Glycosaminoglycans are heterogeneous polysaccharides that mediate important biological functions. There has been considerable interest in deciphering the precise GAG sequences that are responsible for protein interactions. In fact, several GAG oligosaccharides have been discovered to date as targeting proteins with higher level of specificity. Yet, it has been difficult to develop GAG oligosaccharides as drugs. One of the key reasons for this state of art is that GAG synthesis is extremely challenging and is highly structure-specific. Thus, much of the biology and pharmacology of GAG remains unknown and unexploited to date. An alternative approach is to prepare GAG oligosaccharides using enzymatic depolymerization of polymeric GAGs. GAG lyases, including heparinases and chondritinases represent powerful tools that can theoretically generate multiple oligosaccharides in parallel. However, it is difficult to implement such procedures with high consistency. Moreover, GAG lyases can digest GAGs down to disaccharides. A priori, non-polymeric GAGs, or alternatively GAG oligosaccharides containing 4 to 10 residues, would be expected to function better as therapeutic agents because they would be more homogeneous and less non-specific than their polymeric precursors. Thus, we reasoned that immobilization of these enzymes may engineer altered biopolymer processing, which may afford longer oligosaccharides in higher proportions and greater consistency. Heparinase-I and chondroitinase ABC were immobilized on CNBr-activated Sepharose and compared with the free form of the enzyme. Immobilized GAG lyases retained high efficiency of depolymerization over a wide range of pH, temperature and reusability. Most importantly, the immobilized enzyme was found to produce larger proportions of oligosaccharides longer than di- and tetra-saccharides as compared to lyases in the free form. A two dimensional separation involves size exclusion chromatography followed by reversed phase ion-pairing ultra performance liquid chromatography coupled to electrospray ionization mass spectrometry was employed to separate and characterize oligosaccharide structures. We have identified 40 heparin oligosaccharides, including regular and rare structures ranging from dp4 to dp10 and 39 chondroitin sulfate oligosaccharides in high homogeneity and significant yields. Overall, this technology is likely to offer a simple and cost effective route to preparation of larger amounts of sequences that can be expected to bind and modulate protein function.

The hydrophobicity of a surface is an important property in many areas of science and engineering. This is especially the case in mineral processing, where differences in surface hydrophobicity lie at the heart of the separation process of flotation. Chemicals are used to increase and decrease the natural hydrophobicity of minerals to attain a better separation between valuable and worthless material. Polymers are often used to reduce mineral surface hydrophobicity. Decades of empirically based decision making have produced a list of effective depressants. However the detailed study of how these polymer depressants affect surface hydrophobicity and mineral recovery lags behind applied investigations. The aim of this thesis was to study the adsorption of commonly used depressants on model surfaces and to interrogate the action of these polymers in reducing surface hydrophobicity. We have modelled the degree of hydrophobicity of common minerals in order to study polymer depressants with methods not commonly used in studies of surface characterisation in flotation. The model surfaces (self-assembled monolayers, SAMs) allowed us to use the quartz crystal microbalance with dissipation monitoring (QCM-D) to study the adsorption of polymers. The QCM-D can be used to obtain adsorption isotherms, adsorption kinetics, water content of adsorbed layers, and information on the conformation of the adsorbed polymer. The results from the QCM-D were correlated with the contact angle data from the captive bubble measurements, with which we assessed the hydrophobicity of the surface before and after polymer adsorption. Three of the polymers layers were probed with dynamic dewetting studies, in order to test other modes of depressant action. Three types of polymers were studied - a polyacrylamide (Polymer-H), a polyelectrolyte CMC (carboxymethyl cellulose) and a group of dextrins (Dextrin-TY, a phenyl succinate substituted dextrin (PS Dextrin) and a styrene oxide substituted dextrin (SO Dextrin)). These polymers are commonly used or have potential to be used in the depression of talc and graphite. Polymer-H was used to investigate the hydrophobic bonding between a non-ionic polymer depressant and chemically inert and non charged surfaces by probing the influence of substrate hydrophobicity on polymer adsorption