In theoretical medicine, topological indices are defined to test the medicine and pharmacy characteristics, such as melting point, boiling point, toxicity and other biological activities. As basic molecular structures, hexagonal jagged-rectangle and distance-regular structure are widely appeared in medicine, pharmacy and biology engineering. In this paper, we study the chemical properties of hexagonal jagged-rectangle from the mathematical point of view. Several vertex distance-based indices are determined. Furthermore, the Wiener related indices of distance-regular structure are also considered.
A large number of medical experiments have confirmed that the features of drugs have a close correlation with their molecular structure. Drug properties can be obtained by studying the molecular structure of corresponding drugs. The calculation of the topological index of a drug structure enables scientists to have a better understanding of the physical chemistry and biological characteristics of drugs. In this paper, we focus on Hyaluronic Acid-Paclitaxel conjugates which are widely used in the manufacture of anticancer drugs. Several topological indices are determined by virtue of the edge-partition method, and our results remedy the lack of medicine experiments, thus providing a theoretical basis for pharmaceutical engineering.
Isolation toughness is a vital parameter to evaluate the vulnerability of computer networks. In specific network designing stage, it is necessary to find the lower bound of the isolated toughness, and strive to build a network that meets the stability requirements with the least cost. Gao et al.1 conjectured that if a graph
G
with
κ
(
G
)
≥
3
m
+
1
2
satisfies
I
(
G
)
>
7
m
+
5
4
m
+
4
or
I
′
(
G
)
>
7
m
+
5
4
m
+
2
, then
G
is a
(
P
≥
3
,
m
)
‐factor deleted graph. It's proved that this conjecture holds. However, it is found that as the connectivity changes, the tight lower bound of isolated toughness for
(
P
≥
3
,
m
)
‐factor deleted graphs will change as well. Therefore, we propose a new perspective to look into this problem and introduce the concepts of isolated toughness
(
P
≥
3
,
m
)
factor deleted surface and isolated toughness variant
(
P
≥
3
,
m
)
factor deleted surface, where the result of the original conjecture is only a cross‐section on surfaces. The main contribution in this paper is to determine the concrete expression of these two surfaces.
Live ischemia-reperfusion injury is associated with endoplasmic reticulum (ER) stress-induced apoptosis. Activation of peroxisome proliferator-activated receptor-α (PPARα) may inhibit hepatocyte apoptosis induced by oxidative stress and protect against liver injury. This study aimed to investigate the effects of PPARα activation, through a specific agonist, on ER stress-induced apoptosis in human liver hepatocellular carcinoma (HepG2) cells. HepG2 cells were challenged with H2O2 and treated with WY14643, a selective PPARα agonist, in the presence or absence of the PPARα antagonist of MK886. Cell viable assay (MTT) and immunostaining were used to evaluate cell viability. The level of apoptotic cell death was quantified through Annexin V/PI staining. Alanine aminotransferase, asparatate aminotransferase, and malondialdehyde levels were measured to determine the presence of cellular injury and oxidative stress. RT-PCR and Western blot analysis were used to detect mRNA and protein expression of PPARα, BiP, and CHOP. Immunofluorescence was utilized to determine the intracellular localization of CHOP. H2O2 and MK886 both reduced the viability of HepG2 cells, increased oxidative stress and apoptosis, up-regulated the BiP and CHOP expression, and induced CHOP translocation from the cytoplasm to the nucleus. Compared with cells treated with H2O2 alone, pre-administration of WY14643 increased cell viability, attenuated apoptosis, improved cell function, down-regulated BiP and CHOP expression and inhibited CHOP translocation. The effects of WY14643 were completely abolished using the MK886 antagonist. PPARα activation protects against H2O2-induced HepG2 cell apoptosis. The underlying mechanisms may be associated with its activation to suppress excessive ER stress.
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