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.

Protein hydrolysates prepared by Alcalase using ultrasound and microwave pretreated almond meal and their characterization.

The study aimed to optimize ultrasonic (US: 40 kHz/200 W for 10, 20, 30, 40, and 50 min), and microwave (MW: 160 W for 45, 90, 125, 180, and 225 s) pretreatment conditions on protein extraction yield and degree of protein hydrolysis (DH) from almond de-oiled meal, an industrial by-product. First order model was used to describe the kinetics of almond protein hydrolysates obtained with Alcalase. The highest DH, 10.95% was recorded for the US-50 min and 8.87% for MW-45 s; while it was 5.76% for the untreated/control sample. At these optimized pretreatment conditions, a 1.16- and 1.18-fold increment in protein recovery was observed for the US and MW pretreatments, respectively in comparison to the conventional alkaline extraction. The molecular weight distribution recorded for pretreated samples disclosed a significant reduction in the band thickness in comparison with control. Both the pretreatments resulted in a significant increase (P < 0.05) in the antioxidant activity, and TCA solubility index when compared with the control. Results evinced that US and/or MW pretreatments before enzymatic hydrolysis can be a promising approach for the valorization of almond meal for its subsequent use as an ingredient for functional foods/nutraceuticals which otherwise fetches low value as an animal feed.

Proteomic response of Pseudomonas aeruginosa IIPIS-8 during rapid and efficient degradation of naphthalene.

Polycyclic aromatic hydrocarbons (PAHs) are widely distributed in the ecosystem and are of significant concern due to their toxicity and mutagenicity. Bioremediation of PAHs is a popular and benign approach that ameliorates the environment. This study investigated the biodegradation and proteome response of Pseudomonas aeruginosa IIPIS-8 for two-ringed PAH: naphthalene (NAP) to understand proteome alteration during its bioremediation. Rapid biodegradation was observed up to 98 ± 1.26% and 84 ± 1.03%, respectively, for initial concentrations of 100 mg L-1 and 500 mg L-1 of NAP. Degradation followed first-order kinetics with rate constants of 0.12 h-1 and 0.06 h-1 and half-life (t1/2) of 5.7 h and 11.3 h, respectively. Additionally, the occurrence of key ring cleavage and linear chain intermediates, 2,3,4,5,6, -pentamethyl acetophenone, 1-octanol 2-butyl, and hexadecanoic acid supported complete NAP degradation. Proteomics study of IIPIS-8 throws light on the impact of protein expression, in which 415 proteins were quantified in sequential windowed acquisition of all theoretical fragment ion mass spectra (SWATH-MS) analysis, of which 97 were found to be significantly up-regulated and 75 were significantly down-regulated by ≥ 2-fold change (p values ≤ 0.05), during the NAP degradation. The study also listed the up-regulation of several enzymes, including oxido-reductases, hydrolases, and catalases, potentially involved in NAP degradation. Overall, differential protein expression, through proteomics study, demonstrated IIPIS-8's capability to efficiently assimilate NAP in their metabolic pathways even in a high concentration of NAP.

Characterizing the efficiency of low-cost LED lights for conducting laboratory studies to investigate polycyclic aromatic hydrocarbon photodegradation processes.

Polycyclic aromatic hydrocarbons (PAHs) are common contaminants ubiquitously present in various waste products such as biosolids (e.g. wastewater sludges), oil spill residues (e.g. tarballs), road asphalts, and combustion byproducts. In this study, the photodegradation of PAHs is investigated under natural sunlight (cloudy and sunny/clear weather conditions), and using two types of artificial LED light sources. This is the first study to investigate the relative efficiency of low-cost LED light sources for conducting laboratory-scale PAH photodegradation experiments and directly comparing the results against those obtained using natural sunlight. Two types of LED light sources are investigated in this study: a light source with a full-spectrum range (380 nm-780 nm) that can cover the broad wavelength range of solar light reaching the Earth's surface, and a light source with a UV-A range (365 nm) that covers the UV range of the solar spectrum reaching the Earth's surface. The results show that the degradation of high molecular weight (HMW) PAHs is primarily due to photodegradation, and other lighter PAHs are degraded by both photodegradation and evaporation processes. HMW PAH photodegradation reactions follow the first-order degradation kinetics. The degradation rate constants of different PAHs are used to compare the relative efficiency of the light sources. The data show that the full-spectrum LED induced PAH photodegradation rates are similar to the natural sunlight induced rates. Furthermore, when the values of the rate constants are normalized to respective irradiance levels, the normalized rates for HMW PAH photodegradation under both full-spectrum LED light and natural sunlight are almost identical. However, the normalized photodegradation rate constants of HMW PAHs under the UV-A LED light are about two to three orders of magnitude higher than the sunlight as well as the full-spectrum-LED values. Therefore, the UV-A LED light is the optimal low-cost light source for studying PAH photodegradation processes under laboratory conditions.

