Combinatorial Expression Research Articles

Isomonodromic Tau Functions on a Torus as Fredholm Determinants, and Charged Partitions

We prove that the isomonodromic tau function on a torus with Fuchsian singularities and generic monodromies in GL(N,{mathbb {C}}) can be written in terms of a Fredholm determinant of Plemelj operators. We further show that the minor expansion of this Fredholm determinant is described by a series labeled by charged partitions. As an example, we show that in the case of SL(2,{mathbb {C}}) this combinatorial expression takes the form of a dual Nekrasov–Okounkov partition function, or equivalently of a free fermion conformal block on the torus. Based on these results we also propose a definition of the tau function of the Riemann–Hilbert problem on a torus with generic jump on the A-cycle.

Single-cell mapping of combinatorial target antigens for CAR switches using logic gates.

Identification of optimal target antigens that distinguish cancer cells from normal surrounding tissue cells remains a key challenge in chimeric antigen receptor (CAR) cell therapy for tumors with intratumoral heterogeneity. In this study, we dissected tissue complexity to the level of individual cells through the construction of a single-cell expression atlas that integrates ~1.4 million tumor, tumor-infiltrating normal and reference normal cells from 412 tumors and 12 normal organs. We used a two-step screening method using random forest and convolutional neural networks to select gene pairs that contribute most to discrimination between individual malignant and normal cells. Tumor coverage and specificity are evaluated for the AND, OR and NOT logic gates based on the combinatorial expression pattern of the pairing genes across individual single cells. Single-cell transcriptome-coupled epitope profiling validates the AND, OR and NOT switch targets identified in ovarian cancer and colorectal cancer.

Engineering cyanobacteria for converting carbon dioxide into isomaltulose

Isomaltulose is a promising functional sweetener with broad application prospects in the food industry. Currently, isomaltulose is mainly produced through bioconversion processes based on the isomerization of sucrose, the economic feasibility of which is influenced by the cost of sucrose feedstocks, the biocatalyst preparation, and product purification. Cyanobacterial photosynthetic production utilizing solar energy and carbon dioxide represents a promising route for the supply of sugar products, which can promote both carbon reduction and green production. Previously, some cyanobacteria strains have been successfully engineered for synthesis of sucrose, the main feedstock for isomaltulose production. In this work, we introduced different sucrose isomerases into Synechococcus elongatus PCC 7942 and successfully achieved the isomaltulose synthesis and accumulation in the recombinant strains. Combinatory expression of an Escherichia coli sourced sucrose permease CscB with the sucrose isomerases led to efficient secretion of isomaltulose and significantly elevated the final titer. During a 6-day cultivation, 777 mg/L of isomaltulose was produced by the engineered Synechococcus cell factory. This work demonstrated a new route for isomaltulose biosynthesis utilizing carbon dioxide as the substrate, and provided novel understandings for the plasticity of cyanobacterial photosynthetic metabolism network.

Об одном подходе к нахождению сумм кратных числовых рядов

An approach to calculating sums of some types of multiple numerical series is presented. This approach is based on using the formula for the resultant of a polynomial (or an entire function with a finite number of zeros) and an entire function obtained earlier by A.M. Kytmanov and E.K. Myshkina. This formula does not require values of the roots of the functions under study and is a combinatorial expression. By calculating the resultant of a polynomial and an entire function in two different ways, it is possible to obtain a relation for multiple numerical series. For the second way to find the resultant, we use the product of one function at the roots of another. In this article, the sums of some types of multiple numerical series that were previously absent in known reference books are found. They are expressed in terms of well-known special functions such as the Bessel function. This approach to calculating the sums of multiple numerical series differs significantly from the method based on the use of residue integrals associated with a system of equations. The relevance of this problem is determined by the fact that in applied problems, for example, in the equations of chemical kinetics, there are functions and systems of equations consisting of exponential polynomials.

An integrated analysis of the cancer genome atlas data discovers a hierarchical association structure across thirty three cancer types.

