Mixing apples and oranges: Analysis of heterotropic cooperativity in cytochrome P450 3A4

Binding equations for the lipid composition dependence of peripheral membrane-binding proteins

The specific recognition of peripheral membrane-binding proteins for their target membranes is mediated by a complex constellation of various lipid contacts. Despite the inherent complexities of the heterogeneous protein-membrane interface, the binding dependence of such proteins is, surprisingly, often reliably described by simple models such as the Langmuir Adsorption Isotherm or the Hill equation. However, these models were not developed to describe associations with two-dimensional, highly concentrated heterogeneous ligands such as lipid membranes. In particular, these models fail to capture the dependence on the lipid composition, a significant determinant of binding that distinguishes target from non-target membranes. In this work, we present a model that describes the dependence of peripheral proteins on lipid composition through an analytic expression for their association. The resulting membrane-binding equation retains the features of these simple models but completely describes the binding dependence on multiple relevant variables in addition to the lipid composition, such as protein and vesicle concentration. Implicit in this lipid composition dependence is a new form of membrane-based cooperativity that significantly differs from traditional solution-based cooperativity. We introduce the Membrane-Hill number as a measure of this cooperativity and describe its unique properties. We illustrate the utility and interpretational power of our model by analyzing previously published data on two peripheral proteins that associate with phosphatidylserine-containing membranes: The transmembrane immunoglobulin and mucin domain-containing protein 3 (TIM3) that employs calcium in its association, and milk fat globulin epidermal growth factor VIII (MFG-E8) which is completely insensitive to calcium. We also provide binding equations for systems that exhibit more complexity in their membrane-binding.

Midazolam as a Probe for Drug-Drug Interactions Mediated by CYP3A4: Homotropic Allosteric Mechanism of Site-Specific Hydroxylation

We developed an efficient and sensitive probe for drug-drug interactions mediated by human CYP3A4 by using midazolam (MDZ) as a probe substrate. Using global analysis of four parameters over several experimental data sets, we demonstrate that the first MDZ molecule (MDZ1) binds with high affinity at the productive site near the heme iron and gives only hydroxylation at the 1 position (1OH). The second midazolam molecule (MDZ2) binds at an allosteric site at the membrane surface and perturbs the position and mobility of MDZ1 such that the minor hydroxylation product at the 4 position (4OH) is formed in a 1:2 ratio (35%). No increase in catalytic rate is observed after the second MDZ binding. Hence, the site of the 1OH:4OH metabolism ratio is a sensitive probe for drugs, such as progesterone, that bind with high affinity to the allosteric site and serve as effectors. We observe similar changes in the MDZ 1OH:4OH ratio in the presence of progesterone (PGS), suggesting a direct communication between the active and allosteric sites. Mutations introduced into the F-F' loop indicate that residues F213 and D214 are directly involved in allosteric interactions leading to MDZ homotropic cooperativity, and these same residues, together with L211, are involved in heterotropic allosteric interactions in which PGS is the effector and MDZ the substrate. Molecular dynamics simulations provide a mechanistic picture of the origin of this cooperativity. These results show that the midazolam can be used as a sensitive probe for drug-drug interactions in human P450 CYP3A4.

Theoretical explanation for the pharmaceutical incompatibility through the cooperativity effect of the drug-drug intermolecular interactions in the phenobarbital∙∙∙paracetamol∙∙∙H2O complex

In order to reveal the essence of the pharmaceutical incompatibility, the cooperativity effects of the drug-drug intermolecular π∙∙∙π and H∙∙∙O H-bonding interactions involving hydration were evaluated in the phenobarbital∙∙∙paracetamol∙∙∙H₂O complex at the M06-2X/6-311++G** and MP2/6-311++G** levels. The thermodynamic cooperativity effects were also investigated by the statistical thermodynamic method. The results show that the π∙∙∙π stacking ternary complexes with the moderate anti-cooperativity effects are dominant in controling the aggregation process of phenobarbital, paracetamol, and H₂O, as is confirmed by the atoms-in-molecules (AIM) and reduced density gradient (RDG) analyses. Therefore, it can be inferred that the anti-cooperativity effect plays an important role in forming the pharmaceutical incompatibility, and thus a deduction on the formation process of the pharmaceutical incompatibility between phenobarbital and paracetamol, with the hydration effect, is given. Several valuable models that relate the features of molecular surface electrostatic potentials or their statistical parameters, such as the surface areas, average values ([Formula: see text]), variances ([Formula: see text], [Formula: see text] and [Formula: see text]), and product of [Formula: see text] and electrostatic balance parameter (ν) ([Formula: see text]ν), to the values of the cooperativity effects were predicted. The formation of the pharmaceutical incompatibility is a thermodynamic cooperativity process driven by the enthalpy change. Graphical abstract Anti-cooperativity effect plays an important role in forming the pharmaceutical incompatibility.