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.

A procedure for determining the number and pattern of digestible starch fractions in multiphasic food digestograms.

BACKGROUND: Plant-based foods are frequently heterogenous systems, containing multiple starch fractions with distinct digestion rate constants. An unbiased determination of the number and digestion pattern of these fractions is a prerequisite for understanding the digestive characteristics of food. RESULTS: A non-linear least-squares procedure based on a conditional selection of simple first-order kinetics or a combination of parallel and sequential kinetics models was developed. The procedure gave robust results fitting manually generated data, and was applied to in vitro experimental digestion data of retrograded rice starches. By correlating fitting parameters with starch structural parameters, it showed that rice starches with a lower amylose content, longer amylose chains, and amylopectin intermediate chains had more digestible starch fractions after long-term retrogradation. CONCLUSION: This procedure enables the structural basis of starch digestibility and the development of food products with slow starch digestibility to be better understood. © 2022 Society of Chemical Industry.

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.

In situ microbial and phytoremediation of crude oil contaminated soil by Cynodon sp.

Crude oil contamination of land and water leads to their abandonment after heavy oil recovery processes. Analogous to bioremediation, phytoremediation has provided an efficient solution towards land reclamation through enhancement of flora. The present work manifests significance of phytoremediation via reclamation of crude oil contaminated soil collected from Kalol, India. The collected soil was analyzed for pH, oxidation-reduction potential, electrical conductivity (EC), bulk density, particle size, moisture. The experimental work consists three batch units; pot A, pot B and pot C with crude oil contaminated soil, fresh soil and control respectively. While observing plant growth for 120 days, Total Petroleum Hydrocarbon (TPH) was measured at determined intervals for estimation of percentage degradation. After 90 days of pot observation, contaminated soil was inoculated with rhizospheric bacterial inoculum developed from pot A which forms new batch for microbial-remediation as an additional scope to this work. Gas chromatography mass spectroscopy (GC-MS-MS) was carried out for determination of naphthalene contamination. Crude oil degradation in pot A was estimated as 82.16% followed with the affirmation given by degradation kinetics whereas, 60.68% and 36.75% degradation was observed in pot C-control and new batch respectively. Cynodon sp. grown in pot A was confirmed by identification as reported.

Kinetics of zero-valent iron-activated persulfate for methylparaben degradation and the promotion of Cl.

Methylparaben (MP) is an emerging pollutant, and the optimal conditions and kinetics of MP degradation using nano-zero-valent iron-activated persulfate (nZVI/PDS) need to be further investigated. This paper firstly investigated the response surface methodology (RSM) analysis of MP degradation by the heterogeneous system nZVI/PDS and concluded that the initial pH had the most significant effect on MP degradation. The optimal experimental conditions predicted by the RSM were as follows: initial pH 2.75, [nZVI]0 = 2.87 mM, [PDS]0 = 2.18 mM (MP degradation level of 95.30%). First- and second-order kinetic fits were performed for different initial pH levels and different concentrations of MP, nZVI, and PDS. It was determined that k = 0.0365 min-1 (R2 = 0.984) when the initial pH was 3, [PDS]0 = 2 mM, [MP]0 = 20 mg L-1, and [nZVI]0 = 3 mM (MP degradation level of 94.25%). The rest of the conditions were more closely fitted to the second-order reactions. The effects of different concentrations of anions and humic acid (HA) on the MP degradation level and k were examined, and it was found that Cl- could promote MP degradation to 97.69% (increased by 3.65%) and increase the k in accordance with the first-order reaction kinetics (0.0780 min-1, R2 = 0.991). Finally, the analysis of intermediates revealed 5 reaction pathways and 7 reaction intermediates, which inferred a possible reaction mechanism with the recycling performance of nZVI. In this paper, the superiority of nZVI/PDS for the purposes of activating MP degradation was affirmed. The presence of Cl- can enhance the level of MP degradation was confirmed, which provides a new direction for future practical engineering applications.