Cancer cells harbor molecular alterations at all levels of information processing. Genomic/epigenomic and transcriptomic alterations are inter-related between genes, within and across cancer types and may affect clinical phenotypes. Despite the abundant prior studies of integrating cancer multi-omics data, none of them organizes these associations in a hierarchical structure and validates the discoveries in extensive external data. We infer this Integrated Hierarchical Association Structure (IHAS) from the complete data of The Cancer Genome Atlas (TCGA) and compile a compendium of cancer multi-omics associations. Intriguingly, diverse alterations on genomes/epigenomes from multiple cancer types impact transcriptions of 18 Gene Groups. Half of them are further reduced to three Meta Gene Groups enriched with (1) immune and inflammatory responses, (2) embryonic development and neurogenesis, (3) cell cycle process and DNA repair. Over 80% of the clinical/molecular phenotypes reported in TCGA are aligned with the combinatorial expressions of Meta Gene Groups, Gene Groups, and other IHAS subunits. Furthermore, IHAS derived from TCGA is validated in more than 300 external datasets including multi-omics measurements and cellular responses upon drug treatments and gene perturbations in tumors, cancer cell lines, and normal tissues. To sum up, IHAS stratifies patients in terms of molecular signatures of its subunits, selects targeted genes or drugs for precision cancer therapy, and demonstrates that associations between survival times and transcriptional biomarkers may vary with cancer types. These rich information is critical for diagnosis and treatments of cancers.

Combinatorial transient gene expression strategies to enhance terpenoid production in plants.

The monoterpenoid linalool and sesquiterpenoid costunolide are ubiquitous plant components that have been economically exploited for their respective essential oils and pharmaceutical benefits. In general, monoterpenes and sesquiterpenes are produced by the plastid 2-C-methyl-D-erythritol 4-phosphate (MEP) and cytosolic mevalonate (MVA) pathways, respectively. Herein, we investigated the individual and combinatorial potential of MEP and MVA pathway genes in increasing linalool and costunolide production in Nicotiana benthamiana. First, six genes from the MEP (1-deoxy-D-xylulose-5-phosphate synthase, 1-deoxy-D-xylulose 5-phosphate reductoisomerase, 4-diphosphocytidyl-2-C-methyl-D-erythritol kinase, geranyl pyrophosphate synthase, and linalool synthase) and MVA (acetoacetyl-CoA-thiolase, hydroxy-3-methylglutaryl-CoA reductase, farnesyl pyrophosphate synthase, germacrene A synthase, germacrene A oxidase, and costunolide synthase) pathways were separately cloned into the modular cloning (MoClo) golden gateway cassette. Second, the cassettes were transformed individually or in combination into the leaves of N. benthamiana by agroinfiltration. Five days post infiltration (DPI), all selected genes were transiently 5- to 94-fold overexpressed. Quantification using gas chromatography-Q-orbitrap-mass spectrometry (GC-Q-Orbitrap-MS) determined that the individual and combinatorial expression of MEP genes increased linalool production up to 50-90ng.mg-1 fresh leaf weight. Likewise, MVA genes increased costunolide production up to 70-90ng.mg-1 fresh leaf weight. Our findings highlight that the transient expression of MEP and MVA pathway genes (individually or in combination) enhances linalool and costunolide production in plants.

Sustainable Production of Shinorine from Lignocellulosic Biomass by Metabolically Engineered Saccharomyces cerevisiae.

Mycosporine-like amino acids (MAAs) have been used in cosmetics and pharmaceuticals. The purpose of this work was to develop yeast strains for sustainable and economical production of MAAs, especially shinorine. First, genes involved in MAA biosynthetic pathway from Actinosynnema mirum were introduced into Saccharomyces cerevisiae for heterologous shinorine production. Second, combinatorial expression of wild and mutant xylose reductase was adopted in the engineered S. cerevisiae to facilitate xylose utilization in the pentose phosphate pathway. Finally, the accumulation of sedoheptulose 7-phosphate (S7P) was attempted by deleting transaldolase-encoding TAL1 in the pentose phosphate pathway to increase carbon flux toward shinorine production. In fed-batch fermentation, the engineered strain (DXdT-M) produced 751 mg/L shinorine in 71 h. Ultimately, 54 mg/L MAAs was produced by DXdT-M from rice straw hydrolysate. The results suggest that shinorine production by S. cerevisiae might be a promising process for sustainable production and industrial applications.

