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Mathematics for Enzyme Reaction Kinetics and Reactor Performance is the first set in a unique 11 volume-collection on Enzyme Reactor Engineering. This two volume-set relates specifically to the wide mathematical background required for systematic and rational simulation of both reaction kinetics and reactor performance; and to fully understand and capitalize on the modelling concepts developed. It accordingly reviews basic and useful concepts of Algebra (first volume), and Calculus and Statistics (second volume). A brief overview of such native algebraic entities as scalars, vectors, matrices and determinants constitutes the starting point of the first volume; the major features of germane functions are then addressed. Vector operations ensue, followed by calculation of determinants. Finally, exact methods for solution of selected algebraic equations - including sets of linear equations, are considered, as well as numerical methods for utilization at large. The second volume begins with an introduction to basic concepts in calculus, i.e. limits, derivatives, integrals and differential equations; limits, along with continuity, are further expanded afterwards, covering uni- and multivariate cases, as well as classical theorems. After recovering the concept of differential and applying it to generate (regular and partial) derivatives, the most important rules of differentiation of functions, in explicit, implicit and parametric form, are retrieved - together with the nuclear theorems supporting simpler manipulation thereof. The book then tackles strategies to optimize uni- and multivariate functions, before addressing integrals in both indefinite and definite forms. Next, the book touches on the methods of solution of differential equations for practical applications, followed by analytical geometry and vector calculus. Brief coverage of statistics-including continuous probability functions, statistical descriptors and statistical hypothesis testing, brings the second volume to a close.

Background and aims Utilizing drought-tolerant genotypes with appropriate adaptive characteristics is a crucial mitigation strategy to improve wheat productivity in dry conditions. Understanding rhizosphere processes (e.g., enzyme traits) involved in nutrient acquisition and adaptation to drought stress across different genotypes is critical for the development of drought-resistant genotypes. Methods We grew three wheat genotypes with varying drought tolerance -Baran (rainfed drought-tolerant), Sirvan (drought-tolerant), and Marvdasht (non-drought-tolerant)- in rhizoboxes under drought stress. Through in-situ zymography and ex-situ enzyme kinetic analysis, we examined the localization and dynamic behaviors of key enzymes, acid phosphatase (ACP) and β-glucosidase (GLU), in the rhizosphere and their relationship with root traits. Results Baran displayed a more extensive root system with abundant lateral roots compared to other genotypes. Its rhizosphere exhibited a higher hotspot of GLU and ACP than Sirvan (1.5- and 1.2-fold higher, respectively) and Marvdasht (2- and 2.7-fold higher, respectively). Baran also demonstrated a broader enzyme activity expansion in the rhizosphere, showcasing its superior nutrient exploration capability. Drought-tolerant genotypes displayed elevated GLU and ACP activity in the rhizoplane, indicating enhanced root exudation. Notably, V max values of GLU were approximately 2-fold lower in drought-tolerant genotypes than in Marvdasht, revealing an energy conservation strategy in dry conditions. Additionally, drought-tolerant genotypes exhibited a higher affinity of GLU and ACP to substrates, enabling efficient nutrient extraction from soil organic matter despite lower enzyme activity. Conclusion Our findings demonstrate that drought-tolerant genotypes can better withstand water stress by having a broader rhizosphere extent and an effective enzyme system, both of which are primarily facilitated by lateral root growth.

