Kidney disease is a complex disease with several different etiologies and underlying associated pathophysiology. This is reflected by the lack of effective treatment therapies in chronic kidney disease (CKD) that stop disease progression. However, novel strategies, recent scientific breakthroughs, and technological advances have revealed new possibilities for finding novel disease drivers in CKD. This review describes some of the latest advances in the field and brings them together in a more holistic framework as applied to identification and validation of disease drivers in CKD. It uses high-resolution 'patient-centric' omics data sets, advanced in silico tools (systems biology, connectivity mapping, and machine learning) and 'state-of-the-art' experimental systems (complex 3D systems in vitro, CRISPR gene editing, and various model biological systems in vivo). Application of such a framework is expected to increase the likelihood of successful identification of novel drug candidates based on strong human target validation and a better scientific understanding of underlying mechanisms.

For a graph G on the vertex set {0,1,…,n}, the G-parking function ideal MG is a monomial ideal in the polynomial ring R=K[x1,…,xn] such that the vector space dimension of R/MG is given by the determinant of its reduced Laplacian. For any integer k, the k-skeleton ideal MG(k) is the subideal of MG, where the monomial generators correspond to nonempty subsets of [n] of size at most k+1. For a simple graph G, Dochtermann conjectured that the vector space dimension of R/MG(1) is bounded below by the determinant of the reduced signless Laplacian. We show that the Dochtermann conjecture holds for any (multi) graph G. More generally, we prove that this bound holds for ideals JH defined by a larger class of symmetric positive semidefinite n×n matrices H.

Let $${\mathfrak {S}}_n$$ be the set of all permutations of $$[n]=\{1,\ldots ,n\}$$ and let W be the subset consisting of permutations $$\sigma \in {\mathfrak {S}}_n$$ avoiding 132 and 312-patterns. The monomial ideal $$I_W = \big \langle {\mathbf {x}}^{\sigma } = \prod _{i=1}^n x_i^{\sigma (i)} : \sigma \in W \big \rangle $$ in the polynomial ring $$R = k[x_1,\ldots ,x_n]$$ over a field k is called a hypercubic ideal in Kumar and Kumar (Proc. Indian Acad. Sci. (Math Sci.) 126(4) (2016) 479–500). The Alexander dual $$I_W^{[{\mathbf {n}}]}$$ of $$I_W$$ with respect to $${\mathbf {n}}=(n,\ldots ,n)$$ has the minimal cellular resolution supported on the first barycentric subdivision $$\mathbf {Bd}(\Delta _{n-1})$$ of an $$n-1$$ -simplex $$\Delta _{n-1}$$ . We show that the number of standard monomials of the Artinian quotient $$\frac{R}{I_W^{[{\mathbf {n}}]}}$$ equals the number of rooted-labelled unimodal forests on the vertex set [n]. In other words, $$\begin{aligned} \dim _k\left( \frac{R}{I_W^{[{\mathbf {n}}]}}\right) = \sum _{r=1}^n r!~s(n,r) = \mathrm{Per}\left( [m_{ij}]_{n \times n} \right) , \end{aligned}$$ where s(n, r) is the (signless) Stirling number of the first kind and $$\mathrm{Per}([m_{ij}]_{n \times n})$$ is the permanent of the matrix $$[m_{ij}]$$ with $$m_{ii}=i$$ and $$m_{ij}=1$$ for $$i \ne j$$ . For various subsets S of $${\mathfrak {S}}_n$$ consisting of permutations avoiding patterns, the corresponding integer sequences $$\Big \lbrace \dim _k\Big (\frac{R}{I_S^{[{\mathbf {n}}]}}\Big ) \Big \rbrace _{n=1}^{\infty }$$ are identified.

