Simulation of Interstitial Fluid Flow in Ligaments: Comparison among Stokes,Brinkman and Darcy Models

In this paper, we use Stokes, Brinkman and Darcy equations to approximate the porous continuum media of ligament tissues respectively, simulate the flow field with FLUENT software, and study the shear stress on the cell surface due to the interstitial fluid flow. Since the Brinkman equation approaches Stokes equation well in high hydraulic permeability (k_p) condition (k_p ≥1.0×10^-8 m² in our numerical simulation), and it is an approximation to Darcy model in low k_p condition (k_p ≤5.0×10^-12 m² in our numerical simulation), we used the Brinkman model to simulate the interstitial fluid flow in the ligament where k_p is approximately 1.0×10^-16 m². It shows k_p and anisotropic property have a little effect on the flow field, but have a great effect on the shear stress on the membrane of interstitial cells (τ_cell). There is a linear relationship between τ_cell and , when k_p =1.0×10^-16 m² and the maximum τ_cell (τ_cell,max) is approximately 10 Pa. The anisotropic property will affect τ_cell''s distribution on the cell surface. When k_x/k_y>1, low τ_cell dominates the cell, while when k_x/k_y<1, high τ_cell dominants the cell.     

Cellular Microcystin Content in N-Limited Microcystis aeruginosa Can Be Predicted from Growth Rate

Cell quotas of microcystin (Q_MCYST; femtomoles of MCYST per cell), protein, and chlorophyll a (Chl a), cell dry weight, and cell volume were measured over a range of growth rates in N-limited chemostat cultures of the toxic cyanobacterium Microcystis aeruginosa MASH 01-A19. There was a positive linear relationship between Q_MCYST and specific growth rate (μ), from which we propose a generalized model that enables Q_MCYST at any nutrient-limited growth rate to be predicted based on a single batch culture experiment. The model predicts Q_MCYST from μ, μ_max (maximum specific growth rate), Q_MCYSTmax (maximum cell quota), and Q_MCYSTmin (minimum cell quota). Under the conditions examined in this study, we predict a Q_MCYSTmax of 0.129 fmol cell⁻¹ at μ_max and a Q_MCYSTmin of 0.050 fmol cell⁻¹ at μ = 0. Net MCYST production rate (R_MCYST) asymptotes to zero at μ = 0 and reaches a maximum of 0.155 fmol cell⁻¹ day⁻¹ at μ_max. MCYST/dry weight ratio (milligrams per gram [dry weight]) increased linearly with μ, whereas the MCYST/protein ratio reached a maximum at intermediate μ. In contrast, the MCYST/Chl a ratio remained constant. Cell volume correlated negatively with μ, leading to an increase in intracellular MCYST concentration at high μ. Taken together, our results show that fast-growing cells of N-limited M. aeruginosa are smaller, are of lower mass, and have a higher intracellular MCYST quota and concentration than slow-growing cells. The data also highlight the importance of determining cell MCYST quotas, as potentially confusing interpretations can arise from determining MCYST content as a ratio to other cell components.     

Co-assembly of Kv4 α Subunits with K+ Channel-interacting Protein 2 Stabilizes Protein Expression and Promotes Surface Retention of Channel Complexes

Members of the K⁺ channel-interacting protein (KChIP) family bind the distal N termini of members of the Shal subfamily of voltage-gated K⁺ channel (Kv4) pore-forming (α) subunits to generate rapidly activating, rapidly inactivating neuronal A-type (I_A) and cardiac transient outward (I_to) currents. In heterologous cells, KChIP co-expression increases cell surface expression of Kv4 α subunits and Kv4 current densities, findings interpreted to suggest that Kv4·KChIP complex formation enhances forward trafficking of channels (from the endoplasmic reticulum or the Golgi complex) to the surface membrane. The results of experiments here, however, demonstrate that KChIP2 increases cell surface Kv4.2 protein expression (∼40-fold) by an order of magnitude more than the increase in total protein (∼2-fold) or in current densities (∼3-fold), suggesting that mechanisms at the cell surface regulate the functional expression of Kv4.2 channels. Additional experiments demonstrated that KChIP2 decreases the turnover rate of cell surface Kv4.2 protein by inhibiting endocytosis and/or promoting recycling. Unexpectedly, the experiments here also revealed that Kv4.2·KChIP2 complex formation stabilizes not only (total and cell surface) Kv4.2 but also KChIP2 protein expression. This reciprocal protein stabilization and Kv4·KChIP2 complex formation are lost with deletion of the distal (10 amino acids) Kv4.2 N terminus. Taken together, these observations demonstrate that KChIP2 differentially regulates total and cell surface Kv4.2 protein expression and Kv4 current densities.     

