Competition between Self-Assembly and Phase Separation Governs High-Temperature Condensation of a DNA Liquid.

In many biopolymer solutions, attractive interactions that stabilize finite-sized clusters at low concentrations also promote phase separation at high concentrations. Here we study a model biopolymer system that exhibits the opposite behavior, whereby self-assembly of DNA oligonucleotides into finite-sized, stoichiometric clusters tends to inhibit phase separation. We first use microfluidics-based experiments to map a novel phase transition in which the oligonucleotides condense as the temperature increases at high concentrations of divalent cations. We then show that a theoretical model of competition between self-assembly and phase separation quantitatively predicts changes in experimental phase diagrams arising from DNA sequence perturbations. Our results point to a general mechanism by which self-assembly shapes phase boundaries in complex biopolymer solutions.

Low H2O2 consumption Fenton-like catalysts for pollutant cleavage based on the construction of a dual reaction center.

High energy consumption has seriously hindered the development of Fenton-like reactions for the removal of refractory organic pollutants in water. To solve this problem, we designed a novel Fenton-like catalyst (Cu-PAN3) by coprecipitation and carbon thermal reduction. The catalyst exhibits excellent Fenton-like catalytic activity and stability for the degradation of various pollutants with low H2O2 consumption. The experimental results indicate that the dual reaction centers (DRCs) are composed of Cu-N-C and Cu-O-C bridges between copper and graphene-like carbon, which form electron-poor/rich centers on the catalyst surface. H2O2 is mainly reduced at electron-rich Cu centers to free radicals for pollutant degradation. Meanwhile, pollutants can be oxidized by donating electrons to the electron-poor C centers of the catalyst, which inhibits the ineffective decomposition of H2O2 at the electron-poor centers. This therefore significantly reduces the consumption of H2O2 and reduces energy consumption.

Co-adsorption and selective-adsorption of heavy metals and dyes from aqueous solution by bio-based humus/chitosan hydrogels.

An eco-friendly adsorbent was prepared by reverse suspension crosslinking method to remove multiple pollutants from aqueous solution. Both raw materials, derived from humus (HS) and chitosan (CS), are biodegradable and low-cost natural biopolymers. After combining HS with CS, the adsorption capacity was significantly improved due to compensation effects between the two components. HS/CS exhibited the features of amphoteric adsorption through pH adjustment, enabling it to adsorb not only anionic pollutants (Methyl Orange (MO) and Cr(VI)), but also cationic ones (Methylene Blue (MB) and Pb(II)). The adsorption capacities were approximately 242 mg/g, 69 mg/g, 188 mg/g and 57 mg/g for MO, Cr(VI), MB and Pb(II), respectively. HS/CS showed a slight preference for MO in MO/Cr(VI) co-adsorption system, whereas strong selectivity for MB over Pb(II) in MB/Pb(II) system under acidic condition (pH<3.0). This selective behavior would allow for potential applications in separating MB/Pb(II) effluents and selectively recycling Pb(II) in acidic environment. The isothermal and kinetic adsorption behaviors followed Langmuir model and pseudo-second-order model, respectively. The density functional theory (DFT) confirmed that the interaction between metal ions and adsorbents was primarily attributed to chelation and electrostatic adsorption, owing to nitric and oxygenic functional groups. Whereas, the adsorption mechanisms for dyes were involved in electrostatic attraction, H-bond and π-π bond, due to available hydrogen, oxygen, nitrogen atoms and aromatic groups on the surface of adsorbent and adsorbates. The adsorbent could be efficiently regenerated and retained over 90% of its adsorption capacity after five cycles, which has a potential for practical applications in water treatment.

Lean methane combustion over zeolite-supported Pd catalysts: Structure-performance relationship and deactivation mechanism.

