Modeling cell apoptosis for simulating three-dimensional multicellular morphogenesis based on a reversible network reconnection framework

Morphogenesis in multicellular organisms is accompanied by apoptotic cell behaviors: cell shrinkage and cell disappearance. The mechanical effects of these behaviors are spatiotemporally regulated within multicellular dynamics to achieve proper tissue sizes and shapes in three-dimensional (3D) space. To analyze 3D multicellular dynamics, 3D vertex models have been suggested, in which a reversible network reconnection (RNR) model has successfully expressed 3D cell rearrangements during large deformations. To analyze the effects of apoptotic cell behaviors on 3D multicellular morphogenesis, we modeled cell apoptosis based on the RNR model framework. Cell shrinkage was modeled by the potential energy as a function of individual cell times during the apoptotic phase. Cell disappearance was modeled by merging neighboring polyhedrons at their boundary surface according to the topological rules of the RNR model. To establish that the apoptotic cell behaviors could be expressed as modeled, we simulated morphogenesis driven by cell apoptosis in two types of tissue topology: 3D monolayer cell sheet and 3D compacted cell aggregate. In both types of tissue topology, the numerical simulations successfully illustrated that cell aggregates gradually shrank because of successive cell apoptosis. During tissue shrinkage, the number of cells in aggregates decreased while maintaining individual cell size and shape. Moreover, in case of localizing apoptotic cells within a part of the 3D monolayer cell aggregate, the cell apoptosis caused the global tissue bending by pulling on surrounding cells. In case of localizing apoptotic cells on the surface of the 3D compacted cell aggregate, the cell apoptosis caused successive, directional cell rearrangements from the inside to the surface. Thus, the proposed model successfully provided a basis for expressing apoptotic cell behaviors during 3D multicellular morphogenesis based on an RNR model framework.     

Modeling cell proliferation for simulating three-dimensional tissue morphogenesis based on a reversible network reconnection framework

Tissue morphogenesis in multicellular organisms is accompanied by proliferative cell behaviors: cell division (increase in cell number after each cell cycle) and cell growth (increase in cell volume during each cell cycle). These proliferative cell behaviors can be regulated by multicellular dynamics to achieve proper tissue sizes and shapes in three-dimensional (3D) space. To analyze multicellular dynamics, a reversible network reconnection (RNR) model has been suggested, in which each cell shape is expressed by a single polyhedron. In this study, to apply the RNR model to simulate tissue morphogenesis involving proliferative cell behaviors, we model cell proliferation based on a RNR model framework. In this model, cell division was expressed by dividing a polyhedron at a planar surface for which cell division behaviors were characterized by three quantities: timing, intracellular position, and normal direction of the dividing plane. In addition, cell growth was expressed by volume growth as a function of individual cell times within their respective cell cycles. Numerical simulations using the proposed model showed that tissues grew during successive cell divisions with several cell cycle times. During these processes, the cell number in tissues increased while maintaining individual cell size and shape. Furthermore, tissue morphology dramatically changed based on different regulations of cell division directions. Thus, the proposed model successfully provided a basis for expressing proliferative cell behaviors during morphogenesis based on a RNR model framework.     

The computer synthesis of expressive faces.

This paper presents a methodology for the computer synthesis of realistic faces capable of expressive articulations. A sophisticated three-dimensional model of the human face is developed that incorporates a physical model of facial tissue with an anatomical model of facial muscles. The tissue and muscle models are generic, in that their structures are independent of specific facial geometries. To synthesize specific faces, these models are automatically mapped onto geometrically accurate polygonal facial representations constructed by photogrammetry of stereo facial images or by non-uniform meshing of detailed facial topographies acquired by using range sensors. The methodology offers superior realism by utilizing physical modelling to emulate complex tissue deformations in response to coordinated facial muscle activity. To provide realistic muscle actions to the face model, a performance driven animation technique is developed which estimates the dynamic contractions of a performer's facial muscles from video imagery.     

