Inhibitors of lactoperoxidase enzyme.
\r\n\tCell viability is defined as the number of healthy cells in a sample and proliferation of cells is a vital indicator for understanding the mechanisms inaction of certain genes, proteins, and pathways involved in cell survival or death after exposure to toxic agents. The methods used to determine viability are also common for the detection of cell proliferation. A cell viability assay is performed based on the ratio of live and dead cells. This assay is based on an analysis of cell viability in cell culture for evaluating in vitro drug effects in cell-mediated cytotoxicity assays for monitoring cell proliferation. Various methods are involved in performing a cell viability assay, including the dilution method, surface viable count, roll tube technique, nalidixic acid method, fluorogenic dye assay, and the Trypan Blue Cell Viability Assay. The cell viability assays can determine the effect of drug candidates on cells and be used to optimize the cell culture conditions. The parameters that define cell viability can be as diverse as the redox potential of the cell population, the integrity of cell membranes, or the activity of cellular enzymes.
\r\n\tCytotoxicity is the degree to which a substance can cause damage to a cell. Cytotoxicity assays measure the ability of cytotoxic compounds to cause cell damage or cell death. Cytotoxicity assays are widely used in fundamental research and drug discovery to screen libraries for toxic compounds. The cell cytotoxicity and proliferation assays are mainly used for drug screening to detect whether the test molecules have effects on cell proliferation or display direct cytotoxic effects. In a cell-based assay, it is important to know how many viable cells are remaining at the end of the experiment. There are a variety of assay methods based on various cell functions such as enzyme activity, cell membrane permeability, cell adherence, ATP production, co-enzyme production, and nucleotide uptake activity. These methods could be classified in to different categories: (I) dye exclusion methods such as trypan blue dye exclusion assay, (II) methods based on metabolic activity, (III) ATP assay, (IV) sulforhodamine B assay, (V) protease viability marker assay, (VI) clonogenic cell survival assay, (VII) DNA synthesis cell proliferation assays and (V) Raman micro-spectroscopy.
\r\n\tMedical devices have been widely used in various clinical disciplines and these devices have direct contact with the tissues and cells of the body, they should have good physical and chemical properties as well as good biocompatibility. Biocompatibility testing assesses the compatibility of medical devices with a biological system. It studies the interaction between the device and the various types of living tissues and cells exposed to the device when it comes into contact with patients.
\r\n\t
\r\n\tThe book will cover original studies, reviews, all aspects of Cell Viability and Cytotoxicity assays, methods, Biocompatibility of studies of biomedical devices, and related topics.
Peroxidases (POD: H2O2-Oxydoreductase E.C.1.11.1.7) are oxidoreductase enzymes, which catalyze the reactive oxygen species generated during metabolism, and are converted into harmless molecules [1]. These exhibit antioxidant characteristics and catalyze the oxidation of organic and inorganic substrates with hydrogen peroxide being the electron acceptor [2]. Those enzymes are present in eukaryotes, prokaryotes, and photosynthetic cells [3, 4].
\nLPO is generally found in mammalians such as human [5, 6], bovine [7], buffalo [8], goat [9], sheep [10], llama, cow, camel, and mice milk [6, 11], saliva [12], tears [13], and mammary, salivary, and lachrymal glands [6, 14].
\nPeroxidases are frequently used in the studies of metabolic reactions, enzymatic functions, protein structures [15] and in clinical diagnoses, microanalytic applications, and the food and drug industry [16, 17]. Mammalian POD enzymes are localized in milk, saliva, and tears as lactoperoxidases (LPO) [18] and in leukocytes and platelets as myeloperoxidases [6].
\nProsthetic groups of peroxidase are protoheme and are connected to the apoprotein loosely in contrast to many hemoprote [14]. Firstly, protein portion is synthesized in the organisms bearing peroxidases. However, enzymes are not functionally active. The enzyme gets activated by both apoprotein and hem groups [3, 19]. The general formula of the reaction catalyzed by peroxidases is shown below [3].\n
The H2O2 formed during the metabolism having oxidizing property must be quickly removed. The catalase and peroxidase enzymes exhibiting antioxidant properties play this role in cells [20]. The amount of hydrogen peroxide in the cells is removed by catalase in peroxisomes. In other parts of the cells, the peroxidase enzymes utilize various aromatic components as the substrate to [21] neutralize H2O2 [22].
\nThe characteristics of peroxidase enzyme that is isolated from milk are similar to animal and human peroxidases [23]. It displays 55, 54, and 45% similarity with myeloperoxidase (MPO), eosinophilperoxidase (EPO), and thyroidperoxidase (TPO), respectively. Following xanthine oxidase, lactoperoxidase is the most common enzyme in milk and it is also commonly present in whey which is the liquid remaining after milk has been curdled and strained. Each lactoperoxidase enzyme contains an iron molecule. The conformation of the protein is stabilized by a chelated calcium ion [24–26].
\nThe main function of the LPO enzyme is to catalyze the oxidation of thiocyanate with H2O2 to hypothiocyanite having antimicrobial activity [27, 28].\n
The combined action of these three components, which constitute the ‘lactoperoxidase system’, was defined by Reiter and coworkers [29–31]. The biological significance of the system is protection of the lactating mammary gland and the intestinal tract of newborn infants, thereby providing a natural host defence system against invading microorganisms [23]. The LPO catalyzes the oxidation of some halides (I2 and Br2 but not Cl2) to yield the most oxidizable form of I-, that is, I2 [26].\n
The LPO-H2O2-SCN- system shows bacteriostatic effect and thus prevents bacterial growth and development, whereas the LPO-H2O2-I2 system shows bactericidal potency thus killing bacteria. Both SCN- and I2 have shown strong bactericidal effect when present within the system [32, 33].
\nLactoperoxidase (LPO, E.C. 1.11.1.7) is one of the crucial enzymes in milk with oxidoreductase activity. The peroxidase isolated from milk was given the name lactoperoxidase [23] and was the first enzyme reported to be found in milk [34]. The main function of the enzyme is to catalyze the oxidation of molecules in the presence of hydrogen peroxide and to help production of products with a wide antimicrobial activity. Pseudohalogens, thiocyanates, or halogens should function as second substrates for the enzyme to exhibit such antimicrobial effects [23, 29].
\nThe LPO system shows a significant protective effect in bovine milk. The activation of the system depends on the concentration of the two reactants, thiocyanate and hydrogen peroxide. In the presence of hydrogen peroxide, the system catalyzes the transformation of thiocyanate into hypothiocyanate, which has an antibacterial nature [35–37]. The end products of these compounds are oxidized and hence are safe for human health.
\nMany studies show that this system destroys several bacterial and fungal strains [38–42]. Lactoperoxidase has a broad antifungal activity [43, 44]. Mastitis is a bacterial inflammation in mammals. The effects of different concentrations of thiocyanate-H2O2 medium on several antibacterial and antifungal strains were studied to solve this dairy industry issue [45, 46]. They are capable of reducing bacterial growth by damaging the cell membranes and inhibiting activities of several cytoplasmic enzymes.
\nThe LPO enzyme, a glycoprotein consisting of 8–10% carbohydrate, comprises a chain containing 612 amino acids. It consists of a single polypeptide chain of molecular weight approximately 78 kDa [47]. It is a basic protein containing heme as its prosthetic group with an isoelectric pH value of 9.2 [24–26]. Furthermore, it is very active in acidic pH [48]. It is fairly voluminous as a LPO molecule [49]. The Ca2+ ion stabilizes the enzyme. The Ca2+ ion disappears under pH 5.0 and thus reduces the stability of the enzyme [26].
\nThe biocidal activity of the LPO results from the products of the chemical reactions that it catalyzes. Hypothiocyanate, which is the main product of the reaction, interacts with the thiol groups of various proteins, which is critical for the survival of pathogens. The impact of LPO on bacteria results from the oxidation of sulfhydryl. The oxidation of the -SH groups makes the bacterial cytoplasmic membrane lose its ability to transport glucose, potassium ions, amino acids, and peptides [45].
\nThe biological significance of this enzyme results from the fact that it has a natural protection system against the invasion of microorganisms. Besides this antiviral effect, it is reported that it protects animal cells against various damages and peroxidative effects [23, 29–31]. Lactoperoxidase is a significant agent of the defense system against pathogen microorganisms from the digestive system of neonatal babiess. The LPO enzyme functions as a natural compound of the non-immune biological defense system of mammals and it catalyzes the oxidation of the thiocyanate ion into the antibacterial hypothiocyanate [52].