Let $G$ be an (oriented) graph on the vertex set $V = \{ 0, 1,\ldots,n\}$ with root $0$. Postnikov and Shapiro associated a monomial ideal $\mathcal{M}_G$ in the polynomial ring $ R = {\mathbb{K}}[x_1,\ldots,x_n]$ over a field $\mathbb{K}$. A subideal $\mathcal{M}_G^{(k)}$ of $\mathcal{M}_G$ generated by subsets of $\widetilde{V}=V\setminus \{0\}$ of size at most $k+1$ is called a $k$-skeleton ideal of the graph $G$. Many interesting homological and combinatorial properties of $1$-skeleton ideal $\mathcal{M}_G^{(1)}$ are obtained by Dochtermann for certain classes of simple graph $G$. A finite sequence $\mathcal{P}=(p_1,\ldots,p_n) \in \mathbb{N}^n$ is called a spherical $G$-parking function if the monomial $\mathbf{x}^{\mathcal{P}} = \prod_{i=1}^{n} x_i^{p_i} \in \mathcal{M}_G \setminus \mathcal{M}_G^{(n-2)}$. Let ${\rm sPF}(G)$ be the set of all spherical $G$-parking functions. In this paper, a combinatorial description for all multigraded Betti numbers of the $k$-skeleton ideal $\mathcal{M}_{K_{n+1}}^{(k)}$ of the complete graph $K_{n+1}$ on $V$ are given. Also, using DFS burning algorithms of Perkinson-Yang-Yu (for simple graph) and Gaydarov-Hopkins (for multigraph), we give a combinatorial interpretation of spherical $G$-parking functions for the graph $G = K_{n+1}- \{e\}$ obtained from the complete graph $K_{n+1}$ on deleting an edge $e$. In particular, we showed that $|{\rm sPF}(K_{n+1}- \{e_0\} )|= (n-1)^{n-1}$ for an edge $e_0$ through the root $0$, but $|{\rm sPF}(K_{n+1} - \{e_1\})| = (n-1)^{n-3}(n-2)^2$ for an edge $e_1$ not through the root.

In the version of this article initially published, author Volker M. Lauschke had affiliation number 13; the correct affiliation number is 12. The error has been corrected in the HTML and PDF versions of the article.

Let $G$ be a (multi) graph on the vertex set $V=\{0,1,\ldots ,n\}$ with root $0$. The $G$-parking function ideal $\mathcal{M}_G$ is a monomial ideal in the polynomial ring $R=\mathbb{K}[x_1,\ldots ,x_n]$ over a field $\mathbb{K}$ such that $\dim_{\mathbb K}\left(\frac{R}{\mathcal{M}_G}\right)=\det\left(\widetilde{L}_G\right)$, where $\widetilde{L}_G$ is the truncated Laplace matrix of $G$ and $\det\left(\widetilde L_G\right)$ is the determinant of $\widetilde L_G$. In other words, standard monomials of the Artinian quotient $\frac{R}{\mathcal{M}_G}$ correspond bijectively with the spanning trees of $G$. For $0\leq k\leq n-1$, the $k$-skeleton ideal $\mathcal{M}_G^{(k)}$ of $G$ is the monomial subideal $\mathcal{M}_G^{(k)}=\left\langle m_A:\emptyset\neq A\subseteq[n]\text{ and }|A|\leq k+1\right\rangle$ of the $G$-parking function ideal $\mathcal{M}_G=\left\langle m_A : \emptyset \neq A\subseteq[n]\right\rangle\subseteq R$. For a simple graph $G$, Dochtermann conjectured that $\dim_{\mathbb K}\left(\frac{R}{\mathcal{M}_G^{(1)}}\right)\geq\det\left(\widetilde{Q}_G\right)$, where $\widetilde Q_G$ is the truncated signless Laplace matrix of $G$. We show that Dochtermann conjecture holds for any (simple or multi) graph $G$ on $V$.

Background: Alteration of various metabolites has been linked to type 2 diabetes (T2D) and insulin resistance. However, identifying significant associations between metabolites and tissue-specific ...