AimsTree species mixing is an essential measure used to increase soil carbon (C) sinks and enhance nutrient cycling, while enzyme catalysis is the rate-limiting step of soil C mineralization and nutrient release. The study aimed to determine how mixing affects soil C and nitrogen (N) hydrolases kinetics in subtropical plantations.MethodsThe topsoil (0–15 cm) and subsoil (45–60 cm) from two monoculture coniferous plantations and two mixed plantations formed by replanting broad-leaved trees in the two coniferous plantations were collected to analyze the maximum activity (Vmax), half-saturation constant (Km) and catalytic efficiency (Vmax/Km) of four hydrolases involved in C (β-glucosidase, BG; cellobioside, CB) and N (β-N-acetylglucosaminidase, NAG; leucine aminopeptidase, LAP) cycling.ResultsMixing decreased the Vmax of BG but increased the Vmax of NAG in the topsoil, indicating the differential response of C and N enzyme activities to mixing. The Km of NAG and LAP increased, while the Vmax/Km of CB and NAG decreased after mixing in the topsoil. Mixing decreased the Vmax of CB and NAG and the Vmax/Km of BG and CB in the subsoil. The Vmax/Km values of C and N hydrolases were negatively correlated with SOC, total N and mineral N and positively correlated with the aromatic/aliphatic compound ratio, which illustrated that the hydrolases kinetics were mediated by changes in soil quality.ConclusionMixing decreased the catalytic efficiency of soil C and N hydrolases in subtropical plantations, although the mixing effect on soil hydrolase kinetic parameters depended on the enzyme type and soil depth.

Nanopore sensing, a high-resolution DNA sequencing technology, is rapidly expanding into novel and exciting directions of probing specific DNA-enzyme interactions. Although proven excellent for the detecting structural features of bare DNA, quantitative measurements on enzyme-DNA complexes and their real-time activity are lagging and only starting to emerge for long DNA templates. Signal-to-noise requirement and high translocation speeds make it difficult to detect protein bound on biologically relevant plasmid-length DNA. To this end we report accurate position detection of a catalytically active Cas9 bound to its single or multiple target sites on the DNA. Protein position is fingerprinted using event charge deficit (ECD) based analysis of the high signal-to-noise electrical signals as the complex translocates through a glass nanopore. Using a time-dependent assay, we quantify the kinetics of the released products upon enzymatic cleavage of the target DNA by the wild-type Cas9 nuclease. Our approach enables the nanopore-based single-molecule sensing of DNA-protein complexes, for real-time monitoring of biochemical reactions. This may help understand protein binding & localization as well as improve Cas9-based targeting in genome engineering applications. Graphical abstract

Targeting tyrosinase for melanogenesis disorders is an established strategy. Hydroxyl-substituted benzoic and cinnamic acid scaffolds were incorporated into new chemotypes that displayed in vitro inhibitory effects against mushroom and human tyrosinase for the purpose of identifying anti-melanogenic ingredients. The most active compound 2-((4-methoxyphenethyl)amino)-2-oxoethyl (E)-3-(2,4-dihydroxyphenyl) acrylate (Ph9), inhibited mushroom tyrosinase with an IC50 of 0.059 nM, while 2-((4-methoxyphenethyl)amino)-2-oxoethyl cinnamate (Ph6) had an IC50 of 2.1 nM compared to the positive control, kojic acid IC50 16700 nM. Results of human tyrosinase inhibitory activity in A375 human melanoma cells showed that compound (Ph9) and Ph6 exhibited 94.6% and 92.2% inhibitory activity respectively while the positive control kojic acid showed 72.9% inhibition. Enzyme kinetics reflected a mixed type of inhibition for inhibitor Ph9 (Ki 0.093 nM) and non-competitive inhibition for Ph6 (Ki 2.3 nM) revealed from Lineweaver–Burk plots. In silico docking studies with mushroom tyrosinase (PDB ID:2Y9X) predicted possible binding modes in the catalytic site for these active compounds. Ph9 displayed no PAINS (pan-assay interference compounds) alerts. Our results showed that compound Ph9 is a potential candidate for further development of tyrosinase inhibitors.