Zeolites are a promising support for Pd catalysts in lean methane (CH4) combustion. Herein, three types of zeolites (H-MOR, H-ZSM-5 and H-Y) were selected to estimate their structural effects and deactivation mechanisms in CH4 combustion. We show that variations in zeolite structure and surface acidity led to distinct changes in Pd states. Pd/H-MOR with external high-dispersing Pd nanoparticles exhibited the best apparent activity, with activation energy (Ea) at 73 kJ/mol, while Pd/H-ZSM-5 displayed the highest turnover frequency (TOF) at 19.6 × 10-3 sec-1, presumably owing to its large particles with more step sites providing active sites in one particle for CH4 activation. Pd/H-Y with dispersed PdO within pore channels and/or Pd2+ ions on ion-exchange sites yielded the lowest apparent activity and TOF. Furthermore, Pd/H-MOR and Pd/H-ZSM-5 were both stable under a dry condition, but introducing 3 vol.% H2O caused the CH4 conversion rate on Pd/H-MOR drop from 100% to 63% and that on Pd/H-ZSM-5 decreased remarkably from 82% to 36%. The former was shown to originate from zeolite structural dealumination, and the latter principally owed to Pd aggregation and the loss of active PdO.

Nucleation dynamics of a model biomolecular liquid.

Liquid-liquid phase separation in biology has recently been shown to play a major role in the spatial control of biomolecular components within the cell. However, as they are phase transitions, these processes also display nontrivial dynamics. A model phase-separating system of DNA nanostars provides unique access to nucleation physics in a biomolecular context, as phase separation is driven near room temperature by highly thermo-responsive DNA hybridization and at modest DNA concentrations. By measuring the delay time for phase-separated droplets to appear, we demonstrate that the dynamics of DNA nanostar phase separation reflect that of a metastable binary mixture of patchy particles. For sufficiently deep temperature quenches, droplets undergo spinodal decomposition and grow spontaneously, driven by Brownian motion and coalescence of phase-separated droplets, as confirmed by comparing experimental measurements to particle-based simulations. Near the coexistence boundary, droplet growth slows substantially, indicative of a nucleation process. The temperature dependence of droplet appearance times can be predicted by a classical nucleation picture with mean field exponents and demonstrates that a theory previously used to predict equilibrium phase diagrams can also distinguish spinodal and nucleation dynamical regimes. These dynamical principles are relevant to behaviors associated with liquid-liquid phase separating systems, such as their spatial patterning, reaction coupling, and biological function.

In-depth understanding of transport behavior of sulfided nano zerovalent iron/reduced graphene oxide@guar gum slurry: Stability and mobility.

Nanoscale zero-valent iron (NZVI), which has the advantages of small particle size, large specific surface area, and high reactivity, is often injected into contaminated aquifers in the form of slurry. However, the prone to passivation and agglomeration as well as poor stability and mobility of NZVI limit the further application of this technology in fields. Therefore, sulfided NZVI loaded on reduced graphene oxide (S-NZVI/rGO) and guar gum (GG) with shear-thinning properties as stabilizers were used to synthesize S-NZVI/rGO@GG slurries. SEM, TEM, and FT-IR confirmed that the dispersion and anti-passivation of NZVI were optimized in the coupled system. The stability and mobility of the slurry were improved by increasing the GG concentration, enhancing the pH, and decreasing the ionic strength and the presence of Ca2+ ions, respectively. A modified advection-dispersion equation (ADE) was used to simulate the transport experiments considering the strain and physicochemical deposition/release. Meanwhile, colloidal filtration theory (CFT) demonstrated that Brownian motion plays a dominant role in the migration of S-NZVI/rGO@GG slurry, and the maximum migration distance can be increased by appropriately increasing the injection rate. Extended-Derjaguin-Landau-Verwey-Overbeek (XDLVO) theory showed that the excellent stability and migration of S-NZVI/rGO@GG slurry mainly came from the GG spatial forces. This study has important implications for the field injection of S-NZVI/rGO@GG slurry. According to the injection parameters, the injection range of S-NZVI/rGO@GG slurry is effectively controlled, which lays the foundation for the promotion of application in actual fields.

Composition regulates dissolved organic matter adsorption onto iron (oxy)hydroxides and its competition with phosphate: Implications for organic carbon and phosphorus immobilization in lakes.

