邹承鲁作图法的数学证明

邹承鲁于1962年提出了一个判断酶分子中必需基团数目的作图方法.本文对该作图法给出了严格的数学证明,并讨论了一些与实验有关的问题.     

DTNB对人肌肌酸激酶不可逆抑制作用的研究

本文研究了DTNB对人肌肌酸激酶的不可逆抑制作用.研究结果表明,与兔肌肌酸激酶不同,人肌肌酸激酶分子中有四个可反应SH.用邹承鲁作图法定量处理结果表明,在这四个可反应的SH中,有一个快反应SH,两个慢反应SH且这两个慢反应SH是酶的必需基团,此外还有一个反应很慢的SH.用邹承鲁提出的在抑制剂存在条件下,酶活性不可逆改变动力学方法,测定了一系列动力学常数,并对DTNB的作用机制进行了探讨.     

Two theoretical problems concerning the irreversible modification kinetics of enzyme activity

Some years ago, a systematic study on the kinetics of irreversible modification of enzyme activity was presented by Tsou (1988, Adv. Enzymol. Relat. Areas molec. Biol. 61, 381-436). This paper presents a discussion of the theoretical aspects of Tsou's method for the determination of the rate constants for the irreversible modification reaction. Range of validity for the kinetic equations of substrate reaction in the presence of the modifier is discussed quantitatively. The expressions of A, B, v* and [P]infinity for any enzyme catalyzed reaction mechanism are derived.     

Statistical considerations in the estimation of enzyme kinetic parameters by the direct linear plot and other methods

The statistical implications of the direct linear plot for enzyme kinetic data, described in the preceding paper (Eisenthal & Cornish-Bowden, 1974), are discussed for the case of the Michaelis-Menten equation. The plot is shown to lead directly to non-parametric confidence limits for the kinetic parameters, V and K(m), which depend on far less sweeping assumptions about the nature of experimental error than those implicit in the method of least squares. Median estimates of V and K(m) can also be defined, which are shown to be more robust than the least-squares estimates in a wide variety of experimental situations.     

Reducing modeling error of graphical methods for estimating volume of distribution measurements in PIB-PET study

Graphical analysis methods are widely used in positron emission tomography quantification because of their simplicity and model independence. But they may, particularly for reversible kinetics, lead to bias in the estimated parameters. The source of the bias is commonly attributed to noise in the data. Assuming a two-tissue compartmental model, we investigate the bias that originates from modeling error. This bias is an intrinsic property of the simplified linear models used for limited scan durations, and it is exaggerated by random noise and numerical quadrature error. Conditions are derived under which Logan’s graphical method either over-or under-estimates the distribution volume in the noise-free case. The bias caused by modeling error is quantified analytically. The presented analysis shows that the bias of graphical methods is inversely proportional to the dissociation rate. Furthermore, visual examination of the linearity of the Logan plot is not sufficient for guaranteeing that equilibrium has been reached. A new model which retains the elegant properties of graphical analysis methods is presented, along with a numerical algorithm for its solution. We perform simulations with the fibrillar amyloid β radioligand [11C] benzothiazole-aniline using published data from the University of Pittsburgh and Rotterdam groups. The results show that the proposed method significantly reduces the bias due to modeling error. Moreover, the results for data acquired over a 70 min scan duration are at least as good as those obtained using existing methods for data acquired over a 90 min scan duration.     

Kinetics of the modulation of chloroplastic fructose-1,6-bisphosphatase activity by thioredoxin fb

The inactivation of reduced chloroplast fructose-bisphosphatase by oxidized thioredoxin fb has been studied during the enzyme reaction along the principle of Tian and Tsou [Biochemistry (1982) 21, 1028-1032]. A minimum model for this process is presented and its kinetic and equilibrium parameters have been determined. Thioredoxin fb binding to the enzyme is fast relative to catalysis and product desorption. Under quasi-equilibrium conditions oxidized thioredoxin is a non-competitive inhibitor of the enzyme reaction and must bind to a regulatory 'thioredoxin site'. The slow deactivation is thermodynamically favoured, and as expected from binding data, slowed down by the presence of substrate, fructose bisphosphate. The desorption of thioredoxin fb from the enzyme is extremely slow and this small protein may be regarded as a 'regulatory' subunit of fructose-bisphosphatase.     