and reduction of contact angle. Three different model surfaces were used (mixed self-assembled 0.5 SAM, 0.7 SAM or single self-assembled 1.0 SAM monolayers) with advancing contact angles between 75?? and 119??. The study of Polymer-H found that the substrate hydrophobicity is an important factor in adsorption of this polymer and the change in contact angle upon adsorption depends on adsorbed amount. The effectiveness of Polymer-H to reduce surface hydrophobicity was established to correlate with its conformation and morphology. CMC was investigated to find out how a stimulus responsive polymer depressant can be used in flotation. It was established that the adsorbed amount and rate of adsorption of CMC increase with decreasing of pH or increasing of ionic strength. It was shown that the surface hydrophobicity of a CMC pre-adsorbed layer changes with the environment and these alterations are fully reversible. A switch of ionic strength (from 10-2 M KCl to 10-1 M KCl) caused partial dehydration of the adsorbed layer and a decrease of the receding contact angle by 20??. A pH switch (pH = 9 to pH = 3) resulted in a 40?? change in receding contact angle. The CMC investigation showed that the use of a stimulus responsive polymer presents opportunities for exploiting solution conditions as a means to effect a better mineral separation in flotation The adsorption of three dextrin-based polymers on a model hydrophobic surface has been characterized using the quartz crystal microbalance with dissipation monitoring (QCM-D). The three polymers (one standard dextrin and two dextrins with different aromatic group substitutions) exhibited varying affinities and capacity for adsorption on the hydrophobic substrate. The effect of the three polymers on the static contact angle of the surface was studied using captive bubble contact angle measurements. The three polymers were seen to reduce the receding contact angle by similar amounts (approximately 14 degrees) in spite of having varying adsorbed amounts and differences in adsorbed layer water content. Although no differences were observed in the ability of the polymers to reduce the static contact angle, measurements of the dewetting dynamics between a rising air bubble and the polymer covered substrate yielded stark differences between the polymers, with one polymer slowing the dewetting dynamics by an order of magnitude more than the other two polymers. The differences in dewetting behaviour correlate with the adsorbed layer characteristics determined by QCM-D. / Thesis (PhD)--University of South Australia, 2010

Macromolecular interactions play very important roles in regulation of all levels of biological processes. Aberrant macromolecular interactions often result in diseases. By applying a combination of spectroscopy, calorimetry, computation and other techniques, the protein-protein interactions in the system of the Shaw2 Kv channel and the protein-RNA interactions in West Nile virus RNA-cellular protein TIAR complex were explored. In the former system, the results shed light on the local structures of the key channel components and their potential interaction mediated by butanol, a general anesthetic. In the later studies, the binding modes of TIAR RRM2 to oligoU RNAs and West Nile virus RNAs were investigated. These findings provided insights into the basis of the specific cellular protein–viral RNA interaction and preliminary data for the development of strategies on how to interfere with virus replication

The thesis, which contains nine chapters, reports extensive large scale atomistic molecular dynamics (MD) simulation studies of water structure and dynamics at the surface of an anionic micelle, hydration layer of two proteins, and in the grooves of a 38-base pairs long DNA. Understanding the structure and dynamics of water molecules at the surfaces of self-organized assemblies and complex biological macromolecules has become a subject of intense research in recent times. Chapter 1 contains a brief overview of the biomolecular hydration dynamics. Relevant experimental, computational, and theoretical studies of biomolecular hydration and the time scales associated with the water dynamics are discussed. In Chapters 2 and 3, the structure, environment, energetics, and dynamics of constrained water molecules in the aqueous anionic micelle of cesium perfluorooctanoate (CsPFO) have been studied using large scale atomistic molecular dynamics simulations. Based on the number of hydrogen bond (HB) that interfacial water molecule makes with the polar head group (PHG) oxygen of the micelle, we find the existence of three kinds of water at the interface. We introduce a nomenclature to identify the species as IBW2 (form two HBs with two different PHG), IBW1 (form one HB with PHG), and IFW (no HB with PHG). Despite of possessing two strong w-PHG