to scenario (b), using the data documented by Van Baars39. In scenario (a), the volume of saturated soil, Vsoil-sat = 1 m3. The gravimetric water content, Θ, is described as the ratio between the mass of the water, Mw, and the mass of solids, Msolids. For the saturated peat soil at the Wilnis levee, Θ was varying between 600% to 800%, and the unit weight of the saturated peat soil, γsat = 11 kN/m3, and the unit weight of unsaturated peat soil, γunsat = 5 kN/m3 47. The ratio between mass and volume of the solids is assumed to be constant.In the assessment of the failed levee at WilnisMsoil-sat, is equal to sum of mass of water, Mw-sat and mass of solids, Msolid-sat. Thus, for the given Θ of the saturated soil, Msoil-sat = γsat.Vsoil-sat = 11 kN. Using an average Θ of 700%, Mw-sat = 9.63 kN and Msolid-sat = 1.38 kN. Considering the unit weight of water, γw = 9.81 kN/m3, the volume of water in the saturated soil is calculated as Vw-sat = Mw-sat/γw = 0.98 m3 and the volume of solids in the saturated soil is then Vsolid-sat = Vsoil-sat − Vw-sat = 0.02 m3.In the case of fully saturated soil (scenario (a)), the mass of soil, 46. In this case, the mass of water, Mw-unsat reduces to 2.75 kN and the corresponding volume of water in the unsaturated soil is Vw-unsat = 0.28 m3. The mass of solids in the unsaturated soil remains unchanged, Msolid-unsat = 1.38 kN.After a dry period of approximately 100 days, soil samples taken from the crest of the levee show that Θ of the unsaturated soil (scenario (b)) was around 200%3 in the case of a 1 m drop in the phreatic line with the reduction of Θ from 700% to 200%. This correspond to a deformation of 6% of the total height  assuming an isotropic shrinkage of the soil. For an initial Θ of 800% and 600%, about 2% to 10% of shrinkage can be observed, respectively. In case of an anisotropic deformation, mostly on the vertical direction, this range can increase up to approximately 20% in a drought period of 100 days.Hence, the volume change of the soil, ΔV, between the two scenarios is estimated as 0.175 m


Arabidopsis thaliana. The selection of candidate NO-binding proteins identified from the motif search was supported by structural modeling. This approach identified AtLRB3 (At4g01160), a member of the Light Response Bric-a-Brac/Tramtrack/Broad Complex (BTB) family, as a candidate NO-binding protein. AtLRB3 was heterologously expressed and purified, and then tested for NO-response. Spectroscopic data confirmed that AtLRB3 contains a histidine-ligated heme cofactor and importantly, the addition of NO to AtLRB3 yielded absorption characteristics reminiscent of canonical H-NOX proteins. Furthermore, substitution of the heme iron-coordinating histidine at the H-NOX center with a leucine strongly impaired the NO-response. Our finding therefore established AtLRB3 as a NO-interacting protein and future characterizations will focus on resolving the nature of this response.In plants, much like in animals, nitric oxide (NO) has been established as an important gaseous signaling molecule. However, contrary to animal systems, NO-sensitive or NO-responsive proteins that bind NO in the form of a sensor or participating in redox reactions have remained elusive. Here, we applied a search term constructed based on conserved and functionally annotated amino acids at the centers of Heme Nitric Oxide/Oxygen (H-NOX) domains in annotated and experimentally-tested gas-binding proteins from lower and higher eukaryotes, in order to identify candidate NO-binding proteins in  Arabidopsis thaliana flavin monooxygenase  binds NO and has a higher affinity for NO than O2. Moreover, we have also shown that AtNOGC1 acts as a guanylate cyclase (GC) and that this activity can be modulated in an NO-dependent manner in vitro [Nitric oxide (NO) is a reactive oxygen species (ROS) that is utilized as a signaling molecule in many physiological processes in microorganisms, animals, and plants . NO in in vitro . It has in vitro ,15. It iArabidopsis thaliana. One of these proteins is a member of the Light Response Bric-a-Brac/Tramtrack/Broad Complex (BTB) family  and was expressed and tested for responses to NO in vitro.Given the role of NO and the number of NO-dependent processes in plants e.g., growth and development, as well as defense responses, we hypothesize that plants contain NO-sensitive or NO-responsive proteins that can conceivably perceive NO. Here, we have applied a search motif constructed based on conserved amino acids at the heme b accommodating pockets of annotated NO-binding proteins across species and supported by structural modeling , in orde+ channel (GORK) that has subsequently been shown to be directly modulated by ABA [Arabidopsis thaliana.Prokaryotes and eukaryotes harbor complex multi-domain proteins that accommodate functional centers in the form of catalytic centers or auxiliary sites required for binding to organic molecules and protein–protein interactions, which may serve as a highly specific and localized regulatory signal in complex proteins. As such, these seemingly hidden functional centers often fall below the detection limit of BLAST searches. However, such centers may be identified in proteins by applying search motifs (terms) that are built based on consensus amino acids in annotated and experimentally-confirmed proteins across species ,18. Thisd by ABA . Given tTo this end, we extracted an H-NOX motif from an alignment of the centers of NO-binding H-NOX domains from NO-dependent soluble GC of different species, including bacteria, blue-green algae, insects, and mammals . This moThermoanaerobacter tengcongensis, the proline (P) residue at position 14 of the H-NOX motif contributes to structural “flattening” of the distorted heme, resulting in an increased affinity for oxygen [When this motif is used to query the Arabidopsis proteome, it returns four NO-binding candidate proteins: At1g62580, At4g01160, At5g19160, and At5g57690. At1g62580 encodes a flavin monooxygenase that can bind NO , as wellr oxygen . When wer oxygen ,35. Furtr oxygen  and direr oxygen . Finallyr oxygen , and thiIn the next step, we chose to further investigate the Light Response Bric-a-Brac/Tramtrack/Broad Complex protein AtLRB3 B. This pT. tengcongensis [This protein was subsequently modeled C and theongensis . NO bindongensis , leadingongensis . Furtherongensis ,44.To establish the role of AtLRB3 (At4g01160) as an NO-responsive protein, we determined the incorporation of heme into the apoprotein and evaluated the NO response of the holoprotein using UV/Vis spectroscopy. The At4g01160 gene was expressed and the gene product was purified, followed by reconstitution with hemin. The full heme protein showed a distinct Soret