Determination of three-dimensional protein structures from nuclear magnetic resonance data using fragments of known structures

A method to build a three-dimensional protein model from nuclear magnetic resonance (NMR) data using fragments from a data base of crystallographically determined protein structures is presented. The interproton distances derived from the nuclear Overhauser effect (NOE) data are compared to the precalculated distances in the known protein structures. An efficient search algorithm is used, which arranges the distances in matrices akin to a C alpha diagonal distance plot, and compares the NOE distance matrices for short sequential zones of the protein to the data base matrices. After cluster analysis of the fragments found in this way, the structure is built by aligning fragments in overlapping zones. The sequentially long-range NOEs cannot be used in the initial fragments search but are vital to discriminate between several possible combinations of different groups of fragments. The method has been tested on one simulated NOE data set derived from a crystal structure and one experimental NMR data set. The method produces models that have good local structure, but may contain larger global errors. These models can be used as the starting point for further refinement, e.g., by restrained molecular dynamics or interactive graphics.     

Considerations for ecological reconstruction of historic vegetation: Analysis of the spatial uncertainties in the California Vegetation Type Map dataset

Historical ecological data are valuable for reconstructing early environmental and vegetation community conditions and examining change to vegetation communities and disturbance regimes over decadal and longer temporal scales, but these data are not free from error. We examine the spatial uncertainties associated with 18,000 vegetation plots in the decades-old California Vegetation Type Mapping (VTM) dataset that has been digitized for use in modern ecological analysis. We examine the relationship between plot location error and basemap year, basemap scale, plot elevation, plot slope, and general plot habitat type. Bivariate plots and classification and regression tree analysis (CART) confirm that basemap scale and age are the strongest explanation of total error. Total error in spatial location for all plots ranged from 126.9 m to 462.3 m; plots drawn on 15-min (1:62,500-scale) basemaps had total error ranging from 126 m to 199.7 m, and plots drawn on coarser-scale basemaps (1:125,000-scale) had total errors ranging from 241 m to 461.2 m. Relocation of individual VTM plots is considerably easier for plots originally marked on 1:62,500-scale maps produced after 1904, and more difficult for plots originally marked on 1:125,000-scale maps produced before 1898. Biogeographical analyses that rely less on relocating individual plots, such as environmental niche modeling or multivariate analyses can alleviate some of these concerns, but all researchers using these kinds of data need to consider errors in spatial location of plots. The paper also discusses ways in which the differing spatial error might be reported and visualized by those using the dataset, and how the data might be used in modern environmental niche models.     

Determination of rate constants for the irreversible inhibition of acetylcholine esterase by continuously monitoring the substrate reaction in the presence of the inhibitor

The kinetics of the irreversible inhibition of acetylcholinesterase (acetylcholine acetylhydrolase, EC 3.1.1.7) by diisopropyl fluorophosphate and paraoxon have been studied by the approach of following the substrate reaction continuously in the presence of both the substrate and the inhibitor based on kinetic equations previously derived (Tsou, C.-L. (1965) Acta Biochim. Biophys. Sinica 5, 387-417). From determinations of the effects of different concentrations of substrate and the inhibitors on the apparent rate constants for the irreversible inhibition reactions it can be shown that these inhibitors are of the competitive complexing type. Both the reversible dissociation constant for the enzyme inhibitor complex and the rate constant for the subsequent phosphorylation step can be obtained from suitable plots of the experimental data.     

Statistical survey of “saturation analysis” calibration curve data for prednisolone,prednisone and digoxin

An extensive survey of radioimmunoassay calibration data for prednisolone, prednisone and digoxin indicated that the common practice of preparing calibration curves with individual subject's pre-dose plasma or serum, and using this to estimate unknown concentrations for the same subject, is not supported by statistical considerations. Preparation of calibration plots from pooled data is better because this introduces less bias in estimated concentrations. Such a method also saves a great deal of time, since it is not necessary to repeat the calibration procedure each time “unknowns” are being assayed. The data suggest that there is no optimum calibration plot for all radioimmunoassays. Rather, each antibody-drug combination should be investigated thoroughly to determine the best calibration plot for the particular combination. We found that the best calibration plots are; the logistic-logarithmic plot for prednisolone; nonlinear least squares fit to a polyexponential equation for prednisone; and a weighted least squares regression of normalized % bound $\text{versus}$ concentration for digoxin. The error in the radioimmunoassay is usually concentration-dependent, and, in certain regions of the standard curve, is larger than the literature indicates, since, frequently, the error has been gauged from % bound values, but should be gauged from inversely-estimated concentrations.     

