Tools for ADME evaluation.
\\n\\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\\n\\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
Note: Edited in March 2021
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'IntechOpen is proud to announce that 191 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
\n\nThroughout the years, the list has named a total of 261 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\nReleased this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
Note: Edited in March 2021
\n'}],latestNews:[{slug:"intechopen-partners-with-ehs-for-digital-advertising-representation-20210416",title:"IntechOpen Partners with EHS for Digital Advertising Representation"},{slug:"intechopen-signs-new-contract-with-cepiec-china-for-distribution-of-open-access-books-20210319",title:"IntechOpen Signs New Contract with CEPIEC, China for Distribution of Open Access Books"},{slug:"150-million-downloads-and-counting-20210316",title:"150 Million Downloads and Counting"},{slug:"intechopen-secures-indefinite-content-preservation-with-clockss-20210309",title:"IntechOpen Secures Indefinite Content Preservation with CLOCKSS"},{slug:"intechopen-expands-to-all-global-amazon-channels-with-full-catalog-of-books-20210308",title:"IntechOpen Expands to All Global Amazon Channels with Full Catalog of Books"},{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"}]},book:{item:{type:"book",id:"5179",leadTitle:null,fullTitle:"Organic Fertilizers - From Basic Concepts to Applied Outcomes",title:"Organic Fertilizers",subtitle:"From Basic Concepts to Applied Outcomes",reviewType:"peer-reviewed",abstract:"This book, Organic Fertilizers - From Basic Concepts to Applied Outcomes, is intended to provide an overview of emerging researchable issues related to the use of organic fertilizers that highlight recent research activities in applied organic fertilizers toward a sustainable agriculture and environment. We aimed to compile information from a diversity of sources into a single volume to give some real examples extending the concepts in organic fertilizers that may stimulate new research ideas and trends in the relevant fields.",isbn:"978-953-51-2450-4",printIsbn:"978-953-51-2449-8",pdfIsbn:"978-953-51-5436-5",doi:"10.5772/61454",price:139,priceEur:155,priceUsd:179,slug:"organic-fertilizers-from-basic-concepts-to-applied-outcomes",numberOfPages:384,isOpenForSubmission:!1,isInWos:1,hash:"93748f3bd6a9c0240d71ffd350d624b1",bookSignature:"Marcelo L. 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Larramendy, Ph.D., serves as a Professor of Molecular Cell Biology at the School of Natural Sciences and Museum (National University of La Plata, Argentina). He is the appointed Senior Researcher of the National Scientific and Technological Research Council of Argentina and a former member of the Executive Committee of the Latin American Association of Environmental Mutagensis, Teratogenesis and Carcinogenesis. He is the author of more than 450 contributions, including scientific publications, research communications, and conferences worldwide. He is the recipient of several national and international awards. Prof. Larramendy is a regular lecturer at the international A. Hollaender courses organized by the IAEMS and a former guest scientist at NIH (USA) and University of Helsinki (Finland). He is an expert in genetic toxicology and is, or has been, a referee for more than 20 international scientific journals. He was a member of the International Panel of Experts at the International Agency for Research on Cancer (IARC, WHO, Lyon, France) in 2015 for the evaluation of DDT, 2,4-D and Lindane. Presently, Prof. Dr. Larramendy is Head of the Laboratory of Molecular Cytogenetics and Genotoxicology at the UNLP.",institutionString:"National University of La Plata",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"2",totalChapterViews:"0",totalEditedBooks:"18",institution:{name:"National University of La Plata",institutionURL:null,country:{name:"Argentina"}}}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,coeditorOne:{id:"14863",title:"Dr.",name:"Sonia",middleName:null,surname:"Soloneski",slug:"sonia-soloneski",fullName:"Sonia Soloneski",profilePictureURL:"https://mts.intechopen.com/storage/users/14863/images/system/14863.jpg",biography:"Sonia Soloneski has a Ph.D. in Natural Sciences and is an Assistant Professor of Molecular Cell Biology at the School of Natural Sciences and Museum of La Plata, National University of La Plata, Argentina. 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Soto",coverURL:"https://cdn.intechopen.com/books/images_new/8882.jpg",editedByType:"Edited by",editors:[{id:"256002",title:"Ph.D.",name:"Luis",surname:"Soto",slug:"luis-soto",fullName:"Luis Soto"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"66969",title:"ADME Profiling in Drug Discovery and a New Path Paved on Silica",doi:"10.5772/intechopen.86174",slug:"adme-profiling-in-drug-discovery-and-a-new-path-paved-on-silica",body:'Drug discovery and development grew into a wide interdisciplinary field during the last decades and many factors played and play an important role in the successful evolution from a bioactive compound, or so-called new molecular entity (NME), into a potential drug [1]. Herein, we discuss the drug discovery and development (DDD) process where the pharmacokinetic profiling in terms of ADME assessment is concerned. Therefore, we provide a short overview of the
The current state of pharmaceutical DDD estimates that only up to ten compounds out of thousand screened hits would result in optimized leads and enter preclinical testing, with a chance of 9.6% to pass the clinical testing phase [1, 2]. Additionally, the drug approval process is estimated to last in average 15 years, with major expenses in phases II and III of clinical trials, which highlights the drawback a failure in (pre-) clinical testing causes [3, 4, 5, 6], where the overall DDD cost for each drug can reach as high as ~$2.56 billion preapproval rising to $2.87 billion including postapproval investments [6, 7, 8]. From the initial small molecule screened as hit to the optimized lead, a variety of
The drug development phase starts with preclinical testing followed by the clinical stage comprising phase I–III human trials. Each of the phases aims to answer a specific question. Initially, preclinical trials are conducted in animals and can provide information about whether a drug is toxic or not. Compounds that show no toxicity in animals then advance to phase I trials, which will study whether the drug is also safe in healthy humans and provide an initial idea for appropriate dosage. In phase II, the efficacy of the drug is examined in parallel to potential side effects to answer the question if it principally meets the expected performance. Phase II presents the biggest hurdle with a transition success rate as low as 30%. Ultimately, drug candidates enter clinical phase III in which the preliminary results found so far need to be proofed and any adverse reactions monitored to make sure that the drug really helps treating the disease [2, 11].
Starting from the generation of a lead compound assessment, and optimization of pharmacokinetic properties and correlation to pharmacodynamic effects increases in importance as one of the three major attrition causes among toxicity and efficacy [8, 12]. In this sense, it is not surprising that the period between lead and the clinical candidate is sometimes referred to as “valley of death” due to the often occurring failures and dead ends during this time of the DDD process, which results in high costs and missing deadlines [13].
In a long ongoing effort, more and more
Latter approach can save time and resources by eliminating in early stages molecules that have predicted low efficacy against the target or to suggest the next round of chemical modifications [14, 15]. Still, lead generation and/or optimization will eventually also include
When using
Furthermore, the choice of the number and type of molecular descriptors has a high impact, since it influences the accuracy and interpretability of the model. One would expect that using the maximum number of descriptors would be beneficial, but in reality, the risk of overfitting the data or losing the interpretability is a trade-off. This leads to the point that it is fundamental for a “good” model to find the perfect compromise between quality and quantity. Nevertheless, it is crucial to test and train a model and to evaluate its predictability by different means, such as statistical measures and internal and external validation as recommended by organizations as OECD [18], and also includes outlier analysis to reduce the noise in the model. An extensive review of different adequate validation methods is discussed in [19].
As a result of newly achieved advances in computational capability, more complex models and algorithms can now be applied. Despite this, it is still a challenge to create a model for the pharmacokinetic and pharmacodynamic phenomena and interactions within an organism as complex as a mammal, let alone humans [10]. Finally, notwithstanding the apparent linearity, the development of a new chemical entity into a drug is an iterative process, even more, where modeling is concerned, with data from failed attempts being integrated into the new predictions [13].
Pharmacology is a major part of the DDD process and describes the interaction of an organism and the drug. It can be divided into two main branches: while pharmacodynamics (PD) describes what the drug does to the body, pharmacokinetics (PK) is interested in what the body does to the drug [20]. The main processes of PK are absorption, distribution, metabolism, and excretion (ADME), finally complemented by toxicity (ADMET). While ADME tries to maximize the pharmacological performance of a small molecule, toxicology aims to ensure that it causes no harm in any kind of side effect [21].
