Multidimensional curve fitting program for biological data

A program written for use with the IBM-PC can be used to find least squares solutions to linearized multidimensional equations. The program is 'user-friendly' by requiring little from the user except to make decisions; most responses can be entered by a single keystroke. Once data are entered by the user, they can be repeatedly manipulated, graphed, and correlated. Many models relating data variables can be tried relatively easily, and best fit results found. Examples using respiratory mechanical data illustrate the ease of model comparisons.     

A least-squares method for fitting the Hill equatio to data from several animals.

The principle of the method is to solve a set of nonlinear simultaneous equations, given initial estimates of the nonlinear parameters (h, the Hill coefficient, and K, the substrate constant). It can be adapted to fit the Hill equation to sets of data with common values of h and K but different maximum velocities, and an example of this is given. The method is compared with some published alternatives.     

A computer program for linear nonparametric and parametric identification of biological data

A computer program package for parametric and nonparametric linear system identification of both static and dynamic biological data, written for an LSI-11 minicomputer with 28 K of memory, is described. The program has 11 possible commands including an instructional help command. A user can perform nonparametric spectral analysis and estimation of autocorrelation and partial autocorrelation functions of univariate data and estimate nonparametrically the transfer function and possibly an associated noise series of bivariate data. In addition, the commands provide the user the means to derive a parametric autoregressive moving average model for univariate data, to derive a parametric transfer function and noise model for bivariate data, and to perform several model evaluation tests such as pole-zero cancellation, examination of residual whiteness and uncorrelatedness with the input. The program, consisting of a main program and driver subroutine as well as six overlay segments, may be run interactively or automatically.     

A program for fitting of hypnograms and other biological data by orthogonal polynomials.

Many biological phenomenon are nonlinear and poorly approximated by linear regression. The program POLFIT calculates curvilinear regressions by fitting of orthogonal polynomials. This program, as well as two supporting programs (CORREC: disk storage, and CALCML: calculation of cumulated values of series of observations), was primarily designed for the study of the temporal organization of sleep components. They can be used as well for any other kind of biological data.     

A computer program for the graphical and iterative fitting of probability density functions to biological data.

A tutorially-assisted, interactive program, written for a Digital Equipment Corporation LAB-11 minicomputer (PDP-11/20, is described which allows a user to fit (with or without automatic estimation of initial parameter values), by a method of nonlinear least squres, any one of seven different types of probability density functions (p.d.f.'s) to an empirical frequency distribution; the latter of which may be input to the program or formed by the program whenever it is furnished a series of times between events. The iteratively-obtained, "best fit" p.d.f. is displayed on a two color, point-plot display against the background of a point-plot histogram. By selecting any one of nine output modes, the user is allowed: (1) to view histograms successively on the point-plot display, (2) to generate selected p.d.f.'s (3) to "force" p.d.f.'s having known parameters through the histogram data, (4) to obtain Chi-square (x2) and Kolmogorov-Smionov estimates of the goodness of fit to the data, and (5) to apply a special test [Williams and Kloot, 1953] in order to determine whether the least squares estimates of two candidate models are statistically different. The resident driver program and the four overlayable program segments are written in standard FORTRAN IV; except for two plot routines, which are written in PDP-11 assembly language.     

A nomogram for deconvolution of single exponential fluorescence decays.

An extremely rapid technique for deconvolving single exponential luminescence decay data is described that involves essentially no mathematical manipulation of the experimental data. The method permits "real time" measurement of deconvolved luminescence lifetimes with conventional pulsed, lifetime-fluorometers and phosphorimeters. The method assumes that the true luminescence decay of the chromophore is accurately represented by a single exponential decay function.     

A nonparametric test for association with censored data

A nonparametric procedure is proposed for the problem of testing association between two continuous variables when one is subject to arbitrary censoring. The motivation for the procedure derives from our finding that Cox's likelihood procedure may not adequately control the size of the test. The proposed procedure allows the censoring mechanism to depend on the independent variable, is simple computationally, and provides accurate control over the size of the test even for quite small samples. Asymptotic results suggest that it may provide a sensitive alternative to Cox's procedure. An example dealing with survival following operation for myasthenia gravis is provided, wherein a method for testing after adjustment for covariate information is described.     

Two methods for fitting a rectangular hyperbola to data from several animals.

Two methods are described for fitting the Michaelis-Menten equation to sets of data with a common michaelis constant but different maximum velocities. One of them uses the method of least squares, and the other is based on the direct plot of Eisenthal & Cornish-Bowden [Biochem. J. (1974) 139, 715-720].     

A single-parameter family of adjustments for fitting enzyme kinetic models to progress-curve data.

