The Michaelis-Menten Reaction at Low Substrate Concentrations: Pseudo-First-Order Kinetics and Conditions for Timescale Separation

We demonstrate that the Michaelis-Menten reaction mechanism can be accurately approximated by a linear system when the initial substrate concentration is low. This leads to pseudo-first-order kinetics, simplifying mathematical calculations and experimental analysis. Our proof utilizes a monotonicity property of the system and Kamke's comparison theorem. This linear approximation yields a closed-form solution, enabling accurate modeling and estimation of reaction rate constants even without timescale separation. Building on prior work, we establish that the sufficient condition for the validity of this approximation iss 0 ≪ K , where K = k 2 / k 1 is the Van Slyke-Cullen constant. This condition is independent of the initial enzyme concentration. Further, we investigate timescale separation within the linear system, identifying necessary and sufficient conditions and deriving the corresponding reduced one-dimensional equations.

A low-cost and sustainable solution for nitrate removal from secondary effluent: Macroporous ion exchange resin treatment

Macroporous ion exchange resin has excellent selectivity to nitrogen (N), phosphorus (P) and partially soluble refractory organic compounds contained in the secondary effluent of wastewater treatment plants (WWTP). In this study, macroporous ion exchange resins were chosen as an alternative to single biochemical nitrogen removal processes. Various conditions were examined to optimize adsorption performance, and the adsorption mechanism was explored through isotherm fitting, thermodynamic parameter calculation, and kinetic analysis. The experiment demonstrated that the resin exhibited strong selectivity for nitrate (NO3-) and achieved an equilibrium adsorption amount of 9.8924 mg/g and an equilibrium adsorption time of 60 min at 25 °C. The resin denitrification pilot plant demonstrated stable operation for two months and achieved COD<20 mg/L, TN < 1.5 mg/L, and NH4+-N<0.5 mg/L. The removal rates of COD, TP, NH4+-N, NO3--N, and TN were 41.65%, 42.96%, 55.37%, 91.8%, and 90.81%, respectively. After the resin was regenerated, the removal rates of NO3--N, TN and the regeneration recovery rate were above 90%. Through cost analysis, the treatment cost of the pilot plant is only 0.104 $/m3. This study presents a practical, low-cost, and efficient treatment method for the deep treatment of secondary effluent from WWTP in practical engineering, providing new ideas and theoretical guidance.

Comparison of methods for quantitative biomolecular interaction analysis

In order to perform good kinetic experiments, not only the experimental conditions have to be optimized, but the evaluation procedure as well. The focus of this work is the in-depth comparison of different approaches and algorithms to determine kinetic rate constants for biomolecular interaction analysis (BIA). The different algorithms are applied not only to flawless simulated data, but also to real-world measurements. We compare five mathematical approaches for the evaluation of binding curves following pseudo-first-order kinetics with different noise levels. In addition, reflectometric interference spectroscopy (RIfS) measurements of two antibodies are evaluated to determine their binding kinetics. The advantages and disadvantages of the individual approach will be investigated and discussed in detail. In summary, we will raise awareness on how to evaluate and judge results from BIA by using different approaches rather than having to rely on “black box” closed (commercial) software packages.

Mechanistic insight into ultrasound-induced enhancement of electrochemical oxidation of ofloxacin: Multi-response optimization and cost analysis