The big hurdle to overcome is to combine appropriate physicochemical properties of the drug, which would drive its interaction with the organism and show biological activity [22]. Or according to Hodgson: “A chemical cannot be a drug, no matter how active nor how specific its action, unless it is also taken appropriately into the body (absorption), distributed to the right parts of the body, metabolized in a way that does not instantly remove its activity, and eliminated in a suitable manner—a drug must get in, move about, hang around, and then get out” [21].
As already reviewed [23] and suggested by the FDA, PK/PD assessment is one of the main focuses for optimization in the drug development process. This is apparently an idea that was shared among many: whereas ADME evaluation was previously addressed in the late stages of preclinical development, currently it became a major concern throughout the whole DDD process, starting from the very beginnings in drug discovery approaches until the very last steps in lead optimization [21, 24].
For each step in the drug’s path through the body, several parameters determine the destination of the drug. In respect to this, each of those parameters would be addressed directly and individually. Unfortunately, to address experimentally each potential parameter is timely unviable, due to the complexity of the human body where all those parameters influence each other. This is not only restricted to mechanisms within the body between different compartments but also extends to interpersonal variations introduced through gender, age, genetic state, disease, etc. To find an approximation, most of the important variables are indirectly evaluated by either models or surrogates (Table 1). In an approach to characterize the properties of compounds, facilitate calculations, and allow standardization between experiments, descriptors are introduced as numerical representations encoding aspects of the chemical information of a molecule. Examples of descriptors and properties include molecular weight and H-bond donors/acceptors and they can be directly obtained from experimental or generated by computational techniques [25].
Absorption | Physicochemical properties Dissolution and solubility Cell monolayers Artificial membranes | MDCK Caco-2 Transfected cells | Mouse model Knock-out/down mice Humanized mice | QSPR/QSAR pKa log Binding and expression of transporters Inhibition of efflux pumps |
Distribution | PAMPA IAM HAS-coupled (RP-) HPLC | Plasma/tissue binding | Vd Plasma protein binding | Vd Plasma protein binding Activity and expression of transporters |
Metabolism | S9 fraction Liver microsomes Recombinant enzymes | Hepatocytes (HepG2) Isolated tissue Isolated organ | Humanized animals | Half-life Activity and expression of transporters |
Excretion | Isolated tissue Isolated organ Transfected cells | Urine analysis | Half-life prediction |
Tools for ADME evaluation.
For instance, although the perfect approach of PK profiling would also reflect the kinetics of drug administration and concentration at the site of action, most
Each compound possesses individual physicochemical properties, such as solubility or lipophilicity, which are influenced by biochemical properties of the body as the different pH of tissues. Although they can be similar, each compound will behave differently, and it is futile to address
Furthermore, every PK assessment varies depending on the route of administration and requires different models and assays. While some routes depend on absorption mechanisms like oral and transdermal administration, others (i.e., intravenous) directly target the bloodstream and the bioavailability is essentially equal to 100%. Hereafter, we will discuss oral administration parameters of small molecules as the most common form due to many advantages like reliability, safety, price, their experimental approaches, and most common prediction modes [27, 28].
Passive transport across membranes is defined as permeability, which is dependent on lipophilicity, since biological membranes are virtually lipid bilayers, and is by far the most important transport for small molecules, especially in oral absorption [8, 24, 29]. Nonlipophilic compounds normally do not traverse membranes passively, while highly lipophilic molecules run the risk to get stuck within the membranes [30].
Properties utilized for measuring lipophilicity are the logarithm of the partition coefficient (log
Ionizability and lipophilicity provide a strong indication if a compound is likely to be orally absorbed or not [21].
Ultimately, also the molecular size of the compound is involved in successful absorption due to the aforementioned effects on permeability and solubility [31]. Usually, increasing molecular weight by adding new chemical moieties leads to decreased solubility in aqueous solutions [32] and while big lipophilic compounds partition passively along membranes (transcellular), small charged molecules can also cross membranes via tight junctions (paracellular) [26]. For oral absorption in terms of permeability, Lipinski and collaborators already proposed in 1997 [33, 34] that orally active compounds should fit at least three of observed four parameters: molecular weight < 500 g mol−1, log
Despite the criticism and overinterpretation of Lipinski and derived rules, the influence of physicochemical parameters on oral bioavailability and related parameters (as log
As already mentioned, ionizability is one of the most important properties in PK, thus making pKa the physicochemical property with the highest impact.
Early attempts to increase the efficiency of pKa evaluation were reported by Morgan and colleagues by scaling down the classical titration and spectrophotometric methods introducing microscale versions [43].
These alterations, however, could not overcome the principle demands of each technique, which are moderate precision and frequent calibration (potentiometric), and the need for a chromophore within the analyte (spectrophotometric) [44]. Starting in 1998, capillary electrophoresis (CE) was effectively used to determine pKa of many compounds and was further upgraded from Pfizer by implementing pressure-assisted capillary electrophoresis (PACE) as a standard method, which is nowadays readily applied in industry settings showing superior features compared to the aforementioned methods [44, 45]. Other variants such as vacuum-assisted multiplexed capillary electrophoresis also exist (VAMCE) [46]. A different approach better suited for HTS is called pH gradient titration offered from Sirius Analytical Instruments but is still limited due to the UV spectroscopy technology [30].
It is well established that solubility in aqueous media is one of the most important physicochemical properties to be evaluated in oral administration. It is not only necessary for absorption in the GI tract but also a requirement for almost all
On the other hand, generally speaking, lipophilicity is the ability of a compound to dissolve in lipids and/or organic solvents thus being able to pass biological membranes. Descriptors for lipophilicity are the logarithm of the partition coefficient (log
In recent years, a great effort has been made to improve the ability of
General solubility equation as proposed by Yalkowsky and Jain’s [52]:
Modifications in terms of the GSE have been proposed, for instance with the SCRATCH model, which replaces the melting point by molar aqueous activity coefficient, with comparable accuracy (R2 = 0.956, RMSE = 0.859 in a dataset of 883 compounds) [54]. Ali and collaborators suggested replacing the melting point descriptor of the GSE with TPSA, aiming to overcome the issues with compounds with high melting points and also to explicitly take into account the effect of polar and polarizable atoms on the aqueous solubility [55].
The argument that real drugs are actually more soluble than drug-like molecules, filtered by Lipinski’s rule of five [56], pointed out the studies in the direction of more complex models. Indeed, nowadays, the quantitative structure-property relationship (QSPR) models correlating the aqueous solubility with various molecular descriptors are often employed. As an example, Chevillard et al. reported the use of a random forest protocol to select the most accurate model among several available, both in commercial or free software packages, for each compound [57]. They report that the multimodel approach can enlarge the applicability domain given that more accurate results for solubility prediction were obtained in comparison to using individual models. This approach agrees with other reports that consensus of local QSAR models can generate predictive workflows, especially for datasets with large structural diversity [58, 59]. It is worth noting that Lipinski himself recently revisited his own rules [60], in vision of new potential classes of drugs, such as natural products, peptide-like, and fragments, which, despite the validated effect, would defy the original Ro5 limits.
Early pKa measurement proves beneficial in lipophilicity assessment since log
The prediction of ionization state of compounds, which is indicated by the pKa value, is relevant to derive several other physicochemical and ADME properties of drugs, including solubility, lipophilicity, and pharmacokinetic profile. The use of pKa prediction can be placed in two different stages along the DDD, in the beginning with fast models for larger libraries, intending to generate all possible state populations of particular compounds, and/or later on with more refined semiempirical and, computationally expensive, the density functional theory (DFT), in which more accurate ionization states can be accessed. Examples of fast prediction methods for ionization states, which are available as computer programs, are SPARC [61], MoKa [62], and Epik, which use the Hammett and Taft approaches for the pKa prediction [63]. On the other hand, once smaller subsets of molecules are being addressed, the use of semiempirical or density functional theory (DFT) with more computationally expensive models was reported to accurately incorporate the structural features and diversity into the pKa prediction [64, 65].
