A Riemannian manifold analysis of endothelial cell monolayer impedance parameter precision

Endothelial cell adhesion and barrier function play a critical role in many biological and pathophysiological processes. The decomposition of endothelial cell adhesion and barrier function into cell–cell and cell–matrix components using frequency dependent cellular micro-impedance measurements has, therefore, received widespread application. Few if any studies, however, have examined the precision of these model parameters. This study presents a parameter sensitivity analysis of a representative cellular barrier function model using a concise geometric formulation that includes instrumental data acquisition settings. Both model state dependence and instrumental noise distributions are accounted for within the framework of Riemannian manifold theory. Experimentally acquired microimpedance measurements of attached endothelial cells define the model state domain, while experimentally measured noise statistics define the data space Riemannian metric based on the Fisher information matrix. The results of this analysis show that the sensitivity of cell–cell and cell–matrix impedance components are highly model state dependent and several well defined regions of low precision exist. The results of this study further indicate that membrane resistive components can significantly reduce the precision of the remaining parameters in these models. This work was supported by a National Science Foundation CAREER Award (AE), BES-0238905, and in part by the American Heart Association under Grant 0265029B (AE).     

Coccolith volume of the Southern Ocean coccolithophore Emiliania huxleyi as a possible indicator for palaeo‐cell volume

Coccolithophores are a key functional phytoplankton group and produce minute calcite plates (coccoliths) in the sunlit layer of the pelagic ocean. Coccoliths significantly contribute to the sediment record since the Triassic and their geometry have been subject to palaeoceanographic and biological studies to retrieve information on past environmental conditions. Here, we present a comprehensive analysis of coccolith, coccosphere and cell volume data of the Southern Ocean Emiliania huxleyi ecotype A, subject to gradients of temperature, irradiance, carbonate chemistry and macronutrient limitation. All tested environmental drivers significantly affect coccosphere, coccolith and cell volume with driver‐specific sensitivities. However, a highly significant correlation emerged between cell and coccolith volume with V_coccolith = 0.012 ± 0.001 * V_cell + 0.234 ± 0.066 (n = 23, r² = .85, p < .0001, σ_est = 0.127), indicating a primary control of coccolith volume by physiological modulated changes in cell volume. We discuss the possible application of fossil coccolith volume as an indicator for cell volume/size and growth rate and, additionally, illustrate that macronutrient limitation of phosphorus and nitrogen has the predominant influence on coccolith volume in respect to other environmental drivers. Our results provide a solid basis for the application of coccolith volume and geometry as a palaeo‐proxy and shed light on the underlying physiological reasons, offering a valuable tool to investigate the fossil record of the coccolithophore E. huxleyi.     

Three-dimensional modeling of the cochlea by use of an arc fitting approach

Purpose: A cochlea modeling approach is presented allowing for a user defined degree of geometry simplification which automatically adjusts to the patient specific anatomy. Model generation can be performed in a straightforward manner due to error estimation prior to the actual generation, thus minimizing modeling time. Therefore, the presented technique is well suited for a wide range of applications including finite element analyses where geometrical simplifications are often inevitable. Methods: The method is presented for n=5 cochleae which were segmented using a custom software for increased accuracy. The linear basilar membrane cross sections are expanded to areas while the scalae contours are reconstructed by a predefined number of arc segments. Prior to model generation, geometrical errors are evaluated locally for each cross section as well as globally for the resulting models and their basal turn profiles. The final combination of all reconditioned features to a 3D volume is performed in Autodesk Inventor using the loft feature. Results: Due to the volume generation based on cubic splines, low errors could be achieved even for low numbers of arc segments and provided cross sections, both of which correspond to a strong degree of model simplification. Model generation could be performed in a time efficient manner. Conclusion: The proposed simplification method was proven to be well suited for the helical cochlea geometry. The generated output data can be imported into commercial software tools for various analyses representing a time efficient way to create cochlea models optimally suited for the desired task.     

Evaluation of a morphing based method to estimate muscle attachment sites of the lower extremity

To generate subject-specific musculoskeletal models for clinical use, the location of muscle attachment sites needs to be estimated with accurate, fast and preferably automated tools. For this purpose, an automatic method was used to estimate the muscle attachment sites of the lower extremity, based on the assumption of a relation between the bone geometry and the location of muscle attachment sites. The aim of this study was to evaluate the accuracy of this morphing based method. Two cadaver dissections were performed to measure the contours of 72 muscle attachment sites on the pelvis, femur, tibia and calcaneus. The geometry of the bones including the muscle attachment sites was morphed from one cadaver to the other and vice versa. For 69% of the muscle attachment sites, the mean distance between the measured and morphed muscle attachment sites was smaller than 15 mm. Furthermore, the muscle attachment sites that had relatively large distances had shown low sensitivity to these deviations. Therefore, this morphing based method is a promising tool for estimating subject-specific muscle attachment sites in the lower extremity in a fast and automated manner.     

Computational approaches for analyzing the mechanics of atherosclerotic plaques: A review

Vulnerable and stable atherosclerotic plaques are heterogeneous living materials with peculiar mechanical behaviors depending on geometry, composition, loading and boundary conditions. Computational approaches have the potential to characterize the three-dimensional stress/strain distributions in patient-specific diseased arteries of different types and sclerotic morphologies and to estimate the risk of plaque rupture which is the main trigger of acute cardiovascular events. This review article attempts to summarize a few finite element (FE) studies for different vessel types, and how these studies were performed focusing on the used stress measure, inclusion of residual stress, used imaging modality and material model. In addition to histology the most used imaging modalities are described, the most common nonlinear material models and the limited number of models for plaque rupture used for such studies are provided in more detail. A critical discussion on stress measures and threshold stress values for plaque rupture used within the FE studies emphasizes the need to develop a more location and tissue-specific threshold value, and a more appropriate failure criterion. With this addition future FE studies should also consider more advanced strain-energy functions which then fit better to location and tissue-specific experimental data.     