Half-time analysis of the integrated Michaelis equation. Simulation and use of the half-time plot and its direct linear variant in the analysis of some α-chymotrypsin-, papain- and fumarase-catalysed reactions

Substitution of half-time parameters in the integrated form of the Michaelis–Menten equation for any enzyme-catalysed reaction yields an equation that gives a linear relationship between the half-time of the reaction and the substrate concentration at that point of the reaction. The logarithmic term of the integrated equation becomes a constant as a result of the substitution, which means that the use of the half-time plot of the equation requires calculation only of half-time and substrate-concentration values at various stages of the reaction. The half-time method is both simple and exact, being analogous to an [S₀]/v_i against [S₀] plot. A direct linear form of the half-time plot has been devised that allows very simple estimation of Michaelis parameters and/or initial velocities from progress-curve data. This method involves no approximation and is statistically valid. Simulation studies have shown that linear-regression analysis of half-time plots provides unbiased estimates of the Michaelis parameters. Simulation of the effect of error in estimation of the product concentration at infinite time [P_∞] reveals that this is always a cause for concern, such errors being magnified approximately an order of magnitude in the estimate of the Michaelis constant. Both the half-time plot and the direct linear form have been applied to the analysis of a variety of experimental data. The method has been shown to produce excellent results provided certain simple rules are followed regarding criteria of experimental design. A set of rules has been formulated that, if followed, allows progress-curve data to be acquired and analysed in a reliable fashion. It is apparent that the use of modern spectrophotometers in carefully designed experiments allows the collection of data characterized by low noise and accurate [P_∞] estimates. [P_∞] values have been found, in the present work, to be precise to within ±0.2% and noise levels have always been below 0.1% (signal-to-noise ratio1000). As a result of the considerations above, it is concluded that there is little to be feared with regard to the analysis of enzyme kinetics using complete progress curves, despite the generally lukewarm recommendations to be found in the literature. The saving in time, materials and experimental effort amply justify analysis of enzyme kinetics by progress-curve methods. Half-time plots linear to ≥90% of reaction have been obtained for some α-chymotrypsin-, papain- and fumarase-catalysed reactions.     

Detecting and adjusting for small-study effects in meta-analysis

Publication bias and related types of small-study effects threaten the validity of systematic reviews. The existence of small-study effects has been demonstrated in empirical studies. Small-study effects are graphically diagnosed by inspection of the funnel plot. Though observed funnel plot asymmetry cannot be easily linked to a specific reason, tests based on funnel plot asymmetry have been proposed. Beyond a vast range of funnel plot tests, there exist several methods for adjusting treatment effect estimates for these biases. In this article, we consider the trim-and-fill method, the Copas selection model, and more recent regression-based approaches. The methods are exemplified using a meta-analysis from the literature and compared in a simulation study, based on binary response data. They are also applied to a large set of meta-analyses. Some fundamental differences between the approaches are discussed. An assumption common to the trim-and-fill method and the Copas selection model is that the small-study effect is caused by selection. The trim-and-fill method corresponds to an unknown implicit model generated by the symmetry assumption, whereas the Copas selection model is a parametric statistical model. However, it requires a sensitivity analysis. Regression-based approaches are easier to implement and not based on a specific selection model. Both simulations and applications suggest that in the presence of strong selection both the trim-and-fill method and the Copas selection model may not fully eliminate bias, while regression-based approaches seem to be a promising alternative.     

Quantitative analysis of sulpiride in body fluids by high-performance liquid chromatography with fluorescence detection

A high-performance liquid chromatographic method for the analysis of sulpiride, N-ethyl-2-(2-methoxy-5-sulphonamido-benzamido-methyl)-pyrrolidine, in body fluids is described. A structurally related compound, N-ethyl-2-(2,4-dimethoxy-benzamido-methyl)-pyrrolidine, was used as internal standard.A fluorescence detector with excitation maximum at 299 nm and emission maximum at 342 nm was used for the quantitation. The detection limit was about 10 ng/ml in serum and cerebrospinal fluid and about 200 ng/ml in urine. The experimental error was 5–10% in the concentration range 25–100 ng/ml. Some preliminary data from a pharmacokinetic study in healthy volunteers are presented. The half-life for sulpiride in serum was about 8 h. Sulpiride was also measured in cerebrospinal fluid from five drug-treated psychotic patients.     

The effect of ligand heterogeneity on the Scatchard plot. Particular relevance to lipoprotein binding analysis

Computer simulations of equilibrium binding studies of a mixture of two labeled ligands binding competitively to a single class of identical and independent sites (receptors) were performed to investigate how ligand heterogeneity affects the observed data in such studies. The simulated data are presented in Scatchard plots. Ligand heterogeneity was generally found to be indistinguishable from the case of a homogeneous ligand when usual experimental conditions applied (that is, Scatchard plots of the data were straight lines). Some factors that increased the probability of recognizing heterogeneity in the system were identified, however. These are 1) a large difference between the dissociation constants of the two ligands, 2) a high concentration of receptors relative to the dissociation constant of the higher-affinity ligand, 3) a high concentration of the lower-affinity ligand relative to that of the higher-affinity ligand, 4) a high specific activity of the lower-affinity ligand relative to that of the higher-affinity ligand, and 5) lack of experimental error. When ligand heterogeneity (under certain conditions) did cause curvilinearity in the Scatchard plot, the curve formed was always concave-downwards. Thus, ligand heterogeneity may occasionally mimic positive cooperativity, but never mimics negative cooperativity or multiple classes of binding sites. Implications of these findings for equilibrium binding studies involving lipoproteins (which are generally isolated as heterogeneous mixtures of particles) are discussed in detail. These findings are also relevant to equilibrium binding studies using ligands which are mixtures of stereoisomers or which contain chemical or radiochemical impurities.     

