Determination of a constitutive relation for passive myocardium: II. Parameter estimation

In the first paper of this series, we proposed a new transversely isotropic pseudostrain-energy function W for describing the biomechanical behavior of excised noncontracting myocardium. The specific functional form of W was inferred directly from biaxial data to be a polynomial function of two coordinate invariant measures of the finite deformation and five material parameters. In this paper, best-fit values of the material parameters are determined from biaxial data using a nonlinear least-squares regression. These values of the parameters are shown to be well-determined, and the final constitutive relation is shown to have good predictive capabilities. Since the proposed constitutive relation describes much broader classes of in-vitro biaxial data than previously proposed relations, it may be better applicable to analyses of stress in the passive heart.     

Myocardial specificity for initiating endothelial-mesenchymal cell transition in embryonic chick heart correlates with a particulate distribution of fibronectin

The early chick heart tube consists of myocardium and endothelium separated by a myocardially derived basement membrane (MBM). As development proceeds, the endothelium undergoes a transition into mesenchyme in a regionally specific manner; only the atrioventricular (AV) and outflow tract, but not the ventricular endothelium, is transformed into mesenchyme, the progenitor of heart septa and valves. Recent experiments have shown that an EDTA extract of MBM can initiate AV endothelium to form mesenchyme in an in vitro collagen gel culture system. Two-dimensional gel electrophoresis of AV region EDTA extracts showed potentially three isoelectric forms of fibronectin (Fn), while extracts from ventricle contained only two forms. The purpose of the present study was to further investigate the significance of these regional differences by testing of specific myocardial regions (AV vs ventricle) for their ability to induce endothelium to form mesenchyme in vitro, and to immunohistochemically determine if a regionally specific distribution of Fn exists in the MBM that can be correlated with previous electrophoretic data. Embryonic heart regions cultured on three-dimensional collagen gels showed that AV endothelium could only form mesenchyme if cocultured with AV myocardium. Coculture with ventricular myocardial explants did not initiate differentiation of AV endothelium. In contrast, ventricular endothelial cells did not form mesenchyme when cocultured with AV or ventricle myocardium. Immunohistochemical localization of Fn revealed three distinct morphological patterns of distribution in the AV-MBM, i.e., an intense lamina densa staining, diffuse staining in fibrils, and as particles. The Fn localized in particles (0.1 to 0.5 micron in diameter) appeared as a gradient of decreasing concentration extending from the myocardium toward the endothelium. In contrast, no particulate Fn staining was observed in the ventricular region. EDTA extraction selectively depleted the particulate form of Fn. Previous work has shown that this extract, which contains several lower Mr proteins in addition to Fn, is biologically active in initiating mesenchyme formation from AV endothelium in vitro. These results show that a regionally specific interaction of the myocardium with the endothelium is required to initiate the formation of prevalvular mesenchyme. This interaction may be mediated by a multicomponent complex involving Fn and other proteins which appear as a regionally distinct particulate only in areas of endothelial differentiation.     

Myocardial material parameter estimation: a comparison of invariant based orthotropic constitutive equations

This study investigated a number of invariant based orthotropic and transversely isotropic constitutive equations for their suitability to fit three-dimensional simple shear mechanics data of passive myocardial tissue.

A number of orthotropic laws based on Green strain components and one microstructurally based law have previously been investigated to fit experimental measurements of stress-strain behaviour. Here we extend this investigation to include several recently proposed functional forms, i.e. invariant based orthotropic and transversely isotropic constitutive relations.

These laws were compared on the basis of (i) ‘goodness of fit’: how well they fit a set of six shear deformation tests, (ii) ‘variability’: how well determined the material parameters are over the range of experiments. These criteria were utilised to discuss the advantages and disadvantages of the constitutive laws.

It was found that a specific form of the polyconvex type as well as the exponential Fung-type law from the previous study were most suitable for modelling the orthotropic behaviour of myocardium under simple shear.     

