Speckle-type POZ protein (SPOP) is a substrate adaptor in the ubiquitin proteasome system, and plays important roles in cell-cycle control, development, and cancer pathogenesis. SPOP forms linear higher-order oligomers following an isodesmic self-association model. Oligomerization is essential for SPOP’s multivalent interactions with substrates, which facilitate phase separation and localization to biomolecular condensates. Structural characterization of SPOP in its oligomeric state and in solution is, however, challenging due to the inherent conformational and compositional heterogeneity of the oligomeric species. Here, we develop an approach to simultaneously and self-consistently characterize the conformational ensemble and the distribution of oligomeric states of SPOP by combining small-angle X-ray scattering (SAXS) and molecular dynamics (MD) simulations. We build initial conformational ensembles of SPOP oligomers using coarse-grained molecular dynamics simulations, and use a Bayesian/maximum entropy approach to refine the ensembles, along with the distribution of oligomeric states, against a concentration series of SAXS experiments. Our results suggest that SPOP oligomers behave as rigid, helical structures in solution, and that a flexible linker region allows SPOP’s substrate-binding domains to extend away from the core of the oligomers. Additionally, our results are in good agreement with previous characterization of the isodesmic self-association of SPOP. In the future, the approach presented here can be extended to other systems to simultaneously characterize structural heterogeneity and self-assembly. Protein self-association is fundamental for many processes in biology , and it The 374-residue SPOP monomer consists of three domains. From N- to C-terminus, these are the MATH domain , the BTB domain , and the BACK domain . MATH is the substrate binding domain, while the BTB domain mediates interaction with CRL3 . Both thChemical crosslinking experiments have shown that SPOP oligomers form inside cells , and anaThe higher-order self-association of SPOP follows the isodesmic model , in whicmer size . In the ntration . For SPOCG-MALS; . While tCG-MALS; . This maHere, we aimed to determine simultaneously both the distribution of oligomeric states of SPOP and the conformational ensemble of each SPOP oligomer by combining SAXS experiments and MD simulations. SAXS can provide low-resolution information on protein structure in solution, but reports on an ensemble average, which in the case of SPOP is both an average over different oligomeric states and the structural heterogeneity of each oligomeric state. Therefore, SAXS experiments are often combined with MD simulations to provide a full structural model of the system . In the ed value . Using S28–359 (full length is 374 residues), with total protein concentrations ranging from 5 to 40 µM. In order to build structural models to refine against the SAXS data, we first needed to decide which oligomeric species to include in our modelling. To this aim, we used the isodesmic self-association model, which has previously been shown to describe SPOP oligomerization well    and the n (4HS2) . We usedce field  further ce field . It woulce field .We calculated SAXS intensities from our conformational ensembles and, given the relative population of each oligomer from the isodesmic model with  of 1.53 . DespiteAXS data . HoweverTo improve the agreement with the experimental SAXS data further, we aimed to simultaneously refine the conformational ensemble of each oligomer and optimize the distribution of oligomeric states. We developed a self-consistent optimization scheme, in which the isodesmic AXS data . This apremained . The isoed value . To valirfitting . These rrfitting .The previously published CG-MALS data on SPOP clearly precludes a simple dimer–tetramer, dimer–hexamer, dimer–octamer, or dimer–decamer equilibrium in favor of an isodesmic self-association model . To deteWe also wished to examine whether the conformational ensembles of SPOP generated by the MD simulations described the SAXS data better than static structures. As a first comparison, we calculated SAXS profiles from the initial SPOP oligomer structures constructed based on crystal structures. To make the results comparable with our optimized ensembles, we fitted the isodesmic nsembles . This reThe results described above show that the SAXS data fit well to an isodesmic model with a ALS data . This anHaving generated a conformational ensemble of each SPOP oligomer in agreement with the SAXS data, we proceeded to analyze the structures. Reweighting resulted in an increase in the radius of gyration  was expressed and purified as previously described  of the National Synchrotron Light Source II  . Data we28–359 oligomers ranging from the dimer to dodecamer (in steps of dimeric protomer subunits) using a beta version (3.0.4.17) of the Martini 3 force field  we started by removing the last subunit of SPOP 1 and the first subunit of SPOP 2 to ensure that the newly joined subunits were internal and not terminal. We then removed additional subunits from SPOP 2 to reach the desired length of the output oligomer. Then, we selected a random frame from SPOP 1 and SPOP 2, superposed the BTB/BACK domains of the last two subunits of SPOP 1 to the BTB/BACK domains of the first two subunits of SPOP 2, and deleted the first two subunits of SPOP 2. Next, we checked for clashes between the newly joined subunits (shortest interatomic distance <0.4 Å), and rejected the new frame if there was a clash. This approach ensured that the terminal subunits in the constructed oligomer were also the terminal subunits in the MD simulation of the dodecamer, while all internal subunits in the constructed oligomer were also internal in the MD simulation. This approach was repeated to create 15,000 structures of each larger oligomer.We constructed conformational ensembles of larger SPOP3, and the volume of displaced solvent, r0/rm = 1.025, that have been shown to work well for intrinsically disordered and multidomain proteins  fitting the scale and constant background of the SAXS data, (2) fitting the isodesmic LinearRegression function in scikit-learn The following step was repeated for each SAXS experiment in the concentration series. The concentration of each oligomer was calculated using the isodesmic model with the given ctot . The aveIn practice, to avoid modifying the SAXS scale and constant background for every conformer in our ensembles, we instead performed the inverse operation on the experimental SAXS profile:and propagated the experimental errors The isodesmic te Carlo  with simwhere where The following step was repeated for each SAXS experiment in the concentration series. We calculated the oligomer concentrations using the isodesmic model given the new where analysis . The prohttps://github.com/fpesceKU/BLOCKING; where the sum eighting , in whicwhere where Using the ensemble weights obtained from BME reweighting, we calculated new weighted average SAXS intensities, The three steps described above were repeated iteratively to converge on self-consistent values of the SAXS scale and constant background, the isodesmic lue of θ  and then−1 for the Gaussian probability distribution used to generate the new We ran the optimization scheme for 1000 iterations starting with We ran the optimization with a range of itted KA . Thus, wThe optimization scheme outputs a set of conformational weights for each SAXS experiment in the concentration series. We combined these conformational weights to obtain a single set of weights for further analysis, under the assumption that the conformational properties of each SPOP oligomer are independent of protein concentration. The distribution of oligomeric species from the isodesmic model depends on the protein concentration. Thus, each SAXS experiment does not contain the same amount of information on every oligomer; SAXS experiments at lower concentrations have a relatively smaller contribution from large oligomers and vice versa. Therefore, we weighted the averaging of the conformational weights to reflect this mismatch in information. The average weight of conformation where where To determine the uncertainty of the isodesmic gyrate function in Gromacs. End-to-end distances were calculated from ensembles as the distances between the center-of-mass (COM) of the BTB/BACK domains in the terminal subunits using the compute_center_of_mass function in MDTraj , and the equation for conservation of mass:where, −12–1012 µM−1 and selected the where We selected five SPOP substrates with at least 8 SPOP binding motifs  for simuime-step . Frames ue 2.9.3 .compute_contacts function in MDTraj. We also calculated the average distance, R0 is the segment size, curve_fit function in SciPy.We identified SPOP binding motifs in the substrate sequences as five consecutive positions with residues 1: GAVLIMWFPC, 2: STCYNQDEHR, 3: ST, 4: STCYNQDEHR, 5: ST or 1: GAVLIMWFPC, 2: STCYNQDEHR, 3: ST, 4: ST, 5: STCYNQDEHR, where each set of amino acids are allowed at the given position . We calcGiven the concentration of each oligomer from the isodesmic model, the average molecular weight, as measured by CG-MALS, was calculated as:ci is the concentration of oligomer where curve_fit function in SciPy.We fitted the isodesmic  In this important paper, the authors have developed an approach for simultaneously optimizing the conformational ensemble and degrees of oligomerization, and this has been tested by applying it to a specific protein (SPOP). Comparison of the quality of fits with different models also provides valuable insights into structural features important to the assembly of oligomers. The approach, presented with compelling experimental support, is potentially applicable to other systems as well. public reviews designed to be posted alongside the preprint for the benefit of readers; (ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.Our editorial process produces two outputs: (i) Decision letter after peer review:eLife. Your article has been reviewed by 3 peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Volker Dötsch as the Senior Editor. The following individual involved in the review of your submission has agreed to reveal their identity: Sichun Yang (Reviewer #2).Thank you for submitting