Bayesian Estimation in a Generalized Negative Binomial Distribution

A generalized negative binomial (GNB) distribution was introduced by JAIN and CONSUL (1971) and was modified by NELSON (1975). The probability function of the distribution is defined by the function p(x; m, β, θ)= θ^x (1 - θ)^m+βx—x for x=0, 1, …, and zero otherwise, where m>0, 0<θ<1 and β=0 or 1≦β<θ^?1. The Bayes estimators for a number of parametric functions of θ when m and β are known are derived. The prior information on θ may be given by a beta distribution, B(a, b), to which no subjective significance is attached. It has been illustrated that the parameters in the prior distribution can be assigned by a computer. Comparisons are made of the Bayes estimate of P(X=k) to the corresponding ML estimate and the MVU estimate for any given sample to the order n^?1 for different values of k..     

Stereochemistry of nucleic acids and their constituents. IV. Allowed and preferred conformations of nucleosides,nucleoside mono-, di-, tri-, tetraphosphates,nucleic acids and polynucleotides

A uniform notation and convention is suggested to describe the torsional angles in nucleic acids and their derivatives. The torsional angle χ, relating the stereochemistry of the base with respect to the sugar, shows more variation for the β-purine glycosides than for the β-pyrimidine glycosides. This variation is attributed to the fact that the β-purine derivatives may form intramolecular O(5′)-H…N(3) hydrogen bonding. The χ values for the α-purine and α-pyrimidine glycosides show preference for the –syn-clinal (or anti) conformation. The mode of puckering of the sugar also influences the χ value. The various possible conformations for the furanose ring are described by the torsional angles τ₀ τ₁, τ₂, τ₃, τ₄, about the five ring bonds. From an analysis of the torsional angles (ω, ?, ψ, ψ′, ?′, ω′) about the sugar phosphate bonds in the x-ray structures of the known nucleosides, nucleotides, phosphodiesters, nucleic acids, and related compounds, and from a consideration of molecular models, it is found that the possible conformations for the backbone of helical nucleic acids is strikingly limited. Most importantly, the preferred conformation of the nucleotide unit in poly nucleotides and nucleic acids turns out to be the same as that found for the nucleotide in the crystal structure. It is observed that base “stacking” is a consequence of the restricted backbone conformation. The torsional angles are illustrated in the form of conformational “wheels”. Interrelation between the torsion angles about successive pairs of sugar-phosphate bonds are presented in the form of conformational maps: ω,?; ?,ψ; ψ.ψ′; ψ′,?′; ?′,ω′; ω′,ω. The ω′,ω map shows the perferred conformations about the inter-nucleotide bonds of right- and left-handed helices and the possible conformations of phosphodiesters. The preferred conformation of the pyrophosphate and triphosphate is that in which the phosphate oxygens display a staggered arrangement when viewed along the P–P axis. A plausible structure and conformation for the ATPM^2? backbound complex is presented. This structure differs from that proposed by SzentGyorgi in that the metal (only transition metals are considered here) is not bound to the NH₂ nitrogen of adenine, but rather is simultaneously bound to N(7) of the ring and three phosphates (α, β, γ), or N(7) of the ring and two phosphates (β, γ). The remaining metal coordination may be satisfied by solvent–metal or enzyme–metal bonds.     

Minimum energy conformations of DNA dimeric subunits: Potential energy calculations for dGpdC,dApdA, dCpdC,dGpdG, and dTpdT

Minimum energy conformations have been calculated for the deoxydinucleoside phosphates dGpdC, dApdA, dCpdC, dGpdG, and dTpdT. In these potential energy calculations the eight diheldral angles and the sugar pucker were flexible parameters. A substantial survey of conformation space was made in which all staggred combination ofthe dihedral angles ω′,ω, and ψ, in conjuction with C(2′)-endo puker, were used as starting conformers for the energy minimization. The most important conformations in the C(3′)-endo-puckering domain have ψ = g⁺; ω′,ω = g^?,g^?(A-form),g⁺, g⁺, and g^?,t. With C(2′)-endo-type puker the most important conformations have ψ = g⁺; ω′,ω =g^_,g^_(B-form) and g⁺,t; and ψ =t; ω′,ω =g^_,t(Watson-Crick from) and t,g⁺ (skewed). Stacked bases are a persistent feature of the low-energy conformations, the g⁺ conformer being an exception. Freeing the suger puker allowed this conformation to become low energy, with C(3′)-exo puker. It also caused other low-energy forms, such and the Waston-Crick conformation, to become more favourable. Conformation flexibility in the sugar puker and in ψ, as well as the ω′,ω angle pair, is indicated for the dimeric subunits of DNA.     

