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Mathematical Formula Handbook[^2^]



The activity of several well-known anti-malarials, including chloroquine (CQ), is attributed to their ability to inhibit the formation of haemozoin (Hz) in the malaria parasite. The formation of inert Hz, or malaria pigment, from toxic haem acquired from the host red blood cell of the parasite during haemoglobin digestion represents a pathway essential for parasite survival. Inhibition of this critical pathway therefore remains a desirable target for novel anti-malarials. A recent publication described the results of a haem fractionation assay used to directly determine haemoglobin, free haem and Hz in Plasmodium falciparum inoculated with CQ. CQ was shown to cause a dose-dependent increase in cellular-free haem that was correlated with decreased parasite survival. The method provided valuable information but was limited due to its low throughput and high demand on parasite starting material. Here, this haem fractionation assay has been successfully adapted to a higher throughput method in 24-well plates, significantly reducing lead times and starting material volumes.


A higher throughput haem fractionation assay in 24-well plates, containing at most ten million trophozoites was validated against the original published method using CQ and its robustness was confirmed. It provided a minimum six-fold improvement in productivity and 24-fold reduction in starting material volume. The assay was successfully applied to amodiaquine (AQ), which was shown to inhibit Hz formation, while the antifolate pyrimethamine (PYR) and the mitochondrial electron transporter inhibitor atovaquone (Atov) demonstrated no increase in toxic cellular free haem.




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Flow diagram showing the haem fractionation assay: original flask method (left) versus increased throughput plate method (right). The haem fractionation assay is a cellular fractionation technique based on the ability of neutral aqueous pyridine to selectively form a low spin haem-pyridine complex with free haem in the presence of Hz [13]. The original method was performed in 250 ml culture flasks, testing a single drug concentration at a time and performing spectroscopic measurements in a cuvette [12]. The modified method was performed in 24-well plates, testing several drug concentrations, four replicates at a time and using a multiwell plate reader to record absorbance, resulting in a six-fold increase in output. Immature ring stage parasitized red blood cells were inoculated with several different increasing drug concentrations. After 32 h, mature trophozoites were harvested via saponin lysis of erythrocytes. Following hypotonic lysis and centrifugation, SDS treated soluble Hb was measured in the supernatant as a low spin haem-pyridine complex. The pellet was further treated with SDS and pyridine to solubilize free haem, measured in the supernatant following centrifugation. Hz was measured after solubilizing the pellet in NaOH, neutralizing with HCl and treating with pyridine


Excellent advice for good method development practice can be found in several works [18, 30, 40]. In general, nanocarrier formulations are usually composed of a main population, along with reagents in excess or non-encapsulated drug. A requisite for adequate fractionation and quantification is to avoid non-specific particle-membrane and particle-particle interactions. A passing knowledge of these phenomena can be helpful for a rational experimental design.


The application of multivariate analysis in method development has become a staple of chromatographic techniques such as high-performance liquid chromatography (HPLC) for being robust, efficient, and cost-effective [59]. With AF4 becoming increasingly common there have been several attempts at applying multivariate design to the development of methods for the fractionation of proteins and human serum [60], TiO2 nanoparticles [61], and Ag nanoparticles in natural waters [62]. To the best of our knowledge, it has not been applied yet to the fractionation of nanoformulations. In multivariate experimental design, instead of optimizing one parameter at a time (say, first optimize the eluent composition, then the amount of sample injected, etc.), all the parameters are changed together following a statistical design that allows a better representation of the whole process, also taking into account the combined effect of the parameters. The results obtained in the cited studies are in agreement with the theory and the common knowledge of AF4, for example, restating the importance of the eluent composition and cross-flow over most of the other parameters [62]. Multivariate design, while comports some additional effort, may be beneficial, especially for routine applications.


As much as the fractionation improves particle sizing with respect to batch techniques, it may present some rare drawbacks. For example, batch DLS was able to detect the aggregates present in a formulation of poly(lactic-co-glycolic acid) (PLGA) nanoparticles, while said aggregates disappeared when the formulation was analyzed by SdFFF due to the spatial separation among solutes [76]. In a similar fashion, excessively high flows could induce particle disruption due to shear forces [77].


The reactivity and binding properties of polymers can be assessed as well. Recent works employed AF4-UV to compare the binding affinity of different polyphosphazenes for several model proteins, vaccines antigens, and immune receptors. By measuring the quantity of free proteins, at different protein:polymer ratios, it was possible to estimate the maximum binding and the complexation constant of the polymers. In addition, a sharp increase in polyphosphazenes size, implying intermolecular aggregation, was caused by the proteins with the strongest affinities [105]. AF4-UV was also used to verify that the polyphosphazene-complexed E2 glycoprotein retained its antigenicity by incubating the complex with the HC84.26 antibody. The subsequent AF4 fractionation allowed to identify the formed E2-polyphosphazene-HC84.26 complex, proving that the glycoprotein was conformationally intact [106].


Assessing the amount of the unreacted reagent present in the formulation becomes crucial when it can interfere with the activity of the drug. This is the case, for example, of the polycations, widely exploited as complexing agents for nucleic acids and which likely contribute to the endosomal escape via the proton sponge mechanism [121]. Their determination may be hindered by their strong positive charge, which often results in quantitative adsorption on the negatively charged membrane. To prevent sample loss, it may be required to work with a membrane with low surface charge and an eluent at pH close to its isoelectric point, as reported by Ma et al. for chitosan/DNA complexes [122, 123]. While these conditions are optimal for the detection of the polycations and the cationic nanoparticles via online UV-MALS-DLS detection, they result in the quantitative adsorption of the free nucleic acids on the membrane.


When AF4 is preliminary to proteomic analysis, the preservation of the integrity of the corona is of paramount importance, in addition to respecting the conformation and properties of the proteins. The eluent needs to be chosen so as to match the incubation medium, devoid of the macromolecular fraction: for nanoparticles incubated in plasma or serum, PBS or phosphate buffers (PB) are standard choices for the eluent [39, 182, 183, 189], while protein-free intestinal fluid is an option for orally administered drugs [190]. As mentioned above, fractionation carried out with sufficiently mild separation techniques may lead to the retrieval of the corona in its entirety, while harsher conditions would cause the most loosely bound proteins to be washed away. The applications of multiple techniques may thus help to discern which proteins belong to the hard and soft corona. The few studies that systematically compared the performance of centrifugation and AF4 lead to ambiguous results, regarding which of the two techniques can preserve the corona in its pristine conditions. Actually, there is evidence supporting both claims: while AF4 operates in much milder conditions than centrifugation and it is more adapt to fragile systems [182, 183, 189], it is true that proteins with very fast dissociation rate could be washed off by the flow preventing their re-association to the particles [177,178,179].


Aside from particle size, when coupled to suitable detectors, AF4 can provide information about the efficiency of a formulation process and the presence of unreacted reagents and subpopulations. In the case of polydisperse formulations, AF4 can investigate the correlation between drug loading and nanocarrier size distribution, a sort of information that can be difficultly obtained with other techniques. The effect of biological fluids on nanocarrier stability and drug-release can be studied as well. The lack of a sieve or stationary phase set AF4 apart from other chromatographic and filtration techniques and allows working with more broadly dispersed samples, a crucial advantage when it comes to separating molecular drugs or small proteins from nanocarriers, and nanocarriers from particles of micrometric size. We must stress that AF4 does not substitute other fractionation techniques, but it complements them. 2ff7e9595c


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