Deciphering the Cofilin Oligomers via Intermolecular Disulfide Bond Formation: A Coarse-Grained Molecular Dynamics Approach to Understanding Cofilin's Regulation on Actin Filaments.

Cofilin, a key actin-binding protein, orchestrates the dynamics of the actomyosin network through its actin-severing activity and by promoting the recycling of actin monomers. Recent experiments suggest that cofilin forms functionally distinct oligomers via thiol post-translational modifications (PTMs) that promote actin nucleation and assembly. Despite these advances, the structural conformations of cofilin oligomers that modulate actin activity remain elusive because there are combinatorial ways to oxidize thiols in cysteines to form disulfide bonds rapidly. This study employs molecular dynamics simulations to investigate human cofilin 1 as a case study for exploring cofilin dimers via disulfide bond formation. Utilizing a biasing scheme in simulations, we focus on analyzing dimer conformations conducive to disulfide bond formation. Additionally, we explore potential PTMs arising from the examined conformational ensemble. Using the free energy profiling, our simulations unveil a range of probable cofilin dimer structures not represented in current Protein Data Bank entries. These candidate dimers are characterized by their distinct population distributions and relative free energies. Of particular note is a dimer featuring an interface between cysteines 139 and 147 residues, which demonstrates stable free energy characteristics and intriguingly symmetrical geometry. In contrast, the experimentally proposed dimer structure exhibits a less stable free energy profile. We also evaluate frustration quantification based on the energy landscape theory in the protein-protein interactions at the dimer interfaces. Notably, the 39-39 dimer configuration emerges as a promising candidate for forming cofilin tetramers, as substantiated by frustration analysis. Additionally, docking simulations with actin filaments further evaluate the stability of these cofilin dimer-actin complexes. Our findings thus offer a computational framework for understanding the role of thiol PTM of cofilin proteins in regulating oligomerization, and the subsequent cofilin-mediated actin dynamics in the actomyosin network.

The use of multicomponent reactions in the development of bis-boronic acids for the detection of ß-sialic acid.

Sialic acid (SA) is a naturally occurring monosaccharide found in glycoproteins and glycolipids. Changes in the expression of SA are associated with several diseases; thus, the detection of SA is of great significance for biological research, cancer diagnosis, and treatment. Boronic acid analogs have emerged as a promising tool for detecting sugars such as SA due to its reversible covalent bonding ability. In this study, 11 bis-boronic acid compounds and 2 mono-boronic acid compounds were synthesized via a highly efficient Ugi-4CR strategy. The synthesized compounds were subjected to affinity fluorescence binding experiments to evaluate their binding capability to SA. Compound A1 was shown to have a promising binding constant of 2602 ± 100 M-1 at pH = 6.0. Density Functional Theory (DFT) calculations examining the binding modes between A1 and SA indicated that the position of the boronic acid functional group was strongly correlated with its interaction with SA's α-hydroxy acid unit. The DFT calculations were consistent with the observations from the fluorescence experiments, demonstrating that the number and relative positions of the boronic acid functional groups are critical factors in enhancing the binding affinity to SA. DFT calculations of both S and R configuration of A1 indicated that the effect of the S/R configuration of A1 on its binding with ß-sialic acid was insignificant as the Ugi-4CR generated racemic products. A fluorine atom was incorporated into the R2 substituent of A1 as an electron-withdrawing group to produce A5, which possessed a significantly higher capability to bind to SA (Keq = 7015 ± 5 M-1 at pH = 6.0). Finally, A1 and A5 were shown to possess exceptional binding selectivity toward ß-sialic acid under pH of 6.0 and 6.5 while preferring to bind with glucose, fructose, and galactose under pH of 7.0 and 7.5.

Early-Stage Oligomerization of Prion-like Polypeptides Reveals the Molecular Mechanism of Amyloid-Disrupting Capacity by Proline Residues.