\nAlthough peroxidases have similar catalytic mechanisms, they are distinguished for their ability to oxidize halides and pseudohalides. For example, only myeloperoxidase is able to oxidize bromine, iodine, and chlorine at neutral pH. Lactoperoxidase, on the contrary, can only oxidize iodine and thiocyanate but it either cannot or can hardly oxidize brome under the same conditions (Figure 1) [53].
\nThe activation mechanism of the peroxidase enzyme.
In the first step of this mechanism, the peroxidase enzyme reacts with one equivalent of the peroxide to form an Fe (IV)-containing compound I that is the porphyrin cation radical. In the second step, the cation radical takes a proton of the substrate and reduced (substrate)-Fe (IV) form, the substrate becomes radical to lost a proton. The compound II takes a proton from the substrate and return the first reducing form. Also radicalic substrate which are formed with interacting each other are polymerization [54].
\nThe LPO enzyme is covalently bound to the heme group proteins, with the bond occurring between the hydroxyl group of the heme group and the carboxyl group of the protein [14]. Approximately 10% of the molecule is composed of carbohydrates and the molecule contains five main potential glycosylation regions and 15 semi-cysteine residues [11, 23, 45]. The heme group at the catalytic center is protoporphyrin IX, which is covalently bound to the polypeptide chain along with the disulfide bridge. The iron compound, which is a part of the heme group, constitutes 0.07% of LPO. The calcium ion is tightly bound to the enzyme, which ensures the molecular conformation and structural integrity of the enzyme [55].
\nThe activation of the natural antibacterial system has been adopted for protecting raw milk. This system is defined as the lactoperoxidase/thiocyanate/hydrogen peroxide (LPO) system. The antibacterial effect of the system on milk is based on the oxidation of SCN− ions catalyzed by the lactoperoxidase enzyme in the presence of H2O2. The short-lived components, OSCN- ions, generated in this oxidation reaction have bacteriostatic effect [56, 57]. The system is recommended in developing countries where there are no sufficient cooling facilities for collection of raw milk and their transportation to processing centers [57].
\nLPO oxidized the -SH groups of the enzymes in bacteria such as hexokinase and glyceraldehyde-3-phosphate dehydrogenase and tends to lose biological functions of these enzymes. As a result, the bacterial cytoplasmic membranes are damaged structurally, and glucose, purine, pyrimidine, and amino acid uptake as well as protein, DNA, and RNA synthesis are blocked. Thus, bacteria growth and proliferation is prevented (Figure 2) [58].
\nAntibacterial effect of the lactoperoxidase enzyme.
Milk and milk products area rich sources of mineral, protein, vitamin, nutritional elements [56, 57]. Lactoperoxidase showed antifungal activity in apple juice and salt solution. In vitro findings also show that the LPO/H2O2/halide system has a strong virucidal activity against HIV-1 [59].
\nIn conditions of iodine deficiency, the level of SCN ions in milk plays a vital role in thyroid function. The studies showed that when milk containing 19 ml/L thiocyanate ion and iodine at 0.1 mg/l concentration is consumed, the thyroid functions of patients with iodine deficiency did not have any negative symptoms [60].
\nThe measurement of the activity is based on the oxidation of 2, 2\'-azino-bis(3-ethylbenzthiazoline-6-sulfonic acid) (ABTS) chromogenic substrate by H2O2 and observation of the increase in the absorbance caused by the resultant colored compound at 412 nm and pH: 6.0 [61]. For determination of LPO activity with spectrophotometric assay, 2.8 mL of ABTS (1 mM) and 0.1 mL of H2O2 (3.2 mM) were pipetted in the spectrophotometer tube of 3 mL. Enzyme solution of 0.1 mL was added and the tube was turned upside down before it was placed in the spectrophotometer. The increase in the absorbance was observed against blank at 412 nm for 3 min and recorded every 60 sec. Phosphate tampon (0.1 M) at pH: 6.0 was used as blank, instead of the enzyme, while all other solutions were used at the same rates. The following formula was used to determine the activity:\n
A | \n: Absorbance (absorbance read at the end of 1 minute) | \n
b | \n: Path length (1 cm) | \n
c | \n: Concentration (μmol/mL) | \n
ε | \n: Extinction coefficient (32400 M−1 × cm−1) | \n
Df | \n: Dilution coefficient | \n
V | \n: Velocity of the reaction (μmol/mL.min.) | \n
One LPO unit (EU) is defined as the amount of LPO that catalyzes the oxidation of l μmol of substrate (ABTS) per min at 20°C [52].
\n2,2’-azino-bis(3-etilbenztiazolin-6-sülfonik asit (ABTS) [62], p-phenylenediamine [63], pyrogallol, guaiacol, catechol, phenols, aromatic amines, ascorbates, epinephrine, and tetramethylbenzidine [6, 14, 47, 52, 61].
\nTo date, several chromatographic methods have been reported about purification and characterization of the LPO enzyme from bovine milk [14]. For example, CM-Cellulose [64], CM-Sephadex ion-exchange chromatography [46, 64], Sephadex G-100 gel filtration chromatography [6, 64], hydrophobic affinity chromatography on Phenyl-Sepharose CL-4B [5], and Toyopearl-SP cation exchange chromatography [64] are among the methods used in the purification of LPO enzyme from bovine milk. LPO was purified in one stage using the affinity technique and sulfanilamide was used as the ligand [65].
\nThe
To find
The Ki and IC50 values show the inhibitory effect on enzyme. The Ki and IC50 values depend on the inhibitory mechanism. IC50 is the inhibitor concentration required for 50% inhibition and Ki value is the constant.
\nTo investigate the inhibitory effects of some inhibitors on LPO and to determine the IC50 values, the LPO activity was measured in the presence of five different concentrations of inhibitor
The inhibitors of the LPO enzyme were identified in studies on the enzyme [52, 67]. Non-selective monoamine reuptake inhibitors consist of opipramol, lofepramime, dibenzepin, protriptyline, melitracen, butriptyline, dimetacrine, dosulepin, and quinipramine; selective serotonin reuptake inhibitors include alaproclate and etoperidone; non-selective monoamine oxidase inhibitors comprise moclobemide, toloxatone, and isocarboxazid; and other antidepressants are viloxazine, minaprine, bifemelane, oxaflozane, and medifoxamine (Table 1).
\n\nMany inhibitors such as sulfanilamides [65], propofol and derivatives [68, 69], some anesthetic drugs [70], some bacteria [46], some phenolic acid compounds and phenolics [71, 77], avermectins [73], adrenaline, melatonin, serotonin and norepinephrine [45, 73, 74], fungi and bacteria [58], antibiotics [75], hydrazines [52], and some thiocarbamide compounds [67] are assayed and reported as a LPO inhibitor in the literature.
\nInhibitor | \nIC50 | \nKi | \nInhibition type | \nPublication | \n
---|---|---|---|---|
L-Adrenaline | \n34.5 mM | \n2.26 mM | \nNoncompetitive | \nSisecioğlu et al. [74] | \n
Ceftazidime pentahydrate | \n0.048 mM | \n0.018 ±0.0035 mM | \nCompetitive | \nSisecioğlu et al. [76] | \n
Prednisolone | \n0.053 mM | \n0.019 ±0.0005 mM | \nCompetitive | \n\n |
Amikacin sulfate | \n0.26 mM | \n0.04 ±0.015 mM | \nCompetitive | \n\n |
Ceftriaxone sodium | \n0.29 mM | \n0.10 ±0.055 mM | \nCompetitive | \n\n |
Teicoplanin | \n1.016 mM | \n0.13 ±0.022 mM | \nCompetitive | \n\n |
Melatonin | \n1.46 mM | \n0.82 ±0.28 | \nCompetitive | \nSisecioğlu et al. [75] | \n
Serotonin | \n1.29 mM | \n0.26 ±0.04 | \nCompetitive | \n\n |
Norepinephrine | \n67.2 mM | \n62 mM | \nNoncompetitive | \nSisecioğlu et al. 2010b | \n
L-Ascorbic acid (Vitamin Q) | \n2.03 mM | \n0.508 ±0.257 mM | \nCompetitive | \nSisecioğlu et al. [43] | \n
Menadione sodium Bisulfate (Vitamin K3), | \n0.025 mM, | \n0.0107 ±0.0044 mM, | \nCompetitive | \n\n |
Folic acid | \n0.0925 mM | \n0.0218 ±0.0019 mM | \nCompetitive | \n\n |
2,6-Dimethylphenol | \n836.67 nM | \n4442 nM | \n\n | Koksal et al. 2014 | \n
2,6-Di-Tbutylphenol | \n10 nM | \n9 nM | \nCompetitive | \n\n |
Di(2,6-Dimethylphenol) | \n6.86 nM | \n0.53 nM. | \nCompetitive | \n\n |
Di(2,6-Di-Tbutylphenol) | \n185 nM | \n48.33 nM | \nCompetitive | \n\n |
Di(2,6-Diisopropylphenol) | \n154 nM | \n19.33 nM | \nCompetitive | \n\n |
Sulphanilamide | \n0.84 nM | \n3.57 nM | \nCompetitive | \nAtasever et al. [65] | \n
Emamectin benzoate | \n4.33 μM | \n6.82±2.60 μM | \nCompetitive | \nKoksal et al. [73] | \n
Eprinomectin | \n16.90 μM | \n4.80±1.95 μM | \nCompetitive | \n\n |
Moxidectin-Vetranal | \n99.00 μM | \n61.31±9.89 μM | \nCompetitive | \n\n |
Abamectin | \n138.60 μM | \n103.73±34.03 μM | \nCompetitive | \n\n |
Doramectin | \n173.20 μM | \n80.14±29.38 μM | \nCompetitive | \n\n |
Ivermectin | \n231.00 μM | \n519.97±47.62 μM | \nNoncompetitive | \n\n |
Caffeic acid | \n393.61 nM | \n430.033±79.04 nM | \nCompetitive | \nGulcin et al. [72] | \n
Ketamine | \n0.29 mM | \n0.019 ± 0.031 | \nNoncompetitive | \nOzdemir et al. [70] | \n
Bupivacaine | \n0.155 mM | \n0.015 ±0.021 mM | \nNoncompetitive | \n\n |
Inhibitors of lactoperoxidase enzyme.
