A three-dimensional model of the upper tracheobronchial tree

A new model of the upper tracheobronchial tree is proposed to account for the three-dimensional nature of the airway system. In addition to the tube length, the tube diameter, and the branching angle, the model includes information on the orientation angle of each tube relative to its parent tube. The orientation angle, defined as the angle between two successive bifurcations, is useful for calculating the gravitational inclination of each tube. The information on orientation angle is further used to construct a binary coding system for identifying individual tubes in the airway tree. The proposed model is asymmetrical, but the same principles can be readily used to construct a symmetrical one.     

A three-dimensional model of the human pulmonary acinus.

A three-dimensional (3-D) model of the human pulmonary acinus, a gas exchange unit, is constructed with a labyrinthine algorithm generating branching ducts that fill a given space completely. Branching down to the third respiratory bronchioles is generated with the proposed algorithm. A subacinus, a region supplied by the last respiratory bronchiole, is approximated to be a set of cubic cells with a side dimension of 0.5 mm. The labyrinthine algorithm is used to determine a pathway through all cells only once, except at branching points with the smallest path lengths. In choosing each step of a pathway, random variables are used. Resulting labyrinths have equal mean path lengths and equal surface areas of inner walls. An alveolus can be generated by attaching alveolar septa, 0.25 mm long and 0.1 mm wide, to the inner walls. Total alveolar surface area and numbers of alveolar ducts, alveolar sacs, and alveoli in our 3-D acinar model are in good accordance with those reported in the literature.     

First partial three-dimensional model of human monoamine oxidase A

A survey of the major known structural aspects of monoamine oxidase (MAO) is given and a first partial model of human MAO A is presented. This 3D model has been established using secondary structure predictions and fold recognition methods. It shows two α/β domains (the FAD-binding N-terminal and central domains) and an α+β domain. The C-terminal region is predicted to be responsible for anchoring the protein into the mitochondrial membrane and was not modeled. The covalent binding of the flavin cofactor to a cysteine residue is well predicted. The model is validated with experimental data from the literature and should be useful in designing new experimental studies (site-directed mutagenesis, chemical modification, specific antibodies). This first step towards the 3D structure of monoamine oxidase should contribute to a better understanding of the mechanisms of action and inhibition of this drug target in the treatment of clinical depression. Proteins 32:97–110, 1998. © 1998 Wiley-Liss, Inc.     

A three-dimensional model of the human cervical spine for impact simulation

A three-dimensional analytical model of the cervical spine is described. The cervical vertebrae and the head are modeled as rigid bodies which are interconnected by deformable elements representing the intervertebral disks, facet joints, ligaments and muscles. A special pentahedral continuum element for representing the articular facets is described which effectively maintains stability of the cervical spine in both lateral and frontal plane accelerations, which is very difficult with multi-spring models of the facets. A simplified representation is used for the spine and body below the level of T1. The neck musculature is modeled by over 100 muscle elements representing 22 major muscle groups in the neck. The model has been validated for frontal and sideways impact accelerations by simulating published experimental data. Results are also presented to show the effects of the stretch reflex response on the dynamics of the head and neck under moderate acceleration.     

A three-dimensional model of the human facilitative glucose transporter Glut1

The human facilitative transporter Glut1 is the major glucose transporter present in all human cells, has a central role in metabolism, and is an archetype of the superfamily of major protein facilitators. Here we describe a three-dimensional structure of Glut1 based on helical packing schemes proposed for lactose permease and Glut1 and predictions of secondary structure, and refined using energy minimization, molecular dynamics simulations, and quality and environmental scores. The Ramachandran scores and the stereochemical quality of the structure obtained were as good as those for the known structures of the KcsA K(+) channel and aquaporin 1. We found two channels in Glut1. One of them traverses the structure completely, and is lined by many residues known to be solvent-accessible. Since it is delimited by the QLS motif and by several well conserved residues, it may serve as the substrate transport pathway. To validate our structure, we determined the distance between these channels and all the residues for which mutations are known. From the locations of sugar transporter signatures, motifs, and residues important to the transport function, we find that this Glut1 structure is consistent with mutagenesis and biochemical studies. It also accounts for functional deficits in seven pathogenic mutants.     