Interstitial volume modulates the conduction velocity-gap junction relationship

Cardiac conduction through gap junctions is an important determinant of arrhythmia susceptibility. Yet, the relationship between degrees of G(j) uncoupling and conduction velocity (θ) remains controversial. Conflicting results in similar experiments are normally attributed to experimental differences. We hypothesized that interstitial volume modulates conduction velocity and its dependence on G(j). Interstitial volume (V(IS)) was quantified histologically from guinea pig right ventricle. Optical mapping was used to quantify conduction velocity and anisotropy (AR(θ)). Albumin (4 g/l) decreased histologically assessed V(IS), increased transverse θ by 71 ± 10%, and lowered AR(θ). Furthermore, albumin did not change isolated cell size. Conversely, mannitol increased V(IS), decreased transverse θ by 24 ± 4%, and increased AR(θ). Mannitol also decreased cell width by 12%. Furthermore, mannitol was associated with spontaneous ventricular tachycardias in three of eight animals relative to zero of 15 during control. The θ-G(j) relationship was assessed using the G(j) uncoupler carbenoxolone (CBX). Whereas 13 μM CBX did not significantly affect θ during control, it slowed transverse θ by 38 ± 9% during mannitol (edema). These data suggest changes in V(IS) modulate θ, AR(θ), and the θ-G(j) relationship and thereby alter arrhythmia susceptibility. Therefore, V(IS) may underlie arrhythmia susceptibility, particularly in diseases associated with gap junction remodeling.     

ω-Hydroxylation of α-tocopheryl quinone reveals a dual function for cytochrome P450-4F2 in vitamin E metabolism

α-Tocopherol (α-TOH) is the primary lipophilic radical trapping antioxidant in human tissues. Oxidative catabolism of α-tocopherol (αTOH) is initiated by ω-hydroxylation of the terminal carbon (C-13) of the isoprenoid sidechain followed by oxidative transformations that sequentially truncate the chain to yield the 2,5,7,8-tetramethyl(3′carboxyethyl)-6-hydroxychroman (α-CEHC). After conjugation to glucuronic acid, 3′-carboxyethyl-6-hydroxychroman glucuronide is excreted in urine. We report here that the same enzyme that accomplishes this task, the cytochrome P450 monooxygenase CYP-4F2, can also ω-hydroxylate the terminal carbon of α-tocopheryl quinone. A standard sample of ω-OH-α-tocopheryl quinone (ω-OH-α-TQ) was synthesized as a mixture of stereoisomers by allylic oxidation of α-tocotrienol using SeO₂ followed by double-bond reduction and oxidation to the quinone. After incubating human liver microsomes or insect cell microsomes expressing only recombinant human CYP-4F2, cytochrome b5, and NADPH P450 reductase with d₆-α-tocopheryl quinone (d₆-αTQ), we showed that the ω-hydroxylated (13-OH) d₆-α-TQ was produced. We further identified the production of the terminal carboxylic acid d₆-13-COOH-αTQ. The ramifications of this discovery to the understanding of tocopherol utilization and metabolism, including the quantitative importance of the αTQ-ω-hydroxylase pathway in humans, are discussed.     

A calorimetric investigation of the heats of binding of Mg ++ to poly A, to poly U, and to their complexes

The heats of binding of Mg⁺⁺ ions to poly A, poly U, and to their complexes, in the presence of Na⁺ ions, have been measurd calorimetrically. In all cases the heat, ΔH(θ), exhibitis a distinct dependence on the extent of binding, θ, and in the cases of poly A and poly U also on the Na⁺ concentration. The values of ΔH(θ) range from +2 to +3 kcal/mole of Mg⁺⁺ bound at θ = 0 to 1.3 kcal/mole at θ = 0.5 except in poly A where at θ = 0 ΔH(θ) = ?2 to ?3 kcal/mole. This is interpreted as being due to a facilitation of base stacking by the binding of Mg⁺⁺. The extent of facilitation is consistent with current estimates of base stacking. A similar effect but of much smaller magnitude is believed to obtain in poly A poly U. An interpretation of the dependence of ΔH(θ) on θ in terms of simple electrostatic interactions, but neglecting solvent effects, was attempted and found to be inadequate.     