LPO is the second most abundant whey enzyme in bovine milk, [31, 77] and its concentration is approximately 30 mg/L [23]. The peroxidase activity in cow milk is 20 times richer than in human milk and contains 1.2–19.4 units/mL LPO [78]. The mean LPO enzyme activity varies in different species, for example, 1.4 units/mL in cow, 0.34–2.38 units/mL in lamp, 1.5–4.45 units/mL in goat, 0.794 units/mL in buffalo, 22.0 units/mL in pig, and 0.06–0.97 units/mL in human [78].
\nThere is a growing interest in the purification of LPO with increasing applications. The LPO system’s natural biological functions are preferred against antimicrobial chemicals. Lactoperoxidase has many fields of application. It is widely used especially in milk-processing facilities in the milk industry [79]. LPO is used in milk and cheese to reduce the microflora [23]. The LPO enzyme derived from various animal sources has a significant role in the suppression of bacterial growth and helps bacterial inhibition. Inhibition of bacterial growth by the bovine LPO is attributed to the peroxidase system, which contains H2O2 and thiocyanate [9]. The antimicrobial effect of the LPO system occurs naturally in milk. LPO has a bacteriostatic effect on gram-positive and gram-negative bacteria. The antibacterial studies on the LPO enzyme purified from camel milk show that the LPO-thiocyanate and peroxide system leads to significant inhibition of pathogenic bacteria.
\nMost popular applications of the system include food production for preservation of raw milk, pasteurized milk, and cheese milk during storage and/or transportation to the processing plants. The system can be used to avoid the suppression of acidity in yoghurt. In the absence of refrigeration, LPO system is preferable [80] and the system can be used to extend the shelf-life of pasteurized, raw, and cheese milk [79, 81]. This is used for the preservation of emulsions and cosmetics.
\nThe LPO system can ensure an extensive spectrum of antimicrobial properties against bacteria and yeasts when it is composed of LPO, H2O2, SCN-, and I2. Hence, it is preferred in oral care products and cosmetic preservation [82, 83]. The system is used against fish pathogenic bacteria in aquaculture with strong bacterial effects.
\nIn the last decade, a large amount of inelastic neutron and X-ray scattering measurements focused on the study of the collective atomic dynamics of disordered system [1, 2, 3, 4, 5]. Although, across the years, the analysis of the line shape reported in these measurements seldom benefited from the support of a Bayesian inference analysis, the need of this statistical tool is becoming increasingly urgent. As a general premise, it is worth stressing that a scattering measurement somehow resembles a microscope pointed on the dynamics, whose “focus” can be adjusted by suitable choice of the momentum \n
Panel A: The Brillouin light scattering spectral intensity,
One could guess that such a sharp spectral shape does not leave any room for interpretative doubts, also considering that the limiting hydrodynamic spectral profile is exactly known as analytically treatable starting from the application of mass, momentum, and energy conservation laws. Although these statements appear partly true, the very concept of “interpretative doubt” sounds grossly ill-defined before spelling out explicitly the accuracy required to the interpretation one alludes to. Despite its pioneering nature, the quality of the measurements in panel A seems certainly adequate for a precise determination of the side-peak position, probably not much so for a detailed analysis of the spectral tails, which are dominated by the slowly decaying resolution wings. Nonetheless such a shape might still appear a more encouraging candidate for a line shape analysis than its counterpart reported in panel B of \nFigure 1\n which is featured by broad and loosely resolved spectral features, besides a definitely poorer count statistics. Given that the latter result is fairly prototypical of terahertz spectroscopic measurements on simple disordered systems, one might wonder why, thus far, the analysis of these measurements failed to benefit from Bayesian inference methods as routine line shape analysis tools. Aside of hardly justifiable initial mistrusts, a likely explanation is that only recently these spectroscopic techniques transitioned to a mature age in which the very detection of collective modes in amorphous systems can no longer be considered a discovery in itself, and detailed analyses of the spectral shape are more and more common and required. Again, the take-on message of this course of events is that the pivotal issue is the adequacy of a given measurement to provide the sought for information, rather than the quality of the measurement in itself. The unbalance between an unavoidably limited experimental performance and the rapidly increasing interpretative needs dramatically enhances the risk of “good faith overinterpretations” representing a lethal threat for the progress of knowledge.
\n\n
When dealing with neutron or X-ray scattering, the statistical accuracy of spectral acquisition is the primary concern. For the most varied reasons, e.g., relating to the scattering properties of the sample, the integration time, or the count rate of the measurement, the achieved count statistics may either be adequate for a rigorous data analysis or, as often happens, not as good as we would like it to be. In the latter case, the experimental data might not be accurate enough to tell us everything about the physical problem under scrutiny. They could tell us something, but not everything! This is why we need a solid inferential method capable of extracting the maximum amount of information from the data acquired and possibly providing us with a quantitative probabilistic evaluation of the different models that are compatible with the data at hand. Especially when nothing or very little is known about a specific sample or system, the point is, given the observed data, how plausible is a specific model? What is the precision of the conclusions drawn from this model? Are there other possible interpretations of the data at hand? To what extent are different models and interpretations supported by the observed data?
\nA Bayesian inferential approach provides answers to all these questions on a probabilistic basis, along with a sound criterion to integrate any prior knowledge in the process of data analysis. Bayesian inference, in fact, recognizes the importance of including prior knowledge in the analysis. When we do have well-established prior knowledge about a sample property or a general law a physical phenomenon must comply with, it would be insane and pointless not to use this information. Such a prior knowledge, in fact, can protect us from the risk of making mistakes in the description of experimental data, hence in their interpretation. In the Bayesian framework, prior knowledge takes the form of probability statements so that different probabilities, ranging from zero to one, can be attributed to competitive explanations of the data. In this way, less probable explanations are not excluded a priori but simply given a smaller prior probability. The a priori probability of different explanations is then updated, through the Bayes theorem, based on the new information provided by the data. The results of this analysis, thus, assume the form of posterior probabilities. On this basis, one can easily establish which model is most supported by both data and prior knowledge, what are the posterior probabilities of alternative models and those of their parameters, and which provides a ground to appreciate the precision of their estimates. In addition, Bayesian methods naturally embody the Occam’s razor principle, thus favoring simpler models over unnecessarily complex ones. Last but not least, Bayesian estimation algorithms are generally less affected by the presence of local optima in the parameter space and are not sensitive to the starting values used to initialize the estimation process.
\nThe aim of this chapter is to illustrate how Bayesian inference can be used in X-ray and neutron scattering applications. The Bayesian approach proposed here is implemented through an estimation algorithm, which makes use of Markov chains Monte Carlo (MCMC) methods [9, 10] integrated, where appropriate, with a reversible jump (\n
Depending on the problem at hand, our approach to data analysis can be very different. Imagine that we want, as a toy or teaching example, to measure either the neutron or the X-ray scattering spectrum from a system whose spectrum is well-known and its interpretation unanimously agreed. For instance, we aim at extracting the phonon dispersion curve from the thoroughly measured spectral density \n
More often, we face a different problem, as we want to measure for the first time a certain system on which we might not have previous knowledge. Alternatively, we could have prior knowledge about that same system, yet in different thermodynamic or environmental conditions— for instance, a liquid either in bulk or confinement geometries—and possible effects of these peculiar conditions are under scrutiny. Changes could also be very small, and, since detecting them is the focus of our research, it is essential to take the most impartial and noninvasive approach. In this second situation, it would be desirable not to rely too heavily on previous results when choosing the model and to allow the measurement to reveal possible new features.
