A triangulated category
T
whose suspension functor
Σ
satisfies
Σ
m
≅
Id
T
as additive functors is called an
m
-periodic triangulated category. Such a category does not have a tilting object by the ...periodicity. In this paper, we introduce the notion of an
m
-periodic tilting object in an
m
-periodic triangulated category, which is a periodic analogue of a tilting object in a triangulated category, and prove that an
m
-periodic triangulated category having an
m
-periodic tilting object is triangle equivalent to the
m
-periodic derived category of an algebra under some homological assumptions. As an application, we construct a triangle equivalence between the stable category of finitely generated modules over a self-injective algebra and the
m
-periodic derived category of a hereditary algebra.
Essential elements taken up from the soil and distributed throughout the whole plant play diverse roles in different tissues. Cations and anions contribute to maintenance of intracellular osmolarity ...and the formation of membrane potential, while nitrate, ammonium, and sulfate are incorporated into amino acids and other organic compounds. In contrast to these ion species, calcium concentrations are usually kept low in the cytosol and calcium displays unique behavior as a cytosolic signaling molecule. Various environmental stresses stimulate increases in the cytosolic calcium concentration, leading to activation of calcium-regulated protein kinases and downstream signaling pathways. In this review, we summarize the stress responsive regulation of nutrient uptake and balancing by two types of calcium-regulated phosphorylation systems: CPK and CBL-CIPK. CPK is a family of protein kinases activated by calcium. CBL is a group of calcium sensor proteins that interact with CIPK kinases, which phosphorylate their downstream targets. In
, quite a few ion transport systems are regulated by CPKs or CBL-CIPK complexes, including channels/transporters that mediate transport of potassium (KAT1, KAT2, GORK, AKT1, AKT2, HAK5, SPIK), sodium (SOS1), ammonium (AMT1;1, AMT1;2), nitrate and chloride (SLAC1, SLAH2, SLAH3, NRT1.1, NRT2.4, NRT2.5), and proton (AHA2, V-ATPase). CPKs and CBL-CIPKs also play a role in C/N nutrient response and in acquisition of magnesium and iron. This functional regulation by calcium-dependent phosphorylation systems ensures the growth of plants and enables them to acquire tolerance against various environmental stresses. Calcium serves as the key factor for the regulation of membrane transport systems.
Let
R
be a commutative noetherian ring and denote by
mod
R
the category of finitely generated
R
-modules. In this paper, we study KE-closed subcategories of
mod
R
, that is, additive subcategories ...closed under kernels and extensions. We first give a characterization of KE-closed subcategories:
a KE-closed subcategory is a torsion-free class in a torsion-free class
. As an immediate application of the dual statement, we give a conceptual proof of Stanley-Wang’s result about narrow subcategories. Next, we classify the KE-closed subcategories of
mod
R
when
dim
R
≤
1
and when
R
is a two-dimensional normal domain. More precisely, in the former case, we prove that KE-closed subcategories coincide with torsion-free classes in
mod
R
. Moreover, this condition implies
dim
R
≤
1
when
R
is a homomorphic image of a Cohen-Macaulay ring (e.g. a finitely generated algebra over a regular ring). Thus, we give a complete answer for the title.
Abstract
Cesium (Cs+) is known to compete with the macronutrient potassium (K+) inside and outside of plants and to inhibit plant growth at high concentrations. However, the detailed molecular ...mechanisms of how Cs+ exerts its deleterious effects on K+ accumulation in plants are not fully elucidated. Here, we show that mutation in a member of the major K+ channel AKT1–KC1 complex renders Arabidopsis thaliana hypersensitive to Cs+. Higher severity of the phenotype and K+ loss were observed for these mutants in response to Cs+ than to K+ deficiency. Electrophysiological analysis demonstrated that Cs+, but not sodium, rubidium or ammonium, specifically inhibited K+ influx through the AKT1–KC1 complex. In contrast, Cs+ did not inhibit K+ efflux through the homomeric AKT1 channel that occurs in the absence of KC1, leading to a vast loss of K+. Our observation suggests that reduced K+ accumulation due to blockage/competition in AKT1 and other K+ transporters/channels by Cs+ plays a major role in plant growth retardation. This report describes the mechanical role of Cs+ in K+ accumulation, and in turn in plant performance, providing actual evidence at the plant level for what has long been believed, i.e. K+ channels are, therefore AKT1 is, ‘blocked’ by Cs+.
When plants are exposed to drastic environmental changes such as drought, salt or bacterial invasion, rapid stomatal movement confers tolerance to these stresses. This process involves a variety of ...guard cell expressed ion channels and their complex regulation network. Inward K⁺ channels mainly function in stomatal opening. On the other hand, guard cell anion channels play a crucial role in the closing of stomata, which is vital in terms of preventing water loss and bacterial entrance. Massive progress has been made on the research of these anion channels in the last decade. In this review, we focus on the function and regulation of
guard cell anion channels. Starting from SLAC1, a main contributor of stomatal closure, members of SLAHs (SLAC1 homologues), AtNRTs (Nitrate transporters), AtALMTs (Aluminum-activated malate transporters), ABC transporters, AtCLCs (Chloride channels), DTXs (Detoxification efflux carriers), SULTRs (Sulfate transporters), and their regulator components are reviewed. These membrane transport systems are the keys to maintaining cellular ion homeostasis against fluctuating external circumstances.
The Grothendieck monoid of an exact category is a monoid version of the Grothendieck group. We use it to classify Serre subcategories of an exact category and to reconstruct the topology of a ...noetherian scheme. We first construct bijections between (i) the set of Serre subcategories of an exact category, (ii) the set of faces of its Grothendieck monoid, and (iii) the monoid spectrum of its Grothendieck monoid. By using (ii), we classify Serre subcategories of exact categories related to a finite dimensional algebra and a smooth projective curve. For this, we determine the Grothendieck monoid of the category of coherent sheaves on a smooth projective curve. By using (iii), we introduce a topology on the set of Serre subcategories. As a consequence, we recover the topology of a noetherian scheme from the Grothendieck monoid.