Proline cis/trans isomerization governs protein local conformational changes via its local mechanical rigidity. The amyloid-disrupting capacity of proline is widely acknowledged; however, the molecular mechanism is still not clear. To understand how proline residues in polypeptide chains influence amyloid propensity, we study several truncated sequences of the TDP-43 C-terminal region (287-322) and their triple proline variants (308PPP310). We use coarse-grained molecular simulation to study the time evolution of the process of aggregation in the early stages in an effective high-concentration condition (∼25 mM). This ensures the long time scales for protein association at laboratory concentrations. We use several experimentally determined structure templates as initial structures of monomer conformations. We carry out oligomer size analysis and cluster analysis, along with several structural measures, to characterize the size distributions of oligomers and their morphological/structural properties. We show that average oligomer size is not a good indicator of amyloid propensity. Structural order and/or morphological properties are better alternatives. We show that proline variants can efficiently maintain the formation of large "ordered" oligomers of shorter truncated sequences, i.e., 307-322. This "order" maintenance is weakened when using longer truncated sequences (i.e., 287-322), leading to the formation of "disordered" oligomers. From an energy trade-off perspective, if the entropic effect is weak (short sequence length), the shape-complementarity of proline variants effectively guides the oligomerization process to form "ordered" oligomer intermediates. This leads to a distinct aggregation pathway that promotes amyloid formation (on-pathway). Strong entropic effects (long sequence length), however, would cause the formation of "disordered" oligomers. This in turn will suppress amyloid formation (off-pathway). The proline shape-complementary effects provide a guided morphological restraint to facilitate the pathways of amyloid formation. Our study supports the importance of structure-based kinetic heterogeneity of prion-like sequence fragments in driving different aggregation pathways. This work sheds light on the role of morphological and structural order of early-stage oligomeric species in regulating amyloid-disrupting capacity by prolines.

Corrigendum: Fibril Surface-Dependent Amyloid Precursors Revealed by Coarse-Grained Molecular Dynamics Simulation.

[This corrects the article DOI: 10.3389/fmolb.2021.719320.].

The Role of Charge Density Coupled DNA Bending in Transcription Factor Sequence Binding Specificity: A Generic Mechanism for Indirect Readout.

The accurate reading of genetic information during transcription is essential for the expression of genes. Sequence binding specificity very often is attributed to short-range, usually specific interactions between amino acid residues and individual nucleotide bases through hydrogen bonding or hydrophobic contacts: "base readout" (direct readout). In contrast, many proteins recognize DNA sequences in an alternative fashion via "shape readout" (indirect readout), where many elements of the DNA sequence cooperate to localize the transcription factor. In this study, we use a coarse-grained protein-DNA model to investigate the origin of the sequence specificity of the protein PU.1 binding to its binding sites for a series of DNA sequences. We find that the binding specificity of PU.1 is achieved primarily via a nonspecific electrostatically driven DNA mechanism involving the change in the elastic properties of the DNA. To understand the underlying mechanism, we analyze how the mechanical properties of DNA change in relation to the location of the PU.1 bound along DNA. The simulations first show that electrostatic interactions between PU.1 and DNA can cause complex DNA conformational/dynamics changes. Using a semiflexible polymer theory, we find that PU.1 influences the DNA dynamics through a second-order mechanical effect. When PU.1 binds nonspecifically to the DNA via electrostatics, the DNA becomes stiffer and the protein slides along DNA in a search mode. In contrast, once the protein finds its specific binding site, the DNA becomes softer there. PU.1 thus locks into place through configurational entropy effects, which we suggest is a generic mechanism for indirect readout.

Exploring the folding energy landscapes of heme proteins using a hybrid AWSEM-heme model.

Heme is an active center in many proteins. Here we explore computationally the role of heme in protein folding and protein structure. We model heme proteins using a hybrid model employing the AWSEM Hamiltonian, a coarse-grained forcefield for the protein chain along with AMBER, an all-atom forcefield for the heme. We carefully designed transferable force fields that model the interactions between the protein and the heme. The types of protein-ligand interactions in the hybrid model include thioester covalent bonds, coordinated covalent bonds, hydrogen bonds, and electrostatics. We explore the influence of different types of hemes (heme b and heme c) on folding and structure prediction. Including both types of heme improves the quality of protein structure predictions. The free energy landscape shows that both types of heme can act as nucleation sites for protein folding and stabilize the protein folded state. In binding the heme, coordinated covalent bonds and thioester covalent bonds for heme c drive the heme toward the native pocket. The electrostatics also facilitates the search for the binding site.

Fibril Surface-Dependent Amyloid Precursors Revealed by Coarse-Grained Molecular Dynamics Simulation.

