Transglutaminase 2 (TG2) is a multifunctional protein that promotes clearance of apoptotic cells (efferocytosis) acting as integrin β
3
coreceptor. Accumulating evidence indicates that defective efferocytosis contributes to the development of chronic inflammatory diseases. Obesity is characterized by the accumulation of dead adipocytes and inflammatory macrophages in the adipose tissue leading to obesity-related metabolic syndrome. Here, we report that loss of TG2 from bone marrow-derived cells sensitizes for high fat diet (HFD)-induced pathologies. We find that metabolically activated TG2 null macrophages express more phospho-Src and integrin β
3
, unexpectedly clear dying adipocytes more efficiently via lysosomal exocytosis, but produce more pro-inflammatory cytokines than the wild type ones. Anti-inflammatory treatment with an LXR agonist reverts the HFD-induced phenotype in mice lacking TG2 in bone marrow-derived cells with less hepatic steatosis than in wild type mice proving enhanced lipid clearance. Thus it is interesting to speculate whether LXR agonist treatment together with enhancing lysosomal exocytosis could be a beneficial therapeutic strategy in obesity.
The plant hormone ethylene or the gaseous signalling molecule nitric oxide (NO) may enhance salt stress tolerance by maintaining ion homeostasis, first of all K+/Na+ ratio of tissues. Ethylene and NO accumulation increased in the root apices and suspension culture cells of tomato at sublethal salt stress caused by 100 mM NaCl, however, the induction phase of programmed cell death (PCD) was different at lethal salt concentration. The production of ethylene by root apices and the accumulation of NO in the cells of suspension culture did not increase during the initiation of PCD after 250 mM NaCl treatment. Moreover, cells in suspension culture accumulated higher amount of reactive oxygen species which, along with NO deficiency contributed to cell death induction. The absence of ethylene in the apical root segments and the absence of NO accumulation in the cell suspension resulted in similar ion disequilibrium, namely K+/Na+ ratio of 1.41 ± 0.1 and 1.68 ± 0.3 in intact plant tissues and suspension culture cells, respectively that was not tolerated by tomato.
In this paper, we show how the subjects mentioned in the title are related. First we study the structure of partitions of $$A \subseteq \{1, \dots , n\}$$
A
⊆
{
1
,
⋯
,
n
}
in k-sets such that the first $$k-1$$
k
-
1
symmetric polynomials of the elements of the k-sets coincide. Then we apply this result to derive a decomposability result for the polynomial $$f_A(x) := \prod _{x \in A} (x-a)$$
f
A
(
x
)
:
=
∏
x
∈
A
(
x
-
a
)
. Finally we prove two theorems on the structure of the solutions (x, y) of the Diophantine equation $$f_A(x)=P(y)$$
f
A
(
x
)
=
P
(
y
)
where $$P(y)\in \mathbb {Q}[y]$$
P
(
y
)
∈
Q
[
y
]
and on shifted power values of $$f_A(x)$$
f
A
(
x
)
.
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