peak at 408 nm. This peak is concentration-dependent and resembles the range of other proteins with histidine-ligated ferric heme b ,46 FiguA.Importantly, in Arabidopsis thaliana is ferrous, due to the reducing redox potential maintained by the glutathione pool [Next, we used UV/Vis spectroscopy to study the NO response of AtLRB3 under anaerobic conditions. Presumably, the native state of cytosolic AtLRB3 in one pool . Therefoone pool . Furtherone pool . This coone pool ,52, as sone pool ,54.S. oneidensis H-NOX protein with Soret peaks at 403 nm (ferric), 430 nm (ferrous), and 399 nm (ferrous NO-bound form) [Generally, the observed spectroscopic behaviour measured for AtLRB3 resembles that of published H-NOX protein studies, such as the nd form) ,55. Our nd form) . It was nd form) . Correspnd form) . Howevernd form) , which w3NO-) renders NO inert to reduction under physiological conditions and correspondingly, a heme-oxidation mechanism based on an Fe(II) to NO one-electron transfer is unlikely [+ character [We also monitored the behaviour of AtLRB3 after NO-saturation  and a reappearance of the Soret peak at 408 nm indicated the slow release of NO. Concomitantly, the broad absorption at 530 nm reappeared. The UV/Vis signature indicates oxidation of the Fe(II) center by NO and re-coordination of the proximal His to the ferric heme, being consistent with the release of NO from AtLRB3 B. Both tunlikely . In factharacter .2 dimer, which is present in relevant amounts at the higher NO concentration used in this study, is predicted to be quite favorable for heme oxidation (+0.33 V for (NO)2 + 2 e− + 2 H+ → N2O + H2O). Indeed, the reduction of NO to N2O by cytochromes in the ferrous state was demonstrated to occur at NO concentrations above 1 mM, either through the 6c-bis(NO) state [2 complex [In contrast, the reduction potential of the metastable (NO)O) state , an (NO) complex , or the  complex ,64. Excehttp://csb.cse.yzu.edu.tw/SNOSite/Prediction.html [As AtLRB3 was identified based on the conserved amino acids at the centers of H-NOX proteins across species, we probed the H-NOX center of AtLRB3 by site-directed mutagenesis, in order to check if there was indeed any reduced affinity for NO when one or more key amino acids were mutated. Therefore, we generated an AtLRB3/H357L mutant, where a leucine replaced the heme-binding histidine, and investigated its NO binding capability. We selected this mutation as histidine at the H-NOX center was determined in previous studies to be the proximal ligand for the iron of the heme cofactor to which NO binds as a distal ligand . Leucineion.html  and founArabidopsis thaliana, DGK4, harbors an identical H-NOX center, and was shown to be essential for normal pollen tube growth and for the overall development of the plant [We note that in canonical H-NOX proteins, mutating the histidine residue to alanine resulted in the complete loss of the Soret peak. We observed that while the H357L AtLRB3 mutant exhibits spectra identical to the WT, the NO-binding response was clearly diminished, and we have explained this observation by the π-acceptor character of NO. This dissimilarity may also be due to the fact that AtLRB3 only contains key residues in the H-NOX center and does not possess the entire H-NOX domain of canonical H-NOX proteins, which has naturally raised questions regarding its physiological relevance. There is indeed emerging evidence of the biological relevance of such H-NOX centers. For instance, a recent article reported that a protein from he plant . The authe plant . Anotherhe plant  and was he plant . We are The collective experimental data suggest that the AtLRB3 protein contains a heme cofactor that is ligated by histidine 357. We could demonstrate the heme-protein’s ability to function as an NO-responsive protein in vitro, showing NO binding and the plausible formation of a five-coordinate intermediate after histidine displacement, which is required for the NO-dependent signaling of canonical H-NOX proteins. An H357L mutation in the heme-binding pocket results in a diminished NO affinity, and that further supports the assignment of AtLRB3 (At4g01160) as an NO-responsive protein most likely operating through an H-NOX-like pocket. While AtLRB3 harbors an H-NOX-like pocket, AtLRB3 is structurally dissimilar to canonical H-NOX proteins. Therefore, we can expect that the nature of this NO-response, when revealed, may be unique to complex multi-domain plant proteins. Therefore, it is also plausible that AtLRB3 belongs to a new class of heme-sensing proteins with flexible heme binding properties instead of being a canonical NO-sensitive protein. As such, our report can guide subsequent characterization studies on AtLRB3 and possibly also other plant proteins with similar H-NOX centers.Bric-a-Brac/Tramtrack/Broad Complex (BTB) family proteins have been reported to direct the selective ubiquitylation of proteins after their assembly into Cullin3-based ubiquitin ligases . The muArabidopsis thaliana) has been described [lrb1 and Irb2 double mutants display a marked hypersensitivity to red light, but not to far-red or blue light, and are compromised in multiple photomorphogenic processes, and that red light hypersensitivity can be overcome by eliminating phytochrome B (phyB) and phyD from which an effect downstream of these two photoreceptor isoforms was deduced, possibly by affecting the turnover of phyB/D [Recently, a subfamily of nucleus-localized BTB proteins that encode the LIGHT-RESPONSE BTB proteins (LRB) in Arabidopsis  that contains four distinct domains, including the N-terminal BTB domain [. In the case of Keap1, the authors have combined molecular modeling with phylogenetic, chemical, and functional analyses to demonstrate that Keap1 directly recognizes an NO sensor cluster of basic amino acids that facilitate S-nitrosation of C151 [2+ and alkenals) serving as danger messengers. It is therefore tempting to speculate that LRB3 is a  and concluded that Keap1 is a specialized sensor that quantifies stress by monitoring the intracellular concentrations of NO  and cloned into a pENTR221 vector. LR recombination was used to transfer the gene into the vector pDEST17, in order to express the protein in BL21-AI E. coli cells. The pelleted bacterial cells were lysed buffer A . The expressed protein contained an N-terminal His-Tag for affinity purification with Ni-NTA agarose. The lysate was loaded into the pre-filled Ni-NTA column and washed three times with buffer B  and binding protein was eluted with buffer C (250 mM Imidazole added to buffer B). Prior to refolding using FPLC, the denatured purified protein was concentrated and then taken up into buffer D , 0.05% (w/v), polyethylene glycol (PEG), 4 mM reduced glutathione, 0.04 mM oxidized glutathione and a protease inhibitor cocktail (SIGMAFAST); pH 7.8). Gradual removal of urea was obtained by gradient dilution of buffer D with buffer E containing hemin  PEG, 4 mM reduced glutathione, 0.04 mM oxidized glutathione, and the protease inhibitor cocktail; pH 7.8). The refolded protein was then washed again with 10 column volumes of buffer E and eluted with Buffer F (buffer E without hemin and with 500 mM imidazole) (see flowchart in Full-length cDNA of the T. tengcongensis (PDB entry: 3TF0) served as the template for a full-length homology model of AtLRB3, which was generated using Modeller (ver. 9.14) [T. tengcongensis H-NOX protein.The crystal structure of an H-NOX protein from r. 9.14)  accordinr. 