Let S (or T) be the set of permutations of \([n]=\{1,\ldots ,n\}\) avoiding 123 and 132 patterns (or avoiding 123, 132 and 213 patterns). The monomial ideals \(I_S = \langle {\mathbf {x}}^{\sigma } = \prod _{i=1}^n x_i^{\sigma (i)} : \sigma \in S \rangle \) and \(I_T = \langle {\mathbf {x}}^{\sigma } : \sigma \in T \rangle \) in the polynomial ring \(R = k[x_1,\ldots ,x_n]\) over a field k have many interesting properties. The Alexander dual \(I_S^{[{\mathbf {n}}]}\) of \(I_S\) with respect to \({\mathbf {n}}=(n,\ldots ,n)\) has the minimal cellular resolution supported on the order complex \(\mathbf {\Delta }(\Sigma _n)\) of a poset \(\Sigma _n\). The Alexander dual \(I_T^{[{\mathbf {n}}]}\) also has the minimal cellular resolution supported on the order complex \(\mathbf {\Delta } ({\tilde{\Sigma }}_n)\) of a poset \({\tilde{\Sigma }}_n\). The number of standard monomials of the Artinian quotient \(\frac{R}{I_S^{[{\mathbf {n}}]}}\) is given by the number of irreducible (or indecomposable) permutations of \([n+1]\), while the number of standard monomials of the Artinian quotient \(\frac{R}{I_T^{[{\mathbf {n}}]}}\) is given by the number of permutations of \([n+1]\) having no substring \(\{l,l+1\}\).

Björner and Welker studied homology of k-equal partition lattices and obtained interesting identities for (n - 1)!. In this article, simple combinatorial proofs of these identities are discussed.

Background and Objectives. Bile acids (BAs) traversing the enterohepatic circulation (EHC) influence important metabolic pathways. By determining individual serum BAs in relation to markers of metabolic activity, we explored how diurnal variations in their EHC relate to hepatic metabolism in normal humans. Methods. Serum BAs, fibroblast growth factor 19 (FGF19), lipoproteins, glucose/insulin and markers of cholesterol and BA syntheses were monitored for 32 h in 8 healthy males. Studies were conducted at basal state and during initiation of cholestyramine treatment, with and without atorvastatin pretreatment. Time series cross-correlation analysis, Bayesian structural model and Granger causality test were applied. Results. Bile acids synthesis dominated daytime, and cholesterol production at night. Conjugated BAs peaked after food intake, with subsequent FGF19 elevations. BA synthesis was reduced following conjugated BA and FGF19 peaks. Cholestyramine reduced conjugated BAs and FGF19, and increased BA and cholesterol production; the latter effects attenuated by atorvastatin. The relative importance of FGF19 vs. conjugated BAs in this feedback inhibition could not be discriminated. Unconjugated BAs displayed one major peak late at night/early morning that was unrelated to FGF19 and BA synthesis, and abolished by cholestyramine. The normal suppression of serum triglycerides, glucose and insulin observed at night was attenuated by cholestyramine. Conclusions. Conjugated and unconjugated BAs have asynchronous rhythms of EHC in humans. Postprandial transintestinal flux of conjugated BAs increases circulating FGF19 levels and suppresses BA synthesis. Unconjugated BAs peak late at night, indicating a non-postprandial diurnal change in human gut microflora, the physiological implications of which warrants further study.

For an (oriented) graph [Formula: see text] on the vertex set [Formula: see text] (rooted at [Formula: see text]), Postnikov and Shapiro (Trans. Amer. Math. Soc. 356 (2004) 3109–3142) associated a monomial ideal [Formula: see text] in the polynomial ring [Formula: see text] over a field [Formula: see text] such that the number of standard monomials of [Formula: see text] equals the number of (oriented) spanning trees of [Formula: see text] and hence, [Formula: see text], where [Formula: see text] is the truncated Laplace matrix of [Formula: see text]. The standard monomials of [Formula: see text] correspond bijectively to the [Formula: see text]-parking functions. In this paper, we study a monomial ideal [Formula: see text] in [Formula: see text] having rich combinatorial properties. We show that the minimal free resolution of the monomial ideal [Formula: see text] is the cellular resolution supported on a subcomplex of the first barycentric subdivision [Formula: see text] of an [Formula: see text] simplex [Formula: see text]. The integer sequence [Formula: see text] has many interesting properties. In particular, we obtain a formula, [Formula: see text], with [Formula: see text] for [Formula: see text], [Formula: see text] and [Formula: see text] for [Formula: see text], similar to [Formula: see text].