The Activity of σV,an Extracytoplasmic Function σ Factor of Bacillus subtilis,Is Controlled by Regulated Proteolysis of the Anti-σ Factor RsiV

During growth in the environment, bacteria encounter stresses which can delay or inhibit their growth. To defend against these stresses, bacteria induce both resistance and repair mechanisms. Many bacteria regulate these resistance mechanisms using a group of alternative σ factors called extracytoplasmic function (ECF) σ factors. ECF σ factors represent the largest and most diverse family of σ factors. Here, we demonstrate that the activation of a member of the ECF30 subfamily of ECF σ factors, σ^V in Bacillus subtilis, is controlled by the proteolytic destruction of the anti-σ factor RsiV. We will demonstrate that the degradation of RsiV and, thus, the activation of σ^V requires multiple proteolytic steps. Upon exposure to the inducer lysozyme, the extracellular domain of RsiV is removed by an unknown protease, which cleaves at site 1. This cleavage is independent of PrsW, the B. subtilis site 1 protease, which cleaves the anti-σ factor RsiW. Following cleavage by the unknown protease, the N-terminal portion of RsiV requires further processing, which requires the site 2 intramembrane protease RasP. Our data indicate that the N-terminal portion of RsiV from amino acid 1 to 60, which lacks the extracellular domain, is constitutively degraded unless RasP is absent, indicating that RasP cleavage is constitutive. This suggests that the regulatory step in RsiV degradation and, thus, σ^V activation are controlled at the level of the site 1 cleavage. Finally, we provide evidence that increased resistance to lysozyme decreases σ^V activation. Collectively, these data provide evidence that the mechanism for σ^V activation in B. subtilis is controlled by regulated intramembrane proteolysis (RIP) and requires the site 2 protease RasP.     

Na+/K+-ATPase α-subunit (nkaα) Isoforms and Their mRNA Expression Levels,Overall Nkaα Protein Abundance,and Kinetic Properties of Nka in the Skeletal Muscle and Three Electric Organs of the Electric Eel,Electrophorus electricus

This study aimed to obtain the coding cDNA sequences of Na⁺/K⁺-ATPase α (nkaα) isoforms from, and to quantify their mRNA expression in, the skeletal muscle (SM), the main electric organ (EO), the Hunter’s EO and the Sach’s EO of the electric eel, Electrophorus electricus. Four nkaα isoforms (nkaα1c1, nkaα1c2, nkaα2 and nkaα3) were obtained from the SM and the EOs of E. electricus. Based on mRNA expression levels, the major nkaα expressed in the SM and the three EOs of juvenile and adult E. electricus were nkaα1c1 and nkaα2, respectively. Molecular characterization of the deduced Nkaα1c1 and Nkaα2 sequences indicates that they probably have different affinities to Na⁺ and K⁺. Western blotting demonstrated that the protein abundance of Nkaα was barely detectable in the SM, but strongly detected in the main and Hunter’s EOs and weakly in the Sach’s EO of juvenile and adult E. electricus. These results corroborate the fact that the main EO and Hunter’s EO have high densities of Na⁺ channels and produce high voltage discharges while the Sach’s EO produces low voltage discharges. More importantly, there were significant differences in kinetic properties of Nka among the three EOs of juvenile E. electricus. The highest and lowest V _max of Nka were detected in the main EO and the Sach’s EO, respectively, with the Hunter’s EO having a V _max value intermediate between the two, indicating that the metabolic costs of EO discharge could be the highest in the main EO. Furthermore, the Nka from the main EO had the lowest K_m (or highest affinity) for Na⁺ and K⁺ among the three EOs, suggesting that the Nka of the main EO was more effective than those of the other two EOs in maintaining intracellular Na⁺ and K⁺ homeostasis and in clearing extracellular K⁺ after EO discharge.     