your article "Conformational and oligomeric states of SPOP from small-angle X-ray scattering and molecular dynamics simulations" for consideration by The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.Essential revisions:1) Further discuss the potential involvement of non-linear structures and functional implication of the structural features .2) Further clarification of the fitting procedure, including, for example, the importance of sampling different conformations, consideration of violation of the isodesmic model, and alternative experimental validation of the conformation ensemble.Reviewer #1 (Recommendations for the authors):I think the approach and results are well organized and presented. I don't have much to add. The only suggestion I have is to add some discussions regarding the biological implications of the rigid structures established from this work. For example, to what degree such rigidity is relevant to the phase separation behaviors of SPOP?Reviewer #3 (Recommendations for the authors):The work could go further in more thoroughly testing each of the assumptions in light of the experimental data:Does the SAXS data preclude alternate association modes that would give rise to a significant fraction of non-linear structures? The introduction mentions the role of SPOP in condensate formation and one could imagine shorter oligomers associating in different ways than simply growing into single long chains.How would the fit to the SAXS data change if oligomer sizes are distributed differently, not following an isodesmic model?How does the sampling of the conformational ensembles affect the fits? One question would be how the results depend on the number of snapshots extracted from the simulations. Another question would be how consistent the generated domain-domain configurations are with the experimental data. The latter question is addressed in part by showing that a truncated ensemble where the MATH and BTB/BACK domains are in close contact does not lead to a good agreement. What about ensembles that only consist of (i) and (iii), or ensembles that consist only of (ii) and (iii)?Even though there is good agreement between the computational models and the SAXS data, further experimental validation of the proposed oligomers with different techniques may be warranted. While such experiments are likely beyond the scope of this work, some ideas about such experiments may be helpful. Essential revisions:1) Further discuss the potential involvement of non-linear structures and functional implication of the structural features .To address this point, we have added a Discussion section mentioning the possibility of non-linear structures to the manuscript. Additionally, we have added a short discussion of the functional implications of rigid oligomers, in the context of previous work on SPOP phase separation with disordered substrates (https://doi.org/10.1021/jacs.9b10066). We have also performed coarse-grained molecular dynamics simulations of several disordered SPOP substrates to investigate the relationship between the spacing of binding motifs in SPOP substrates and the substrate binding sites in SPOP oligomers given by our proposed conformational ensembles.2) Further clarification of the fitting procedure, including, for example, the importance of sampling different conformations, consideration of violation of the isodesmic model, and alternative experimental validation of the conformation ensemble.To address these points, we have performed additional analysis of the SAXS data and compared the results to an alternative measure of self-association. We have added an analysis in which use other thermodynamic models of self-association and compare the results to the SAXS data. We have also compared the model derived from the SAXS data to previously (but independently) measured CGMALS data. We tested the effect of the structural ensembles on the agreement with the SAXS data, both by subsampling the existing ensembles and by testing the agreement gained by using conformational ensembles compared to using individual (static) structures. The results from these analyses are consistent with the previous conclusions of the manuscript, and we thank the reviewers for the suggestions.Reviewer #1 (Recommendations for the authors):I think the approach and results are well organized and presented. I don't have much to add. The only suggestion I have is to add some discussions regarding the biological implications of the rigid structures established from this work. For example, to what degree such rigidity is relevant to the phase separation behaviors of SPOP?Following the suggestion from the reviewer, we have added results and discussion on the more biological implications. We have performed new molecular dynamics simulations of several disordered SPOP substrates to investigate the relationship between the spacing of binding motifs in SPOP substrates and the distances between substrate binding sites in SPOP oligomers. These results provide some functional context for the linear structures and spacing of the MATH domains in SPOP. Another potential function of rigidity has been explored in earlier work by Schmit et al. (https://doi.org/10.1021/jacs.9b10066), where it is proposed that the rigidity of SPOP oligomers is important to avoid a high entropic penalty upon stacking cross-bound oligomers in the dense phase. Our results are consistent with this model, and we have now included this in the Discussion section of the manuscript.Reviewer #3 (Recommendations for the authors):The work could go further in more thoroughly testing each of the assumptions in light of the experimental data:Does the SAXS data preclude alternate association modes that would give rise to a significant fraction of non-linear structures? The introduction mentions the role of SPOP in condensate formation and one could imagine shorter oligomers associating in different ways than simply growing into single long chains.We agree with the reviewer that, in the current work, we cannot strictly exclude that other non-linear models of self-association are consistent with the SAXS data. However, we show that the simple model of linear oligomers based only on the interfaces seen in crystal structures are consistent with the SAXS data including fitting a concentration-dependence consistent with an isodesmic model. Thus, we would argue that linear oligomers are the most plausible model based on this and other existing experimental evidence: 1. The only known interfaces for SPOP selfassociation are the BACK-BACK and BTB-BTB interfaces; 2. Removal or mutation of either the BACK-BACK or BTB-BTB interface results in abolishment of higher-order oligomerization; 3. Linear isodesmic self-association is consistent with both the SAXS and CG-MALS data; 4. Native mass spectrometry shows that higher-order oligomers are formed through the self-association of dimers, with every step of subunit-addition populated(https://doi.org/10.15252/embj.201593169). To make this assumption clearer to the reader, we have added a paragraph discussing this in the Discussion section.How would the fit to the SAXS data change if oligomer sizes are distributed differently, not following an isodesmic model?We agree with the reviewer that it is useful to examine whether the SAXS data directly support the isodesmic model over other simple self-association models, independently of the previous existing evidence for the isodesmic model. To examine this problem further, we have now tested the agreement with the SAXS data modelling either (i) monodisperse oligomers or (ii) dimer-oligomer equilibria for a range of oligomer sizes; our results show that the isodesmic model gives better agreement with the SAXS data than any of these models. Additionally, it has previously been shown that CG-MALS experiments (covering a wider range of concentrations than our SAXS experiments) clearly exclude the possibility of smaller monodisperse oligomers (https://doi.org/10.15252/embj.201593169).How does the sampling of the conformational ensembles affect the fits? One question would be how the results depend on the number of snapshots extracted from the simulations. Another question would be how consistent the generated domain-domain configurations are with the experimental data. The latter question is addressed in part by showing that a truncated ensemble where the MATH and BTB/BACK domains are in close contact does not lead to a good agreement. What about ensembles that only consist of (i) and (iii), or ensembles that consist only of (ii) and (iii)?We agree with the reviewer that the manuscript would benefit from further analysis of how the agreement with the SAXS data is affected by the ensembles and the sampled conformations. To address the first point, we have tested how well single conformers drawn from the ensembles agree with the SAXS data. This analysis shows that a full ensemble is needed for optimal agreement with SAXS, but in line with the overall rigidity of oligomers, a small number of “well-selected” single structures can also give reasonable agreement with the SAXS data. To address the second point, we have added an analysis where we subsample the ensembles and assess the effect on the agreement with the SAXS data. The results from this analysis are consistent with the results from reweighting and restraining the simulations. However, we were not able to subsample ensembles with only a subset of the MATH configurations, as suggested by the reviewer, because the configurations of the MATH domains are not coordinated across different subunits, making it very unlikely to observe all MATH domains in an oligomer in the same configuration in a given frame. Addressing this problem in further detail would require extensive new simulations which we deem to be beyond the scope of this work.Even though there is good agreement between the computational models and the SAXS data, further experimental validation of the proposed oligomers with different techniques may be warranted. While such experiments are likely beyond the scope of this work, some ideas about such experiments may be helpful.We agree with the reviewer that further experimental validation would be interesting. We have added a direct comparison with CG-MALS data using data predicted from our SAXS-derived model of oligomerization.


