Mucosal folding in biologic vessels

A two-layer model is used to simulate the mechanical behavior of an airway or other biological vessel under external compressive stress or smooth muscle constriction sufficient to cause longitudinal mucosal buckling. Analytic andfinite element numerical methods are used to examine the onset of buckling. Post-buckling solutions are obtained by finite element analysis, then verified with large-scale physical model experiments. The two-layer model provides insight into how the stiffness of a vessel wall changes due to changes in the geometry and intrinsic material stiffnesses of the wall components. Specifically, it predicts that the number of mucosal folds in the buckled state is diminished most by increased thickness of the inner collagen-rich layer, and relatively little by increased thickness of the outer submucosal layer. An increase in the ratio of the inner to outer material stiffnesses causes an intermediate reduction in the number of folds. Results are cast in a simple form that can easily be used to predict buckling in a variety of vessels. The model quantitatively confirms that an increase in the thickness of the inner layer leads to a reduction in the number of mucosal folds, and further, that this can lead to increased vessel collapse at high levels of smooth muscle constriction.     

Possible role of differential growth in airway wall remodeling in asthma

Airway remodeling in patients with chronic asthma is characterized by a thickening of the airway walls. It has been demonstrated in previous theoretical models that this change in thickness can have an important mechanical effect on the properties of the wall, in particular on the phenomenon of mucosal folding induced by smooth muscle contraction. In this paper, we present a model for mucosal folding of the airway in the context of growth. The airway is modeled as a bilayered cylindrical tube, with both geometric and material nonlinearities accounted for via the theory of finite elasticity. Growth is incorporated into the model through the theory of morphoelasticity. We explore a range of growth possibilities, allowing for anisotropic growth as well as different growth rates in each layer. Such nonuniform growth, referred to as differential growth, can change the properties of the material beyond geometrical changes through the generation of residual stresses. We demonstrate that differential growth can have a dramatic impact on mucosal folding, in particular on the critical pressure needed to induce folding, the buckling pattern, as well as airway narrowing. We conclude that growth may be an important component in airway remodeling.     

Structure and Mechanics of Supporting Cells in the Guinea Pig Organ of Corti

The mechanical properties of the mammalian organ of Corti determine its sensitivity to sound frequency and intensity, and the structure of supporting cells changes progressively with frequency along the cochlea. From the apex (low frequency) to the base (high frequency) of the guinea pig cochlea inner pillar cells decrease in length incrementally from 75–55 µm whilst the number of axial microtubules increases from 1,300–2,100. The respective values for outer pillar cells are 120–65 µm and 1,500–3,000. This correlates with a progressive decrease in the length of the outer hair cells from >100 µm to 20 µm. Deiters''cell bodies vary from 60–50 µm long with relatively little change in microtubule number. Their phalangeal processes reflect the lengths of outer hair cells but their microtubule numbers do not change systematically. Correlations between cell length, microtubule number and cochlear location are poor below 1 kHz. Cell stiffness was estimated from direct mechanical measurements made previously from isolated inner and outer pillar cells. We estimate that between 200 Hz and 20 kHz axial stiffness, bending stiffness and buckling limits increase, respectively,∼3, 6 and 4 fold for outer pillar cells, ∼2, 3 and 2.5 fold for inner pillar cells and ∼7, 20 and 24 fold for the phalangeal processes of Deiters''cells. There was little change in the Deiters''cell bodies for any parameter. Compensating for effective cell length the pillar cells are likely to be considerably stiffer than Deiters''cells with buckling limits 10–40 times greater. These data show a clear relationship between cell mechanics and frequency. However, measurements from single cells alone are insufficient and they must be combined with more accurate details of how the multicellular architecture influences the mechanical properties of the whole organ.     

Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests.

Observation of cell membrane buckling and cell folding in micropipette aspiration experiments was used to evaluate the bending rigidity of the red blood cell membrane. The suction pressure required to buckle the membrane surface initially was found to be about one-half to two-thirds of the pressure that caused the cell to fold and move up the pipet. A simple analytical model for buckling of a membrane disk supported at inner and outer radii correlates well with the observed buckling pressures vs. pipet radii. The buckling pressure is predicted to increase in inverse proportion to the cube of the pipet radius; also, the buckling pressure depends inversely on the radial distance to the toroidal rim of the cell, normalized by the pipet radius. As such, the pressure required to buckle the membrane with 1 X 10(-4) cm diam pipet would be about four times greater than with a 2 X 10(-4) cm pipet. This is the behavior observed experimentally. Based on analysis of the observed buckling data, the membrane bending or curvature elastic modulus is calculated to be 1.8 X 10(-12) dyn-cm.     