Amyloid peptides are known to self-assemble into larger aggregates that are linked to the pathogenesis of many neurodegenerative disorders. In contrast to primary nucleation, recent experimental and theoretical studies have shown that many toxic oligomeric species are generated through secondary processes on a pre-existing fibrillar surface. Nucleation, for example, can also occur along the surface of a pre-existing fibril-secondary nucleation-as opposed to the primary one. However, explicit pathways are still not clear. In this study, we use molecular dynamics simulation to explore the free energy landscape of a free Abeta monomer binding to an existing fibrillar surface. We specifically look into several potential Abeta structural precursors that might precede some secondary events, including elongation and secondary nucleation. We find that the overall process of surface-dependent events can be described at least by the following three stages: 1. Free diffusion 2. Downhill guiding 3. Dock and lock. And we show that the outcome of adding a new monomer onto a pre-existing fibril is pathway-dependent, which leads to different secondary processes. To understand structural details, we have identified several monomeric amyloid precursors over the fibrillar surfaces and characterize their heterogeneity using a probability contact map analysis. Using the frustration analysis (a bioinformatics tool), we show that surface heterogeneity correlates with the energy frustration of specific local residues that form binding sites on the fibrillar structure. We further investigate the helical twisting of protofilaments of different sizes and observe a length dependence on the filament twisting. This work presents a comprehensive survey over the properties of fibril growth using a combination of several openMM-based platforms, including the GPU-enabled openAWSEM package for coarse-grained modeling, MDTraj for trajectory analysis, and pyEMMA for free energy calculation. This combined approach makes long-timescale simulation for aggregation systems as well as all-in-one analysis feasible. We show that this protocol allows us to explore fibril stability, surface binding affinity/heterogeneity, as well as fibrillar twisting. All these properties are important for understanding the molecular mechanism of surface-catalyzed secondary processes of fibril growth.

Modeling Protein Aggregation Kinetics: The Method of Second Stochasticization.

The nucleation of protein aggregates and their growth are important in determining the structure of the cell's membraneless organelles as well as the pathogenesis of many diseases. The large number of molecular types of such aggregates along with the intrinsically stochastic nature of aggregation challenges our theoretical and computational abilities. Kinetic Monte Carlo simulation using the Gillespie algorithm is a powerful tool for modeling stochastic kinetics, but it is computationally demanding when a large number of diverse species is involved. To explore the mechanisms and statistics of aggregation more efficiently, we introduce a new approach to model stochastic aggregation kinetics which introduces noise into already statistically averaged equations obtained using mathematical moment closure schemes. Stochastic moment equations summarize succinctly the dynamics of the large diversity of species with different molecularity involved in aggregation but still take into account the stochastic fluctuations that accompany not only primary and secondary nucleation but also aggregate elongation, dissociation, and fragmentation. This method of "second stochasticization" works well where the fluctuations are modest in magnitude as is often encountered in vivo where the number of protein copies in some computations can be in the hundreds to thousands. Simulations using second stochasticization reveal a scaling law that correlates the size of the fluctuations in aggregate size and number with the total number of monomers. This scaling law is confirmed using experimental data. We believe second stochasticization schemes will prove valuable for bridging the gap between in vivo cell biology and detailed modeling. (The code is released on https://github.com/MYTLab/stoch-agg.).

AWSEM-Suite: a protein structure prediction server based on template-guided, coevolutionary-enhanced optimized folding landscapes.

The accurate and reliable prediction of the 3D structures of proteins and their assemblies remains difficult even though the number of solved structures soars and prediction techniques improve. In this study, a free and open access web server, AWSEM-Suite, whose goal is to predict monomeric protein tertiary structures from sequence is described. The model underlying the server's predictions is a coarse-grained protein force field which has its roots in neural network ideas that has been optimized using energy landscape theory. Employing physically motivated potentials and knowledge-based local structure biasing terms, the addition of homologous template and co-evolutionary restraints to AWSEM-Suite greatly improves the predictive power of pure AWSEM structure prediction. From the independent evaluation metrics released in the CASP13 experiment, AWSEM-Suite proves to be a reasonably accurate algorithm for free modeling, standing at the eighth position in the free modeling category of CASP13. The AWSEM-Suite server also features a front end with a user-friendly interface. The AWSEM-Suite server is a powerful tool for predicting monomeric protein tertiary structures that is most useful when a suitable structure template is not available. The AWSEM-Suite server is freely available at: https://awsem.rice.edu.

Multiple Binding Configurations of Fis Protein Pairs on DNA: Facilitated Dissociation versus Cooperative Dissociation.