On an approach for evaluating certain trigonometric character sums using the discrete time heat kernel

In this article we develop a general method by which one can explicitly evaluate certain sums of nth powers of products of d≥1 elementary trigonometric functions evaluated at m=(m1,…,md)-th roots of unity. Our approach is to first identify the individual terms in the expression under consideration as eigenvalues of a discrete Laplace operator associated to a graph whose vertices form a d-dimensional discrete torus Gm which depends on m. The sums in question are then related to the nth step of a Markov chain on Gm. The Markov chain admits the interpretation as a particular random walk, also viewed as a discrete time and discrete space heat diffusion, so then the sum in question is related to special values of the associated heat kernel. Our evaluation follows by deriving a combinatorial expression for the heat kernel, which is obtained by periodizing the heat kernel on the infinite lattice Zd which covers Gm.

Combinatorial co-expression of xanthine dehydrogenase and chaperone XdhC from Acinetobacter baumannii and Rhodobacter capsulatus and their applications in decreasing purine content in food

This study investigated the combinatorial expression of xanthine dehydrogenase (XDH) and chaperone XdhC from Acinetobacter baumannii and Rhodobacter capsulatus and their applications in decreasing purine content in the beer, beef and yeast. Naturally occurring xdhABC gene clusters of A. baumannii CICC 10254 and R. capsulatus CGMCC 1.3366 as well as two refactored clusters constructed by exchanging their xdhC genes were overexpressed in Escherichia coli and purified to near homogeneity. RcXDH chaperoned by AbXdhC showed nearly the same catalytic performance as that by RcXdhC, except for the decreased substrate affinity. While the AbXDH co-expressed with RcXdhC displayed enhanced acidic adaptation but weakened catalytic activity. All the XDHs degraded purines in beer, beef and yeast extract effectively, indicating potential applications in low-purine foods to prevent hyperuricemia and gout. The study also presents a method for exploiting the better chaperone XdhC and novel XDHs by functional complement activity using existing XdhCs such as RcXdhC.

Overcoming Heterogeneity in AML with a Novel or-Gated Hitcar-1XX Platform

Target heterogeneity limits therapeutic success of conventional CAR therapies in B cell and other malignancies. Therefore, novel concepts for efficient combinatorial targeting are urgently needed. Several OR-gated targeting approaches based on CARs have been described and include dual CARs (T cells co-expressing two CARs), tandem CARs (T cells expressing a single bi-specific CAR) and pooled single CAR-T cells (T cells expressing a single CAR). Clinical efficacy of such OR-gated CAR therapies is still under ongoing investigation, and emerging pre-clinical data suggests that optimization of OR-gated approaches requires fine-tuning of combinatorial CAR signaling to balance effector and memory functions, avoiding premature differentiation and eventual exhaustion. Here, we present a novel OR-gated platform based on co-expression of a CAR and a HIT (HLA-Independent TCR), which we previously described to afford T cells with increased antigen sensitivity (Mansilla-Soto et al., Nature Medicine 2022). Since HIT receptors do not incorporate engineered co-stimulatory domains like conventional CARs, we hypothesized that T cells co-expressing CAR and HIT display limited differentiation in comparison to dual CAR T cells, thus resulting in improved long-term anti-tumor activity. We termed this novel OR-gated therapy HITCAR and evaluated it in the setting of AML which stands out with a high degree of inter- and intra-individual phenotypic heterogeneity. We selected two target antigens which we had previously demonstrated to have a favorable and non-overlapping expression profile in normal hematopoietic cells and other tissues (Perna et al., Cancer Cell 2017). We selected a lower-density target for the HIT, using its increased sensitivity to avoid antigen-low escape, and selected a higher-density target for the CAR. We utilized an NSG xenograft model for target heterogeneity, based on co-engraftment of engineered MOLM13 AML cell line populations endogenously expressing either HIT target alone, CAR target alone, or both. To identify an optimal HITCAR design, we treated target-heterogeneous MOLM13 AML-bearing mice with HITCAR T cells containing different CAR architectures and found that only the 28z1XX CAR allowed for complete AML remission and long-term survival in conjunction with the HIT. All other CAR architectures failed to control AML long-term, highlighting the importance for fine-tuned CAR signaling in combination with HIT. We then selected the superior HITCAR-1XX and compared it to dual CARs containing BBz and 28z1XX architectures. In our NSG AML xenograft heterogeneity model, the HITCAR-1XX induced complete AML remission while the alternative dual CARs failed to control AML. T cell phenotyping demonstrated a less differentiated T cell phenotype over time with HITCAR-1XX as compared to the alternative dual CARs, supporting our hypothesis. Further validation of our HITCAR-1XX platform in clinically relevant AML PDX models is ongoing. Overall, we established a novel OR-gated HITCAR T cell platform based on combinatorial expression of HIT and CAR which can be applied to overcome target heterogeneity in various malignancies. In the setting of AML, we compared different HITCAR configurations and identified HITCAR-1XX as most promising. Furthermore, we demonstrated superiority of HITCAR-1XX over alternative dual CAR designs, highlighting its high potential for clinical translation.