Multipermutohedron ideals have rich combinatorial properties. An explicit combinatorial formula for the multigraded Betti numbers of a multipermutohedron ideal and their Alexander duals are known. Also, the dimension of the Artinian quotient of an Alexander dual of a multipermutohedron ideal is the number of generalized parking functions. In this paper, monomial ideals which are certain variants of multipermutohedron ideals are studied. Multigraded Betti numbers of these variant monomial ideals and their Alexander duals are obtained. Further, many interesting combinatorial properties of multipermutohedron ideals are extended to these variant monomial ideals.

Nonhuman primates (NHP) are important biomedical animal models for the study of human disease. Of these, the most widely used models in biomedical research currently are from the genus Macaca. However, evolutionary genetic divergence between human and NHP species makes human-based probes inefficient for the capture of genomic regions of NHP for sequencing and study. Here we introduce a new method to resequence the exome of NHP species by a designed capture approach specifically targeted to the NHP, and demonstrate its superior performance on four NHP species or subspecies. Detailed investigation on biomedically relevant genes demonstrated superior capture by the new approach. We identified 28 genes that appeared to be pseudogenized and inactivated in macaque. Finally, we identified 187 genes showing strong evidence for positive selection across all branches of the primate phylogeny including many novel findings.

An Alexander dual of a multipermutohedron ideal has many combinatorial properties. The standard monomials of an Artinian quotient of such a dual correspond bijectively to some λ-parking functions, and many interesting properties of these Artinian quotients are obtained by Postnikov and Shapiro (Trans. Am. Math. Soc. 356 (2004) 3109–3142). Using the multigraded Hilbert series of an Artinian quotient of an Alexander dual of multipermutohedron ideals, we obtained a simple proof of Steck determinant formula for enumeration of λ-parking functions. A combinatorial formula for all the multigraded Betti numbers of an Alexander dual of multipermutohedron ideals are also obtained.

A Permutohedron supports the cellular resolution minimally resolving the associated Permutohedron ideal. The aim of this paper is to study multipermutohedron ideals and obtain combinatorial formula for their multigraded Betti numbers.

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.

Delineation of phosphorylation-based signaling networks requires reliable data about the underlying cellular kinase-substrate interactions. We report a chemical genetics and quantitative phosphoproteomics approach that encompasses cellular kinase activation in combination with comparative replicate mass spectrometry analyses of cells expressing either inhibitor-sensitive or resistant kinase variant. We applied this workflow to Plk1 (Polo-like kinase 1) in mitotic cells and induced cellular Plk1 activity by wash-out of the bulky kinase inhibitor 3-MB-PP1, which targets a mutant kinase version with an enlarged catalytic pocket while not interfering with wild-type Plk1. We quantified more than 20,000 distinct phosphorylation sites by SILAC, approximately half of which were measured in at least two independent experiments in cells expressing mutant and wild-type Plk1. Based on replicate phosphorylation site quantifications in both mutant and wild-type Plk1 cells, our chemical genetic proteomics concept enabled stringent comparative statistics by significance analysis of microarrays, which unveiled more than 350 cellular downstream targets of Plk1 validated by full concordance of both statistical and experimental data. Our data point to hitherto poorly characterized aspects in Plk1-controlled mitotic progression and provide a largely extended resource for functional studies. We anticipate the described strategies to be of general utility for systematic and confident identification of cellular protein kinase substrates.

We study clean group rings and also the group rings whose every element is a sum of two units. We also prove that if R is an Abelian exchange ring and G is a locally finite group, then the group ring RG has stable range one.