Dissolved organic matter (DOM) is a heterogeneous pool of compounds and exhibits diverse adsorption characteristics with or without phosphorous (P) competition. The impacts of these factors on the burial and mobilization of organic carbon and P in aquatic ecosystems remain uncertain. In this study, an algae-derived DOM (ADOM) and a commercially available humic acid (HA) with distinct compositions were assessed for their adsorption behaviors onto iron (oxy)hydroxides (FeOx), both in the absence and presence of phosphate. ADOM contained less aromatics but more protein-like and highly unsaturated structures with oxygen compounds (HUSO) than HA. The adsorption capacity of FeOx was significantly greater for ADOM than for HA. Protein-like and HUSO compounds in ADOM and humic-like compounds and macromolecular aromatics in HA were preferentially adsorbed by FeOx. Moreover, ADOM demonstrated a stronger inhibitory effect on phosphate adsorption than HA. This observation suggests that the substantial release of autochthonous ADOM by algae could elevate internal P loading and pose challenges for the restoration of restore eutrophic lakes. The presence of phosphate suppressed the adsorption of protein-like compounds in ADOM onto FeOx, resulting in an increase in the relative abundance of protein-like compounds and a decrease in the relative abundance of humic-like compounds in post-adsorption ADOM. In contrast, phosphate exhibited no discernible impact on the compositional fractionation of HA. Collectively, our results show the source-composition characters of DOM influence the immobilization of both DOM and P in aquatic ecosystems through adsorption processes. The preferential adsorption of proteinaceous compounds within ADOM and aromatics within HA highlights the potential for the attachment with FeOx to diminish the original source-specific signatures of DOM, thereby contributing to the shared DOM characteristics observed across diverse aquatic environments.

Pollution characteristics and quantitative source apportionment of heavy metals within a zinc smelting site by GIS-based PMF and APCS-MLR models.

The abandoned smelters present a substantial pollution threat to the nearby soil and groundwater. In this study, 63 surface soil samples were collected from a zinc smelter to quantitatively describe the pollution characteristics, ecological risks, and source apportionment of heavy metal(loid)s (HMs). The results revealed that the average contents of Zn, Cd, Pb, As, and Hg were 0.4, 12.2, 3.3, 5.3, and 12.7 times higher than the risk screening values of the construction sites, respectively. Notably, the smelter was accumulated heavily with Cd and Hg, and the contribution of Cd (0.38) and Hg (0.53) to ecological risk was 91.58%. ZZ3 and ZZ7 were the most polluted workshops, accounting for 25.7% and 35.0% of the pollution load and ecological risk, respectively. The influence of soil parent materials on pollution was minor compared to various workshops within the smelter. Combined with PMF, APCS-MLR and GIS analysis, four sources of HMs were identified: P1(25.5%) and A3(18.4%) were atmospheric deposition from the electric defogging workshop and surface runoff from the smelter; P2(32.7%) and A2(20.9%) were surface runoff of As-Pb foul acid; P3(14.5%) and A4(49.8%) were atmospheric deposition from the leach slag drying workshop; P4(27.3%) and A1(10.8%) were the smelting process of zinc products. This paper described the distribution characteristics and specific sources of HMs in different process workshops, providing a new perspective for the precise remediation of the smelter by determining the priority control factors.

Photocatalytic degradation of antibiotic sulfamethizole by visible light activated perovskite LaZnO3.

In this work, the perovskite LaZnO3 was synthesized via sol-gel method and applied for photocatalytic treatment of sulfamethizole (SMZ) antibiotics under visible light activation. SMZ was almost completely degraded (99.2% ± 0.3%) within 4 hr by photocatalyst LaZnO3 at the optimal dosage of 1.1 g/L, with a mineralization proportion of 58.7% ± 0.4%. The efficient performance of LaZnO3 can be attributed to its wide-range light absorption and the appropriate energy band edge levels, which facilitate the formation of active agents such as ·O2-, h+, and ·OH. The integration of RP-HPLC/Q-TOF-MS and DFT-based computational techniques revealed three degradation pathways of SMZ, which were initiated by the deamination reaction at the aniline ring, the breakdown of the sulfonamide moieties, and a process known as Smile-type rearrangement and SO2 intrusion. Corresponding toxicity of SMZ and the intermediates were analyzed by quantitative structure activity relationship (QSAR), indicating the effectiveness of LaZnO3-based photocatalysis in preventing secondary pollution of the intermediates to the ecosystem during the degradation process. The visible-light-activated photocatalyst LaZnO3 exhibited efficient performance in the occurrence of inorganic anions and maintained high durability across multiple recycling tests, making it a promising candidate for practical antibiotic treatment.