\nThe two situations mentioned above notably differ in the amount of information available on the system before analyzing the data. In the first case, we have a complete knowledge of the system, while, in the second case, this knowledge is partial or even lacking at all. In this second situation, a traditional approach would consist in either best fitting a model we deem adequate for the data, e.g., well-assessed for the considered sample, albeit only in different thermodynamic or environmental conditions, or fitting competing models to establish the one best performing based on criteria agreed upon, e.g., the chi-square value. Following the first path, we hinge too much on a specific model and on previous partial knowledge, thus jeopardizing the chance of new findings. On the other hand, the second path would be less coercive at the cost of completely ignoring previous partial knowledge. In addition, the model chosen would be simply the one providing the best fit, but no assessment can be made on the plausibility of this or any other fitting model, based on the data measured. Conversely, a Bayesian approach to data analysis would, instead, allow to assign a different prior probability to the different models (accounting for the uncertainty of available information on the system) and, then, revise these probabilities in the light of the data to deliver the posterior probability of each model, conditional on the data at hand.
\nThe Bayes theorem stems from the theorem of compound probability and from the definition of conditional probability. If we consider two events \n
where \n
From Eq. (1), we immediately get:
\nwhich is nothing else than the Bayes theorem.
\nLet us now consider \n
where \n
Let us consider the different elements of Eq. (4), starting with the prior distribution (or simply prior) \n
Just to make a few examples, it might be possible that a certain parameter \n
In other situations, the information available on the parameters might be more vague. For example, we might simply know that a certain parameter must be nonnegative or that it must range in a limited interval, as often the case of neutron scattering hampered by severe kinematic constraints. Nonnegative parameters can be a priori assumed to follow, for example, a truncated Gaussian or a gamma distribution, and, if no other information is available, the prior distribution will be adjusted to make allowance for a large parameter variability, reflecting the noninformative initial guess. Parameters having random or hardly quantifiable variations within limited windows can be assumed to approximately follow a uniform distribution over such a window. Also, whenever feasible, any mutual entanglement between parameters, as well as any selection, conservation, or sum rule, should be embodied in a usable distribution function complementing our prior knowledge \n
Notice that, even if it is common practice to assume that the parameters are a priori independently distributed, correlation between them can be naturally induced by the data, through the combination of the likelihood and the prior. Parameters can be a posteriori correlated, even if they are a priori independent.
\nThe likelihood function is the joint probability of the observed data, conditional on the model adopted and its parameter values. Notice that for continuous data, the likelihood becomes a density of probability. Let \n
The left side of Eq. (6) is the likelihood function for the observed sample \n
To be more specific, we can consider spectroscopic data. The observable directly accessed by a spectroscopic measurement is the spectrum of the correlation function of density fluctuation, or dynamic structure factor \n
where \n
Under the assumption above, the likelihood function is:
\nConditional on a certain value of the parameter vector \n
The term on the left-hand side of Eq. (3) is the joint posterior distribution of the model parameters, given prior knowledge and measured data, i.e.,
Sketch of how the prior distribution and therefore our prior knowledge about a model parameter are changed by the data evidence.
The term in the denominator of Eq. (3):
\nis generally called the marginal likelihood and represents the probability of observing the measured data \n
For this reason, Bayesian inference usually needs to resort to MCMC methods to simulate the joint posterior distribution. MCMC algorithms, in fact, allow to draw values from distributions known up to a normalizing constant, as is often the case for \n
To illustrate an interesting point, let us go back to the example considered before, in which we want to analyze spectroscopic data that can be modeled as in Eq. (7) and for which the likelihood is given in Eq. (8). Imagine to have no prior information at all on the parameters of the model so that the only sensible choice for the prior is a uniform distribution on the parameter space. Then, from Eqs. (8) and (10), it follows that:
\nwhich implies that the posterior distribution is a multivariate Gaussian. As already mentioned, parameters can be estimated taking the mean of the posterior distribution, which, for a Gaussian distribution, corresponds to the median, mode, and maximum of the distribution. Therefore Bayesian parameter estimates are obtained as those values of \n
Despite the asymptotic equivalence, sometimes parameters are much easier estimated in a Bayesian rather than in a frequentist perspective. Frequentist estimation, in fact, is generally based on least squares or maximum likelihood methods, and this might be a problem in the presence of local optima. If, for example, the starting values of the parameters, needed to initialize the optimization algorithm, are close to a local optimum, the algorithm might be trapped in this suboptimal solution. As a consequence, different starting values might determine different solutions and, thus, parameter estimates. The Bayesian estimate of a parameter, as stated before, is instead obtained as the mean of its posterior distribution, marginalized with respect to all other parameters. This estimation procedure does not involve any minimization or maximization, and, thus, the fitting algorithm does not risk to get trapped in local optima, and the results are independent from starting values used in the MCMC algorithm used to simulate the posterior distribution (see Section 3.6). It might happen, obviously, that the posterior of one or more parameters is bimodal or multimodal. The presence of different parameter regions with high posterior density might suggest that the data show some evidence in favor of a more complex model but not enough for this model to have the highest posterior probability. In this case, it is not reasonable to use the mean as a point estimate for the parameters, since it might fall in a low posterior density region, and the mode of the posterior distribution can be used in its place. In such situations of posterior multimodality, it is evident how the whole posterior distribution conveys a much richer information than the simple parameter estimate.
\nEven if Bayesian and classical analysis asymptotically give the same results, Bayesian results always have a probabilistic interpretation, and this is particularly relevant when we need to compare different models and determine, for instance, the number of spectral excitations (in the frequency domain) or the number of relaxations (in the time domain). In addition, the Bayesian method represents a natural implementation of the Occam’s razor [18, 19, 20]: this principle is intrinsic to Bayesian inference and is a simple consequence of the adoption of the Bayes theorem. In model choice problems, in fact, the posterior probabilities of the different models naturally penalize complex solutions with respect to simple ones, thus conforming to the parsimony principle.
\nTo see this, consider Eq. (4), and imagine that the parameter vector also includes a model indicator parameter \n
Now, consider for simplicity just two possible models, the first one, denoted as \n
As already stated, Bayesian inference completely relies on the joint posterior distribution \n
Parameter updating.
where \n
Concerning the proposal distribution, this should be chosen as a distribution from which it is easy to sample. It could be, for instance, a normal distribution centered on the current value of the parameter and with a certain variance which can be adjusted and used as a tuning parameter. This locution alludes to the circumstance that adjustments of this parameter can literally tune the step of the parameter updates. For a normal proposal distribution, a large variance allows the new value \n
When the parameter vector also includes a model indicator parameter, a further move needs to be considered to update this parameter and to allow the algorithm to explore different models. This move is a reversible jump [11] step, which is specifically designed to allow the Markov chain to move between states having different dimensions (since the dimension of the parameter space varies accordingly to the model considered).
\nAs a final remark, consider that when the MCMC algorithm reaches convergence, after a so called “burn-in” period, the draws not only effectively represent samples from the joint posterior distribution but are also theoretically independent from the starting values of each parameter. Few examples about this point are shown in \nTable 1\n of Ref. [12]. Notice, however, that the time required to reach convergence might vary a lot depending on the data and the prior. For example, peaked unimodal posterior distributions (i.e., highly informative data) generally speed up convergence, as well as the availability of an important prior information, which reduces the size of the effectively accessible parameter space. On the contrary, the presence of many high posterior density regions can hinder and slow down convergence.
