Cryo-EM model validation recommendations based on outcomes of the 2019 EMDataResource challenge

This paper describes outcomes of the 2019 Cryo-EM Model Challenge. The goals were to (1) assess the quality of models that can be produced from cryogenic electron microscopy (cryo-EM) maps using current modeling software, (2) evaluate reproducibility of modeling results from different software developers and users and (3) compare performance of current metrics used for model evaluation, particularly Fit-to-Map metrics, with focus on near-atomic resolution. Our findings demonstrate the relatively high accuracy and reproducibility of cryo-EM models derived by 13 participating teams from four benchmark maps, including three forming a resolution series (1.8 to 3.1 Å). The results permit specific recommendations to be made about validating near-atomic cryo-EM structures both in the context of individual experiments and structure data archives such as the Protein Data Bank. We recommend the adoption of multiple scoring parameters to provide full and objective annotation and assessment of the model, reflective of the observed cryo-EM map density.

Comparative analysis of methods for evaluation of protein models against native structures

MOTIVATION

Measuring discrepancies between protein models and native structures is at the heart of development of protein structure prediction methods and comparison of their performance. A number of different evaluation methods have been developed; however, their comprehensive and unbiased comparison has not been performed.

RESULTS

We carried out a comparative analysis of several popular model assessment methods (RMSD, TM-score, GDT, QCS, CAD-score, LDDT, SphereGrinder and RPF) to reveal their relative strengths and weaknesses. The analysis, performed on a large and diverse model set derived in the course of three latest community-wide CASP experiments (CASP10-12), had two major directions. First, we looked at general differences between the scores by analyzing distribution, correspondence and correlation of their values as well as differences in selecting best models. Second, we examined the score differences taking into account various structural properties of models (stereochemistry, hydrogen bonds, packing of domains and chain fragments, missing residues, protein length and secondary structure). Our results provide a solid basis for an informed selection of the most appropriate score or combination of scores depending on the task at hand.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Assessment of chemical-crosslink-assisted protein structure modeling in CASP13

With the advance of experimental procedures obtaining chemical crosslinking information is becoming a fast and routine practice. Information on crosslinks can greatly enhance the accuracy of protein structure modeling. Here, we review the current state of the art in modeling protein structures with the assistance of experimentally determined chemical crosslinks within the framework of the 13th meeting of Critical Assessment of Structure Prediction approaches. This largest-to-date blind assessment reveals benefits of using data assistance in difficult to model protein structure prediction cases. However, in a broader context, it also suggests that with the unprecedented advance in accuracy to predict contacts in recent years, experimental crosslinks will be useful only if their specificity and accuracy further improved and they are better integrated into computational workflows.

Cryo-electron microscopy targets in CASP13: Overview and evaluation of results

Structures of seven CASP13 targets were determined using cryo-electron microscopy (cryo-EM) technique with resolution between 3.0 and 4.0 Å. We provide an overview of the experimentally derived structures and describe results of the numerical evaluation of the submitted models. The evaluation is carried out by comparing coordinates of models to those of reference structures (CASP-style evaluation), as well as checking goodness-of-fit of modeled structures to the cryo-EM density maps. The performance of contributing research groups in the CASP-style evaluation is measured in terms of backbone accuracy, all-atom local geometry and similarity of inter-subunit interfaces. The results on the cryo-EM targets are compared with those on the whole set of eighty CASP13 targets. A posteriori refinement of the best models in their corresponding cryo-EM density maps resulted in structures that are very close to the reference structure, including some regions with better fit to the density.

Assessing the accuracy of contact predictions in CASP13

The accuracy of sequence-based tertiary contact predictions was assessed in a blind prediction experiment at the CASP13 meeting. After 4 years of significant improvements in prediction accuracy, another dramatic advance has taken place since CASP12 was held 2 years ago. The precision of predicting the top L/5 contacts in the free modeling category, where L is the corresponding length of the protein in residues, has exceeded 70%. As a comparison, the best-performing group at CASP12 with a 47% precision would have finished below the top 1/3 of the CASP13 groups. Extensively trained deep neural network approaches dominate the top performing algorithms, which appear to efficiently integrate information on coevolving residues and interacting fragments or possibly utilize memories of sequence similarities and sometimes can deliver accurate results even in the absence of virtually any target specific evolutionary information. If the current performance is evaluated by F-score on L contacts, it stands around 24% right now, which, despite the tremendous impact and advance in improving its utility for structure modeling, also suggests that there is much room left for further improvement.