Allosteric Interactions in Human Cytochrome P450 CYP3A4: The Role of Phenylalanine 213

The role of Phe213 in the allosteric mechanism of human cytochrome P450 CYP3A4 was studied using a combination of progesterone (PGS) and carbamazepine (CBZ) as probe substrates. We expressed, purified, and incorporated into POPC Nanodiscs three mutants, F213A, F213S, and F213Y, and compared them with wild-type (WT) CYP3A4 by monitoring spectral titration, the rate of NADPH oxidation, and steady-state product turnover rates with pure substrates and substrate mixtures. All mutants demonstrated higher activity with CBZ, lower activity with PGS, and a reduced level of activation of CBZ epoxidation by PGS, which was most pronounced in the F213A mutant. Using all-atom molecular dynamics simulations, we compared the dynamics of WT CYP3A4 and the F213A mutant incorporated into the lipid bilayer and the effect of the presence of the PGS molecule at the allosteric peripheral site and evaluated the critical role of Phe213 in mediating the heterotropic allosteric interactions in CYP3A4.

Steroid bioconjugation to a CYP3A4 allosteric site and its effect on substrate binding and coupling efficiency

Human cytochrome P450 3A4 (CYP3A4) is an important drug metabolizing enzyme involved in a number of drug-drug and food-drug interactions. As such, much effort has been devoted into investigating its mechanism of interaction with ligands. CYP3A4 has one of the highest levels of substrate promiscuity for an enzyme, and can even bind multiple ligands simultaneously. The location and orientation of these ligands depend on the chemical structure and stoichiometry, and are generally poorly understood. In the case of the steroid testosterone, up to three copies of the molecule can associate with the enzyme at once, likely two in the active site and one at a postulated allosteric site. Recently, we demonstrated that steroid bioconjugation at the allosteric site results in an increase in activity of CYP3A4 toward testosterone and 7-benzyloxy-4-trifluoromethylcoumarin oxidation. Here, using the established bioconjugation methodology, we show how steroid bioconjugation at the allosteric site affects the heme spin state, the binding affinity (K_S) of CYP3A4 for testosterone, as well as the enzyme coupling efficiency.

Membrane-embedded substrate recognition by cytochrome P450 3A4

Cytochrome P450 3A4 (CYP3A4) is the dominant xenobiotic-metabolizing enzyme in the liver and intestine and is involved in the disposition of more than 50% of drugs. Because of its ability to bind multiple substrates, its reaction kinetics are complex, and its association with the microsomal membrane confounds our understanding of how this enzyme recognizes and recruits diverse substrates. Testosterone (TST) hydroxylation is the prototypical CYP3A4 reaction, displaying positive homotropic cooperativity with three binding sites. Here, exploiting the capability of accelerated molecular dynamics (aMD) to sample events in the millisecond regime, I performed >25-μs aMD simulations in the presence of three TST molecules. These simulations identified high-occupancy surface-binding sites as well as a pathway for TST ingress into the CYP3A4 active site originating in the membrane. Adaptive biasing force analysis of the latter pathway revealed a metastable intermediate that could constitute a third binding site at high TST concentrations. Prompted by the observation that interactions between TST and the G'-helix mobilize the ligand into the active site, a free-energy analysis of TST distribution in the membrane was conducted and revealed that the depth of the G'-helix is optimal for extracting TST. In summary, these simulations confirm separate, but adjacent substrate-binding sites within the enzyme and the existence of an auxiliary TST-binding site. The broader impact of these simulations is that they support a mechanism in which cytochromes P450 directly recruit membrane-solubilized substrates.