Glycosaminoglycan network geometry may contribute to anisotropic hydraulic permeability in cartilage under compression.

Resistance to fluid flow within cartilage extracellular matrix is provided primarily by a dense network of rod-like glycosaminoglycans (GAGs). If the geometrical organization of this network is random, the hydraulic permeability tensor of cartilage is expected to be isotropic. However, experimental data have suggested that hydraulic permeability may become anisotropic when the matrix is mechanically compressed, contributing to cartilage biomechanical functions such as lubrication. We hypothesized that this may be due to preferred GAG rod orientations and directionally-dependent reduction of inter-GAG spacings which reflect molecular responses to tissue deformations. To examine this hypothesis, we developed a model for effects of compression which allows the GAG rod network to deform consistently with tissue-scale deformations but while still respecting limitations imposed by molecular structure. This network deformation model was combined with a perturbation analysis of a classical analytical model for hydraulic permeability based on molecular structure. Finite element analyses were undertaken to ensure that this approach exhibited results similar to those emerging from more exact calculations. Model predictions for effects of uniaxial confined compression on the hydraulic permeability tensor were consistent with previous experimental results. Permeability decreased more rapidly in the direction perpendicular to compression than in the parallel direction, for matrix solid volume fractions associated with fluid transport in articular cartilage. GAG network deformations may therefore introduce anisotropy to the permeability (and other GAG-associated matrix properties) as physiological compression is applied, and play an important role in cartilage lubrication and other biomechanical functions.     

Modeling mechanical strains and stresses in soft tissues of the shoulder during load carriage based on load-bearing open MRI

Shoulder strain is a major limiting factor associated with load carriage. Despite advances in backpack designs, there are still reports of shoulder discomfort, loss of sensorimotor functions, and brachial plexus syndrome. The current study is aimed at characterizing mechanical loading conditions (strains and stresses) that develop within the shoulder's soft tissues when carrying a backpack. Open MRI scans were used for reconstructing a three-dimensional geometrical model of an unloaded shoulder and for measuring the soft tissue deformations caused by a 25-kg backpack; subsequently, a subject-specific finite element (FE) model for nonlinear, large-deformation stress-strain analyses was developed. Skin pressure distributions under the backpack strap were used as reference data and for verifying the numerical solutions. The parameters of the model were adjusted to fit the calculated tissue deformations to those obtained by MRI. The MRI scans revealed significant compression of the soft tissues of the shoulder, with substantial deformations in the area of the subclavian muscle and the brachial plexus. The maximal pressure values exerted by a 25-kg load were substantial and reached ～90 kPa. In the muscle surrounding the brachial plexus, the model predicted maximal compressive strain of 0.14 and maximal tensile strain of 0.13, which might be injurious for the underlying neural tissue. In conclusion, the FE model provided some insights regarding the potential mechanisms underlying brachial plexus injuries related to load carriage. The large tissue deformations and pressure hotspots that were observed are likely to result in tissue damage, which may hamper neural function if sustained for long time exposures.     

Density functional and electrostatics study of oxidized and reduced ribonucleotide reductase; comparisons with methane monooxygenase

A combined broken symmetry density functional and electrostatics approach has been used to examine the active sites of the resting (RNR(ox)) and reduced (RNR(red)) forms of class I type ribonucleotide reductase in the protein and solvent environment. Active site cluster geometries and Heisenberg J values are discussed in the context of the available protein data. The total electrostatic interaction energy in the protein comprises a large reaction field component and a much smaller protein field term, the former suggesting strong dielectric polarization between the cluster and protein-solvent dielectrics; the latter is indicative of a very weak link to the protein environment. Decomposition of the protein field term elucidates the major electrostatic interactions between amino acid residues in the RNR R2 local environment and the active site cluster, enabling an energetic comparison of structurally equivalent residues with a related diiron protein, methane monooxygenase.     