Optimal design of protein docking potentials: efficiency and limitations

Protein-protein docking is a challenging computational problem in functional genomics, particularly when one or both proteins undergo conformational change(s) upon binding. The major challenge is to define scoring function soft enough to tolerate these changes and specific enough to distinguish between near-native and "misdocked" conformations. Using a linear programming technique, we derived protein docking potentials (PDPs) that comply with this requirement. We considered a set of 63 nonredundant complexes to this aim, and generated 400,000 putative docked complexes (decoys) based on shape complementarity criterion for each complex. The PDPs were required to yield for the native (correctly docked) structure a potential energy lower than those of all the nonnative (misdocked) structures. The energy constraints applied to all complexes led to ca. 25 million inequalities, the simultaneous solution of which yielded an optimal set of PDPs that discriminated the correctly docked (up to 4.0 A root-mean-square deviation from known complex structure) structure among the 85 top-ranking (0.02%) decoys in 59/63 examined bound-bound cases. The high performance of the potentials was further verified in jackknife tests and by ranking putative docked conformation submitted to CAPRI. In addition to their utility in identifying correctly folded complexes, the PDPs reveal biologically meaningful features that distinguish docking potentials from folding potentials.     

Habitat geometry, population viscosity and the rate of genetic drift

In all natural populations, individuals located close to one another tend to interact more than those further apart. The extent of population viscosity can have important implications for ecological and evolutionary processes. Here we develop a spatially explicit population model to examine how the rate of genetic drift depends upon both spatial population structure and habitat geometry. The results show that the time to fixation for a new and selectively neutral mutation is dramatically increased in viscous populations. Furthermore, in viscous populations the time to fixation depends critically on habitat geometry. Fixation time for populations of identical size increases markedly as landscape width decreases and length increases. We suggest that similar effects will also be important in metapopulations, with the spatial arrangement of subpopulations and their connectivity likely to determine the rate of drift. We argue that the recent increases in computer power should facilitate major advances in our understanding of evolutionary landscape ecology over the next few years, and suggest that the time is ripe for a unification of spatial population dynamics theory, landscape ecology and population genetics.     

Parabolic movement primitives and cortical states: merging optimality with geometric invariance

Previous studies have suggested that several types of rules govern the generation of complex arm movements. One class of rules consists of optimizing an objective function (e.g., maximizing motion smoothness). Another class consists of geometric and kinematic constraints, for instance the coupling between speed and curvature during drawing movements as expressed by the two-thirds power law. It has also been suggested that complex movements are composed of simpler elements or primitives. However, the ability to unify the different rules has remained an open problem. We address this issue by identifying movement paths whose generation according to the two-thirds power law yields maximally smooth trajectories. Using equi-affine differential geometry we derive a mathematical condition which these paths must obey. Among all possible solutions only parabolic paths minimize hand jerk, obey the two-thirds power law and are invariant under equi-affine transformations (which preserve the fit to the two-thirds power law). Affine transformations can be used to generate any parabolic stroke from an arbitrary parabolic template, and a few parabolic strokes may be concatenated to compactly form a complex path. To test the possibility that parabolic elements are used to generate planar movements, we analyze monkeys’ scribbling trajectories. Practiced scribbles are well approximated by long parabolic strokes. Of the motor cortical neurons recorded during scribbling more were related to equi-affine than to Euclidean speed. Unsupervised segmentation of simulta- neously recorded multiple neuron activity yields states related to distinct parabolic elements. We thus suggest that the cortical representation of movements is state-dependent and that parabolic elements are building blocks used by the motor system to generate complex movements.     

Two Hg(II) complexes with a capped trigonal prismatic geometry derived from multidentate macrocyclic ligands containing N and S donors, with coordinated anions

Two Hg(II) complexes [HgL′(ClO₄)₂] (1) and [HgL(ClO₄)]ClO₄ (2) derived from the macrocyclic ligands, 4-(pyridin-2-ylmethyl)-1,7-dithia-4,10-diazacyclododecane (L′) and 7-(pyridin-2-ylmethyl)-1,4,10-trithia-7,13-diazacyclopentadecane (L), have been crystallographically characterised. Ligand L and its Hg(II) complex were isolated unexpectedly, and a possible formation pathway of the ligand is proposed. By including weakly bound O atoms from the perchlorate ions, the Hg atoms in both complexes are seven-coordinate and possess capped trigonal prismatic geometries. These uncommon structures for Hg(II) complexes were achieved mainly by the relatively large size of the metal ion and the steric effect from the macrocycles. In both complexes, strong hydrogen bonding between the amine hydrogen atom and a perchlorate ion was observed. For complex 1, the interaction is N(3)-H(15)···O(8) at 2.08(12) Å where O(8) is of the same anion as one of the coordinated O atoms; in complex 2, a similar hydrogen bond, N(7)-H(7)···O(32), with a distance of 2.25 Å, is formed to the coordinated anion, but the second anion remains discrete.