As already seen, lipophilicity (log
Cell culture methods have been applied to study intestinal absorption for several decades already [66]. Finding the correct model or cell line is crucial to assess the desired parameters such as passive or active transport. In general, it cannot be distinguished between the different transport mechanisms when using cell culture approaches, but several models exist to shift the focus on one of the parameters.
Two main cell lines are in use as models for intestinal absorption: Caco-2 and MDCK cells. Caco-2 cells are derived from a human colorectal carcinoma and possess many of the typical properties of the small intestine, therefore representing a well-established and validated assay system for absorption, permeability, and secretion studies [21, 67]. This assay is mainly used for rank ordering of compounds in terms of oral absorption and permeability in early phases of drug design. Unfortunately, results obtained in different batches and laboratories vary heavily due to several reasons, which make control compound usage necessary and represent a drawback of the technique [26]. Additional disadvantages include long preparation times (about 3 weeks) and no specific permeation mechanism evaluation. Caco-2 assays are usually used as a primary assay followed and complemented by other
As already stated above, transcellular permeation either occurs passively via diffusion of lipophilic molecules or is driven by membrane transporters. Important transporter includes ATP-dependent efflux transporter such as MRP2, BCRP, and P-gp and the organic solute transporter and the multidrug resistance protein 3 (MRP3) on the luminal and basolateral membranes, respectively [26].
Madin-Darby canine kidney (MDCK) cells are an alternative to Caco-2 cell-based assays and the next most common cell line for passive permeability assessment as well as drug-receptor interaction [70]. MDCK cells also are ideal for transfection and overexpression experiments with human transporters and receptors due to the lack of P-glycoprotein [68, 71]. For instance, the MDCK-MDR1 cell line overexpresses the multidrug resistance protein 1 (MDR1, P-glycoprotein) and can be used in concert with other cell-based assays to specifically address the influence of MDR1 in drug efflux [72].
Immobilized artificial membranes (IAMs) were already used very early on for lipophilicity determination and are gaining interest again in recent years for direct permeability measures [25]. IAMs are also intensively used in the measurement of the volume of distribution to mimic
The parallel artificial membrane permeability assay (PAMPA) [73] is a cheap and fast
Although high-throughput applications of newly developed and standardized techniques allow gathering of an exorbitant amount of data, it is crucial to also (cor)relate the physicochemical and biomimetic properties to structural features of the compound. This will facilitate the development of QSPRs and allows the construction of
When dealing with oral administration, it is important to note that the drug is not only confronted with the hurdles of solubility and permeability in the absorption process but is also facing metabolizing mechanisms (
Permeability has a direct influence on the drug absorption rate and, as discussed, despite the several
However, we are far from a model that can predict overall permeability and, the current status, rather focuses on individual compartments and tissues, such as the gastrointestinal (GI) tract, skin, buccal membrane, and the blood-brain barrier (BBB). Since the first BBB permeability correlations with log
Log
Finally, beyond the usual ADME parameters of interest in DDD, there are several other unusual ones that also can be predicted; as examples, we here point the permeability of the models for skin permeability, which evolved from simple diffusion models based on molecular weight and
Oral bioavailability is defined as the amount of drug that reaches the site of action after oral administration and is influenced by factors like drug solubility and dissolution, chemical and enzymatic stability in the gastric and intestinal lumen, interacting luminal contents (food), gastrointestinal transit time, enterocyte permeability, and intestinal and hepatic metabolism [24]. Recently, bioavailability has been also described as the rate and speed of the drug to reach systemic bloodstream, considering the initial formulation as the starting point.
Oral administration includes a pharmaceutical phase—prior to PK and PD phases—that comprises disintegration and dissolution of the dosage form. When using oral dosage forms, the shape and chemical composition (
Following the pharmaceutical phase, absorption is the first step in the pharmacokinetic phase and is defined as the movement of the drug from the site of administration to the bloodstream. The main properties determining the rate of oral absorption for small molecules are permeability and solubility [87].
As such, the rate of dissolution and ionization, which are described by the Noyes-Whitney and Henderson-Hasselbalch equation, respectively, is the key factors in lead optimization for oral administration and is complemented by lipophilicity as an additional factor influencing membrane permeation and solubility of the compound [31].
Dissolution can be expressed by a function of the aqueous solubility of a compound, the surface area of the administered tablet (or the particles in other solid formulation), and a specific dissolution rate constant. Altering any of these parameters directly affects the dissolution profile [26]. While solubility is an endpoint value indicating the amount of a compound that is soluble in a solvent, dissolution describes the kinetic process of a compound being solved in a solvent [88].
On the other hand, ionization reflects if a compound is present in the charged or uncharged state and is at least influenced by two major parameters. The physicochemical property responsible for ionization is the pKa and describes the ionization state of that entity at a given pH. It is also referred to as aqueous ionization constant [30]. Thereby, it is directly influenced by the pH of the environment, the second parameter, which drastically changes on the way through the GI tract, from about pH 1 to 8 in the stomach and ileum, respectively.
The determination of the ionization state of a compound in the gastrointestinal system (stomach, jejunum, ileum, and colon) is crucial for absorption since it not only influences the solubility of a compound but also the lipophilicity and permeability [26, 30, 89]. About 60–70% of all drugs (effective 1999) are ionizable, which underlines the role that ionization plays in ADME assessment [30, 90]. While charged molecules easily dissolve in aqueous systems (GI tract), they do not permeate membranes via passive diffusion and are reliant on active transport. The contrary is true for uncharged molecules, which pass biological membranes passively but show low solubility in aqueous solutions. Mechanisms of drug absorption include passive diffusion, active transport, and receptor-mediated endocytosis, which are influenced by different factors and can themselves influence the bioavailability.
Similar to model and prediction, the absorption of a drug is a complex process, which is influenced not only by the physicochemical properties of drugs themselves but also by the physiological state of the tissue in question. As such, there are a large number of prediction models available, which were generated based on the physicochemical properties involved in the absorption process, such as membrane permeability and drug solubility. These models can help formulation scientists to optimize drugs with poor absorption due to low aqueous solubility.
Initial absorption models can be separated into dispersion and compartmental models [91]. While dispersion models treat the GI as a continuous system, with variable pH and surface area, compartmental models take into account physiological factors such as transporters. The compartmental absorption transit (CAT) was one of the first models to regard distinct physiological properties, such as the minimal absorption in the stomach and colon, while assuming some mathematical simplifications, such as the instant dissolution of the drug and linear kinetics [92]. CAT was further modified as advanced CAT (ACAT), by including nonlinear absorption kinetics and the effects of the first-pass metabolism. ACAT also considers the gastrointestinal tract as nine subsections, each with unique physicochemical properties, such as pH, allowed solubility, particle size, and permeability [93]. Novel developments have included other absorption routes other than the GI, which have been recently included in commercially available software, such as oral absorption for the development of sublingual zolpidem tablets [94]. The absorption constant (Ka, expressed in terms of h−1 min−1), or also called first-order absorption rate constant (to not be confounded with pKa), is employed in most of the aforementioned models and is determined as a result from the changes in mass of absorbable drug over time at the site of administration. Ka can be derived from the decrease in the drug amount of absorbable present at the site of administration over time; however, it is often indirectly determined by the drug amounts measured in the blood and/or urine.
Along physicochemical models, which have a global application, machine-learning techniques were extensively employed to model absorption (as comprehensively reviewed by Kumar et al. [95]) and are inclined to be local models, since they are mostly based on a small, homogeneous dataset that influences their applicability domain.
After being absorbed and entering the circulatory system, the drug moves reversibly between different compartments within the body, which is described as distribution and influenced by several physicochemical properties of the drug and biological factors of the body. One of the most important properties is lipophilicity, and as such log
Volume distribution (Vd) is defined by the ratio between the amount of drug in the body (A) and the drug concentration in plasma (C, comprising both free drug and protein-bound drug):
The parameter describing protein binding is the plasma protein affinity constant Ki. Many efforts to determine distribution led to chromatography-based methods, such as (RP-)HPLC to mimic
A method to address plasma protein binding is the use of HSA and other plasma proteins (
To calculate the Vd “a priori”/nonexperimentally, plasma protein binding, experimental log
Expanding these studies, the work of Lombardo and Jing generated a set of models to predict the Vd in the steady state (Vss), using a dataset of 1096 diverse compounds [104]. They compared models generated by linear (PLS) with nonlinear (Random Forest) models, recommending the latter, with 33 descriptors, as the optimal method for Vss prediction.