9.14) . All strr. 9.14) . StructuChanges in the heme-accommodating domain during the binding of NO were followed using UV/Vis absorption spectroscopy. Here, spectral characteristics are strongly indicative of the type of heme which is present and are influenced by the heme environment, thereby providing a valuable tool for observing changes in the surrounding heme . In moreTo show heme b incorporation, the spectra of air-exposed protein (89 μg/mL), as well as spectra with added hemin , were measured using a TECAN Infinite M1000 microplate reader. Spectra of unfolded protein (500 μg/mL) and BSA (1 mg/mL) with or without added hemin were measured as a control.NO binding was monitored in a glove box (InerTec AG) under nitrogen atmosphere using a TECAN Infinite 200 microplate reader. All solutions were flushed for 20 min with argon to remove oxygen before transfer into the glove box. The heme b-containing protein (400 μg/mL) was reduced chemically by adding sodium dithionite to a final concentration of 8 mM. Then, the NO donor diethylamine/nitric oxide complex (DEA NONOate) was immediately added in increments to the ferrous heme-protein. The Soret peak was monitored and DEA NONOate addition was continued until the absorption frequency remained constant, which indicates NO saturation. Over 24 h, repeated recordings of UV/Vis spectra were used to observe the slow diffusion of NO from the heme center.Arabidopsis thaliana. Furthermore, the selection of candidate H-NOX center-containing proteins was supported by structural modeling. We then demonstrated that a recombinant Light Response Bric-a-Brac/Tramtrack/Broad Complex (BTB) family protein binds NO with spectral characteristics reminiscent of canonical H-NOX proteins. Our data shows that AtLRB3 incorporates a histidine-coordinated heme cofactor with a characteristic Soret peak at 408 nm for the oxidized protein that shifts to 418 nm after chemical reduction with sodium dithionite. AtLRB3 binds NO, resulting in a 5-coordinate complex after histidine dissociation, as indicated by the Soret peak shift to 398 nm, reported in the literature for NO-bound 5-coordinate H-NOX proteins. Importantly, we have also demonstrated the reversibility of NO-binding by measuring spectra post-NO saturation indicating NO dissociation, while a mutant with a replacement of the heme-binding histidine with leucine yielded strongly reduced affinity for NO and thus showed slower binding of NO with faster dissociation. Taken together, the NO-binding dynamics of AtLRB3 and the AtLRB3/H357 mutant have assigned AtLRB3 as an NO-responsive protein. Further work will ascertain the exact nature of this NO response , as well as its associated biological roles. If indeed more NO-responsive plant proteins of a similar nature will be discovered, many more important cellular and physiological functions directly or indirectly linked to NO might also be discovered.We have used aligned centers of H-NOX domains from bacteria, blue-green algae, and mammals to extract a consensus motif based on functionally-assigned and conserved amino acid residues at the heme-accommodating pockets, in order to search for candidate NO-binding molecules in


A nonlinear hybrid method is developed for multiscale analysis of a bearing‐capacity test of a real‐scale segmental tunnel ring subjected to point loads. The structural analysis consists of two parts. Part I refers to modeling of bending‐induced tensile cracking of the segments, resulting from the external loading. The segments are subdivided into elements, according to the crack spacing. Each element is either intact or contains one central crack band, flanked by lateral undamaged domains. A multiscale model for tensile softening of concrete is used to describe the progressive deterioration of the crack bands. After iterative determination of their state of damage, the effective bending and extensional stiffnesses of the corresponding elements are quantified by means of Voigt‐Reuss‐Hill estimates. The effective stiffnesses are used for linear‐elastic simulations of the segmental tunnel ring. Part II refers to the relative rotation angles at the joints, which are estimated from monitoring data, using the Bernoulli‐Euler hypothesis. Since the validity of this hypothesis is questionable for neck‐like joints, the relative rotation angles are post‐processed such that they refer to rigid body displacements of the segments. The following conclusions are drawn: The presented approach yields good estimates of crack widths. Relative rotation angles at the joints mainly result in rigid body displacements of the segments, governing the convergences. Because realistic interface models are lacking, hybrid analysis based on displacement‐monitoring data allows for performing ultimate‐load analysis of segmental tunnel rings. This will be achieved with the help of experimental data from monitoring of the displacement discontinuities at the joints during the real‐scale test. These data are used as input for the structural analysis. The analysis is based on the linear theory of slender circular arches.The linings of tunnels, excavated by boring machines, consist of segmental rings. The individual segments are made of precast reinforced concrete. The interaction with the ground massand the relative rotation angles. BlomComputation of the internal forces as occurring in a continuous linear‐elastic ring, subjected to the external loading.Computation of the relative rotation angles at the joints as functions of the normal forces and the bending moments transmitted across the joints, making use of spring models.