A nonparametric method for fitting a single exponential to biological data.

A nonparametric (“median”) method for fitting a single exponential to biological data is described. Its performance compared with that of least-squares alternatives has been assessed by analyzing simulated experimental data. The method appears to be reliable and relatively efficient.     

Pseudoelasticity of excised visceral pleura

A pseudostrain-energy function is proposed for describing the behavior of excised sheets of canine visceral pleura. Pseudoelastic material constants are determined from experimental biaxial data by employing a nonlinear least-squares algorithm. The agreement between theory and experiment is shown to be quite good. Furthermore, the visceral pleura studied appears to be inelastic and to exhibit in-plane isotropy. Comparison with previous works is discussed.     

A method of graphically analyzing substrate-inhibition kinetics

A model of substrate inhibition for enzyme catalysis was extended to describe the kinetics of photosynthetic production of ethylene by a recombinant cyanobacterium, which exhibits light-inhibition behavior similar to the substrate-inhibition behavior in enzyme reactions. To check the validity of the model against the experimental data, the model equation, which contains three kinetic parameters, was transformed so that a linear plot of the data could be made. The plot yielded reasonable linearity, and the parameter values could be estimated from the plot. The linear-plot approach was then applied to other inhibition kinetics including substrate inhibition of enzyme reactions and inhibitory growth of bacteria, whose analyses would otherwise require nonlinear least-squares fits or data measured in constrained ranges. Plots for three totally different systems all showed reasonable linearity, which enabled visual validation of the assumed kinetics. Parameter values evaluated from the plots were compared with results of nonlinear least-squares fits. A normalized linear plot for all the results discussed in this work is also presented, where dimensionless rates as a function of dimensionless concentration lie in a straight line. The linear-plot approach is expected to be complementary to nonlinear least-squares fits and other currently used methods in analyses of substrate-inhibition kinetics. Copyright 1999 John Wiley & Sons, Inc.     

Weighted least-squares likelihood ratio test for branch testing in phylogenies reconstructed from distance measures

A variety of analytical methods is available for branch testing in distance-based phylogenies. However, these methods are rarely used, possibly because the estimation of some of their statistics, especially the covariances, is not always feasible. We show that these difficulties can be overcome if some simplifying assumptions are made, namely distance independence. The weighted least-squares likelihood ratio test (WLS-LRT) we propose is easy to perform, using only the distances and some of their associated variances. If no variances are known, the use of the Felsenstein F-test, also based on weighted least squares, is discussed. Using simulated data and a data set of 43 mammalian mitochondrial sequences we demonstrate that the WLS-LRT performs as well as the generalized least-squares test, and indeed better for a large number of taxa data set. We thus show that the assumption of independence does not negatively affect the reliability or the accuracy of the least-squares approach. The results of the WLS-LRT are no worse than the results of the bootstrap methods, such as the Felsenstein bootstrap selection probability test and the Dopazo test. We also show that WLS-LRT can be applied in instances where other analytical methods are inappropriate. This point is illustrated by analyzing the relationships between human immunodeficiency virus type 1 (HIV-1) sequences isolated from various organs of different individuals.     

A user's experience with a standard non-linear regression program (BMDP3R).

A study was made to test and compare the behavior of a standard non-linear regression program (BMDP3R) in fitting data from six classical least-squares problems. The use of three program control parameters is discussed and four measures of regression failure are utilized to give a quantitative reference of success. Recommendations are given to aid the user of packaged programs in the parameter estimation of non-linear regression models.     

Why, when, and how biochemists should use least squares.

One of the most commonly used methods for the analysis of experimental data in the biochemical literature is nonlinear least squares (regression). This group of methods are also commonly misused. The purpose of this article is to review the assumptions inherent in the use of least-squares techniques and how these assumptions govern the ways that least-squares techniques can and should be used. Since these assumptions pertain to the nature of the experimental data to be analyzed they also dictate many aspects of the data collection protocol. The examination of these assumptions includes a discussion of questions like: Why would a biochemist want to use nonlinear least-squares techniques? When is it appropriate for a biochemist to use nonlinear least-squares techniques? What confidence can be assigned to the results of a nonlinear least-squares analysis?     

(1)H NMR spectroscopy of serum reveals unique metabolic fingerprints associated with subtypes of surgically induced osteoarthritis in sheep

Osteoarthritis (OA) is a highly prevalent joint disease. Its slow progressive nature and the correlation between pathological changes and clinical symptoms mean that OA is often well advanced by the time of diagnosis. In the absence of any specific pharmacological treatments, there is a pressing need to develop robust biomarkers for OA. We have adopted a nuclear magnetic resonance (NMR)-based metabolomic strategy to identify molecular responses to surgically induced OA in an animal model. Sheep underwent one of three types of surgical procedure (sham (control), meniscal destabilization, MD or anterior cruciate ligament transaction, ACLT), and for every animal a serum sample was collected both pre- and postoperatively, thus, affording two types of "control" data for comparison. 1D (1)H NMR spectra were acquired from each sample at 800 MHz and the digitized spectral data were analyzed using principal components analysis and partial least-squares regression discriminant analysis. Our approach, combined with the study design, allowed us to separate the metabolic responses to surgical intervention from those associated with OA. We were able to identify dimethyl sulfone (DMSO(2)) as being increased in MD after 4 weeks, while ACLT-induced OA exhibited increased 3-methylhistidine and decreased branched chain amino acids (BCAAs). The findings are discussed in the context of interpretation of metabolomic results in studies of human disease, and the selection of appropriate "control" data sets.     

