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Articles published on General Folding
- Research Article
- 10.1038/s42004-025-01636-6
- Aug 1, 2025
- Communications Chemistry
- Peng Tao + 1 more
Existing experimental results indicate potential disparities between cotranslational protein folding in vivo and free folding in vitro, yet the microscopic mechanisms responsible for these differences remain elusive. In this study, we devised a general protein cotranslational folding (GPCTF) simulations framework by modeling the ribosomal exit tunnel and translation process. Utilizing the GPCTF framework, we conducted extensive molecular dynamics simulations on three proteins of varying topologies, generating over 8 milliseconds of total trajectories. When compared to free folding, cotranslational folding enables the nascent peptide to adopt a more helix-rich structure with less nonnative interactions upon expulsion from the ribosomal exit tunnel. Notably, subsequent folding of this structure adheres to the same pathway as free folding, but with different ratios of folding pathways, modulated by the translation speed. This investigation illuminates the pathway regulation mechanism inherent to cotranslational folding and successfully reconciles discrepancies in pre-existing experimental results, offering significant insights into the protein folding process in vivo.
- Research Article
- 10.2174/0124681873291766240724055136
- Jun 1, 2025
- Current Nanomedicine
- Ivan Mazoni + 5 more
Background: This work is the third part of our initiative to fully describe the internal protein nano environments (NEs) for the three existing types of secondary structure elements (SSE). In our previous work, the NE of both the α-helix and the β-sheet were analyzed. The focus of this and previous research is improving our understanding of the SSEs: α-helices, β-sheets and turns, within protein structures. We found that the structural similarities between turns and α-helices are very high and turns may be considered as the “incomplete” initiation of α-helices. The knowledge we were able to compile during this work might be essential for predicting a tertiary structure of proteins, with higher precision and subsequently being in a more favourable position with regard to designing drugs for certain protein structure/function related diseases. Considering that the formation of secondary structure elements is a crucial step in the general folding of protein 3D structure, an important contribution of this work is augmenting the efficiency of estimating if modelled structures, for example, are predicting SSEs in full agreement to necessary/required/ sufficient values of respective SSEs nanoenvironment descriptors. During exactly that modelling phase, preceding the more precise final 3D protein structure construction, our Dictionary of Most Relevant Nanoenvironment Descriptors is able to answer some fundamental questions regarding SSE correctness with regard to nanoenvironment characteristics found to be generally required. Expanding this vision, our current work is part of an effort by our laboratory to create a “dictionary of internal protein nanoenvironments” - DIPN. The ten most studied internal protein nanoenvironments are described in DIPN in physicochemical and structural terms, and this knowledge is now available to be used to aid drug design - probably the most important area of application for the results we are presenting here. Methods: In the current paper, STING´s database of physical-chemical and structural descriptors was used to gather the necessary information to characterize the NE of loops, or, as they are often called, turns. Given that approximately 20% of all protein-type residues form turns, research in this field is essential, and analysis of the obtained results will further contribute to our comprehension of how proteins fold. In addition, the results in this paper will contribute to the better training of algorithms that evaluate the degree of overall protein structure quality and, consequently, structure prediction. This is currently very important given we are witnessing a revolution in algorithms employing artificial intelligence for protein structure prediction. Powered by the STING’s database (wide-ranging protein structure information source), statistical testing was used to retrieve a set of descriptors that fully delineate the NE of turns. By collecting such data, it is then possible to list the variances with respect to the NE of α-helices and β-sheets and, by doing so, establish the most relevant NE descriptors (MRND) for each of the three SSEs. Results: The results show that the α-helical and β-sheet Nes, as well as the amino acid residue composition, all behave in a similar fashion as a “key and lock” system. In other words, it is necessary for a set of specific descriptors to assume respective specific values (within the bounds of a very definite value region) to construct the specific secondary structure element NE at a certain protein location. Conclusion: Consequently, there is a set of descriptors that act together and are required to satisfy specific conditions for secondary structure element occurrences. The very same requirement, we found, occurs in the case of turns.
- Research Article
- 10.1016/j.jsb.2025.108173
- Mar 1, 2025
- Journal of structural biology
- David Salom + 1 more
Structure and self-association of Arrestin-1.