The Vd of drugs is greatly influenced by binding to plasma proteins with several machine-learning–based models generated to predict this interaction. Protein-protein interaction (PPI) information derived from molecular docking was employed to derive a PPI-QSAR model for a small dataset of antibiotics (65 unique compounds), which resulted in an accurate model (R2 = 0.86 for the test set) [105]. Additionally, global quantitative models using an array of classification and regression models using physicochemical and molecular descriptors derived from a dataset of 794 compounds were shown to correctly classify the binding status of the test set compounds and could be used as a prescreening [106]. Another recent QSAR study using an extensively curated training set of 967 diverse pharmaceuticals aimed to predict plasma protein-bound fractions (fb) using models generated by six machine-learning algorithms with 26 molecular descriptors [107]. This study is particularly interesting where the applicability domain is concerned allowing to differentiate whether the classification derives from (un-)favorable regions.
del Amo et al. recently reported one of the first QSPR models to predict intravitreal volume of distribution and clearance of small molecules [108]; the model relies on the Log
Recently, as a novel approach bridging the animal experiments with human results, it was shown that in PXB mice, a chimeric mice linage with a humanized liver, plasma concentration-time profiles could be used to infer human’s compound half-life [110].
Volume of distribution is also closely related to half-life and clearance parameters. As the Vd is a relative measurement of the free concentration of drug in the blood, this same amount could be excreted by kidneys in the glomerular filtration (clearance). Consecutively, the rate of clearance (discussed below in Excretion section) directly influences the amount of available drug. Naturally, the concentration of free drug that can bind its molecular target is related to the therapeutic dosage and the half-life of the administered drug (as seen in Eq. (4)).
Half-life definition. Half-life is calculated by a ratio between the Napierian logarithm multiplied by the volume of distribution (Vd) and renal clearance (CL):
Drug metabolism normally involves enzymatic modification or degradation of the compound to facilitate excretion via one of the major clearance organs: liver, kidney, spleen, or bile. While phase I enzymatic reactions include modifications such as oxidation, hydrolysis, and reduction to either introduce a functional group to the molecule or make it accessible, phase II reactions are conjugation mechanisms (
When available, the 3D structure of those proteins could be employed in molecular docking and molecular dynamics simulations aiming to predict the binding affinity of drugs or drug candidates aiming the estimation of a PK profile [112]. The metabolism prediction combines mathematical models to predict whether the target compound could be a substrate of a specific enzyme in combination with metabolism site predictions. Usually, those initial predictions are followed by molecular docking simulations and quantum mechanics simulations due to the dependency of electronics structure from both substrate and enzyme in catalyzed reaction [113, 114].
Nowadays, several attempts have been made to develop
IDSite approach aims to overcome the ligand-based bias of SOM prediction by using it as a part of a large framework, more precisely by combining it with molecular docking, where an atom can be considered a significant SOM by a P450 enzyme when accessible to the reactive heme iron center, and/or quantum calculations, where the candidate atom must have some degree of reactivity in the absence of the enzyme [119]. Similarly, the work of Kingsley et al. combined different approaches into a framework to predict CYP2C9 substrates. They validated the predictions from SMARTCyp in an ensemble docking, followed by a QSAR model to account for influences of both the inherent reactivity of each atom and the physical structure of the CYP2C9 binding site [120]. This combined approach resulted in 88% of true SOMs accurately predicted among the top ranked sites.
Excretion is guided by one of the major clearance organs, and the assessment of clearance behavior sometimes involves isolated organs or tissues [24]. Humans rely on the kidney clearance as a major route for xenobiotic excretion, despite other available routes such as feces, bile, sweat, and breath. The excretion pathways directly impact the concentration of available drugs and are often measured in terms of half-life and the initial administered dose.
The renal clearance of a drug is another important parameter, which is usually employed to predict drug excretion. Experimentally, clearance is defined by the drug concentration drug along a defined time of renal excretion by a linear equation (Eq. (5)).
Equation for renal clearance.
Gombar et al. developed SVM- and MLR-based QSAR models to predict both systemic clearance and apparent volume of distribution from intravenous data [121] using as input structural fingerprints and electro-topological states (so-called E-states), respectively. The model performed with high accuracy, despite the highly diverse initial dataset employed for its generation, which points the importance of those models in early steps of the drug-discovery pipeline.
Also, the work of Kusama et al. established a chemoinformatic-based classification model to predict the major clearance pathways of 141 approved drugs based on four physicochemical parameters: charge, molecular weight, lipophilicity, and protein unbound fraction in plasma, resulting in a final model with an accuracy of 88% [122]. This model approach was further refined by using support vector machine and increasing the number of relevant descriptors [123]. In order to better model the biotransformation processes, often the major triggers of excretion, the work of Berellini et al. used ELASTICO (Enhanced Leave Analog-Structural, Therapeutic, Ionization Class Out) to provide an appropriate sampling during the validation process. Their partial least-square models resulted in a highly accurate model derived from 754 compounds [124].
On another topic, ABCB1, also known as P-glycoprotein (P-gp or MDR1), is a membrane protein member of the ATP-binding cassette (ABC) transporters superfamily. Together with the hERG channel and CYP3A4, P-gp is one of the most widely studied antitarget, where its inhibition could bring consequences for several processes, such as the absorption, distribution, and excretion of drugs. Classical studies used chemometric methods to describe bioavailability in terms of P-gp and CYP enzyme activities, generating QSAR models based on 805 unique drug molecules with high accuracy (R2 = 0.80 for the test set) [125]. Alternatively, an approach to predict P-glycoprotein inhibition using molecular interaction fields, derived from a literature collection of more than 1200 structures, generated a pharmacophore model for competitive P-gp inhibition [126].
The most recent reported studies involving prediction of drug clearance, both from human and rat hepatic
As the pinnacle of ADME
One of PBPK models’ important features is the perspective for the mechanistic and prospective prediction of a drug’s pharmacokinetic profiles. The use of drug-dependent parameters includes, but is not limited to, physicochemical properties, solubility and permeability values, and also the role of individual enzymes and transporters in the metabolism. Those parameters can be determined
Name | Description | Link/reference |
---|---|---|
ADME prediction | ||
vNN-ADMET | Public web server for ADMET property prediction based on 15 nearest neighbor models. | https://vnnadmet.bhsai.org/ [132] |
Swiss-ADME | Public web server for ADME property prediction. It has a very unique Log | http://www.swissadme.ch [133] |
pkCSM | ADME web server based on chemical fragment similarity (the so-called graph-based signatures). | http://biosig.unimelb.edu.au/pkcsm/ [134] |
ADMETlab | Web server using similarity-based ADME calculator models and drug-likeness analyses. | http://admet.scbdd.com/home/index/ [135] |
Schrodinger—QikProp | Calculates pKa; Log | https://www.schrodinger.com/ QikProp, Schrödinger, LLC, NY, 2019 |
DDI-Predictor | DDI-Predictor is able to make quantitative predictions of drug exposure even in cases where the interaction has not been studied yet. | https://www.ddi-predictor.org |
PBPK models and platforms | ||
GastroPlus | Comprises 10 different modules including PBPK modeling and | www.simulations-plus.com |
PKSIM | PBK modeling tool with integrated database of anatomical and physiological parameters for humans, mouse, rat, dog, and monkey. Can model different scenarios depending on the chosen building blocks. | www.systemsbiology.com/products/pk-sim.html |
Simcyp | Incorporates databases of genetic, physiological, and epidemiological information to enable simulation of different populations and species, ultimately is able to predict ADME parameters. | www.simcyp.com |
ADMEWORKS DDI Simulator | As a differential is able to predict drug-drug interactions using nonlinear models. | http://www.fqs.pl/chemistry_ materials_life_science/products/ddi_simulator |
Tools for ADME prediction and PBPK modeling.
