Well-Composed Cell Complexes

Well-composed 3D digital images, which are 3D binary digital images whose boundary surface is made up by 2D manifolds, enjoy important topological and geometric properties that turn out to be advantageous for some applications. In this paper, we present a method to transform the cubical complex associated to a 3D binary digital image (which is not generally a well-composed image) into a cell complex that is homotopy equivalent to the first one and whose boundary surface is composed by 2D manifolds. This way, the new representation of the digital image can benefit from the application of algorithms that are developed over surfaces embedded in ℝ3

Strong Euler well-composedness

In this paper, we define a new flavour of well-composedness, called strong Euler well composedness. In the general setting of regular cell complexes, a regular cell complex of dimension n is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is 1, which is the Euler characteristic of an (n−1)-dimensional ball. Working in the particular setting of cubical complexes canonically associated with nD pictures, we formally prove in this paper that strong Euler well-composedness implies digital well-composedness in any dimension n ≥ 2 and that the converse is not true when n ≥ 4Ministerio de Ciencia, Innovación y Universidades PID2019-107339GB-I00Junta de Andalucía P20_0114

EVOLUTION OF PROTEIN COMPLEXES IN BACTERIAL SPECIES

Protein complexes are composed of two or more associated polypeptide chains that may have different functions. Protein complexes play a critical role for all processes in life and are considered as highly conserved in evolution. In previous studies, protein complexes from E. coli or Mycoplasma pneumoniae have been characterized experimentally, revealing that a typical bacterial cell has on the order of 500 protein complexes. Using gene homology (orthology), these experimentally-observed complexes can be used to predict protein complexes across many species of bacteria. Surprisingly, the majority of protein complexes is not conserved, demonstrating an unexpected evolutionary flexibility. The current research investigates the evolution of 174 well-characterized (“reference”) protein complexes from E. coli that have three or more subunits. More specifically, we study the evolutionary flexibility by using evidence and patterns of the presence or absence of the subunits across a range of 894 bacterial species and to interpret whether the evolution is due to the loss or gain of a subunit in the protein complex. The purpose of this study is to determine how the presence or absence of a subunit affects the protein complexes’ functionality. We discuss the functional changes observed in a protein complex due to the presence or absence of a particular subunit by using a statistical approach and by confirming its significance.https://scholarscompass.vcu.edu/uresposters/1253/thumbnail.jp

Efficiently Storing Well-Composed Polyhedral Complexes Computed Over 3D Binary Images

A 3D binary image I can be naturally represented by a combinatorial-algebraic structure called cubical complex and denoted by Q(I ), whose basic building blocks are vertices, edges, square faces and cubes. In Gonzalez-Diaz et al. (Discret Appl Math 183:59–77, 2015), we presented a method to “locally repair” Q(I ) to obtain a polyhedral complex P(I ) (whose basic building blocks are vertices, edges, specific polygons and polyhedra), homotopy equivalent to Q(I ), satisfying that its boundary surface is a 2D manifold. P(I ) is called a well-composed polyhedral complex over the picture I . Besides, we developed a new codification system for P(I ), encoding geometric information of the cells of P(I ) under the form of a 3D grayscale image, and the boundary face relations of the cells of P(I ) under the form of a set of structuring elements. In this paper, we build upon (Gonzalez-Diaz et al. 2015) and prove that, to retrieve topological and geometric information of P(I ), it is enough to store just one 3D point per polyhedron and hence neither grayscale image nor set of structuring elements are needed. From this “minimal” codification of P(I ), we finally present a method to compute the 2-cells in the boundary surface of P(I ).Ministerio de Economía y Competitividad MTM2015-67072-

3D Well-composed Polyhedral Complexes

A binary three-dimensional (3D) image $I$ is well-composed if the boundary surface of its continuous analog is a 2D manifold. Since 3D images are not often well-composed, there are several voxel-based methods ("repairing" algorithms) for turning them into well-composed ones but these methods either do not guarantee the topological equivalence between the original image and its corresponding well-composed one or involve sub-sampling the whole image. In this paper, we present a method to locally "repair" the cubical complex $Q(I)$ (embedded in $\mathbb{R}^3$) associated to $I$ to obtain a polyhedral complex $P(I)$ homotopy equivalent to $Q(I)$ such that the boundary of every connected component of $P(I)$ is a 2D manifold. The reparation is performed via a new codification system for $P(I)$ under the form of a 3D grayscale image that allows an efficient access to cells and their faces

Encoding Specific 3D Polyhedral Complexes Using 3D Binary Images

We build upon the work developed in [4] in which we presented a method to “locally repair” the cubical complex Q(I) associated to a 3D binary image I, to obtain a “well-composed” polyhedral complex P(I), homotopy equivalent to Q(I). There, we developed a new codification system for P(I), called ExtendedCubeMap (ECM) representation, that encodes: (1) the (geometric) information of the cells of P(I) (i.e., which cells are presented and where), under the form of a 3D grayscale image gP ; (2) the boundary face relations between the cells of P(I), under the form of a set BP of structuring elements. In this paper, we simplify ECM representations, proving that geometric and topological information of cells can be encoded using just a 3D binary image, without the need of using colors or sets of structuring elements. We also outline a possible application in which well-composed polyhedral complexes can be useful.Junta de Andalucía FQM-369Ministerio de Economía y Competitividad MTM2012-32706Ministerio de Economía y Competitividad MTM2015-67072-

A practical method for efficient and optimal production of Seleno‐methionine‐labeled recombinant protein complexes in the insect cells

The use of Seleno‐methionine (SeMet) incorporated protein crystals for single or multi‐wavelength anomalous diffraction (SAD or MAD) to facilitate phasing has become almost synonymous with modern X‐ray crystallography. The anomalous signals from SeMets can be used for phasing as well as sequence markers for subsequent model building. The production of large quantities of SeMet incorporated recombinant proteins is relatively straightforward when expressed in Escherichia coli. In contrast, production of SeMet substituted recombinant proteins expressed in the insect cells is not as robust due to the toxicity of SeMet in eukaryotic systems. Previous protocols for SeMet‐incorporation in the insect cells are laborious, and more suited for secreted proteins. In addition, these protocols have generally not addressed the SeMet toxicity issue, and typically result in low recovery of the labeled proteins. Here we report that SeMet toxicity can be circumvented by fully infecting insect cells with baculovirus. Quantitatively controlling infection levels using our Titer Estimation of Quality Control (TEQC) method allow for the incorporation of substantial amounts of SeMet, resulting in an efficient and optimal production of labeled recombinant protein complexes. With the method described here, we were able to consistently reach incorporation levels of about 75% and protein yield of 60–90% compared with native protein expression

Neuro-Insular Complexes in the Human Pancreas

It is well known that pancreatic islets are complex structures composed of endodermally derived endocrine cells, integrated with endothelial cells and other cells, originating from the mesoderm, and innervated by nerve fibers that have a neuroectodermal origin. In our studies, we focused on the interactions between the structures of the nervous system and endocrine cells, the so-called neuro-insular complexes, in the human pancreas. In this chapter, we present our results and literature data concerning the morphological organization of neuro-insular complexes in humans and other mammals. We also discuss the possible functional role of neuro-insular complexes, such as the involvement of the nervous system in the regulation and synchronization of islet hormone secretion and the morphogenetic plasticity of the endocrine pancreas in adults, as well as in the regulation of endocrine cell proliferation and maturation during prenatal development of the pancreas