N-myristoylation and S-acylation promote protein membrane association, allowing regulation of membrane proteins. However, how widespread this targeting mechanism is in plant signaling processes ...remains unknown.
Through bioinformatics analyses, we determined that among plant protein kinase families, the occurrence of motifs indicative for dual lipidation by N-myristoylation and S-acylation is restricted to only five kinase families, including the Ca2+-regulated CDPK-SnRK and CBL protein families. We demonstrated N-myristoylation of CDPK-SnRKs and CBLs by incorporation of radiolabeled myristic acid. We focused on CPK6 and CBL5 as model cases and examined the impact of dual lipidation on their function by fluorescence microscopy, electrophysiology and functional complementation of Arabidopsis mutants.
We found that both lipid modifications were required for proper targeting of CBL5 and CPK6 to the plasma membrane. Moreover, we identified CBL5–CIPK11 complexes as phosphorylating and activating the guard cell anion channel SLAC1. SLAC1 activation by CPK6 or CBL5–CIPK11 was strictly dependent on dual lipid modification, and loss of CPK6 lipid modification prevented functional complementation of cpk3 cpk6 guard cell mutant phenotypes.
Our findings establish the general importance of dual lipid modification for Ca2+ signaling processes, and demonstrate their requirement for guard cell anion channel regulation.
Summary
Glutamine is a product of ammonium (NH4+) assimilation catalyzed by glutamine synthetase (GS) and glutamate synthase (GOGAT). The growth of NH4+‐preferring paddy rice (Oryza sativa L.) ...depends on root NH4+ assimilation and the subsequent root‐to‐shoot allocation of glutamine; however, little is known about the mechanism of glutamine storage in roots. Here, using transcriptome and reverse genetics analyses, we show that the rice amino acid transporter‐like 6 (OsATL6) protein exports glutamine to the root vacuoles under NH4+‐replete conditions. OsATL6 was expressed, along with OsGS1;2 and OsNADH‐GOGAT1, in wild‐type (WT) roots fed with sufficient NH4Cl, and was induced by glutamine treatment. We generated two independent Tos17 retrotransposon insertion mutants showing reduced OsATL6 expression to determine the function of OsATL6. Compared with segregants lacking the Tos17 insertion, the OsATL6 knock‐down mutant seedlings exhibited lower root glutamine content but higher glutamine concentration in the xylem sap and greater shoot growth under NH4+‐replete conditions. The transient expression of monomeric red fluorescent protein‐fused OsATL6 in onion epidermal cells confirmed the tonoplast localization of OsATL6. When OsATL6 was expressed in Xenopus laevis oocytes, glutamine efflux from the cell into the acidic bath solution increased. Under sufficient NH4+ supply, OsATL6 transiently accumulated in sclerenchyma and pericycle cells, which are located adjacent to the Casparian strip, thus obstructing the apoplastic solute path, and in vascular parenchyma cells of WT roots before the peak accumulation of GS1;2 and NADH‐GOGAT1 occurred. These findings suggest that OsATL6 temporarily stores excess glutamine, produced by NH4+ assimilation, in root vacuoles before it can be translocated to the shoot.
Significance Statement
We show that the rice amino acid transporter‐like protein OsATL6 acts as a vacuolar glutamine exporter and plays a key role in the temporary vacuolar storage of excess glutamine produced during ammonium assimilation in roots. Therefore, OsATL6 affects the root‐to‐shoot allocation of glutamine and plant growth under ammonium‐replete conditions.
The m-periodic derived category of an abelian category is a natural Z/mZ-periodic analogue of the usual derived category. We determine the Grothendieck group of the periodic derived category of a ...skeletally small abelian category with enough projectives. In particular, we prove that the Grothendieck group of the m-periodic derived category of finitely generated modules over an Artin algebra is a free Z-module if m is even, and is an F2-vector space if m is odd. Moreover, in both cases of parity of m, the rank of the Grothendieck group is equal to the number of isomorphism classes of simple modules in both cases. As an application, we prove that the number of non-isomorphic summands of a strict periodic tilting object T, which was introduced by the author in 6 as a periodic analogue of tilting objects, is independent of the choice of T.
Potassium (K) is a major essential element in plant cells, and KUP/HAK/KT-type K
+
transporters participate in the absorption of K
+
into roots and in the long-distance transport to above-ground ...parts. In
Arabidopsis thaliana
, KUP9 is involved in the transport of K
+
and Cs
+
in roots. In this study, we investigated KUP9 function in relation to the K
+
status of the plant. The expression of
KUP9
was upregulated in older leaves on K
+
-depleted medium, compared to the expression of the other 12 KUP genes in the
KUP/HAK/KT
family in Arabidopsis. When grown on low K
+
medium, the
kup9
mutant had reduced chlorophyll content in seedlings and chlorosis in older rosette leaves. Tissue-specific expression of
KUP9
determined by
KUP9
promoter:GUS assay depended on the K
+
status of the plants: In K
+
sufficient medium,
KUP9
was expressed in the leaf blade towards the leaf tip, whereas in K
+
depleted medium expression was mainly found in the petioles. In accordance with this, K
+
accumulated in the roots of
kup9
plants. The short-term
43
K
+
tracer measurement showed that
43
K was transferred at a lower rate in roots and shoots of
kup9
, compared to the wild type. These data show that KUP9 participates in the distribution of K
+
in leaves and K
+
absorption in roots under low K
+
conditions.
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