Small angle X-ray scattering-assisted protein structure prediction in CASP13 and emergence of solution structure differences

Small angle X-ray scattering (SAXS) measures comprehensive distance information on a protein's structure, which can constrain and guide computational structure prediction algorithms. Here, we evaluate structure predictions of 11 monomeric and oligomeric proteins for which SAXS data were collected and provided to predictors in the 13th round of the Critical Assessment of protein Structure Prediction (CASP13). The category for SAXS-assisted predictions made gains in certain areas for CASP13 compared to CASP12. Improvements included higher quality data with size exclusion chromatography-SAXS (SEC-SAXS) and better selection of targets and communication of results by CASP organizers. In several cases, we can track improvements in model accuracy with use of SAXS data. For hard multimeric targets where regular folding algorithms were unsuccessful, SAXS data helped predictors to build models better resembling the global shape of the target. For most models, however, no significant improvement in model accuracy at the domain level was registered from use of SAXS data, when rigorously comparing SAXS-assisted models to the best regular server predictions. To promote future progress in this category, we identify successes, challenges, and opportunities for improved strategies in prediction, assessment, and communication of SAXS data to predictors. An important observation is that, for many targets, SAXS data were inconsistent with crystal structures, suggesting that these proteins adopt different conformation(s) in solution. This CASP13 result, if representative of PDB structures and future CASP targets, may have substantive implications for the structure training databases used for machine learning, CASP, and use of prediction models for biology.

Assessment of protein model structure accuracy estimation in CASP13: Challenges in the era of deep learning

Scoring model structure is an essential component of protein structure prediction that can affect the prediction accuracy tremendously. Users of protein structure prediction results also need to score models to select the best models for their application studies. In Critical Assessment of techniques for protein Structure Prediction (CASP), model accuracy estimation methods have been tested in a blind fashion by providing models submitted by the tertiary structure prediction servers for scoring. In CASP13, model accuracy estimation results were evaluated in terms of both global and local structure accuracy. Global structure accuracy estimation was evaluated by the quality of the models selected by the global structure scores and by the absolute estimates of the global scores. Residue-wise, local structure accuracy estimations were evaluated by three different measures. A new measure introduced in CASP13 evaluates the ability to predict inaccurately modeled regions that may be improved by refinement. An intensive comparative analysis on CASP13 and the previous CASPs revealed that the tertiary structure models generated by the CASP13 servers show very distinct features. Higher consensus toward models of higher global accuracy appeared even for free modeling targets, and many models of high global accuracy were not well optimized at the atomic level. This is related to the new technology in CASP13, deep learning for tertiary contact prediction. The tertiary model structures generated by deep learning pose a new challenge for EMA (estimation of model accuracy) method developers. Model accuracy estimation itself is also an area where deep learning can potentially have an impact, although current EMA methods have not fully explored that direction.

Assessment of protein assembly prediction in CASP13

We present the assembly category assessment in the 13th edition of the CASP community-wide experiment. For the second time, protein assemblies constitute an independent assessment category. Compared to the last edition we see a clear uptake in participation, more oligomeric targets released, and consistent, albeit modest, improvement of the predictions quality. Looking at the tertiary structure predictions, we observe that ignoring the oligomeric state of the targets hinders modeling success. We also note that some contact prediction groups successfully predicted homomeric interfacial contacts, though it appears that these predictions were not used for assembly modeling. Homology modeling with sizeable human intervention appears to form the basis of the assembly prediction techniques in this round of CASP. Future developments should see more integrated approaches where subunits are modeled in the context of the assemblies they form.

CASP13 target classification into tertiary structure prediction categories

Protein target structures for the Critical Assessment of Structure Prediction round 13 (CASP13) were split into evaluation units (EUs) based on their structural domains, the domain organization of available templates, and the performance of servers on whole targets compared to split target domains. Eighty targets were split into 112 EUs. The EUs were classified into categories suitable for assessment of high accuracy modeling (or template-based modeling [TBM]) and topology (or free modeling [FM]) based on target difficulty. Assignment into assessment categories considered the following criteria: (a) the evolutionary relationship of target domains to existing fold space as defined by the Evolutionary Classification of Protein Domains (ECOD) database; (b) the clustering of target domains using eight objective sequence, structure, and performance measures; and (c) the placement of target domains in a scatter plot of target difficulty against server performance used in the previous CASP. Generally, target domains with good server predictions had close template homologs and were classified as TBM. Alternately, targets with poor server predictions represent a mixture of fast evolving homologs, structure analogs, and new folds, and were classified as FM or FM/TBM overlap.