Crystal structure of the GABA(A)-receptor-associated protein, GABARAP

The GABA_A-receptor-associated protein (GABARAP) is a member of a growing family of intracellular membrane trafficking and/or fusion proteins and has been implicated in plasma membrane targeting and/or recycling of GABA_A receptors. GABARAP is localized on intracellular membranes such as the trans-Golgi network, binds to the γ 2 subunit of GABA_A receptors and interacts with microtubules and the N-ethylmaleimide-sensitive factor. We report the X-ray crystal structure of mammalian GABARAP at 2.0 Å resolution. GABARAP consists of an N-terminal basic helical region, which has been implicated in tubulin binding, and a core structure with a conserved ubiquitin-like fold. Consistent with the high extent of sequence conservation among GABARAP homologues from plants to mammals, one face of the core structure is absolutely conserved while the opposite face shows considerable divergence. These features are in agreement with the conserved surface mediating protein–protein interactions shared by all members of the family, whereas the non-conserved surface region may play specific roles, such as docking to particular membrane receptors.     

Functional Characterization of CaVα2δ Mutations Associated with Sudden Cardiac Death

L-type Ca²⁺ channels play a critical role in cardiac rhythmicity. These ion channels are oligomeric complexes formed by the pore-forming Ca_Vα1 with the auxiliary Ca_Vβ and Ca_Vα2δ subunits. Ca_Vα2δ increases the peak current density and improves the voltage-dependent activation gating of Ca_V1.2 channels without increasing the surface expression of the Ca_Vα1 subunit. The functional impact of genetic variants of CACNA2D1 (the gene encoding for Ca_Vα2δ), associated with shorter repolarization QT intervals (the time interval between the Q and the T waves on the cardiac electrocardiogram), was investigated after recombinant expression of the full complement of L-type Ca_V1.2 subunits in human embryonic kidney 293 cells. By performing side-by-side high resolution flow cytometry assays and whole-cell patch clamp recordings, we revealed that the surface density of the Ca_Vα2δ wild-type protein correlates with the peak current density. Furthermore, the cell surface density of Ca_Vα2δ mutants S755T, Q917H, and S956T was not significantly different from the cell surface density of the Ca_Vα2δ wild-type protein expressed under the same conditions. In contrast, the cell surface expression of Ca_Vα2δ D550Y, Ca_Vα2δ S709N, and the double mutant D550Y/Q917H was reduced, respectively, by ≈30–33% for the single mutants and by 60% for the latter. The cell surface density of D550Y/Q917H was more significantly impaired than protein stability, suggesting that surface trafficking of Ca_Vα2δ was disrupted by the double mutation. Co-expression with D550Y/Q917H significantly decreased Ca_V1.2 currents as compared with results obtained with Ca_Vα2δ wild type. It is concluded that D550Y/Q917H reduced inward Ca²⁺ currents through a defect in the cell surface trafficking of Ca_Vα2δ. Altogether, our results provide novel insight in the molecular mechanism underlying the modulation of Ca_V1.2 currents by Ca_Vα2δ.     

Activation of αVβ3 on Vascular Cells Controls Recognition of Prothrombin

Regulation of vascular homeostasis depends upon collaboration between cells of the vessel wall and blood coagulation system. A direct interaction between integrin α_Vβ₃ on endothelial cells and smooth muscle cells and prothrombin, the pivotal proenzyme of the blood coagulation system, is demonstrated and activation of the integrin is required for receptor engagement. Evidence that prothrombin is a ligand for α_Vβ₃ on these cells include: (a) prothrombin binds to purified α_Vβ₃ via a RGD recognition specificity; (b) prothrombin supports α_Vβ₃-mediated adhesion of stimulated endothelial cells and smooth muscle cells; and (c) endothelial cells, either in suspension and in a monolayer, recognize soluble prothrombin via α_Vβ₃. α_Vβ₃-mediated cell adhesion to prothrombin, but not to fibrinogen, required activation of the receptor. Thus, the functionality of the α_Vβ₃ receptor is ligand defined, and prothrombin and fibrinogen represent activation- dependent and activation-independent ligands. Activation of α_Vβ₃ could be induced not only by model agonists, PMA and Mn²⁺, but also by a physiologically relevant agonist, ADP. Inhibition of protein kinase C and calpain prevented activation of α_Vβ₃ on vascular cells, suggesting that these molecules are involved in the inside-out signaling events that activate the integrin. The capacity of α_Vβ₃ to interact with prothrombin may play a significant role in the maintenance of hemostasis; and, at a general level, ligand selection by α_Vβ₃ may be controlled by the activation state of this integrin.     

