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Fractional SIR Epidemic Model of Childhood Disease with Mittag-Leffler Memory
Published in Devendra Kumar, Jagdev Singh, Fractional Calculus in Medical and Health Science, 2020
P. Veeresha, D. G. Prakasha, Devendra Kumar
The kernel of mathematical tools for demonstrating the practical difficulties exist in real life is as old as the conception of the world. The development of science and technology is magnetizing the considerations of the authors with the help of mathematical models to understand, describe, and predict the future behavior of the natural phenomena. A mathematical model is a representation of a system with the aid of mathematical theories, rules, formulas, and methods. Humankind has invented the most influential mathematical concepts known as calculus with the integral and differential operators, which can model and simulate numerous mechanisms that have arisen in environments of past decades. Recently, many researchers pointed out that classical derivatives fail to capture essential physical properties like long-range, anomalous diffusion, random walk, non-Markovian processes, and most importantly heterogeneous behaviours. Hence, many scientists and mathematicians find out that the classical differential operators are not always suitable tools to model the non-linear phenomena.
Atomic Force Microscopy of Biomembranes
Published in Qiu-Xing Jiang, New Techniques for Studying Biomembranes, 2020
Yi Ruan, Lorena Redondo-Morata, Simon Scheuring
Another interesting result is on the process of protein insertion via anomalous diffusion analysis of Lysenin, a 33 kDa protein extracted from the coleomic fluid of the earthworm Eisenia fetida. In a highly organized, crowded and clustered mosaic membrane of lipids and proteins, it has been difficult to correlate protein diffusion properties and domain formation and local molecular details because single molecule fluorescence microscopy does not allow observing directly unlabeled molecules in a crowded environment. Munguira et al.51 presented a novel method to analyze lysenin in a highly crowded environment and documented coexistence of different diffusion regimes within one membrane using HS-AFM, in Figure 5.9.
Kinetic Thinking: Back to the Future
Published in Clive R. Bagshaw, Biomolecular Kinetics, 2017
Regarding the forward direction of Equation 10.4, the calculated collision frequency of 7 × 109 M−1 s−1 ignores charge and tunneling effects, which would favor faster association, but another major factor comes from the anomalous diffusion coefficient of H3O+ compared to similarly sized ions. Grotthus accounted for this behavior in 1806 before water was known to have an H:O stoichiometry of 2:1 [698,699]. The idea then resurfaced 100 years later, when the molecular properties of water were better understood. The Grotthuss mechanism envisages that protons are rapidly exchanged between adjacent water molecules, so cutting down on the distance an individual proton has to move is analogous to a bucket brigade (Figure 10.2). The reaction is formally represented as
Vision of bacterial ghosts as drug carriers mandates accepting the effect of cell membrane on drug loading
Published in Drug Development and Industrial Pharmacy, 2020
Fars K. Alanazi, Abdulaziz A. Alsuwyeh, Nazrul Haq, Mounir M. Salem-Bekhit, Abdullah Al-Dhfyan, Faiyaz Shakeel
Short-term release can be described as zero-order model based on the highest R2 value among all applied models (R2 = 0.9780). In this model, drug released from vector that do not disintegrate and release the drug slowly like in osmotic systems. The short-term release was further examined using Korsmeyer–Peppas model to describe the release mechanisms. Using this model, the data of the release-exponent (n) describes the release mechanism of the drug [30]. In Table 3, n value was equal to 0.9595 (0.5 < n < 1.0) which indicated that the DOX release is governed by anomalous or non-Fickian diffusion. Anomalous diffusion or non-Fickian diffusion refers to combination of both diffusion and erosion controlled rate release. In case of BGs is probably due to the diffusion.
Facile development, characterization, and evaluation of novel bicalutamide loaded pH-sensitive mesoporous silica nanoparticles for enhanced prostate cancer therapy
Published in Drug Development and Industrial Pharmacy, 2019
Seema Saroj, Sadhana J. Rajput
However, at higher pH like 7.4, it might be possible that drug release could be hindered due to strong forces acting as a barrier. Variation of zeta potential with a change in pH for PAA-MSNs is shown in Figure 11. The zeta potential continuously decreased with increments in pH value. For determining the release mechanism involved the cumulative percentage release data were incorporated into three kinetic models for zero order, Higuchi and Korsmeyer Peppas model. The best fit model for determining the release of BIC from MSNs matrix was found to be Korsmeyer Peppas model. PAA-MSNs exhibited n value lying across 0.43 and 0.85 which is a proof of the existence of an anomalous diffusion mechanism. Anomalous diffusion combines both Fickian and Non-Fickian diffusion. Both diffusion and swelling are relative. In case of anomalous transport, polymeric relaxation and solvent diffusion both are almost similar in magnitudes. In case of n value up to 0.5, the BIC release is mainly diffusion controlled. Here the rate of solvent diffusion is at a much higher level than the polymeric relaxation process. Furthermore, n value greater than 0.85 indicates swelling governed diffusion process. Swelling is credited to the expansion of polymer employed [40]. A n value of greater than 1 means there exists a Super case II model. Here, we observed that for non-functionalized MCM-41 NPs the BIC release followed Fickian diffusion and not much pH dependency was seen. However, in case of PAA-MSNs, a highly pH-responsive and sustained release was obtained for greater than 72 h. Release mechanisms are summarized in Table 2.
Tailor-made pH-sensitive polyacrylic acid functionalized mesoporous silica nanoparticles for efficient and controlled delivery of anti-cancer drug Etoposide
Published in Drug Development and Industrial Pharmacy, 2018
Seema Saroj, Sadhana J. Rajput
For determining the release mechanism, release data were fitted to three models namely Korsmeyer–Peppas, zero order and Higuchi model. The best fit model was found to be Korsmeyer–Peppas and the diffusion exponential value (n) was used for determination of type of release mechanism playing role in diffusion of ETS from mesoporous matrix. For ETS@MCM-41-PAA n value was found to be 0.52. The n value between 0.43 and 0.85 signals a non-Fickian anomalous diffusion mechanism present. The anomalous diffusion was observed which combines both Fickian and non-Fickian release mechanisms. Fickian diffusion might be there due to weak interaction between the drug and the non-functionalized silica surface. The diffusion and swelling rated both are commensurable. In Anomalous transport, the velocity of solvent diffusion and the polymeric relaxation possess similar magnitudes [33]. In primary case of Fickian diffusion, n = 0.5 the drug release is extensively governed by diffusion. The solvent transport rate or diffusion is way higher than the polymeric chain relaxation process. In any case n value >0.85 stands for a swelling controlled diffusion process, attributed to the expansion of polymer used [34]. For Fickian diffusion ETS released is governed by diffusion and solvent transport rate or diffusion is much greater than the process of polymeric chain relaxation. Moreover, if n value is greater than unity, it signifies Super case II model [33]. Thus, it can be assumed that for MCM-41-PAA the anomalous mechanism based drug release is controlled both by diffusion and polymer swelling. Furthermore, in case of ETS-MCM-41, not much pronounced pH-dependent release was observed and the mechanism of release was Fickian (Figure 11(a)).