Distribution of evaluation scores for the models submitted to the second cryo-EM model challenge

142 protein structure models were submitted to second Cryo-EM model challenge (2015–2016). Accuracy of the models was evaluated with 54 evaluation scores. Results of the descriptive statistical analysis of the scores are provided in this article.

Assessment of contact predictions in CASP12: Co-evolution and deep learning coming of age

Following up on the encouraging results of residue-residue contact prediction in the CASP11 experiment, we present the analysis of predictions submitted for CASP12. The submissions include predictions of 34 groups for 38 domains classified as free modeling targets which are not accessible to homology-based modeling due to a lack of structural templates. CASP11 saw a rise of coevolution-based methods outperforming other approaches. The improvement of these methods coupled to machine learning and sequence database growth are most likely the main driver for a significant improvement in average precision from 27% in CASP11 to 47% in CASP12. In more than half of the targets, especially those with many homologous sequences accessible, precisions above 90% were achieved with the best predictors reaching a precision of 100% in some cases. We furthermore tested the impact of using these contacts as restraints in ab initio modeling of 14 single-domain free modeling targets using Rosetta. Adding contacts to the Rosetta calculations resulted in improvements of up to 26% in GDT_TS within the top five structures.

Evaluation of the template-based modeling in CASP12

The article describes results of numerical evaluation of CASP12 models submitted on targets for which structural templates could be identified and for which servers produced models of relatively high accuracy. The emphasis is on analysis of details of models, and how well the models compete with experimental structures. Performance of contributing research groups is measured in terms of backbone accuracy, all-atom local geometry, and the ability to estimate local errors in models. Separate analyses for all participating groups and automatic servers were carried out. Compared with the last CASP, two years ago, there have been significant improvements in a number of areas, particularly the accuracy of protein backbone atoms, accuracy of sequence alignment between models and available structures, increased accuracy over that which can be obtained from simple copying of a closest template, and accuracy of modeling of sub-structures not present in the closest template. These advancements are likely associated with more effective strategies to build non-template regions of the targets ab initio, better algorithms to combine information from multiple templates, enhanced refinement methods, and better methods for estimating model accuracy.

Assessment of protein assembly prediction in CASP12

We present the results of the first independent assessment of protein assemblies in CASP. A total of 1624 oligomeric models were submitted by 108 predictor groups for the 30 oligomeric targets in the CASP12 edition. We evaluated the accuracy of oligomeric predictions by comparison to their reference structures at the interface patch and residue contact levels. We find that interface patches are more reliably predicted than the specific residue contacts. Whereas none of the 15 hard oligomeric targets have successful predictions for the residue contacts at the interface, six have models with resemblance in the interface patch. Successful predictions of interface patch and contacts exist for all targets suitable for homology modeling, with at least one group improving over the best available template for each target. However, the participation in protein assembly prediction is low and uneven. Three human groups are closely ranked at the top by overall performance, but a server outperforms all other predictors for targets suitable for homology modeling. The state of the art of protein assembly prediction methods is in development and has apparent room for improvement, especially for assemblies without templates.

Assessment of model accuracy estimations in CASP12

The record high 42 model accuracy estimation methods were tested in CASP12. The paper presents results of the assessment of these methods in the whole-model and per-residue accuracy modes. Scores from four different model evaluation packages were used as the "ground truth" for assessing accuracy of methods' estimates. They include a rigid-body score-GDT_TS, and three local-structure based scores-LDDT, CAD and SphereGrinder. The ability of methods to identify best models from among several available, predict model's absolute accuracy score, distinguish between good and bad models, predict accuracy of the coordinate error self-estimates, and discriminate between reliable and unreliable regions in the models was assessed. Single-model methods advanced to the point where they are better than clustering methods in picking the best models from decoy sets. On the other hand, consensus methods, taking advantage of the availability of large number of models for the same target protein, are still better in distinguishing between good and bad models and predicting local accuracy of models. The best accuracy estimation methods were shown to perform better with respect to the frozen in time reference clustering method and the results of the best method in the corresponding class of methods from the previous CASP. Top performing single-model methods were shown to do better than all but three CASP12 tertiary structure predictors when evaluated as model selectors.

