Strategy for Generating Sequence-Defined Aptamer Reagent Sets for Detecting Protein Contaminants in Biotherapeutics.

Biologic drugs are typically manufactured in mammalian host cells, and it is critical from a drug safety and efficacy perspective to detect and remove host cell proteins (HCPs) during production. This is currently achieved with sets of polyclonal antibodies (pAbs), but these suffer from critical shortcomings because their composition is inherently undefined, and they cannot detect nonimmunogenic HCPs. In this work, we report a high-throughput screening and array-based binding characterization strategy that we employed to generate a set of aptamers that overcomes these limitations to achieve sensitive, broad-spectrum detection of HCPs from the widely used Chinese hamster ovary (CHO) cell line. We identified a set of 32 DNA aptamers that achieve better sensitivity than a commercial pAb reagent set and can detect a comparable number of HCPs over a broad range of isoelectric points and sizes. Importantly, these aptamers detect multiple contaminants that are known to be responsible for therapeutic antibody degradation and toxicity in patients. Because HCP aptamer reagents are sequence-defined and chemically synthesized, we believe they may enable safer production of biologic drugs, and this strategy should be broadly applicable for the generation of HCP detection reagents for other cell lines.

Decomposing Dynamical Couplings in Mutated scFv Antibody Fragments into Stabilizing and Destabilizing Effects.

Conformational fluctuations within scFv antibodies are characterized by a novel perturbation-response decomposition of molecular dynamics trajectories. Both perturbation and response profiles are stratified into stabilizing and destabilizing conditions. The linker between the VH and VL domains exhibits the dominant dynamical response by being coupled to nearly the entire protein, responding to both stabilizing and destabilizing perturbations. Perturbations within complementarity-determining regions (CDR) induce rich behavior in dynamic response. Among many effects, stabilizing any CDR loop in the VH domain triggers a destabilizing response in all CDR loops in the VL domain and vice versa. Destabilizing residues within the VL domain are likely to stabilize all CDR loops in the VH domain, and, when these residues are not buried, the CDR loops in the VL domain are also likely to be stabilized. These effects, described by shifts in normal mode characteristics, initiate a propensity for dynamic allostery with possible functional implications in bispecific antibodies.

Mutations in Antibody Fragments Modulate Allosteric Response Via Hydrogen-Bond Network Fluctuations.

A mechanical perturbation method that locally restricts conformational entropy along the protein backbone is used to identify putative allosteric sites in a series of antibody fragments. The method is based on a distance constraint model that integrates mechanical and thermodynamic viewpoints of protein structure wherein mechanical clamps that mimic substrate or cosolute binding are introduced. Across a set of six single chain-Fv fragments of the anti-lymphotoxin-ß receptor antibody, statistically significant responses are obtained by averaging over 10 representative structures sampled from a molecular dynamics simulation. As expected, the introduced clamps locally rigidify the protein, but long-ranged increases in both rigidity and flexibility are also frequently observed. Expanding our analysis to every molecular dynamics frame demonstrates that the allosteric responses are modulated by fluctuations within the hydrogen-bond network where the native ensemble is comprised of conformations that both are, and are not, affected by the perturbation in question. Population shifts induced by the mutations alter the allosteric response by adjusting which hydrogen-bond networks are the most probable. These effects are compared using response maps that track changes across each single chain-Fv fragment, thus providing valuable insight into how sensitive allosteric mechanisms are to mutations.

Rigidity Emerges during Antibody Evolution in Three Distinct Antibody Systems: Evidence from QSFR Analysis of Fab Fragments.

The effects of somatic mutations that transform polyspecific germline (GL) antibodies to affinity mature (AM) antibodies with monospecificity are compared among three GL-AM Fab pairs. In particular, changes in conformational flexibility are assessed using a Distance Constraint Model (DCM). We have previously established that the DCM can be robustly applied across a series of antibody fragments (VL to Fab), and subsequently, the DCM was combined with molecular dynamics (MD) simulations to similarly characterize five thermostabilizing scFv mutants. The DCM is an ensemble based statistical mechanical approach that accounts for enthalpy/entropy compensation due to network rigidity, which has been quite successful in elucidating conformational flexibility and Quantitative Stability/Flexibility Relationships (QSFR) in proteins. Applied to three disparate antibody systems changes in QSFR quantities indicate that the VH domain is typically rigidified, whereas the VL domain and CDR L2 loop become more flexible during affinity maturation. The increase in CDR H3 loop rigidity is consistent with other studies in the literature. The redistribution of conformational flexibility is largely controlled by nonspecific changes in the H-bond network, although certain Arg to Asp salt bridges create highly localized rigidity increases. Taken together, these results reveal an intricate flexibility/rigidity response that accompanies affinity maturation.