Genotypic variability in vulnerability of leaf xylem to cavitation in water-stressed and well-irrigated sugarcane

Genotypic variability in vulnerability of leaf xylem to water-stress-induced cavitation was determined in four sugarcane (Saccharum sp.) clones using detached leaf segments in a hydraulic conductivity apparatus. Vulnerability curves were constructed by plotting the percentage of maximum conductivity versus leaf water potential (ψ_I) and fitting curves using a Weibull function. The ψ_I at which each clone lost 10, 50, and 80% of maximum conductivity was determined. Maximum conductivity per unit of leaf width was positively associated with metaxylem vessel diameter. The commercial clone H65-7052 exhibited the highest and the nondomesticated S. spontaneum exhibited the lowest conductivity. All four clones lost substantial conductivity at values of ψ_I less negative than −1.4 MPa, but H65-7052 was able to maintain 50% conductivity to lower ψ_I than the other clones. S. spontaneum sustained the most negative ψ_I (−1.99 MPa) before reaching the 80% conductivity loss point. Clone H69-8235 was consistently the most vulnerable to initial loss of conductivity. These vulnerability functions were used in conjunction with field measurements of ψ_I to estimate diurnal losses in leaf hydraulic conductivity under irrigated and droughted conditions. H69-8235 lost up to 50% of its conductivity during the day, even when well irrigated, and more than 80% when subjected to drought. The other clones exhibited lower conductivity losses. These losses are apparently reversed overnight by root pressure. Despite their close genetic relationships, these clones exhibited large differences in conductivity, in the vulnerability of their xylem to cavitation, and in gas exchange behavior. The potential for altering water relations by selecting for particular hydraulic characteristics is discussed.     

Solution structure of psi32-modified anticodon stem-loop of Escherichia coli tRNAPhe

Nucleoside base modifications can alter the structures and dynamics of RNA molecules and are important in tRNAs for maintaining translational fidelity and efficiency. The unmodified anticodon stem–loop from Escherichia coli tRNA^Phe forms a trinucleotide loop in solution, but Mg²⁺ and dimethylallyl modification of A₃₇ N6 destabilize the loop-proximal base pairs and increase the mobility of the loop nucleotides. The anticodon arm has three additional modifications, ψ₃₂, ψ₃₉, and A₃₇ C2-thiomethyl. We have used NMR spectroscopy to investigate the structural and dynamical effects of ψ₃₂ on the anticodon stem-loop from E.coli tRNA^Phe. The ψ₃₂ modification does not significantly alter the structure of the anticodon stem–loop relative to the unmodified parent molecule. The stem of the RNA molecule includes base pairs ψ₃₂-A₃₈ and U₃₃–A₃₇ and the base of ψ₃₂ stacks between U₃₃ and A₃₁. The glycosidic bond of ψ₃₂ is in the anti configuration and is paired with A₃₈ in a Watson–Crick geometry, unlike residue 32 in most crystal structures of tRNA. The ψ₃₂ modification increases the melting temperature of the stem by ~3.5°C, although the ψ₃₂ and U₃₃ imino resonances are exchange broadened. The results suggest that ψ₃₂ functions to preserve the stem integrity in the presence of additional loop modifications or after reorganization of the loop into a translationally functional conformation.     

The Structure of Mytilus Smooth Muscle and the Electrical Constants of the Resting Muscle

The individual muscle fibers of the anterior byssus retractor muscle (ABRM) of Mytilus edulis L. are uninucleate, 1.2–1.8 mm in length, 5 µm in diameter, and organized into bundles 100–200 µm in diameter, surrounded by connective tissue. Some bundles run the length of the whole muscle. Adjacent muscle cell membranes are interconnected by nexuses at frequent intervals. Specialized attachments exist between muscle fibers and connective tissue. Electrical constants of the resting muscle membrane were measured with intracellular recording electrodes and both extracellular and intracellular current-passing electrodes. With an intracellular current-passing electrode, the time constant τ, was 4.3 ± 1.5 ms. With current delivered via an extracellular electrode τ was 68.3 ± 15 ms. The space constant, λ, was 1.8 mm ± 0.4. The membrane input resistance, R_eff, ranged from 23 to 51 MΩ. The observations that values of τ depend on the method of passing current, and that the value of λ is large relative to fiber length and diameter are considered evidence that the individual muscle fibers are electrically interconnected within bundles in a three-dimensional network. Estimations are made of the membrane resistance, R_m, to compare the values to fast and slow striated muscle fibers and mammalian smooth muscles. The implications of this study in reinterpreting previous mechanical and electrical studies are discussed.     