Migration mechanism of atrazine in the simulated lake icing process at different freezing temperatures based on density function theory.

Atrazine causes concern due to its resistant to biodegradation and could be accumulated in aquatic organisms, causing pollution in lakes. This study measured the concentration of atrazine in ice and the water under ice through a simulated icing experiment and calculated the distribution coefficient K to characterize its migration ability in the freezing process. Furthermore, density functional theory (DFT) calculations were employed to expatiate the migration law of atrazine during icing process. According to the results, it could release more energy into the environment when atrazine staying in water phase (-15.077 kcal/mol) than staying in ice phase (-14.388 kcal/mol), therefore it was beneficial for the migration of atrazine from ice to water. This explains that during the freezing process, the concentration of atrazine in the ice was lower than that in the water. Thermodynamic calculations indicated that when the temperature decreases from 268 to 248 K, the internal energy contribution of the compound of atrazine and ice molecule (water cluster) decreases at the same vibrational frequency, resulting in an increase in the free energy difference of the compound from -167.946 to -165.390 kcal/mol. This demonstrated the diminished migratory capacity of atrazine. This study revealed the environmental behavior of atrazine during lake freezing, which was beneficial for the management of atrazine and other pollutants during freezing and environmental protection.

Pore-blocking steric mass-action model for adsorption of bioparticles.

The steric mass-action (SMA) model has been widely reported to describe the adsorption of proteins in different types of chromatographic adsorbents. Here in the present work, a pore-blocking steric mass-action model (PB-SMA) was developed for the adsorption of large-size bioparticles, which usually exhibit the unique pore-blocking characteristic on the adsorbent and thus lead to a fraction of ligands in the deep channels physically inaccessible to bioparticles adsorption, instead of being shielded due to steric hindrance by adsorbed bioparticles. This unique phenomenon was taken into account by introducing an additional parameter, Lin, which is defined as the inaccessible ligand densities in the physically blocked pore area, into the PB-SMA model. This fraction of ligand densities (Lin) will be deducted from the total ligand (Lt) for model development, thus the steric factor (σ) in the proposed PB-SMA will reflect the steric shielding effect on binding sites by adsorbed bioparticles more accurately than the conventional SMA model, which assumes that all ligands on the adsorbent have the same accessibility to the bioparticles. Based on a series of model assumptions, a PB-SMA model was firstly developed for inactivated foot-and-mouth disease virus (iFMDV) adsorption on immobilized metal affinity chromatography (IMAC) adsorbents. Model parameters for static adsorption including equilibrium constant (K), characteristic number of binding sites (n), and steric factor (σ) were determined. Compared with those derived from the conventional SMA model, the σ values derived from the PB-SMA model were dozens of times smaller and much closer to the theoretical maximum number of ligands shielded by a single adsorbed iFMDV, indicating the modified model was more accurate for bioparticles adsorption. The applicability of the PB-SMA model was further validated by the adsorption of hepatitis B surface antigen virus-like particles (HBsAg VLPs) on an ion exchange adsorbent with reasonably improved accuracy. Thus, it is considered that the PB-SMA model would be more accurate in describing the adsorption of bioparticles on different types of chromatographic adsorbents.

A mechanistic kinetic model for lipid oxidation in Tween 20-stabilized O/W emulsions.

Models predicting lipid oxidation in oil-in-water (O/W) emulsions are a requirement for developing effective antioxidant solutions. Existing models do, however, not include explicit equations that account for composition and structural features of O/W emulsions. To bridge this gap, a mechanistic kinetic model for lipid oxidation in emulsions is presented, describing the emulsion as a one-dimensional three phase (headspace, water, and oil) system. Variation in oil droplet sizes, overall surface area of oil/water interface, oxidation of emulsifiers, and the presence of catalytic transition metals were accounted for. For adequate predictions, the overall surface area of oil/water interface needs to be determined from the droplet size distribution obtained by dynamic and static light scattering (DLS, SLS). The kinetic model predicted well the formation of oxidation products in both mono- and polydisperse emulsions, with and without presence of catalytic transition metals.

Simulation and parameter determination of the net sorption of phenanthrene by sediment particles.