Study on reaction mechanism and Langmuir-Hinshelwood kinetic model of catalytic denitrification by Fe0 and bimetallic catalyst.

The focus of this research was on the catalytic reduction of nitrate to nitrogen gas for the water conservation. Zero-valent iron (Fe0) with bimetallic catalyst that carrier supported palladium (Pd) and copper (Cu) was innovatively applied in this study. First, XPS (X-ray photoelectron spectroscopy) analyses and experiments were conducted to study the mechanism of the catalytic reduction of nitrate. In the catalytic reaction, which is regarded as a stepwise process, Fe0 was the electron provider; Pd and Cu supported on carrier played indispensable but distinct roles. The kinetics suggested that the process was better reflected by first-order kinetics of the Langmuir-Hinshelwood model. Additionally, first-order kinetics of the catalytic reaction under the effect of catalysts with different carriers (SiO2, silica gel, kaolin, diatomite, γ-Al2O3, graphene) were further studied. Pd-Cu/graphene catalyst showed higher catalytic performance compared with other catalysts.

Performance of EDTA modified magnetic ZnFe2O4 during photocatalytic reduction of Cr(VI) in aqueous solution under UV irradiation.

The photocatalytic reduction of toxic Cr(VI) to non-pernicious Cr(III) using ZnFe2O4/EDTA (ethylenediaminetetraacetic acid) under UV irradiation was evaluated. The reduction of Cr(VI) with bare ZnFe2O4 under UV irradiation was negligible. However, the Cr(VI) in the solution was completely reduced within 3 h after the introduction of EDTA. EDTA could consume valence band holes and could be oxidized by holes into inorganic products. Therefore, photo-generated electrons could be used to reduce Cr(VI) to Cr(III). The effect of concentration of EDTA, ZnFe2O4 photocatalyst dosages, and initial pH on the photocatalytic reduction of Cr(VI) was investigated. The results revealed that the photocatalytic reduction of Cr(VI) accelerated by increasing EDTA concentration and ZnFe2O4 dosage. The present reduction process confirms the pseudo-first-order kinetic reaction. The quasi reduction rate constant increased from 3.5 x 10-4 min-1 to 2.6 x 10-2 min-1 with the increase in initial EDTA concentration from 0 to 1000 mg L-1. The acidic solution is preferable for the photocatalytic reduction of Cr(VI). The entire reduction of Cr(VI) was carried out within 2 h under the optimum conditions with pH 2, 20 mg ZnFe2O4, and 500 mg L-1 EDTA. The formation of [Cr-EDTA]3+ complex may be advantageous to accelerate the Cr(VI) reduction. A probable mechanism for the photocatalytic Cr(VI) reduction was speculated here.

Role of climate change variables (standing water and rainfall) on dissipation of chlorantraniliprole from a simulated rice ecosystem.

Chlorantraniliprole (CAP) is extensively used for rice pest management. Lack of information on the role of standing water and amount and timing of rainfall on CAP dissipation in rice ecosystem could hamper its prospective use. Present study was performed to investigate the effects of different water regimes (saturated, 5 and 10 cm standing water) and simulated rainfall (40 and 100 mm occurred at 4, 8 and 24 h after CAP application) on leaching, surface runoff and dissipation of CAP into components of rice ecosystem. The results showed highest concentration of CAP residues in soil and plant under saturated condition followed by 5 and 10 cm standing water conditions. Whereas, the highest concentration of CAP in leachates was detected under 10 cm standing water (12.19 ng mL-1). The results revealed large amount of leaching (21.99 ng mL-1) and surface runoff (42.25 ng mL-1) losses of CAP when 100 mm rainfall occurred at 4 h after pesticide application. The total quantity of CAP residues in soil and plant was highest when rainfall occurred at 24 h after pesticide application under both the rainfall amounts. Water stagnation and high intensity rainfall occurred shortly after pesticide application will contribute to pesticide loss to non-target sites through surface run-off and leaching. There will be less pesticide available in soil for plant uptake which may not be sufficient to kill the target organisms.

