Analysis and application of an equilibrium model for in vitro bioassay systems with three components: Receptor, hormone and hormone-binding-protein

A simple theoretical framework is presented for bioassay studies using three component in vitro systems. An equilibrium model is used to derive equations useful for predicting changes in biological response after addition of hormone-binding-protein or as a consequence of increased hormone affinity. Sets of possible solutions for receptor occupancy and binding protein occupancy are found for typical values of receptor and binding protein affinity constants. Unique equilibrium solutions are dictated by the initial condition of total hormone concentration. According to the occupancy theory of drug action, increasing the affinity of a hormone for its receptor will result in a proportional increase in biological potency. However, the three component model predicts that the magnitude of increase in biological potency will be a small fraction of the proportional increase in affinity. With typical initial conditions a two-fold increase in hormone affinity for its receptor is predicted to result in only a 33% increase in biological response. Under the same conditions an Ii-fold increase in hormone affinity for receptor would be needed to produce a two-fold increase in biological potency. Some currently used bioassay systems may be unrecognized three component systems and gross errors in biopotency estimates will result if the effect of binding protein is not calculated. An algorithm derived from the three component model is used to predict changes in biological response after addition of binding protein to in vitro systems. The algorithm is tested by application to a published data set from an experimental study in an in vitro system (Lim et al., 1990, Endocrinology 127, 1287-1291). Predicted changes show good agreement (within 8%) with experimental observations. (C) 1998 Academic Press Limited.

Structure determination of the three disulfide bond isomers of alpha-conotoxin GI: A model for the role of disulfide bonds in structural stability

The three possible disulfide bonded isomers of alpha-conotoxin GI have been selectively synthesised and their structures determined by H-1 NMR spectroscopy. alpha-Conotoxin GI derives from the venom of Conus geographus and is a useful neuropharmacological tool as it selectively binds to the nicotinic acetylcholine receptor (nAChR), a ligand-gated ion channel involved in nerve signal transmission. The peptide has the sequence ECCNPACGRHYSC-NH2, and the three disulfide bonded isomers are referred to as GI(2-7;3-13), GI(2-13;3-7) and GI(2-3;7-13). The NMR structure for the native isomer GI(2-7;3-13) is of excellent quality, with a backbone pairwise RMSD of 0.16 Angstrom for a family of 35 structures, and comprises primarily a distorted 3(10),, helix between residues 5 to 11. The two non-native isomers exhibit multiple conformers in solution, with the major populated forms being different in structure both from each other and from the native form. Structure-activity relationships for the native GI(2-7;3-13) as well as the role of the disulfide bonds on folding and stability of the three isomers are examined. It is concluded that the disulfide bonds in alpha-conotoxin GI play a crucial part in determining both the structure and stability of the peptide. A trend for increased conformational heterogeneity was observed in the order of GI(2-7;3-13) < GI(2-13;3-7) < GI(2-3;7-13). It was found that the peptide bond joining Cys2 to Cys3 in GI(2-3;7-13) is predominantly trans, rather than cis as theoretically predicted. These structural data are used to interpret the varying nAChR binding of the non-native forms. A model for the binding of native GI(2-7;3-13) to the mammalian nAChR is proposed, with an alpha-subunit binding face made up of Cys2, Asn4, Pro5, Ala6 and Cys7 and a selectivity face, comprised of Arg9 and His10. These two faces orient the molecule between the alpha and delta subunits of the receptor. The structure of the CCNPAC sequence of the native GI(2-7;3-13) is compared to the structure of the identical sequence from the toxic domain of heat-stable enterotoxins, which forms part of the receptor binding region of the enterotoxins, but which has a different disulfide connectivity. (C) 1998 Academic Press Limited.

Phase diagram of the one-dimensional Holstein model of spinless fermions

The one-dimensional Holstein model of spinless fermions interacting with dispersionless phonons is studied using a new variant of the density matrix renormalization group. By examining various low-energy excitations of finite chains, the metal-insulator phase boundary is determined precisely and agrees with the predictions of strong coupling theory in the antiadiabatic regime and is consistent with renormalization group arguments in the adiabatic regime. The Luttinger liquid parameters, determined by finite-size scaling, are consistent with a Kosterlitz-Thouless transition.

A phase-segregated model for plant cell culture: The effect of cell volume fraction

Plant cells are characterized by low water content, so the fraction of cell volume (volume fraction) in a vessel is large compared with other cell systems, even if the cell concentrations are the same. Therefore, concentration of plant cells should preferably be expressed by the liquid volume basis rather than by the total vessel volume basis. In this paper, a new model is proposed to analyze behavior of a plant cell culture by dividing the cell suspension into the biotic- and abiotic-phases, Using this model, we analyzed the cell-growth and the alkaloid production by Catharanthus roseus, Large errors in the simulated results were observed if the phase-segregation was not considered.

New integrable boundary conditions for the q-deformed supersymmetric U model and Bethe ansatz equations

New classes of integrable boundary conditions for the q-deformed (or two-parameter) supersymmetric U model are presented. The boundary systems are solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. (C) 1998 Elsevier Science B.V.