A validated three-dimensional computational model of a human knee joint

This paper presents a three-dimensional finite element tibio-femoral joint model of a human knee that was validated using experimental data. The geometry of the joint model was obtained from magnetic resonance (MR) images of a cadaveric knee specimen. The same specimen was biomechanically tested using a robotic/universal force-moment sensor (UFS) system and knee kinematic data under anterior-posterior tibial loads (up to 100 N) were obtained. In the finite element model (FEM), cartilage was modeled as an elastic material, ligaments were represented as nonlinear elastic springs, and menisci were simulated by equivalent-resistance springs. Reference lengths (zero-load lengths) of the ligaments and stiffness of the meniscus springs were estimated using an optimization procedure that involved the minimization of the differences between the kinematics predicted by the model and those obtained experimentally. The joint kinematics and in-situ forces in the ligaments in response to axial tibial moments of up to 10 Nm were calculated using the model and were compared with published experimental data on knee specimens. It was also demonstrated that the equivalent-resistance springs representing the menisci are important for accurate calculation of knee kinematics. Thus, the methodology developed in this study can be a valuable tool for further analysis of knee joint function and could serve as a step toward the development of more advanced computational knee models.     

A fractal continuum model of the pulmonary arterial tree.

The extant morphometric data from the intrapulmonary arteries of dog, human, and cat lungs produce graphs of the log of the vessel number, (N) or length (l) in each level vs. the log of the mean diameter (D) in each level that are sufficiently linear to suggest that a scale-independent self-similar or fractal structure may underlie the observed relationships. These data can be correlated by the following formulas: Nj = a1Dj-beta 1, and lj = a2Dj beta 2, where j denotes the level (order or generation) number measured from the largest vessel at the entrance to the arterial tree to the smallest vessel at the entrance to the capillary bed. With the hemodynamic resistance (R) represented by Rj = 128 microliterj/(Nj pi Dj4) and the vascular volume (Q) by Qj = Nj pi Dj2lj/4, the continuous cumulative distribution of vascular resistance (Rcum) vs. cumulative vascular volume (Qcum) (where Rcum and Qcum represent the total resistance or volume, respectively, upstream from the jth level) can be calculated from [formula: see text] where r = Dj/Dj+1 is a constant independent of j. Analogous equations are developed for the inertance and compliance distributions, providing simple formulas to represent the hemodynamic consequences of the pulmonary arterial tree structure.     

A three-dimensional model of differentiation of immortalized human bronchial epithelial cells

A therapeutic approach being investigated for a variety of pathologies is tissue regeneration using a patient's own cells. Such studies have been hampered due to the difficulty in growing epithelial cells for prolonged periods in culture. Replicative senescence due to short telomeres and p16 induced by culture stress work together to inhibit cell growth. Forced expression of telomerase (hTERT) can prevent replicative senescence, and expression of the cell cycle protein cdk4 can sequester p16, thereby immortalizing epithelial cells in culture. In the present study, we used this method to immortalize human bronchial epithelial cells (HBECs) to determine whether immortalized HBECs retain the ability to differentiate normally. HBECs were plated atop contracted collagen gels containing lung fibroblasts. This three-dimensional (3D) tissue model was cultured initially submerged, then raised to the air/liquid interface for up to 28 days. Normal differentiation was assessed by the presence of ciliated cells, goblet (mucin-producing) cells, and basal epithelial cells. Scanning electron microscopic observations revealed both ciliated and non-ciliated cells in these 3D tissues. Histological examination revealed the presence of mucin-producing cells, and immunohistochemistry using antibodies against p63 and keratin 14 showed the presence of basal cells. These results demonstrate that immortalized HBECs retain the capacity to differentiate into each of three cell types: basal, mucin-producing, and columnar ciliated epithelial cells. Such cells will be useful cellular reagents for research in aging, cancer progression, as well as normal bronchial epithelial differentiation and will help progress the use of engineered cells to enhance tissue regeneration.     

A three-dimensional model of aromatase cytochrome P450.

P450 hemeproteins comprise a large gene superfamily that catalyzes monooxygenase reactions in the presence of a redox partner. Because the mammalian members are, without exception, membrane-bound proteins, they have resisted structure-function analysis by means of X-ray crystallographic methods. Among P450-catalyzed reactions, the aromatase reaction that catalyzes the conversion of C19 steroids to estrogens is one of the most complex and least understood. Thus, to better understand the reaction mechanism, we have constructed a three-dimensional model of P450arom not only to examine the active site and those residues potentially involved in catalysis, but to study other important structural features such as substrate recognition and redox-partner binding, which require examination of the entire molecule (excepting the putative membrane-spanning region). This model of P450arom was built based on a "core structure" identified from the structures of the soluble, bacterial P450s (P450cam, P450terp, and P450BM-P) rather than by molecular replacement, after which the less conserved elements and loops were added in a rational fashion. Minimization and dynamic simulations were used to optimize the model and the reasonableness of the structure was evaluated. From this model we have postulated a membrane-associated hydrophobic region of aliphatic and aromatic residues involved in substrate recognition, a redox-partner binding region that may be unique compared to other P450s, as well as residues involved in active site orientation of substrates and an inhibitor of P450arom, namely vorozole. We also have proposed a scheme for the reaction mechanism in which a "threonine switch" determines whether oxygen insertion into the substrate molecule involves an oxygen radical or a peroxide intermediate.     