“Correction” of the computed relative rotation angles such that they correlate with rigid body displacements of the segments, which do not activate internal forces.The first analytical models for structural analysis of segmental tunnel rings were simply based on closed rings, without explicit consideration of the joints, see the pioneering developments of Morganregular service loads and coefficients of lateral ground pressure around 0.9, see, e.g. Blom.bearing‐capacity test of a segmental tunnel ring, which was subjected to point loads, simulating a coefficient of lateral ground pressure as small as 0.65.The pronounced anisotropy of the external loading resulted in significant bending of the tested ring, which produced tensile cracking of the segments. This has raised the need for modeling bending‐induced tensile cracking of the segments.The external loading was increased up to the bearing capacity of the ring, such that plastic hinges occurred at several joints during the test. This has raised the need for consideration of the nontrivial joint behavior, based on monitoring data that were recorded during the test.This approach was validated for linear implies that the segments are considered to behave linearly elastic. Accordingly, their structural behavior can be described by means of transfer relations, representing analytical solutions of the linear theory of circular arches. The term hybrid implies that the structural simulations do not only use the external loading as input, but also the measured discontinuities that have developed at the joints during structural testing. With this modeling approach, Zhang et al.The present paper refers to the extension of the linear hybrid method developed by Zhang et al.The assumption that the relative rotation angles at the joints are related to rigid body displacements will be checked. This will be accomplished by comparing the results from two structural simulations: (1) nonlinear hybrid analysis, based on relative rotation angles referring to rigid body displacements of the segments and (2) an alternative nonlinear hybrid analysis, based on relative rotation angles, which are estimated from structural monitoring data. However, they are not post‐processed in order to enforce a correlation with rigid body displacements of the segments.The significance of accounting for bending‐induced tensile cracking of the segments will be assessed. This will be accomplished by comparing the results from two structural simulations: (1) nonlinear hybrid analysis accounting for tensile cracking and (2) linear hybrid analysis, disregarding tensile cracking.The first central goal of the present work is to extend the described linear hybrid method towards consideration of the nonlinearities associated with bending‐induced tensile cracking of the segments. The second central goal is to organize the nonlinear hybrid method such that it follows the conceptual lines of BlomThe paper is organized as follows. Section 2R of the centerline of the ring was 2.925 m, see Figure φ is measured from the crown.Inspired by other tests on segmental tunnel linings described in the open literature,H, and their axial length, B, amounted to 35 cm and 1.2 m, respectively. As for the concrete, the maximum size of the aggregates, dmax, was equal to 2 cm. The composition details of the concrete is listed in Table fc, reached 28 days after production, amounted to 58 MPa. As for the reinforcement, Chinese hot‐rolled steel rebars with specification HRB 335 were used; see Figure Es, and the yield stress of the reinforcement, fy, amounted to 210 GPa and 335 MPa, respectively. The concrete cover was 6 cm.The ring consisted of six reinforced concrete segments. Their thickness, φ1  =  8°, φ2  =  73°, φ3  =  138°, φ4  =  222°, φ5  =  287°, and φ6  =  352°. Neighboring segments were connected with two steel bolts each. The bolts had a diameter, d, amounting to 30 mm and a yield stress, fb, amounting to 400 MPa, see Figure The joints were positioned at angular coordinates Compressive loading was imposed by three groups of altogether 24 hydraulic jacks, see Figure φ1  =  8°, φ2  =  73°, and φ5  =  287°. Load step 40 was very close to the bearing capacity of the tested segmental tunnel ring, because the convergences of the structure became so large that a kinematic mechanism began to develop.within the segments.The structural behavior was monitored carefully during the entire bearing‐capacity test. Displacement monitoring referred to circumferential displacement discontinuities across both the inner and the outer gaps of the joints  where Structural analysis of the bearing‐capacity test is based on the following transfer relations, representing analytical solutions of the linear theory of slender circular arches, see Zhang et al.R, EA, and EI denote the radius of the axis of the arch, the extensional stiffness, and the bending stiffness, respectively. Further, θ stands for the cross‐sectional rotation, u and v denote the radial and the circumferential displacement, respectively, and N, M, and V stand for the axial force, the bending moment, and the shear force, respectively. The vector on the left‐hand side of Equation φ. The vector on the right‐hand side of Equation i”), i.e. to the circumferential position φ  =  0. The top‐left 6 × 6 submatrix of the transfer matrix in Equation L”). The latter represent analytical solutions for radial point loads and relative rotation angles at the joints.In Equations P, imposed at position φp, read asH(φ − φj) stands for the Heaviside function. The load integrals for the relative rotation angle, Δθj, at the joint located at φ  =  φj, read asThe load integrals for a radial point load closed ring. They read as The six integration constants are obtained as follows. Without loss of generality, the three integration constants, representing kinematic quantities, may be set equal to zero, i.e. ui=vi=θi=ui=vi=θi=Equations 3.2rigid body displacements of the segments. This allows for subdividing hybrid analyses into two load cases. Load case I refers to the point loads, while the relative rotation angles are set equal to zero. Thus, the corresponding structural analysis may be interpreted as referring to a closed ring without joints, which is subjected to the point loads. This part of the hybrid analysis requires consideration of bending‐induced tensile cracking of the segments. Load case II refers to the relative rotation angles at the joints and to the rigid body displacements of the segments, caused by these relative rotations, while the point loads are set equal to zero. Finally, the two load cases will be superimposed. Such a superposition is admissible, even though the analysis of load case I is nonlinear, because (1) superposition of load case II only means addition of rigid body displacements and (2) equilibrium equations are formulated for the undeformed configuration.The aim of the following considerations is to carry out a hybrid analysis of the bearing‐capacity test described in Section The extension of the linear