Liver steatosis is a chronic liver disease that is becoming one of the most important global health problems, due to its direct connection with metabolic syndrome, its significant impact on patients’ socioeconomic status and frailty, and the occurrence of advanced chronic liver disease. In recent years, there has been rapid technological progress in the ultrasound-based diagnostics field that can help us to quantitatively assess liver steatosis, including continuous attenuation parameters in A and B ultrasound modes, backscatter coefficients  and ultrasound envelope statistic parametric imaging. The methods used in this field are widely available, have favorable time and financial profiles, and are well accepted by patients. Less is known about their reliability in defining the presence and degree of liver steatosis. Numerous study reports have shown the methods’ favorable negative and positive predictive values in comparison with reference investigations (liver biopsy and MRI). Important research has also evaluated the role of these methods in diagnosing and monitoring non-alcoholic fatty liver disease (NAFLD). Since NAFLD is becoming the dominant global cause of liver cirrhosis, and due to the close but complex interplay of liver steatosis with the coexistence of liver fibrosis, knowledge regarding NAFLD’s influence on the progression of liver fibrosis is of crucial importance. Study findings, therefore, indicate the possibility of using these same diagnostic methods to evaluate the impact of NAFLD on the patient’s liver fibrosis progression risk, metabolic risk factors, cardiovascular complications, and the occurrence of hepatocellular carcinoma. The mentioned areas are particularly important in light of the fact that most of the known chronic liver disease etiologies are increasingly intertwined with the simultaneous presence of NAFLD. In the last twenty years, significant progress has been made in the field of chronic liver disease (CLD) regarding the non-invasive evaluation of its main consequence, liver fibrosis (LF). With the progress of elastographic techniques, pragmatic threshold values have been defined, which enable advanced chronic liver disease  diagnosis to be reliably defined and in a timely manner . AdditioThe evolution of elastographic techniques has contributed to the emergence of ultrasound-based applications that help in assessing and grading LS, both of which are important for prognosis and management decisions that involve CLD patients . The artLS is evaluated through liver tissue histological examination and is defined as the presence of >5% (>10% for the purpose of studies) fat cells in the liver parenchyma. As a non-invasive alternative, the use of CT examination is possible where LS causes a characteristic Hounsfield unit value decrease, but the examination is limited by poor sensitivity and by exposure to ionizing radiation . In receThe following section is a brief overview of the qnUS methods intended for LS evaluation and their technical and clinical features. Only qnUS techniques that report the indexed LS study results are listed. Due to the rapid progress and large number of different technologies, it is very likely that some of the methods or devices are not mentioned in the article. The technical aspect of the applications is intentionally described in a short summary; the reader can refer to the proposed guidelines for a more detailed description . A summaThe presence of fat cells in the liver tissue causes changes in the tissue’s physical properties, which is advantageously exploited by various ultrasound (US) imaging techniques. Liver US can be used due to the wide B-mode US availability, so as to assess the presence of LS when the steatosis degree exceeds 20% of the liver tissue. LS can be graded based on a higher liver echogenicity than that of the renal cortex, impaired visualization of the intrahepatic vessels, and impaired visualization of the diaphragm and posterior right hepatic lobe, due to US signal attenuation ,4. This Another semi-quantitative method, the HRI  assessment, is available on certain US apparatuses where a difference between the liver and kidney echo signal intensities can be calculated. This B-mode ratio has limited value in differentiating higher LS grades, but good performance when detecting LS .Related to this field are qnUS methods, which ensure short bedside examinations, the expression of the final results in numerical form, and non-invasiveness. The methods of this field define various acoustic parameters, which are obtained from raw US data .Methods that define the attenuation coefficient monitor the US signal energy loss as it travels through the tissue. The loss is greater as the liver infiltration with fatty tissue progresses. The main methods of this area are the controlled attenuation parameter (CAP) obtained with a transient elastography device and B-mode ultrasound-guided attenuation imaging .® (Echosens). The study is not time-consuming, is operator-independent, can be carried out by operators without experience in medical imaging and can be used simultaneously for liver stiffness measurement. The CAP numerical value is expressed in dB/m (decibels per meter); its values range from 100 to 400 dB/m, and the final result is the median value of 10 valid measurements . The measurement is probably influenced by female gender (unclear), body mass index (BMI), and the presence of metabolic syndrome ,8,9,10. 3%. The mThe CAP measurement protocol has not been officially defined. Clinical use follows the LF measurement protocol specified by the manufacturer. Studies show conflicting results regarding the impact of the interquartile range (IQR) on the median CAP value reliability. A study by Myers et al. reported that the IQR showed no effect on the final outcome . On the In the studies that compared the LS grade assessment against liver biopsy, it was reported that, compared to MRI-PDFF, CAP defined S2 or S3 with a moderate predictive probability  ,15,16. SThe proposed cut-off values differ in the reported studies, but they are generally comparable if we divide them between the general population area and the NAFLD subpopulation. 2 is added to the final result .A study comparison was also made between the LS CAP assessment and the parameters included in the Aixplorer Mach30 (sound speed plane-wave ultrasound (SSp.PLUS), attenuation plane-wave ultrasound (Att.PLUS), and viscosity plane-wave ultraSound (Vi.PLUS). The cited study defined a suitable correlation between CAP values and SSp.PLUS values. The Att.PLUS correlation with CAP values was not proven .Ultrasound Envelope Statistic Parametric ImagingThis method takes advantage of the US images’ properties, which contain speckle patterns that appear in a granular form. Speckle patterns are generated by the US signal scattering due to microstructures in the tissue; therefore, speckle statistics with the backscatter envelope can describe the tissue-scattering characteristics . VariousAcoustic structure quantification is available on Canon Medical Systems devices and uses a statistical model, which, in the final calculation stage, is converted into a focal disturbance ratio (FD ratio). In fatty livers, the FD ratio theoretically decreases and the mean FD ratio can be used for LS analysis. A special feature of this technology is that the FD ratio measured in the intercostal and subcostal views does not show a significant difference and shows good agreement with the LS assessment .The Nakagami distribution is a generalized statistical model that uses the Nakagami parameter to define scattering characteristics within a tissue. Early studies revealed a significant positive correlation between the Nakagami parameter and the liver tissue lipid concentrations. The method is available as tissue scatter distribution imaging , and the TSI image acquisition process is similar to that of TAI . AccordiThe majority of the data in this area are represented by the use of CAP. The use of the remaining qUS technologies is still the subject of current research and will be important in future clinical evaluations. A summation of the possible clinical use of this area’s most important study data is shown in CAP can be used as a screening tool due to its negative predictive value that is sufficiently sensitive and specific at the suggested threshold values ,9,12. InIn an extensive cross-sectional study on a large number of patients without CLD, it was determined that CAP-defined NAFLD is dependent on weight gain during the 1- and 10-year observation periods. Patients who significantly increased their body weight had a significantly higher risk of developing NAFLD . In the A study by Grgurevic et al. demonstrated that LF progression, which is a major NAFLD complication promotor, is likely to be slow. In the NAFLD and DM2 group, LF evaluation at a two-year interval is recommended . CAP assA study that evaluated the occurrence of cardiovascular complications and their association with CAP in DM2 patients demonstrated that an elevated CAP value is associated with the occurrence of both total and incident myocardial infarction or chronic kidney disease development . PreviouWith nomenclature change proposals (NAFLD vs. MAFLD), the question arises as to whether the diagnostic methods from the NAFLD era would also have value in the MALFD field. A report from the NHANES III  cohort showed that the use of CAP to define LS is, as expected, remarkably comparable in both nomenclature scenarios. It also states that both designations have a similar clinical profile and long-term outcomes. However, there is an important difference, as increased liver-related mortality among NAFLD patients is driven by insulin resistance, but among MAFLD patients, it is primarily driven by coexisting AFLD .An important NAFLD clinical area is the impact of weight loss interventions on LS. Unfortunately, in the last major study in this field, the researchers failed to demonstrate a significant benefit of planned weight reduction on CAP-estimated LS, despite the clear impact of lower body weight on the CAP value itself and its favorable impact on anthropometric and metabolic indicators in both the control and intervention study arms. This result could be a consequence of the current pandemic, so the authors suggest larger trials