Pan-Cancer Analysis Identifies MNX1 and Associated Antisense Transcripts as Biomarkers for Cancer.

The identification of diagnostic and prognostic biomarkers is a major objective in improving clinical outcomes in cancer, which has been facilitated by the availability of high-throughput gene expression data. A growing interest in non-coding genomic regions has identified dysregulation of long non-coding RNAs (lncRNAs) in several malignancies, suggesting a potential use as biomarkers. In this study, we leveraged data from large-scale sequencing projects to uncover the expression patterns of the MNX1 gene and its associated lncRNAs MNX1-AS1 and MNX1-AS2 in solid tumours. Despite many reports describing MNX1 overexpression in several cancers, limited studies exist on MNX1-AS1 and MNX1-AS2 and their potential as biomarkers. By employing clustering methods to visualise multi-gene relationships, we identified a discriminative power of the three genes in distinguishing tumour vs. normal samples in several cancers of the gastrointestinal tract and reproductive systems, as well as in discerning oesophageal and testicular cancer histological subtypes. Notably, the expressions of MNX1 and its antisenses also correlated with clinical features and endpoints, uncovering previously unreported associations. This work highlights the advantages of using combinatory expression patterns of non-coding transcripts of differentially expressed genes as clinical evaluators and identifies MNX1, MNX1-AS1, and MNX1-AS2 expressions as robust candidate biomarkers for clinical applications.

Expression level of the reprogramming factor NeuroD1 is critical for neuronal conversion efficiency from different cell types

Several transcription factors, including NeuroD1, have been shown to act as neuronal reprogramming factors (RFs) that induce neuronal conversion from somatic cells. However, it remains unexplored whether expression levels of RFs in the original cells affect reprogramming efficiency. Here, we show that the neuronal reprogramming efficiency from two distinct glial cell types, microglia and astrocytes, is substantially dependent on the expression level of NeuroD1: low expression failed to induce neuronal reprogramming, whereas elevated NeuroD1 expression dramatically improved reprogramming efficiency in both cell types. Moreover, even under conditions where NeuroD1 expression was too low to induce effective conversion by itself, combined expression of three RFs (Ascl1, Brn2, and NeuroD1) facilitated the breaking down of cellular barriers, inducing neuronal reprogramming. Thus, our results suggest that a sufficiently high expression level of RFs, or alternatively their combinatorial expression, is the key to achieving efficient neuronal reprogramming from different cells.

Integrated transcriptomics and miRNAomics provide insights into the complex multi-tiered regulatory networks associated with coleoptile senescence in rice.