CASP11 statistics and the prediction center evaluation system

We outline the role of the Protein Structure Prediction Center (predictioncenter.org) in conducting the CASP11 and CASP ROLL experiments, discuss the experiment statistics, and provide an overview of the present CASP infrastructure. The biggest changes compared to the previous CASPs are the implementation of the evaluation system incorporating practically all evaluation measures, statistical tests, and visualization tools historically used by the CASP assessors, the expansion of the infrastructure to incorporate new categories of contact-assisted and multimeric predictions, and the redesign of the assessors' web-workspace enabling assessments based on multiple measures for different group categories and target sets. Proteins 2016; 84(Suppl 1):15-19. © 2016 Wiley Periodicals, Inc.

Assessment of CASP11 contact-assisted predictions

We present an overview of contact-assisted predictions in the eleventh round of critical assessment of protein structure prediction (CASP11), which included four categories: predicted contacts (Tp), correct contacts (Tc), simulated sparse NMR contacts (Ts), and cross-linking contacts (Tx). Comparison of assisted to unassisted model quality highlighted a relatively poor overall performance in CASP11 using predicted Tp and crosslinked Tx contact information. However, average model quality significantly improved in the correct Tc and simulated NMR Ts categories for most targets, where maximum improvement of unassisted models reached an impressive 70 GDT_TS. Comparison of the performance in the correct Tc category to CASP10 suggested the improvement in CASP11 model quality originated from an increased number of provided contacts per target. Group rankings based on a combination of scores used in the CASP11 free modeling (FM) assessment for each category highlight four top-performing groups, with three from the Lee lab and one from the Baker lab. We used the overall performance of these groups in each category to develop hypotheses for their relative outperformance in the correct Tc and simulated NMR Ts categories, which stemmed from the fraction of correct contacts provided (correct Tc category) and a reduced fraction of correct contacts offset by an increased coverage of the correct contacts (simulated NMR Ts category). Proteins 2016; 84(Suppl 1):164-180. © 2016 Wiley Periodicals, Inc.

CASP 11 target classification

Protein target structures for the Critical Assessment of Structure Prediction round 11 (CASP11) and CASP ROLL were split into domains and classified into categories suitable for assessment of template-based modeling (TBM) and free modeling (FM) based on their evolutionary relatedness to existing structures classified by the Evolutionary Classification of Protein Domains (ECOD) database. First, target structures were divided into domain-based evaluation units. Target splits were based on the domain organization of available templates as well as the performance of servers on whole targets compared to split target domains. Second, evaluation units were classified into TBM and FM categories using a combination of measures that evaluate prediction quality and template detectability. Generally, target domains with sequence-related templates and good server prediction performance were classified as TBM, whereas targets without sequence-identifiable templates and low server performance were classified as FM. As in previous CASP experiments, the boundaries for classification were blurred due to the presence of significant insertions and deteriorations in the targets with respect to homologous templates, as well as the presence of templates with partial coverage of new folds. The FM category included 45 target domains, which represents an unprecedented number of difficult CASP targets provided for modeling. Proteins 2016; 84(Suppl 1):20-33. © 2016 Wiley Periodicals, Inc.

Evaluation of free modeling targets in CASP11 and ROLL

We present an assessment of 'template-free modeling' (FM) in CASP11and ROLL. Community-wide server performance suggested the use of automated scores similar to previous CASPs would provide a good system of evaluating performance, even in the absence of comprehensive manual assessment. The CASP11 FM category included several outstanding examples, including successful prediction by the Baker group of a 256-residue target (T0806-D1) that lacked sequence similarity to any existing template. The top server model prediction by Zhang's Quark, which was apparently selected and refined by several manual groups, encompassed the entire fold of target T0837-D1. Methods from the same two groups tended to dominate overall CASP11 FM and ROLL rankings. Comparison of top FM predictions with those from the previous CASP experiment revealed progress in the category, particularly reflected in high prediction accuracy for larger protein domains. FM prediction models for two cases were sufficient to provide functional insights that were otherwise not obtainable by traditional sequence analysis methods. Importantly, CASP11 abstracts revealed that alignment-based contact prediction methods brought about much of the CASP11 progress, producing both of the functionally relevant models as well as several of the other outstanding structure predictions. These methodological advances enabled de novo modeling of much larger domain structures than was previously possible and allowed prediction of functional sites. Proteins 2016; 84(Suppl 1):51-66. © 2015 Wiley Periodicals, Inc.