- Research Article
3
- 10.1038/s41467-024-55601-3
- Jan 22, 2025
- Nature Communications
- David Z Bushhouse + 2 more
Riboswitches are ligand-responsive gene-regulatory RNA elements that perform key roles in maintaining cellular homeostasis. Understanding how riboswitch sensitivity to ligand (EC50) is controlled is critical to explain how highly conserved aptamer domains are deployed in a variety of contexts with different sensitivity demands. Here we uncover roles by which RNA folding dynamics control riboswitch sensitivity in cells. By investigating the Clostridium beijerinckii pfl ZTP riboswitch, we identify multiple mechanistic routes of altering expression platform sequence and structure to slow RNA folding, all of which enhance riboswitch sensitivity. Applying these methods to riboswitches with diverse aptamer architectures and regulatory mechanisms demonstrates the generality of our findings, indicating that any riboswitch that operates in a kinetic regime can be sensitized by slowing expression platform folding. Our results add to the growing suite of knowledge and approaches that can be used to rationally program cotranscriptional RNA folding for biotechnology applications, and suggest general RNA folding principles for understanding dynamic RNA systems in other areas of biology.
- Research Article
- 10.5510/ogp20250201062
- Jan 1, 2025
- SOCAR Proceedings
- V Y Kerimov + 3 more
To study the reservoirs of the South Caspian basin, models of the distribution of natural reservoirs, paleogeographic sedimentation settings, lithological and facies schemes, thickness maps, sedimentation velocity maps, and a scheme for determining the boundaries of sedimentation depocenters based on the results of lithological, paleogeographic, and sedimentary-facies studies were developed. Paleogeographic reconstructions have shown that fluvial-delta complexes played a significant role in the formation of sedimentary complexes in the South Caspian basin. The general geological background of the SKB is characterized by: sharp lithofacial and filtration-capacitive heterogeneity of the section, which was built up in separate Cenozoic intervals in an environment of nonequilibrium avalanche sedimentation; rhythmicity of the productive stratum-red-colored stratum (PT-CT), expressed in periodic vertical substitution of clay differences with sandy ones; lens-forming regionally consistent wedging of the stratigraphic components of the PT section. CT both in the direction of rising and sinking of general folding; Lithologicalpaleogeographic and lithological-facies studies indicate the existence of favorable conditions for the formation of lithological and stratigraphic traps of oil and gas in clinoform complexes in the South Caspian basin. The results of these studies are of key importance for practical applicationin the field ofin the planning of geological exploration. Reservoir maps and litho-facies schemes provide a reasonable choice of the location of project wells in the most promising areas of reservoir development. Models of paleogeographic settings make it possible to predict the distribution of sand bodies in ancient delta complexes, and sedimentation rate maps help to assess the degree of rock consolidation and predict abnormal reservoir pressures. Keywords: South Caspian basin; paleogeography; lithologic-facies schemes; sedimentation rates; depocenters; reservoirs; clinoforms.
- Research Article
- 10.3233/fi-242195
- Sep 20, 2024
- Fundamenta Informaticae
- Jaime Arias + 4 more
This paper presents a concrete and a symbolic rewriting logic semantics for parametric time Petri nets with inhibitor arcs (PITPNs), a flexible model of timed systems where parameters are allowed in firing bounds. We prove that our semantics is bisimilar to the “standard” semantics of PITPNs. This allows us to use the rewriting logic tool Maude, combined with SMT solving, to provide sound and complete formal analyses for PITPNs. We develop and implement a new general folding approach for symbolic reachability, so that Maude-with-SMT reachability analysis terminates whenever the parametric state-class graph of the PITPN is finite. Our work opens up the possibility of using the many formal analysis capabilities of Maude—including full LTL model checking, analysis with user-defined execution strategies, and even statistical model checking—for such nets. We illustrate this by explaining how almost all formal analysis and parameter synthesis methods supported by the state-of-the-art PITPN tool Roméo can be performed using Maude with SMT. In addition, we also support analysis and parameter synthesis from parametric initial markings, as well as full LTL model checking and analysis with user-defined execution strategies. Experiments show that our methods outperform Roméo in many cases.