\n\n | \n\n | \n
---|---|
1 | \n8.47 | \n
2 | \n61.83 | \n
3 | \n23.91 | \n
4 | \n4.41 | \n
5 | \n1.12 | \n
6 | \n0.26 | \n
Posterior distribution for the number of time correlation decay channels for a polymer solution of polyethylene glycol with a molecular weight of \n
One of the models commonly used to analyze either neutron or X-ray scattering data is the so-called damped harmonic oscillator (DHO) profile, which we report here below:
\nwhere \n
To fit the experimental data, the model in Eq. (14) needs to be convoluted with the instrument resolution, and it can conceivably sit on top of an unknown linear background. Overall, the final model used to approximate the measured line shape is given by:
\nwhere \n
For IXS, Eqs. (14–16) are still formally valid although the instrument resolution function has usually a slightly more complex shape which appears in the convolution of Eq. (15) either as approximated by an analytical model or measured from the signal of an almost elastic scatterer; obviously, in the latter case, the convolution is computed numerically. The final model is further corrupted by an additive Gaussian noise, having a variance that, for instance, can be taken proportional to each data point. Thus, the experimental data points are given by:
\nwith
\nwhere \n
The whole parameter vector for the model in Eq. (17) is \n
Bayesian inference is, then, based on the joint posterior of the whole parameter vector \n
Once the convergence is attained, after a burn-in period, at each sweep \n
from the joint posterior \n
where each row is a particular draw of the whole parameter vector \n
Once a particular model with, let us say, \n
In assessing convergence, a valuable tool is provided by trace plots, which show the sampled values of a parameter over the sweeps of the algorithm. Ideally, a trace plot should exhibit rapid up-and-down variation with no long-term trends or drifts. Imagining to break up this plot into a few horizontal sections, the trace within any section should not look much different from the trace in any other section. This indicates that the algorithm has converged to the posterior distribution of the parameters. Other convergence criteria can be found, for example, in Ref. [23]. \nFigure 4\n shows the trace plots of three DHO-mode frequencies \n
Typical trace plots for the three DHO-mode frequencies as obtained after the first 1000 (a), 10000 (b) and 100000 (c) sweeps of the algorithm for IXS data on pure water at room temperature and at a wave vector transfer
In \nFigure 5\n, we report an example of Bayesian analysis applied to neutron Brillouin scattering data from liquid gold [12] at different values of the momentum transfer \n
Dynamic structure factor of liquid gold at five
Even in this straightforward case, however, additional insights can be obtained from the posterior distributions delivered by the Bayesian inference. For example, in \nFigure 6\n, it can be noticed that, as the value of \n
Posterior probability for the number of modes
To investigate these issues, one can look, for example, at the posterior distributions for the excitation frequency \n
Simulated posterior distributions for the excitation frequency
The shape of these posterior distributions provides a measure of the precision with which the parameter is estimated. For example, \n
Data discussed in Ref. [25] provide another example of the efficacy of Bayesian inference in enforcing the parsimony principle. Specifically, we refer to the case of an IXS measurement from a suspension of gold nanoparticles in water which has been analyzed with a model similar to the one in Eq. (14), yet with the DHO terms replaced by Dirac delta functions, due to the extremely narrow width of the measured excitations. For all \n
Posterior probability for the number of
As a further remark, we would like to stress again the fact that results from Bayesian inference are always to be interpreted in a probabilistic nuance. For instance, we stated before that the oscillation mode \n
Time correlation function decays can be modeled in terms of an expansion of the intermediate scattering function \n
where \n
The value of \n
Let us consider one of the datasets in Ref. [15], representing the time correlation decay of a polymer solution of polyethylene glycol with a molecular weight of \n
The most visited model is the one with two exponential functions. The fit is shown in the figure below (\nFigure 9\n).
\n\n
The values reported in \nTable 1\n clearly show that the posterior distribution of \n
Posterior probability for the number of
When we model a spectroscopic dataset through a homogeneous mixture, e.g., a linear combination of exponentials, Lorentzians or DHO functions, the posterior distribution for the number of components always has at least a maximum, unless the data are so scarcely informative that the posterior for \n
\n
Let us introduce a quantity which could resemble the \n
which measures the distance between the experimental data and the best fit determined with the \n
\n | \n\n | \n
---|---|
\n\n | \n\n\n | \n
\n\n | \n\n\n | \n
\n\n | \n\n\n | \n
\n\n | \n\n\n | \n
\n\n | \n\n\n | \n
\n\n | \n\n\n | \n
Values of the quantity \n
Nevertheless, \n
In summary, we have here shown some of the opportunity offered by a Bayesian inference analysis of experimental results and, in particular, those obtained with spectroscopic methods. As possible future development, it appears very promising the opportunity of applying similar methods to the joint analysis of complementary time or frequency-resolved measurements. Also, we can envisage the use of more informative priors implementing the fulfillment of sum rules of the spectra or any other known physical constraint of the measurement. We are confident that, in the long run, these methods will improve the rigor of routine data analysis protocols, supporting a probability-based, unprejudiced interpretation of the experimental outcome.
\nThis work used resources of the National Synchrotron Light Source II, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-SC 0012704. The open access fee was covered by FILL2030, a European Union project within the European Commission’s Horizon 2020 Research and Innovation programme under grant agreement N°731096.
\nWe would like to thank U. Bafile, E. Guarini, F. Formisano, and M. Maccarini for the very stimulating discussions.
\nAuthors are listed below with their open access chapters linked via author name:
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Pati",coverURL:"https://cdn.intechopen.com/books/images_new/6778.jpg",editedByType:"Edited by",editors:[{id:"174737",title:"Dr.",name:"Abhijit",middleName:null,surname:"Ray",slug:"abhijit-ray",fullName:"Abhijit Ray"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"5913",title:"Redox",subtitle:"Principles and Advanced Applications",isOpenForSubmission:!1,hash:"bc323da5a080b0f626da4c6099b5193a",slug:"redox-principles-and-advanced-applications",bookSignature:"Mohammed Awad Ali Khalid",coverURL:"https://cdn.intechopen.com/books/images_new/5913.jpg",editedByType:"Edited by",editors:[{id:"137240",title:"Prof.",name:"Mohammed",middleName:null,surname:"Khalid",slug:"mohammed-khalid",fullName:"Mohammed Khalid"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"5381",title:"Ionic Liquids",subtitle:"Progress and Developments in",isOpenForSubmission:!1,hash:"e87c37c4d014c11121453605e6d0f37a",slug:"progress-and-developments-in-ionic-liquids",bookSignature:"Scott Handy",coverURL:"https://cdn.intechopen.com/books/images_new/5381.jpg",editedByType:"Edited by",editors:[{id:"42658",title:"Prof.",name:"Scott",middleName:null,surname:"Handy",slug:"scott-handy",fullName:"Scott Handy"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4599",title:"Ion Exchange",subtitle:"Studies and Applications",isOpenForSubmission:!1,hash:"2e45cfed818bc38f70a214561b0a1e21",slug:"ion-exchange-studies-and-applications",bookSignature:"Ayben Kilislioglu",coverURL:"https://cdn.intechopen.com/books/images_new/4599.jpg",editedByType:"Edited by",editors:[{id:"139903",title:"Prof.",name:"Ayben",middleName:null,surname:"Kilislioglu",slug:"ayben-kilislioglu",fullName:"Ayben Kilislioglu"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4524",title:"Field Effect Electroosmosis",subtitle:"A Novel Phenomenon in Electrokinetics and its Applications in Capillary Electrophoresis",isOpenForSubmission:!1,hash:"565f91c26b8f3a3c73d9e28145d7b269",slug:"field-effect-electroosmosis-a-novel-phenomenon-in-electrokinetics-and-its-applications-in-capillary-electrophoresis",bookSignature:"Kiumars