Biomechanical experiments on excised myocardium: theoretical considerations

Both the specific functional form of a constitutive relation and the particular material parameters must be determined from experiments. Constitutive formulations based on experimental data are valid, however, only when the experimentally measured stresses closely represent the actual distribution of stress in a specimen. In this paper, we present theoretical considerations to help experimentalists identify conditions under which biaxial data obtained from thin slabs of non-contracting myocardium satisfy the above criterion. In particular, we present both a general framework to investigate, and specific numerical examples to illustrate, the influence of certain distributions of muscle fibers, in-plane shearing strains and particular stretching protocols on the distribution of stress within biaxially tested myocardial specimens.     

The size and form of chromosomes are constant in the nucleus, but highly variable in bacteria, mitochondria and chloroplasts

From cytological examination, the size and form of the chromosomes in the eukaryotic nucleus are invariant across generations, leading to the expectation that constancy of inheritance likely depends on constancy of the chromosomal DNA molecule conveying the constant phenotype. Indeed, except for rare mutations, major phenotypic traits appear largely without change from generation to generation. Thus, when it was discovered that the inheritance of traits for bacteria, mitochondria and chloroplasts was also constant, it was assumed that chromosomes in those locations were also constant. Such has not turned out to be the case, however; those chromosomes are highly variable in structure. I propose, therefore, that only for the nucleus is there a requirement that a chromosome be "finished" (contain only fully replicated genomes) before it may segregate to daughter cells. This requirement does not apply to the variable chromosomes among chloroplasts, mitochondria and bacteria.     

Conserved water molecular dynamics of the different X-ray structures of rusticyanin: an unique aquation potentiality of the ligand bonded Cu++ center

The invariant water molecular interaction involving in the Rusticyanin of Thiobacillus ferrooxidans is thought to be important for its molecular complexation with other proteins at differential acidophilic situation. The comparative analysis of the different x-ray, energy minimized, and auto solvated structures of Rusticyanin revealed the presence of five specific invariant bound water molecules (among the approximately 150 water molecules per monomer) in the crystals. The five W 205, W 206, W 112, W 214, and W 221 water molecules (in Rusticyanin PDB code: 1RCY) were seem to be invariant in all the seven structures (PDB codes: 1RCY, 1A3Z, 1A8Z, 1E3O, 1GY1, 1GY2, 2CAL). Among the five conserved water molecules the W 221 (of 1 RCY or the equivalent water molecules in the other oxidized form of Rusticyanin structures) had endowed an interesting coordination potentiality to Cu(+2) ion during the energy minimization. The W 221 was observed to approach toward the tetrahedrally bonded Cu(+2) ion through the opposite (or trans) route of metal-bonded Met 148. This direct water molecular coordination affected the tetrahedral geometry of Cu(+2) to trigonal bipyramidal. Presumably this structural dynamics at the Cu(+2) center could involve in the electron transport process during protein-protein complexation.     

Invariance in species-abundance distributions

Many attempts to explain the species-abundance distribution (SAD) assume that it has a universal functional form which applies to most assemblages. However, if such a form does exist, then it has to be invariant under changes in the area of the study plot (the addition of neighboring areas or subdivision of the original area) and changes in taxonomic composition (the addition of sister taxa or subdivision to subtaxa). We developed a theory for such an area-and-taxon invariant SAD and derived a formula for such a distribution. Both the log-normal and our area-and-taxon invariant distribution fitted data well. However, the log-normal distributions of two adjoined sub-assemblages cannot be composed into a log-normal distribution for the resulting assemblage, and the SAD composed from two log-normal distributions fits the SAD for the assemblage poorly in comparison to the area-and-taxon invariant distribution. Observed abundance patterns therefore reveal area-and-taxon invariant properties absent in log-normal distributions, suggesting that multiplicative models generating log-normal-like SADs (including the power-fraction model) cannot be universally valid, as they necessarily apply only to particular scales and taxa. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Cellular organization of the embryonic lobster heart