- Research Article
- 10.18799/24131830/2024/6/4369
- Jun 27, 2024
- Bulletin of the Tomsk Polytechnic University Geo Assets Engineering
- Yury G Paktovsky + 7 more
Relevance. Relationship with the Takata formation of diamond reservoir rocks and previously discovered deposits and the presence of prospects for discovering new ones in the zone of the forward folds of the Urals. Aim. To reconstruct the conditions of sedimentation and composition of rocks, the source of the removal of terrigenous rocks of the Takata formation based on the results of studying the "Yuzhnaya Rassolnaya" section. Objects. Terrigenous rocks of the Takata formation in the "Yuzhnaya Rassolnaya" section located in the western part of the alluvial diamond deposit "Yuzhnaya Rassolnaya" in the Krasnovishersky district of the Perm Territory. Methods. Lithofacies analysis, petrographic study of thin sections in transmitted light using crossed nicol methods, determination of the content of rock-forming oxides by X-ray fluorescence on an S8 Tiger (Bruker) spectrometer, analysis of rock-forming elements on glassy disks. Impurity and microimpurity elements (with a content of <5%) were determined using a certified method for defining elements by inductively coupled plasma mass spectrometry according to the method, STO TGU 048-2012. The analysis was performed by ICP-MS on an Agilent 7500cx quadrupole mass spectrometer (Agilent Technologies Inc., USA) using an internal (In Internal standard, Inorganic Ventures, USA) and an external standard SGD-2A (GSO 8670-2005). Results. Lithological-facial, mineralogical, petrographic, lithogeochemical studies of Takata terrigenous deposits were carried out in the "Yuzhnaya Rassolnaya" section in the area of the Polyudovo-Kolchima anticlinorium of the Western Ural folding zone, which made it possible to clarify the sources of matter and sedimentation conditions. The formation of sediments occurred in a transitional sedimentation environment. A transgressive sequence is observed from bottom to top. Terrigenous rocks of the Takata formation include rocks of the first and second sedimentation cycles. They were cut off due to the destruction of primary igneous (acidic and basic compositions) and metamorphic rocks, as well as sedimentary rocks. The totality of the material characteristics of the terrigenous rocks of the Takata formation, taking into account the published data, allowed us to assume that sedimentation of the rocks occurred on the passive continental margin, with the supply of clastic material due to the erosion of internal raised blocks of the foundation of the East European Platform. The activation of the latter occurred in the Emsian time with the manifestation of general lithospheric folding. At the same time, water flows carrying weathering products from the East European Platform eroded sedimentary rocks of the Riphean, Vendian, Ordovician and Silurian, which fragments we observe in small quantities when describing thin sections.
- Research Article
- 10.1021/acs.biochem.3c00714
- May 20, 2024
- Biochemistry
- Rainier-Numa Georges + 5 more
Transketolases (TKs) are key enzymes of the pentose phosphate pathway, regulating several other critical pathways in cells. Considering their metabolic importance, TKs are expected to be conserved throughout evolution. However, Tittmann et al. (J Biol Chem, 2010, 285(41): 31559-31570) demonstrated that Homo sapiens TK (hsTK) possesses several structural and kinetic differences compared to bacterial TKs. Here, we study 14 TKs from pathogenic bacteria, fungi, and parasites and compare them with hsTK using biochemical, bioinformatic, and structural approaches. For this purpose, six new TK structures are solved by X-ray crystallography, including the TK of Plasmodium falciparum. All of these TKs have the same general fold as bacterial TKs. This comparative study shows that hsTK greatly differs from TKs from pathogens in terms of enzymatic activity, spatial positions of the active site, and monomer-monomer interface residues. An ubiquitous structural pattern is identified in all TKs as a six-residue histidyl crown around the TK cofactor (thiamine pyrophosphate), except for hsTK containing only five residues in the crown. Residue mapping of the monomer-monomer interface and the active site reveals that hsTK contains more unique residues than other TKs. From an evolutionary standpoint, TKs from animals (including H. sapiens) and Schistosoma sp. belong to a distinct structural group from TKs of bacteria, plants, fungi, and parasites, mostly based on a different linker between domains, raising hypotheses regarding evolution and regulation.
- Research Article
13
- 10.1063/4.0000247
- Mar 1, 2024
- Structural Dynamics
- Georgii Khusainov + 2 more
Macromolecular crystallography has historically provided the atomic structures of proteins fundamental to cellular functions. However, the advent of cryo-electron microscopy for structure determination of large and increasingly smaller and flexible proteins signaled a paradigm shift in structural biology. The extensive structural and sequence data from crystallography and advanced sequencing techniques have been pivotal for training computational models for accurate structure prediction, unveiling the general fold of most proteins. Here, we present a perspective on the rise of time-resolved crystallography as the new frontier of macromolecular structure determination. We trace the evolution from the pioneering time-resolved crystallography methods to modern serial crystallography, highlighting the synergy between rapid detection technologies and state-of-the-art x-ray sources. These innovations are redefining our exploration of protein dynamics, with high-resolution crystallography uniquely positioned to elucidate rapid dynamic processes at ambient temperatures, thus deepening our understanding of protein functionality. We propose that the integration of dynamic structural data with machine learning advancements will unlock predictive capabilities for protein kinetics, revolutionizing dynamics like macromolecular crystallography revolutionized structural biology.