Dissipation of Pendimethalin in Soil Under Direct Seeded and Transplanted Rice Field.

The dissipation of pendimethalin applied in direct seeded rice (DSR) and transplanted rice (TPR) field at 1.0 and 2.0 kg a.i. ha-1 followed biphasic first order kinetics (R2 > 0.91) and was comparatively faster under flooded TPR than DSR. The half-life (DT50) of pendimethalin in the soil ranged from 2.22 to 2.80 days in the initial phase and 23.51 to 24.66 days in the final phase in TPR for both application rates. However in DSR, DT50 varied from 3.67 to 4.35 days in the initial phase and 34.19 to 34.99 days in the final phase. Residues of pendimethalin in soil samples analyzed by HPLC and GC-MS/MS were below the detection limit (< 0.003 µg g-1) for both the application rates in DSR and TPR whereas 0.003-0.009 µg g-1 and 0.003-0.008 µg g-1 residues of pendimethalin were found in rice grain and straw samples, respectively.

Pharmacokinetic studies of naproxen amides of some amino acid esters with promising colorectal cancer chemopreventive activity.

Naproxen (nap) is belonging to Non-steriodal anti-inflammatory drugs (NSAIDs) group of drugs that characterized by their free carboxylic group. The therapeutic activity of nap is usually accompanied by GI untoward side effects. Recently synthesized naproxen amides of some amino acid esters prodrugs to mask the free carboxylic group were reported. Those prodrugs showed a promising colorectal cancer chemopreventive activity. The current study aims to investigate the fate and hydrolysis of the prodrugs kinetically in different pH conditions, simulated gastric and intestinal fluids with pHs of 1.2, 5.5 and 7.4 in vitro at 37 °C. The effect of enzymes on the hydrolysis of prodrugs was also studied through incubation of these prodrugs at 37 °C in human plasma and rat liver homogenates. The pharmacokinetic parameters of selected prodrugs and the liberated nap were studied after oral and intraperitoneal administration in male wistar rats. The results showed the hydrolysis of naproxen amides of amino acid esters to nap through two steps first by degradation of the ester moiety to form the amide of nap with amino acid and the second was through the degradation of the amide link to liberate nap. The two reactions were followed and studied kinetically where K1 and K2 (rate constants of degradation) is reported. The hydrolysis of prodrugs was faster in liver homogenates than in plasma. The relative bioavailability of the liberated nap in vivo was higher in case of prodrug containing ethyl glycinate moiety than that occupied l-valine ethyl ester moiety. Each of nap. prodrugs containing ethyl glycinate and l-valine ethyl ester moieties appears promising in liberating nap, decreasing direct GI side effect and consequently their colorectal cancer chemopreventive activity.

Modeling the effect of adsorption on the degradation rate of propiconazole in profiles of Polish Luvisols.

Laboratory adsorption and degradation studies were carried out to determine the effect of time-dependent adsorption on propiconazole degradation rates in samples from three Polish Luvisols. Strong propiconazole adsorption (organic carbon normalized adsorption coefficients Koc in the range of 1217-7777 mL/g) was observed in batch experiments, with a typical biphasic mechanism with a fast initial step followed by the time-dependent step, which finished within 48 h in the majority of soils. The time-dependent step observed in incubation experiments was longer (duration from 5 to 23 d), and its contribution to total adsorption was from 20% to 34%. The half-lives obtained at 25 °C and 40% maximum water holding capacity of soil, were in the range of 34.7-112.9 d in the Ap horizon and in the range of 42.3-448.8 d for subsoils. The very strong correlations, between degradation rates in pore water and soil organic carbon and soil microbial activity, indicated that microbial degradation of propiconazole was most likely the only significant process responsible for the decay of this compound under aerobic conditions for the whole of the examined soil profiles. Modeling of the processes showed that only models coupling adsorption and degradation were able to correctly describe the experimental data. The analysis of the bioavailability factor values showed that degradation was not limited by the rate of propiconazole desorption from soil, but sorption affected the degradation rate by decreasing its availability for microorganisms.