Ghowsi",coverURL:"https://cdn.intechopen.com/books/images_new/4524.jpg",editedByType:"Edited by",editors:[{id:"145098",title:"Prof.",name:"Kiumars",middleName:null,surname:"Ghowsi",slug:"kiumars-ghowsi",fullName:"Kiumars Ghowsi"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"2437",title:"Electrochemistry",subtitle:null,isOpenForSubmission:!1,hash:"4d77896d92a0b2f69168537e0b57c8ab",slug:"electrochemistry",bookSignature:"Mohammed A. A. Khalid",coverURL:"https://cdn.intechopen.com/books/images_new/2437.jpg",editedByType:"Edited by",editors:[{id:"40312",title:"Dr.",name:"Mohammed",middleName:"Awad",surname:"Khalid",slug:"mohammed-khalid",fullName:"Mohammed Khalid"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3476",title:"Developments in Electrochemistry",subtitle:null,isOpenForSubmission:!1,hash:"a0d070ce0c17777f7605b91a0beac07e",slug:"developments-in-electrochemistry",bookSignature:"Jang H. Chun",coverURL:"https://cdn.intechopen.com/books/images_new/3476.jpg",editedByType:"Edited by",editors:[{id:"164636",title:"Prof.",name:"Jang Ho",middleName:null,surname:"Chun",slug:"jang-ho-chun",fullName:"Jang Ho Chun"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"2549",title:"Ion Exchange Technologies",subtitle:null,isOpenForSubmission:!1,hash:"d5d70a346ca433c501e5968f54286740",slug:"ion-exchange-technologies",bookSignature:"Ayben Kilislioğlu",coverURL:"https://cdn.intechopen.com/books/images_new/2549.jpg",editedByType:"Edited by",editors:[{id:"139903",title:"Prof.",name:"Ayben",middleName:null,surname:"Kilislioglu",slug:"ayben-kilislioglu",fullName:"Ayben Kilislioglu"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"2264",title:"Scanning Probe Microscopy",subtitle:"Physical Property Characterization at Nanoscale",isOpenForSubmission:!1,hash:"5a969e2a47b3e08d1e8c1ff3c3503fcf",slug:"scanning-probe-microscopy-physical-property-characterization-at-nanoscale",bookSignature:"Vijay Nalladega",coverURL:"https://cdn.intechopen.com/books/images_new/2264.jpg",editedByType:"Edited by",editors:[{id:"105093",title:"Dr.",name:"Vijay",middleName:null,surname:"Nalladega",slug:"vijay-nalladega",fullName:"Vijay Nalladega"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}],booksByTopicTotal:20,seriesByTopicCollection:[],seriesByTopicTotal:0,mostCitedChapters:[{id:"40697",doi:"10.5772/51040",title:"Selective Removal of Heavy Metal Ions from Waters and Waste Waters Using Ion Exchange Methods",slug:"selective-removal-of-heavy-metal-ions-from-waters-and-waste-waters-using-ion-exchange-methods",totalDownloads:19274,totalCrossrefCites:36,totalDimensionsCites:93,abstract:null,book:{id:"2549",slug:"ion-exchange-technologies",title:"Ion Exchange Technologies",fullTitle:"Ion Exchange Technologies"},signatures:"Zbigniew Hubicki and Dorota Kołodyńska",authors:[{id:"42116",title:"Dr.",name:"Dorota",middleName:null,surname:"Kołodyńska",slug:"dorota-kolodynska",fullName:"Dorota Kołodyńska"},{id:"141883",title:"Prof.",name:"Zbigniew",middleName:null,surname:"Hubicki",slug:"zbigniew-hubicki",fullName:"Zbigniew Hubicki"}]},{id:"33450",doi:"10.5772/37583",title:"Measurement of the Nanoscale Roughness by Atomic Force Microscopy: Basic Principles and Applications",slug:"measurement-of-the-nanoscale-roughness-by-atomic-force-microscopy-basic-principles-and-applications",totalDownloads:21229,totalCrossrefCites:20,totalDimensionsCites:88,abstract:null,book:{id:"2282",slug:"atomic-force-microscopy-imaging-measuring-and-manipulating-surfaces-at-the-atomic-scale",title:"Atomic Force Microscopy",fullTitle:"Atomic Force Microscopy - Imaging, Measuring and Manipulating Surfaces at the Atomic Scale"},signatures:"R.R.L. De Oliveira, D.A.C. Albuquerque, T.G.S. Cruz, F.M. Yamaji and F.L. Leite",authors:[{id:"1164",title:"Dr.",name:"Fabio",middleName:"Lima",surname:"Leite",slug:"fabio-leite",fullName:"Fabio Leite"},{id:"136651",title:"MSc.",name:"Ricardo",middleName:null,surname:"De Oliveira",slug:"ricardo-de-oliveira",fullName:"Ricardo De Oliveira"},{id:"136652",title:"M.Sc.",name:"Diego",middleName:"Aparecido Carvalho",surname:"Albuquerque",slug:"diego-albuquerque",fullName:"Diego Albuquerque"},{id:"136653",title:"Prof.",name:"Tersio",middleName:null,surname:"Cruz",slug:"tersio-cruz",fullName:"Tersio Cruz"},{id:"136657",title:"Prof.",name:"Fabio",middleName:null,surname:"Yamaji",slug:"fabio-yamaji",fullName:"Fabio Yamaji"}]},{id:"49054",doi:"10.5772/60952",title:"Anion Exchange Resins as Effective Sorbents for Removal of Acid, Reactive, and Direct Dyes from Textile Wastewaters",slug:"anion-exchange-resins-as-effective-sorbents-for-removal-of-acid-reactive-and-direct-dyes-from-textil",totalDownloads:3146,totalCrossrefCites:24,totalDimensionsCites:46,abstract:"Coloured wastewaters are a consequence of batch processes in both dye-manufacturing and dye-consuming industries. Dyes are widely used in a number of industries, such as textile and leather dyeing, food, cosmetics, paper printing, gasoline, with the textile industry as the largest consumer. Dyeing as a fundamental operation during textile fibre processing causes the production of more or less coloured wastewaters, depending on the degree of fixation of dyes on substrates, which varies with the nature of substances, desired intensity of coloration, and application method. Dye bearing effluents are considered to be a very complex and inconsistent mixture of many pollutants ranging from dyes, dressing substances, alkalis, oils, detergents, salts of organic and inorganic acids to heavy metals.Thus after dyeing wastewaters are characterized not only by intensive and difficult for removal colour but also by high pH, suspended and dissolved solids, chemical and biochemical oxygen demands. Ion exchange is a very versatile and effective tool for treatment of aqueous hazardous wastes including dyes. The role of ion exchange in dye effluents treatment is to reduce the magnitude of hazardous load by converting them into a form in which they can be reused, leaving behind less toxic substances in their places or to facilitate ultimate disposal by reducing the hydraulic flow of the stream bearing toxic substances. Another significant feature of the ion exchange process is that it has the ability to separate as well as to concentrate pollutants. Taking into account high capacity and selectivity of ion exchange resins for different dyes, they seem to be proper materials for dyes sorption from textile effluents. The aim of the paper is to study the removal of the acid, reactive and direct textile dyes such as C.I. Acid Orange 7, C.I. Reactive Black 5 and C.I. Direct Blue 71 on the commercially available anion exchangers (Lewatit MonoPlus MP 62, Lewatit MonoPlus MP 64, Lewatit MonoPlus MP 500, Lewatit MonoPlus M 500, Amberlite IRA 67, Amberlite IRA 478RF, Amberlite IRA 458 and Amberlite IRA 958) differing not only in basicity of the functional groups but also in composition and structure of the matrix. Comparison of the sorption parameters obtained by the batch method taking into account influence of phase contact time, dyes initial concentration and solution pH were discussed in detail. Desorption conditions depending on the dyes sorption mechanism were also presented. Influence of the auxiliaries typically present in textile effluents such as inorganic electrolytes and different surfactants on the amounts of dyes retained by the anion exchangers was presented. The adsorption behaviour of the polyacrylic Amberlite IRA 958 demonstrates that it can be a promising adsorbent for the textile wastewater treatment. The results obtained with raw textile wastewaters purification confirmed this statement.",book:{id:"4599",slug:"ion-exchange-studies-and-applications",title:"Ion Exchange",fullTitle:"Ion Exchange - Studies and Applications"},signatures:"Monika Wawrzkiewicz and Zbigniew Hubicki",authors:[{id:"141883",title:"Prof.",name:"Zbigniew",middleName:null,surname:"Hubicki",slug:"zbigniew-hubicki",fullName:"Zbigniew Hubicki"},{id:"173310",title:"Dr.",name:"Monika",middleName:null,surname:"Wawrzkiewicz",slug:"monika-wawrzkiewicz",fullName:"Monika Wawrzkiewicz"}]},{id:"25422",doi:"10.5772/28293",title:"Electrochemical Polymerization of Aniline",slug:"electrochemical-polymerization-of-aniline",totalDownloads:11436,totalCrossrefCites:3,totalDimensionsCites:29,abstract:null,book:{id:"607",slug:"electropolymerization",title:"Electropolymerization",fullTitle:"Electropolymerization"},signatures:"Milica M. Gvozdenović, Branimir Z. Jugović, Jasmina S. Stevanović, Tomislav Lj. Trišović and Branimir N. Grgur",authors:[{id:"73400",title:"Dr.",name:"Milica",middleName:null,surname:"Gvozdenović",slug:"milica-gvozdenovic",fullName:"Milica