- Research Article
4
- 10.1128/spectrum.01975-23
- Oct 4, 2023
- Microbiology Spectrum
- Frédéric Kerff + 7 more
In Streptomyces scabiei, the main causative agent of common scab disease of root and tuber crops, the interaction between the substrate-binding protein (SBP) CebE (CebEscab) and cellotriose released by the plant host (KD in the nanomolar range) is the first event for the onset of its pathogenic lifestyle. Here, we report the structure of CebEscab in complex with cellotriose at a resolution of 1.55 Å, adopting a general fold of the B subcluster of SBPs. The interaction between CebEscab and cellotriose involves multiple direct or water-mediated hydrogen bonds and hydrophobic interactions, with the glucose monomer at the non-reducing end occupying the most conserved part of the substrate-binding cleft. As main interactions between the two domains of CebE involve cellotriose itself, the closed conformational state of CebE is performed via an induced-fit ligand binding mechanism where cellotriose binding triggers the domain movement. Analysis of regulon predictions revealed that the signaling pathway from CebE-mediated cellotriose transport to the transcriptional activation of thaxtomin phytotoxin biosynthesis is conserved in Streptomyces spp. causing common scab, except for Streptomyces ipomoeae, which specifically colonizes sweet potatoes and responds to other and yet unknown virulence elicitors. Interestingly, strains belonging to the pathogenic species turgidiscabies and caniscabiei have a cellotriose-binding protein orthologous to the CebE protein of the saprophytic species Streptomyces reticuli with lower affinity for its substrate (KD in the micromolar range), suggesting higher cellotriose concentrations for perception of their host. Our work also provides the structural basis for the uptake of cellobiose and cellotriose by non-pathogenic cellulose-decomposing Streptomyces species.IMPORTANCECommon scab is a disease caused by a few Streptomyces species that affects important root and tuber crops including potato, beet, radish, and parsnip, resulting in major economic losses worldwide. In this work, we unveiled the molecular basis of host recognition by these pathogens by solving the structure of the sugar-binding protein CebE of Streptomyces scabiei in complex with cellotriose, the main elicitor of the pathogenic lifestyle of these bacteria. We further revealed that the signaling pathway from CebE-mediated transport of cellotriose is conserved in all pathogenic species except Streptomyces ipomoeae, which causes soft rot disease in sweet potatoes. Our work also provides the structural basis of the uptake of cellobiose and cellotriose in saprophytic Streptomyces species, the first step activating the expression of the enzymatic system degrading the most abundant polysaccharide on earth, cellulose.
- Research Article
2
- 10.1111/febs.16964
- Sep 29, 2023
- The FEBS Journal
- Sara Košenina + 4 more
The botulinum neurotoxin-like toxin from Weissella oryzae (BoNT/Wo) is one of the BoNT-like toxins recently identified outside of the Clostridium genus. We show that, like the canonical BoNTs, BoNT/Wo forms a complex with its non-toxic non-hemagglutinin (NTNH) partner, which in traditional BoNT serotypes protects the toxin from proteases and the acidic environment of the hosts' guts. We here report the cryo-EM structure of the 300 kDa BoNT/Wo-NTNH/Wo complex together with pH stability studies of the complex. The structure reveals molecular details of the toxin's interactions with its protective partner. The overall structural arrangement is similar to other reported BoNT-NTNH complexes, but NTNH/Wo uniquely contains two extra bacterial immunoglobulin-like (Big) domains on the C-terminus. Although the function of these Big domains is unknown, they are structurally most similar to bacterial proteins involved in adhesion to host cells. In addition, the BoNT/Wo protease domain contains an internal disulfide bond not seen in other BoNTs. Mass photometry analysis revealed that the BoNT/Wo-NTNH/Wo complex is stable under acidic conditions and may dissociate at neutral to basic pH. These findings established that BoNT/Wo-NTNH/Wo shares the general fold of canonical BoNT-NTNH complexes. The presence of unique structural features suggests that it may have an alternative mode of activation, translocation and recognition of host cells, raising interesting questions about the activity and the mechanism of action of BoNT/Wo as well as about its target environment, receptors and substrates.