We have investigated the rapid phosphorylation of proteins in B-lymphocytes incubated with the tumour-promoting phorbol ester 12-O-tetradecanoylphorbol 13-acetate (TPA), anti-Ig and combinations of TPA and the Ca2+ ionophore ionomycin. Two-dimensional electrophoretic analysis was used to identify the proteins phosphorylated in cells preincubated with [32P]Pi. TPA induced a characteristic pattern of labelled proteins, four of which (pp85, pp76, pp66 and pp63) showed a dose-dependent incorporation of 32P on serine residues. The phosphorylation of pp63 and pp66, in particular, correlated with the mitogenic dose-response curve. Addition of the Ca2+ ionophore ionomycin to B-cells also stimulated a characteristic incorporation of 32P into proteins, which included pp63 and pp66. With combined doses of TPA and ionomycin, these two proteins show an enhanced phosphorylation, which correlated well with the synergistic enhancement of proliferation shown by this combination of agents. Protein kinase C (PKC) was partially purified from B-cells and separated into alpha and beta subtypes. The activation of both PKCs was assessed with increasing doses of TPA and concentrations of Ca2+ of 0.1 microM and 2 microM. For both forms of PKC, in particular the beta form, higher concentrations of Ca2+ shifted the dose-response curve for TPA to the left and increased the maximum activation. Anti-Ig, which stimulated B-cells by cross-linking surface immunoglobulin and causing hydrolysis of PtdIns(4,5)P2, also caused increased phosphorylation of several proteins, which again included pp63 and pp66. These data suggest that PKC, particularly the beta form, is involved in the early part of the proliferation cascade for human B-lymphocytes. It is most probably activated in a synergistic manner by the increased Ca2+ and diacylglycerol levels which result from the earlier hydrolysis of PtdIns(4,5)P2.     

A method of selecting data points for fitting the maximum biomass-density line for stands undergoing self-thinning

Abstract A problem that has always existed in self-thinning studies is the lack of objectivity in determining which data points to include when fitting the maximum biomass-density line. This paper demonstrates a more objective method of selecting data points using data from 12 even-aged Pinus radiata stands undergoing self-thinning. The method involves the division of a cluster of data points into a specified number of intervals. From each interval, that point having the maximum stand biomass is selected to contribute to the fitting process. This process is repeated a specified number of times using an increasing number of intervals. Each time an estimate of the line is obtained. From these estimates, one can be chosen to represent the maximum biomass-density line. The method may also be useful in other areas involving the definition of a boundary condition.     

A Bayesian nonparametric method for prediction in EST analysis

Background  

Expressed sequence tags (ESTs) analyses are a fundamental tool for gene identification in organisms. Given a preliminary EST sample from a certain library, several statistical prediction problems arise. In particular, it is of interest to estimate how many new genes can be detected in a future EST sample of given size and also to determine the gene discovery rate: these estimates represent the basis for deciding whether to proceed sequencing the library and, in case of a positive decision, a guideline for selecting the size of the new sample. Such information is also useful for establishing sequencing efficiency in experimental design and for measuring the degree of redundancy of an EST library.     

A Fourier method for the analysis of exponential decay curves.

A method based on the Fourier convolution theorem is developed for the analysis of data composed of random noise, plus an unknown constant "base line," plus a sum of (or an integral over a continuous spectrum of) exponential decay functions. The Fourier method's usual serious practical limitation of needing high accuracy data over a very wide range is eliminated by the introduction of convergence parameters and a Gaussian taper window. A computer program is described for the analysis of discrete spectra, where the data involves only a sum of exponentials. The program is completely automatic in that the only necessary inputs are the raw data (not necessarily in equal intervals of time); no potentially biased initial guesses concerning either the number or the values of the components are needed. The outputs include the number of components, the amplitudes and time constants together with their estimated errors, and a spectral plot of the solution. The limiting resolving power of the method is studied by analyzing a wide range of simulated two-, three-, and four-component data. The results seem to indicate that the method is applicable over a considerably wider range of conditions than nonlinear least squares or the method of moments.     

Financing a future for public biological data.

MOTIVATION: The public web-based biological database infrastructure is a source of both wonder and worry. Users delight in the ever increasing amounts of information available; database administrators and curators worry about long-term financial support. An earlier study of 153 biological databases (Ellis and Kalumbi, Nature Biotechnol., 16, 1323-1324, 1998) determined that near future (1-5 year) funding for over two-thirds of them was uncertain. More detailed data are required to determine the magnitude of the problem and offer possible solutions. METHODS: This study examines the finances and use statistics of a few of these organizations in more depth, and reviews several economic models that may help sustain them. RESULTS: Six organizations were studied. Their administrative overhead is fairly low; non-administrative personnel and computer-related costs account for 77% of expenses. One smaller, more specialized US database, in 1997, had 60% of total access from US domains; a majority (56%) of its US accesses came from commercial domains, although only 2% of the 153 databases originally studied received any industrial support. The most popular model used to gain industrial support is asymmetric pricing: preferentially charging the commercial users of a database. At least five biological databases have recently begun using this model. Advertising is another model which may be useful for the more general, more heavily used sites. Microcommerce has promise, especially for databases that do not attract advertisers, but needs further testing. The least income reported for any of the databases studied was $50,000/year; applying this rate to 400 biological databases (a lower limit of the number of such databases, many of which require far larger resources) would mean annual support need of at least $20 million. To obtain this level of support is challenging, yet failure to accept the challenge could be catastrophic. CONTACT: lynda@tc.umn. edu     

A general approach to simultaneous model fitting and variable elimination in response models for biological data with many more variables than observations

Background  

With the advent of high throughput biotechnology data acquisition platforms such as micro arrays, SNP chips and mass spectrometers, data sets with many more variables than observations are now routinely being collected. Finding relationships between response variables of interest and variables in such data sets is an important problem akin to finding needles in a haystack. Whilst methods for a number of response types have been developed a general approach has been lacking.