Spectroscopic studies of the cytochrome P450 reaction mechanisms

The cytochrome P450 monooxygenases (P450s) are thiolate heme proteins that can, often under physiological conditions, catalyze many distinct oxidative transformations on a wide variety of molecules, including relatively simple alkanes or fatty acids, as well as more complex compounds such as steroids and exogenous pollutants. They perform such impressive chemistry utilizing a sophisticated catalytic cycle that involves a series of consecutive chemical transformations of heme prosthetic group. Each of these steps provides a unique spectral signature that reflects changes in oxidation or spin states, deformation of the porphyrin ring or alteration of dioxygen moieties. For a long time, the focus of cytochrome P450 research was to understand the underlying reaction mechanism of each enzymatic step, with the biggest challenge being identification and characterization of the powerful oxidizing intermediates. Spectroscopic methods, such as electronic absorption (UV-Vis), electron paramagnetic resonance (EPR), nuclear magnetic resonance (NMR), electron nuclear double resonance (ENDOR), Mössbauer, X-ray absorption (XAS), and resonance Raman (rR), have been useful tools in providing multifaceted and detailed mechanistic insights into the biophysics and biochemistry of these fascinating enzymes. The combination of spectroscopic techniques with novel approaches, such as cryoreduction and Nanodisc technology, allowed for generation, trapping and characterizing long sought transient intermediates, a task that has been difficult to achieve using other methods. Results obtained from the UV-Vis, rR and EPR spectroscopies are the main focus of this review, while the remaining spectroscopic techniques are briefly summarized. This article is part of a Special Issue entitled: Cytochrome P450 biodiversity and biotechnology, edited by Erika Plettner, Gianfranco Gilardi, Luet Wong, Vlada Urlacher, Jared Goldstone.

Drug-Drug Interactions between Atorvastatin and Dronedarone Mediated by Monomeric CYP3A4

Heterotropic interactions between atorvastatin (ARVS) and dronedarone (DND) have been deciphered using global analysis of the results of binding and turnover experiments for pure drugs and their mixtures. The in vivo presence of atorvastatin lactone (ARVL) was explicitly taken into account by using pure ARVL in analogous experiments. Both ARVL and ARVS inhibit DND binding and metabolism, while a significantly higher affinity of CYP3A4 for ARVL makes the latter the main modulator of activity (effector) in this system. Molecular dynamics simulations reveal significantly different modes of interactions of DND and ARVL with the substrate binding pocket and with a peripheral allosteric site. Interactions of both substrates with residues F213 and F219 at the allosteric site play a critical role in the communication of conformational changes induced by effector binding to productive binding of the substrate at the catalytic site.

Use of bioconjugation with cytochrome P450 enzymes

Bioconjugation, defined as chemical modification of biomolecules, is widely employed in biological and biophysical studies. It can expand functional diversity and enable applications ranging from biocatalysis, biosensing and even therapy. This review summarizes how chemical modifications of cytochrome P450 enzymes (P450s or CYPs) have contributed to improving our understanding of these enzymes. Genetic modifications of P450s have also proven very useful but are not covered in this review. Bioconjugation has served to gain structural information and investigate the mechanism of P450s via photoaffinity labeling, mechanism-based inhibition (MBI) and fluorescence studies. P450 surface acetylation and protein cross-linking have contributed to the investigation of protein complexes formation involving P450 and its redox partner or other P450 enzymes. Finally, covalent immobilization on polymer surfaces or electrodes has benefited the areas of biocatalysis and biosensor design. This article is part of a Special Issue entitled: Cytochrome P450 biodiversity and biotechnology, edited by Erika Plettner, Gianfranco Gilardi, Luet Wong, Vlada Urlacher, Jared Goldstone.

Allosteric Activation of Cytochrome P450 3A4 via Progesterone Bioconjugation

Human cytochrome P450 3A4 (CYP3A4) is responsible for the metabolism of the majority of drugs. As such, it is implicated in many adverse drug-drug and food-drug interactions, and is of significant interest to the pharmaceutical industry. This enzyme is known to simultaneously bind multiple ligands and display atypical enzyme kinetics, suggestive of allostery and cooperativity. As well, evidence of a postulated peripheral allosteric binding site has provoked debate around its significance and location. We report the use of bioconjugation to study the significance of substrate binding at the proposed allosteric site and its effect on CYP3A4 activity. CYP3A4 mutants were created and covalently modified with various small molecules including progesterone. The labeled mutants displayed enhanced kinetic stability and improved activity in testosterone and 7-benzyloxy-(4-trifluoromethyl)coumarin oxidation assays. Our work applies a new strategy to study cytochrome P450 allostery and supports the hypothesis that substrate binding at the postulated allosteric site of CYP3A4 may induce functional cooperativity.