New encouraging developments in contact prediction: Assessment of the CASP11 results

This article provides a report on the state-of-the-art in the prediction of intra-molecular residue-residue contacts in proteins based on the assessment of the predictions submitted to the CASP11 experiment. The assessment emphasis is placed on the accuracy in predicting long-range contacts. Twenty-nine groups participated in contact prediction in CASP11. At least eight of them used the recently developed evolutionary coupling techniques, with the top group (CONSIP2) reaching precision of 27% on target proteins that could not be modeled by homology. This result indicates a breakthrough in the development of methods based on the correlated mutation approach. Successful prediction of contacts was shown to be practically helpful in modeling three-dimensional structures; in particular target T0806 was modeled exceedingly well with accuracy not yet seen for ab initio targets of this size (>250 residues). Proteins 2016; 84(Suppl 1):131-144. © 2015 Wiley Periodicals, Inc.

Methods of model accuracy estimation can help selecting the best models from decoy sets: Assessment of model accuracy estimations in CASP11

The article presents assessment of the model accuracy estimation methods participating in CASP11. The results of the assessment are expected to be useful to both-developers of the methods and users who way too often are presented with structural models without annotations of accuracy. The main emphasis is placed on the ability of techniques to identify the best models from among several available. Bivariate descriptive statistics and ROC analysis are used to additionally assess the overall correctness of the predicted model accuracy scores, the correlation between the predicted and observed accuracy of models, the effectiveness in distinguishing between good and bad models, the ability to discriminate between reliable and unreliable regions in models, and the accuracy of the coordinate error self-estimates. A rigid-body measure (GDT_TS) and three local-structure-based scores (LDDT, CADaa, and SphereGrinder) are used as reference measures for evaluating methods' performance. Consensus methods, taking advantage of the availability of several models for the same target protein, perform well on the majority of tasks. Methods that predict accuracy on the basis of a single model perform comparably to consensus methods in picking the best models and in the estimation of how accurate is the local structure. More groups than in previous experiments submitted reasonable error estimates of their own models, most likely in response to a recommendation from CASP and the increasing demand from users. Proteins 2016; 84(Suppl 1):349-369. © 2015 Wiley Periodicals, Inc.

Assessment of the assessment: evaluation of the model quality estimates in CASP10

The article presents an assessment of the ability of the thirty-seven model quality assessment (MQA) methods participating in CASP10 to provide an a priori estimation of the quality of structural models, and of the 67 tertiary structure prediction groups to provide confidence estimates for their predicted coordinates. The assessment of MQA predictors is based on the methods used in previous CASPs, such as correlation between the predicted and observed quality of the models (both at the global and local levels), accuracy of methods in distinguishing between good and bad models as well as good and bad regions within them, and ability to identify the best models in the decoy sets. Several numerical evaluations were used in our analysis for the first time, such as comparison of global and local quality predictors with reference (baseline) predictors and a ROC analysis of the predictors' ability to differentiate between the well and poorly modeled regions. For the evaluation of the reliability of self-assessment of the coordinate errors, we used the correlation between the predicted and observed deviations of the coordinates and a ROC analysis of correctly identified errors in the models. A modified two-stage procedure for testing MQA methods in CASP10 whereby a small number of models spanning the whole range of model accuracy was released first followed by the release of a larger number of models of more uniform quality, allowed a more thorough analysis of abilities and inabilities of different types of methods. Clustering methods were shown to have an advantage over the single- and quasi-single- model methods on the larger datasets. At the same time, the evaluation revealed that the size of the dataset has smaller influence on the global quality assessment scores (for both clustering and nonclustering methods), than its diversity. Narrowing the quality range of the assessed models caused significant decrease in accuracy of ranking for global quality predictors but essentially did not change the results for local predictors. Self-assessment error estimates submitted by the majority of groups were poor overall, with two research groups showing significantly better results than the remaining ones.