transfer relations to consideration of bending‐induced tensile damage of the segments is carried out in the framework of multiscale structural analysis, see Figure estimates of the relative rotation angles are computed, based on the assumption of a linear distribution of circumferential displacement jumps along the radial length of the joints, i.e. on the Bernoulli‐Euler hypothesis. In this context, it is noteworthy that joints represent structural necks. The corresponding stress concentrations invalidate the Bernoulli‐Euler hypothesis. This raises the need to improve the estimates of the relative rotation angles. The improvement is carried out at the structural scale of the segmental tunnel ring. In more detail, following scientific work by Blomrigid body displacements of the segments.Quantification of the relative rotation angles at the joints is based on the experimental data illustrated in Figure 3.3The mean field homogenization methods of continuum micromechanics allow for estimating homogenized properties of microheterogeneous materials.E, ν, and fc denote Young's modulus, Poisson ratio, and the uniaxial compressive strength of concrete. The model‐predicted compressive strength ν=0.24,fc=62.0MPft, ft,dam, and Edam denote the uniaxial tensile strength of the concrete, its tensile strength during softening, and its Young's modulus during softening, respectively. Further, ω denotes the damage variable, which is equal to the crack density parameter by Budiansky and O'Connell.Homogenization of the uniaxial tensile strength and of the tensile softening behavior is carried out, using the model by Hlobil et al.3.17MPa,ft,dam(ω)396ω·ft,Edam(ω)=13.4ℓcs, see Figure fib Model Code Linear‐elastic behavior of the segments are restricted to the first four load steps.This value agrees with the experimentally measured crack spacing, amounting to 50 cm, see Liu et al.M(φ) and the one of the normal force N(φ) are averaged along each of the 34 elements. The averaged quantities, M‾(e) and N‾(e), are obtained as Structural analysis is organized in an incremental‐iterative fashion. Each one of the 40 load steps refers to one increment of the simulation. Within each increment, an iterative solution procedure is implemented. Each iteration step consists of an “elastic predictor‐step,” which is followed, if required, by “damage corrector‐steps.” Based on the results of the “elastic predictor‐step,” it is checked whether or not a “damage corrector‐step” is required. To this end, both the distribution of the bending moment e labels the number of the simulation element, i.e.  e  ∈  , and ψ denotes a local angular coordinate of the element, such that ψ  =  0 refers to the initial cross‐section and ψ=ψf(e) to the final cross‐section of the element. Insertion of M(ψ) and N(ψ) according to the fourth line and the fifth line of the transfer relations In Equations Mi(e), Ni(e), and Vi(e) denote the bending moment, the normal force, and the shear force at the initial cross‐section of the element, and Pe). The element remains undamaged as long as the normal strains in the circumferential direction are smaller than or equal to the elastic limit: EAini(e) and EIini(e) denote the initial (undamaged) values of the extensional stiffness and of the bending stiffness, respectively, see Table cbd), which requires “damage corrector‐steps.”In Equations  limit: 1ε=N‾(e)Eℓcbd, measured normal to the crack planes, amounts to three times the maximum aggregate size,EA and EI of the undamaged lateral zones remain equal to their initial values, EAini and EIini, while those of the crack band decrease with increasing damage.The typical width of a crack band in the concrete, EAcbd, and of the bending stiffness, EIcbd, of the crack band is based on (1) the Bernoulli‐Euler hypothesis, (2) linear‐elastic behavior of steel both in tension and in compression, and (3) linear‐elastic behavior of concrete in compression as well as linear‐elastic, nonlinear‐softening of concrete in tension according to Equations linear distribution of the normal strain in the circumferential direction prevails inside every crack band. Thus, εcbd(e) and κcbd(e) stand for the normal strain in the circumferential direction at the centerline of the crack band and for the change of curvature of this line, respectively. Both εcbd(e) and κcbd(e) are unknown and will be identified such that the stress resultants of the crack band, nl =εcbdAsc and Ast denote the cross‐sectional area of the reinforcement in compression and tension, respectively. Equating the expressions on the right‐hand sides of εcbd(e) and κcbd(e). They are solved numerically by the relaxation method.Because of the layer‐wise constant stresses, the integrals in Equations EAcbd(e) and the bending stiffness EIcbd(e) of the crack band are computed as described in the following. The general definitions of the stiffness quantities read as Thereafter, the extensional stiffness Rcbd(e) denotes the radial coordinate of the neutral axis of the crack band. It is computed as follows: Consideration of linear‐elastic, nonlinear‐softening behavior of concrete in tension leads to layer‐wise constant Young's moduli of concrete, see Figure EA‾(e) and EI‾(e), respectively, of a damaged simulation element. These quantities are estimated based on the Voigt‐Reuss‐Hill average,The next task is to quantify the effective extensional and the bending stiffness, fcbd(e) stands for the volume fraction of the crack band relative to the total volume of the element, such that (1−fcbd(e)) is the volume fraction of the intact lateral parts of the element relative to its total volume. Denoting the volume of the element as Ve) and EI‾(e) are accepted only if they are smaller than the values obtained at the end of the previous load increment.Computed values of •EA‾(e) and EI‾(e) are larger than the values obtained at the end of the previous load increment, unloading will take place. This implies that damage remains constant. Thus, the values of EA‾(e) and EI‾(e), obtained at the end of the previous load increment, are considered for further analysis.If the computed values of Structural analysis starts with load step 1. The initial values of the extensional stiffnesses and the bending stiffnesses are listed in Table Once the updated stiffnesses are identified, they are assigned to the corresponding simulation elements. This marks the end of the iteration step.The next iteration step starts with a structural simulation of the entire segmental tunnel ring. This is followed by calculating the element‐wise average bending moments and normal forces according to Equations 3.6final results from the nonlinear hybrid analysis of the bearing‐capacity tests of Section The results