Coleoptile is the small conical, short-lived, sheath-like organ that safeguards the first leaf and shoot apex in cereals. It is also the first leaf-like organ to senesce that provides nutrition to the developing shoot and is, therefore, believed to play a crucial role in seedling establishment in rice and other grasses. Though histochemical studies have helped in understanding the pattern of cell death in senescing rice coleoptiles, genome-wide expression changes during coleoptile senescence have not yet been explored. With an aim to investigate the gene regulation underlying the coleoptile senescence (CS), we performed a combinatorial whole genome expression analysis by sequencing transcriptome and miRNAome of senescing coleoptiles. Transcriptome analysis revealed extensive reprogramming of 3439 genes belonging to several categories, the most prominent of which encoded for transporters, transcription factors (TFs), signaling components, cell wall organization enzymes, redox homeostasis, stress response and hormone metabolism. Small RNA sequencing identified 41 known and 21 novel miRNAs that were differentially expressed during CS. Comparison of gene expression and miRNA profiles generated for CS with publicly available leaf senescence (LS) datasets revealed that the two aging programs are remarkably distinct at molecular level in rice. Integration of expression data of transcriptome and miRNAome identified high confidence 140 miRNA-mRNA pairs forming 42 modules, thereby demonstrating multi-tiered regulation of CS. The present study has generated a comprehensive resource of the molecular networks that enrich our understanding of the fundamental pathways regulating coleoptile senescence in rice.

Explicit Calculation of Structural Commutation Relations for Stochastic and Dynamical Graph Grammar Rule Operators in Biological Morphodynamics.

Many emergent, non-fundamental models of complex systems can be described naturally by the temporal evolution of spatial structures with some nontrivial discretized topology, such as a graph with suitable parameter vectors labeling its vertices. For example, the cytoskeleton of a single cell, such as the cortical microtubule network in a plant cell or the actin filaments in a synapse, comprises many interconnected polymers whose topology is naturally graph-like and dynamic. The same can be said for cells connected dynamically in a developing tissue. There is a mathematical framework suitable for expressing such emergent dynamics, "stochastic parameterized graph grammars," composed of a collection of the graph- and parameter-altering rules, each of which has a time-evolution operator that suitably moves probability. These rule-level operators form an operator algebra, much like particle creation/annihilation operators or Lie group generators. Here, we present an explicit and constructive calculation, in terms of elementary basis operators and standard component notation, of what turns out to be a general combinatorial expression for the operator algebra that reduces products and, therefore, commutators of graph grammar rule operators to equivalent integer-weighted sums of such operators. We show how these results extend to "dynamical graph grammars," which include rules that bear local differential equation dynamics for some continuous-valued parameters. Commutators of such time-evolution operators have analytic uses, including deriving efficient simulation algorithms and approximations and estimating their errors. The resulting formalism is complementary to spatial models in the form of partial differential equations or stochastic reaction-diffusion processes. We discuss the potential application of this framework to the remodeling dynamics of the microtubule cytoskeleton in cortical microtubule networks relevant to plant development and of the actin cytoskeleton in, for example, a growing or shrinking synaptic spine head. Both cytoskeletal systems underlie biological morphodynamics.

A conserved molecular template underlies color pattern diversity in estrildid finches.

The color patterns that adorn animals’ coats not only exhibit extensive diversity linked to various ecological functions but also display recurrences in geometry, orientation, or body location. How processes of pattern formation shape such phenotypic trends remains a mystery. Here, we surveyed plumage color patterns in passerine finches displaying extreme apparent variation and identified a conserved set of color domains. We linked these domains to putative embryonic skin regions instructed by early developmental tissues and outlined by the combinatory expression of few genetic markers. We found that this embryonic prepattern is largely conserved in birds displaying drastic color differences in the adult, interspecies variation resulting from the masking or display of each domain depending on their coloration. This work showed that a simple molecular landscape serves as common spatial template to extensive color pattern variation in finches, revealing that early conserved landmarks and molecular pathways are a major cause of phenotypic trends.