Background Cellobiohydrolase from glycoside hydrolase family 7 is a major component of commercial enzymatic mixtures for lignocellulosic biomass degradation. For many years, Trichoderma reesei Cel7A (TrCel7A) has served as a model to understand structure–function relationships of processive cellobiohydrolases. The architecture of TrCel7A includes an N-glycosylated catalytic domain, which is connected to a carbohydrate-binding module through a flexible, O-glycosylated linker. Depending on the fungal expression host, glycosylation can vary not only in glycoforms, but also in site occupancy, leading to a complex pattern of glycans, which can affect the enzyme’s stability and kinetics. Results Two expression hosts, Aspergillus oryzae and Trichoderma reesei, were utilized to successfully express wild-types TrCel7A (WTAo and WTTr) and the triple N-glycosylation site deficient mutants TrCel7A N45Q, N270Q, N384Q (ΔN-glycAo and ΔN-glycTr). Also, we expressed single N-glycosylation site deficient mutants TrCel7A (N45QAo, N270QAo, N384QAo). The TrCel7A enzymes were studied by steady-state kinetics under both substrate- and enzyme-saturating conditions using different cellulosic substrates. The Michaelis constant (KM) was consistently found to be lowered for the variants with reduced N-glycosylation content, and for the triple deficient mutants, it was less than half of the WTs’ value on some substrates. The ability of the enzyme to combine productively with sites on the cellulose surface followed a similar pattern on all tested substrates. Thus, site density (number of sites per gram cellulose) was 30–60% higher for the single deficient variants compared to the WT, and about twofold larger for the triple deficient enzyme. Molecular dynamic simulation of the N-glycan mutants TrCel7A revealed higher number of contacts between CD and cellulose crystal upon removal of glycans at position N45 and N384. Conclusions The kinetic changes of TrCel7A imposed by removal of N-linked glycans reflected modifications of substrate accessibility. The presence of N-glycans with extended structures increased KM and decreased attack site density of TrCel7A likely due to steric hindrance effect and distance between the enzyme and the cellulose surface, preventing the enzyme from achieving optimal conformation. This knowledge could be applied to modify enzyme glycosylation to engineer enzyme with higher activity on the insoluble substrates.

Non-digestible polysaccharides are of great significance to human and animal intestinal health. Cellulose, arabinoxylan, β−glucan and glucomannan were selected in the present study to investigate the fermentation characteristics and fiber-degrading enzyme kinetics by inoculating pig fecal microbiota in vitro. Our results showed that fermentation of arabinoxylan and β-glucan produced the highest amount of acetate and lactate, respectively. The abundance of Prevotella_9 was the highest in β-glucan group and positively correlated with lactate and acetate. Glucomannan fermentation produced the highest amount of butyrate, and the abundance of Lachnospiraceae_XPB_1014_group and Bacteroides were the lowest. A significant negative correlation was found between Lachnospiraceae_XPB_1014_group, Bacteroides and butyrate. Exo-β-1,4-xylanase had the highest activity at 24 h during arabinoxylan fermentation. The activity of β-glucosidase and β-mannosidase at 36 h were higher than those at 15 h in the glucomannan group. The abundance of Prevotella_9 was positively correlated with β-glucosidase while Lachnospiraceae_XPB_1014_group and Bacteroides were negatively correlated with β-xylosidase. Our findings demonstrated the β-glucan and arabinoxylan promote proliferation of Prevotella_9, with the preference to secret β-glucosidase, β-mannosidase and the potential to produce lactate and acetate. Butyrate production can be improved by inhibiting the proliferation of Lachnospiraceae_XPB_1014_group and Bacteroides, which have the lack of potential to secret β-xylosidase.