Photodegradation of organophosphorus pesticides in honey medium.

Honey can be polluted due to environmental pollution and misuse of beekeeping practices. In the present study, photodegradation experiments of organophosphorus pesticides (coumaphos, methyl parathion and fenitrothion) in honey medium were conducted using Atlas Suntest simulator CPS+ as a sunlight producer. Photodegradation experiments were conducted under three different intensities as 250W/m(2), 500W/m(2) and 750W/m(2) to evaluate the impact of sunlight intensity on removal of OPs in honey medium. Significant decreases of three OPs' concentrations were observed. Coumaphos showed the highest degradability, reaching a degradation percentage of 90 percent within 15min. After 1h irradiation, residual percentages of coumaphos were 6.62 percent for 250W/m(2), 3.48 percent for 500W/m(2) and 2.98 percent for 750W/m(2), respectively. Methyl parathion and fenitrothion also could be removed through photodegradation efficiently. After 1h irradiation, the residual percentages of methyl parathion and fenitrothion under 750W/m(2) sunlight irradiation were 26.89 percent and 16.70 percent, respectively. Intensity of sunlight showed a positive impact on removal of OPs in honey medium. The higher intensity, the lower residual percentage. Photodegradation of three OPs fitted well with pseudo-first order kinetics. Half-lives calculated from pseudo-first order kinetics were 17.61min (250W/m(2)), 16.67min (500W/m(2)) and 17.58min (750W/m(2)) for coumaphos, 57.62min (250W/m(2)), 34.13min (500W/m(2)) and 31.69min (750W/m(2)) for methyl parathion and 144.70min (250W/m(2)), 95.47min (500W/m(2)) and 22.57min (750W/m(2)) for fenitrothion, respectively. Most of the three OPs could dissipate in a short time under sunlight irradiation. Photodegradation could be accepted as an appropriate method for the removal of OPs in honey medium.

Biodegradation kinetics of organic micropollutants in biofilters for advanced wastewater treatment - Impact of operational conditions and biomass origin on removal.

Biofiltration processes are often part of advanced wastewater treatment (aWWT) technologies for the removal of organic micropollutants (OMP) from conventional wastewater treatment plant (WWTP) effluents. Although biological effects are not always the main focus of these technologies (e.g. filtration through granular activated carbon), they have been shown to contribute significantly to total OMP removal. While OMP biodegradation kinetics in conventional biological wastewater treatment are well researched, no systematic comparison to biomass from aWWT is available. This biomass faces different growth conditions and higher OMP concentrations relative to the background organic matter. Adaptation to these conditions could be possible and could lead to faster OMP biodegradation kinetics, which would show in a larger pseudo first-order biodegradation kinetic constant kbiol. In this work, kbiol values for biomass obtained from aWWT biofilters were determined by evaluating OMP removals measured in lab-scale biofilters using a mechanistic model of the experimental setup. A comparison to kbiol values from literature for conventional wastewater treatment (with nutrient removal) revealed similar OMP biodegradation kinetics without any advantages of biomass from aWWT. A conceptual evaluation of influencing factors on OMP removal in biofilters showed that operational parameters (such as the biomass concentration or the empty bed contact time) and the affinity of OMPs to adsorb on biomass have a significant additional effect on biological OMP removal. Therefore, kbiol values alone are not sufficient to estimate biological OMP removal in biofilters and further information about the system is required.

Design, Development and In-Vitro Characterization of Insulin Loaded Topical Pluronic-Lecithin Based Organogel Formulation for the Management of Diabetic Wound.