Lipids of the tropical seagrass Thallassia hemprichii

The component sterols, alcohols, hydrocarbons, monocarboxylic, α,ω-dicarboxylic and α- and ω-hydroxy acids from the leaves and roots of the tropical seagrass Thallassia hemprichii are reported. The leaves contained significant concentrations of cholest-5-en-3β-ol, a sterol not normally detected in either higher plants or seagrasses. The lower abundance of polyunsaturated fatty acids found in both the leaves and roots compared to other seagrass species may be a result of the warmer waters from which this species was collected. Solvent-extractable, long-chain (> C₂₂)α,ω-diacids, α- and ω-hydroxy and monocarboxylic acids were also isolated from the leaves. The distribution pattern of these lipids should enable these components along with other distinctive components to be used as chemical markers for this seagrass.     

Studies on the conformation of amino acids. IX. Conformations of butyl, seryl, threonyl, cystennyl, and valyl residues in a dipeptide unit

Potential energies of conformation of a dipeptide unit with butyl, seryl, threonyl, eysteinyl, and valyl side groups have been computed by using classical energy expressions. The presence of a γ-atom introduces characteristic restrictions on the backbone rotational angles ? and ψ the γ-atom itself is restricted to three staggered positions about the C^α—C^β bond. The important results are that a γ-carbon in position I (χ¹ ? 60°) cannot be accommodated in the standard right-and left-handed α-helices, whereas a γ-oxygen or sulfur could easily be accommodated in the right-handed α-helix. Further, a γ-carbon or a heteroatom in position II (χ¹ ? 180°) does not favor a conformation ψ ? 180°, compared to two other positions. The valyl side group significantly reduces the allowed ? and ψ values and energetically prefers a β-conformation compared to right-or left-handed α-helical conformations. The less favorable α-helical conformation is possible only for γ (III, II) combination of the valyl residue. The observed ?, ψ, and χ¹ values of all the amino acid residues in the three protein molecules, lysozyme, myoglobin, and chymotrypsin are compared with the theoretical predictions and the agreement is excellent. The results bring out the important fact that even in large molecules, the conformation of local segments are predominantly governed by the short-range intramolecular interactions.     

Unconditional Non-Asymptotic One-Sided Tests for Independent Binomial Proportions When the Interest Lies in Showing Non-Inferiority and/or Superiority

For two independent binomial proportions Barnard (1947) has introduced a method to construct a non-asymptotic unconditional test by maximisation of the probabilities over the ‘classical’ null hypothesis H₀= {(θ₁, θ₂) ∈ [0, 1]²: θ₁ = θ₂}. It is shown that this method is also useful when studying test problems for different null hypotheses such as, for example, shifted null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ θ₁ ± Δ } for non-inferiority and 1-sided superiority problems (including the classical null hypothesis with a 1-sided alternative hypothesis). We will derive some results for the more general ‘shifted’ null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ g(θ₁ )} where g is a non decreasing curvilinear function of θ₁. Two examples for such null hypotheses in the regulatory setting are given. It is shown that the usual asymptotic approximations by the normal distribution may be quite unreliable. Non-asymptotic unconditional tests (and the corresponding p-values) may, therefore, be an alternative, particularly because the effort to compute non-asymptotic unconditional p-values for such more complex situations does not increase as compared to the classical situation. For ‘classical’ null hypotheses it is known that the number of possible p-values derived by the unconditional method is very large, albeit finite, and the same is true for the null hypotheses studied in this paper. In most of the situations investigated it becomes obvious that Barnard's CSM test (1947) when adapted to the respective null space is again a very powerful test. A theorem is provided which in addition to allowing fast algorithms to compute unconditional non-asymptotical p-values fills a methodological gap in the calculation of exact unconditional p-values as it is implemented, for example, in Stat Xact 3 for Windows (1995).     

A comparison of lipid components of the fresh and dead leaves and pneumatophores of the mangrove Avicennia marina

The component hydrocarbons, sterols, alcohols, monobasic, α,ω-dibasic and ω-hydroxy acids of the fresh hand decayed leaves and the pneumatophores of the mangrove Avicennia marina are reported in detail. From the quantitative comparisons which can be drawn, relative changes in the lipid classes occurring during leaf decay can be highlighted. These base-line data are important to our understanding of inputs to marine intertidal sediments. During leaf decay the only significant changes were a reduction in the total absolute concentrations of monobasic acids due largely to a decrease in concentration of the C₁₈ polyunsaturated fatty acids, and an enhancement of the concentrations of the long-chain monobasic acids, ω-hydroxy acids and α,ω-dibasic acids. This resistance to degradation shown by the cutin derived acids (α,ω-dibasic, ω-hydroxy and long-chain monobasic acids) relative to the cellular and wax derived lipids may allow these cutin components to be used as quantitative markers of A. marina in mangrove associated sediments.     