Gvozdenović"},{id:"78801",title:"Dr.",name:"Branimir",middleName:null,surname:"Jugović",slug:"branimir-jugovic",fullName:"Branimir Jugović"},{id:"78807",title:"Dr.",name:"Jasmina",middleName:null,surname:"Stevanović",slug:"jasmina-stevanovic",fullName:"Jasmina Stevanović"},{id:"120374",title:"Dr.",name:"Tomislav",middleName:null,surname:"Trišović",slug:"tomislav-trisovic",fullName:"Tomislav Trišović"},{id:"120376",title:"Prof.",name:"Branimir",middleName:null,surname:"Grgur",slug:"branimir-grgur",fullName:"Branimir Grgur"}]},{id:"52110",doi:"10.5772/64935",title:"Electrodeposition from Deep Eutectic Solvents",slug:"electrodeposition-from-deep-eutectic-solvents",totalDownloads:3440,totalCrossrefCites:5,totalDimensionsCites:27,abstract:"Deep eutectic solvents constitute a class of compounds sharing many similarities with properly named ionic liquids. The accepted definition of ionic liquid is a fluid (liquid for T<100 °C) consisting of ions, while DES are eutectic mixtures of Lewis or Brønsted acids and bases. Their most attractive properties are the wide potential windows and the chemical properties largely different from aqueous solutions. In the last few decades, the possibility to electrodeposit decorative and functional coatings employing deep eutectic solvents as electrolytes has been widely investigated. A large number of the deposition procedures described in literature, however, cannot find application in the industrial practice due to competition with existing processes, cost or difficult scalability. From one side, there is the real potential to replace existing plating protocols and to find niche applications for high added-value productions; to the other one, this paves the path towards the electrodeposition of metals and alloys thermodynamically impossible to be obtained via usual aqueous solution processes. The main aim of this chapter is therefore the critical discussion of the applicability of deep eutectic solvents to the electrodeposition of metals and alloys, with a particular attention to the industrial and applicative point of view.",book:{id:"5381",slug:"progress-and-developments-in-ionic-liquids",title:"Ionic Liquids",fullTitle:"Progress and Developments in Ionic Liquids"},signatures:"R. Bernasconi, G. Panzeri, A. Accogli, F. Liberale, L. Nobili and L.\nMagagnin",authors:[{id:"188210",title:"Associate Prof.",name:"Luca",middleName:null,surname:"Magagnin",slug:"luca-magagnin",fullName:"Luca Magagnin"},{id:"194387",title:"MSc.",name:"Roberto",middleName:null,surname:"Bernasconi",slug:"roberto-bernasconi",fullName:"Roberto Bernasconi"},{id:"194388",title:"MSc.",name:"Gabriele",middleName:null,surname:"Panzeri",slug:"gabriele-panzeri",fullName:"Gabriele Panzeri"},{id:"194389",title:"MSc.",name:"Alessandra",middleName:null,surname:"Accogli",slug:"alessandra-accogli",fullName:"Alessandra Accogli"},{id:"194390",title:"MSc.",name:"Francesco",middleName:null,surname:"Liberale",slug:"francesco-liberale",fullName:"Francesco Liberale"},{id:"194391",title:"Prof.",name:"Luca",middleName:null,surname:"Nobili",slug:"luca-nobili",fullName:"Luca Nobili"}]}],mostDownloadedChaptersLast30Days:[{id:"52110",title:"Electrodeposition from Deep Eutectic Solvents",slug:"electrodeposition-from-deep-eutectic-solvents",totalDownloads:3433,totalCrossrefCites:5,totalDimensionsCites:27,abstract:"Deep eutectic solvents constitute a class of compounds sharing many similarities with properly named ionic liquids. The accepted definition of ionic liquid is a fluid (liquid for T<100 °C) consisting of ions, while DES are eutectic mixtures of Lewis or Brønsted acids and bases. Their most attractive properties are the wide potential windows and the chemical properties largely different from aqueous solutions. In the last few decades, the possibility to electrodeposit decorative and functional coatings employing deep eutectic solvents as electrolytes has been widely investigated. A large number of the deposition procedures described in literature, however, cannot find application in the industrial practice due to competition with existing processes, cost or difficult scalability. From one side, there is the real potential to replace existing plating protocols and to find niche applications for high added-value productions; to the other one, this paves the path towards the electrodeposition of metals and alloys thermodynamically impossible to be obtained via usual aqueous solution processes. The main aim of this chapter is therefore the critical discussion of the applicability of deep eutectic solvents to the electrodeposition of metals and alloys, with a particular attention to the industrial and applicative point of view.",book:{id:"5381",slug:"progress-and-developments-in-ionic-liquids",title:"Ionic Liquids",fullTitle:"Progress and Developments in Ionic Liquids"},signatures:"R. Bernasconi, G. Panzeri, A. Accogli, F. Liberale, L. Nobili and L.\nMagagnin",authors:[{id:"188210",title:"Associate Prof.",name:"Luca",middleName:null,surname:"Magagnin",slug:"luca-magagnin",fullName:"Luca Magagnin"},{id:"194387",title:"MSc.",name:"Roberto",middleName:null,surname:"Bernasconi",slug:"roberto-bernasconi",fullName:"Roberto Bernasconi"},{id:"194388",title:"MSc.",name:"Gabriele",middleName:null,surname:"Panzeri",slug:"gabriele-panzeri",fullName:"Gabriele Panzeri"},{id:"194389",title:"MSc.",name:"Alessandra",middleName:null,surname:"Accogli",slug:"alessandra-accogli",fullName:"Alessandra Accogli"},{id:"194390",title:"MSc.",name:"Francesco",middleName:null,surname:"Liberale",slug:"francesco-liberale",fullName:"Francesco Liberale"},{id:"194391",title:"Prof.",name:"Luca",middleName:null,surname:"Nobili",slug:"luca-nobili",fullName:"Luca Nobili"}]},{id:"74147",title:"Electrochemical Impedance Spectroscopy (EIS): A Review Study of Basic Aspects of the Corrosion Mechanism Applied to Steels",slug:"electrochemical-impedance-spectroscopy-eis-a-review-study-of-basic-aspects-of-the-corrosion-mechanis",totalDownloads:2382,totalCrossrefCites:9,totalDimensionsCites:13,abstract:"AC impedance measurements have been applied for over twenty years in electrochemistry and physics to investigate the electrical properties of conductive materials and their interfaces using an external electrical impulse (VOLTAGE, V or CURRENT, I) as driving force. Furthermore, its application has recently appeared to be destined in the Biotechnology field as an effective tool for rapid microbiologic diagnosis of living organism in situ. However, there is no doubt that the electrochemical impedance spectroscopy (EIS) is still one of the most useful techniques around the world for metal corrosion control and its monitoring. Corrosion has long been recognized as one of the most expensive stumbling blocks that concern many industries and government agencies, because it is a steel destructive phenomenon that occurs due to the chemical interaction with aqueous environments and takes place at the interface between metal and electrolyte producing an electrical charge transfer or ion diffusion process. Consequently, it is experimentally possible to determine through the EIS technique the mechanism and control that kinectics of corrosion reactions encounter. First, EIS data is collected through a potentiostat/galvanostat apparatus. After, it is fitted to a mathematical model (i.e. an equivalent electrical circuit, EEC) for its interpretation and analysis, fundamentally seeking a meaningful physical interpretation. Finally, this review reports some basic aspects of the corrosion mechanism applied to steels through the experimental EIS response using Nyquist or Bode plots. Examples are given for different applied electrochemical impedance cases in which steel is under study intentionally exposed to a corrosive aqueous solution by applying a sinusoidal potential at various test conditions.",book:{id:"10054",slug:"electrochemical-impedance-spectroscopy",title:"Electrochemical Impedance Spectroscopy",fullTitle:"Electrochemical Impedance Spectroscopy"},signatures:"Héctor Herrera Hernández, Adriana M. Ruiz Reynoso, Juan C. Trinidad González, Carlos O. González Morán, José G. Miranda Hernández, Araceli Mandujano Ruiz, Jorge Morales Hernández and Ricardo Orozco Cruz",authors:[{id:"114381",title:"Dr.",name:"Jorge",middleName:null,surname:"Morales-Hernandez",slug:"jorge-morales-hernandez",fullName:"Jorge Morales-Hernandez"},{id:"215540",title:"Dr.",name:"Araceli",middleName:null,surname:"Mandujano Ruiz",slug:"araceli-mandujano-ruiz",fullName:"Araceli Mandujano Ruiz"},{id:"268773",title:"Dr.",name:"Hector",middleName:null,surname:"Herrera Hernandez",slug:"hector-herrera-hernandez",fullName:"Hector Herrera Hernandez"},{id:"268774",title:"Dr.",name:"Carlos O.",middleName:null,surname:"Gonzalez Moran",slug:"carlos-o.