Folding kinetics of the outer membrane proteins OmpA and FomA into phospholipid bilayers

The folding mechanism of outer membrane proteins (OMPs) of Gram-negative bacteria into lipid bilayers has been studied using OmpA of E. coli and FomA of F. nucleatum as examples. Both, OmpA and FomA are soluble in unfolded form in urea and insert and fold into phospholipid bilayers upon strong dilution of the denaturant urea. OmpA is a structural protein and forms a small ion channel, composed of an 8-stranded transmembrane beta-barrel domain. FomA is a voltage-dependent porin, predicted to form a 14 stranded beta-barrel. Both OMPs fold into a range of model membranes of very different phospholipid compositions. Three membrane-bound folding intermediates of OmpA were discovered in folding studies with dioleoylphosphatidylcholine bilayers that demonstrated a highly synchronized mechanism of secondary and tertiary structure formation of beta-barrel membrane proteins. A study on FomA folding into lipid bilayers indicated the presence of parallel folding pathways for OMPs with larger transmembrane beta-barrels.     

Linked opening angle and histological and mechanical aspects of the proximal pulmonary arteries of healthy and pulmonary hypertensive rats and calves

Understanding how arterial remodeling changes the mechanical behavior of pulmonary arteries (PAs) is important to the evaluation of pulmonary vascular function. Early and current efforts have focused on the arteries' histological changes, their mechanical properties under in vitro mechanical testing, and their zero-stress and no-load states. However, the linkage between the histology and mechanical behavior is still not well understood. To explore this linkage, we investigated the geometry, residual stretch, and histology of proximal PAs in both adult rat and neonatal calf hypoxic models of pulmonary hypertension (PH), compared their changes due to chronic hypoxia across species, and proposed a two-layer mechanical model of artery to relate the opening angle to the stiffness ratio of the PA outer to inner layer. We found that the proximal PA remodeling in calves was quite different from that in rats. In rats, the arterial wall thickness, inner diameter, and outer layer thickness fraction all increased dramatically in PH and the opening angle decreased significantly, whereas in calves, only the arterial wall thickness increased in PH. The proposed model predicted that the stiffness ratio of the calf proximal PAs changed very little from control to hypertensive group, while the decrease of opening angle in rat proximal PAs in response to chronic hypoxia was approximately linear to the increase of the stiffness ratio. We conclude that the arterial remodeling in rat and calf proximal PAs is different and the change of opening angle can be linked to the change of the arterial histological structure and mechanics.     

All-atom ab initio folding of a diverse set of proteins

Natural proteins fold to a unique, thermodynamically dominant state. Modeling of the folding process and prediction of the native fold of proteins are two major unsolved problems in biophysics. Here, we show successful all-atom ab initio folding of a representative diverse set of proteins by using a minimalist transferable-energy model that consists of two-body atom-atom interactions, hydrogen bonding, and a local sequence-energy term that models sequence-specific chain stiffness. Starting from a random coil, the native-like structure was observed during replica exchange Monte Carlo (REMC) simulation for most proteins regardless of their structural classes; the lowest energy structure was close to native-in the range of 2-6 A root-mean-square deviation (rmsd). Our results demonstrate that the successful folding of a protein chain to its native state is governed by only a few crucial energetic terms.     

Anisotropic and inhomogeneous tensile behavior of the human anulus fibrosus: experimental measurement and material model predictions

The anulus fibrosus (AF) of the intervertebral disc exhibits spatial variations in structure and composition that give rise to both anisotropy and inhomogeneity in its material behaviors in tension. In this study, the tensile moduli and Poisson's ratios were measured in samples of human AF along circumferential, axial, and radial directions at inner and outer sites. There was evidence of significant inhomogeneity in the linear-region circumferential tensile modulus (17.4+/-14.3 MPa versus 5.6+/-4.7 MPa, outer versus inner sites) and the Poisson's ratio v21 (0.67+/-0.22 versus 1.6+/-0.7, outer versus inner), but not in the axial modulus (0.8+/-0.9 MPa) or the Poisson's ratios V12 (1.8+/-1.4) or v13 (0.6+/-0.7). These properties were implemented in a linear an isotropic material model of the AF to determine a complete set of model properties and to predict material behaviors for the AF under idealized kinematic states. These predictions demonstrate that interactions between fiber populations in the multilamellae AF significantly contribute to the material behavior, suggesting that a model for th     