bonds, the concentration of the IBW2 species is rather low due to entropic effect. The ion solvation dynamics study at the interface shows the presence of a slow component, with a relaxation time 1-2 order of magnitude slower than that in the corresponding bulk solvent in agreement with the experimental results. Both the translational and orientational dynamics of the water molecules near the micellar surface is found to be much slower than those in the bulk. The HB between the PHG of the micelle and the water molecule has almost 13 times longer life time than that in the bulk between two tagged water molecules. In Chapter 4, we present results of extensive atomistic MD simulation studies of the structure and dynamics of aqueous protein solution of the toxic domain of Enterotoxin (1ETN) and the chicken villin headpiece sub-domain containing 36 amino acid residues (HP-36). Reduced water structure and the faster water dynamics around the active site of these proteins have been observed which may have biological significance. Chapter 5 presents an extensive atomistic molecular dynamics simulations study of water dynamics in the hydration layer of a 38 base long hydrated DNA duplex. The computed rotational time correlation function (TCF) of the minor groove water dipoles is found to be markedly non-exponential with a slow component at long time. The constrained water molecule is also found to exhibit anisotropic diffusion in both the major and minor grooves. At short-to-intermediate times, translational motion of water molecules in minor groove is sub-diffusive. Chapter 6 presents the study of water entropy in both the grooves DNA. The average values of the entropy of water at 300K in both the grooves of DNA are found to be significantly lower than that in bulk water. We propose that the configurational entropy of water in the grooves can be used as a measure of the mobility (or micro viscosity) of water molecules in a given domain. In Chapter 7, we study the specific DNA base-water hydrogen bond lifetime (HBLT) dynamics at the major and the minor grooves of a hydrated duplex. The base-water HBLT correlation functions are in general multi-exponential and the average lifetime depends significantly on the specificity of the DNA sequence. The average HBLT is longer in the minor groove than that in the major groove by almost a factor of 2. Chapter 8 presents the solvation dynamics of constituent bases of aqueous DNA duplex. The solvation TCFs of the four individual bases display highly non-exponential decay with time. An interesting negative cross-correlation between water and counterions is observed which makes an important contribution to relaxation at intermediate to longer times. In the concluding note, Chapter 9 presents a brief summary of the outcome of the thesis and suggests several relevant problems that may prove w orthwhile to be addressed in future

The thesis focuses on elastic polymer material that is biodegradable and compatible with human cells and tissues. The presented research describes polymer synthesis, material processing, physico-chemical investigation and biological tests performed on this novel biomaterial.

The hydrophobicity of a surface is an important property in many areas of science and engineering. This is especially the case in mineral processing, where differences in surface hydrophobicity lie at the heart of the separation process of flotation. Chemicals are used to increase and decrease the natural hydrophobicity of minerals to attain a better separation between valuable and worthless material. Polymers are often used to reduce mineral surface hydrophobicity. Decades of empirically based decision making have produced a list of effective depressants. However the detailed study of how these polymer depressants affect surface hydrophobicity and mineral recovery lags behind applied investigations. The aim of this thesis was to study the adsorption of commonly used depressants on model surfaces and to interrogate the action of these polymers in reducing surface hydrophobicity. We have modelled the degree of hydrophobicity of common minerals in order to study polymer depressants with methods not commonly used in studies of surface characterisation in flotation. The model surfaces (self-assembled monolayers, SAMs) allowed us to use the quartz crystal microbalance with dissipation monitoring (QCM-D) to study the adsorption of polymers. The QCM-D can be used to obtain adsorption isotherms, adsorption kinetics, water content of adsorbed layers, and information on the conformation of the adsorbed polymer. The results from the QCM-D were correlated with the contact angle data from the captive bubble measurements, with which we assessed the hydrophobicity of the surface before and after polymer adsorption. Three of the polymers layers were probed with dynamic dewetting studies, in