Summary The cellular organization of the embryonic heart of the lobster Homarus americanus was examined in 6-week and 6-month-old animals. The heart wall consists of an outer adventitial layer of fibroblast cells and an inner layer of transversely striated myocardial cells. Present in close association with the myocardium are cardiac neurons, hemocytes and so-called storage cells.Adjacent fibroblasts form fasciae adhaerentes and gap junctions. Adherent junctions also occur between fibroblasts and myocardial cells. Intercalated discs and differentiated membrane regions of close apposition (4 nm) occur between adjacent myocardial cells.The cardiac neurons form a ganglion that contains four small and five large somata. Regions of neuropil are present. Motor axons arising from the cardiac ganglion form neuromuscular synapses with the myocardial cells.The storage cells contain large inclusions and form gap junctions with the myocardial cells. They may supply nutritive material to the developing myocardium.The heart at 6 weeks is about 200 m long and 160 m wide. At 6 months, it is about 300 m long and 250 m wide. The myocardium at 6 weeks is one cell layer thick, and the cells are from 2–6 m in maximum width. At 6 months the myocardium is 2–4 cells thick, and the cells are from 6–12 m in width. Therefore, the myocardium grows by an increase in the number and size of the myocardial cells.     

Conserved Water Molecular Dynamics of the Different X-ray Structures of Rusticyanin: An Unique Aquation Potentiality of the Ligand Bonded Cu++ Center

Abstract

The invariant water molecular interaction involving in the Rusticyanin of Thiobacillus ferrooxidans is thought to be important for its molecular complexation with other proteins at differential acidophilic situation. The comparative analysis of the different x-ray, energy minimized, and auto solvated structures of Rusticyanin revealed the presence of five specific invariant bound water molecules (among the ~ 150 water molecules per monomer) in the crystals. The five W 205, W 206, W 112, W 214, and W 221 water molecules (in Rusticyanin PDB code: 1RCY) were seem to be invariant in all the seven structures (PDB codes: 1RCY, 1A3Z, 1A8Z, 1E3O, 1GY1, 1GY2, 2CAL). Among the five conserved water molecules the W 221 (of 1 RCY or the equivalent water molecules in the other oxidized form of Rusticyanin structures) had endowed an interesting coordination potentiality to Cu⁺² ion during the energy minimization. The W 221 was observed to approach toward the tetrahedrally bonded Cu⁺² ion through the opposite (or trans) route of metal-bonded Met 148. This direct water molecular coordination affected the tetrahedral geometry of Cu⁺² to trigonal bipyramidal. Presumably this structural dynamics at the Cu⁺² center could involve in the electron transport process during protein-protein complexation.     

Conserved water-mediated H-bonding dynamics of catalytic Asn 175 in plant thiol protease

The role of invariant water molecules in the activity of plant cysteine protease is ubiquitous in nature. On analysing the 11 different Protein DataBank (PDB) structures of plant thiol proteases, the two invariant water molecules W1 and W2 (W220 and W222 in the template 1PPN structure) were observed to form H-bonds with the O_b atom of Asn 175. Extensive energy minimization and molecular dynamics simulation studies up to 2 ns on all the PDB and solvated structures clearly revealed the involvement of the H-bonding association of the two water molecules in fixing the orientation of the asparagine residue of the catalytic triad. From this study, it is suggested that H-bonding of the water molecule at the W1 invariant site better stabilizes the Asn residue at the active site of the catalytic triad.     