with more intensive weight-loss interventions . It is iAn interesting Chinese study identified a typical negative correlation between vitamin D3 and osteocalcin values, bone metabolism metabulators, and elevated CAP values .Insights from the sarcopenic obesity  field are important because this condition is crucially related to NAFLD-related frailty and mortality . The resIndividual studies have looked at the use of the CAP, both to assess the degree of LS and to assess LS regression in patients who were bariatric surgery candidates. In a study by Kim et al., a decrease in CAP values that was relative to the surgery’s success in patients with morbid obesity was observed . In the With the transition of HIV infection to that of chronic disease form, research that defines the impact of NALFD in these patients is interesting, particularly because, due to the underlying disease and treatment impact, lipodystrophy is often present. A study by Lemoine et al. with MRI-PDFF as a control showed that CAP can accurately define moderate to severe LS in HIV patients and those with coexisting metabolic syndrome, and/or persistently elevated liver enzymes, and/or clinical lipodystrophy, in comparison to the general population . CAP-assThere are interesting data regarding the impact of LS in patients with HBV and HCV infections. The study findings by Seto et al. indicate that CAP-defined LS was an important factor that independently influenced the LF rate progression in the HBV patient group. LF risk progression was slightly lower in treated patients . A studyThe CAP in combination with liver stiffness measurement (LSM) could be useful to assess the risk of HCC occurrence according to the findings of a study on a general population cohort without HBV or HCV infection and in a cohort with NAFLD and chronic HCV infection ,67,68. DStudies in the cACLD NAFLD/NASH field show a mild, but significantly positive, CAP association with liver-related events, while the absence of CAP-estimated LS exhibited an inverse association with the same events. These results might reflect the negative prognostic LS loss meaning in this specific etiology . AccordiqnUS technologies used for LS evaluation are extremely important when taking into account that the disease has become highly prevalent, its close connection with metabolic syndrome development, its independent impact on patients’ mortality and frailty, and the socioeconomic consequences. The advantages of the methods described in this article are often the (current) disadvantages of the field. A large number of different applications are (currently) poorly validated by studies. There are a large number of studies in small- to medium-sized populations and diagnostic value assessments based only on retrograde meta-analyses. There are also a significant number of studies that use the CAP as a clinical outcome control test, although it has not yet been fully validated. Investigations regarding LS clinical outcomes should be based on comparisons with MRI-PDFF or histological tissue analysis to the greatest extent possible.It is of significant and positive importance that many studies within this area define the concrete role of attenuation assessment (mainly with CAP) for clinical decision making regarding NAFLD exclusion, patients with increased cardiovascular risk stratification, HCC risk assessment , and LS evaluation in the ACLD subgroup.It will be important to define the impact of these non-invasive and widely available methods regarding the area of NAFLD medical interventions, such as the impact of intentional weight reduction and the treatment of metabolic syndrome factors; the importance of LS monitoring in CLD, other than NAFLD, where etiological treatment is possible; the ability to assess ACLD decompensation risk and prognostication in the coronary disease field.Of particular note is the ability of all the listed applications to identify both LS and LF in the same clinical examination. The interplay between LS and LF in the CLD domain is complex, but this possibly shows the important influence on the progression of the portal hypertension stage in the NAFLD ACLD group.Future challenges include the creation of study-supported pragmatic and clinically useful threshold values (CAP and other applications) that would be similar to those used in the LF field. At the same time, it is important to define how to assess LS timeline dynamics (LS progression/regression) and the impact of these dynamics on metabolic risk assessment and LF prognostication. Studies in this field should focus on hard clinical end points and multi-factorial CLDs, and, at the same time, translate the study results to the primary medical care level. Due to the rapid emergence of new applications, it is also necessary to validate how reliable these methods are according to the field’s golden standard (MRI-PDFF).qnUS techniques allow us to quantitatively assess LS with moderate to very good accuracy.The advantage of these methods is the simplicity of the examinations and their non-invasiveness, as well as favorable time and financial profiles.These advantages are clinically important as LS is a major medical challenge, both in terms of the extremely high prevalence of the disease and also because of its possible serious consequences (the appearance of metabolic syndrome and progression to liver cirrhosis).With technological advancements, the presented qnUS methods could gradually take over the current golden standards in this field and facilitate early LS detection and prognostication regarding the role of LS in patients’ metabolic risk stratification and ACLD development.


Feature selection plays a very significant role for the success of pattern recognition and data mining. Based on the maximal relevance and minimal redundancy (mRMR) method, combined with feature subset, this paper proposes an improved maximal relevance and minimal redundancy (ImRMR) feature selection method based on feature subset. In ImRMR, the Pearson correlation coefficient and mutual information are first used to measure the relevance of a single feature to the sample category, and a factor is introduced to adjust the weights of the two measurement criteria. And an equal grouping method is exploited to generate candidate feature subsets according to the ranking features. Then, the relevance and redundancy of candidate feature subsets are calculated and the ordered sequence of these feature subsets is gained by incremental search method. Finally, the final optimal feature subset is obtained from these feature subsets by combining the sequence forward search method and the classification learning algorithm. Experiments are conducted on seven datasets. The results show that ImRMR can effectively remove irrelevant and redundant features, which can not only reduce the dimension of sample features and time of model training and prediction, but also improve the classification performance. With the development of machine learning and artificial intelligence, more and more rich information is obtained from research objects, but some irrelevant and redundant features are added, which leads to higher feature dimensions. For the classification learning, the good learning samples are the key to train the classifier. The irrelevant or redundant information of the samples will increase the complexity of the classification algorithm as well as the time of training and prediction, and directly affect the classification performance. Therefore, it is necessary to select the optimal features that can best represent the characteristic of object, and eliminate irrelevant and redundant features to improve the efficiency of the classifier .m features through the genetic algorithm wrapper. The embedded method puts the feature selection process into the learning algorithm, which is a compromise between the filter method and the wrapper method. For example, Xu et al. [K-nearest neighbor method. Because both the wrapper and embedded methods have certain dependencies on the classification learning algorithm, and are prone to problems such as overfitting and low efficiency. The filter method has high efficiency and is suitable for various data types. The method has strong versatility and low algorithm complexity.Feature selection is the process of selecting the optimal feature subset from the raw feature set to reduce the dimension of the feature space . Its puru et al.  proposedu et al. . Liu et u et al.  proposedIn the filter method, the feature metric is the key factor. That the maximal relevance and minimal redundancy (mRMR) criterion is a filter feature metric for pattern recognition , it aimsF-measure) to determine the effectiveness of the proposed method. Experiments show that the proposed feature selection method on random forest classifier outperforms the original mRMR and other methods.This paper adopts a supervised learning method to perform feature selection on these datasets through ImRMR, and uses advanced machine learning classification algorithm (random forest) to classify these features. In this study, 70% of each dataset was randomly selected for the training dataset, and the remaining 30% was used for the test dataset. We conduct extensive experiments and evaluate on various performance metrics  filtering method to remove the noise features in ransomware, and selected the most relevant feature subset to characterize the real behavior of ransomware. EmRMR requires only a small amount of evaluation, avoiding unnecessary calculations inherent in the original mRMR [In addition, many scholars have improved the mRMR to obtain better feature selection results. Feng and Zhang improved the mRMR by using conditional mutual information formula and three-dimensional calculation to determine the candidate connection of each attribute node in Bayesian network classifier. The method enhanced the reliability and robustness of small sample calculation . Yao et g et al.  improvedg et al.  used thenal mRMR . Combinenal mRMR .The existing improved methods for mRMR are based on the calculation of correlation and redundancy of a single feature, they ignore the joint contribution of multiple features, and do not take into account the calculation of redundancy and correlation between feature subsets. We propose an improve mRMR (ImRMR) based on feature