Use of two-block partial least-squares to study covariation in shape

The relatively new two-block partial least-squares method for analyzing the covariance between two sets of variables is described and contrasted with the well-known method of canonical correlation analysis. Their statistical properties, type of answers, and visualization techniques are discussed. Examples are given to show its usefulness in comparing two sets of variables--especially when one or both of the sets of variables are shape variables from a geometric morphometric study.     

Application of splines to the calculation of bacterial swimming speed distributions.

A new method of extracting information about bacterial speeds from photon correlation spectroscopy is presented. This method has the advantage that an estimation of the translational speed distribution is directly varied so as to achieve a best least-squares fit to the experimental autocorrelation function. The theory of spline approximations to continuous functions is briefly outlined. The importance of the previously disregarded diffusional component of bacterial motion is discussed. Experimental data from Salmonella at a low scattering angle is analyzed by this method of spline approximation and the distribution of translational speeds is obtained.     

The graduation of secondary structure elements

A method of graduating (i.e., least-squares fitting) a smooth polynomial curve through long elements of protein secondary structure is described. It uses the Chebyshev polynomials of a discrete (integer) variable with several restraints to prevent artifactual curvatures. A new recursion formula is given which allows the evaluation of the polynomials on rational-number points as well as on the integer points. High-order splines suitable for interpolation between integer points are also discussed. The new method finds applications in graphics and in structural analysis.     

A Method of Estimation of Change Points in Multiphasic Growth Models

The least-squares estimation (LSE) of change points and the phase parameters is considered for two growth models with piecewise continuously connected exponential and stationary phases. The calculation of a LSE is reduced to the solution of a finite number of simpler least-squares problems for which methods of calculation are well known.     

508. Aloe Descoingsii

Summary.  Aloe descoingsii Reynolds, the smallest Aloe species in the world, endemic to Madagascar, is described and illustrated. Its history, ecology and conservation status are discussed. Its habitat is shown.     

Refinement of the structure of bovine seminal ribonuclease

We report here the refinement at 2.5-Å resolution of the x-ray crystal structure of bovine seminal ribonuclease, a dimeric covalent enzyme. The protein, which crystallizes with one molecule in the asymmetric unit, consists of two subunits of identical chemical sequences, related by an almost exact binary axis. The tertiary structure of the subunits is similar to that of the pancreatic enzyme, which shows similar catalytic properties. The refinement was carried out using the restrained least-squares procedure both in the reciprocal and real spaces. The assemblage of the subunits in the dimer is described and discussed.     

Evaluation of distribution-free confidence limits for enzyme kinetic parameters

Monte Carlo experiments have been used to test the robustness of distribution-free confidence limits for the parameters of the Michaelis-Menten equation (Porter & Trager, 1977). When used in conjunction with the modified form of the direct linear plot (Cornish-Bowden & Eisenthal, 1978), they prove to be more robust than least-squares confidence limits. In circumstances where the least-squares assumptions are correct, the distribution-free confidence limits define the parameters somewhat less precisely than the corresponding least-squares confidence limits, but this effect is negligible unless there are eight or fewer observations.     

Methods for multiple-marker mapping of quantitative trait loci in half-sib populations

In this paper we consider the detection of individual loci controlling quantitative traits of interest (quantitative trait loci or QTLs) in the large half-sib family structure found in some species. Two simple approaches using multiple markers are proposed, one using least squares and the other maximum likelihood. These methods are intended to provide a relatively fast screening of the entire genome to pinpoint regions of interest for further investigation. They are compared with a more traditional single-marker least-squares approach. The use of multiple markers is shown to increase power and has the advantage of providing an estimate for the location of the QTL. The maximum-likelihood and the least-squares approaches using multiple markers give similar power and estimates for the QTL location, although the likelihood approach also provides estimates of the QTL effect and sire heterozygote frequency. A number of assumptions have been made in order to make the likelihood calculations feasible, however, and computationally it is still more demanding than the least-squares approach. The least-squares approach using multiple markers provides a fast method that can easily be extended to include additional effects.     

Optimal recognition of neuronal waveforms

Statistically optimal methods for identifying single unit activity in multiple unit recordings are discussed. These methods take into account both the nerve impulse waveforms and the firing patterns of the units. A generalized least-squares fit procedure is shown to be the optimal recognition scheme under some reasonable statistical assumptions, but the amount of computation becomes prohibitively large when the method is applied to the problem of sorting superimposed waveforms. A linear filter technique which relies on simultaneous recording from several electrodes in shown to give good separation of superimposed waveforms. An iterative recognition procedure can be applied to improve the results and reduce the number of recording electrodes required.     

507. Aloe Calcairophila

Summary.  Aloe calcairophila Reynolds, a miniature aloe, endemic to Madagascar, is described and illustrated. Its ecology and conservation status are discussed. Its habitat on Cipolins dominated by Aloe capitata var cipolinicola , is shown.     

786. STROBILANTHES ATTENUATA

Strobilanthes attenuata (Nees) Nees is described and illustrated. Its extensive synonomy is discussed and its principal characteristics are highlighted. Its introduction to countries with a temperate climate is chronicled and successful experience of its cultivation in England is described.     

733. CARPINUS TSCHONOSKII

The east Asian hornbeam, Carpinus tschonoskii Maxim., is illustrated and described. Its distribution in the wild and the distinctness of related species are discussed. Its behaviour in cultivation is reported.     

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.