The biology and functional morphology of Arca noae (Bivalvia: Arcidae) from the Adriatic Sea, Croatia, with a discussion on the evolution of the bivalve mantle margin

In the Croatian Adriatic, Arca noae occurs from the low intertidal to a depth of 60 m; it can live for > 15 years and is either solitary or forms byssally attached clumps with Modiolus barbatus. The shell is anteriorly foreshortened and posteriorly elongate. The major inhalant flow is from the posterior although a remnant anterior stream is retained. There are no anterior but huge posterior byssal retractor muscles and both anterior and posterior pedal retractors. The ctenidia are of Type B(1a) and the ctenidial–labial palp junction is Category 3. The ctenidia collect, filter and undertake the primary sorting of potential food in the inhalant water. The labial palps are small with simple re‐sorting tracks on the ridges of their inner surfaces. The ciliary currents of the mantle cavity appear largely concerned with the rejection of particulate material. The mantle margin comprises an outer and an (either) inner or middle fold. The outer fold is divided into outer and inner components that secrete the shell and are photo‐sensory, respectively. The latter bears a large number of pallial eyes, especially posteriorly. The inner/middle mantle fold of A. noae, possibly representative of simpler, more primitive conditions, may have differentiated into distinct folds in other recent representatives of the Bivalvia.     

Beta-barrel proteins that reside in the Escherichia coli outer membrane in vivo demonstrate varied folding behavior in vitro

Little is known about the dynamic process of membrane protein folding, and few models exist to explore it. In this study we doubled the number of Escherichia coli outer membrane proteins (OMPs) for which folding into lipid bilayers has been systematically investigated. We cloned, expressed, and folded nine OMPs: outer membrane protein X (OmpX), OmpW, OmpA, the crcA gene product (PagP), OmpT, outer membrane phospholipase A (OmpLa), the fadl gene product (FadL), the yaet gene product (Omp85), and OmpF. These proteins fold into the same bilayer in vivo and share a transmembrane beta-barrel motif but vary in sequence and barrel size. We quantified the ability of these OMPs to fold into a matrix of bilayer environments. Several trends emerged from these experiments: higher pH values, thinner bilayers, and increased bilayer curvature promote folding of all OMPs. Increasing the incubation temperature promoted folding of several OMPs but inhibited folding of others. We discovered that OMPs do not have the same ability to fold into any single bilayer environment. This suggests that although environmental factors influence folding, OMPs also have intrinsic qualities that profoundly modulate their folding. To rationalize the differences in folding efficiency, we performed kinetic and thermal denaturation experiments, the results of which demonstrated that OMPs employ different strategies to achieve the observed folding efficiency.     

Folding of the β-Barrel Membrane Protein OmpA into Nanodiscs

Nanodiscs (NDs) are an excellent alternative to small unilamellar vesicles (SUVs) for studies of membrane protein structure, but it has not yet been shown that membrane proteins are able to spontaneously fold and insert into a solution of freely diffusing NDs. In this article, we present SDS-PAGE differential mobility studies combined with fluorescence, circular dichroism, and ultraviolet resonance Raman spectroscopy to confirm the spontaneous folding of outer membrane protein A (OmpA) into preformed NDs. Folded OmpA in NDs was incubated with Arg-C protease, resulting in the digestion of OmpA to membrane-protected fragments with an apparent molecular mass of ∼26 kDa (major component) and ∼24 kDa (minor component). The OmpA folding yields were greater than 88% in both NDs and SUVs. An OmpA adsorbed intermediate on NDs could be isolated at low temperature and induced to fold via an increase in temperature, analogous to the temperature-jump experiments on SUVs. The circular dichroism spectra of OmpA in NDs and SUVs were similar and indicated β-barrel secondary structure. Further evidence of OmpA folding into NDs was provided by ultraviolet resonance Raman spectroscopy, which revealed the intense 785 cm⁻¹ structural marker for folded OmpA in NDs. The primary difference between folding in NDs and SUVs was the kinetics; the rate of folding was two- to threefold slower in NDs compared to in SUVs, and this decreased rate can tentatively be attributed to the properties of NDs. These data indicate that NDs may be an excellent alternative to SUVs for folding experiments and offer benefits of optical clarity, sample homogeneity, control of ND:protein ratios, and greater stability.     