subsets. The proposed method and performance evaluation will be discussed in the following sections.Maximal relevance and minimal redundancy (mRMR) is a filter feature measurement criterion, which calculates the redundancy between features and the correlation between features and class based on mutual information The mutual information mentclass2pt{minimGiven a sample feature set entclass1pt{minimaThe redundancy of all features in The mRMR method seeks the optimal features of the samples with maximal relevance Incremental search is used to quickly and efficiently select the optimal feature set. Given the raw feature set The mRMR method measures the contribution of feature by calculating the relevance and redundancy of individual feature. The joint contribution of multiple features is ignored. Relevance and redundancy are only based on mutual information measures. Therefore, to obtain the optimal feature subset, from the perspective of feature subset, this paper uses two measurement criteria, Pearson correlation coefficient and mutual information to evaluate the relevance and redundancy of the feature subsets. A weight factor is introduced to tradeoff the two measurement criteria.The whole process of proposed ImRMR is shown in Fig. α is introduced to adjust the weight of the two indicators. The features are ranked on relevance. The relevance Given a sample set of  subsets . The relThe range of feature subsets This paper exploits an equal grouping method (EGM) to generate candidate feature subsets. According to the ranking features with relevance, each feature is assigned to a group one by one. When the first-round assignation has finished, the feature will be assigned to a group reversely till the end of the round, and keep going the assignation and swapping directions until all the features assigned to the groups.For example, suppose the number of features entclass1pt{minimaCalculate the relevance of all individual features in each candidate feature subset according to Eq. Calculate the relevance mentclasspt{minimaCombined with Eq. where By calculating the contribution of each candidate feature subset, the ranking sequence of these feature subsets is obtained. It is mainly divided into the following three steps.Take out the features of the feature subsets sequence in turn to find features sequence. The optimal feature subset is obtained according to the ranking features sequence and the SFS search strategy.The feature selection algorithm based on ImRMR and SFS is descripted as follows.In addition, for the ImRMR algorithm, the same Different The hardware platform is a laptop computer with 16G RAM and 11th Gen Intel(R) Core(TM) i7-11370H @ 3.30 GHz CPU. The operating system is Windows 10 64-bit. MATLAB 2018b is the data processing, programming and running platform as well WEKA 3.8.5.Seven datasets were involved in experiments. Five of them are provided by the UCI Machine Learning Repository : Musk daEach dataset is divided into training set and test set as the ratio of 7:3. The information of datasets are listed in Table Two groups experimental scheme are designed. One group compared the proposed method of EGM with the method of randomly selecting features to generate candidate feature subsets. And the other compared the ImRMR with other feature selection methods, such as mRMR, InfoGain (IG) , SymmetrThe four feature selection methods of IG, SU, GR RfF and the classification method of random forest involved in the experiment are all built-in methods in WEKA 3.8.5, which are implemented by MATLAB 2018b calling the interface of WEKA 3.8.5, and the parameters of each feature selection method are default parameters. The mRMR method has no parameter settings, and F-measure.Random forest is an ensemble learning method based on bagging, which can handle classification problems and regression problems well, and is one of the most widely used machine learning methods at present. To verify effectiveness of the proposed ImRMR feature selection method, the random forest classifier is adopted to obtain classification results of the selected optimal feature subset. Each experiment is repeated 30 times independently, and the average of the experimental results is taken as the final result. The evaluation indicators include accuracy rate, dimensionality reduction rate, comprehensive rate, precision, recall and The accuracy rate is used to evaluate the proportion of correctly identified samples to the total number of samples in the prediction results. Its calculation is shown in Eq. The dimensionality reduction rate as an evaluation indictor is introduced, as shown in Eq. The comprehensive rate considers the accuracy rate and the dimensionality reduction rate, as shown in Eq. The precision is used to evaluate the proportion of all predicted correct samples that contain actual correct samples. Its calculation is shown in Eq. The recall rate is the percentage of in all samples where the correct sample is predicted to be correct. Its calculation is shown in Eq. F-measure is precision and recall weighted harmonic mean. F-measure calculation is shown in Eq. In this group experiments, EGM and the method of random grouping are, respectively, applied to the generating candidate feature subsets part of ImRMR, namely ImRMR-EGM and ImRMR-RS. The random grouping method is different from EGM only in that the features of its grouping are randomly assigned, and other parts are consistent with EGM.F-measure and the comprehensive rate when the classification accuracy obtained by the ImRMR-EGM and ImRMR-RS feature selection of the seven datasets reached the maximum value, the performances of the two methods are compared. The experimental results are shown in Table Using SFS search strategy, by recording the dimensionality reduction rate, the accuracy rate, precision, recall, Seen from Table F-measure of ImRMR-EGM are higher than ImRMR-RS. Therefore, the EGM has achieved good results in generating candidate feature subsets, which outperforms the random grouping method.In seven datasets, the comprehensive rate of ImRMR-EGM is higher than that of ImRMR-RS by 0.14–5.42%. And in most cases, the accuracy, precision, recall and F-measure and comprehensive rate when the classification accuracy reaches the maximum.Experiments with ImRMR and other five feature selection methods are conducted on seven datasets. Combine SFS search strategy, the results of various feature selection methods are classified by random forest. Their performances are compared with the evaluation indices including dimensionality reduction rate, accuracy rate, precision, recall, The experimental results are shown in Table F-measure and precision on seven sets of datasets. Therefore, from a comprehensive comparison, the ImRMR feature selection method is superior to the five feature selection methods.Seen from Table From the above comparative experiments, experimental results show that the proposed ImRMR method can effectively remove irrelevant and redundant features, which can not only reduce the dimension of sample features, but also achieve better classification and recognition results.Recently, various researchers have analyzed various feature selection methods due to improved accuracy results. Table To further explore the effectiveness of the feature subset selected by the ImRMR, the sequence forward selection feature subset method (SFSFs) is used for the ranking feature subsets sequence to verify the pros and cons of the feature subset.The optimal feature subset starts with an empty set;The first feature subset in the ordered feature subset set is added for the first time, and then the feature subset is added iteratively according to the order, which is combined with the selected feature subset to form a new feature subset;This process continues until the classification accuracy of the newly mapped training set is greater than or equal to the raw classification accuracy, and the corresponding feature subset is the selected optimal feature subset.The steps of the SFSFs are as below.F-measure and precision when the classification accuracy with feature selection is greater than or equal to that of the raw datasets.The feature selection method based on SFSFs is shown in Fig. The experimental results are shown in Table F-measure and precision on the seven datasets in most cases. Therefore, in a comprehensive comparison, with SFSFs the ImRMR feature selection method is superior to the five feature selection methods such as mRMR, IG, SU, GR, and RfF, and can effectively measure the contribution of feature subset to obtain an effective ranking feature subsets sequence.From Table Extend the method to more datasets.This study currently proposes EGM to divide candidate feature subsets. Other more feature subset division methods are needed to be explored to improve the quality of candidate feature subsets.This study only uses Pearson correlation coefficient and mutual information to measure correlation and redundancy. In the next work, we will try to explore other measurement criteria to improve the effectiveness of the selected features.This paper improves mRMR based on feature subsets, and proposes the ImRMR method, which is used to select efficient feature sets, reduce the dimension of feature sets, and improve the classification performance of samples. There still exists more issues to carry out in the future work, and some of the most important points are listed below:In this paper, considering the joint contribution between multiple features, the proposed ImRMR method expands the feature selection process based on feature subset.EGM is used to divide the raw feature set into multiple different candidate feature subsets. Two criteria of Pearson’s correlation coefficient and mutual information are used to calculate the correlation and redundancy of candidate feature subsets, and weights are introduced to tradeoff both criteria. Then the SFS search strategy is combined for the ranking feature subsets sequence to obtain the optimal feature subset. Compared with five methods, including mRMR, InfoGain, Symmetrical Uncert, GainRatio, and ReliefF, experimental results verified the effectiveness on seven datasets. In most cases, ImRMR outperforms the other methods, and can effectively obtain the optimal feature subset and improve the performance of the classification.