-gonzalez-moran",fullName:"Carlos O. Gonzalez Moran"},{id:"314695",title:"Dr.",name:"Adriana Mercedes",middleName:null,surname:"Ruiz Reynoso",slug:"adriana-mercedes-ruiz-reynoso",fullName:"Adriana Mercedes Ruiz Reynoso"}]},{id:"62242",title:"Oxygen Reduction Reaction",slug:"oxygen-reduction-reaction",totalDownloads:3951,totalCrossrefCites:8,totalDimensionsCites:17,abstract:"In this chapter, the oxygen reduction reaction (ORR), which is one of the most important reactions in energy conversion systems such as fuel cells, including its reaction kinetics, is presented. Recent developments in electrocatalysts for ORR in fuel cells, including low and non-Pt electrocatalysts, metal oxides, transition metal macrocycles and chalgogenides, are discussed. Understanding of the interdependence of size, shape and activity of the electrocatalysts is evaluated. The recent development of ORR electrocatalysts with novel nanostructures is also reported. The mechanism catalysed by these electrocatalysts is presented. Finally, the perspectives of future trends for ORR are discussed.",book:{id:"6778",slug:"electrocatalysts-for-fuel-cells-and-hydrogen-evolution-theory-to-design",title:"Electrocatalysts for Fuel Cells and Hydrogen Evolution",fullTitle:"Electrocatalysts for Fuel Cells and Hydrogen Evolution - Theory to Design"},signatures:"Lindiwe Khotseng",authors:[{id:"236596",title:"Dr.",name:"Lindiwe",middleName:null,surname:"Khotseng",slug:"lindiwe-khotseng",fullName:"Lindiwe Khotseng"}]},{id:"40709",title:"The Role of Ion Exchange Chromatography in Purification and Characterization of Molecules",slug:"the-role-of-ion-exchange-chromatography-in-purification-and-characterization-of-molecules",totalDownloads:12894,totalCrossrefCites:2,totalDimensionsCites:9,abstract:null,book:{id:"2549",slug:"ion-exchange-technologies",title:"Ion Exchange Technologies",fullTitle:"Ion Exchange Technologies"},signatures:"Hidayat Ullah Khan",authors:[{id:"140538",title:"Dr.",name:"Hidayat",middleName:null,surname:"Khan",slug:"hidayat-khan",fullName:"Hidayat Khan"}]},{id:"49055",title:"Ion Exchange Method for Removal and Separation of Noble Metal Ions",slug:"ion-exchange-method-for-removal-and-separation-of-noble-metal-ions",totalDownloads:2981,totalCrossrefCites:5,totalDimensionsCites:11,abstract:"Ion exchange has been widely applied in technology of chemical separation of noble metal ions. This is associated with dissemination of methods using various ion exchange resins which are indispensable in many fields of chemical industry. Due to small amounts of noble elements in nature and constant impoverishment of their natural raw materials, of particular importance are physicochemical methods of their recovery from the second sources e.g. worn out converters of exhausted gases, chemical catalysts, dental alloys, anodic sludges from cooper and nickiel electrorefining as well as waste waters and running off waters from refineries containing trace amount of noble metals. It should be stated that these waste materials are usually pyro- and hydrometallurgically processed. Recovery of noble metals, from such raw materials requires individual approach to each material and application of selective methods for their removal. Moreover, separation of noble metals, particularly platinum metals and gold from geological samples, industrial products, synthetic mixtures along with other elements is a problem of significant importance nowadays. In the paper the research on the applicability of different types of ion exchangers for the separation of noble metals will be presented. The effect of the different parameters on their separation will be also discussed. The examples of the removal of noble metals chlorocomplexes will also be presented in detail.",book:{id:"4599",slug:"ion-exchange-studies-and-applications",title:"Ion Exchange",fullTitle:"Ion Exchange - Studies and Applications"},signatures:"Zbigniew Hubicki, Monika Wawrzkiewicz, Grzegorz Wójcik, Dorota\nKołodyńska and Anna Wołowicz",authors:[{id:"141883",title:"Prof.",name:"Zbigniew",middleName:null,surname:"Hubicki",slug:"zbigniew-hubicki",fullName:"Zbigniew Hubicki"},{id:"173610",title:"Dr.",name:"Dorota",middleName:null,surname:"Kołodyńska",slug:"dorota-kolodynska",fullName:"Dorota Kołodyńska"}]}],onlineFirstChaptersFilter:{topicId:"505",limit:6,offset:0},onlineFirstChaptersCollection:[],onlineFirstChaptersTotal:0},preDownload:{success:null,errors:{}},subscriptionForm:{success:null,errors:{}},aboutIntechopen:{},privacyPolicy:{},peerReviewing:{},howOpenAccessPublishingWithIntechopenWorks:{},sponsorshipBooks:{sponsorshipBooks:[],offset:8,limit:8,total:0},allSeries:{pteSeriesList:[{id:"14",title:"Artificial Intelligence",numberOfPublishedBooks:9,numberOfPublishedChapters:87,numberOfOpenTopics:6,numberOfUpcomingTopics:0,issn:"2633-1403",doi:"10.5772/intechopen.79920",isOpenForSubmission:!0},{id:"7",title:"Biomedical Engineering",numberOfPublishedBooks:12,numberOfPublishedChapters:98,numberOfOpenTopics:3,numberOfUpcomingTopics:0,issn:"2631-5343",doi:"10.5772/intechopen.71985",isOpenForSubmission:!0}],lsSeriesList:[{id:"11",title:"Biochemistry",numberOfPublishedBooks:27,numberOfPublishedChapters:287,numberOfOpenTopics:4,numberOfUpcomingTopics:0,issn:"2632-0983",doi:"10.5772/intechopen.72877",isOpenForSubmission:!0},{id:"25",title:"Environmental Sciences",numberOfPublishedBooks:1,numberOfPublishedChapters:9,numberOfOpenTopics:4,numberOfUpcomingTopics:0,issn:"2754-6713",doi:"10.5772/intechopen.100362",isOpenForSubmission:!0},{id:"10",title:"Physiology",numberOfPublishedBooks:11,numberOfPublishedChapters:139,numberOfOpenTopics:4,numberOfUpcomingTopics:0,issn:"2631-8261",doi:"10.5772/intechopen.72796",isOpenForSubmission:!0}],hsSeriesList:[{id:"3",title:"Dentistry",numberOfPublishedBooks:8,numberOfPublishedChapters:129,numberOfOpenTopics:0,numberOfUpcomingTopics:2,issn:"2631-6218",doi:"10.5772/intechopen.71199",isOpenForSubmission:!1},{id:"6",title:"Infectious Diseases",numberOfPublishedBooks:13,numberOfPublishedChapters:107,numberOfOpenTopics:3,numberOfUpcomingTopics:1,issn:"2631-6188",doi:"10.5772/intechopen.71852",isOpenForSubmission:!0},{id:"13",title:"Veterinary Medicine and Science",numberOfPublishedBooks:10,numberOfPublishedChapters:103,numberOfOpenTopics:3,numberOfUpcomingTopics:0,issn:"2632-0517",doi:"10.5772/intechopen.73681",isOpenForSubmission:!0}],sshSeriesList:[{id:"22",title:"Business, Management and Economics",numberOfPublishedBooks:1,numberOfPublishedChapters:12,numberOfOpenTopics:2,numberOfUpcomingTopics:1,issn:null,doi:"10.5772/intechopen.100359",isOpenForSubmission:!0},{id:"23",title:"Education and Human Development",numberOfPublishedBooks:0,numberOfPublishedChapters:0,numberOfOpenTopics:2,numberOfUpcomingTopics:0,issn:null,doi:"10.5772/intechopen.100360",isOpenForSubmission:!1},{id:"24",title:"Sustainable Development",numberOfPublishedBooks:0,numberOfPublishedChapters:10,numberOfOpenTopics:4,numberOfUpcomingTopics:1,issn:null,doi:"10.5772/intechopen.100361",isOpenForSubmission:!0}],testimonialsList:[{id:"13",text:"The collaboration with and support of the technical staff of IntechOpen is fantastic. The whole process of submitting an article and editing of the submitted article goes extremely smooth and fast, the number of reads and downloads of chapters is high, and the contributions are also frequently cited.",author:{id:"55578",name:"Antonio",surname:"Jurado-Navas",institutionString:null,profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRisIQAS/Profile_Picture_1626166543950",slug:"antonio-jurado-navas",institution:{id:"720",name:"University of Malaga",country:{id:null,name:"Spain"}}}},{id:"6",text:"It is great to work with the IntechOpen to produce a worthwhile collection of research that also becomes a great educational resource and guide for future research endeavors.",author:{id:"259298",name:"Edward",surname:"Narayan",institutionString:null,profilePictureURL:"https://mts.intechopen.com/storage/users/259298/images/system/259298.jpeg",slug:"edward-narayan",institution:{id:"3",name:"University of Queensland",country:{id:null,name:"Australia"}}}}]},series:{item:{id:"25",title:"Environmental Sciences",doi:"10.5772/intechopen.100362",issn:"2754-6713",scope:"\r\n\tScientists have long researched to understand the environment and man’s place in it. 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