New Delhi metallo-β-lactamase-1 (NDM-1), expressed in different Gram-negative bacteria, is a versatile enzyme capable of hydrolyzing β-lactam rings containing antibiotics such as penicillins, cephalosporins, and even carbapenems. Multidrug resistance in bacteria mediated by NDM-1 is an emerging threat to the public health, with an enormous economic burden. There is a scarcity in the availability of specific NDM-1 inhibitors, and also a lag in the development of new inhibitors in pharmaceutical industries. In order to identify novel inhibitors of NDM-1, we screened a library of more than 20 million compounds, available at the MCULE purchasable database. Virtual screening led to the identification of six potential inhibitors, namely, MCULE-1996250788-0-2, MCULE-8777613195-0-12, MCULE-2896881895-0-14, MCULE-5843881524-0-3, MCULE-4937132985-0-1, and MCULE-7157846117-0-1. Furthermore, analyses by molecular docking and ADME properties showed that MCULE-8777613195-0-12 was the most suitable inhibitor against NDM-1. An analysis of the binding pose revealed that MCULE-8777613195-0-12 formed four hydrogen bonds with the catalytic residues of NDM-1 (His120, His122, His189, and Cys208) and interacted with other key residues. Molecular dynamics simulation and principal component analysis confirmed the stability of the NDM-1 and MCULE-8777613195-0-12 complex. The in vitro enzyme kinetics showed that the catalytic efficiency (i.e., kcat/Km) of NDM-1 on various antibiotics decreased significantly in the presence of MCULE-8777613195-0-12, due to poor catalytic proficiency (kcat) and affinity (Km). The IC50 value of MCULE-8777613195-0-12 (54.2 µM) was comparable to that of a known inhibitor, i.e., D-captopril (10.3 µM). In sum, MCULE-8777613195-0-12 may serve as a scaffold to further design/develop more potent inhibitors of NDM-1 and other β-lactamases.

Background Molecular-scale mechanisms of the enzymatic breakdown of cellulosic biomass into fermentable sugars are still poorly understood, with a need for independent measurements of enzyme kinetic parameters. We measured binding times of cellobiohydrolase Trichoderma reesei Cel7A (Cel7A) on celluloses using wild-type Cel7A (WTintact), the catalytically deficient mutant Cel7A E212Q (E212Qintact) and their proteolytically isolated catalytic domains (CD) (WTcore and E212Qcore, respectively). The binding time distributions were obtained from time-resolved, super-resolution images of fluorescently labeled enzymes on cellulose obtained with total internal reflection fluorescence microscopy. Results Binding of WTintact and E212Qintact on the recalcitrant algal cellulose (AC) showed two bound populations: ~ 85% bound with shorter residence times of < 15 s while ~ 15% were effectively immobilized. The similarity between binding times of the WT and E212Q suggests that the single point mutation in the enzyme active site does not affect the thermodynamics of binding of this enzyme. The isolated catalytic domains, WTcore and E212Qcore, exhibited three binding populations on AC: ~ 75% bound with short residence times of ~ 15 s (similar to the intact enzymes), ~ 20% bound for < 100 s and ~ 5% that were effectively immobilized. Conclusions Cel7A binding to cellulose is driven by the interactions between the catalytic domain and cellulose. The cellulose-binding module (CBM) and linker increase the affinity of Cel7A to cellulose likely by facilitating recognition and complexation at the substrate interface. The increased affinity of Cel7A to cellulose by the CBM and linker comes at the cost of increasing the population of immobilized enzyme on cellulose. The residence time (or inversely the dissociation rates) of Cel7A on cellulose is not catalysis limited.

When enzyme inhibition by either the product or excess substrate occurs, it is possible to determine the characteristic kinetic parameters based on [P]/ t measurements, even when a large proportion of the substrate is converted. The advantages of various approaches are discussed. Most of them allow a good estimation of the V and K m values. Conversely, the determination of K p (product inhibition) and K i (inhibition by excess substrate) can be more challenging. In the first case, determination of the type of inhibition requires more complex experiments that are beyond the scope of the present contribution. In the second, the inhibition constant K i can only be roughly estimated. In an experimental approach, we compared the results obtained either with initial rate measurements or with 50 to 60% conversion of the substrate. Similar values of V and K m were obtained. Measurements involving the conversion of a large proportion of substrate are particularly advantageous when the assay method is difficult or time-consuming, or when obtaining the substrate presents experimental difficulties or involves substantial costs.