The N-terminal Domain Allosterically Regulates Cleavage and Activation of the Epithelial Sodium Channel

The epithelial sodium channel (ENaC) is activated upon endoproteolytic cleavage of specific segments in the extracellular domains of the α- and γ-subunits. Cleavage is accomplished by intracellular proteases prior to membrane insertion and by surface-expressed or extracellular soluble proteases once ENaC resides at the cell surface. These cleavage events are partially regulated by intracellular signaling through an unknown allosteric mechanism. Here, using a combination of computational and experimental techniques, we show that the intracellular N terminus of γ-ENaC undergoes secondary structural transitions upon interaction with phosphoinositides. From ab initio folding simulations of the N termini in the presence and absence of phosphatidylinositol 4,5-bisphosphate (PIP₂), we found that PIP₂ increases α-helical propensity in the N terminus of γ-ENaC. Electrophysiology and mutation experiments revealed that a highly conserved cluster of lysines in the γ-ENaC N terminus regulates accessibility of extracellular cleavage sites in γ-ENaC. We also show that conditions that decrease PIP₂ or enhance ubiquitination sharply limit access of the γ-ENaC extracellular domain to proteases. Further, the efficiency of allosteric control of ENaC proteolysis is dependent on Tyr³⁷⁰ in γ-ENaC. Our findings provide an allosteric mechanism for ENaC activation regulated by the N termini and sheds light on a potential general mechanism of channel and receptor activation.     

Complex Role of Collybistin and Gephyrin in GABAA Receptor Clustering

Gephyrin and collybistin are key components of GABA_A receptor (GABA_AR) clustering. Nonetheless, resolving the molecular interactions between the plethora of GABA_AR subunits and these clustering proteins is a significant challenge. We report a direct interaction of GABA_AR α2 and α3 subunit intracellular M3–M4 domain (but not α1, α4, α5, α6, β1–3, or γ1–3) with gephyrin. Curiously, GABA_AR α2, but not α3, binds to both gephyrin and collybistin using overlapping sites. The reciprocal binding sites on gephyrin for collybistin and GABA_AR α2 also overlap at the start of the gephyrin E domain. This suggests that although GABA_AR α3 interacts with gephyrin, GABA_AR α2, collybistin, and gephyrin form a trimeric complex. In support of this proposal, tri-hybrid interactions between GABA_AR α2 and collybistin or GABA_AR α2 and gephyrin are strengthened in the presence of gephyrin or collybistin, respectively. Collybistin and gephyrin also compete for binding to GABA_AR α2 in co-immunoprecipitation experiments and co-localize in transfected cells in both intracellular and submembrane aggregates. Interestingly, GABA_AR α2 is capable of “activating ” collybistin isoforms harboring the regulatory SH3 domain, enabling targeting of gephyrin to the submembrane aggregates. The GABA_AR α2-collybistin interaction was disrupted by a pathogenic mutation in the collybistin SH3 domain (p.G55A) that causes X-linked intellectual disability and seizures by disrupting GABA_AR and gephyrin clustering. Because immunohistochemistry in retina revealed a preferential co-localization of collybistin with α2 subunit containing GABA_ARs, but not GlyRs or other GABA_AR subtypes, we propose that the collybistin-gephyrin complex has an intimate role in the clustering of GABA_ARs containing the α2 subunit.     

