A beta-cyclodextrin based fiber-optic chemical sensor: a fractal analysis

A fractal analysis is presented for the binding of pyrene in solution to beta-cyclodextrin attached to a fiber-optic chemical sensor. The specific (k(l)) and non-specific binding rate coefficients and the fractal dimension (D(f)) (specific binding case only) both tend to increase as the pyrene concentration in solution increases from 12.4 to 124 ng ml(-1). Predictive relations for the binding rate coefficient (specific as well as non-specific binding) and for D(f) (specific binding case only) as a function of pyrene concentration are provided. These relations fit the calculated k(l) and D(f) values in the pyrene concentration range reasonably well. Fractal analysis data seem to indicate that an increase in the pyrene concentration in solution increases the "ruggedness" or inhomogeneity on the fiber-optic biosensor surface. The fractal analysis provides novel physical insights into the reactions occuring on the fiber-optic chemical surface and should assist in the design of fiber-optic chemical sensors.     

评《马氏决策过程》

（《马氏决策过程》,侯振挺、郭先平著,长沙,湖南科技出版社,1997,中文版,386页,定价：28元）马尔可夫决策过程是概率论的运筹学的理论研究和实际应用中极其重要的领域之一．随着中国和国际上对马尔可夫决策过程（MarkovDecisionProcesses,简记为MDP）研究的新进展,许     

Analyte-receptor binding kinetics for biosensor applications

The diffusion-limited binding kinetics of antigen (analyte), in solution with antibody (receptor) immobilized on a biosensor surface, is analyzed within a fractal framework. Most of the data presented is adequately described by a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot. A single example of a dual-fractal analysis is also presented. It is of interest to note that the binding-rate coefficient (k) and the fractal dimension (D_f) both exhibit changes in the same and in the reverse direction for the antigen-antibody systems analyzed. Binding-rate coefficient expressions, as a function of the D_f developed for the antigen-antibody binding systems, indicate the high sensitivity of thek on the D_f when both a single- and a dual-fractal analysis are used. For example, for a single-fractal analysis, and for the binding of antibody Mab 0.5β in solution to gpl20 peptide immobilized on a BIAcore biosensor, the order of dependence on the D_f was 4.0926. For a dual-fractal analysis, and for the binding of 25-100 ng/mL TRITC-LPS (lipopolysaccharide) in solution with polymyxin B immobilized on a fiberoptic biosensor, the order of dependence of the binding-rate coefficients, k₁ and k₂ on the fractal dimensions, D_f1 and D_f2, were 7.6335 and-11.55, respectively. The fractional order of dependence of thek(s) on the D_f(s) further reinforces the fractal nature of the system. Thek(s) expressions developed as a function of the D_f(s) are of particular value, since they provide a means to better control biosensor performance, by linking it to the heterogeneity on the surface, and further emphasize, in a quantitative sense, the importance of the nature of the surface in biosensor performance.     

Mass spectra of sterically crowded trialkylsilyl derivatives of nucleosides

The electron impact mass spectra of tert-butyldimethylsilyl-, cyclo-tetramethylene-tert-butylsilyl and cyclo-tetramethylene-isopropylsilyl- ether derivatives of ribo- and 2′-deoxyribonucleosides are described in detail. The interpretation of fragmentation pathways of full and mixed derivatives was aided by metastable ion decomposition studies, precise mass and deuterium labelling measurements, and spectra of mixed derivatives containing the ‘passive’ (in these spectra) trimethylsilyl group. The sterically crowded silyl groups have a powerful fragmentation directing effect. Elimination of a bulky radical, R˙ (tert-butyl or isopropyl), from the molecular ion produces the siliconium ion [M? R]⁺, which is the precursor for most of the other prominent ions in the spectra. These arise from ‘siliconium ion rearrangements’ resulting from the interaction of the positively charged siliconium ion center with electron dense regions (i.e. oxygens) in the molecule, to form cyclic silyloxonium ions which subsequently decompose. Since the interacting oxygen and silicon must be sterically accessible, the fragment ion types and their abundances are very dependent upon structure. Consequently, [M? R]⁺ ions formed from 2′, 3′ or 5′-O-silyl groups give rise to different sets of daughter ions which, for the most part, are not found, or have very low abundances, in the mass spectra of underivatized or trimethylsilylated nucleosides. Detailed information on sugar and base moieties and isomeric substitution is readily obtained.     

Simulation model for anomalous precession of the perihelion of mercury's orbit

The ‘anomalous perihelion precession’ of Mercury, announced by Le Verrier in 1859, was a highly controversial topic for more than half a century and invoked many alternative theories until 1916, when Einstein presented his theory of general relativity as an alternative theory of gravitation and showed perihelion precession to be one of its potential manifestations. As perihelion precession was a directly derived result of the full General Theory and not just the Equivalence Principle, Einstein viewed it as the most critical test of his theory. This paper presents the computed value of the anomalous perihelion precession of Mercury's orbit using a new relativistic simulation model that employs a simple transformation factor for mass and time, proposed in an earlier paper. This computed value compares well with the prediction of general relativity and is, also, in complete agreement with the observed value within its range of uncertainty. No general relativistic equations have been used for computing the results presented in this paper.     

A simplified strategy for the synthesis of dideoxyribonucleotide blocks

The rapid synthesis of dideoxyribonucleotide blocks in 60–85% isolated yields has been achieved by combining the phosphorylation and condensation steps in a sequential reaction series which also allows the recovery of unreacted nucleotides.     