Universal method for the determination of nonionic surfactant content in the presence of protein.

A new analytical method has been developed for the quantitative determination of ethylene glycol-containing nonionic surfactants, such as polyethylene glycol 8000, polysorbate 80, and Pluronic F-68. These surfactants are commonly used in pharmaceutical protein preparations, thus, testing in the presence of protein is required. This method is based on the capillary gas chromatographic analysis of ethylene glycol diacetate formed by hydrolysis and acetylation of surfactants that contain ethylene glycol. Protein samples containing free surfactants were hydrolyzed and acetylated with acetic anhydride in the presence of p-toluene sulfonic acid. Acetylated ethylene glycol was extracted with dichloromethane and analyzed by gas chromatography using a flame ionization detector. The amount of nonionic surfactant in the sample was determined by comparing the released ethylene glycol diacetate signal to that measured from calibration standards. The limits of quantitation of the method were 5.0 µg/mL for polyethylene glycol 8000 and Pluronic F-68, and 50 µg/mL for polysorbate 80. This method can be applied to determine the polyethylene glycol content in PEGylated proteins or the final concentration of polysorbate 80 in a protein drug in a quality control environment.

Nucleic acid binding and chaperone properties of HIV-1 Gag and nucleocapsid proteins.

The Gag polyprotein of HIV-1 is essential for retroviral replication and packaging. The nucleocapsid (NC) protein is the primary region for the interaction of Gag with nucleic acids. In this study, we examine the interactions of Gag and its NC cleavage products (NCp15, NCp9 and NCp7) with nucleic acids using solution and single molecule experiments. The NC cleavage products bound DNA with comparable affinity and strongly destabilized the DNA duplex. In contrast, the binding constant of Gag to DNA was found to be approximately 10-fold higher than that of the NC proteins, and its destabilizing effect on dsDNA was negligible. These findings are consistent with the primary function of Gag as a nucleic acid binding and packaging protein and the primary function of the NC proteins as nucleic acid chaperones. Also, our results suggest that NCp7's capability for fast sequence-nonspecific nucleic acid duplex destabilization, as well as its ability to facilitate nucleic acid strand annealing by inducing electrostatic attraction between strands, likely optimize the fully processed NC protein to facilitate complex nucleic acid secondary structure rearrangements. In contrast, Gag's stronger DNA binding and aggregation capabilities likely make it an effective chaperone for processes that do not require significant duplex destabilization.

Biophysical characterization of influenza virus subpopulations using field flow fractionation and multiangle light scattering: correlation of particle counts, size distribution and infectivity.

Adequate biophysical characterization of influenza virions is important for vaccine development. The influenza virus vaccines are produced from the allantoic fluid of developing chicken embryos. The process of viral replication produces a heterogeneous mixture of infectious and non-infectious viral particles with varying states of aggregation. The study of the relative distribution and behavior of different subpopulations and their inter-correlation can assist in the development of a robust process for a live virus vaccine. This report describes a field flow fractionation and multiangle light scattering (FFF-MALS) method optimized for the analysis of size distribution and total particle counts. The FFF-MALS method was compared with several other methods such as transmission electron microscopy (TEM), atomic force microscopy (AFM), size exclusion chromatography followed by MALS (SEC-MALS), quantitative reverse transcription polymerase chain reaction (RT Q-PCR), median tissue culture dose (TCID(50)), and the fluorescent focus assay (FFA). The correlation between the various methods for determining total particle counts, infectivity and size distribution is reported. The pros and cons of each of the analytical methods are discussed.

HIV-1 nucleocapsid protein as a nucleic acid chaperone: spectroscopic study of its helix-destabilizing properties, structural binding specificity, and annealing activity.