- Research Article
13
- 10.1016/j.celrep.2023.113134
- Sep 1, 2023
- Cell Reports
- Yan Li + 4 more
The organization and dynamics of chromatin fiber play crucial roles in regulating DNA accessibility for gene expression. Here we combine cryoelectron tomography (cryo-ET), sub-volume averaging, and 3D segmentation to visualize the invitro and invivo chromatin fibers folding by linker histone. We discover that an increased nucleosome repeat length and prolonged fiber length do not change the two-start helical architecture in reconstituted chromatin of homogeneous composition. Additionally, an isolated chromatin fiber with heterogeneous composition was observed, which includes short-range regions compatible with two-start helix. Invivo, sub-volume averaging reveals similar subunits of two-start helical architecture in transcriptionally inactive chromatin in frog erythrocyte nuclei. Strikingly, unambiguous DNA trajectories that displayed a zigzag pattern universally between alternate N/N+2 nucleosomes were further determined by cryo-ET with voltage phase plate. Therefore, these structural similarities suggest a general folding mode of chromatin induced by linker histone, and heterogeneous compositions mainly affect local conformation rather than changing the overall architecture.
- Research Article
3
- 10.1016/j.molcel.2023.07.028
- Aug 18, 2023
- Molecular Cell
- Alexander J Mcquown + 6 more
A Zpr1 co-chaperone mediates folding of eukaryotic translation elongation factor 1A via a GTPase cycle
- Research Article
8
- 10.1021/acs.jpclett.3c00926
- May 23, 2023
- The Journal of Physical Chemistry Letters
- Hung N Do + 1 more
We have developed a new deep boosted molecular dynamics (DBMD) method. Probabilistic Bayesian neural network models were implemented to construct boost potentials that exhibit Gaussian distribution with minimized anharmonicity, thereby allowing for accurate energetic reweighting and enhanced sampling of molecular simulations. DBMD was demonstrated on model systems of alanine dipeptide and the fast-folding protein and RNA structures. For alanine dipeptide, 30 ns DBMD simulations captured up to 83-125 times more backbone dihedral transitions than 1 μs conventional molecular dynamics (cMD) simulations and were able to accurately reproduce the original free energy profiles. Moreover, DBMD sampled multiple folding and unfolding events within 300 ns simulations of the chignolin model protein and identified low-energy conformational states comparable to previous simulation findings. Finally, DBMD captured a general folding pathway of three hairpin RNAs with the GCAA, GAAA, and UUCG tetraloops. Based on a deep learning neural network, DBMD provides a powerful and generally applicable approach to boosting biomolecular simulations. DBMD is available with open source in OpenMM at https://github.com/MiaoLab20/DBMD/.
- Research Article
- 10.1002/prot.26480
- Apr 4, 2023
- Proteins: Structure, Function, and Bioinformatics
- Andrew D Sanders + 2 more
In this perspective, we propose that the folding energy landscapes of model proteases including pepsin and alpha-lytic protease (αLP), which lack thermodynamic stability and fold on the order of months to millennia, respectively, should be viewed as not evolved and fundamentally distinct from their extended zymogen forms. These proteases have evolved to fold with prosegment domains and robustly self-assemble as expected. In this manner, general protein folding principles are strengthened. In support of our view, αLP and pepsin exhibit hallmarks of frustration associated with unevolved folding landscapes, such as non-cooperativity, memory effects, and substantial kinetic trapping. The evolutionary implications of this folding strategy are considered in detail. Direct applications of this folding strategy on enzyme design, finding new drug targets, and constructing tunable folding landscapes are also discussed. Together with certain proteases, growing examples of other folding "exceptions"-including protein fold switching, functional misfolding, and prevalent inability to refold-suggests a paradigm shift in which proteins may evolve to exist in a wide range of energy landscapes and structures traditionally thought to be avoided in nature.