As a master transcription regulator, the Fis protein influences over two hundred genes of E. coli. The Fis protein's nonspecific binding to DNA is widely acknowledged, and its kinetics of dissociation from DNA is strongly influenced by its surroundings: the dissociation rate increases as the concentration of the Fis protein in the solution phase increases. In this study, we use computational methods to explore the global binding energy landscape of the Fis1:Fis2:DNA ternary complex. The complex contains a binary-Fis molecular dyad whose formation relies on complex structural rearrangements. The simulations allow us to distinguish several different pathways for the dissociation of the protein from DNA with different functional outcomes and involving different protein stoichiometries: (1) simple exchange of proteins and (2) cooperative unbinding of two Fis proteins to yield bare DNA. In the case of exchange, the protein on the DNA is replaced by the solution-phase protein through competition for DNA binding sites. This process seen in fluorescence imaging experiments has been called facilitated dissociation. In the latter case of cooperative unbinding of pairs, two neighboring Fis proteins on DNA form a unique binary-Fis configuration via protein-protein interactions, which in turn leads to the codissociation of both molecules simultaneously, a process akin to the "molecular stripping" seen in the NFκB/IκB genetic broadcasting system. This simulation shows that the existence of multiple binding configurations of transcription factors can have a significant impact on the kinetics and outcome of transcription factor dissociation from DNA, with important implications for the systems biology of gene regulation by Fis.

Structural and Dynamical Order of a Disordered Protein: Molecular Insights into Conformational Switching of PAGE4 at the Systems Level.

Folded proteins show a high degree of structural order and undergo (fairly constrained) collective motions related to their functions. On the other hand, intrinsically disordered proteins (IDPs), while lacking a well-defined three-dimensional structure, do exhibit some structural and dynamical ordering, but are less constrained in their motions than folded proteins. The larger structural plasticity of IDPs emphasizes the importance of entropically driven motions. Many IDPs undergo function-related disorder-to-order transitions driven by their interaction with specific binding partners. As experimental techniques become more sensitive and become better integrated with computational simulations, we are beginning to see how the modest structural ordering and large amplitude collective motions of IDPs endow them with an ability to mediate multiple interactions with different partners in the cell. To illustrate these points, here, we use Prostate-associated gene 4 (PAGE4), an IDP implicated in prostate cancer (PCa) as an example. We first review our previous efforts using molecular dynamics simulations based on atomistic AWSEM to study the conformational dynamics of PAGE4 and how its motions change in its different physiologically relevant phosphorylated forms. Our simulations quantitatively reproduced experimental observations and revealed how structural and dynamical ordering are encoded in the sequence of PAGE4 and can be modulated by different extents of phosphorylation by the kinases HIPK1 and CLK2. This ordering is reflected in changing populations of certain secondary structural elements as well as in the regularity of its collective motions. These ordered features are directly correlated with the functional interactions of WT-PAGE4, HIPK1-PAGE4 and CLK2-PAGE4 with the AP-1 signaling axis. These interactions give rise to repeated transitions between (high HIPK1-PAGE4, low CLK2-PAGE4) and (low HIPK1-PAGE4, high CLK2-PAGE4) cell phenotypes, which possess differing sensitivities to the standard PCa therapies, such as androgen deprivation therapy (ADT). We argue that, although the structural plasticity of an IDP is important in promoting promiscuous interactions, the modulation of the structural ordering is important for sculpting its interactions so as to rewire with agility biomolecular interaction networks with significant functional consequences.

PAGE4 and Conformational Switching: Insights from Molecular Dynamics Simulations and Implications for Prostate Cancer.