Examination by the molecular orbital method of the intrinsic conformation preferences of nucleic acid sequence]

This paper reports a systematic PCILO study of the conformation of the nucleic acid backbone. The authors principally studied the ω′ and ω phosphodiester torsion angles of the disugar triphosphate model as a simultaneous function of (1) the sugar nature, ribose or deoxyribose, (2) the different combinations of the sugar ring puckers C(2′)-endo-C(2′)-endo, C(3′)-endo-C(3′)-endo, C(3′)-endo-C(2′)-endo, and C(2′)-endo-C(3′)-endo, and (3) the different conformations around the ψ(C4′–C5′) exocyclic bond. The dependence of the (ω′,ω) conformational energy maps upon these different factors, is discussed. The results are in very good agreement with the observed structures of ribonucleic (RNA10, RNA11, A′-RNA12, tRNA^Phe) and deoxyribonucleic acids (D-DNA, C-DNA 9.3, B-DNA 10, A-DNA 11). Thus the validity of this model, the disugar triphosphate unit, is ensured. The main conclusions that can be drawn from this systematic study are the following:

• 1 The torsion around P-05′ (angle ω) is, as a general rule, more flexible than the torsion around P-03′ (angle ω′).
• 2 There is no notable difference between the ribose–triphosphate units and the deoxyribose–triphosphate units for the C(3′)-endo–C(3′)-endo and C(3′)-endo–C(2′)-endo sugar puckers.
• 3 The deoxyribose–triphosphate units with C(2′)-endo–C(2′)-endo and C(2′)-endo–C(3′)-endo sugar puckers show much more ω′ flexibility than the ribose–triphosphate units with the same sugar puckers and cis position for the 2′hydroxyl group.
• 4 The preferred values of ω′ are independent of the sugar nature (ribose or deoxyribose) and of ψ values; they are correlated with the sugar pucker of the first sugar-phosphate unit:
  • C(3′)-endo-C(3′)-endo and C(3′)-endo-C(2′)-endo puckers ? ω′ ? 240° (g^? region)
  • C(2′)-endo-C(2′)-endo and C(2′)-endo-C(3′)-endo puckers ? ω′ 180° (t region)
• 5 The preferred values of ω are independent of the nature and the puckering of the sugars; they are correlated with the rotational state of the torsion angle ψ(C4′–C5′): ψ ? 60° (gg) ? ω ? 300° (g^?), ψ ? 180° (gt) or 300° (tg) ? ω ? 60° (g⁺)

     

Quantum chemical studies on the conformational structure of nucleic acids. IV. Calculation of backbone structure by CNDO method

Quantum chemical calculations using the CNDO/2 method, have been carried out to determine the energetically favoured ranges of the torsional angles (φ′, ω′, ω, φ, ψ) which fix the conformational structure of nucleic acid backbone. The two dimensional isoenergy maps have been constructed in the (ω′, ω) and (φ, ψ) hyperspaces. The variation of total energy with respect to φ′ has also been studied. The results show that the non-bonding interactions play a major role in the conformational stability of nucleic acids and polynucleotides. The theoretical predictions show good correspondence with the experimental data (X-ray and ¹³C NMR) as well as the other reported theoretical calculations (EHT, PCILO and classical potential functions). The most favoured structure has the conformational angles close to 240, 290, 290, 180 and 60° and these values lead to a helical structure with a pitch of 34 Å and about ten nucleotide units per turn of the helix. The proposed models of Watson &; Crick, DNA-B and DNA-C lie in high energy regions.     

