A unified view of LCRs across species

Low complexity regions (LCRs) in proteins play a major role in the higher order assemblies of organisms, such as the nucleolus and extracellular matrix. Despite recent focus on how certain features affect the function of LCRs in intracellular higher order assemblies, the relationships between LCRs within proteins, captured by their type and copy number, has yet to be systematically studied. Furthermore, we still lack a unified view of how the sequences, features, relationships and functions of LCRs relate to each other. Here, we developed a systematic and comprehensive approach using dotplot matrices and dimensionality reduction to define LCR relationships proteome-wide and to create a map of LCR sequences capable of integrating any LCR features. As a proof of concept of the importance of LCR relationships, we demonstrate the biological significance of LCR copy number for higher order assembly of the nucleolar protein RPA43 both in vitro and in vivo. Using the LCR map, we revealed the boundaries and connections between regions of sequence space occupied by LCRs, and that LCRs of certain higher order assemblies populated specific regions of sequence space. The integration of LCR relationships and the LCR map provided a unified view of LCRs which uncovered the distribution, distinguishing features, and conserved prevalence of glutamic acid-rich LCRs among nucleolar proteins. When applied across multiple species, this approach highlights how differential occupancy of certain regions of LCR sequence space corresponds to the conservation and emergence of higher order assemblies, such as the plant cell wall or metazoan extracellular matrix. Additionally, we identified previously undescribed regions of LCR sequence space, including a teleost-specific threonine/histidine-rich cluster which exhibits signatures of higher order assemblies. By providing this unified view of LCRs, our approach enables discovery of how LCRs encode higher order assemblies of organisms.

Nonexpansive Mappings on New Premodular Special Space of Sequences

For different premodular, which is a generalization of modular, defined by weighted Orlicz sequence space and its prequasi operator ideal, we have examined the existence of a fixed point for both Kannan contraction and nonexpansive mappings acting on these spaces. Some numerous numerical experiments and practical applications are presented to support our results.

Some Fixed Point Results in Premodular Special Space of Sequences and Their Associated Pre-Quasi-Operator Ideal

A weighted Nakano sequence space and the s -numbers it contains are the subject of this article, which explains the concept of the pre-quasi-norm and its operator ideal. We show that both Kannan contraction and nonexpansive mappings acting on these spaces have a fixed point. A slew of numerical experiments back up our findings. The presence of summable equations’ solutions is shown to be useful in a number of ways. Weight and power of the weighted Nakano sequence space are used to define the parameters for this technique, resulting in customizable solutions.

Predictive profiling of SARS-CoV-2 variants by deep mutational learning

The continual evolution of the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) and the emergence of variants that show resistance to vaccines and neutralizing antibodies threaten to prolong the coronavirus disease 2019 (COVID-19) pandemic. Selection and emergence of SARS-CoV-2 variants are driven in part by mutations within the viral spike protein and in particular the ACE2 receptor-binding domain (RBD), a primary target site for neutralizing antibodies. Here, we develop deep mutational learning (DML), a machine learning-guided protein engineering technology, which is used to interrogate a massive sequence space of combinatorial mutations, representing billions of RBD variants, by accurately predicting their impact on ACE2 binding and antibody escape. A highly diverse landscape of possible SARS-CoV-2 variants is identified that could emerge from a multitude of evolutionary trajectories. DML may be used for predictive profiling on current and prospective variants, including highly mutated variants such as omicron (B.1.1.529), thus supporting decision making for public heath as well as guiding the development of therapeutic antibody treatments and vaccines for COVID-19.

Hierarchical length and sequence preferences establish a single major piRNA 3'-end

PIWI-interacting RNAs (piRNAs) guard germline genomes against the deleterious action of retroviruses and other mobile genetic elements. How piRNAs faithfully discriminate between self and non-self to restrict all mobile elements while sparing essential genes remains a key outstanding question in genome biology. PiRNAs use extensive base-pairing to recognize their targets and variable 3'ends could change the specificity and efficacy of piRNA silencing. Here, we identify conserved rules that ensure the generation of a single major piRNA 3'end in flies and mice. Our data suggest that the PIWI proteins initially define a short interval on pre-piRNAs that grants access to the ZUC-processor complex. Within this Goldilocks zone, the preference of the ZUC-processor to cut in front of a Uridine determines the ultimate processing site. We observe a mouse-specific roadblock that relocates the Goldilocks zone and generates an opportunity for consecutive trimming by PNLDC1. Our data reveal a conserved hierarchy between length and sequence preferences that controls the piRNA sequence space. The unanticipated precision of 3'end formation bolsters the emerging understanding that the functional piRNA sequence space is tightly controlled to ensure effective defense.

On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences

Let F denote the factorable matrix and X ∈ {ℓp , c 0, c, ℓ ∞}. In this study, we introduce the domains X(F) of the factorable matrix in the spaces X. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spaces X(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (ℓ p (F), ℓ ∞), (ℓ p (F), f) and (X, Y(F)) of matrix transformations, where Y denotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrix F and derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrix F. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.

Individualized VDJ recombination predisposes the available Ig sequence space

The process of recombination between variable (V), diversity (D), and joining (J) immunoglobulin (Ig) gene segments determines an individual's naive Ig repertoire and, consequently, (auto)antigen recognition. VDJ recombination follows probabilistic rules that can be modeled statistically. So far, it remains unknown whether VDJ recombination rules differ between individuals. If these rules differed, identical (auto)antigen-specific Ig sequences would be generated with individual-specific probabilities, signifying that the available Ig sequence space is individual specific. We devised a sensitivity-tested distance measure that enables inter-individual comparison of VDJ recombination models. We discovered, accounting for several sources of noise as well as allelic variation in Ig sequencing data, that not only unrelated individuals but also human monozygotic twins and even inbred mice possess statistically distinguishable immunoglobulin recombination models. This suggests that, in addition to genetic, there is also nongenetic modulation of VDJ recombination. We demonstrate that population-wide individualized VDJ recombination can result in orders of magnitude of difference in the probability to generate (auto)antigen-specific Ig sequences. Our findings have implications for immune receptor–based individualized medicine approaches relevant to vaccination, infection, and autoimmunity.