Impairment of ATP hydrolysis decreases adenosine A1 receptor tonus favoring cholinergic nerve hyperactivity in the obstructed human urinary bladder

This study was designed to investigate whether reduced adenosine formation linked to deficits in extracellular ATP hydrolysis by NTPDases contributes to detrusor neuromodulatory changes associated with bladder outlet obstruction in men with benign prostatic hyperplasia (BPH). The kinetics of ATP catabolism and adenosine formation as well as the role of P1 receptor agonists on muscle tension and nerve-evoked [³H]ACh release were evaluated in mucosal-denuded detrusor strips from BPH patients (n = 31) and control organ donors (n = 23). The neurogenic release of ATP and [³H]ACh was higher (P < 0.05) in detrusor strips from BPH patients. The extracellular hydrolysis of ATP and, subsequent, adenosine formation was slower (t_1/2 73 vs. 36 min, P < 0.05) in BPH detrusor strips. The A₁ receptor-mediated inhibition of evoked [³H]ACh release by adenosine (100 μM), NECA (1 μM), and R-PIA (0.3 μM) was enhanced in BPH bladders. Relaxation of detrusor contractions induced by acetylcholine required 30-fold higher concentrations of adenosine. Despite VAChT-positive cholinergic nerves exhibiting higher A₁ immunoreactivity in BPH bladders, the endogenous adenosine tonus revealed by adenosine deaminase is missing. Restoration of A₁ inhibition was achieved by favoring (1) ATP hydrolysis with apyrase (2 U mL⁻¹) or (2) extracellular adenosine accumulation with dipyridamole or EHNA, as these drugs inhibit adenosine uptake and deamination, respectively. In conclusion, reduced ATP hydrolysis leads to deficient adenosine formation and A₁ receptor-mediated inhibition of cholinergic nerve activity in the obstructed human bladder. Thus, we propose that pharmacological manipulation of endogenous adenosine levels and/or A₁ receptor activation might be useful to control bladder overactivity in BPH patients.     

Hyperpolarization-Activated Current (Ih) Is Reduced in Hippocampal Neurons from Gabra5?/? Mice

Changes in the expression of γ-aminobutyric acid type A (GABA_A) receptors can either drive or mediate homeostatic alterations in neuronal excitability. A homeostatic relationship between α5 subunit-containing GABA_A (α5GABA_A) receptors that generate a tonic inhibitory conductance, and HCN channels that generate a hyperpolarization-activated cation current (I_h) was recently described for cortical neurons, where a reduction in I_h was accompanied by a reciprocal increase in the expression of α5GABA_A receptors resulting in the preservation of dendritosomatic synaptic function. Here, we report that in mice that lack the α5 subunit gene (Gabra5−/−), cultured embryonic hippocampal pyramidal neurons and ex vivo CA1 hippocampal neurons unexpectedly exhibited a decrease in I_h current density (by 40% and 28%, respectively), compared with neurons from wild-type (WT) mice. The resting membrane potential and membrane hyperpolarization induced by blockade of I_h with ZD-7288 were similar in cultured WT and Gabra5−/− neurons. In contrast, membrane hyperpolarization measured after a train of action potentials was lower in Gabra5−/− neurons than in WT neurons. Also, membrane impedance measured in response to low frequency stimulation was greater in cultured Gabra5−/− neurons. Finally, the expression of HCN1 protein that generates I_h was reduced by 41% in the hippocampus of Gabra5−/− mice. These data indicate that loss of a tonic GABAergic inhibitory conductance was followed by a compensatory reduction in I_h. The results further suggest that the maintenance of resting membrane potential is preferentially maintained in mature and immature hippocampal neurons through the homeostatic co-regulation of structurally and biophysically distinct cation and anion channels.     

Structural Flexibility of CaV1.2 and CaV2.2 I-II Proximal Linker Fragments in?Solution

Voltage-dependent calcium channels (Ca_V) enable the inward flow of calcium currents for a wide range of cells. Ca_V1 and Ca_V2 subtype α1 subunits form the conducting pore using four repeated membrane domains connected by intracellular linkers. The domain I-II linker connects to the membrane gate (IS6), forming an α-helix, and is bound to the Ca_Vβ subunit. Previous studies indicated that this region may or may not form a continuous helix depending on the Ca_V subtype, thereby modulating channel activation and inactivation properties. Here, we used small-angle x-ray scattering and ensemble modeling analysis to investigate the solution structure of these linkers, extending from the membrane domain and including the Ca_Vβ-binding site, called the proximal linker (PL). The results demonstrate that the Ca_V1.2 PL is more flexible than the Ca_V2.2 PL, the flexibility is intrinsic and not dependent on Ca_Vβ binding, and the flexibility can be most easily explained by the presence of conserved glycines. Our analysis also provides a robust example of investigating protein domains in which flexibility plays an essential role.