Early PBPK models, such as the work of Varma et al., described another layer of complexity by including drug-drug interactions (DDI). The dosing time-dependent model considering the interaction between repaglinide with rifampicin was able to predict repaglinide plasma concentrations along a day. The model also predicted the drug interaction with other CYP3A4 and OATP1B1 inhibitors, which could result in further DDIs. Reports of DDI leading to complications in patients with particular genotype stimulated studies such as the one performed by Fermier et al. [131], where the effects of polymorphic cytochromes provided the basis for a more accurate DDI prediction.
During recent years, larger molecules (LM) have gained in significance and popularity, due to achievements and approvals, as new molecular entities. These “
The main differences between small and large molecules, despite the molecular weight, the number of heavy atoms, and torsions, can be found in the physicochemical properties, such as permeability, oral bioavailability, stability, specificity, and immunogenicity [138, 139]. New parameters, unique for large molecules, are also of interest, such as the physical particle size and the hydrodynamic radius, which has a dramatic effect on the absorption. Both parameters are related to the overall shape and correlate well with MW for globular proteins, but not necessarily for unstructured or highly modified entities. As a result, biologics are normally administered parenterally, only targeting extracellular structures; they are also more likely to trigger an immune response; and their production costs are considerably higher [139]. Interestingly, with the exception of the costs, these disadvantages can potentially be circumvented by appropriate delivery systems, for example, nanoparticle-based delivery to facilitate membrane permeation.
Other parameters, such as charges, which were previously modeled by pKa in case of small molecules, are heavily heterogeneous in LMs. The charge can be represented by the use of isoelectric points (pI), which are calculated from the available amino-acid sequence, and surface charge, which can use individual pKa’s and structural information to be inferred. Overall protein charge often influences the biologic excretion [140], since negatively charged molecules undergo less renal filtration disregarding size effect [141].
While representing difficulties in the development of new molecular entities, the aforementioned properties also offer special advantages that small molecules cannot cover. As such, LMs normally have longer t1/2, slower clearance, and higher selectivity; are multifunctional; and rarely expose drug interactions [139]. Apart from those, it was suggested that only 2–5% of the human genes can be targeted by small molecules, offering a niche for LMs’ application against several diseases [138].
The increasing effort and development of new technologies, driven by the belief in higher success rates, enabled the latest advances in the field [138]. For instance, currently, peptide drugs only account for ~2% of the drug market but are in use in a wide range of diseases such as acromegaly and multiple sclerosis, together with different cancer types such as prostate and breast cancer.
Several other biologics are currently in use, namely monoclonal antibodies (mAbs) and bispecific antibodies (bsAbs), as example agents that activate or enhance the immunologic response. Of special interest in cancer therapy is a subclass of bsAbs, so-called bispecific T-cell engager (BiTEs), which can recruit CD3 cells at the tumor site by binding to both cell types thereby directing the immunological response [142].
Other interesting examples for biologics comprise hormones (e.g., insulin), cytokines (such as erythropoietin, EPO; IL-1; IL-2; IL-6) [143], nucleic acids such as siRNA (ONPATTRO) [144], and aptamers (Pegaptanib) [145]. While such a broad spectrum of molecule classes offers also a wide range of treatments, at the same time, it exacerbates the need for new developments since every molecule type exhibits different properties. In the field of predicting the biologics activity against specific targets, classical modeling tools, such as Monte Carlo sampling, genetic algorithms, docking, and molecular dynamics simulation, were adapted or even developed anew to accommodate the specifics (as extensively reviewed by [146, 147]).
On the other hand, the absence of standard techniques to assess ADME properties hampers the PK profiling and thus further development [136]. In fact, the current knowledge of LM pharmacokinetics is even impaired compared to the basic knowledge of ADME principles for small molecules in the 1980s [136]. Although the basic PK principles are similar between SMs and LMs, the specific mechanisms influencing each step of ADME are different. To begin with, the route of administration between them can differ, which leads to different mechanisms of absorption and first-pass metabolism. Furthermore, LMs are not metabolized by CYPs but can still trigger the release of pro-inflammatory cytokines leading to heavy side effects known as cytokine storm [136, 139]. Also, other modifications play a role in biologics ADME, namely glycosylation, PEGylation, and neonatal Fc receptor (FcRn) interactions [139, 148]. Unfortunately, up until now, most of the evaluation of those factors is only addressed on
In this regard, the development of
The main difficulties in PK profiling lie in the high costs and comparable low throughput of
What distinguishes the DDD “then” and “now” is principally two main changes. First, in the past, pharmaceutical companies as well as academic laboratories were not that concerned with ADMET assessment in the early stages of drug discovery (hit and lead generation) and only addressed PK from preclinical stages on forward. Instead, HTS/HCS, genomics, and computational chemistry were high-profile areas. Today, almost all pharmaceutical big-players have shifted pharmacokinetic profiling to discovery phases. However, only the future will tell whether those changes will yield fruit.
Second, CADD became more and more part of the DDD pipeline in different stages facilitating fast screening of compounds
The authors would like to acknowledge the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP grants 2018/08820-0, 2017/03966-4, and 2015/26722-8). The authors would like to thank Prof Dr. José Eduardo Gonçalves for his valuable comments on the manuscript.
The authors declare no conflict of interest.
ORCID numbers of all authors:
Thales Kronenberger: 0000-0001-6933-7590
Carsten Wrenger: 0000-0001-5987-1749
Vinicius Goncalves Maltarollo: 0000-0001-9675-5907
Arne Krüger: 0000-0002-5531-9508
Stability constant of the formation of metal complexes is used to measure interaction strength of reagents. From this process, metal ion and ligand interaction formed the two types of metal complexes; one is supramolecular complexes known as host-guest complexes [1] and the other is anion-containing complexes. In the solution it provides and calculates the required information about the concentration of metal complexes.
Solubility, light, absorption conductance, partitioning behavior, conductance, and chemical reactivity are the complex characteristics which are different from their components. It is determined by various numerical and graphical methods which calculate the equilibrium constants. This is based on or related to a quantity, and this is called the complex formation function.
During the displacement process at the time of metal complex formation, some ions disappear and form a bonding between metal ions and ligands. It may be considered due to displacement of a proton from a ligand species or ions or molecules causing a drop in the pH values of the solution [2]. Irving and Rossotti developed a technique for the calculation of stability constant, and it is called potentiometric technique.
To determine the stability constant, Bjerrum has used a very simple method, and that is metal salt solubility method. For the studies of a larger different variety of polycarboxylic acid-, oxime-, phenol-containing metal complexes, Martel and Calvin used the potentiometric technique for calculating the stability constant. Those ligands [3, 4] which are uncharged are also examined, and their stability constant calculations are determined by the limitations inherent in the ligand solubility method. The limitations of the metal salt solubility method and the result of solubility methods are compared with this. M-L, MLM, and (M3) L are some types of examples of metal-ligand bonding. One thing is common, and that is these entire types metal complexes all have one ligand.
The solubility method can only usefully be applied to studies of such complexes, and it is best applied for ML; in such types of system, only ML is formed. Jacqueline Gonzalez and his co-worker propose to explore the coordination chemistry of calcium complexes. Jacqueline and et al. followed this technique for evaluate the as partial model of the manganese-calcium cluster and spectrophotometric studies of metal complexes, i.e., they were carried calcium(II)-1,4-butanediamine in acetonitrile and calcium(II)-1,2-ethylendiamine, calcium(II)-1,3-propanediamine by them.
Spectrophotometric programming of HypSpec and received data allows the determination of the formation of solubility constants. The logarithmic values, log β110 = 5.25 for calcium(II)-1,3-propanediamine, log β110 = 4.072 for calcium(II)-1,4-butanediamine, and log β110 = 4.69 for calcium(II)-1,2-ethylendiamine, are obtained for the formation constants [5]. The structure of Cimetidine and histamine H2-receptor is a chelating agent. Syed Ahmad Tirmizi has examined Ni(II) cimetidine complex spectrophotometrically and found an absorption peak maximum of 622 nm with respect to different temperatures.