Assessment of protein disorder region predictions in CASP10

The article presents the assessment of disorder region predictions submitted to CASP10. The evaluation is based on the three measures tested in previous CASPs: (i) balanced accuracy, (ii) the Matthews correlation coefficient for the binary predictions, and (iii) the area under the curve in the receiver operating characteristic (ROC) analysis of predictions using probability annotation. We also performed new analyses such as comparison of the submitted predictions with those obtained with a Naïve disorder prediction method and with predictions from the disorder prediction databases D2P2 and MobiDB. On average, the methods participating in CASP10 demonstrated slightly better performance than those in CASP9.

CASP prediction center infrastructure and evaluation measures in CASP10 and CASP ROLL

The Protein Structure Prediction Center at the University of California, Davis, supports the CASP experiments by identifying prediction targets, accepting predictions, performing standard evaluations, assisting independent CASP assessors, presenting and archiving results, and facilitating information exchange relating to CASP and structure prediction in general. We provide an overview of the CASP infrastructure implemented at the Center, and summarize standard measures used for evaluating predictions in the latest round of CASP. Several components were introduced or significantly redesigned for CASP10, in particular an improved assessors' common web-workspace; a Sphere Grinder visualization tool for analyzing local accuracy of predictions; brand new blocks for evaluation contact prediction and contact-assisted structure prediction; expanded evaluation and visualization tools for tertiary structure, refinement and quality assessment. Technical aspects of conducting the CASP10 and CASP ROLL experiments and relevant statistics are also provided.

Evaluation of residue-residue contact prediction in CASP10

We present the results of the assessment of the intramolecular residue-residue contact predictions from 26 prediction groups participating in the 10th round of the CASP experiment. The most recently developed direct coupling analysis methods did not take part in the experiment likely because they require a very deep sequence alignment not available for any of the 114 CASP10 targets. The performance of contact prediction methods was evaluated with the measures used in previous CASPs (i.e., prediction accuracy and the difference between the distribution of the predicted contacts and that of all pairs of residues in the target protein), as well as new measures, such as the Matthews correlation coefficient, the area under the precision-recall curve and the ranks of the first correctly and incorrectly predicted contact. We also evaluated the ability to detect interdomain contacts and tested whether the difficulty of predicting contacts depends upon the protein length and the depth of the family sequence alignment. The analyses were carried out on the target domains for which structural homologs did not exist or were difficult to identify. The evaluation was performed for all types of contacts (short, medium, and long-range), with emphasis placed on long-range contacts, i.e. those involving residues separated by at least 24 residues along the sequence. The assessment suggests that the best CASP10 contact prediction methods perform at approximately the same level, and comparably to those participating in CASP9.

Evaluation of residue-residue contact predictions in CASP9

This work presents the results of the assessment of the intramolecular residue-residue contact predictions submitted to CASP9. The methodology for the assessment does not differ from that used in previous CASPs, with two basic evaluation measures being the precision in recognizing contacts and the difference between the distribution of distances in the subset of predicted contact pairs versus all pairs of residues in the structure. The emphasis is placed on the prediction of long-range contacts (i.e., contacts between residues separated by at least 24 residues along sequence) in target proteins that cannot be easily modeled by homology. Although there is considerable activity in the field, the current analysis reports no discernable progress since CASP8.

Evaluation of disorder predictions in CASP9

Lack of stable three-dimensional structure, or intrinsic disorder, is a common phenomenon in proteins. Naturally, unstructured regions are proven to be essential for carrying function by many proteins, and therefore identification of such regions is an important issue. CASP has been assessing the state of the art in predicting disorder regions from amino acid sequence since 2002. Here, we present the results of the evaluation of the disorder predictions submitted to CASP9. The assessment is based on the evaluation measures and procedures used in previous CASPs. The balanced accuracy and the Matthews correlation coefficient were chosen as basic measures for evaluating the correctness of binary classifications. The area under the receiver operating characteristic curve was the measure of choice for evaluating probability-based predictions of disorder. The CASP9 methods are shown to perform slightly better than the CASP7 methods but not better than the methods in CASP8. It was also shown that capability of most CASP9 methods to predict disorder decreases with increasing minimum disorder segment length.