Assembly of infectious retroviral particles involves recognition of specific sequences on the viral RNA by the nucleocapsid (NC) domain of the Gag polyprotein, and subsequent stoichiometric binding of the processed NC protein along the entire length of the RNA. NC proteins also act as nucleic acid chaperones. They accelerate nucleic acid hybridization and strand exchange, which may be critical during the initial stages of reverse transcription. In order to better understand these properties, we have studied the nucleic acid helix-destabilizing t(m)-depressing) and binding activities of HIV-1 NCp7 protein with a variety of substrates, and the real-time kinetics of NC-induced strand exchange. At low ionic strength (0.01 M Na phosphate, pH 7.0) and saturating levels of protein, NCp7 displays moderate helix-destabilizing activity on double-stranded DNA. Saturating levels of NCp7 lowered the t(m) of a synthetic 28 base-pair 28(+)/28(-) oligonucleotide duplex by about 10 deg. C (51 to 41 degrees C). The presence of single-stranded calf thymus DNA (equimolar with duplex) eliminated the t(m) depression, whereas double-stranded calf thymus DNA only altered the t(m) of the 28-mer duplex by about 2 deg. C. Similar effects were seen with duplexes with single-stranded overhangs or internal single-stranded gaps. Binding experiments utilizing intrinsic tryptophan quenching indicated significant affinity (K(d) about 0.1 microM) for both single-stranded and double-stranded forms of the 28-mer in 0.01 M sodium phosphate at 25 degrees C, although long-chain (calf thymus double-stranded) DNA displayed a much lower affinity. The effects of NCp7 on the kinetics of nucleic acid annealing, strand exchange, and strand displacement were determined by use of oligonucleotides with end-labeled fluorophores serving as donor-acceptor pairs. NCp7 accelerated all these reactions. In the strand exchange reaction, an imperfect duplex, 28(+)/21(-), was reacted with a perfect complement, 28(-). The kinetics of 28(+)/28(-) annealing in this reaction did not conform to a simple bimolecular model, but could be well fit to the sum of two exponential decays. Addition of stoichiometric levels of NCp7 increased the rate constants of both components, and significantly increased the fraction of exchange associated with the rapid process. Increasing levels of 28(-) also increased the rapid fraction, as well as the rapid rate constant. This concentration dependence indicates that, although the kinetic decays appear biexponential, at least one of the steps is bimolecular. Simple annealing reactions, 28(+) with 28(-), could be fit to single-exponential decays, and their magnitudes in the presence of NCp7 were comparable to the rapid step of annealing observed for exchange reactions, suggesting that this step is connected with annealing. Strand dissociation during exchange was monitored by placing the fluorescent acceptor on the 21(-) strand. The results, though complex, suggest that the slow step of exchange is largely associated with the dissociation of the shorter oligonucleotide. Analogous experiments were performed with variants of these oligonucleotides, and the results are in line with the 28(+)/21(-)/28(-) experiments. On the basis of an analysis of the effect of increasing levels of 28(-) on the formation of the perfect 28 bp duplex from the imperfect duplex, we propose that NCp7 forms a ternary complex intermediate with imperfect duplex and 28(-), and suggest several ways by which such an intermediate would facilitate strand exchange.

Mechanism of reversible self-association of a monoclonal antibody: role of electrostatic and hydrophobic interactions.

Reversible self-association of protein therapeutics, the phenomenon of formation of native reversible oligomeric species as a result of noncovalent intermolecular interactions, can add additional manufacturing, stability, delivery, and safety complexities in biopharmaceutical development. Its early detection, characterization, and mitigation can therefore contribute to the success of drug development. A variety of structural and environmental factors can contribute to the modulation of self-association with mechanisms still elusive in some cases due to the inherent structural complexity of proteins. By combining the capabilities of dynamic and static light scattering techniques, the modulatory effects of a variety of solution conditions on a model IgG1's (mAbA) intermolecular interactions have been utilized to derive mechanism of its self-association at relatively low-protein concentration. The analysis of the effect of pH, buffer type, Hofmeister salts, and aromatic amino acids utilizing light scattering supported a combined role of hydrophobic and electrostatic interactions in mAbA self-association. Fitting of the data into the equilibrium models obtained from the multiangle static light scattering provided the enthalpic and entropic contributions of self-association, highlighting the more dominant effect of electrostatic interactions. In addition, studies of the Fab and Fc fragments of mAbA suggested the key role of the former in observed self-association.