Nanodiscs in Membrane Biochemistry and Biophysics

Membrane proteins play a most important part in metabolism, signaling, cell motility, transport, development, and many other biochemical and biophysical processes which constitute fundamentals of life on the molecular level. Detailed understanding of these processes is necessary for the progress of life sciences and biomedical applications. Nanodiscs provide a new and powerful tool for a broad spectrum of biochemical and biophysical studies of membrane proteins and are commonly acknowledged as an optimal membrane mimetic system that provides control over size, composition, and specific functional modifications on the nanometer scale. In this review we attempted to combine a comprehensive list of various applications of nanodisc technology with systematic analysis of the most attractive features of this system and advantages provided by nanodiscs for structural and mechanistic studies of membrane proteins.

Mechanism of drug-drug interactions mediated by human cytochrome P450 CYP3A4 monomer

Using Nanodiscs, we quantitate the heterotropic interaction between two different drugs mediated by monomeric CYP3A4 incorporated into a nativelike membrane environment. The mechanism of this interaction is deciphered by global analysis of multiple-turnover experiments performed under identical conditions using the pure substrates progesterone (PGS) and carbamazepine (CBZ) and their mixtures. Activation of CBZ epoxidation and simultaneous inhibition of PGS hydroxylation are measured and quantitated through differences in their respective affinities for both a remote allosteric site and the productive catalytic site near the heme iron. Preferred binding of PGS at the allosteric site and a stronger preference for CBZ binding at the productive site give rise to a nontrivial drug-drug interaction. Molecular dynamics simulations indicate functionally important conformational changes caused by PGS binding at the allosteric site and by two CBZ molecules positioned inside the substrate binding pocket. Structural changes involving Phe-213, Phe-219, and Phe-241 are thought to be responsible for the observed synergetic effects and positive allosteric interactions between these two substrates. Such a mechanism is likely of general relevance to the mutual heterotropic effects caused by biologically active compounds that exhibit different patterns of interaction with the distinct allosteric and productive sites of CYP3A4, as well as other xenobiotic metabolizing cytochromes P450 that are also involved in drug-drug interactions. Importantly, this work demonstrates that a monomeric CYP3A4 can display the full spectrum of activation and cooperative effects that are observed in hepatic membranes.

Current Approaches for Investigating and Predicting Cytochrome P450 3A4-Ligand Interactions

Cytochrome P450 3A4 (CYP3A4) is the major and most important drug-metabolizing enzyme in humans that oxidizes and clears over a half of all administered pharmaceuticals. This is possible because CYP3A4 is promiscuous with respect to substrate binding and has the ability to catalyze diverse oxidative chemistries in addition to traditional hydroxylation reactions. Furthermore, CYP3A4 binds and oxidizes a number of substrates in a cooperative manner and can be both induced and inactivated by drugs. In vivo, CYP3A4 inhibition could lead to undesired drug-drug interactions and drug toxicity, a major reason for late-stage clinical failures and withdrawal of marketed pharmaceuticals. Owing to its central role in drug metabolism, many aspects of CYP3A4 catalysis have been extensively studied by various techniques. Here, we give an overview of experimental and theoretical methods currently used for investigation and prediction of CYP3A4-ligand interactions, a defining factor in drug metabolism, with an emphasis on the problems addressed and conclusions derived from the studies.

Molecular analysis of resistance to acaricidal spirocyclic tetronic acids in Tetranychus urticae: CYP392E10 metabolizes spirodiclofen, but not its corresponding enol