The COVID-19 pandemic has brought to the fore the need for policy makers toreceive timely and ongoing scientific guidance in response to this recentlyemerged human infectious disease. Fitting mathematical models of infectiousdisease transmission to the available epidemiological data provide a keystatistical tool for understanding the many quantities of interest that are notexplicit in the underlying epidemiological data streams. Of these, the effectivereproduction number,  The virus was identified as a novel strain of coronavirus on 7 January 2020, subsequently named severe acute respiratory syndrome coronavirus 2(SARS-CoV-2), causing the respiratory syndrome known as COVID-19. The outbreak hassince developed into a global pandemic. As of 3 August 2020, the number of confirmedCOVID-19 cases was approaching 18 million, with more than 685,000 deaths occurring worldwide. Faced with these threats, there is a need for robust predictive models thatcan help policy makers by quantifying the impact of a range of potential responses.However, as is often stated, models are only as good as the data that underpin them;it is therefore important to examine, in some detail, the parameter inferencemethods and agreement between model predictions and data.In late 2019, accounts emerged from Wuhan city in China of a virus of unknown originthat was leading to a cluster of pneumonia cases.In the UK, the first cases of COVID-19 were reported on 31 January 2020 in the cityof York. Cases continued to be reported sporadically throughout February and by theend of the month, guidance was issued stating that travellers from the high-riskepidemic hotspots of Hubei province in China, Iran and South Korea shouldself-isolate upon arrival in the UK. By mid-March, as the number of cases began torise, there was advice against all non-essential travel and, over the coming days,several social-distancing measures were introduced including the closing of schools,non-essential shops, pubs and restaurants. This culminated in the introduction of aUK lockdown, announced on the evening of 23 March 2020, whereby the public wereinstructed to remain at home with four exceptions: shopping for essentials; anymedical emergency; for one form of exercise per day; and to travel to work ifabsolutely necessary. By mid-April 2020, these stringent mitigation strategies beganto have an effect, as the number of confirmed cases and deaths as a result of thedisease began to decline. As the number of daily confirmed cases continued todecline during April, May and June, measures to ease lockdown restrictions began,with the reopening of some non-essential businesses and allowing small groups ofindividuals from different households to meet up outdoors, whilst maintaining socialdistancing. This was followed by gradually reopening primary schools in England from1 June 2020 and all non-essential retail outlets from 15 June 2020. Predictivemodels for the UK are therefore faced with a changing set of behaviours againstwhich historic data must be judged and an uncertain future of potential additionalrelaxations. Note, the effective reproduction number differs from the basic reproductionnumber, Throughout, a significant factor in the decision-making process was the value of theeffective reproduction number, The initial understanding of key epidemiological characteristics for a newly emergentinfectious disease is, by its very nature of being novel, extremely limited andoften biased towards early severe cases. Developing models of infectious diseasedynamics enables us to challenge and improve our mechanistic understanding of theunderlying epidemiological processes based on a variety of data sources. One waysuch insights can be garnered is through model fitting/parameter inference, theprocess of estimating the parameters of the mathematical model from data. The taskof fitting a model to data is often challenging, partly due to the necessarycomplexity of the model in use, but also because of data limitations and the need toassimilate information from multiple sources of data. In full, the posterior distribution of the parameters  Simulating this Markov chain thus allows us to draw sets of parameters fromthe joint posterior distribution.Throughout this work, the process of model fitting is performed under a Bayesianparadigm, where knowledge of the parameters are modelled through random variablesand have joint probability distributions. with examples during the present pandemic including analyses of the effect ofnon-pharmaceutical interventions (NPIs) on curbing the outbreak of COVID-19 in the UK..Adopting a Bayesian approach to parameter inference means parameter uncertainty maythen be propagated if using the model to make projections. This affords models withmechanistic aspects, through computational simulation, the capability of providingan estimated range of predicted possibilities given the evidence presentlyavailable. Thus, models can demonstrate important principles about outbreaks, to the available public health data streams and estimating keyepidemiological quantities such as In this paper, we present the inference scheme, and its subsequent refinements,employed for calibrating the Warwick SARS-CoV-2 transmission and COVID-19 disease modelWe begin by describing our mechanistic transmission model for SARS-CoV-2 in Section2, detailing in Section 3 how the effects of social distancing are incorporatedwithin the model framework. To fit the model to data streams pertaining to criticalcare, such as hospital admissions and bed occupancy, Section 4 expresses howepidemiological outcomes were mapped onto these quantities. In Section 5, we outlinehow these components are incorporated into the likelihood function and the adoptedMCMC scheme. The estimated parameters are then used to measure epidemiologicalmeasures of interest, such as the growth rate (The closing sections draw attention to how model frameworks may evolve during adisease outbreak as more data streams become available and we collectively gain abetter understanding of the epidemiology (Section 7). We explore how keyepidemiological quantities, in particular the reproduction number Here we present the University of Warwick SEIR-type compartmental age-structuredmodel, developed to simulate the spread of SARS-CoV-2 within regions of the UK.Matched to a variety of epidemiological data, the model operates and is fitted todata from the seven NHS regions in England  and the three devolvednations . The model incorporates multiplelayers of heterogeneity, through partitioning the population into five-year ageclasses, tracking symptomatic and asymptomatic transmission, accounting forhousehold saturation of transmission and household quarantining.The population is stratified into multiple compartments with respect to SARS-CoV-2infection status : individThe model is deterministic in structure, based on a large set of coupled ordinarydifferential equations (ODEs). The continuous results from these ODEs are nevergoing to precisely match the discrete integer-valued data. We therefore assume thatthe observed data are an imprecise measure of the modelled quantities and representthis through a distribution  centred around the solutionof the ODEs.We provide a description of the model parameters in  although other sources such as POLYMOD could be used, with the modification of these contact patterns to modelsocial distancing measures explained in Section 3. The forces of infection govern the non-linear transmission of infection. Wepartition the infectious pressure exerted on a given age group 14 Therefore, we instead make a number of approximationsin our model to achieve a comparable effect.We wanted our model to be able to capture both individual-level quarantining andisolation of households with identified cases. In a standard ODE framework, theincorporation of the household structure increases the dimensionality of thesystem. Combined with the inclusion of other heterogeneities, such as agestructure, the result can be a system whose dimensionality results in modelcalibration and simulation only being achievable at a large computationalexpense.We make the simplification that all within household transmission originates fromthe first infected individual within the household , a next-generation approach can be used to relate thenumbers of newly infected individuals in the various categories in consecutive generations. We argue that a low  yet children do not appear to play a major role intransmission.19 To some extent, the separation into symptomatic , the ISARIC WHO Clinical Characterisation Protocol UK (CCP-UK) databasesourced from the COVID-19 Clinical Information Network (CO-CIN),23 and the PHEsero-surveillance of blood donors. CHESS data is used to define the probabilities of different outcomes  is highly biased by the testingprotocols at any given point in time. It is therefore necessary to convert infectionestimates into quantities of interest that can be compared to data. We consideredsix such quantities which we calculated from the number of newly detectablesymptomatic infections on a given day However, these distributions all represent a national average and do not thereforereflect regional differences. We therefore define regional scalings of the three keyprobabilities  and the impactof observable quantities (with the delay to deaths being multiple weeks). Secondly,they cannot readily utilise multiple data streams. Finally, they can only be used toextrapolate into the future – extending the period of exponential behaviour – theycannot predict the impact of further changes to the policy. Our approach is toinstead fit the ODE model to multiple data streams, and then use the daily incidenceto calculate the growth rate. Since we use a deterministic set of ODEs, theinstantaneous growth rate There has been a strong emphasis  on the value of thereproductive number , there areinevitably different time scales from when a change in policy or adherence occursand when its impact is observed in key quantities. We briefly assess this problem inAs mentioned in Section 7, the number of phases used to describe the reduction intransmission due to lockdown has changed as the situation, model and data evolved.The model began with just two phases; before and after lockdown. However, in lateMay 2020, following the policy changes on 13 May 2020, we explored having threephases. Having three phases is equivalent to assuming the same level of adherence tothe lockdown and social-distancing measures throughout the epidemic, with changes intransmission occurring only due to the changing policy on 23 March 2020 and 13 May2020. However, a different number of phases can be explored  could lead to biased results.Hospital admissions for COVID-19 are comprised of two measures: We now wish to compare how the fits made weekly (or more frequently) from late Marchto early June 2020 compare to later results. We note that this period also sawconsiderable development of the model structure as more data streams becameavailable.We used a fit to the data performed on 14 June 2020  to infer thechange in NPIs and adherence, The