An electron microscope study of the formation of the periostracum in the freshwater bivalve, Anodonta cygnea

The periostracum and cells lining the periostracal groove of Anodonta cygnea L. have been studied at the electron microscope level. The cells lining the inner face of the outer fold differ in fine structural details, five cell types being recognized. Along the length of the outer surface of the middle fold, to which the periostracum is closely applied, only two cell types are evident. At the base of the periostracal groove the two epithelia are separated by a bulbous region containing a group of basal cells which initiate the periostracum. The periostracum, which is homogenously electron-lucid, originates in the intercellular space between a basal cell and the first cell of the middle fold. It increases in thickness in the periostracal groove due to the secretory activity of the different outer fold cells. The cells of the middle fold do not appear to be involved in periostracum formation.     

Biomechanics and functional anatomy of hollow-stemmed sphenopsids. I. Equisetum giganteum (Equisetaceae)

The hollow stem of Equisetum giganteum owes its mechanical stability to an outer ring of strengthening tissue, which provides stiffness and strength in the longitudinal direction, but also to an inner lining of turgid parenchyma, which lends resistance to local buckling. With a height >2.5 m isolated stems are mechanically unstable. However, in dense stands individual stems support each other by interlacing with their side branches, the typical growth habit of semi-self-supporters.     

Constraining local structure can speed up folding by promoting structural polarization of the folding pathway

The pathway which proteins take to fold can be influenced from the earliest events of structure formation. In this light, it was both predicted and confirmed that increasing the stiffness of a beta hairpin turn decreased the size of the transition state ensemble (TSE), while increasing the folding rate. Thus, there appears to be a relationship between conformationally restricting the TSE and increasing the folding rate, at least for beta hairpin turns. In this study, we hypothesize that the enormous sampling necessary to fold even two-state folding proteins in silico could be reduced if local structure constraints were used to restrict structural heterogeneity by polarizing folding pathways or forcing folding into preferred routes. Using a Gō model, we fold Chymotrypsin Inhibitor 2 (CI-2) and the src SH3 domain after constraining local sequence windows to their native structure by rigid body dynamics (RBD). Trajectories were monitored for any changes to the folding pathway and differences in the kinetics compared with unconstrained simulations. Constraining local structure decreases folding time two-fold for 41% of src SH3 windows and 45% of CI-2 windows. For both proteins, folding times are never significantly increased after constraining any window. Structural polarization of the folding pathway appears to explain these rate increases. Folding rate enhancements are consistent with the goal to reduce sampling time necessary to reach native structures during folding simulations. As anticipated, not all constrained windows showed an equal decrease in folding time. We conclude by analyzing these differences and explain why RBD may be the preferred way to constrain structure.     

Interactions between folding factors and bacterial outer membrane proteins

The outer membrane is the first line of contact between Gram-negative bacteria and their external environment. Embedded in the outer membrane are integral outer membrane proteins (OMPs) that perform a diverse range of tasks. OMPs are synthesized in the cytoplasm and are translocated across the inner membrane and probably diffuse through the periplasm before they are inserted into the outer membrane in a folded and biologically active form. Passage through the periplasm presents a number of challenges, due to the hydrophobic nature of the OMPs and the choice of membranes into which they can insert. Recently, a number of periplasmic proteins and one OMP have been shown to play a role in OMP biogenesis. In this review, we describe what is known about these folding factors and how they function in a biological context. In particular, we focus on how they interact with the OMPs at the molecular level and present a comprehensive overview of data relating to a possible effect on OMP folding yield and kinetics. Furthermore, we discuss the role of lipo-chaperones, i.e. lipopolysaccharide and phospholipids, in OMP folding. Important advances have clearly been made in the field, but much work remains to be done, particularly in terms of describing the biophysical basis for the chaperone-OMP interactions which so intricately regulate OMP biogenesis.     

Modeling mechanical stresses as a factor in the etiology of benign vocal fold lesions

Vocal fold tissue lesions such as nodules and polyps are thought to develop in response to mechanical stress that occurs during vocal fold collision. Two computational models of vocal fold collision during voice production are used to investigate this hypothesis. A one-dimensional lumped mass model, whose parameters are derived from vocal fold tissue dimensions and material properties, predicts stress perpendicular to the direction of impact (normal stress). A previously published three-dimensional finite element model that incorporates the same dimensions and properties predicts the entire stress tensor. The hypothesis is supported by predictions from the finite element model that three components of normal stress and one component of shear stress are increased during collision in the typical location of lesions (i.e. the center of the superior medial edge of the vocal fold in the middle of the vibrating and contact region). The lumped mass model predicts that mechanical stress is negatively correlated with mucosal thickness (increased by voice warm-up and hydration), is positively correlated with driving force (proportional to voice intensity), and is affected by voice production method. These relationships are consistent with clinical observations of vocal fold lesion risk factors and have implications for improving prevention and treatment of benign vocal fold lesions.     