Formation, isolation, spectroscopic properties, and calculated properties of some isomers of C(60)H(36)

Isomers of C(60)H(36) and He@C(60)H(36) have been synthesized by the Birch or dihydroanthracene reduction of C(60) and isolated by preparative high-pressure liquid chromatography. (3)He, (13)C, and (1)H NMR spectroscopic properties were then determined. A comparison of experimental chemical shifts against those computed using density functional theory (B3LYP) with polarized triple- and double-zeta basis sets for He and C,H, respectively, allowed provisional assignment of structure for several isomers to be made. Theoretical calculations have also been carried out to identify low-energy structures. The transfer hydrogenation method using dihydroanthracene gives a major C(60)H(36) isomer and a minor C(60)H(36) isomer with C(3) symmetry as determined by the (13)C NMR spectrum of C(60)H(36) and the (3)He NMR spectrum of the corresponding sample of (3)He@C(60)H(36). In view of the HPLC retention times and the (3)He chemical shifts observed for the Birch and dihydroanthracene reduction products, the two isomers generated by the latter procedure can be only minor isomers of the Birch reduction. A significant energy barrier apparently exists in the dihydroanthracene reduction of C(60) for the conversion of the C(3) and C(1) symmetry isomers of C(60)H(36) to the T symmetry isomer previously predicted by many calculations to be among the most stable C(60)H(36) isomers. Many of the (1)H NMR signals exhibited by C(60)H(36) (and C(60)H(18), previously reported) are unusually deshielded compared to "ordinary" organic compounds, presumably because the unusual structures of C(60)H(36) and C(60)H(18) result in chemical shift tensors with one or more unusual principal values. Calculations clearly show a relationship between exceptionally deshielded protons beta to a benzene ring in C(60)H(18) and C(60)H(36) and relatively long C-C bonds associated with these protons. The additional information obtained from 1D and 2D (1)H NMR spectra obtained at ultrahigh field strengths (up to 900 MHz) will serve as a critical test of chemical shifts to be obtained from future calculations on different C(60)H(36) isomers.     

An Evaluation of Cellular Analyte-Receptor Binding Kinetics Utilizing Biosensors: A Fractal Analysis

A fractal analysis is presented for cellular analyte-receptor binding kinetics utilizing biosensors. Data taken from the literature can be modeled by using (a) a single-fractal analysis and (b) a single- and a dual-fractal analysis. Case (b) represents a change in the binding mechanism as the reaction progresses on the biosensor surface. Relationships are presented for the binding rate coefficient(s) as a function of the fractal dimension for the single-fractal analysis examples. In general, the binding rate coefficient is rather sensitive to the degree of heterogeneity that exists on the biosensor surface. For example, for the binding of mutagenized and back-mutagenized forms of peptide E1037 in solution to salivary agglutinin immobilized on a sensor chip, the order of dependence of the binding rate coefficient, k, on the fractal dimension, D(f), is 13.2. It is of interest to note that examples are presented where the binding coefficient (k) exhibits an increase as the fractal dimension (D(f)) or the degree of heterogeneity increases on the surface. The predictive relationships presented provide further physical insights into the binding reactions occurring on the surface. These should assist us in understanding the cellular binding reaction occurring on surfaces, even though the analysis presented is for the cases where the cellular "receptor" is actually immobilized on a biosensor or other surface. The analysis suggests possible modulations of cell surfaces in desired directions to help manipulate the binding rate coefficients (or affinities). In general, the technique presented is applicable for the most part to other reactions occurring on different types of biosensors or other surfaces. Copyright 2000 Academic Press.     

A Fractal Analysis Approach for the Evaluation of Hybridization Kinetics in Biosensors

The diffusion-limited hybridization kinetics of analyte in solution to a receptor immobilized on a biosensor or immunosensor surface is analyzed within a fractal framework. The data may be analyzed by a single- or a dual-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot (Sigmaplot, Scientific Graphing Software, User's Manual, Jandel Scientific, CA, 1993). It is of interest to note that the binding rate coefficient and the fractal dimension both exhibit changes, in general, in the same direction for both the single-fractal and the dual-fractal analysis examples presented. The binding rate coefficient expression developed as a function of the analyte concentration in solution and the fractal dimension is of particular value since it provides a means to better control biosensor or immunosensor performance. Copyright 2001 Academic Press.     

Antibody-antigen binding kinetics a model for multivalency antibodies for large antigen systems

This work presents a theoretical analysis of the influence of multivalency of antigen on external mass transfer-limited binding kinetics to divalent antibody for biosensor applications to polycyclic-aromatic systems. Both cases are considered wherein the antigen is in solution and the antibody is either covalently or noncovalently attached to a cylindrical fiber-optic biosensor, and the antibody is in solution and the antigen is attached to the surface. Both single-step and dual-step binding processes are considered. The rate of attachment of antigen to antibody (or vice versa) is linear for the valencies (or reaction orders) analyzed in the time frame (100 min) considered. The rate of attainment of saturation levels of antigen or antibody in solution close to the surface is very rapid (within 20 min). An increase in the valency of the antigen in solution has the effect of decreasing the order of reaction (for valency, Ν ≥ 1). An increase in the number of steps increases the order of reaction, as expected. An increase in the valency of the antigen in solution decreases the saturation level of the antigen close to the surface and the rate of antigen attachment to the antibody on the surface for all Damkohler numbers. A decrease in the diffusional limitations decreases the effect of valency (or reaction order) on saturation levels of c_s/c₀. Nondimensional plots presented in the analysis help extend the analysis to different antigen-antibody systems. An increase in the valency of the antibody in solution has the effect of increasing the order of reaction (for Ν < 2). The effects in this case are reverse to those described earlier. For valency greater than2, the reaction order is dependent on the antigen valency, whether it is in solution or immobilized on the surface. The general analysis presented here should be applicable to most surface reactions that involve ligand-receptor binding wherein multiple-binding sites are involved on either the receptor or the ligand.