A three-dimensional whole-body model to predict human walking on level ground

Predictive simulation of human walking has great potential in clinical motion analysis and rehabilitation engineering assessment, but large computational cost and reliance on measurement data to provide initial guess have limited its wide use. We developed a computationally efficient model combining optimization and inverse dynamics to predict three-dimensional whole-body motions and forces during human walking without relying on measurement data. Using the model, we explored two different optimization objectives, mechanical energy expenditure and the time integral of normalized joint torque. Of the two criteria, the sum of the time integrals of the normalized joint torques produced a more realistic walking gait. The reason for this difference is that most of the mechanical energy expenditure is in the sagittal plane (based on measurement data) and this leads to difficulty in prediction in the other two planes. We conclude that mechanical energy may only account for part of the complex performance criteria driving human walking in three dimensions.

     

A three-dimensional mathematical model of the human masticatory system predicting maximum possible bite forces

A three-dimensional mathematical model of the human masticatory system, containing 16 muscle forces and two joint reaction forces, is described. The model allows simulation of static bite forces and concomitant joint reaction forces for various bite point locations and mandibular positions. The system parameters for the model were obtained from a cadaver head. Maximum possible bite forces were computed using optimization techniques; the optimization criterion we used was the minimizing of the relative activity of the most active muscle. The model predicts that at each specific bite point, bite forces can be generated in a wide range of directions, and that the magnitude of the maximum bite force depends on its direction. The relationship between bite force direction and its maximum magnitude depends on bite point location and mandibular position. In general, the direction of the largest possible bite force does not coincide with the direction perpendicular to the occlusal plane.     

A model for the three-dimensional structure of human plasma vitronectin from small-angle scattering measurements

Small-angle X-ray scattering (SAXS) measurements were used to characterize vitronectin, a circulatory protein found in human plasma that functions in regulating cell adhesion and migration, as well as proteolytic cascades that affect blood coagulation, fibrinolysis, and pericellular proteolysis. SAXS measurements were taken over a 3-fold range of protein concentrations, yielding data that characterize a monodisperse system of particles with an average radius of gyration of 30.3 +/- 0.6 A and a maximum linear dimension of 110 A. Shape restoration was applied to the data to produce two models of the solution structure of the ligand-free protein. A low-resolution model of the protein was generated that indicates the protein to be roughly peanut-shaped. A better understanding of the domain structure of vitronectin resulted from low-resolution models developed from available high-resolution structures of the domains. These domains include the N-terminal domain that was determined experimentally by NMR [Mayasundari, A., Whittemore, N. A., Serpersu, E. H., and Peterson, C. B. (2004) J. Biol. Chem. 279, 29359-29366] and the docked structure of the central and C-terminal domains that were determined by computational threading [Xu, D., Baburaj, K., Peterson, C. B., and Xu, Y. (2001) Proteins: Struct., Funct., Genet. 44, 312-320]. This model provides an indication of the disposition of the central domain and C-terminal heparin-binding domains of vitronectin with respect to the N-terminal somatomedin B (SMB) domain. This model constructed from the available domain structures, which agrees with the low-resolution model produced from the SAXS data, shows the SMB domain well separated from the central and heparin-binding domains by a disordered linker (residues 54-130). Also, binding sites within the SMB domain are predicted to be well exposed to the surrounding solvent for ease of access to its various ligands.     

A model of the mechanics of airway narrowing

To examine the interaction between airway smooth muscle shortening and airway wall thickening on changes in pulmonary resistance, we have developed a model of the tracheobronchial tree that allows simulation of the mechanisms involved in airway narrowing. The model is based on the symmetrical dichotomous branching tracheobronchial tree as described by Weibel and uses fluid dynamic equations proposed by Pedley et al. to calculate inspiratory resistance during quiet tidal breathing. To allow for changes in lung volume, we used the airway pressure-area curves developed by Lambert et al. The model is easily implemented with a spreadsheet and personal computer that allows calculation of total and regional pulmonary resistance. At each airway generation in the model, provision is made for airway wall thickness, the maximal airway smooth muscle shortening achievable, and an S-shaped dose-response relationship to describe smooth muscle shortening. To test the validity of the model, we compared pressure-flow curves generated with the model with measurements of pulmonary resistance while normal subjects breathed air and 20% O2-80% He at a variety of lung volumes. By simulating progressive airway smooth muscle shortening, realistic pulmonary resistance vs. dose-response curves were produced. We conclude that this model provides realistic estimates of pulmonary resistance and shows potential for examining the various mechanisms that could produce excessive airway narrowing in disease.     