Probing cell identity hierarchies by fate titration and collision during direct reprogramming

Despite the therapeutic promise of direct reprogramming, basic principles concerning fate erasure and the mechanisms to resolve cell identity conflicts remain unclear. To tackle these fundamental questions, we established a single‐cell protocol for the simultaneous analysis of multiple cell fate conversion events based on combinatorial and traceable reprogramming factor expression: Collide‐seq. Collide‐seq revealed the lack of a common mechanism through which fibroblast‐specific gene expression loss is initiated. Moreover, we found that the transcriptome of converting cells abruptly changes when a critical level of each reprogramming factor is attained, with higher or lower levels not contributing to major changes. By simultaneously inducing multiple competing reprogramming factors, we also found a deterministic system, in which titration of fates against each other yields dominant or colliding fates. By investigating one collision in detail, we show that reprogramming factors can disturb cell identity programs independent of their ability to bind their target genes. Taken together, Collide‐seq has shed light on several fundamental principles of fate conversion that may aid in improving current reprogramming paradigms.

GB_SynP: A Modular dCas9-Regulated Synthetic Promoter Collection for Fine-Tuned Recombinant Gene Expression in Plants.

Programmable transcriptional factors based on the CRISPR architecture are becoming commonly used in plants for endogenous gene regulation. In plants, a potent CRISPR tool for gene induction is the so-called dCasEV2.1 activation system, which has shown remarkable genome-wide specificity combined with a strong activation capacity. To explore the ability of dCasEV2.1 to act as a transactivator for orthogonal synthetic promoters, a collection of DNA parts was created (GB_SynP) for combinatorial synthetic promoter building. The collection includes (i) minimal promoter parts with the TATA box and 5′UTR regions, (ii) proximal parts containing single or multiple copies of the target sequence for the gRNA, thus functioning as regulatory cis boxes, and (iii) sequence-randomized distal parts that ensure the adequate length of the resulting promoter. A total of 35 promoters were assembled using the GB_SynP collection, showing in all cases minimal background and predictable activation levels depending on the proximal parts used. GB_SynP was also employed in a combinatorial expression analysis of an autoluminescence pathway in Nicotiana benthamiana, showing the value of this tool in extracting important biological information such as the determination of the limiting steps in an enzymatic pathway.

KG-Sombor index of Kragujevac trees

The paper is concerned with the KG-Sombor index (\(KG\)), a recently introduced vertex-and-edge-degree-based version of the Sombor index, applied to Kragujevac trees (\(Kg\)). A general combinatorial expression for \(KG(Kg)\) is established. The species with minimum and maximum \(KG(Kg)\)-values are determined.

Subtype-specific survival and regeneration of retinal ganglion cells in response to injury.

Retinal ganglion cells (RGCs) are a heterogeneous population of neurons that function synchronously to convey visual information through the optic nerve to retinorecipient target areas in the brain. Injury or disease to the optic nerve results in RGC degeneration and loss of visual function, as few RGCs survive, and even fewer can be provoked to regenerate their axons. Despite causative insults being broadly shared, regeneration studies demonstrate that RGC types exhibit differential resilience to injury and undergo selective survival and regeneration of their axons. While most early studies have identified these RGC types based their morphological and physiological characteristics, recent advances in transgenic and gene sequencing technologies have further enabled type identification based on unique molecular features. In this review, we provide an overview of the well characterized RGC types and identify those shown to preferentially survive and regenerate in various regeneration models. Furthermore, we discuss cellular characteristics of both the resilient and susceptible RGC types including the combinatorial expression of different molecular markers that identify these specific populations. Lastly, we discuss potential molecular mechanisms and genes found to be selectively expressed by specific types that may contribute to their reparative capacity. Together, we describe the studies that lay the important groundwork for identifying factors that promote neural regeneration and help advance the development of targeted therapy for the treatment of RGC degeneration as well as neurodegenerative diseases in general.

Cracking the combinatorial code of neuronal wiring

How transcription factors orchestrate the combinatorial expression of cell-surface proteins that, in turn, specify the wiring of the nervous system is an open question. In this issue of Neuron, Xie etal. reveal a new, unexpected layer of complexity.