AIM: To develop and characterize the topical insulin-loaded organogel formulation for the management of diabetic wounds. OBJECTIVES: To formulate and evaluate organogel of insulin that can serve as a topical administration for promoting enhanced wound healing in diabetic patients by providing sustained and localized delivery of drug to the wound site. METHODOLOGY: The insulin organogel formulated by the micro-emulsion method involves mixing the "aqueous and oil phases" at high shear. Physical and chemical properties, as well as an in vitro study with a Franz diffusion chamber, were used to evaluate the prepared organogel. RESULTS: All formulations proved to be off-white, homogeneous, washable, and had a pH between 6 and 6.5; moreover, they were non-irritating and skin-compatible. Formulations F1-F6 had viscosity ranging from 2058 to 3168 cps, spreadability ranges of 0.35 to 0.52 g*cm/s, and gel transition ranges of 28.33 to 35.33 °C. In formulations F1-F3, the concentration of lecithin was gradually increased, and in formulations F4-F6, the concentration of PF-127 was increased, resulting in a decrease in gel transition temperature, an increase in viscosity, and a gradual change in spreadability. The higher-viscosity formulations were much more stable and had better drug release. All formulations were fitted to a kinetic model belonging to first-order kinetics. However, after examining the parameter evaluation, it was found that the formulations F2 and F6 were better suited to the kinetic model and were consistent with the first-order and Higuchi models in Korsmeyer-Peppas F2 (r2 = 0.9544 and n = 1.0412); F6 (r2 = 0.9019 and n = 1.0822), which was a confirmation of the sustainability of the release system with matrix diffusion and drug delivery mechanisms that were based on the Super-Case II transport. CONCLUSION: Further research and clinical trials are needed to validate its efficacy, optimize the formulation, and establish its long-term safety. Topical insulin organogel has the potential to revolutionize diabetic wound management by improving healing outcomes, reducing complications, and raising the standard of living for those who have diabetes.

First-order compartment model solutions - Exponential sums and beyond.

First-order compartment models are common tools for modelling many biological processes, including pharmacokinetics. Given the compartments and the transfer rates, solutions for the time-dependent quantity (or concentration) curves can normally be described by a sum of exponentials. This paper investigates cases that go beyond simple sums of exponentials. With specific relations between the transfer rate constants, two exponential rate constants can be equal, in which case the normal solution cannot be used. The conditions for this to occur are discussed, and advice is provided on how to circumvent these cases. An example of an analytic solution is given for the rare case where an exact equality is the expected result. Furthermore, for models with at least three compartments, cases exist where the solution to a real-valued model involves complex-valued exponential rate constants. This leads to solutions with an oscillatory element in the solution for the tracer concentration, i.e., there are cases where the solution is not a simple sum of (real-valued) exponentials but also includes sine and cosine functions. Detailed solutions for three-compartment cases are given. As a tentative conclusion of the analysis, oscillatory solutions appear to be tied to cases with a cyclic element in the model itself.

A superabsorbent and pH-responsive copolymer-hydrogel based on acemannan from Aloe vera (Aloe barbadensis M.): A smart material for drug delivery.

Combining natural polysaccharides with synthetic materials improves their functional properties which are essential for designing sustained-release drug delivery systems. In this context, the Aloe vera leaf mucilage/hydrogel (ALH) was reacted with acrylic acid (AA) to synthesize a copolymerized hydrogel, i.e., ALH-grafted-Polyacrylic acid (ALH-g-PAA) through free radical copolymerization. Concentrations of the crosslinker N,N'-methylene-bis-acrylamide (MBA), and the initiator potassium persulfate (KPS) were optimized to study their effects on ALH-g-PAA swelling. The FTIR and solid-state NMR (CP/MAS 13C NMR) spectra witnessed the formation of ALH-g-PAA. Scanning electron microscopy (SEM) analysis revealed superporous nature of ALH-g-PAA. The gel fraction (%) of ALH-g-PAA was directly related to the concentrations of AA and MBA whereas the sol fraction was inversely related to the concentrations of AA and MBA. The porosity (%) of ALH-g-PAA directly depends on the concentration of AA and MBA. The ALH-g-PAA swelled admirably at pH 7.4 and insignificantly at pH 1.2. The ALH-g-PAA offered on/off switching properties at pH 7.4/1.2. The metoprolol tartrate was loaded on different formulations of ALH-g-PAA. The ALH-g-PAA showed pH, time, and swelling-dependent release of metoprolol tartrate (MT) for 24 h following the first-order kinetic and Korsmeyer-Peppas model. Haemocompatibility studies ascertained the non-thrombogenic and non-hemolytic behavior of ALH-g-PAA.