Syed Ahmad Tirmizi have been used to taken 1:2 ratio of metal and cimetidine compound for the formation of metal complex and this satisfied by molar ratio data. The data, 1.40–2.4 × 108, was calculated using the continuous variation method and stability constant at room temperature, and by using the mole ratio method, this value at 40°C was 1.24–2.4 × 108. In the formation of lead(II) metal complexes with 1-(aminomethyl) cyclohexene, Thanavelan et al. found the formation of their binary and ternary complexes. Glycine, l-proline, l-alanine, l-isoleucine, l-valine, and l-leucine are α-amino acids, and these are important biologically [6]. These α-amino acids are also investigated by potentiometric technique at 32°C. The mixed ligands were also studied using these methods. 50% (v/v) DMSO-water medium used for the determination of acidity constants and their stability constants these type ligands. In a stepwise manner, the ternary complexes were synthesized.
Using the stability constant method, these ternary complexes were found out, and using the parameters such as Δ log
The above acids (gallic and aliphatic dicarboxylic acid) were taken to determine the acidity constants. For the purpose of determining the stability constant, binary and ternary complexes were carried in the aqueous medium using the experimental conditions as stated above. The potentiometric pH-metric titration curves are inferred for the binary complexes and ternary complexes at different ratios, and formation of ternary metal complex formation was in a stepwise manner that provided an easy way to calculate stability constants for the formation of metal complexes.
The values of Δ log
A study by Kathrina and Pekar suggests that pH plays an important role in the formation of metal complexes. When epigallocatechin gallate and gallic acid combine with copper(II) to form metal complexes, the pH changes its speculation. We have been able to determine its pH in frozen and fluid state with the help of multifrequency EPR spectroscopy [8]. With the help of this spectroscopy, it is able to detect that each polyphenol exhibits the formation of three different mononuclear species. If the pH ranges 4–8 for di- or polymeric complex of Cu(II), then it conjectures such metal complexes. It is only at alkaline pH values.
The line width in fluid solutions by molecular motion exhibits an incomplete average of the parameters of anisotropy spin Hamilton. If the complexes are different, then their rotational correlation times for this also vary. The analysis of the LyCEP anisotropy of the fluid solution spectra is performed using the parameters determined by the simulation of the rigid boundary spectra. Its result suggests that pH increases its value by affecting its molecular mass. It is a polyphenol ligand complex with copper, showing the coordination of an increasing number of its molecules or increasing participation of polyphenol dimers used as ligands in the copper coordination region.
The study by Vishenkova and his co-worker [8] provides the investigation of electrochemical properties of triphenylmethane dyes using a voltammetric method with constant-current potential sweep. Malachite green (MG) and basic fuchsin (BF) have been chosen as representatives of the triphenylmethane dyes [9]. The electrochemical behavior of MG and BF on the surface of a mercury film electrode depending on pH, the nature of background electrolyte, and scan rate of potential sweep has been investigated.
Using a voltammetric method with a constant-current potential sweep examines the electrical properties of triphenylmethane dye. In order to find out the solution of MG and BF, certain registration conditions have been prescribed for it, which have proved to be quite useful. The reduction peak for the currents of MG and BF has demonstrated that it increases linearly with respect to their concentration as 9.0 × 10−5–7.0 × 10−3 mol/dm3 for MG and 6.0 × 10−5–8.0 × 10−3 mol/dm3 for BF and correlation coefficients of these values are 0.9987 for MG and 0.9961 for BF [10].
5.0 × 10−5 and 2.0 × 10−5 mol/dm3 are the values used as the detection limit of MG and BF, respectively. Stability constants are a very useful technique whose size is huge. Due to its usefulness, it has acquired an umbrella right in the fields of chemistry, biology, and medicine. No science subject is untouched by this. Stability constants of metal complexes are widely used in the various areas like pharmaceuticals as well as biological processes, separation techniques, analytical processes, etc. In the presented chapter, we have tried to explain this in detail by focusing our attention on the applications and solutions of stability of metal complexes in solution.
Stability or formation or binding constant is the type of equilibrium constant used for the formation of metal complexes in the solution. Acutely, stability constant is applicable to measure the strength of interactions between the ligands and metal ions that are involved in complex formation in the solution [11]. A generally these 1-4 equations are expressed as the following ways:
Thus
K1, K2, K3, … Kn are the equilibrium constants and these are also called stepwise stability constants. The formation of the metal-ligand-n complex may also be expressed as equilibrium constants by the following steps:
The parameters K and β are related together, and these are expressed in the following example:
Now the numerator and denominator are multiplied together with the use of [metal-ligand] [metal-ligand2], and after the rearranging we get the following equation:
Now we expressed it as the following:
From the above relation, it is clear that the overall stability constant βn is equal to the product of the successive (i.e., stepwise) stability constants, K1, K2, K3,…Kn. This in other words means that the value of stability constants for a given complex is actually made up of a number of stepwise stability constants. The term stability is used without qualification to mean that the complex exists under a suitable condition and that it is possible to store the complex for an appreciable amount of time. The term stability is commonly used because coordination compounds are stable in one reagent but dissociate or dissolve in the presence of another regent. It is also possible that the term stability can be referred as an action of heat or light or compound. The stability of complex [13] is expressed qualitatively in terms of thermodynamic stability and kinetic stability.
In a chemical reaction, chemical equilibrium is a state in which the concentration of reactants and products does not change over time. Often this condition occurs when the speed of forward reaction becomes the same as the speed of reverse reaction. It is worth noting that the velocities of the forward and backward reaction are not zero at this stage but are equal.
If hydrogen and iodine are kept together in molecular proportions in a closed process vessel at high temperature (500°C), the following action begins:
In this activity, hydrogen iodide is formed by combining hydrogen and iodine, and the amount of hydrogen iodide increases with time. In contrast to this action, if the pure hydrogen iodide gas is heated to 500°C in the reaction, the compound is dissolved by reverse action, which causes hydrogen iodide to dissolve into hydrogen and iodine, and the ratio of these products increases over time. This is expressed in the following reaction:
For the formation of metal chelates, the thermodynamic technique provides a very significant information. Thermodynamics is a very useful technique in distinguishing between enthalpic effects and entropic effects. The bond strengths are totally effected by enthalpic effect, and this does not make any difference in the whole solution in order/disorder. Based on thermodynamics the chelate effect below can be best explained. The change of standard Gibbs free energy for equilibrium constant is response:
Where:
R = gas constant
T = absolute temperature
At 25°C,
ΔG = (− 5.708 kJ mol−1) · log β.
The enthalpy term creates free energy, i.e.,
For metal complexes, thermodynamic stability and kinetic stability are two interpretations of the stability constant in the solution. If reaction moves from reactants to products, it refers to a change in its energy as shown in the above equation. But for the reactivity, kinetic stability is responsible for this system, and this refers to ligand species [14].
Stable and unstable are thermodynamic terms, while labile and inert are kinetic terms. As a rule of thumb, those complexes which react completely within about 1 minute at 25°C are considered labile, and those complexes which take longer time than this to react are considered inert. [Ni(CN)4]2− is thermodynamically stable but kinetically inert because it rapidly exchanges ligands.
The metal complexes [Co(NH3)6]3+ and such types of other complexes are kinetically inert, but these are thermodynamically unstable. We may expect the complex to decompose in the presence of acid immediately because the complex is thermodynamically unstable. The rate is of the order of 1025 for the decomposition in acidic solution. Hence, it is thermodynamically unstable. However, nothing happens to the complex when it is kept in acidic solution for several days. While considering the stability of a complex, always the condition must be specified. Under what condition, the complex which is stable or unstable must be specified such as acidic and also basic condition, temperature, reactant, etc.
A complex may be stable with respect to a particular condition but with respect to another. In brief, a stable complex need not be inert and similarly, and an unstable complex need not be labile. It is the measure of extent of formation or transformation of complex under a given set of conditions at equilibrium [15].
Thermodynamic stability has an important role in determining the bond strength between metal ligands. Some complexes are stable, but as soon as they are introduced into aqueous solution, it is seen that these complexes have an effect on stability and fall apart. For an example, we take the [Co (SCN)4]2+ complex. The ion bond of this complex is very weak and breaks down quickly to form other compounds. But when [Fe(CN)6]3− is dissolved in water, it does not test Fe3+ by any sensitive reagent, which shows that this complex is more stable in aqueous solution. So it is indicated that thermodynamic stability deals with metal-ligand bond energy, stability constant, and other thermodynamic parameters.