The distribution of polycyclic aromatic hydrocarbons (PAHs) in the ocean is affected by the sorption-desorption process of sediment particles. This process is determined by the concentration of PAHs in seawater, water temperature, and organic matter content of sediment particles. Quantitative relationships between the net sorption rates (=the difference of sorption and desorption rates) and these factors have not been established yet and used in PAH transport models. In this study, phenanthrene was chosen as the representative of PAHs. Three groups of experimental data were collected to address the dependence of the net sorption processes on the initial concentration, water temperature, and organic carbon content representing organic matter content. One-site and two-compartment mass-transfer models were tested to represent the experimental data using various parameters. The results showed that the two-compartment mass-transfer model performed better than the one-site mass-transfer model. The parameters of the two-compartment mass-transfer model include the sorption rate coefficients kafand kas (L g-1 min-1), and the desorption rate coefficients kdf and kds (min-1). The parameters at different temperatures and organic carbon contents were obtained by numerical simulations. Linear relationships were obtained between the parameters and water temperature, as well as organic carbon content. kaf, kas and kdf decreased linearly, while kds increased linearly with temperature. kaf, kas and kdf increased linearly, while kds decreased linearly with organic carbon content. The r2 values between the simulation results based on the relationships and the experimental results reached 0.96-0.99, which supports the application of the model to simulate sorption-desorption processes at different water temperatures and organic carbon contents in a realistic ocean.

Phosphate adsorption on dried alum sludge: Modeling and application to treatment of dairy effluents.

This study evaluates Alum sludge from drinking water treatment plants for the efficient and cost-effective removal of phosphates from aqueous solutions. Extensive characterization and batch experiments have established that optimal phosphate removal was achieved with a sludge dosage of 20 g L-1 (at an initial phosphate concentration of 100 mg L-1), a pH of 5, a temperature of 23 °C, and a stirring speed of 200 rpm. These conditions significantly reduced phosphate levels, ensuring compliance with legal discharge limits. The Langmuir isotherm, pseudo-second-order kinetic and intraparticle diffusion models best described the adsorption process, highlighting the spontaneous and endothermic nature of the phenomenon. The sludge effectively reduced phosphate concentrations to acceptable levels when applied to dairy effluents. This study underscores the potential of Alum sludge as a viable solution for phosphate management in environmental cleanup efforts.

Comparison of numerical calculations and ALOHA modeling in consequence assessment of chlorine gas emissions from ethylene dichloride reactors.

Incidents involving chemical storage tanks in the petrochemical industry are significant events with severe consequences. Within the petrochemical industry, EDC is a sector that produces ethylene dichloride through the reaction of chlorine and ethylene. The present research was conducted to evaluate the consequences of chlorine gas released from the EDC reactor in a petrochemical industry in southern Iran. Data regarding reactor specifications were obtained from the factory's technical office, while climatic data was acquired from the Meteorological Organization. The consequences of chlorine gas release from the reactor were assessed in four predefined scenarios using numerical calculation methods and modeling with the ALOHA software. The numerical calculation method involved thermodynamic fluid path analysis, discharge coefficient calculations, and wind speed impact analysis. The hazard radius was determined based on the ERPG1-2-3 index. Results showed that in the scenario of chlorine gas release from EDC reactors, according to the ALOHA model, an increase in wind speed from 3 to 7 m/h led to an expanded dispersion radius. At a radius of 700 m from the reactor, the maximum outdoor concentration reached 3.12 ppm, decreasing to 2.27 ppm at 800 m and further to 1.53 ppm at 1000 m. The comparison of numerical calculations and modeling using the ALOHA software indicates the desirable conformity of the results with each other. The R2 coefficient for evaluating the conformity of the results was 0.9964, indicating the desired efficiency of the model in evaluating the consequences of the release of toxic gasses from the EDC tank. The results of this research can be useful in designing the site and emergency response plan.

Carbon-based molecular properties efficiently predicted by deep learning-based quantum chemical simulation with large language models.