time profile of the predicted growth rate illustrates how the imposition oflockdown measures on 23 March 2020 led to une 2020 .The relative strength of lockdown restrictions parameter, bove 0 . As the bove 0 .Using parameters drawn from the posterior distributions, the model producespredictive posterior distributions for multiple health outcome quantities that havea strong quantitative correspondence to the regional observations . We reco to the available health care, mortality and serological data streams. We havefocused on the period May–June 2020, which corresponds to the first wave of theoutbreak; a brief account of further refinements is given below. The work wedescribe was performed under extreme time pressures, working from limited initialknowledge and with data sources of varying quality. There are therefore assumptionsin the model that with time and hindsight we have refined and compared to other morerecently available data sources; similarly, the focus on hotspots of infectionduring the summer and the rise in cases into autumn 2020 has shaped much of ourmethodology. This article relates the model formulation that was used to understandthe dynamics, predict cases and advise policy during the first wave.In this study, we have provided an overview of the evolving MCMC inference schemeemployed for calibrating the Warwick COVID-19 modelA comparison of model short-term predictions and data over time (i.e. as the outbreakhas progressed) demonstrated an observable decline in the error – suggesting thatour model and inference methods have improved. We have considered in some detail thechoice of data sets used to infer model parameters and the impact of this choice onthe key emergent properties of the growth rate wth rate  and may wth rate . Howeverwth rate  is shown comparing intra-chain with inter-chain variability . Yet, in the midst of a global public health emergency such as apandemic, there are extremely short time scales over which the results need to begenerated. In this instance, the speed of the epidemic meant that results needed tobe produced every 2–3 days. Results were required even if full convergence had notbeen achieved, precluding any regular assessment of convergence and mixing – on thebasis that a reasonable but imperfect answer was better than none. These reflections signpost that attention should be paid to ensuring adequateresearch support is provided to permit the design of more robust and efficient waysof performing statistical inference for complex models in real-time.It is important that uncertainty in the parameters governing the transmissiondynamics, and its influence on predicted outcomes, be robustly conveyed. Without it,decision-makers will be missing meaningful information and may assume a false senseof precision. MCMC methodologies were a suitable choice for inferring parameters inour model framework, since we were able to evaluate the likelihood function quicklyenough to make the approach feasible. However, a fundamental part of assessingwhether your empirical estimates of the posterior distributions is valid and robust,which we have omitted to discuss thus far, is the use of MCMC convergencediagnostics. In the early stages of code development, we were checking convergenceusing the Gelman–Rubin test,2628 We also recognise theappropriate mathematical structure of the model is also uncertain. Our methodologyis formulated around deterministic differential equations that work well for largepopulations and significant levels of infection. On the other hand, stochasticeffects are ignored and stochastic approaches may be needed when modelling lowinfection level regimes. In addition, a subset of our parameters had fixed valuesthroughout our analyses, which means we may have underestimated the overall amountof parameter uncertainty.Nevertheless, for some model formulations and data, it may not be possible to writedown or evaluate the likelihood function. In these circumstances, an alternativeapproach to parameter inference is via simulation-based, likelihood-free methods,such as approximate Bayesian computation. This is particularly crucial as new interventions are introduced orsignificant policy changes occur, such as the relaxation of multiple NPIs duringMay, June and July of 2020 or the introduction of the nationwide ‘test and trace’ protocol. Predicting the impact of such changes will inevitability be delayed by thelag between deployment and the effects on observable quantities  is documented here  and 8 anantities  as well ; and the development and delivery of vaccines from December 2020 onwards. The two variants have necessitated an increase in the dimension of the ODEsas at least two variants need to be modelled simultaneously ; the two new variants alsorequire the estimation of variant-specific parameters governing their relativetransmission rates and the proportion of infected individuals that require hospitaltreatment or die from the disease. The spread of these two variants is captured by looking at ‘S-gene failures’:the TaqPath system used to perform polymerase chain reaction (PCR) tests in manyregions of the country fails to detect the S-gene of Alpha due to a point mutation.The rise of Alpha is therefore determined by the increase of S-gene failures, whilethe decline of Delta is captured by the decline of S-gene failures. Vaccination alsorequires a large number of parameters: in particular, the vaccine efficacy after oneand two doses against infection, symptoms, severe illness and hospitalisation,death, and against both Alpha and Delta variants are needed within the model. Wetreat these additional parameters as inputs to the model, based on the estimationsmade by Public Health England.Multiple refinements to the model structure and approaches have been realised sinceJune 2020 and more are still possible. The three biggest changes have been forced byexternal events: the rise and spread of the Alpha (B.1.1.7) variant during thelatter part of 2020; the rise and spread of the Delta (B.1.617.2) in April and Mayof 2021 is incorporated into the likelihood and helps to anchor the total number ofpreviously infected individuals in each region. More consideration has been given todetecting changes in the strength of social distancing (Other changes to the model structure include using the proportion of community (knownas Pillar 2) PCR samples that are positive rather than the number of positive tests.We feel that this proportion is less likely to be biased by changes in testingbehaviour, and so provide a more stable estimate of the level of infection in thecommunity. We also no longer use serology data from blood-donors, as again this islikely to suffer from a number of confounding factors. Instead, data from thenational REACT 2 study36 while significant mortality is due to infection in carehomes38 suggests that additional compartments capturing thesecomponents could greatly improve model realism if the necessary data were availablethroughout the course of the epidemic. Similarly, schools, universities and someworkplaces pose additional risks, so there is merit in considering how theseamplifiers of community infection could be incorporated within the generalframework.3941 Additionally,if in a regime with much lower levels of infection in the community, it may beprudent to adopt a stochastic model formulation at a finer spatial resolution tocapture localised outbreak clusters, although the potential heterogeneity in localparameters may preclude accurate prediction at this scale.Despite all of these improvements over the last year, there are still aspects thatcould be further improved. The understanding that infection may be partially drivenby nosocomial transmission,In summary, if epidemiological models are to be used as part of the scientificdiscussion of controlling a disease outbreak it is vital that these models capturecurrent biological understanding and are continually matched to all available datain real-time. Our work on COVID-19 presented here highlights some of the challengeswith predicting a novel outbreak in a rapidly changing environment. Probably thegreatest weakness is the time that it inevitably takes to respond – both in terms ofdeveloping the appropriate model and inference structure, and the mechanisms toprocess any data sources, but also in terms of delay between real-world changes andtheir detection within any inference scheme. Both of these can be shortened bywell-informed preparations; having the necessary suite of models supported by thelatest most efficient inference techniques could be hugely beneficial when rapid androbust predictive results are required.Click here for additional data file.Supplemental material, sj-pdf-1-smm-10.1177_09622802211070257 for Fitting to theUK COVID-19 outbreak, short-term forecasts and estimating the reproductivenumber by Matt J. Keeling, Louise Dyson, Glen Guyver-Fletcher, Alex Holmes,Malcolm G Semple, , Michael J. Tildesley and Edward M. Hill in StatisticalMethods in Medical Research


Facial ageing is a result of superficial wrinkling combined with changes to the underlying soft tissues and skeleton. The influence of tooth loss, as a geriatric characteristic, on facial appearance is still poorly explained. The aim was to evaluate the facial characteristics of older adults, correlate these characteristics with the dentition and make comparisons with young adults using a non-invasive 3D methodology.P < 0.05).90 participants older than 65 years, classified into 3 subgroups  and 30 young adults were evaluated. Their faces were scanned with an optical Artec 3D-scanner. Cephalometric analyses were made using the RapidForm computer program. An independent t-test and ANOVA were used for the comparisons. Pairwise, post-hoc tests were applied with respect to the significant differences , narrower upper- and lower-lip vermilions and larger facial and lower-facial-height angles, resulting in a flat facial profile.The facial changes due to ageing are the most pronounced in the edentulous. In comparison with the toothed, they have a smaller facial height due to the smaller lower facial height, larger nasolabial angle, smaller mouth width, shorter upper lip and narrower lip vermilions. Their profile is flatter and their lips are more retruded.The proportions of the whole face are changed in older adults and they are the most expressed when this is combined with tooth loss.The online version contains supplementary material available at 10.1186/s12877-022-03190-5. The face is the most important part of the human body in the psychosocial sense. The negative impacts of exposure to the sun, smoking and a low BMI with respect to facial ageing are known and do not correspond with a high social status, a low depression score and being married, which are associated with a younger look . The infDental caries and periodontal disease are the main causative factors of tooth loss and, eventually, if untreated, lead to edentulism . In the Facial ageing represents the transition from youth, where there is an optimal relationship between the bone morphology and the volume of the soft-tissue envelope, to