Prostate-associated gene 4 (PAGE4) is an intrinsically disordered protein implicated in prostate cancer. Thestress-response kinase homeodomain-interacting protein kinase 1 (HIPK1) phosphorylates two residues in PAGE4, serine 9 and threonine 51. Phosphorylation of these two residues facilitates the interaction of PAGE4 with activator protein-1 (AP-1) transcription factor complex to potentiate AP-1's activity. In contrast, hyperphosphorylation of PAGE4 by CDC-like kinase 2 (CLK2) attenuates this interaction with AP-1. Small-angleX-ray scattering and single-molecule fluorescence resonance energy transfer measurements have shown that PAGE4 expands upon hyperphosphorylation and that this expansion is localized to its N-terminal half. To understand the interactions underlying this structural transition, we performed molecular dynamics simulations using Atomistic AWSEM, a multi-scale molecular model that combines atomistic and coarse-grained simulation approaches. Our simulations show that electrostatic interactions drive transient formation of an N-terminal loop, the destabilization of which accounts for the dramatic change in size upon hyperphosphorylation. Phosphorylation also changes the preference of secondary structure formation of the PAGE4 ensemble, which leads to a transition between states that display different degrees of disorder. Finally, we construct a mechanism-based mathematical model that allows us to capture the interactions ofdifferent phosphoforms of PAGE4 with AP-1 and its downstream target, the androgen receptor (AR)-a key therapeutic target in prostate cancer. Our model predicts intracellular oscillatory dynamics of HIPK1-PAGE4, CLK2-PAGE4, and AR activity, indicating phenotypic heterogeneity in an isogenic cell population. Thus, conformational switching of PAGE4 may potentially affect the efficiency of therapeutically targeting AR activity.

Comparing the Aggregation Free Energy Landscapes of Amyloid Beta(1-42) and Amyloid Beta(1-40).

Using a predictive coarse-grained protein force field, we compute and compare the free energy landscapes and relative stabilities of amyloid-ß protein (1-42) and amyloid-ß protein (1-40) in their monomeric and oligomeric forms up to the octamer. At the same concentration, the aggregation free energy profile of Aß42 is more downhill, with a computed solubility that is about 10 times smaller than that of Aß40. At a concentration of 40 µM, the clear free energy barrier between the pre-fibrillar tetramer form and the fibrillar pentamer in the Aß40 aggregation landscape disappears for Aß42, suggesting that the Aß42 tetramer has a more diverse structural range. To further compare the landscapes, we develop a cluster analysis based on the structural similarity between configurations and use it to construct an oligomerization map that captures the paths of easy interconversion between different but structurally similar states of oligomers for both species. A taxonomy of the oligomer species based on ß-sheet stacking topologies is proposed. The comparison of the two oligomerization maps highlights several key differences in the landscapes that can be attributed to the two additional C-terminal residues that Aß40 lacks. In general, the two terminal residues strongly stabilize the oligomeric structures for Aß42 relative to Aß40, and greatly facilitate the conversion from pre-fibrillar trimers to fibrillar tetramers.

Exploring the aggregation free energy landscape of the amyloid-ß protein (1-40).

A predictive coarse-grained protein force field [associative memory, water-mediated, structure, and energy model for molecular dynamics (AWSEM)-MD] is used to study the energy landscapes and relative stabilities of amyloid-ß protein (1-40) in the monomer and all of its oligomeric forms up to an octamer. We find that an isolated monomer is mainly disordered with a short α-helix formed at the central hydrophobic core region (L17-D23). A less stable hairpin structure, however, becomes increasingly more stable in oligomers, where hydrogen bonds can form between neighboring monomers. We explore the structure and stability of both prefibrillar oligomers that consist of mainly antiparallel ß-sheets and fibrillar oligomers with only parallel ß-sheets. Prefibrillar oligomers are polymorphic but typically take on a cylindrin-like shape composed of mostly antiparallel ß-strands. At the concentration of the simulation, the aggregation free energy landscape is nearly downhill. We use umbrella sampling along a structural progress coordinate for interconversion between prefibrillar and fibrillar forms to identify a conversion pathway between these forms. The fibrillar oligomer only becomes favored over its prefibrillar counterpart in the pentamer where an interconversion bottleneck appears. The structural characterization of the pathway along with statistical mechanical perturbation theory allow us to evaluate the effects of concentration on the free energy landscape of aggregation as well as the effects of the Dutch and Arctic mutations associated with early onset of Alzheimer's disease.

Molecular Mechanism of Facilitated Dissociation of Fis Protein from DNA.

Fis protein is a nucleoid-associated protein that plays many roles in transcriptional regulation and DNA site-specific recombination. In contrast to the naïve expectation based on stoichiometry, recent single-molecule studies have shown that the dissociation of Fis protein from DNA is accelerated by increasing the concentration of the Fis protein. Because the detailed molecular mechanism of facilitated dissociation is still not clear, in this study, we employ computational methods to explore the binding landscapes of Fis:DNA complexes with various stoichiometries. When two Fis molecules are present, simulations uncover a ternary complex, where the originally bound Fis protein is partially dissociated from DNA. The simulations support a three-state sequential kinetic model (N ⇄ I → D) for facilitated dissociation, thus explaining the concentration-dependent dissociation.