of load case I refer to The discussion of the results from load case I starts with the internal force distributions at the level of the entire segmental tunnel ring. The computed bending moments, normal forces, and shear forces are symmetric/antisymmetric with respect to the “vertical” axis passing through the center and the crown of the segmental tunnel ring, see Figure fy  =  335 MPa, underlines the validity of the assumption of linear‐elastic behavior of steel, all the way up to the bearing capacity of the ring, see Figure fc  =  62 MPa, see Figure r  =  rt) is multiplied by the size of this zone, equal to three times the maximum aggregate size, see Equation A comparison of the computed axial stresses of the reinforcement bars with the yield stress of steel, The local extreme values of the crack widths are obtained in the lateral regions and at the bottom, see Figure M‐N interaction diagrams, analogous to the strategy proposed for concrete hinges by Kalliauer et al.two types of failure envelopes: initial contact area of the segments  is used as a local kinematic hypothesis for the joints. Thus, the relative rotation angles are quantified as the difference of the circumferential displacement jumps, Δvjo−Δvji, measured at the inner and the outer surface, see Figure ℓs  =  410 mm, see Figure First estimates of the relative rotation angles at the joints are based on the assumption of a Mi  =  Ni  =  Vi  =  0. Considering The estimated relative rotation angles do not relate to rigid body displacements only. This can be shown by means of the transfer relations, see not refer to purely rigid body displacements of the segments. The underlying problem is the Bernoulli‐Euler hypothesis, which does not strictly apply to neck‐like joints. Thus, the estimates of the relative rotation angles need to be improved. Replacing the Bernoulli‐Euler hypothesis by a better local kinematic assumption for the neck‐like joints is, unfortunately, out of reach. As a remedy, the relative rotation angles are improved, based on considerations referring to the global scale of the entire segmental tunnel ring. Notably, this improvement is carried out in two steps.The estimates of the relative rotation angles according to Equation symmetrization of the relative rotation angles illustrated in Figure The first improvement step refers to This is motivated by the fact that the external loading was symmetric with respect to the vertical axis of the ring and that the deformed configuration of the ring during the entire bearing‐capacity test was almost symmetric.Δθ1corr, Δθ2corr, and Δθ3corr are added to the symmetrized values, Δθ1sym, Δθ2sym, and Δθ3sym, in order to obtain relative rotation angles referring to rigid body displacements (index rbd). Thus, Δθ1corr, Δθ2corr, and Δθ3corr are unknown. Inserting the expressions φj  =  1,2,…,6  =  , the following two conditions for the three unknowns Δθ1corr, Δθ2corr, Δθ3corr: This improvement step refers to enforcing the conditions Δθ2corr and Δθ3corr as functions of the known symmetrized relative rotation angles and of the unknown improved increment Δθ1corr, which is the last remaining unknown. Equations infinitely many solutions for Δθ1corr, because there are infinitely many rigid body displacements that can be described by means of the improvement strategy expressed by Equation smallest improved increments. Herein, these increments are defined as the minimum of their sum of squares. Thus, the sought solution follows from the additional condition Equations Δθ2corr and Δθ3corr according to Equations Δθ1corr as Inserting the expressions for Inserting this result into Equations The improved estimates of the relative rotation angles, which by definition refer to rigid body displacements, are quite similar to the symmetrized relative rotation angles  the external forces and (2) the relative rotation angles, derived from the monitoring data based on the Bernoulli‐Euler hypothesis, see Equation larger internal forces of the segmental tunnel ring as compared with the analysis described in Section The present hybrid analysis delivers From the analysis, it is concluded that it is more realistic to assume that relative rotation angles result in rigid body displacements of the segments, as compared with the alternative approach of assuming that the Bernoulli‐Euler hypothesis applies to neck‐like joints between two neighboring segments. This corroborates the proposed mode of post‐processing the relative rotation angles such that they refer to rigid body displacements of the segments.4.2The hybrid analysis described in Section The linear‐elastic version of load case I, “point loads,” refers to a continuous ring without joints, characterized by a uniform bending stiffness and a uniform extensional stiffness. The transfer relations  monitoring data concerning displacement discontinuities in the circumferential direction, recorded across the joints both at the inner and the outer surface of the segments, and (2) the Bernoulli‐Euler hypothesis deliver first estimates only. They are not sufficiently reliable for structural analysis. The underlying reason is that the circumferential displacement discontinuities at the joints are actually •local kinematic assumption for the joints, it is recommended to improve the estimated relative rotation angles, at the global scale of the entire segmental tunnel ring, such that they result in rigid body displacements of all segments, as described in Section As long as the Bernoulli‐Euler hypothesis cannot be replaced by a better Quantification of the relative rotation angles, developing at the joints during structural testing, is a nontrivial task.•As regards the analyzed real‐scale test, it was shown that rigid body displacements of the segments are responsible for approximately 95% of the convergences, while the deformation of the segments contributes to approximately 5% only. The latter contribution was estimated reliably with and without consideration of bending‐induced tensile cracking of the segments. As for practical purposes, it is, therefore, recommended to calculate the deformations of the segments under the assumption of linear‐elastic behavior, even if the tensile strength of concrete is exceeded in the simulations.•The relative rotation angles governed the bearing capacity of the tested segmental tunnel ring, although the relative rotation angles at the joints were related, as a good approximation, to rigid body displacements of the segments. Thus, they had no significant influence on the internal forces of the segments. This can be explained as follows: The bearing capacity of the segmental tunnel ring is related to the development of a kinematic mechanism. The latter results from the development of plastic hinges at two pairs of joints, herein the two top joints and the two lateral joints.The rigid body displacements resulting from the relative rotation angles govern the structural convergences and the bearing capacity of the tested segmental tunnel ring.