Lipid components of the seagrasses Posidonia australis and Heterozostera tasmanica as indicators of carbon source

The component hydrocarbons, sterols, alcohols, monocarboxylic, α, ω-dicarboxylic and ω-hydroxy acids of the seagrasses Posidonia australis and Heterozostera tasmanica and a sample of P. australis detritus are reported. The fresh leaves of P. australis and P. australis detritus are characterized by a distinctive distribution of solvent-extractable long-chain monocarboxylic, α, ω-dicarboxylic and ω-hydroxy acids. This distinctive pattern should enable these lipid components along with other distinctive components to be used as chemical markers of the seagrass P. australis. H. tasmanica is characterized by (1) higher relative concentrations of 16:2ω6 and 16:3ω3 than P. australis, (2) the absence of the distinctive distribution pattern of long-chain monocarboxylic and ω-hydroxy acids observed for P. australis, (3) the absence of α, ω-diacids and (4) a lower absolute concentration of ω-hydroxy acids than P. australis.     

Active site model of (R)-selective ω-transaminase and its application to the production of d-amino acids

ω-Transaminase (ω-TA) is one of the important biocatalytic toolkits owing to its unique enzyme property which enables the transfer of an amino group between primary amines and carbonyl compounds. In addition to preparation of chiral amines, ω-TA reactions have been exploited for the asymmetric synthesis of l-amino acids using (S)-selective ω-TAs. However, despite the availability of (R)-selective ω-TAs, catalytic utility of the ω-TAs has not been explored for the production of d-amino acids. Here, we investigated the substrate specificity of (R)-selective ω-TAs from Aspergillus terreus and Aspergillus fumigatus and demonstrated the asymmetric synthesis of d-amino acids from α-keto acids. Substrate specificity toward d-amino acids and α-keto acids revealed that the two (R)-selective ω-TAs possess strict steric constraints in the small binding pocket that precludes the entry of a substituent larger than an ethyl group, which is reminiscent of (S)-selective ω-TAs. Molecular models of the active site bound to an external aldimine were constructed and used to explain the observed substrate specificity and stereoselectivity. α-Methylbenzylamine (α-MBA) showed the highest amino donor reactivity among five primary amines (benzylamine, α-MBA, α-ethylbenzylamine, 1-aminoindan, and isopropylamine), leading us to employ α-MBA as an amino donor for the amination of 5 reactive α-keto acids (pyruvate, 2-oxobutyrate, fluoropyruvate, hydroxypyruvate, and 2-oxopentanoate) among 17 ones tested. Unlike the previously characterized (S)-selective ω-TAs, the enzyme activity of the (R)-selective ω-TAs was not inhibited by acetophenone (i.e., a deamination product of α-MBA). Using racemic α-MBA as an amino donor, five d-amino acids (d-alanine, d-homoalanine, d-fluoroalanine, d-serine, and d-norvaline) were synthesized with excellent product enantiopurity (enantiomeric excess >99.7 %).     

ψ-Constrained Simulations of Protein Folding Transition States: Implications for Calculating ?

ψ-analysis has been used to identify interresidue contacts in the transition state ensemble (TSE) of ubiquitin and other proteins. The magnitude of ψ depends on the degree to which an inserted bihistidine (biHis) metal ion binding site is formed in the TSE. A ψ equal to zero or one indicates that the biHis site is absent or fully native-like, respectively, while a fractional ψ implies that in the TSE, the biHis site recovers only part of the binding-induced stabilization of the native state. All-atom Langevin dynamics simulations of the TSE are performed with restrictions imposed only on the distances between the pairs of residues with experimentally determined ψ of unity. When a site with a fractional ψ lies adjacent to a site with ψ = 1, the fractional ψ generally signifies that the “fractional site” has a distorted geometry in the TSE. When a fractional site is distal to the sites with ψ = 1, however, the histidines sample configurations in which the site is absent. The simulations indicate that the ψ = 1 sites by themselves can be used to generate a well-defined TSE having near-native topology. ? values calculated from the TS simulations exhibit mixed agreement with the experimental values. The origin and implication of the disparities are discussed.     

A practical route to long-chain non-natural α,ω-diamino acids

An efficient method for the synthesis of long-chain α,ω-diamino acids, starting from natural α-amino acids, has been developed. The long-chain skeleton has been generated through condensation between a protected aldehyde, derived from l-aspartic acid, and an ylide obtained from an ω-hydroxy-alkyl phosphonium salt. After conversion of the ω-hydroxy group into an amine, catalytic hydrogenation produced the N,N′-protected α,ω-diamino acid. The present route to α,ω-diamino acids allows the modulation of the chain length depending on the length of the ylide used for the Wittig olefination reaction.     