Improving the Accuracy of Sampling Field Plots for Plant-Parasitic Nematodes

The validity of nematode data from field experiments depends largely on how well samples represent the nematode population. Data from an intensive sampling of three field plots before and after spring cultivation were used to compare eight simulated sampling schemes. Average deviation from the plot mean ranged from 10% to 34% before cultivation and from 7% to 16% after cultivation. Samples taken from only the plant row erred most before cultivation but were comparable to other schemes after cultivation. Several schemes achieved a 25% deviation or less in 90% of the sample simulations. Sampling a nematode population usually involves subsampling a composite bulk sample, however, and this increases error by an estimable amount. A random sample with 35 cores and four random subsamples estimated mean plot densities within 25% with probabilities ranging from 0.77 to 0.85. The probability of a sample-subsample combination coming within a specified percent error of the true mean can be extended cautiously to any field mean and variance more-or-less independent of species and area using formulae presented herein. The most economical method of increasing sample accuracy was to increase the number of soil cores.     

Systematic detection of errors in genetic linkage data.

Construction of dense genetic linkage maps is hampered, in practice, by the occurrence of laboratory typing errors. Even relatively low error rates cause substantial map expansion and interfere with the determination of correct genetic order. Here, we describe a systematic method for overcoming these difficulties, based on incorporating the possibility of error into the usual likelihood model for linkage analysis. Using this approach, it is possible to construct genetic maps allowing for error and to identify the typings most likely to be in error. The method has been implemented for F2 intercrosses between two inbred strains, a situation relevant to the construction of genetic maps in experimental organisms. Tests involving both simulated and real data are presented, showing that the method detects the vast majority of errors.     

The role of intermolecular electrostatic cooperative interactions causing cryoprecipitation of human monoclonal immunoglobin M

A chemical modification of carboxylic groups of monoclonal human cryoglobulin M has been studied. The modification by a chromophoric carbodiimide was accompanied by complete loss of IgM cryoprecipitating properties. The number of carboxylic groups important for biological activity was estimated by the Tsou method and found to be 2. The cryoprecipitation dependence on ionic strength has been investigated and the number of ions per binding site isolated upon formation of intermolecular ion couples has been estimated. Mechanism of cryoprecipitation stipulated by intermolecular cooperative electrostatic interactions is proposed.     

Lateral mobility in membranes as detected by fluorescence recovery after photobleaching.

The evaluation of lateral diffusion coefficients of membrane components by the technique of fluorescence recovery after photobleaching (FRAP) is often complicated by uncertainties in the values of the intensities F(O), immediately after bleaching, and F(infinity), after full recovery. These uncertainties arise from instrumental settling time immediately after bleaching and from cell, tissue, microscope, or laser beam movements at the long times required to measure F(infinity). We have developed a method for precise analysis of FRAP data that minimizes these problems. The method is based on the observation that a plot of the reciprocal function R(tau) = F(infinity)/[F(infinity)-F(tau)] is linear over a large time range when (a) the laser beam has a Gaussian profile, (b) recovery involves a single diffusion coefficient, and (c) there is no membrane flow. Moreover, the ratio of intercept to slope of the linear plot is equal to tau 1/2, the time required for the bleached fluorescence to rise to 50% of the full recovery value, F(infinity). The lateral diffusion coefficient D is related to tau 1/2 by tau 1/2 = beta w2/4D where beta is a defined parameter and w is the effective radius of the focused laser beam. These results are shown to indicate that the recovery of fluorescence F(tau) can be represented over a large range of percent bleach, and recovery time tau by the relatively simple expression F(tau) = [ F(o) + F(infinity) (tau/tau 1/2)]/[1 + tau/tau 1/2)]. FRAP data can therefore be easily evaluated by a nonlinear regression analysis with this equation or by a linear fit to the reciprocal function R(tau). It is shown that any error in F(infinity) can be easily detected in a plot of R(tau) vs. tau which deviates significantly from a straight line when F(infinity) is in error by as little as 5%. A scheme for evaluating D by linear analysis is presented. It is also shown that the linear reciprocal plot provides a simple method for detecting flow or multiple diffusion coefficients and for establishing conditions (data precision, differences in multiple diffusion coefficients, magnitude of flow rate compared to lateral diffusion) under which flow or multiple diffusion coefficients can be detected. These aspects are discussed in some detail.