The prediction of thermodynamic properties of carbon-based molecules based on their geometrical conformation using fluctuation and density functional theories has achieved great success in the field of energy chemistry, while the excessive computational cost provides both opportunities and challenges for the integration of machine learning. In this work, a deep learning-based quantum chemical prediction model was constructed for efficient prediction of thermodynamic properties of carbon-based molecules. We constructed a novel framework - encoding the 3D information into a large language model (LLM), which in turn generates a 2D SMILES string, while embedding a learnable encoding designed to preserve the integrity of the original 3D information, providing better structural information for the model. Additionally, we have designed an equivariant learning module to encompass representations of conformations and feature learning for conformational sampling. This framework aims to predict thermodynamic properties more accurately than learning from 2D topology alone, while providing faster computational speeds than conventional simulations. By combining machine learning and quantum chemistry, we pioneer efficient practical applications in the field of energy chemistry. Our model advances the integration of data-driven and physics-based modeling to unlock novel insights into carbon-based molecules.

Leveraging Language Model Multitasking To Predict C-H Borylation Selectivity.

C-H borylation is a high-value transformation in the synthesis of lead candidates for the pharmaceutical industry because a wide array of downstream coupling reactions is available. However, predicting its regioselectivity, especially in drug-like molecules that may contain multiple heterocycles, is not a trivial task. Using a data set of borylation reactions from Reaxys, we explored how a language model originally trained on USPTO_500_MT, a broad-scope set of patent data, can be used to predict the C-H borylation reaction product in different modes: product generation and site reactivity classification. Our fine-tuned T5Chem multitask language model can generate the correct product in 79% of cases. It can also classify the reactive aromatic C-H bonds with 95% accuracy and 88% positive predictive value, exceeding purpose-developed graph-based neural networks.

Data-driven, explainable machine learning model for predicting volatile organic compounds' standard vaporization enthalpy.

The accurate prediction of standard vaporization enthalpy (ΔvapHm°) for volatile organic compounds (VOCs) is of paramount importance in environmental chemistry, industrial applications and regulatory compliance. To overcome traditional experimental methods for predicting ΔvapHm° of VOCs, machine learning (ML) models enable a high-throughput, cost-effective property estimation. But despite a rising momentum, existing ML algorithms still present limitations in prediction accuracy and broad chemical applications. In this work, we present a data driven, explainable supervised ML model to predict ΔvapHm° of VOCs. The model was built on an established experimental database of 2410 unique molecules and 223 VOCs categorized by chemical groups. Using supervised ML regression algorithms, the Random Forest successfully predicted VOCs' ΔvapHm° with a mean absolute error of 3.02 kJ mol-1 and a 95% test score. The model was successfully validated through the prediction of ΔvapHm° for a known database of VOCs and through molecular group hold-out tests. Through chemical feature importance analysis, this explainable model revealed that VOC polarizability, connectivity indexes and electrotopological state are key for the model's prediction accuracy. We thus present a replicable and explainable model, which can be further expanded towards the prediction of other thermodynamic properties of VOCs.

Modeling of phosphate speciation on goethite surface: Effects of humic acid.

Iron (hydr)oxides and humic acid (HA) are important active components in soils and usually coexist in the environment. The effects of HA on the adsorption and subsequent immobilization of phosphate on iron (hydr)oxide surface are of great importance in studies of soil fertility and eutrophication. In this study, two types of goethite with different particle sizes were prepared to investigate the phosphate adsorption behaviors and complexation mechanisms in the absence or presence of HA by combining multiple characterization and modeling studies. The adsorption capacity of micro- (M-Goe) and nano-sized goethite (N-Goe) for phosphate was 2.02 and 2.04 µmol/m2, which decreased by ∼25% and ∼45% in the presence of 100 and 200 mg/L HA, respectively. Moreover, an increase in equilibrium phosphate concentration significantly decreased the adsorption amount of goethite for HA. Charge distribution-multisite surface complexation (CD-MUSIC) and natural organic matter-charge distribution (NOM-CD) modeling identified five phosphate complexes and their corresponding affinity constants (logKP). Among these phosphate complexes, FeOPO2OH, (FeO)2PO2, and (FeO)2POOH species were predominant complexes on the surface of both M-Goe and N-Goe across a wide range of pH and initial phosphate concentrations. The presence of HA had little effect on the coordination mode and logKP of phosphate on goethite surface. These results and the obtained model parameters shed new lights on the interfacial reactivity of phosphate at the goethite-water interface in the presence of HA, and may facilitate further prediction of the environmental fate of phosphate in soils and sediments.

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 is s 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.