order to test other modes of depressant action. Three types of polymers were studied - a polyacrylamide (Polymer-H), a polyelectrolyte CMC (carboxymethyl cellulose) and a group of dextrins (Dextrin-TY, a phenyl succinate substituted dextrin (PS Dextrin) and a styrene oxide substituted dextrin (SO Dextrin)). These polymers are commonly used or have potential to be used in the depression of talc and graphite. Polymer-H was used to investigate the hydrophobic bonding between a non-ionic polymer depressant and chemically inert and non charged surfaces by probing the influence of substrate hydrophobicity on polymer adsorption and reduction of contact angle. Three different model surfaces were used (mixed self-assembled 0.5 SAM, 0.7 SAM or single self-assembled 1.0 SAM monolayers) with advancing contact angles between 75?? and 119??. The study of Polymer-H found that the substrate hydrophobicity is an important factor in adsorption of this polymer and the change in contact angle upon adsorption depends on adsorbed amount. The effectiveness of Polymer-H to reduce surface hydrophobicity was established to correlate with its conformation and morphology. CMC was investigated to find out how a stimulus responsive polymer depressant can be used in flotation. It was established that the adsorbed amount and rate of adsorption of CMC increase with decreasing of pH or increasing of ionic strength. It was shown that the surface hydrophobicity of a CMC pre-adsorbed layer changes with the environment and these alterations are fully reversible. A switch of ionic strength (from 10-2 M KCl to 10-1 M KCl) caused partial dehydration of the adsorbed layer and a decrease of the receding contact angle by 20??. A pH switch (pH = 9 to pH = 3) resulted in a 40?? change in receding contact angle. The CMC investigation showed that the use of a stimulus responsive polymer presents opportunities for exploiting solution conditions as a means to effect a better mineral separation in flotation The adsorption of three dextrin-based polymers on a model hydrophobic surface has been characterized using the quartz crystal microbalance with dissipation monitoring (QCM-D). The three polymers (one standard dextrin and two dextrins with different aromatic group substitutions) exhibited varying affinities and capacity for adsorption on the hydrophobic substrate. The effect of the three polymers on the static contact angle of the surface was studied using captive bubble contact angle measurements. The three polymers were seen to reduce the receding contact angle by similar amounts (approximately 14 degrees) in spite of having varying adsorbed amounts and differences in adsorbed layer water content. Although no differences were observed in the ability of the polymers to reduce the static contact angle, measurements of the dewetting dynamics between a rising air bubble and the polymer covered substrate yielded stark differences between the polymers, with one polymer slowing the dewetting dynamics by an order of magnitude more than the other two polymers. The differences in dewetting behaviour correlate with the adsorbed layer characteristics determined by QCM-D. / Thesis (PhD)--University of South Australia, 2010

In a 4-cell C. elegans embryo the ventral blastomere EMS requires polarity signaling from its posterior sister cell, P2. This signaling event enables EMS to orient its division spindle along the anterior-posterior (A/P) axis and to specify the endoderm fate of its posterior daughter cell, E. Wnt pathway components have been implicated in mediating P2/EMS signaling. However, no single mutants or various mutant combinations of the Wnt pathway components disrupt EMS polarity completely. Here we describe the identification of a pathway that is defined by two tyrosine kinase related proteins, SRC-1 and MES-1, which function in parallel with Wnt signaling to specify endoderm and to orient the division axis of EMS. We show that SRC-1, a C. elegans homolog of c-Src, functions downstream of MES-1 to specifically enhance phosphotyrosine accumulation at the P2/EMS junction in order to control cell fate and mitotic spindle orientation in both the P2 and EMS cells. In the canonical Wnt pathway, GSK-3 is conserved across species and acts as a negative regulator. However, in C. elegans we find that GSK-3 functions in a positive manner and in parallel with other components in the Wnt pathway to specify endoderm during embryogenesis. In addition, we also show that GSK-3 regulates C. elegans germline development, a function of GSK-3 that is not associated with Wnt signaling. It is required for the differentiation of somatic gonadal cells as well as the regulation of meiotic cell cycle in germ cells. Our results indicate that GSK-3 modulates multiple signaling pathways to regulate both embryogenesis and germline development in C. elegans.