Protein Frustratometer 2: a tool to localize energetic frustration in protein molecules, now with electrostatics.

The protein frustratometer is an energy landscape theory-inspired algorithm that aims at localizing and quantifying the energetic frustration present in protein molecules. Frustration is a useful concept for analyzing proteins' biological behavior. It compares the energy distributions of the native state with respect to structural decoys. The network of minimally frustrated interactions encompasses the folding core of the molecule. Sites of high local frustration often correlate with functional regions such as binding sites and regions involved in allosteric transitions. We present here an upgraded version of a webserver that measures local frustration. The new implementation that allows the inclusion of electrostatic energy terms, important to the interactions with nucleic acids, is significantly faster than the previous version enabling the analysis of large macromolecular complexes within a user-friendly interface. The webserver is freely available at URL: http://frustratometer.qb.fcen.uba.ar.

Intrinsic coordination for revealing local structural changes in protein folding-unfolding.

With a deformed object of a rigid rod inside, the local dislocations may be tracked relatively easily with respect to the internal rigid rod. We apply this concept on protein folding-unfolding to track the internal structural changes of an unfolded protein in solution. Proposed here is a protein internal coordination based on the major axis X of an ellipsoidal protein and the stable intrinsic transition dipole moment µ of the protein during unfolding. In this methodology, small-angle X-ray scattering (SAXS) is used to provide the protein global morphologies in the native and unfolded states. Furthermore, time-resolved fluorescence anisotropy (TRFA) provides the relative orientation between X and µ of Trp59 of the model protein cytochrome c. Hence observed in the protein unfolding with denaturants, acid, urea, or GuHCl, is the elongation of the native protein conformation along a reoriented protein major axis; accompanied are the different extents of relocations of the terminal α helices and loop structures of the protein in the corresponding unfolding.

Electrostatics, structure prediction, and the energy landscapes for protein folding and binding.

While being long in range and therefore weakly specific, electrostatic interactions are able to modulate the stability and folding landscapes of some proteins. The relevance of electrostatic forces for steering the docking of proteins to each other is widely acknowledged, however, the role of electrostatics in establishing specifically funneled landscapes and their relevance for protein structure prediction are still not clear. By introducing Debye-Hückel potentials that mimic long-range electrostatic forces into the Associative memory, Water mediated, Structure, and Energy Model (AWSEM), a transferable protein model capable of predicting tertiary structures, we assess the effects of electrostatics on the landscapes of thirteen monomeric proteins and four dimers. For the monomers, we find that adding electrostatic interactions does not improve structure prediction. Simulations of ribosomal protein S6 show, however, that folding stability depends monotonically on electrostatic strength. The trend in predicted melting temperatures of the S6 variants agrees with experimental observations. Electrostatic effects can play a range of roles in binding. The binding of the protein complex KIX-pKID is largely assisted by electrostatic interactions, which provide direct charge-charge stabilization of the native state and contribute to the funneling of the binding landscape. In contrast, for several other proteins, including the DNA-binding protein FIS, electrostatics causes frustration in the DNA-binding region, which favors its binding with DNA but not with its protein partner. This study highlights the importance of long-range electrostatics in functional responses to problems where proteins interact with their charged partners, such as DNA, RNA, as well as membranes.

Thermodynamics of protein folding using a modified Wako-Saitô-Muñoz-Eaton model.

Herein, we propose a modified version of the Wako-Saitô-Muñoz-Eaton (WSME) model. The proposed model introduces an empirical temperature parameter for the hypothetical structural units (i.e., foldons) in proteins to include site-dependent thermodynamic behavior. The thermodynamics for both our proposed model and the original WSME model were investigated. For a system with beta-hairpin topology, a mathematical treatment (contact-pair treatment) to facilitate the calculation of its partition function was developed. The results show that the proposed model provides better insight into the site-dependent thermodynamic behavior of the system, compared with the original WSME model. From this site-dependent point of view, the relationship between probe-dependent experimental results and model's thermodynamic predictions can be explained. The model allows for suggesting a general principle to identify foldon behavior. We also find that the backbone hydrogen bonds may play a role of structural constraints in modulating the cooperative system. Thus, our study may contribute to the understanding of the fundamental principles for the thermodynamics of protein folding.