The elastic behavior of the urinary bladder for large deformations

The purpose of this paper is to investigate the theoretical basis for the pressure-distension behavior of the urinary bladder. A finite strain theory is developed for hollow spherical structures and it is shown that the Treloar model is a good prototype only for rubber balloons. The pressure-extension ratio relationship is inverted to lead a general form of strain energy function, and fitted by an empirical relation involving one exponential. The following form of strain energy function is derived: W(lambda, lambda, lambda -2) = C1 (P(1), a) + P(1)C2 (a, lambda)ea(lambda -1). Where C1(P(1), a) is a constant (N m-2), P(1) is the initial pressure, a is the rate of pressure increase and C2 (a, lambda) a third degree polynomial relation. P(1) and a are experimentally determined through volumetric pressure-distension data. It is verified that this type of energy function is also valid for uniaxial loading experiments by testing strips coming from the same bladder for which P(1) and a were computed. There is a good agreement between the experimental points and the theoretical stress-strain relation. Finally, the strain energy function is plotted as a function of the first strain invariant and appears to be of an exponential nature.     

Physical invariant strain energy function for passive myocardium

Principal axis formulations are regularly used in isotropic elasticity, but they are not often used in dealing with anisotropic problems. In this paper, based on a principal axis technique, we develop a physical invariant orthotropic constitutive equation for incompressible solids, where it contains only a one variable (general) function. The corresponding strain energy function depends on six invariants that have immediate physical interpretation. These invariants are useful in facilitating an experiment to obtain a specific constitutive equation for a particular type of materials. The explicit appearance of the classical ground-state constants in the constitutive equation simplifies the calculation for their admissible values. A specific constitutive model is proposed for passive myocardium, and the model fits reasonably well with existing simple shear and biaxial experimental data. It is also able to predict a set of data from a simple shear experiment.     

A symmetrical approach to the analysis of cardiocyte electrical and contractile activity]

Based on the systemic symmetrical approach, experimentally determined parameters of action potential and contractile response of frog myocardial strip were analyzed prior to and after the administration of several physiologically active drugs (caffeine, neoepinephrine, nembutal, ouabain) into the perfusate. It was shown that the satisfactory functional state of preparation was characterized by an interrelation between parameters in the form of a harmonic proportion with relatively constant coefficient. When the functional state of subject is affected by a physiologically active substance, the interrelation between the parameters is considerably changed. Based on the analysis of the data of literature, it was found that the interrelation between temporary parameters of action potential in various structures from human heart has the form of a harmonic proportion with a constant coefficient close to the invariant of "Gold Wurf" proportion. The similarity is underlined of principles of cardiac function temporary arrangement at levels of cell, organ and organism.     

On constitutive relations and finite deformations of passive cardiac tissue: I. A pseudostrain-energy function

A three-dimensional constitutive relation for passive cardiac tissue is formulated in terms of a structurally motivated pseudostrain-energy function, W, while the mathematical simplicity of phenomenological approaches is preserved. A specific functional form of W is proposed on the basis of limited structural information and multiaxial experimental data. The material parameters are determined in a least-squared sense from both uniaxial and biaxial data. Our results suggest that (1) multiaxially-loaded cardiac tissue is nearly transversely-isotropic with respect to local muscle fiber directions, at least for a limited range of strain histories, (2) material parameters determined from uniaxial papillary muscle data result in gross underestimates of the stresses in multiaxially-loaded specimens, and (3) material parameters determined from equibiaxial tests predict the behavior of the tissue under various nonequibiaxial stretching protocols reasonably well.     

Conformational changes in DNA and soft modes

In this paper we explore the applicability of the soft mode approach to study the conformational transitions of DNA. It is believed that the A-B conformation change is a first order transition. Soft mode theories only apply to the initial stages of a first order transition. However the mode softening in such a case can be the initiating factor which ultimately leads to the transition. The first order transition is, then, a breakdown of what otherwise would have been a true second order transition. The mode softening is causally connected to onset of the transition. We use the eigenvectors obtained from lattice dynamics calculations to identify the softmode. We use the eigenvector projections to form a force constant matrix that is required to drive a mode soft. We explore the methods by which this force constant matrix can be formed. We suggest that the breaking of specific "water bridges" between phosphate groups in the two single strands can drive the conformation change.     