THE ANATOMY OF CALLOCARDIA HUNGERFORDI (BIVALVIA: VENERIDAE) AND THE ORIGIN OF ITS SHELL CAMOUFLAGE

Callocardia hungerfordi (Veneridae: Pitarinae) lives in subtidalmuds (220 to 240m C.D.) and is covered by a dense mat of mudthat, effectively, camouflages the shell. The periostracum is two layered. The inner layer is thick andpleated, the outer thin and perforated. From the outer surfaceof the inner layer develop numerous, delicate (0.5 mm in diameter),calcified, periostracal needles. These penetrate the outer periostracum.Mucus produced from sub-epithelial glands in the inner surfaceof the mantle, slides over the cuticle-covered epithelium ofthe inner and outer surfaces of the inner fold and the innersurface of the middle mantle fold to coat the outer surfaceof the periostracum and its calcified needles. Increased productionat some times produces solidified strands of mucus which bindmud and detrital material into their fabric to create the shellcamouflage. Calcified periostracal needles have been identified in othervenerids, including some members of the Pitarinae, but how theyare secreted and how the covering they attract is producedand, thus, how the whole structure functions, has not been explained. (Received 7 December 1998; accepted 5 February 1999)     

The major outer membrane protein of Fusobacterium nucleatum (FomA) folds and inserts into lipid bilayers via parallel folding pathways

Membrane protein insertion and folding was studied for the major outer membrane protein of Fusobacterium nucleatum (FomA), which is a voltage-dependent general diffusion porin. The transmembrane domain of FomA forms a beta-barrel that is predicted to consist of 14 beta-strands. Here, unfolded FomA is shown to insert and fold spontaneously and quantitatively into phospholipid bilayers upon dilution of the denaturant urea, which was shown previously only for outer membrane protein A (OmpA) of Escherichia coli. Folding of FomA is demonstrated by circular dichroism and fluorescence spectroscopy, by SDS-polyacrylamide gel electrophoresis, and by single-channel recordings. Refolded FomA had a single-channel conductance of 1.1 nS at 1 M KCl, in agreement with the conductance of FomA isolated from membranes in native form. In contrast to OmpA, which forms a smaller eight-stranded beta-barrel domain, folding kinetics of the larger FomA were slower and provided evidence for parallel folding pathways of FomA into lipid bilayers. Two pathways were observed independent of membrane thickness with two different lipid bilayers, which were either composed of dicapryl phosphatidylcholine or dioleoyl phosphatidylcholine. This is the first observation of parallel membrane insertion and folding pathways of a beta-barrel membrane protein from an unfolded state in urea into lipid bilayers. The kinetics of both folding pathways depended on the chain length of the lipid and on temperature with estimated activation energies of 19 kJ/mol (dicapryl phosphatidylcholine) and 70 kJ/mol (dioleoyl phosphatidylcholine) for the faster pathways.     

Multiple folding pathways of the SH3 domain

Experimental observations suggest that proteins follow different folding pathways under different environmental conditions. We perform molecular dynamics simulations of a model of the c-Crk SH3 domain over a broad range of temperatures, and identify distinct pathways in the folding transition. We determine the kinetic partition temperature-the temperature for which the c-Crk SH3 domain undergoes a rapid folding transition with minimal kinetic barriers-and observe that below this temperature the model protein may undergo a folding transition by multiple folding pathways via only one or two intermediates. Our findings suggest the hypothesis that the SH3 domain, a protein fold for which only two-state folding kinetics was observed in previous experiments, may exhibit intermediate states under conditions that strongly stabilize the native state.     

Is protein folding rate dependent on number of folding stages? Modeling of protein folding with ferredoxin-like fold

Statistical analysis of protein folding rates has been done for 84 proteins with available experimental data. A surprising result is that the proteins with multi-state kinetics from the size range of 50–100 amino acid residues (a.a.) fold as fast as proteins with two-state kinetics from the same size range. At the same time, the proteins with two-state kinetics from the size range 101–151 a.a. fold faster than those from the size range 50–100 a.a. Moreover, it turns out unexpectedly that usually in the group of structural homologs from the size range 50–100 a.a., proteins with multi-state kinetics fold faster than those with two-state kinetics. The protein folding for six proteins with a ferredoxin-like fold and with a similar size has been modeled using Monte Carlo simulations and dynamic programming. Good correlation between experimental folding rates, some structural parameters, and the number of Monte Carlo steps has been obtained. It is shown that a protein with multi-state kinetics actually folds three times faster than its structural homologs.