The primary goal of my thesis research was to characterize the basis for the hypersensitive response of glycogen phosphorylase to catecholamine stimulation in primary culture diabetic cardiomyocytes. Toward this goal, I have investigated several key regulatory sites in this signaling pathway which could promote the hypersensitive activation of phosphorylase. Specifically, I investigated (1) which adrenergic receptors are involved in mediating the hypersensitive response of glycogen phosphorylase to epinephrine stimulation; (2) whether the presence of fatty acid metabolites affects phosphorylase activation; (3) whether the hypersensitive response of phosphorylase results from altered signal transduction through the β-adrenergic receptor system or from a post-receptor defect; and (4) the potential role for phosphorylase kinase in mediating the hypersensitive response of phosphorylase to catecholamine stimulation. The basis for adrenergic receptor mediation of the catecholamine-induced activation of glycogen phosphorylase was investigated in adult rat cardiomyocytes isolated from normal and alloxan-diabetic animals. Cells derived from diabetic animals exhibited a hypersensitive response to epinephrine stimulation which was apparent 3 hours after cell isolation and was further enhanced upon maintenance of the myocytes in culture for 24 hours. Normal cells initially lacked the hypersensitive response to epinephrine stimulation although upon maintenance of these cells in culture for 24 hours, the hypersensitive response was acquired in vitro. To assess alpha- and beta- adrenergic mediation of the response, normal and diabetic cardiomyocytes were incubated with propranolol, a β-receptor antagonist, prior to direct α1receptor stimulation with phenylephrine. Both normal and diabetic myocytes failed to undergo activation of phosphorylase in 3 or 24 hour cell cultures. In addition, the effects of epinephrine on phosphorylase activation were completely inhibited by propranolol whereas prazosin, an α-receptor antagonist, was unsuccessful. This data suggests that the hypersensitive response of glycogen phosphorylase in normal and diabetic cardiomyocytes is solely mediated through β-adrenergic receptor activation. Since the accumulation of various fatty acid metabolites can affect certain enzymes and signal transduction pathways within the cell, the potential effect of various fatty acid metabolites on phosphorylase activation was investigated. To determine the potential effects of fatty acid metabolites on phosphorylase activation in cultured cardiomyocytes, normal and alloxan-diabetic cells were incubated with either carnitine or palmitoylcarnitine prior to stimulation with epinephrine. Pretreatment of cardiomyocytes with or without carnitine or palmitoylcarnitine for 3 or 24 hours before epinephrine stimulation failed to alter phosphorylase activation. The addition of exogenous carnitine in the absence and presence of insulin was also unsuccessful in attenuating the hypersensitive phosphorylase activation response in 3 and 24 hour, normal and alloxan-diabetic derived cardiomyocytes. To determine if carnitine palmitoyltransferase 1 (CPT-1) activity was responsible for the hypersensitive response of phosphorylase in the diabetic myocytes, both normal and diabetic myocytes were maintained for 3 and 24 hours in the absence and presence of etomoxir, a CPT-1 inhibitor. Subsequent activation of phosphorylase by epinephrine in normal and diabetic myocytes was unaltered in the presence of etomoxir. Collectively, these data fail to support a critical role for fatty acid metabolite involvement in the hypersensitive activation of glycogen phosphorylase in acute, alloxan-diabetic cardiomyocytes. To assess potential G-protein involvement in the response, normal and diabetic-derived myocytes were incubated with either cholera or pertussis toxin prior to hormonal stimulation. Pretreatment of cardiomyocytes with cholera toxin resulted in a potentiated response to epinephrine stimulation whereas pertussis toxin did not affect the activation of this signaling pathway. To determine if the enhanced response of phosphorylase activation resulted from an alteration in adenylyl cyclase activation, the cells were challenged with forskolin. After 3 hours in primary culture, diabetic cardiomyocytes exhibited a hypersensitive response to forskolin stimulation relative to normal cells. However, after 24 hours in culture, both normal and diabetic myocytes responded identically to forskolin challenge. The present data suggest that a cholera toxin sensitive G-protein mediates the hypersensitive response of glycogen phosphorylase to catecholamine stimulation in diabetic cardiomyocytes. This response, which is present in alloxan-diabetic cells, and is induced in vitroin normal cardiomyocytes, is primarily due to a defect at a post-receptor site. To assess the role of phosphorylase kinase in the hypersensitive activation of glycogen phosphorylase in the diabetic heart, phosphorylase kinase activity was measured initially in perfused hearts (to optimize the assay parameters) and subsequently in primary culture cardiomyocytes. Results from these experiments demonstrate that the present method for measuring phosphorylase kinase activity is a reliable indicator of the enzyme's activity in the heart, although the assay conditions must be further optimized before this system can be applied to the measurement of phosphorylase kinase activity in primary cultured cardiomyocytes.