This example also suggests that thermodynamic stability refers to the stability and instability of complexes. The measurement of the extent to which one type of species is converted to another species can be determined by thermodynamic stability until equilibrium is achieved. For example, tetracyanonickelate is a thermodynamically stable and kinetic labile complex. But the example of hexa-amine cobalt(III) cation is just the opposite:
Thermodynamics is used to express the difference between stability and inertia. For the stable complex, large positive free energies have been obtained from ΔG0 reaction. The ΔH0, standard enthalpy change for this reaction, is related to the equilibrium constant, βn, by the well thermodynamic equation:
For similar complexes of various ions of the same charge of a particular transition series and particular ligand, ΔS0 values would not differ substantially, and hence a change in ΔH0 value would be related to change in βn values. So the order of values of ΔH0 is also the order of the βn value.
Kinetic stability is referred to the rate of reaction between the metal ions and ligand proceeds at equilibrium or used for the formation of metal complexes. To take a decision for kinetic stability of any complexes, time is a factor which plays an important role for this. It deals between the rate of reaction and what is the mechanism of this metal complex reaction.
As we discuss above in thermodynamic stability, kinetic stability is referred for the complexes at which complex is inert or labile. The term “inert” was used by Tube for the thermally stable complex and for reactive complexes the term ‘labile’ used [16]. The naturally occurring chlorophyll is the example of polydentate ligand. This complex is extremely inert due to exchange of Mg2+ ion in the aqueous media.
The nature of central atom of metal complexes, dimension, its degree of oxidation, electronic structure of these complexes, and so many other properties of complexes are affected by the stability constant. Some of the following factors described are as follows.
In the coordination chemistry, metal complexes are formed by the interaction between metal ions and ligands. For these type of compounds, metal ions are the coordination center, and the ligand or complexing agents are oriented surrounding it. These metal ions mostly are the transition elements. For the determination of stability constant, some important characteristics of these metal complexes may be as given below.
Ligands are oriented around the central metal ions in the metal complexes. The sizes of these metal ions determine the number of ligand species that will be attached or ordinated (dative covalent) in the bond formation. If the sizes of these metal ions are increased, the stability of coordination compound defiantly decreased. Zn(II) metal ions are the central atoms in their complexes, and due to their lower size (0.74A°) as compared to Cd(II) size (0.97A°), metal ions are formed more stable.
Hence, Al3+ ion has the greatest nuclear charge, but its size is the smallest, and the ion N3− has the smallest nuclear charge, and its size is the largest [17]. Inert atoms like neon do not participate in the formation of the covalent or ionic compound, and these atoms are not included in isoelectronic series; hence, it is not easy to measure the radius of this type of atoms.
The properties of stability depend on the size of the metal ion used in the complexes and the total charge thereon. If the size of these metal ions is small and the total charge is high, then their complexes will be more stable. That is, their ratio will depend on the charge/radius. This can be demonstrated through the following reaction:
An ionic charge is the electric charge of an ion which is formed by the gain (negative charge) or loss (positive charge) of one or more electrons from an atom or group of atoms. If we talk about the stability of the coordination compounds, we find that the total charge of their central metal ions affects their stability, so when we change their charge, their stability in a range of constant can be determined by propagating of error [18]. If the charge of the central metal ion is high and the size is small, the stability of the compound is high:
In general, the most stable coordination bonds can cause smaller and highly charged rations to form more stable coordination compounds.
When an electron pair attracts a central ion toward itself, a strong stability complex is formed, and this is due to electron donation from ligand → metal ion. This donation process is increasing the bond stability of metal complexes exerted the polarizing effect on certain metal ions. Li+, Na+, Mg2+, Ca2+, Al3+, etc. are such type of metal cation which is not able to attract so strongly from a highly electronegative containing stable complexes, and these atoms are O, N, F, Au, Hg, Ag, Pd, Pt, and Pb. Such type of ligands that contains P, S, As, Br and I atom are formed stable complex because these accepts electron from M → π-bonding. Hg2+, Pb2+, Cd2+, and Bi3+ metal ions are also electronegative ions which form insoluble salts of metal sulfide which are insoluble in aqueous medium.
Volatile ligands may be lost at higher temperature. This is exemplified by the loss of water by hydrates and ammonia:
The transformation of certain coordination compounds from one to another is shown as follows:
A ligand is an ion or small molecule that binds to a metal atom (in chemistry) or to a biomolecule (in biochemistry) to form a complex, such as the iron-cyanide coordination complex Prussian blue or the iron-containing blood-protein hemoglobin. The ligands are arranged in spectrochemical series which are based on the order of their field strength. It is not possible to form the entire series by studying complexes with a single metal ion; the series has been developed by overlapping different sequences obtained from spectroscopic studies [19]. The order of common ligands according to their increasing ligand field strength is
The above spectrochemical series help us to for determination of strength of ligands. The left last ligand is as weaker ligand. These weaker ligand cannot forcible binding the 3d electron and resultant outer octahedral complexes formed. It is as-
Increasing the oxidation number the value of Δ increased.
Δ increases from top to bottom.
However, when we consider the metal ion, the following two useful trends are observed:
Δ increases with increasing oxidation number.
Δ increases down a group. For the determination of stability constant, the nature of the ligand plays an important role.
The following factors described the nature of ligands.
The size and charge are two factors that affect the production of metal complexes. The less charges and small sizes of ligands are more favorable for less stable bond formation with metal and ligand. But if this condition just opposite the product of metal and ligand will be a more stable compound. So, less nuclear charge and more size= less stable complex whereas if more nuclear charge and small in size= less stable complex. We take fluoride as an example because due to their smaller size than other halide and their highest electro negativity than the other halides formed more stable complexes. So, fluoride ion complexes are more stable than the other halides:
As compared to S2− ion, O22− ions formed more stable complexes.
It is suggested by Calvin and Wilson that the metal complexes will be more stable if the basic character or strength of ligands is higher. It means that the donating power of ligands to central metal ions is high [20].
It means that the donating power of ligands to central metal ions is high. In the case of complex formation of aliphatic diamines and aromatic diamines, the stable complex is formed by aliphatic diamines, while an unstable coordination complex is formed with aromatic diamines. So, from the above discussion, we find that the stability will be grater if the e-donation power is greater.
Thus it is clear that greater basic power of electron-donating species will form always a stable complex. NH3, CN−, and F− behaved as ligands and formed stable complexes; on the other hand, these are more basic in nature.
We know that if the concentration of coordination group is higher, these coordination compounds will exist in the water as solution. It is noted that greater coordinating tendency show the water molecules than the coordinating group which is originally present. SCN− (thiocynate) ions are present in higher concentration; with the Co2+ metal ion, it formed a blue-colored complex which is stable in state, but on dilution of water medium, a pink color is generated in place of blue, or blue color complex is destroyed by [Co(H2O)6]2+, and now if we added further SCN−, the pink color will not appear:
Now it is clear that H2O and SCN− are in competition for the formation of Co(II) metal-containing complex compound. In the case of tetra-amine cupric sulfate metal complex, ammonia acts as a donor atom or ligand. If the concentration of NH3 is lower in the reaction, copper hydroxide is formed but at higher concentration formed tetra-amine cupric sulfate as in the following reaction:
For a metal ion, chelating ligand is enhanced and affinity it and this is known as chelate effect and compared it with non-chelating and monodentate ligand or the multidentate ligand is acts as chelating agent. Ethylenediamine is a simple chelating agent (Figure 1).
Structure of ethylenediamine.
Due to the bidentate nature of ethylenediamine, it forms two bonds with metal ion or central atom. Water forms a complex with Ni(II) metal ion, but due to its monodentate nature, it is not a chelating ligand (Figures 2 and 3).
Structure of chelating configuration of ethylenediamine ligand.
Structure of chelate with three ethylenediamine ligands.