Hepatic disposition and metabolite kinetics of a homologous series of diflunisal esters

The hepatic disposition and metabolite kinetics of a homologous series of diflunisal O-acyl esters (acetyl, butanoyl, pentanoyl, anti hexanoyl) were determined using a single-pass perfused in situ rat liver preparation. The experiments were conducted using 2% BSA Krebs-Henseleit buffer (pH 7.4), and perfusions were performed at 30 mL/min in each liver. O-Acyl esters of diflunisal and pregenerated diflunisal were injected separately into the portal vein. The venous outflow samples containing the esters and metabolite diflunisal were analyzed by high performance liquid chromatography (HPLC). The normalized outflow concentration-time profiles for each parent ester and the formed metabolite, diflunisal, were analyzed using statistical moments analysis and the two-compartment dispersion model. Data (presented as mean +/- standard error for triplicate experiments) was compared using ANOVA repeated measures, significance level P < 0.05. The hepatic availability (AUC'), the fraction of the injected dose recovered in the outflowing perfusate, for O-acetyldiflunisal (C2D = 0.21 +/- 0.03) was significantly lower than the other esters (0.34-0.38). However, R-N/f(u), the removal efficiency number R-N divided by the unbound fraction in perfusate f(u), which represents the removal efficiency of unbound ester by the liver, was significantly higher for the most lipophilic ester (O-hexanoyldiflunisal, C6D = 16.50 +/- 0.22) compared to the other members of the series (9.57 to 11.17). The most lipophilic ester, C6D, had the largest permeability surface area (PS) product (94.52 +/- 38.20 mt min-l g-l liver) and tissue distribution value VT (35.62 +/- 11.33 mL g(-1) liver) in this series. The MTT of these O-acyl esters of diflunisal were not significantly different from one another. However, the metabolite diflunisal MTTs tended to increase with the increase in the parent ester lipophilicity (11.41 +/- 2.19 s for C2D to 38.63 +/- 9.81 s for C6D). The two-compartment dispersion model equations adequately described the outflow profiles for the parent esters and the metabolite diflunisal formed from the O-acyl esters of diflunisal in the liver.

Shift of the subharmonic resonances and suppression of fluorescence in a two-level atom driven by a bichromatic field

We study the behavior of a two-level atom that is driven by a bichromatic field consisting of a strong resonant component and a weaker tunable component. In addition to the splitting of the energy levels (the multiphoton AC Stark effect), we find that the weaker component also shifts the subharmonic resonances, an effect we attribute to a dynamic Stark shift. When the weaker component is tuned to a shifted resonance, no fluorescence occurs at either the frequency of the strong component or the three-photon mixing frequency. Results are obtained with numerical techniques and explained in terms of the dressed-atom model of the system. (C) 1998 Optical Society of America [S0740-3224(98)01508-2] OCIS codes: 270.4180, 270.6620, 270.0270.

Modification of the in vivo four-point loading model for studying mechanically induced bone adaptation

We modified the noninvasive, in vivo technique for strain application in the tibiae of rats (Turner et al,, Bone 12:73-79, 1991), The original model applies four-point bending to right tibiae via an open-loop, stepper-motor-driven spring linkage, Depending on the magnitude of applied load, the model produces new bone formation at periosteal (Ps) or endocortical surfaces (Ec.S). Due to the spring linkage, however, the range of frequencies at which loads can be applied is limited. The modified system replaces this design with an electromagnetic vibrator. A load transducer in series with the loading points allows calibration, the loaders' position to be adjusted, and cyclic loading completed under load central as a closed servo-loop. Two experiments were conducted to validate the modified system: (1) a strain gauge was applied to the lateral surface of the right tibia of 5 adult female rats and strains measured at applied loads from 10 to 60 N; and (2) the bone formation response was determined in 28 adult female Sprague-Dawley rats. Loading was applied as a haversine wave with a frequency of 2 Hz for 18 sec, every second day for 10 days. Peak bending loads mere applied at 33, 40, 52, and 64 N, and a sham-loading group tr as included at 64 N, Strains in the tibiae were linear between 10 and 60 N, and the average peak strain at the Ps.S at 60 N was 2664 +/- 250 microstrain, consistent with the results of Turner's group. Lamellar bone formation was stimulated at the Ec.S by applied bending, but not by sham loading. Bending strains above a loading threshold of 40 N increased Ec Lamellar hone formation rate, bone forming surface, and mineral apposition rate with a dose response similar to that reported by Turner et al, (J Bone Miner Res 9:87-97, 1994). We conclude that the modified loading system offers precision for applied loads of between 0 and 70 N, versatility in the selection of loading rates up to 20 Hz, and a reproducible bone formation response in the rat tibia, Adjustment of the loader also enables study of mechanical usage in murine tibia, an advantage with respect to the increasing variety of transgenic strains available in bone and mineral research. (Bone 23:307-310; 1998) (C) 1998 by Elsevier Science Inc. All rights reserved.

Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

On uniquely determining cell-wall material properties with the compression experiment

A finite element model (FEM) of the cell-compression experiment has been developed in dimensionless form to extract the fundamental cell-wall-material properties (i.e. the constitutive equation and its parameters) from experiment force-displacement data. The FEM simulates the compression of a thin-walled, liquid-filled sphere between two flat surfaces. The cell-wall was taken to be permeable and the FEM therefore accounts for volume loss during compression. Previous models assume an impermeable wall and hence a conserved cell volume during compression. A parametric study was conducted for structural parameters representative of yeast. It was shown that the common approach of assuming reasonable values for unmeasured parameters (e.g. cell-wall thickness, initial radial stretch) can give rise to nonunique solutions for both the form and constants in the cell-wall constitutive relationship. Similarly, measurement errors can also lead to an incorrectly defined cell-wall constitutive relationship. Unique determination of the fundamental wall properties by cell compression requires accurate and precise measurement of a minimum set of parameters (initial cell radius, initial cell-wall thickness, and the volume loss during compression). In the absence of such measurements the derived constitutive relationship may be in considerable error, and should be evaluated against its ability to predict the outcome of other mechanical experiments. (C) 1998 Elsevier Science Ltd. All rights reserved.

A mathematical model for estimating the extent of solute- and water-flux heterogeneity in multiple sample percolation experiments

Multiple sampling is widely used in vadose zone percolation experiments to investigate the extent in which soil structure heterogeneities influence the spatial and temporal distributions of water and solutes. In this note, a simple, robust, mathematical model, based on the beta-statistical distribution, is proposed as a method of quantifying the magnitude of heterogeneity in such experiments. The model relies on fitting two parameters, alpha and zeta to the cumulative elution curves generated in multiple-sample percolation experiments. The model does not require knowledge of the soil structure. A homogeneous or uniform distribution of a solute and/or soil-water is indicated by alpha = zeta = 1, Using these parameters, a heterogeneity index (HI) is defined as root 3 times the ratio of the standard deviation and mean. Uniform or homogeneous flow of water or solutes is indicated by HI = 1 and heterogeneity is indicated by HI > 1. A large value for this index may indicate preferential flow. The heterogeneity index relies only on knowledge of the elution curves generated from multiple sample percolation experiments and is, therefore, easily calculated. The index may also be used to describe and compare the differences in solute and soil-water percolation from different experiments. The use of this index is discussed for several different leaching experiments. (C) 1999 Elsevier Science B.V. All rights reserved.

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons are studied by means of the boundary graded quantum inverse scattering method. The boundary K-matrices depending on the local magnetic moments of the impurities are presented as non-trivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, the model Hamiltonian is diagonalized and the Bethe ansatz equations are derived. It is interesting to note that our model exhibits a free parameter in the bulk Hamiltonian but no free parameter exists on the boundaries. This is in sharp contrast to the impurity models arising from the supersymmetric t-J and extended Hubbard models where there is no free parameter in the bulk but there is a free parameter on each boundary.

High level of aspartic acid-bond isomerization during the synthesis of an N-linked tau glycopeptide

An increased degree of utilization of the potential N-glycosylation site In the fourth repeat unit of the human tau protein may be involved in the inability of tau to bind to the corresponding tubulin sequence(s) and in the subsequent development of the paired helical filaments of Alzheimer's disease. To model these processes, we synthesized the octadecapeptide spanning this region without sugar, and with the addition of an N-acetyl-glucosamine moiety. The carbohydrate-protected, glycosylated asparagine was incorporated as a building block during conventional Fmoc-solid phase peptide synthesis. While the crude non-glycosylated analog was obtained as a single peptide, two peptides with, the identical, expected masses, in approximately equal amounts, were detected after the cleavage of the peracetylated glycopeptide. Surprisingly, the two glycopeptides switched positions on the reversed-phase high performance liquid chromatogram after removal of the sugar-protecting acetyl groups. Nuclear magnetic resonance spectroscopy and peptide sequencing identified the more hydrophobic deprotected peak as the target peptide, and the more hydrophilic deprotected peak as a peptide analog in which the aspartic acid-bond just preceding the glycosylated asparagine residue was isomerized resulting in the formation of a beta-peptide. The anomalous chromatographic behavior of the acetylated beta-isomer could be explained on the basis of the generation of an extended hydrophobic surface which is not present in any of the other three glycopeptide variants. Repetition of the syntheses, with altered conditions and reagents, revealed reproducibly high levels of aspartic acid-bond isomerization of the glycopeptide as well as lack of isomerization for the non-glycosylated parent analog. If similar increased aspartic acid-bond isomerization occurs in vivo, a protein modification well known to take place for both the amyloid deposits and the neurofibrillary tangles in Alzheimer's disease, this process may explain the aggregation of glycosylated tau into the paired helical filaments in the affected brains. Copyright (C) 1999 European Peptide Society and John Wiley & Sons, Ltd.