Extracting Labeled Topological Patterns from Samples of Networks

An advanced graph theoretical approach is introduced that enables a higher level of functional interpretation of samples of directed networks with identical fixed pairwise different vertex labels that are drawn from a particular population. Compared to the analysis of single networks, their investigation promises to yield more detailed information about the represented system. Often patterns of directed edges in sample element networks are too intractable for a direct evaluation and interpretation. The new approach addresses the problem of simplifying topological information and characterizes such a sample of networks by finding its locatable characteristic topological patterns. These patterns, essentially sample-specific network motifs with vertex labeling, might represent the essence of the intricate topological information contained in all sample element networks and provides as well a means of differentiating network samples. Central to the accurateness of this approach is the null model and its properties, which is needed to assign significance to topological patterns. As a proof of principle the proposed approach has been applied to the analysis of networks that represent brain connectivity before and during painful stimulation in patients with major depression and in healthy subjects. The accomplished reduction of topological information enables a cautious functional interpretation of the altered neuronal processing of pain in both groups.     

An elastic network model based on the structure of the red blood cell membrane skeleton.

A finite element network model has been developed to predict the macroscopic elastic shear modulus and the area expansion modulus of the red blood cell (RBC) membrane skeleton on the basis of its microstructure. The topological organization of connections between spectrin molecules is represented by the edges of a random Delaunay triangulation, and the elasticity of an individual spectrin molecule is represented by the spring constant, K, for a linear spring element. The model network is subjected to deformations by prescribing nodal displacements on the boundary. The positions of internal nodes are computed by the finite element program. The average response of the network is used to compute the shear modulus (mu) and area expansion modulus (kappa) for the corresponding effective continuum. For networks with a moderate degree of randomness, this model predicts mu/K = 0.45 and kappa/K = 0.90 in small deformations. These results are consistent with previous computational models and experimental estimates of the ratio mu/kappa. This model also predicts that the elastic moduli vary by 20% or more in networks with varying degrees of randomness. In large deformations, mu increases as a cubic function of the extension ratio lambda 1, with mu/K = 0.62 when lambda 1 = 1.5.     

Measuring the Deformation of Cells within a Piece of Compressed Potato Tuber Tissue

For the successful mathematical mechanical modelling of livingplant tissues, relationships between cellular deformations andtissue deformation need to be investigated. In previous workthese relationships have often been assumed. In this paper thedeformation of living cells within potato tuber tissue is measuredusing light microscopy and image analysis and is analysed inrelation to applied tissue deformations. The cell wall deformationwas found to depend upon the orientation of the cell wall faceswith respect to the global axes of the tissue and the appliedtissue deformation. Some faces experienced compression, whichreduced their surface area; others were deformed in bi-axialtension, thus increasing their surface area. These deformationswere successfully related to the global tissue deformations,using a simple constant volume affine deformation model, upto compressive deformations of 20% of specimen height. Somedeviation from the model was observed due to the bending ofcell walls in compression. Copyright 2000 Annals of Botany Company Potato tuber tissue, Solanum tuberosum, mechanical properties, cell walls, strain, re-orientation     

A computer simulation of geometrical configurations during cell division

A process of cell division in the blastular wall of the starfish, Asterina pectinifera, was observed, and an attempt was made to model with a computer simulation the way in which cell number increases in such a tissue. Dividing cells at stages between the 2(11)-cell and the beginning of rotation were observed to shift these positions to the outer surface of the cell sheet by rounding up, after which they divide and slip back into the sheet as two columnar daughter cells. The change of a polygonal pattern of the blastular wall by cell division was simulated by making use of geometrical models of polygonal cells and the rule of the direction of cell division which was confirmed by observation. The simulation proves valid for describing changes of polygonal patterns of cell sheets including dividing cells.     