Ligand migration in the truncated hemoglobin of Mycobacterium tuberculosis

The truncated hemoglobin of Mycobacterium tuberculosis (Mt-trHbO) is a small heme protein belonging to the hemoglobin superfamily. Truncated hemoglobins (trHbs) are believed to have functional roles such as terminal oxidases and oxygen sensors involved in the response to oxidative and nitrosative stress, nitric oxide (NO) detoxification, O?/NO chemistry, O? delivery under hypoxic conditions, and long-term ligand storage. Based on sequence similarities, they are classified into three groups. Experimental studies revealed that all trHbs display a 2-on-2 α-helical sandwich fold rather than the 3-on-3 α-helical sandwich fold of the classical hemoglobin fold. Using locally enhanced sampling (LESMD) molecular dynamics, the ligand-binding escape pathways from the distal heme binding cavity of Mt-trHbO were determined to better understand how this protein functions. The importance of specific residues, such as the group II and III invariant W(G8) residue, can be seen in terms of ligand diffusion pathways and ligand dynamics. LESMD simulations show that the wild-type Mt-trHbO has three diffusion pathways while the W(G8)F Mt-trHbO mutant has only two. The W(G8) residue plays a critical role in ligand binding and stabilization and helps regulate the rate of ligand escape from the distal heme pocket. Thus, this invariant residue is important in creating ligand diffusion pathways and possibly in the enzymatic functions of this protein.     

Myocardial material parameter estimation

The passive material properties of myocardium play a major role in diastolic performance of the heart. In particular, the shear behaviour is thought to play an important mechanical role due to the laminar architecture of myocardium. We have previously compared a number of myocardial constitutive relations with the aim to extract their suitability for inverse material parameter estimation. The previous study assumed a homogeneous deformation. In the present study we relaxed the homogeneous assumption by implementing these laws into a finite element environment in order to obtain more realistic measures for the suitability of these laws in both their ability to fit a given set of experimental data, as well as their stability in the finite element environment. In particular, we examined five constitutive laws and compare them on the basis of (i) "goodness of fit": how well they fit a set of six shear deformation tests, (ii) "determinability": how well determined the objective function is at the optimal parameter fit, and (iii) "variability": how well determined the material parameters are over the range of experiments. Furthermore, we compared the FE results with those from the previous study.It was found that the same material law as in the previous study, the orthotropic Fung-type "Costa-Law", was the most suitable for inverse material parameter estimation for myocardium in simple shear.     

A simulation study of the reaction of human heart to biphasic electrical shocks

Background

This article presents a study, which examines the effects of biphasic electrical shocks on human ventricular tissue. The effects of this type of shock are not yet fully understood. Animal experiments showed the superiority of biphasic shocks over monophasic ones in defibrillation. A mathematical computer simulation can increase the knowledge of human heart behavior.

Methods

The research presented in this article was done with different models representing a three-dimensional wedge of ventricular myocardium. The electrophysiology was described with Priebe-Beuckelmann model. The realistic fiber twist, which is specific to human myocardium was included. Planar electrodes were placed at the ends of the longest side of the virtual cardiac wedge, in a bath medium. They were sources of electrical shocks, which varied in magnitude from 0.1 to 5 V. In a second arrangement ring electrodes were placed directly on myocardium for getting a better view on secondary electrical sources. The electrical reaction of the tissue was generated with a bidomain model.

Results

The reaction of the tissue to the electrical shock was specific to the initial imposed characteristics. Depolarization appeared in the first 5 ms in different locations. A further study of the cardiac tissue behavior revealed, which features influence the response of the considered muscle. It was shown that the time needed by the tissue to be totally depolarized is much shorter when a biphasic shock is applied. Each simulation ended only after complete repolarization was achieved. This created the possibility of gathering information from all states corresponding to one cycle of the cardiac rhythm.

Conclusions

The differences between the reaction of the homogeneous tissue and a tissue, which contains cleavage planes, reveals important aspects of superiority of biphasic pulses. ...     