- Research Article
13
- 10.1016/j.molcel.2022.12.012
- Jan 1, 2023
- Molecular Cell
- Ibrahim M Sabbarini + 8 more
Zinc-finger protein Zpr1 is a bespoke chaperone essential for eEF1A biogenesis
- Research Article
- 10.1206/3993.1
- Dec 13, 2022
- American Museum Novitates
- David E Vrech + 3 more
The spermatozoa of scorpions are often bundled together, forming a type of sperm conjugation known as a sperm package. Sperm packages may be found inside the testes and seminal vesicles but vanish in the female atrium, leaving free spermatozoa. Previous studies, based on a limited number of taxa, suggested a diversity of sperm package morphology across the order Scorpiones C.L. Koch, 1850. However, the sperm packages of most scorpion taxa remained unknown. The present study provides the first systematic survey of sperm package morphology across the order, covering 89 exemplar species in 66 genera and 19 families representing all suprafamilial ranks, with a more detailed investigation of the family Bothriuridae Simon, 1880. Whereas all exemplar species of scorpions exhibit sperm packages, Buthida Soleglad and Fet, 2003, including Chaerilidae Pocock, 1893, and most Buthidae C.L. Koch, 1837, present unorganized sperm or loosely organized bundles. Although the details vary, three main types of sperm packages may be recognized in all other families: single folded; straight; and multiple folded. Subtypes may be identified according to general shape and folding patterns, mainly among sperm packages that are folded multiple times. Single-folded sperm packages are the most common type observed in the order. Although most sperm packages lack a covering, a conspicuous secretion sheath may be evident, e.g., in some Chactidae Pocock, 1893. Sperm packages vary in length from 112–354 µm and bent sperm packages are not necessarily longer than straight sperm packages. Four exemplar species of Bothriuridae reveal that variation in sperm count within a single sperm package is consistent with the count derived in spermatogenesis. The diversity of sperm packages suggests a path from free spermatozoa, via bent sperm packages, to other forms. Sperm packages may aid in the transport, cooperation, competition, and survival of spermatozoa. The diverse morphology, function, and evolution of sperm packages merit further investigation.
- Research Article
3
- 10.1093/bioinformatics/btac384
- Jun 8, 2022
- Bioinformatics (Oxford, England)
- Adam Midlik + 5 more
Every protein family has a set of characteristic secondary structures. However, due to individual variations, a single structure is not enough to represent the whole family. OverProt can create a secondary structure consensus, showing the general fold of the family as well as its variation. Our server provides precomputed results for all CATH superfamilies and user-defined computations, visualized by an interactive viewer, which shows the secondary structure element type, length, frequency of occurrence, spatial variability and β-connectivity. OverProt Server is freely available at https://overprot.ncbr.muni.cz. Supplementary data are available at Bioinformatics online.
- Research Article
19
- 10.1126/sciadv.abl6293
- Mar 4, 2022
- Science Advances
- Mohsin M Naqvi + 8 more
The collapse of polypeptides is thought important to protein folding, aggregation, intrinsic disorder, and phase separation. However, whether polypeptide collapse is modulated in cells to control protein states is unclear. Here, using integrated protein manipulation and imaging, we show that the chaperonin GroEL-ES can accelerate the folding of proteins by strengthening their collapse. GroEL induces contractile forces in substrate chains, which draws them into the cavity and triggers a general compaction and discrete folding transitions, even for slow-folding proteins. This collapse enhancement is strongest in the nucleotide-bound states of GroEL and is aided by GroES binding to the cavity rim and by the amphiphilic C-terminal tails at the cavity bottom. Collapse modulation is distinct from other proposed GroEL-ES folding acceleration mechanisms, including steric confinement and misfold unfolding. Given the prevalence of collapse throughout the proteome, we conjecture that collapse modulation is more generally relevant within the protein quality control machinery.
- Research Article
- 10.3390/app112411856
- Dec 13, 2021
- Applied Sciences
- Yiyang Jia + 1 more
In this paper, we compare the performance of three different folding models when they are applied to three different map folding settings. Precisely, the three folding models include the simple folding model, the simple folding–unfolding model, and the general folding model. The different map folding settings are discussed by comparing different folded states, i.e., different overlapping orders on the set of the squares of 1 × n maps, the squares of m × n maps, and the squares lying on the boundary of m × n maps. These folding models are abstracts of manual works and robotics. We clarify the relationship between their reachable final folded states under different settings and give proof of all the inclusion relationships between every two of these sets. In addition, there are nine distinct problems with the three folding models applied to three folding settings. We give the optimal linear time solutions to all the unsolved ones: the valid total overlapping order problems of 1 × n maps, m × n maps, as well as the valid boundary overlapping order problems of m × n maps with the three different folding models. Our work gives the conclusion of the research field where the folding models and the overlapping orders of map folding are concerned.