Voro3D: 3D Voronoi tessellations applied to protein structures

SUMMARY: Voro3D is an original easy-to-use tool, which provides a brand new point of view on protein structures through the three-dimensional (3D) Voronoi tessellations. To construct the Voronoi cells associated with each amino acid by a number of different tessellation methods, Voro3D uses a protein structure file in the PDB format as an input. After calculation, different structural properties of interest like secondary structures assignment, environment accessibility and exact contact matrices can be derived without any geometrical cut-off. Voro3D provides also a visualization of these tessellations superimposed on the associated protein structure, from which it is possible to model a polygonal protein surface using a model solvent or to quantify, for instance, the contact areas between a protein and a ligand. AVAILABILITY: The software executable file for PC using Windows 98, 2000, NT, XP can be freely downloaded at http://www.lmcp.jussieu.fr/~mornon/voronoi.html CONTACT: franck.dupuis@sanofi-aventis.com; jean-paul-mornon@imcp.jussieu.fr.     

Topological Progression in Proliferating Epithelia Is Driven by a Unique Variation in Polygon Distribution

Morphogenesis is consequence of lots of small coordinated variations that occur during development. In proliferating stages, tissue growth is coupled to changes in shape and organization. A number of studies have analyzed the topological properties of proliferating epithelia using the Drosophila wing disc as a model. These works are based in the existence of a fixed distribution of these epithelial cells according to their number of sides. Cell division, cell rearrangements or a combination of both mechanisms have been proposed to be responsible for this polygonal assembling. Here, we have used different system biology methods to compare images from two close proliferative stages that present high morphological similarity. This approach enables us to search for traces of epithelial organization. First, we show that geometrical and network characteristics of individual cells are mainly dependent on their number of sides. Second, we find a significant divergence between the distribution of polygons in epithelia from mid-third instar larva versus early prepupa. We show that this alteration propagates into changes in epithelial organization. Remarkably, only the variation in polygon distribution driven by morphogenesis leads to progression in epithelial organization. In addition, we identify the relevant features that characterize these rearrangements. Our results reveal signs of epithelial homogenization during the growing phase, before the planar cell polarity pathway leads to the hexagonal packing of the epithelium during pupal stages.     

Nonatomic solvent-driven Voronoi tessellation of proteins: an open tool to analyze protein folds

A three-dimensional Voronoi tessellation of folded proteins is used to analyze geometrical and topological properties of a set of proteins. To each amino acid is associated a central point surrounded by a Voronoi cell. Voronoi cells describe the packing of the amino acids. Special attention is given to reproduction of the protein surface. Once the Voronoi cells are built, a lot of tools from geometrical analysis can be applied to investigate the protein structure; volume of cells, number of faces per cell, and number of sides per face are the usual signatures of the protein structure. A distinct difference between faces related to primary, secondary, and tertiary structures has been observed. Faces threaded by the main-chain have on average more than six edges, whereas those related to helical packing of the amino acid chain have less than five edges. The faces on the protein surface have on average five edges within 1% error. The average number of faces on the protein surface for a given type of amino acid brings a new point of view in the characterization of the exposition to the solvent and the classification of amino acid as hydrophilic or hydrophobic. It may be a convenient tool for model validation.     

Texture analysis of the 3D collagen network and automatic classification of the physiology of articular cartilage

A close relationship has been found between the 3D collagen structure and physiological condition of articular cartilage (AC). Studying the 3D collagen network in AC offers a way to determine the condition of the cartilage. However, traditional qualitative studies are time consuming and subjective. This study aims to develop a computer vision-based classifier to automatically determine the condition of AC tissue based on the structural characteristics of the collagen network. Texture analysis was applied to quantitatively characterise the 3D collagen structure in normal (International Cartilage Repair Society, ICRS, grade 0), aged (ICRS grade 1) and osteoarthritic cartilages (ICRS grade 2). Principle component techniques and linear discriminant analysis were then used to classify the microstructural characteristics of the 3D collagen meshwork and the condition of the AC. The 3D collagen meshwork in the three physiological condition groups displayed distinctive characteristics. Texture analysis indicated a significant difference in the mean texture parameters of the 3D collagen network between groups. The principle component and linear discriminant analysis of the texture data allowed for the development of a classifier for identifying the physiological status of the AC with an expected prediction error of 4.23%. An automatic image analysis classifier has been developed to predict the physiological condition of AC (from ICRS grade 0 to 2) based on texture data from the 3D collagen network in the tissue.     