Trehalose-containing lipooligosaccharide antigens of Mycobacterium sp.: presence of a mono-O-methyltri-O-acyltrehalose "core"

We have described the surface antigens of Mycobacterium kansasii as trehalose-containing lipooligosaccharides (LOS) which at the nonreducing "epitope" end bear a unique amino sugar containing diglycosyl unit, whereas the putative reducing end consists of an acylated alpha, alpha-trehalose-containing tetraglucosyl "core" [Hunter, S. W., Jardine, I., Yanagihara, D. L., & Brennan, P. J. (1985) Biochemistry 24, 2798-2805]. The presence of a new variation on this core, in Mycobacterium szulgai, is now reported, ----3)beta-D-Glcp-(1----6)alpha-D-Glcp(1----1)3,4,6-tri-O-acyl-2-O- Me-alpha-D-Glcp, representing the first example of an O-methyltrehalose unit in nature. The simplest of the LOS class of glycolipids in M. szulgai was defined as alpha-L-2-O-Me-Fucp(1----3)alpha-L-Rhap(1----3)alpha-L-Rh ap(1----3) beta-D-Glcp(1----6)alpha-D-Glcp(1----1)3,4,6-tri-O-acyl-2-O-Me-alpha-D-G lcp. Further glycosylation of this nonantigen, by an incompletely defined 6-deoxyhexosyl residue, confers specific antigenicity on the organism. Thus, these extraordinary structures, in a manner analogous to the better known lipopolysaccharides from rough variants of Enterobactericiae, are highly amphipathic and display variability not only in the immunogenic, distal region but also in the "invariant" lipophilic core. The contribution of these glycolipids to the hydrophobic barrier, the pseudo outer membrane of mycobacteria, is discussed.     

Amino acid substitutions at tryptophan-51 of cytochrome c peroxidase: effects on coordination, species preference for cytochrome c, and electron transfer.

Amino acid replacements of an aromatic residue, Trp-51, which is in contact with the heme of yeast cytochrome c peroxidase have a number of significant effects on the kinetics and coordination state of the enzyme. Six mutants at this site (W51F, W51M, W51T, W51C, W51A, and W51G) were examined. Optical and EPR spectra show that each of these mutations introduces a shift from the 5-coordinate to 6-coordinate form, and slightly increases the asymmetry of the heme ligand field. Conversion from a 6-coordinate high-spin form at pH 5 to a 6-coordinate low-spin form at pH 7 is observed for several of the variants (W51F, W51T, and W51A), while W51G and W51C appear as predominantly low-spin species between pH 5 and 7. Addition of 50% glycerol prevents the facile conversion to the low-spin conformation for W51F, W51T, and W51A, and only W51F can be stabilized in a 5-coordinate configuration by glycerol. For the oxidation of cytochrome c by H2O2, three of the variants (W51F, W51M, and W51T) exhibit values of kcat(app) that are greater than for the wild-type enzyme, while the other mutations give decreased rates of enzyme turnover. Unlike the wild-type enzyme, which functions more efficiently with cytochrome c from yeast than with the horse heart protein, the mutant W51F does not show a preference for substrate from its native organism. The three mutants which exhibit increased values of kcat(app) show a pH optimum at 6.8 compared with that of 5.25 for the wild-type enzyme when measured with horse heart cytochrome c. This shift in pH optimum is not observed with yeast cytochrome c. Construction of single and multiple mutations at Trp-51, Ile-53, and Gly-152 shows that these kinetic properties are not due to natural amino acid variations observed at these sites. Pre-steady-state kinetics show that the bimolecular rate constant for the fast phase of the reaction of the enzyme with H2O2 is only slightly decreased from 3.03 (0.09) X 10(7) to 2.2 (0.1) X 10(7) M-1 s-1 for W51F and to 1.5 (0.1) X 10(7) M-1 s-1 for W51A. The slow phase of the reaction (4.9 s-1) which contributes approximately 30% to the amplitude of the change for the wild-type enzyme is not observed for W51F or W51A.(ABSTRACT TRUNCATED AT 400 WORDS)