The dentate cheater of ligand provides bonding strength to the metal ion or central atom, and as the number of dentate increased, the tightness also increased. This phenomenon is known as chelating effect, whereas the formation of metal complexes with these chelating ligands is called chelation:
or
Some factors are of much importance for chelation as follows.
The sizes of the chelating ring are increased as well as the stability of metal complex decreased. According to Schwarzenbach, connecting bridges form the chelating rings. The elongated ring predominates when long bridges connect to the ligand to form a long ring. It is usually observed that an increased a chelate ring size leads to a decrease in complex stability.
He interpreted this statement. The entropy of complex will be change if the size of chelating ring is increased, i.e., second donor atom is allowed by the chelating ring. As the size of chelating ring increased, the stability should be increased with entropy effect. Four-membered ring compounds are unstable, whereas five-membered are more stable. So the chelating ring increased its size and the stability of the formed metal complexes.
The number of chelating rings also decides the stability of complexes. Non-chelating metal compounds are less stable than chelating compounds. These numbers increase the thermodynamic volume, and this is also known as an entropy term. In recent years ligands capable of occupying as many as six coordination positions on a single metal ion have been described. The studies on the formation constants of coordination compounds with these ligands have been reported. The numbers of ligand or chelating agents are affecting the stability of metal complexes so as these numbers go up and down, the stability will also vary with it.
For the Ni(II) complexes with ethylenediamine as chelating agent, its log K1 value is 7.9 and if chelating agents are trine and penten, then the log K1 values are 7.9 and 19.3, respectively. If the metal ion change Zn is used in place of Ni (II), then the values of log K1 for ethylenediamine, trine, and penten are 6.0, 12.1, and 16.2, respectively. The log βMY values of metal ions are given in Table 1.
Metal ion | log βMY (25°C, I = 0.1 M) |
---|---|
Ca2+ | 11.2 |
Cu2+ | 19.8 |
Fe3+ | 24.9 |
Metal ion vs. log βMY values.
Ni(NH3)62+ is an octahedral metal complex, and at 25 °C its log β6 value is 8.3, but Ni(ethylenediamine)32+ complex is also octahedral in geometry, with 18.4 as the value of log β6. The calculated stability value of Ni(ethylenediamine)32+ 1010 times is more stable because three rings are formed as chelating rings by ethylenediamine as compared to no such ring is formed. Ethylenediaminetetraacetate (EDTA) is a hexadentate ligand that usually formed stable metal complexes due to its chelating power.
A special effect in molecules is when the atoms occupy space. This is called steric effect. Energy is needed to bring these atoms closer to each other. These electrons run away from near atoms. There can be many ways of generating it. We know the repulsion between valence electrons as the steric effect which increases the energy of the current system [21]. Favorable or unfavorable any response is created.
For example, if the static effect is greater than that of a product in a metal complex formation process, then the static increase would favor this reaction. But if the case is opposite, the skepticism will be toward retardation.
This effect will mainly depend on the conformational states, and the minimum steric interaction theory can also be considered. The effect of secondary steric is seen on receptor binding produced by an alternative such as:
Reduced access to a critical group.
Stick barrier.
Electronic resonance substitution bond by repulsion.
Population of a conformer changes due to active shielding effect.
The macrocyclic effect is exactly like the image of the chelate effect. It means the principle of both is the same. But the macrocyclic effect suggests cyclic deformation of the ligand. Macrocyclic ligands are more tainted than chelating agents. Rather, their compounds are more stable due to their cyclically constrained constriction. It requires some entropy in the body to react with the metal ion. For example, for a tetradentate cyclic ligand, we can use heme-B which forms a metal complex using Fe+2 ions in biological systems (Figure 4).
Structure of hemoglobin is the biological complex compound which contains Fe(II) metal ion.
The n-dentate chelating agents play an important role for the formation of more stable metal complexes as compared to n-unidentate ligands. But the n-dentate macrocyclic ligand gives more stable environment in the metal complexes as compared to open-chain ligands. This change is very favorable for entropy (ΔS) and enthalpy (ΔH) change.
There are so many parameters to determination of formation constants or stability constant in solution for all types of chelating agents. These numerous parameters or techniques are refractive index, conductance, temperature, distribution coefficients, refractive index, nuclear magnetic resonance volume changes, and optical activity.
Solubility products are helpful and used for the insoluble salt that metal ions formed and complexes which are also formed by metal ions and are more soluble. The formation constant is observed in presence of donor atoms by measuring increased solubility.
To determine the solubility constant, it involves the distribution of the ligands or any complex species; metal ions are present in two immiscible solvents like water and carbon tetrachloride, benzene, etc.
In this method metal ions or ligands are present in solution and on exchanger. A solid polymers containing with positive and negative ions are ion exchange resins. These are insoluble in nature. This technique is helpful to determine the metal ions in resin phase, liquid phase, or even in radioactive metal. This method is also helpful to determine the polarizing effect of metal ions on the stability of ligands like Cu(II) and Zn(II) with amino acid complex formation.
At the equilibrium free metal and ions are present in the solution, and using the different electrometric techniques as described determines its stability constant.
This method is based upon the titration method or follows its principle. A stranded acid-base solution used as titrate and which is titrated, it may be strong base or strong acid follows as potentiometrically. The concentration of solution using 103− M does not decomposed during the reaction process, and this method is useful for protonated and nonprotonated ligands.
This is the graphic method used to determine the stability constant in producing metal complex formation by plotting a polarograph between the absences of substances and the presence of substances. During the complex formation, the presence of metal ions produced a shift in the half-wave potential in the solution.
If a complex is relatively slow to form and also decomposes at measurable rate, it is possible, in favorable situations, to determine the equilibrium constant.
This involves the study of the equilibrium constant of slow complex formation reactions. The use of tracer technique is extremely useful for determining the concentrations of dissociation products of the coordination compound.
This method is based on the study of the effect of an equilibrium concentration of some ions on the function at a definite organ of a living organism. The equilibrium concentration of the ion studied may be determined by the action of this organ in systems with complex formation.
The solution of 25 ml is adopted by preparing at the 1.0 × 10−5 M ligand or 1.0 × 10−5 M concentration and 1.0 × 10−5 M for the metal ion:
The solutions containing the metal ions were considered both at a pH sufficiently high to give almost complete complexation and at a pH value selected in order to obtain an equilibrium system of ligand and complexes.
In order to avoid modification of the spectral behavior of the ligand due to pH variations, it has been verified that the range of pH considered in all cases does not affect absorbance values. Use the collected pH values adopted for the determinations as well as selected wavelengths. The ionic strengths calculated from the composition of solutions allowed activity coefficient corrections. Absorbance values were determined at wavelengths in the range 430–700 nm, every 2 nm.
For a successive metal complex formation, use this method. If ligand is protonate and the produced complex has maximum number of donate atoms of ligands, a selective light is absorbed by this complex, while for determination of stability constant, it is just known about the composition of formed species.
Bjerrum (1941) used the method stepwise addition of the ligands to coordination sphere for the formation of complex. So, complex metal–ligand-n forms as the following steps [22]. The equilibrium constants, K1, K2, K3, … Kn are called stepwise stability constants. The formation of the complex metal-ligandn may also be expressed by the following steps and equilibrium constants.
Where:
M = central metal cation
L = monodentate ligand
N = maximum coordination number for the metal ion M for the ligand
If a complex ion is slow to reach equilibrium, it is often possible to apply the method of isotopic dilution to determine the equilibrium concentration of one or more of the species. Most often radioactive isotopes are used.
This method was extensively used by Werner and others to study metal complexes. In the case of a series of complexes of Co(III) and Pt(IV), Werner assigned the correct formulae on the basis of their molar conductance values measured in freshly prepared dilute solutions. In some cases, the conductance of the solution increased with time due to a chemical change, e.g.,
It is concluded that the information presented is very important to determine the stability constant of the ligand metal complexes. Some methods like spectrophotometric method, Bjerrum’s method, distribution method, ion exchange method, electrometric techniques, and potentiometric method have a huge contribution in quantitative analysis by easily finding the stability constants of metal complexes in aqueous solutions.
All the authors thank the Library of University of Delhi for reference books, journals, etc. which helped us a lot in reviewing the chapter.
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