•Carrying out hybrid analyses with and without the assumption that relative rotation angles at the joints are associated with rigid body displacements of the segments, it was shown that these rotation angles are unlikely to result in significant internal forces of the segments. This conclusion is consistent with similar findings of Blom•linear hybrid analyses, disregarding tensile cracking of the segments. This conclusion is consistent with similar findings of Winkler et al.Carrying out hybrid analyses with and without consideration of bending‐induced tensile cracking, it was shown that the internal forces can be estimated reliably by means of As for estimating the internal forces experienced by the segments, structural analysis may be restricted to the external loading.nonlinear analysis is nonetheless useful in the framework of durability analysis of segmental tunnel rings.•When it comes to the design of reinforced concrete structures, the definition of serviceability limit states (SLS) includes limitations of the opening of cracks. These limitations ensure that the reinforcement is durably protected from corrosion‐inducing media. In the present analysis, crack openings were determined reliably, based on the employed multiscale model for quantification of the deterioration of the crack bands, as described in Sections The presented mode of two failure envelopes, representing M‐N interaction diagrams.The joints of the analyzed segmental tunnel ring can be described by inner failure envelope refers to the largest resistance of the joints that can be established, based on the initial contact area between neighboring segments, see Figure The Once the inner failure envelope is reached, relative rotation angles will increase significantly at almost constant loading. Adjacent to the compressed inner or outer surface of the joints, the large relative rotation will close the initial gap between the segments. Once segment‐to‐segment contact is established in this region, the joint will stiffen, as described in Liu et al.outer failure envelope refers to the maximum resistance of the joints. It can be established, based on both the initial contact area and the additional contact area, available after having reached the inner failure envelope, see Figure The The failure process of the joints governed the behavior of the analyzed segmental tunnel ring, from load step 4 to load step 40.linear‐elastic ring subjected to the external loading in order to compute the internal forces and the structural displacements. This task can be accomplished comfortably, even in case of many point loads, with only one transfer matrix describing the entire ring structure.Analyze a continuous nonlinear model for crack bands as described in Sections As for quantification of crack‐opening displacements, which are relevant to durability design, determine the positions of the maximum bending moments and continue the analysis with the Evaluate the internal forces at the position of the joints and use “interface models” to compute the relative rotation angles of the joints.Post‐process the obtained relative rotation angles as described in Section Compute the structural displacements associated with the rigid body displacements of the segments, which result from the relative rotation angles at the joints. Again, this task can be accomplished comfortably, no matter how many joints have to be considered and where they are located, with only one transfer matrix, describing the entire ring structure.Superimpose the displacements, obtained in steps 1 and 5, to obtain the total displacements of the segmental tunnel ring.It is recommended to organize structural analyses of segmental tunnel rings in form of the following six steps:As long as realistic interface models are not available, the combination of displacement‐monitoring data and hybrid analysis remains a prime candidate for structural analysis of segmental tunnel rings, loaded all the way up to their bearing capacity.


The cell wall (CW) of bacteria is an intricate arrangement of macromolecules, at least constituted of peptidoglycan (PG) but also of (lipo)teichoic acids, various polysaccharides, polyglutamate and/or proteins. During bacterial growth and division, there is a constant balance between CW degradation and biosynthesis. The CW is remodeled by bacterial hydrolases, whose activities are carefully regulated to maintain cell integrity or lead to bacterial death. Each cell wall hydrolase (CWH) has a specific role regarding the PG: (i) cell wall amidase (CWA) cleaves the amide bond between N-acetylmuramic acid and L-alanine residue at the N-terminal of the stem peptide, (ii) cell wall glycosidase (CWG) catalyses the hydrolysis of the glycosidic linkages, whereas (iii) cell wall peptidase (CWP) cleaves amide bonds between amino acids within the PG chain. After an exhaustive overview of all known conserved catalytic domains responsible for CWA, CWG, and CWP activities, this review stresses that the CWHs frequently display a modular architecture combining multiple and/or different catalytic domains, including some lytic transglycosylases as well as CW binding domains. From there, direct physiological and collateral roles of CWHs in bacterial cells are further discussed. The first bacterial cell wall hydrolase (CWH) was discovered in 1921 by the Scottish bacteriologist Sir Alexander Fleming, who is well known for his 1928 discovery of the antibiotic penicillin Fleming, . He had The bacterial cell wall (CW) is a complex arrangement of macromolecules that varies depending on the species of bacteria and whether they are parietal monoderm bacteria , lipopolysaccharidic diderm bacteria  or mycolate diderm bacteria   constitutes the third residue of the stem peptide. In cocci species, though, a lysine residue is found at this position  or mycomembrane has been intensively investigated  and can also be called PG amidases (PGAs) or amidases in the scientific literature Young, . They hyE. coli AmpD is one of the most investigated CWHs with a NALAA-2 domain , which remains poorly understood . E. coli, the NALAA-3 AmiA and AmiC were shown to result in the release of the L-Ala-D-Glu-mDAP tripeptide and L-Ala-D-Glu-mDAP-D-Ala tetrapeptide. Like NALAA-2, NALAA-3 is a zinc-dependent amidase, which structure has been solved . In Streptococcus pneumoniae belonging to Siphoviridae family, encodes a NALAA-5 CW degrading enzyme . Dp-1, a