Spirodiclofen is one of the most recently developed acaricides and belongs to the new family of spirocyclic tetronic acids (ketoenols). This new acaricidal family is an important chemical tool in resistance management strategies providing sustainable control of spider mites such as Tetranychus urticae. Spirodiclofen targets lipid biosynthesis mediated by direct inhibition of acetyl coenzyme A carboxylase (ACCase). In this study, we investigated two genetically distant spider mite strains with high resistance to spirodiclofen. Despite the strong resistance levels to spirodiclofen (up to 680-fold), only limited cross-resistance with other members of this group such as spiromesifen and spirotetramat could be detected. Amplification and sequencing of the ACCase gene from resistant and susceptible strains did not reveal common non-synonymous mutations, and expression levels of ACCase were similar in both resistant and susceptible strains, indicating the absence of target-site resistance. Furthermore, we collected genome-wide expression data of susceptible and resistant T. urticae strains using microarray technology. Analysis of differentially expressed genes revealed a broad response, but within the overlap of two resistant strains, several cytochrome P450s were prominent. Quantitative PCR confirmed the constitutive over-expression of CYP392E7 and CYP392E10 in resistant strains, and CYP392E10 expression was highly induced by spirodiclofen. Furthermore, stage specific expression profiling revealed that expression levels were not significantly different between developing stages, but very low in eggs, matching the age-dependent resistance pattern previously observed. Functional expression of CYP392E7 and CYP392E10 confirmed that CYP392E10 (but not CYP392E7) metabolizes spirodiclofen by hydroxylation as identified by LC-MS/MS, and revealed cooperative substrate binding and a Km of 43 μM spirodiclofen. CYP392E10 also metabolizes spiromesifen, but not spirotetramat. Surprisingly, no metabolism of the hydrolyzed spirodiclofen-enol metabolite could be detected. These findings are discussed in the light of a likely resistance mechanism.

Nanodiscs in the studies of membrane-bound cytochrome P450 enzymes

Cytochromes P450 from eukaryotes and their native redox partners cytochrome P450 reductases both belong to the class of monotopic membrane proteins containing one transmembrane anchor. Incorporation into the lipid bilayer significantly affects their equilibrium and kinetic properties and plays an important role in their interactions. We describe here the detailed protocols developed in our group for the functional self-assembly of mammalian cytochromes P450 and cytochrome P450 reductases into Nanodiscs with controlled lipid composition. The resulting preparations are fully functional, homogeneous in size, composition and oligomerization state of the heme enzyme, and show an improved stability with respect to P420 formation. We provide a brief overview of applications of Nanodisc technology to the biophysical and biochemical mechanistic studies of cytochromes P450 involved in steroidogenesis, and of the most abundant xenobiotic-metabolizing human cytochrome P450 CYP3A4.

Optimization of the bacterial cytochrome P450 BM3 system for the production of human drug metabolites

Drug metabolism in human liver is a process involving many different enzymes. Among them, a number of cytochromes P450 isoforms catalyze the oxidation of most of the drugs commercially available. Each P450 isoform acts on more than one drug, and one drug may be oxidized by more than one enzyme. As a result, multiple products may be obtained from the same drug, and as the metabolites can be biologically active and may cause adverse drug reactions (ADRs), the metabolic profile of a new drug has to be known before this can be commercialized. Therefore, the metabolites of a certain drug must be identified, synthesized and tested for toxicity. Their synthesis must be in sufficient quantities to be used for metabolic tests. This review focuses on the progresses done in the field of the optimization of a bacterial self-sufficient and efficient cytochrome P450, P450 BM3 from Bacillus megaterium, used for the production of metabolites of human enzymes. The progress made in the improvement of its catalytic performance towards drugs, the substitution of the costly NADPH cofactor and its immobilization and scale-up of the process for industrial application are reported.

A novel type of allosteric regulation: functional cooperativity in monomeric proteins

Cooperative functional properties and allosteric regulation in cytochromes P450 play an important role in xenobiotic metabolism and define one of the main mechanisms of drug-drug interactions. Recent experimental results suggest that ability to bind simultaneously two or more small organic molecules can be the essential feature of cytochrome P450 fold, and often results in rich and complex pattern of allosteric behavior. Manifestations of non-Michaelis kinetics include homotropic and heterotropic activation and inhibition effects depending on the stoichiometric ratios of substrate and effector, changes in the regio- and stereospecificity of catalytic transformations, and often give rise to the clinically important drug-drug interactions. In addition, functional response of P450 systems is modulated by the presence of specific and non-specific effector molecules, metal ions, membrane incorporation, formation of homo- and hetero-oligomers, and interactions with the protein redox partners. In this article we briefly overview the main factors contributing to the allosteric effects in cytochromes P450 with the main focus on the sources of cooperative behavior in xenobiotic metabolizing monomeric heme enzymes with their conformational flexibility and extremely broad substrate specificity. The novel mechanism of functional cooperativity in P450 enzymes does not require substantial binding cooperativity, rather it implies the presence of one or more binding sites with higher affinity than the single catalytically active site in the vicinity of the heme iron.