Modulation of the Hydration Water Around Monoclonal Antibodies on Addition of Excipients Detected by Terahertz Time-Domain Spectroscopy.

Terahertz time-domain spectroscopy (THz-TDS) has been shown to detect overlapping extended hydration layers around proteins. Here, we used THz-TDS to detect modulation of the extended hydration layer around monoclonal antibodies (mAbs) by the introduction of commonly used excipients. Proline and sucrose altered the hydration layer around a mAb (mAb1), which was observed as a negative shift in the plateau in absorbance above ~100 mg/mL mAb1 (~70,000 water molecules per mAb); arginine had no effect. At lower concentrations of ~10 mg/mL mAb1 (~700,000 water molecules per mAb) proline and arginine modulated the hydration layer, which was observed as a negative shift in the relative absorbance, whereas sucrose had no effect. The changes in the extended hydration layer were not translated to shifts in the thermal stability or protein:protein interaction parameter. The hydration layer of a second mAb (mAb2) was further shown to be modulated by more complex formulations composed of two or more excipients; although the differences in terahertz absorbance were not predictive of viscosity or long-term stability. THz-TDS promises to be a useful tool for understanding a protein's interaction with excipients in solution and the challenge will be to determine how to apply this knowledge to protein formulation.

Characterisation of Stress-Induced Aggregate Size Distributions and Morphological Changes of a Bi-Specific Antibody Using Orthogonal Techniques.

A critical step in monoclonal antibody (mAb) screening and formulation selection is the ability of the mAb to resist aggregation following exposure to environmental stresses. Regulatory authorities welcome not only information on the presence of micron-sized particles, but often any information on sub-visible particles in the size range obtained by orthogonal sizing techniques. The present study demonstrates the power of combining established techniques such as dynamic light scattering (DLS) and micro-flow imaging (MFI), with novel analyses such as raster image correlation spectroscopy (RICS) that offer to bridge existent particle sizing gaps in this area. The influence of thermal and freeze-thaw stress treatments on particle size and morphology was assessed for a bi-specific antibody (mAb2). Aggregation of mAb2 was confirmed to be concentration- and treatment-dependent following thermal stress and freeze-thaw cycling. Particle size and count data show concentration- and treatment-dependent behaviour of aggregate counts, morphological descriptors and particle size distributions. Complementarity in particle size output was observed between all approaches utilised, where RICS bridged the analytical size gap (∼0.5-5 µm) between DLS and MFI. Overall, this study highlights the potential of orthogonal image analyses such as RICS (analytical size gap) and MFI (particle morphology) for formulation screening.

Fluorescence and nucleic acid binding properties of bovine leukemia virus nucleocapsid protein.

We used the intrinsic fluorescence of bovine leukemia virus p12, a nucleocapsid protein with two tryptophan-containing zinc fingers (ZFs), to study its conformation and binding to single-stranded nucleic acids. Spectral emission maxima suggested solvent-exposed tryptophans. A peptide derived from ZF1 had a higher quantum yield and longer average lifetime (tau) than ZF2. BLV p12 tau and rotational correlation time were greater than ZF values, but all de-metallated sequences gave similar results. Apo p12 showed reduced fluorescence intensity, tau and loss of secondary structure. DNA-binding affinity of p12 was in the nanomolar range, and decreased 14-fold after Zn++ ejection. Nucleobase preference of BLV p12 was different from the closely related HTLV-1 but similar to HIV-1 and SIV nucleocapsids, both phylogenetically distant.

Bisimidazoacridones: 2. Steady-state and time-resolved fluorescence studies of their diverse interactions with DNA.

Several bisimidazoacridones (BIA) are potent, selective antineoplastic agents, whereas others have potent anti-human immunodeficiency virus activity. BIA are bifunctional agents that consist of two imidazoacridone (IA) chromophores held together by various linkers. Interaction of BIA with DNA has been postulated to be required for their biological activity. Fluorescence data on free and bound BIA suggest that the binding of BIA and similar drugs to DNA is driven by a transfer of hydrophobic molecules from aqueous media to the more amphiphilic DNA environment. Binding to DNA was sensitive to sequence and depended on the length and rigidity of the linker. Time-resolved fluorescence measurements showed that BIA adopt an extended conformation upon binding and that all of the molecules are tightly associated with DNA. Gel-shift and melting assays indicated that one of the aromatic residues of BIA is intercalated, whereas the other, together with a linker, resides in a groove, probably the minor groove. A continuum of structures may be possible where intercalation and classical minor groove binding are limiting structures. In general, the hypothesis for the mechanism of action of BIA wherein the unintercalated residue, accessible for additional interactions, captures a critical protein involved in repair or transcription, is consistent with this model.