In this paper, a hybrid advanced oxidation process of sonoelectrochemical, in which ultrasound and electrochemical are applied simultaneously, has been used for the degradation of ofloxacin (bio-recalcitrant pharmaceutical pollutant). Response surface methodology based central composite design was applied to understand the parametric effects of ultrasonic power, current density, initial pH, and electrolyte dose. Enhanced ofloxacin degradation was obtained using sonoelectrochemical (≈95%) process in comparison to the electrochemical (≈60.6%) and sonolysis alone (≈7.2%) after 120 min treatment time. Multi-response optimization was used so as to maximize COD removal (70.12%) and minimize specific energy consumption (11.92 kWh (g COD removed)^-1)at the optimized parametric condition of pH = 6.3 (natural pH), ultrasonic power = 54 W, current density = 213 A m^-2, and Na₂SO₄ electrolyte dose = 2.0 g L^-1. It was revealed that ^•OH radicals contribute major to the ofloxacin degradation reaction among the other oxidizing agents. Degradation of the ofloxacin followed pseudo-first-order kinetics with a higher reaction rate, which confirmed the synergistic effect of 34% between ultrasound and electrochemical approaches. The degradation pathway of ofloxacin removal was elucidated at optimum condition by the temporal evolution of the intermediate compounds and final products using gas chromatography coupled with mass spectroscopy (GC-MS), liquid chromatography-mass spectroscopy (LC-MS), high-resolution mass spectroscopy (HR-MS), and Fourier transform infrared spectroscopy (FTIR). Atomic force microscopy (AFM) and field emission scanning electron microscope (FE-SEM) coupled with energy dispersed X-ray (EDX) were used to determine the morphology of electrodes. Operational cost analysis was done based on the reactor employed in the present study.

Electro-oxidation of Ofloxacin antibiotic by dimensionally stable Ti/RuO2 anode: Evaluation and mechanistic approach

Present study investigates the potential of Ti/RuO₂ electrode for degradation and mineralization of Ofloxacin (OFLX) antibiotic from synthetic wastewater by electro-oxidation (EO) method, not reported earlier. Effects of various EO parameters such as applied current (I), initial pH, initial OFLX concentration (C₀) and supporting electrolyte concentration on %OFLX removal efficiency and %TOC removal efficiency were systematically studied and reported. Decay kinetics of OFLX by varying C₀ and applied I were also studied. Additionally, mineralization current efficiency and specific energy consumption of OFLX mineralization were evaluated. Moreover, mode of oxidation method involved (direct and/or indirect oxidation) was also explored. Major OFLX transformation products during EO were identified using UPLC-Q-TOF-MS, and possible degradation reaction mechanism was proposed. Furthermore, operating cost analysis was performed to check the economic feasibility of the EO process. The optimum pH and current (I) were found to be ≈6.8 (natural pH of OFLX wastewater) and 1 A, respectively. Mineralization current efficiency decreased from 7.8% to 4.9% with increase in I value from 0.25 to 1 A. ≈80% of OFLX removal in 30 min of electrolysis and 46.3% TOC removal in 240 min of electrolysis at I = 1 A were observed. Pseudo-first-order kinetic model best fitted the experimental data showing R² value ≈ 0.99 for all the C_o and applied I studied.

Photodegradation of diphenylarsinic acid by UV-C light: Implication for its remediation

Diphenylarsinic acid (DPAA) is a major contaminant in environments polluted by chemical weapons and abandoned after World Wars I and II and poses high risks to biota but remediation methods for this contaminant are rare. Here, the photodegradtion of DPAA was studied under high-pressure Hg lamp irradiation. DPAA was degraded completely into inorganic arsenic species in 30 min under UV-C irradiation. The photodegradation of DPAA depended mainly on its direct photolysis through excited-state DPAA. By contrast, the generation of (1)O2 during the photodegradation of DPAA was confirmed by electron paramagnetic resonance (EPR) studies, but (1)O2 had little effect on the photodegradation of DPAA. Phtotodegradation of DPAA was also studied in soil leachates and groundwater and the photolytic rate of DPAA was controlled by the total organic carbon (TOC) content in soil leachates and by the NO3(-) concentration in groundwater. Finally, studies on the effects of common solutes on the photodegradation of DPAA show that Cl(-) can increase the photolytic rate of DPAA by prolonging the lifetime of excited-state DPAA. Moreover, NO3(-), NO2(-), and humic acid (HA) can decrease the photolytic rate of DPAA by suppressing the production of excited-state DPAA. This research shows the detailed mechanism of DPAA photodegradation and provides a new and effective method for DPAA decontamination.