L'objectif de cette thèse est l'étude des conséquences de la thermo-oxydation sur la structure chimique et le comportement mécanique d'un Ethylène Propylène Diène Monomère (EPDM). Afin de déterminer les modifications à différentes échelles structurales, quatre formulations modèles sont étudiées : la gomme pure, les matrices vulcanisées stabilisée et non stabilisée et l'élastomère industriel. L'ensemble des échantillons est vieilli entre 70 et 170°C dans l'air ou sous vide puis caractérisé par divers outils analytiques. La thermogravimétrie donne accès aux variations de masse résultant de l'incorporation d'oxygène et l'émission de composés volatils. L'analyse infrarouge permet de suivre les évolutions des espèces chimiques. Les essais de gonflement, de chromatographie et de spectrométrie mécanique permettent de calculer les nombres de coupures de chaînes et d'actes de réticulation à chaque instant. Sur la base de ces résultats, un modèle cinétique général de thermo-oxydation de la matrice EPDM est proposé et en partie validé. Les conséquences du vieillissement thermique sur le comportement mécanique de l'élastomère industriel sont mises en évidence par des essais de traction uniaxiale et de multi-relaxation à température ambiante et vitesse de déformation initiale de 10-3 s-1. L'impact du vieillissement thermique sur les propriétés ultimes et les réponses à l'équilibre et hors équilibre est examiné. Un critère prédictif de rupture basé sur la mécanique de la rupture est proposé. Enfin, le couplage vieillissement thermique - contrainte mécanique est étudié par des essais relaxation de contraintes continues entre 130 et 170°C dans l'air. Les modifications de la microstructure pendant le vieillissement thermique sont intégrées dans les équations constitutives du modèle mécanique macroscopique afin de proposer un outil de prédiction du comportement à long terme de l'élastomère industriel. La simulation numérique montre une bonne adéquation avec les résultats expérimentaux. / The aim of this work is to study the consequences of the thermal oxidation on the chemical structure and mechanical behavior of an Ethylene-Propylene-Diene Monomer (EPDM). In order to determine the structural changes at different scales, four model formulations have been considered: free additive gum, stabilized and unstabilized vulcanized matrix and industrial rubber. All samples were aged between 70 and 170°C in air or vacuum and characterized by several analytical tools. Thermogravimetry gives access to weight variations due to oxygen grafting and volatile compounds release. Infrared analysis is used to follow chemical species evolutions. Swelling tests, chromatographic and mechanical spectrometry tests allow calculating the number of chain scission and cross-linking events at any time. Based on these results, a general kinetic model is proposed and partially validated for EPDM matrix thermal oxidation. The consequences of thermal ageing on the mechanical behavior of the industrial rubber are pointed out by monotonic tensile and stress relaxation tests at room temperature and a 10-3 s-1- initial strain rate. The impact of thermal ageing on ultimate properties and equilibrium and non-equilibrium response are examined. Finally, the coupling between thermal ageing and mechanical stress is studied by continuous stress relaxation tests between 130 et 170°C in air. The microstructural modifications during thermal ageing are introduced into the constitutive equations of the macroscopic mechanical model in order to propose a predictif tool of the long time behavior of the industrial rubber. The numerical simulation is in good agreement with experimental results.

The goal of this thesis has been to throw light on a selection of open problems in chemical and biological physics using the general principles of statistical mechanics. These problems are all broadly concerned with the role of fluctuations in the dynamics of macromolecular systems. More specifically, they are concerned with identifying the microscopic roots of a number of interesting and unusual effects, including fractional viscoelasticity, anomalous chain cyclization dynamics in crowded environments, subdifffusion in hair bundles, symmetries in the work distributions of stretched polymers, heterogeneities in the geometries of reptation channels in polymer melts, and non-Gaussianity in the distributions of the end products of gene expression. I have shown here that all these effects are expressions of essentially the same underlying process of stochasticity, which can be described in terms of the dynamics of a point particle or a continuous curve that evolves in simple potentials under the action of white or colored Gaussian noise [8]. I have also shown that this minimal model of time-dependent behavior in condensed phases is amenable to analysis, often exactly, by path integral methods [13-15], which are naturally suited to the treatment of random processes in many-body physics. The results of such analyses are theoretical expressions for various experimentally measured quantities, comparisons with which form the basis for developing physical intuition about the phenomena under study. The general success of this approach to the study of stochasticity in biophysics and molecular biology holds out hopes of its application to other unsolved problems in these fields. These include electrical transport in DNA [143], quantum coherence in photosynthesis [144], power generation in molecular motors [145], cell signaling and chemotaxis [146], space dependent diffusion [147], and self-organization of active matter [148], to name a few. Most of these problems are characterized by non-linearities of one kind or another, so they add a new layer of complexity to the problems considered in this thesis. Although path integral and related field theoretic methods are equipped to handle such complexities, the attendant calculations are expected to be non-trivial, and the challenge to theory will be to devise effective approximation schemes for these methods, or to develop new and more sophisticated methods altogether.