Thermodynamic stability and flexibility characteristics of antibody fragment complexes.

Free energy landscapes, backbone flexibility and residue-residue couplings for being co-rigid or co-flexible are calculated from the minimal Distance Constraint Model (mDCM) on an exploratory dataset consisting of VL, scFv and Fab antibody fragments. Experimental heat capacity curves are reproduced markedly well, and an analysis of quantitative stability/flexibility relationships (QSFR) is applied to a representative VL domain and several complexes in the scFv and Fab forms. Global flexibility in the denatured ensemble typically decreases in the larger complexes due to domain-domain interfaces. Slight decreases in global flexibility also occur in the native state of the larger fragments, but with a concurrent large increase in correlated flexibility. Typically, a VL fragment has more co-rigid residue pairs when isolated compared to the scFv and Fab forms, where correlated flexibility appears upon complex formation. This context dependence on residue- residue couplings in the VL domain across length scales of a complex is consistent with the evolutionary hypothesis of antibody maturation. In comparing two scFv mutants with similar thermodynamic stability, local and long-ranged changes in backbone flexibility are observed. In the case of anti-p24 HIV-1 Fab, a variety of QSFR metrics were found to be atypical, which includes comparatively greater co-flexibility in the VH domain and less co-flexibility in the VL domain. Interestingly, this fragment is the only example of a polyspecific antibody in our dataset. Finally, the mDCM method is extended to cases where thermodynamic data is incomplete, enabling high throughput QSFR studies on large numbers of antibody fragments and their complexes.

Redistribution of flexibility in stabilizing antibody fragment mutants follows Le Châtelier's principle.

Le Châtelier's principle is the cornerstone of our understanding of chemical equilibria. When a system at equilibrium undergoes a change in concentration or thermodynamic state (i.e., temperature, pressure, etc.), La Châtelier's principle states that an equilibrium shift will occur to offset the perturbation and a new equilibrium is established. We demonstrate that the effects of stabilizing mutations on the rigidity ⇔ flexibility equilibrium within the native state ensemble manifest themselves through enthalpy-entropy compensation as the protein structure adjusts to restore the global balance between the two. Specifically, we characterize the effects of mutation to single chain fragments of the anti-lymphotoxin-ß receptor antibody using a computational Distance Constraint Model. Statistically significant changes in the distribution of both rigidity and flexibility within the molecular structure is typically observed, where the local perturbations often lead to distal shifts in flexibility and rigidity profiles. Nevertheless, the net gain or loss in flexibility of individual mutants can be skewed. Despite all mutants being exclusively stabilizing in this dataset, increased flexibility is slightly more common than increased rigidity. Mechanistically the redistribution of flexibility is largely controlled by changes in the H-bond network. For example, a stabilizing mutation can induce an increase in rigidity locally due to the formation of new H-bonds, and simultaneously break H-bonds elsewhere leading to increased flexibility distant from the mutation site via Le Châtelier. Increased flexibility within the VH ß4/ß5 loop is a noteworthy illustration of this long-range effect.

The effect of palmitoylation on the conformation and physical stability of a model peptide hormone.

Peptides are ideal drug candidates due to their potency and specificity, but suffer from a short half-life and low membrane permeability. Acylation can overcome these limitations but the consequences to stability under different formulation conditions and stresses are largely unreported. Using synchrotron radiation circular dichroism (SRCD), we show that palmitoylation of a 28 amino acid peptide hormone (pI 9.82) induced a structural transition from 310-helix to α-helix, irrespective of buffer type and pH investigated (5.5-8.0) when compared to the non acylated analogues. These conformational preferences were retained in the presence of non-ionic micelles but not anionic micelles, which induced an α-helical structure for all peptides. Palmitoylation promoted an irreversible peptide denaturation under thermal stress at pH ≥ 6.5 and increased the propensity for loss of helical structure under high photon flux (here used as a novel accelerated photostability test). The presence of either ionic or non-ionic micelles did not recover these conformational changes over the same irradiation period. These results demonstrate that acylation can change peptide conformation and decrease thermal-/photo-stability, with important consequences for drug-development strategies.

