Glycosylation, a prevalent post-translational modification, plays a pivotal role in regulating intricate cellular processes by covalently attaching glycans to macromolecules. Dysregulated glycosylation is linked to a spectrum of diseases, encompassing cancer, neurodegenerative disorders, congenital disorders, infections, and inflammation. This review delves into the intricate interplay between glycosylation and protein conformation, with a specific focus on the profound impact of N-glycans on the selection of distinct protein conformations, characterized by distinct interactomes – namely protein assemblies - under normal and pathological conditions across various diseases. We begin by examining the spike protein of the SARS virus, illustrating how N-glycans regulate the infectivity of pathogenic agents. Subsequently, we utilize the prion protein and the chaperone glucose-regulated protein 94 as examples, exploring instances where N-glycosylation transforms physiological protein structures into disease-associated forms. Unraveling these connections provides valuable insights into potential therapeutic avenues and a deeper comprehension of the molecular intricacies that underlie disease conditions. This exploration of glycosylation's influence on protein conformation effectively bridges the gap between the glycome and disease, offering a comprehensive perspective on the therapeutic implications of targeting conformational mutants and their pathologic assemblies in various diseases. The goal is to unravel the nuances of these post-translational modifications, shedding light on how they contribute to the intricate interplay between protein conformation, assembly and disease.

The following system of equations {x_1 \cdot x_1=x_2, x_2 \cdot x_2=x_3, 2^{2^{x_1}}=x_3, x_4 \cdot x_5=x_2, x_6 \cdot x_7=x_2} has exactly one solution in ({\mathbb N}\{0,1})^7, namely (2,4,16,2,2,2,2). Hypothesis 1 states that if a system of equations S \subseteq {x_i \cdot x_j=x_k: i,j,k \in {1,...,7}} \cup {2^{2^{x_j}}=x_k: j,k \in {1,...,7}} has at most five equations and at most finitely many solutions in ({\mathbb N}\{0,1})^7, then each such solution (x_1,...,x_7) satisfies x_1,...,x_7 \leq 16. Hypothesis 1 implies that there are infinitely many composite numbers of the form 2^{2^{n}}+1. Hypotheses 2 and 3 are of similar kind. Hypothesis 2 implies that if the equation x!+1=y^2 has at most finitely many solutions in positive integers x and y, then each such solution (x,y) belongs to the set {(4,5),(5,11),(7,71)}. Hypothesis 3 implies that if the equation x(x+1)=y! has at most finitely many solutions in positive integers x and y, then each such solution (x,y) belongs to the set {(1,2),(2,3)}. We describe semi-algorithms sem_j (j=1,2,3) that never terminate. For every j \in {1,2,3}, if Hypothesis j is true, then sem_j endlessly prints consecutive positive integers starting from 1. For every j \in {1,2,3}, if Hypothesis j is false, then sem_j prints a finite number (including zero) of consecutive positive integers starting from 1.

Manzamines are complex polycyclic marine-derived β-carboline alkaloids with reported anticancer, immunostimulatory, anti-inflammatory, antibacterial, antiviral, antimalarial, neuritogenic, hyperlipidemia and atherosclerosis suppression bioactivities, putatively associated with inhibition of glycogen synthase kinase-3, cyclin-dependent kinase 5, and vacuolar ATPases. We hypothesized that additional and yet undiscovered molecular targets might be associated with Manzamine A (MZA) reported pharmacological properties. We report herein for the first time to our knowledge that MZA inhibited a 90kDa ribosomal protein kinase S6 (RSK1) when screened against a panel of 30 protein kinases. Furthermore in vitro RSK kinase assays demonstrated a 10-fold selectivity in potency of MZA against RSK1 versus RSK2. MZA’s differential binding and selectivity toward the two isoforms is also supported by computational docking experiments. Specifically, the RSK1-MZA (N- and C-termini) complexes appear to have stronger interactions and preferable energetics contrary to the RSK2-MZA ones. In addition, our computational strategy suggests that MZA binds to the N-terminal kinase domain of RSK1 rather than the C-terminal domain. RSK is a vertebrate family of cytosolic serine-threonine kinases that act downstream of the ras-ERK1/2 (extracellular-signal-regulated kinase 1/2) pathway, which phosphorylates substrates shown to regulate several cellular processes including growth, survival and proliferation. Consequently, our findings have lead us to hypothesize that MZA and the 80 currently known manzamine-type alkaloids isolated from several sponge genera, may have novel pharmacological properties.

In this paper, we first define the concepts of r-fuzzy soft α-open (semi-open and δ-open) sets on fuzzy soft topological spaces based on the article Aygunoglu et al. (Hacet. J. Math. Stat., 43 (2014), 193-208), and the relations of these sets with each other are established. In addition, we introduce the concepts of fuzzy soft δ-closure (δ-interior) operators, and study some properties of them. Also, the concept of r-fuzzy soft δ-connected sets is introduced and studied with help of fuzzy soft δ-closure operators. Thereafter, we define the concepts of fuzzy soft α-continuous (β-continuous, semi-continuous, pre-continuous and δ-continuous) functions, which are weaker forms of fuzzy soft continuity, and some properties of these functions along with their mutual relationships are discussed. Moreover, a decomposition of fuzzy soft α-continuity and a decomposition of fuzzy soft semi-continuity is obtained. Finally, as a weaker form of a fuzzy soft continuity, the concepts of fuzzy soft almost (weakly) continuous functions are defined, and some properties are specified. Additionally, we explore the notion of continuity in a very general setting called, fuzzy soft (L, M, N, O)-continuous functions and a historical justification is introduced.

In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. To do this, its randomness is estimated using three metrics, of which algorithmic complexity is the only one capable of revealing both transitions towards the chaotic regime and the algorithmic contribution of certain states to the transition diagram and their relationship with the order they occupy in the temporal evolution of the respective RBN.