bacteriophage of http://www.cazy.org). CW glycosidases (CWGs), also called PG glycosidases (PGGs), can be broadly differentiated into (i) N-acetylglucosaminidases, and (ii) lysozymes , leading to the formation of a glucide hemiacetal or hemiketal Holtje, . Glycosiysozymes .N-acetylglucosaminidases hydrolyse the glycosidic bond in different oligosaccharide substrates including the CW, chitin and N-glycans by cleaving specifically between N-acetyl-β-D-glucosamine residues and contiguous monosaccharides -1,6-anhydro-MurNAc disaccharide  with a conserved Asp-His dyad is involved in CW lysis  where the active catalytic site is formed by a tetrad of Tyr-Ala-Thr-Asp amino acid residues together with a highly conserved glutamic acid residue  and lytic transglycosylases (LTGs) cleave the same β1,4-glycosidic bond but in two different ways. While its hydrolysis by lysozymes result in a product with a terminal reducing MurNAc residue without a ring, LTGs are not hydrolases but cleave the bond between MurNAc and GlcNAc with the concomitant formation of a 1,6-anhydro ring at the MurNAc residue  and corresponds to lysozymes of type C almost uniquely found in species of the superkingdom Eukaryota  and corresponds to phage lysozymes (type P), which structure has been solved only for the bacteriophage P22 lysozyme  and corresponds to the lysozymes of type B such as Cpl-1, produced by the phage Cp-1, which specifically lyses several serotypes of A CW peptidase (CWP) cleaves the amide bonds between amino acids in PG Holtje, . CWPs, aS. saprophyticus, a highly-conserved Cys-His-Glu-Asn tetrad relaying the active site was further evidenced  with the unique feature to be potentially involved in two different CW cleavage activities  and proteins of this superfamily are ubiquitous papain-like cysteine peptidases involved in the catalysis of the Enterococcus faecium, the structure of the D-Ala-D-Ala dipeptidase VanX has been solved and revealed a Zn-dependent catalytic mechanism  and can be further discriminated into four subfamilies, namely from PM15A to PM15D. In Staphylococcus simulans is one of the best studied PM23. In its active form, lysostaphin cuts the peptide bond between the third and fourth glycine residues of the pentaglycine cross-link in the PG of Staphylococcus . Lysostaphin from E. coli cleaves the D-alanyl-meso-2,6-diamino-pimelyl amide bond in PG . The PM74 D,D-endopeptidase MepA from The PS11 domain is approximately 235 amino acids long (IPR001967) and is systematically associated with another C-terminal domain (IPR012907), which is organized into a sandwich of two anti-parallel β-sheets. The function of this C-terminal domain is unknown, but it could mediate interaction with other CW synthesizing enzymes . Together with PS13 and PS66 domains, little experimental work has been dedicated to PM14 domain. In E. coli exhibits both D,D-carboxypeptidase and D,D-endopeptidase activities . The PS13 PBP4 from E. coli is a L,D-carboxypeptidase releasing the terminal D-alanine residue from the tetrapeptide L-Ala-γ-D-Glu-meso-A2pm-D-Ala . The PS66 LdcA from Mycobacterium tuberculosis harbors a TP domain and has been the subject of intense structural investigations, especially for the study of drugs blocking the enzyme activity through PG cross-linking . The L,D-transpeptidase LdtMt2 from Besides the different catalytic domains involved in PG hydrolysis and reviewed here above, numerous CWHs have CW binding domains –5. In baE. coli, the AMIN  domain allows proper localization of the enzyme at the division site through binding to the PG , one of the most frequent CW binding domains found in CWHs, is found at the N- or C-terminal of a protein  domains can be found, from SH3 of type 1 (SH3-1) to SH3-9 –3. The SActually, more than one CW binding domain can be found in some CWHs –6. WhileThe different catalytic domains reviewed above can be found individually or in combination in various CWHs . CWHs wiB. subtilis , where only the first 165 amino acids are kept, an activity twofold higher than that of the native protein was observed  harbors a central GHF-73 domain and a C-terminal CHAP domain  of the mature protein, and that a hydrolytic activity can only be detected at acidic pH in renaturing conditions, this suggests that interaction with the negatively charged CW is favored by a positive or neutral charge of the protein. Unlike CWAs, some CWGs and CWPs can combine two different types of glycosidase or peptidase catalytic domains, e.g., PS11 and PS13 , TG , MltA , MltG  and RlpA  domains  and YebA (belonging to PM23), are collectively required for cell growth and PG incorporation  the synthesis of MurNAc pentapeptide precursor  is lethal  and PG hydrolases , T3SS and T4SS, as well as surface organelles, including type 4 pili (T4P) and flagella  exhibits a GHF-73, whose CWG activity is essential for flagella assembly as it degrades the PG locally to enable the formation of the rod structure in the periplasmic space   was originally considered as a virulence factor per se, named Iap (invasion-associated protein) or P60 (protein of 60 KDa) at the time. Actually, it appeared to be primarily a CWH inducing septation default and consequently mislocalisation of key cell-surface virulence factors, namely the internalin InlA and the actin polymerisation factor ActA  and the more specific designations of CWA, CWG, and CWP, for which conserved motifs and/or three-dimensional structures are clearly established. Besides, the combination of these latter terms, such as CWA-CWG or CWA-CWG-CWP, better reflect the modular organization of the numerous CWHs exhibiting multiple catalytic sites. This comprehensive review of the diversity of conserved domains exhibiting CWH catalytic activity will help scientists in the field to describe the enzymes at hand. While the association of different catalytic properties generally results in synergistic effects, the CW binding motifs that can be found along the monopolypeptide, generally improve the efficiency of the enzymatic activity (Shoseyov et al., AV and MD wrote the first overall draft of the manuscript and drew the original pictures. SL, RT, MP, and CP wrote sections of the manuscript. MD, SL, and RT contributed to conceptualize the overarching aims. MD had management as well as coordination responsibility for the execution of the work. MD and CP contributed to the acquisition of the financial supports and resources leading to this publication. All authors contributed to the critical revision of the manuscript, read and approved the submitted version.CP is permanent employee of BioFilm Control and declare his company provided support in the form of salary. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.