A systematic multitechnique approach for detection and characterization of reversible self-association during formulation development of therapeutic antibodies.

In addition to controlling typical instabilities such as physical and chemical degradations, understanding monoclonal antibodies' (mAbs) solution behavior is a key step in designing and developing process and formulation controls during their development. Reversible self-association (RSA), a unique solution property in which native, reversible oligomeric species are formed as a result of the noncovalent intermolecular interactions has been recognized as a developability risk with the potential to negatively impact manufacturing, storage stability, and delivery of mAbs. Therefore, its identification, characterization, and mitigation are key requirements during formulation development. Considering the large number of available analytical methods, choice of the employed technique is an important contributing factor for successful investigation of RSA. Herein, a multitechnique (dynamic light scattering, multiangle static light scattering, and analytical ultracentrifugation) approach is employed to comprehensively characterize the self-association of a model immunoglobulin G1 molecule. Studies herein discuss an effective approach for detection and characterization of RSA during biopharmaceutical development based on the capabilities of each technique, their complementarity, and more importantly their suitability for the stage of development in which RSA is investigated.

A systematic multitechnique approach for detection and characterization of reversible self-association during formulation development of therapeutic antibodies.

In addition to controlling typical instabilities such as physical and chemical degradations, understanding monoclonal antibodies' (mAbs) solution behavior is a key step in designing and developing process and formulation controls during their development. Reversible self-association (RSA), a unique solution property in which native, reversible oligomeric species are formed as a result of the noncovalent intermolecular interactions has been recognized as a developability risk with the potential to negatively impact manufacturing, storage stability, and delivery of mAbs. Therefore, its identification, characterization, and mitigation are key requirements during formulation development. Considering the large number of available analytical methods, choice of the employed technique is an important contributing factor for successful investigation of RSA. Herein, a multitechnique (dynamic light scattering, multiangle static light scattering, and analytical ultracentrifugation) approach is employed to comprehensively characterize the self-association of a model immunoglobulin G1 molecule. Studies herein discuss an effective approach for detection and characterization of RSA during biopharmaceutical development based on the capabilities of each technique, their complementarity, and more importantly their suitability for the stage of development in which RSA is investigated.

Evaluation of a synthetic peptide as a replacement for the recombinant fusion protein of respiratory syncytial virus in a potency ELISA.

This report describes the development of a potency ELISA using a peptide derived from the motavizumab binding epitope of respiratory syncytial virus (RSV) F-protein. Motavizumab is an antibody therapeutic studied for the prevention of RSV disease. It binds to the RSV glycoprotein F (F-protein), blocking the ability of RSV to fuse with target cells. This binding is the basis for a potency ELISA, however, due to inefficient F-protein production, development of an alternative ligand for the potency ELISA was investigated. A series of synthetic peptides spanning the motavizumab epitope on F-protein were evaluated for motavizumab binding activity. A 26-mer peptide was identified with desirable motavizumab binding kinetics, as shown by ELISA and surface plasmon resonance. The peptide corresponds to a portion of the motavizumab binding domain on the F-protein, and is referred to as F-peptide. The binding of motavizumab to the F-peptide is used in a new motavizumab potency ELISA, which was shown to be robust and statistically comparable to the F-protein ELISA. In addition, based on a qualitative observation, this new ELISA may be able to detect motavizumab degradation with greater sensitivity compared to the F-protein ELISA.

Improved particle counting and size distribution determination of aggregated virus populations by asymmetric flow field-flow fractionation and multiangle light scattering techniques.

A method using a combination of asymmetric flow field-flow fractionation (AFFFF) and multiangle light scattering (MALS) techniques has been shown to improve the estimation of virus particle counts and the amount of aggregated virus in laboratory samples. The method is based on the spherical particle counting approach given by Wyatt and Weida in 2004, with additional modifications. The new method was tested by analyzing polystyrene beads and adenovirus samples, both having a well-characterized particle size and concentration. Influenza virus samples were analyzed by the new AFFFF-MALS technique, and particle size and aggregate state were compared with results from atomic force microscopy analysis. The limitations and source of possible errors for the new AFFFF-MALS analysis are discussed.