Yeast DNA damage-inducible Rnr3 has a very low catalytic activity strongly stimulated after the formation of a cross-talking Rnr1/Rnr3 complex

The ribonucleotide reductase system in Saccharomyces cerevisiae includes four genes (RNR1 and RNR3 encoding the large subunit and RNR2 and RNR4 encoding the small subunit). RNR3 expression, nearly undetectable during normal growth, is strongly induced by DNA damage. Yet an rnr3 null mutant has no obvious phenotype even under DNA damaging conditions, and the contribution of RNR3 to ribonucleotide reduction is not clear. To investigate the role of RNR3 we expressed and characterized the Rnr3 protein. The in vitro activity of Rnr3 was less than 1% of the Rnr1 activity. However, a strong synergism between Rnr3 and Rnr1 was observed, most clearly demonstrated in experiments with the catalytically inactive Rnr1-C428A mutant, which increased the endogenous activity of Rnr3 by at least 10-fold. In vivo, the levels of Rnr3 after DNA damage never reached more than one-tenth of the Rnr1 levels. We propose that heterodimerization of Rnr3 with Rnr1 facilitates the recruitment of Rnr3 to the ribonucleotide reductase holoenzyme, which may be important when Rnr1 is limiting for dNTP production. In complex with inactive Rnr1-C428A, the activity of Rnr3 is controlled by effector binding to Rnr1-C428A. This result indicates cross-talk between the Rnr1 and Rnr3 polypeptides of the large subunit.     

Three-dimensional tissue cultures: current trends and beyond

Life science research focuses on deciphering the biochemical mechanisms that regulate cell proliferation and function and largely depends on the use of tissue culture methods in which cells are grown on two-dimensional hard plastic or glass surfaces. However, the flat surface of the tissue culture plate represents a poor topological approximation of the complex three-dimensional (3D) architecture of a tissue or organ composed of various cell types, extracellular matrix (ECM) and interstitial fluids. Moreover, if we consider a cell as a perfectly defined volume, flattened cells have full access to the environment and limited cell-to-cell contact. However if the cell is a cube in a simple cuboidal epithelium, then its access to the lumen is limited to one face, with the opposite face facing the basal membrane and the remaining four faces lying in close contact with neighbouring cells. This is of great importance when considering the access of viruses and bacteria to the cell surface, the excretion of soluble factors or proteins or the signalling within or between cells. This short review discusses various cell culture approaches to improve the simulation of the 3D environment of cells.     

The Non-Proliferative Nature of Ascidian Folliculogenesis as a Model of Highly Ordered Cellular Topology Distinct from Proliferative Epithelia

Previous studies have addressed why and how mono‐stratified epithelia adopt a polygonal topology. One major additional, and yet unanswered question is how the frequency of different cell shapes is achieved and whether the same distribution applies between non-proliferative and proliferative epithelia. We compared different proliferative and non-proliferative epithelia from a range of organisms as well as Drosophila melanogaster mutants, deficient for apoptosis or hyperproliferative. We show that the distribution of cell shapes in non‐proliferative epithelia (follicular cells of five species of tunicates) is distinctly, and more stringently organized than proliferative ones (cultured epithelial cells and Drosophila melanogaster imaginal discs). The discrepancy is not supported by geometrical constraints (spherical versus flat monolayers), number of cells, or apoptosis events. We have developed a theoretical model of epithelial morphogenesis, based on the physics of divided media, that takes into account biological parameters such as cell‐cell contact adhesions and tensions, cell and tissue growth, and which reproduces the effects of proliferation by increasing the topological heterogeneity observed experimentally. We therefore present a model for the morphogenesis of epithelia where, in a proliferative context, an extended distribution of cell shapes (range of 4 to 10 neighbors per cell) contrasts with the narrower range of 5-7 neighbors per cell that characterizes non proliferative epithelia.