On Analysis of Topological Aspects for Subdivision of Kragujevac Tree Networks

In this paper, we have taken review of certain topological topological characteristics of subdivision and the line graph of subdivision of Kragujevac tree. A Kragujevac tree is denoted by K , K ∈ Kg q = r 2 t + 1 + 1 , r , with order r 2 t + 1 + 1 and size r 2 t + 1 , respectively. We have computed the Zagreb polynomials, forgotten polynomial, and M-polynomial for Kragujevac tree. Moreover, we have computed topological indices like Zagreb-type indices, reduced reciprocal Randić indices, family of Gourava indices as well as forgotten index. Further, some topological indices that can be directly derived from M-polynomial, i.e., first and second Zagreb index, modified second Zagreb index, Randić and reciprocal Randić index, symmetric division and harmonic index, and inverse sum and augmented Zagreb index are also computed.

On Computation Degree-Based Topological Descriptors for Planar Octahedron Networks

A molecular graph is used to represent a chemical molecule in chemical graph theory, which is a branch of graph theory. A graph is considered to be linked if there is at least one link between its vertices. A topological index is a number that describes a graph’s topology. Cheminformatics is a relatively young discipline that brings together the field of sciences. Cheminformatics helps in establishing QSAR and QSPR models to find the characteristics of the chemical compound. We compute the first and second modified K-Banhatti indices, harmonic K-Banhatti index, symmetric division index, augmented Zagreb index, and inverse sum index and also provide the numerical results.

Asymmetric cell division of mammary stem cells

Somatic stem cells are distinguished by their capacity to regenerate themselves and also to produce daughter cells that will differentiate. Self-renewal is achieved through the process of asymmetric cell division which helps to sustain tissue morphogenesis as well as maintain homeostasis. Asymmetric cell division results in the development of two daughter cells with different fates after a single mitosis. Only one daughter cell maintains “stemness” while the other differentiates and achieves a non-stem cell fate. Stem cells also have the capacity to undergo symmetric division of cells that results in the development of two daughter cells which are identical. Symmetric division results in the expansion of the stem cell population. Imbalances and deregulations in these processes can result in diseases such as cancer. Adult mammary stem cells (MaSCs) are a group of cells that play a critical role in the expansion of the mammary gland during puberty and any subsequent pregnancies. Furthermore, given the relatively long lifespans and their capability to undergo self-renewal, adult stem cells have been suggested as ideal candidates for transformation events that lead to the development of cancer. With the possibility that MaSCs can act as the source cells for distinct breast cancer types; understanding their regulation is an important field of research. In this review, we discuss asymmetric cell division in breast/mammary stem cells and implications on further research. We focus on the background history of asymmetric cell division, asymmetric cell division monitoring techniques, identified molecular mechanisms of asymmetric stem cell division, and the role asymmetric cell division may play in breast cancer.

Overexpression of Flii during Murine Embryonic Development Increases Symmetrical Division of Epidermal Progenitor Cells

Epidermal progenitor cells divide symmetrically and asymmetrically to form stratified epidermis and hair follicles during late embryonic development. Flightless I (Flii), an actin remodelling protein, is implicated in Wnt/β-cat and integrin signalling pathways that govern cell division. This study investigated the effect of altering Flii on the divisional orientation of epidermal progenitor cells (EpSCs) in the basal layer during late murine embryonic development and early adolescence. The effect of altering Flii expression on asymmetric vs. symmetric division was assessed in vitro in adult human primary keratinocytes and in vivo at late embryonic development stages (E16, E17 and E19) as well as adolescence (P21 day-old) in mice with altered Flii expression (Flii knockdown: Flii+/−, wild type: WT, transgenic Flii overexpressing: FliiTg/Tg) using Western blot and immunohistochemistry. Flii+/− embryonic skin showed increased asymmetrical cell division of EpSCs with an increase in epidermal stratification and elevated talin, activated-Itgb1 and Par3 expression. FliiTg/Tg led to increased symmetrical cell division of EpSCs with increased cell proliferation rate, an elevated epidermal SOX9, Flap1 and β-cat expression, a thinner epidermis, but increased hair follicle number and depth. Flii promotes symmetric division of epidermal progenitor cells during murine embryonic development.

Deceleration of cell cycle underpins a switch from proliferative- to terminal division in plant stomatal lineage

Differentiation of specialized cell types from self-renewing progenitors requires precise cell cycle control. Plant stomata are generated through asymmetric divisions of a stem-cell-like precursor meristemoid followed by the single symmetric division that creates an adjustable pore surrounded by paired guard cells. The stomatal-lineage-specific transcription factor MUTE terminates the asymmetric divisions and triggers differentiation. However, the role of cell cycle machinery in this transition remains unknown. Through time-lapse imaging, we discover that the symmetric division is slower than the asymmetric division. We identify a plant-specific cyclin-dependent kinase inhibitor, SIAMESE-RELATED4 (SMR4), as a molecular brake that decelerates cell cycle during this transition. SMR4 is directly induced by MUTE and transiently accumulates in differentiating meristemoids. SMR4 physically and functionally associates with CYCD3;1 and extends G1-phase of asymmetric divisions. By contrast, SMR4 fails to interact with CYCD5;1, a MUTE-induced G1 cyclin, and permits the symmetric division. Our work unravels a molecular framework of the proliferation-to-differentiation switch within the stomatal lineage and suggests that a timely proliferative cell cycle is critical for the stomatal fate specification.

M-Polynomials and Degree-Based Topological Indices of the Molecule Copper(I) Oxide

Topological indices are numerical parameters used to study the physical and chemical residences of compounds. Degree-based topological indices have been studied extensively and can be correlated with many properties of the understudy compounds. In the factors of degree-based topological indices, M-polynomial played an important role. In this paper, we derived closed formulas for some well-known degree-based topological indices like first and second Zagreb indices, the modified Zagreb index, the symmetric division index, the harmonic index, the Randić index and inverse Randić index, and the augmented Zagreb index using calculus.