Interactions of cytochrome P450s with their ligands

Cytochrome P450s (CYPs) are heme-containing monooxygenases that contribute to an enormous range of enzymatic function including biosynthetic and detoxification roles. This review summarizes recent studies concerning interactions of CYPs with ligands including substrates, inhibitors, and diatomic heme-ligating molecules. These studies highlight the complexity in the relationship between the heme spin state and active site occupancy, the roles of water in directing protein-ligand and ligand-heme interactions, and the details of interactions between heme and gaseous diatomic CYP ligands. Both kinetic and thermodynamic aspects of ligand binding are considered.

Defining CYP3A4 structural responses to substrate binding. Raman spectroscopic studies of a nanodisc-incorporated mammalian cytochrome P450

Resonance Raman (RR) spectroscopy is used to help define active site structural responses of nanodisc-incorporated CYP3A4 to the binding of three substrates: bromocriptine (BC), erythromycin (ERY), and testosterone (TST). We demonstrate that nanodisc-incorporated assemblies reveal much more well-defined active site RR spectroscopic responses as compared to those normally obtained with the conventional, detergent-stabilized, sampling strategies. While ERY and BC are known to bind to CYP3A4 with a 1:1 stoichiometry, only the BC induces a substantial conversion from low- to high-spin state, as clearly manifested in the RR spectra acquired herein. The third substrate, TST, displays significant homotropic interactions within CYP3A4, the active site binding up to 3 molecules of this substrate, with the functional properties varying in response to binding of individual substrate molecules. While such behavior seemingly suggests the possibility that each substrate binding event induces functionally important heme structural changes, up to this time spectroscopic evidence for such structural changes has not been available. The current RR spectroscopic studies show clearly that accommodation of different size substrates, and different loading of TST, do not significantly affect the structure of the substrate-bound ferric heme. However, it is here demonstrated that the nature and number of bound substrates do have an extraordinary influence on the conformation of bound exogenous ligands, such as CO or dioxygen and its reduced forms, implying an effective mechanism whereby substrate structure can impact reactivity of intermediates so as to influence function, as reflected in the diverse reactivity of this drug metabolizing cytochrome.

Analysis of heterotropic cooperativity in cytochrome P450 3A4 using alpha-naphthoflavone and testosterone

Cytochrome P450 3A4 (CYP3A4) displays non-Michaelis-Menten kinetics for many of the substrates it metabolizes, including testosterone (TST) and α-naphthoflavone (ANF). Heterotropic effects between these two substrates can further complicate the metabolic profile of the enzyme. In this work, monomeric CYP3A4 solubilized in Nanodiscs has been studied for its ability to interact with varying molar ratios of ANF and TST. Comparison of the observed heme spin state, NADPH consumption, and product formation rates with a non-cooperative model calculated from a linear combination of the global analysis of each substrate reveals a detailed landscape of the heterotropic interactions and indicates negligible binding cooperativity between ANF and TST. The observed effect of ANF on the kinetics of TST metabolism is due to the additive action of the second substrate with no specific allosteric effects.

Cytochromes P450 in nanodiscs

Nanodiscs have proven to be a versatile tool for the study all types of membrane proteins, including receptors, transporters, enzymes and viral antigens. The self-assembled Nanodisc system provides a robust and common means for rendering these targets soluble in aqueous media while providing a native like bilayer environment that maintains functional activity. This system has thus provided a means for studying the extensive collection of membrane bound cytochromes P450 with the same biochemical and biophysical tools that have been previously limited to use with the soluble P450s. These include a plethora of spectroscopic, kinetic and surface based methods. Significant improvements in homogeneity and stability of these preparations open new possibilities for detailed analysis of equilibrium and steady-state kinetic characteristics of catalytic mechanisms of human cytochromes P450 involved in xenobiotic metabolism and in steroid biosynthesis. The experimental methods developed for physico-chemical and functional studies of membrane cytochromes P450 incorporated in Nanodiscs allow for more detailed understanding of the scientific questions along the lines pioneered by Professor Klaus Ruckpaul and his array of colleagues and collaborators.