A three-dimensional model of the human transglutaminase 1: insights into the understanding of lamellar ichthyosis

The stratum corneum, the outer layer of the epidermis, serves as a protective barrier to isolate the skin from the external environment. Keratinocyte transglutaminase 1 (TGase 1) catalyzes amide crosslinking between glutamine and lysine residues on precursor proteins forming the impermeable layers of the epidermal cell envelopes (CE), the highly insoluble membranous structures of the stratum corneum. Patients with the autosomal recessive skin disorder lamellar ichthyosis (LI) appear to have deficient cross-linking of the cell envelope due to mutations identified in TGase 1, linking this enzyme to LI. In the absence of a crystal structure, molecular modeling was used to generate the structure of TGase 1. We have mapped the known mutations of TGase 1 from our survey obtained from a search of PubMed and successfully predicted the impact of these mutations on LI. Furthermore, we have identified Ca²⁺ binding sites and propose that Ca²⁺ induces a cis to trans isomerization in residues near the active site as part of the enzyme transamidation activation. Docking experiments suggest that substrate binding subsequently induces the reverse cis to trans isomerization, which may be a significant part of the catalytic process. These results give an interpretation at the molecular level of previously reported mutations and lead to further insights into the structural model of TGase 1, providing a new basis for understanding LI. Figure Ribbon image of the model of the human TGase 1 structure. The side chains of residues reported to be mutated in patients with LI (34 amino acid mutation sites) are shown as spheres. This paper is dedicated to the memory of Dr. Peter M. Steinert (April 7, 2003).     

Pulsatile non-Newtonian flow characteristics in a three-dimensional human carotid bifurcation model.

Numerical analysis of flow phenomena and wall shear stresses in the human carotid artery bifurcation has been carried out using a three-dimensional geometrical model. The primary aim of this study is the detailed discussion of non-Newtonian flow velocity and wall shear stress during the pulse cycle. A comparison of non-Newtonian and Newtonian results is also presented. The applied non-Newtonian behavior of blood is based on measured dynamic viscosity. In the foreground of discussion are the flow characteristics in the carotid sinus. The investigation shows complex flow patterns especially in the carotid sinus where flow separation occurs at the outer wall throughout the systolic deceleration phase. The changing sign of the velocity near the outer sinus wall results in oscillating shear stress during the pulse cycle. At the outer wall of the sinus at maximum diameter level the shear stress ranges from -1.92 N/m2 to 1.22 N/m2 with a time-averaged value of 0.04 N/m2. At the inner wall of the sinus at maximum diameter level the shear stress range is from 1.16 N/m2 to 4.18 N/m2 with a mean of 1.97 N/m2. The comparison of non-Newtonian and Newtonian results indicates unchanged flow phenomena and rather minor differences in the basic flow characteristics.     

A conceptual model of tree behaviour improves the visual assessment of tree condition

A conceptual model describing the response of two Australian floodplain eucalypts, river red gum (Eucalyptus camaldulensis) and black box (Eucalyptus largiflorens), to changes in water availability was developed based on field observations. This model was incorporated into a percentage based visual method estimating two tree crown parameters, crown extent and density. Extent is the amount of foliage at the periphery of the assessable crown; density is the density of assessable crown foliage. Polychoric correlation was used to determine the level of agreement between two experienced observers assessing river red gum and black box trees using a simple percentage scale and a percentage scale supported by the conceptual model. Trees were evaluated using the model by determining their position on a trajectory of water stress related decline and response. In both cases observer estimates of crown extent and density were significantly correlated. With the exception of red gum crown density the correlation coefficients were higher for the model supported scale. Using a conceptual model of tree response to water availability improved observer agreement. Supporting subjective assessment systems with a conceptual model is recommended to improve observer agreement in cases where a distinct model of the dominant stressor can be defined.     

A model for the three-dimensional structure of glucagon

A literature search on the structural aspects of glucagon in dilute aqueous solution has been undertaken. We have found that a compact, well-defined structure must exist and propose a model for that structure. In doing so, care was taken to distinguish between the raw data themselves and the interpretations drawn from them, and to bring about a model consistent with as much of the data as possible. The model building was performed on Corey-Pauling-Koltun (CPK) space-filling models using secondary structure prediction rules, experimental data such as fluorescence quenching, circular dichroism, NMR and high resolution dark field electron microscopy, and was guided by a hierarchy of intramolecular interactions which places hydrophobic bonding first and hydrogen bonding second. This last criterion places a strict requirement on the model-building to maximize contacts among complementary hydrophobic surfaces; this means that no empty spaces are allowed inside the folded molecule. The resultant model is consistent with all the relevant data. Furthermore, as demanded by any structure building exercise, the model suggests structure-function relationships. One of the predictions drawn from the structure—the binding of guanosine-5′-triphosphate (GTP)—has been confirmed by a preliminary experiment (reported elsewhere). Another aspect of the structure suggests a subtle mechanism for allostery.