the imbalances between these components that lead to the stigma of an aged face . This isThe irreversible alveolar ridge resorption of both jaws follows the loss of teeth, while the mean number of lost teeth increases with age . The losThe loss of supporting bones and teeth strongly influences the covering soft tissues and leads to the formation of wrinkles and compensatory mechanisms of the mimic muscles . Senile So far there is no reliable study that would determine the influence of edentulism on the facial appearance of older adults. The aim of our research was to objectively evaluate the characteristics of older adults’ faces in correlation with dentition and compare them with the young adults’ faces using a non-invasive 3D methodology.The study included 90 participants older than 65 years  and 30 controls . The inclusion criteria were no craniofacial anomaly, no history of major facial trauma, no history of plastic or orthognathic surgery, no facial paresis and no tremor. Male participants with facial hair were excluded to avoid artefacts. The older adults were classified into three subgroups. The first subgroup consisted of completely edentulous participants , the second subgroup consisted of partially edentulous participants  and the third subgroup were toothed participants . The edentulous subgroup contained participants who had lost all their teeth at least 5 years previously . In the partially edentulous subgroup, there were participants with 5 or more teeth. They had unstable occlusion, the intecuspal position was not repeatable and the vertical dimension of the occlusion was not maintained. The average number of teeth in the partially edentulous women was 11 ± 5 teeth and in the partially edentulous men, 9 ± 4 teeth. Two-thirds of these teeth were in the intercanine region and one-third in the transcanine region. The missing teeth were not replaced with fixed prosthodontics, but the participants had partial dentures, which were removed during the scanning. In the toothed subgroup were participants with a stable occlusion, a repeatable intecuspal position and the vertical dimension of the occlusion was maintained. They had all their teeth in the intercanine region and 3 or more functional dental units of posterior teeth. A premolar in occlusal contact was counted as 1 occlusal unit and the whole molar crown in the occlusal contact was counted as 2 occlusal units. They had no removable dentures. The subjects in the control group had complete dentition with second molars. A flowchart with the composition of the groups is shown in Fig. The 3D facial scans were obtained from all the participants using an Artec 3D scanner, which uses the flying-triangulation method for the surface scanning . It is aDuring the image acquisition, special attention was given to positioning the participant and relaxing the facial musculature. The participants were sat in a relaxed posture with a natural head position, looking to the front with a relaxed mouth-closed position (without contractions of the mouth muscles). The instructions were to not to swallow and keep both eyes open during the acquisition of the image, which took less than 10 seconds. The natural position of the head was achieved by moving it up and down a few times and then stopping the movement and looking into the distance. The relaxed mouth-closed position was achieved with repeated wide opening and closing of the mouth until light contact of the lips was achieved. All dentures were removed from the mouth.The 3D surface images were then further processed using Artec Studio software to obtain 3D scans in STL format. A subsequent analysis was then conducted using the computer program RapidForm 2006 (INUS Technology Inc.). The 3D cephalometric analyses of 39 superficial facial landmarks were determined on 3D facial scans  were included in the experimental group and 30 participants  were in the control group. The average body-mass index (BMI) of the older adults was 27.2 in the male group and 26.6 in the female group. In the control group the BMIs were significantly lower . The sex, age and BMI of the participants in the three research subgroups and the control group are presented in Table p = 0.001), and close to statistical significance (p = 0.071) in the female group. The older adults had longer faces than the control group, and statistically significant (p = 0.000) in the male group. They had a longer middle facial height in comparison to the control group, statistically significant only in the male group (p = 0.010) and a larger lower facial height than the controls. Facial height and lower facial height were significantly smaller in the completely edentulous subgroup than in the toothed subgroup for both sexes.The facial width of the older adults was larger in both sexes compared to the control group. The difference in the male group was statistically significant (p = 0.072). The upper- and lower-lip rednesses were statistically significantly narrower in the group of older adults for both sexes, while the completely edentulous subgroup had the narrowest rednesses,The completely edentulous participants of both sexes had statistically significant narrower mouths than the toothed. The upper-lip height was longer in the group of older adults, and close to statistical significance in the male group (p = 0.084).Older men had statistically significant longer noses than the young adults, but no statistical significance was found in the female group (p = 0.000) larger facial angle than the young adults. The largest facial angle was found for the completely edentulous participants, and this is statistically significant for the females.Older adults, especially the completely and partially edentulous, had statistically significant longer distances between the upper and lower lips and the E-line. They had a statistically significant (p = 0.000) smaller in the group of older adults in comparison with the control group.The soft-tissue ANB angle was significantly ; the older adults had significantly higher BMIs than the younger ones, but there were no obese subjects among them. There were no differences in BMIs between our subgroups of old adults and there were no differences regarding the sex in the group of old adults. Also, it is known that, for example, high-BMI-conditioned changes to the face are ethnically and racially conditioned . So we hDifferent studies have shown that the face becomes wider with age . In our Among the facial heights we excluded the parameter known as the upper facial height, because of the large variability in the position of the trichion point, especially in the male group. Some studies found that the total facial height increases with age and the same was observed in our study, but some studies have shown consistency in facial height in spite of tooth loss . We assuThe facial height and the lower facial height were smaller in the completely edentulous subgroup. Barlett et al. have studied skull differences in the toothed and edentulous older adults and discovered a shortening of the facial height, because of a shortening of the lower facial height as a result of teeth loosening and atrophy in both jaws . When coApart from the eyes, the most recognizable part of every face is the mouth. Ageing has no impact on the width of the mouth, but tooth loss does. The completely edentulous participants had narrower mouths than the toothed. Sex dimorphism is observed for this parameter, with men having wider mouths than women . The uppThe nose is a very significant part of the face and has his own characteristics. In our study we identified nose prolongation with age, no matter the shape and the size of the nose. Older men had longer noses than the young adults. The prolongation of the nose is a consequence of the intrinsic loosening of the lower lateral alar cartilages and the supporting ligaments . We discIn the profile view of the scan we investigated the distance between the upper and lower lip and the aesthetic line (E-line). Ageing and tooth loss have an important influence on these two parameters. Longer distances between the upper and lower lip and the E-line in the group older of adults means they have poorer facial aesthetics.The angles that we studied were the facial angle, the soft-tissue ANB angle, the angle of the lower facial height and the nasolabial angle. Older adults had a larger facial angle than the young adults, which means they had a flatter profile.In our study we placed the soft-tissue points a, n, b corresponding to the bone points in the skeletal angle ANB. In a systematic review of the existing literature we did not find any study relating to the soft-tissue ANB-angle changes in connection with dentition. The soft-tissue ANB angle was smaller in the group of older adults, which is a result of a narrowing of the upper lip and changing the a point position. The change was larger in the female group, because of the more voluminous upper lip. The soft-tissue ANB decreases with tooth loss as a result of maxilla and mandibular atrophy. After loosening of the teeth, especially in the upper jaw, the upper lip is retruded. The statistically significant differences were just in the female subgroups, which means that it is a sex-dependent parameter.The greater lower-facial-height angle in the group of older adults indicates the retrusion of the perioral tissues. With tooth loss there was a tendency to increase the angle. Studies have shown that the skeletal angle ANB, the inclination of the incisors and canines – supporting the upper lip and ptosis of tip of the nose – have the main impact on the nasolabial angle . In our We wanted to simplify the facial changes due to ageing with facial ratios, but this did not prove to be a good indicator. For the ratio between the facial height and the width there were no statistically significant differences, because of the changes in both directions.The study by Pucciarelli et al. has some similarities with ours when comparing the facial characteristics of older, toothed participants with edentulous ones  In generOur goal was to quantify the facial changes observed in an ageing face. We also wanted to evaluate the influence of edentulism. Age influences the facial width and leads to a longer total facial height, as a result of a longer middle facial height. The upper lip is longer and the nose is larger in the elderly. The upper- and lower-lip rednesses are narrower. The facial and the lower-facial-height angles are larger, resulting in a flat facial profile. The nasolabial angle is smaller due to the nose ptosis.The facial changes in the elderly are the most pronounced in the completely edentulous. In comparison with the toothed group, they have a smaller facial height due to the smaller lower facial height and the larger nasolabial angle. The mouth width is smaller, the upper lip is shorter, and there is a narrower upper- and lower-lip redness. Their profile is flatter and both lips more retruded than in the subjects with teeth.Our study confirmed the influence of edentulism on the facial characteristics of older adults.Additional file 1.