Disruption of mouse cytochrome p450 4f14 (Cyp4f14 gene) causes severe perturbations in vitamin E metabolism

Vitamin E is a family of naturally occurring and structurally related lipophilic antioxidants, one of which, α-tocopherol (α-TOH), selectively accumulates in vertebrate tissues. The ω-hydroxylase cytochrome P450-4F2 (CYP4F2) is the only human enzyme shown to metabolize vitamin E. Using cDNA cloning, cell culture expression, and activity assays, we identified Cyp4f14 as a functional murine ortholog of CYP4F2. We then investigated the effect of Cyp4f14 deletion on vitamin E metabolism and status in vivo. Cyp4f14-null mice exhibited substrate-specific reductions in liver microsomal vitamin E-ω-hydroxylase activity ranging from 93% (γ-TOH) to 48% (γ-tocotrienol). In vivo data obtained from metabolic cage studies showed whole-body reductions in metabolism of γ-TOH of 90% and of 68% for δ- and α-TOH. This metabolic deficit in Cyp4f14(-/-) mice was partially offset by increased fecal excretion of nonmetabolized tocopherols and of novel ω-1- and ω-2-hydroxytocopherols. 12'-OH-γ-TOH represented 41% of whole-body production of γ-TOH metabolites in Cyp4f14(-/-) mice fed a soybean oil diet. Despite these counterbalancing mechanisms, Cyp4f14-null mice fed this diet for 6 weeks hyper-accumulated γ-TOH (2-fold increase over wild-type littermates) in all tissues and appeared normal. We conclude that CYP4F14 is the major but not the only vitamin E-ω-hydroxylase in mice. Its disruption significantly impairs whole-body vitamin E metabolism and alters the widely conserved phenotype of preferential tissue deposition of α-TOH. This model animal and its derivatives will be valuable in determining the biological actions of specific tocopherols and tocotrienols in vivo.     

A quantitative analysis of excluded-site effects for highly cooperative binding systems

Binding isotherms can provide quantitive information regarding the stability of a molecular complex. Theorectical studies in recent years have been directed to systems in which a single ligand can exclude more than one polymer site (excluded-site effect). This system has minium of thre parameters to describe the binding data: the intrinsic binding constant, B; the remote-neighbor cooperative paramaters, σ_q and the number of excluded sites, q. It is suggested in the present communication that precise values for these three parameters can be obtained by utilizing the characteristics of two forms of data representation: θ vs ln m and θ/m vs θ, where θ is the degree of saturation (0?θ?1) and m is the molality of free ligand. The matrix generation method is used to obtain empirical equations relating the midpoint location and slope at the midpoint of the θ vs ln m plot to the three molecular parameters. A modified Scatchard theory is also presented for highly cooperative systems, which results in an expression relaing the maximum in the θ/m vs θ plot to the molecular parameters σ_q and q, thus providing the third equation for the three unknown parameters. The novel method f analysis is illustrated with the AMP-poly(L -arginine) and oligocytidylate–T7 DNA sstems.     

Conformational Studies of Dextran [α-(1⇒6)-D-Glucan]

Abstract

A theoretical conformational study of dextran, a (l?6)-linked α-D-glucan polysaccharide, has been made to allow an explicit comparison with earlier results on pustulan, the corresponding (1 ?6)-linked β-D-glucan. The nonbonded, torsional and hydrogen bond contributions to potential energy were calculated as a function of rotational angles φ, ψ, and ω The (φ, ψ, ω)-space of the disaccharide and of helices contain many local energy minima with very small energy differences. A comparison of (1?6)-α-D-glucans with (1?6)-β-D-glucans indicates significant differences in conformational behavior. Specifically, our results shed light on the fact that dextran does not gel, whereas pustulan does. The difference in tendency to gel may be related to the fact that dextran has no particularly favored conformations with structural regularity whereas pustulan does.     

Consistency of the Asymptotic Quasi-Likelihood Estimate on Linear Models

Consider a model y_t = f_t(θ) + M_t, 0 ⩽ t ⩽ T where θ∈ Θ in an unknown parameter, f_t(θ) is a linear predictable process, M_t is a martingale difference, and the nature of E(M²_t/ℱ_t—1) is unknown. This paper presents an estimating procedure for θ based on the asymptotic quasi-likelihood methodology. Conditions under which the asymptotic quasi-likelihood estimate converges to the true parameter θ₀ are discussed. This method is applied to several simulated examples, and estimates of the unknown parameter are obtained by means of a two-stage technique. Comparison is made between the estimates obtained via this method and those obtained via the ordinary least squares method. Discussion is provided on the application of the model.