A versatile digital computer program for non-linear regression analysis

1.

1. A general purpose digital computer program is described for application to biological experiments that require a non-linear regression analysis. The mathematical function, or model, to be fitted to a given set of experimental data is written as a section within the program. Given initial estimates for the parameters of the function, the program uses an iterative procedure to adjust the parameters until the sum of squares of residuals has converged to a minimum.     

INAKT - an interactive non-linear regression program for enzyme inactivation and affinity labelling studies

An interactive program for analysing enzyme activity-time data using non-linear regression analysis is described. Protection studies can also be dealt with. The program computes inactivation rates, dissociation constants and promotion or inhibition parameters with their standard errors. It can also be used to distinguish different inactivation models. The program is written in SIMULA and is menu-oriented for refining or correcting data at the different levels of computing.     

Analysis of progress curves by simulations generated by numerical integration.

A highly flexible computer program written in FORTRAN is presented which fits computer-generated simulations to experimental progress-curve data by an iterative non-linear weighted least-squares procedure. This fitting procedure allows kinetic rate constants to be determined from the experimental progress curves. Although the numerical integration of the rate equations by a previously described method [Barshop, Wrenn & Frieden (1983) Anal. Biochem. 130, 134-145] is used here to generate predicted curves, any routine capable of the integration of a set of differential equations can be used. The fitting program described is designed to be widely applicable, easy to learn and convenient to use. The use, behaviour and power of the program is explored by using simulated test data.     

Steady state enzyme kinetics: Experimental design and data analysis by microcomputer

One of the most time-consuming, yet essential, operations involved in the steady state kinetic study of enzymes is the design and optimization of experimental conditions. A computer program was developed for the Sinclair ZX-81 (or TS-1000, 1500) microcomputer which will optimize substrate concentration for preliminary and subsequently more refined kinetic analysis of one, two or three substrate systems. This program also analyzes the data collected from these studies by linear regression, weighted linear regression of weighted non-linear regression. In addition to the above program several of the enzyme kinetic statistical analysis programs of Cleland (1979) have been translated from FORTRAN into BASIC and implemented on the ZX-81 and the TRS-80 model II. Inexpensive commercially available software was used to overcome the inability of the ZX-81 to read data files from magnetic tape making the data analysis programs easier to use.     

A free derivate program for non-linear regression analysis of enzyme kinetics to be used on small computers

A non-linear regression program, written in BASIC, is describe. The program uses the Marquardt's algorithm as modified by Reich et al. (Eur. J. Biochem., 26 (1972) pp.368–379). The user only supplies the expression to fit, since the program uses numerical differentiation. It is possible to fit models of 1 substrate, 2 substrates, 1 substrates and 1 inhibitor, and 2 substrates and 1 inhibitor. Likewise, several weighting patterns, as well as a simple or robust regression, can be selected.     

The effect of pH on enzyme-catalysed reactions: A computer program to determine pK values of enzyme ionisable groups from kinetic data

The paper describes a non-linear multiple regression program to analyse the kinetic parameters V_m and K_m as functions of pH, assuming that the activity of particular enzyme forms is determined by the ionisation of two groups, the active form of the enzyme being the half-ionised species.     

Relational database model for DNA mutations and a software program for implementation of the model

A relational database model for describing DNA mutations is presented. The model was developed in conjunction with the human hprt database and was succesful in representing over 1800 hprt mutations. Mutants showing aberrant mRNA splicing can be adequately described using the model, as well as mutants showing more than one mutation. The basic aspects of the relational model should be applicable to mutations in a variety of genes. A data entry program developed using Microsoft Access 2.0 is also described that implements the relational model The data entry program ensures that relational integrity is maintained between the tables and automatically generates key fields as needed. The program also has the ability to convert between the various numbering schemes that are used to decribed base pair location in the hprt gene. The program and source code are placed in the public domain so that other experimenters can adapt the program for use with other genes.     

SHAM, a method for biexponential curve resolution using initial slope, height, area and moment of the experimental decay type curve.

A method for biexponesitial fitting of decay type curves is described. Basically the four unknowns are calculated from four curve parameters, viz. the initial slope (S), the initial height (H), the area (A) and the first time moment (M) with extrapolation to infinity being accomplished algebraically. The SHAM algorithm was considerably faster than a conventional iterative regression analysis (Gauss) and the results of the two methods were quite comparable both in synthetic and real data. The latter stemmed from ¹³³xenon wash-out studies of regional blood flow in the human brain. Fast analysis of such data was the primary aim of developing the new method.     

Regression imputation of missing values in longitudinal data sets

A stand-alone, menu-driven PC program, written in GAUSS, which can be used to estimate missing observations in longitudinal data sets is described and made available to interested readers. The program is limited to the situation in which we have complete data on N cases at each of the planned times of measurement t₁, t₂,…, t_T; and we wish to use this information, together with the non-missing values for n additional cases, to estimate the missing values for those cases. The augmented data matrix may be saved in an ASCII file and subsequently imported into programs requiring complete data. The use of the program is illustrated. Ten percent of the observations in a data set consisting of mandibular ramus height measurements for N = 12 young male rhesus monkeys measured at T = 5 time points are randomly discarded. The augmented data matrix is used to determine the lowest degree polynomial adequate to fit the average growth curve (AGC); the regression coefficients are estimated and confidence intervals for them are determined; and confidence bands for the AGC are constructed. The results are compared with those obtained when the original complete data set is used.     

Creation of an in vitro biomechanical model of the trachea using rapid prototyping

Previous in vitro models of the airways are either rigid or, if flexible, have not matched in vivo compliance characteristics. Rapid prototyping provides a quickly evolving approach that can be used to directly produce in vitro airway models using either rigid or flexible polymers. The objective of this study was to use rapid prototyping to directly produce a flexible hollow model that matches the biomechanical compliance of the trachea. The airway model consisted of a previously developed characteristic mouth–throat region, the trachea, and a portion of the main bronchi. Compliance of the tracheal region was known from a previous in vivo imaging study that reported cross-sectional areas over a range of internal pressures. The compliance of the tracheal region was matched to the in vivo data for a specific flexible resin by iteratively selecting the thicknesses and other dimensions of tracheal wall components. Seven iterative models were produced and illustrated highly non-linear expansion consisting of initial rapid size increase, a transition region, and continued slower size increase as pressure was increased. Thickness of the esophageal interface membrane and initial trachea indention were identified as key parameters with the final model correctly predicting all phases of expansion within a value of 5% of the in vivo data. Applications of the current biomechanical model are related to endotracheal intubation and include determination of effective mucus suctioning and evaluation of cuff sealing with respect to gases and secretions.     

Abnormal cytoplasmic bundles of filaments in the Neurospora crassa snowflake colonial mutant contain P59Nc

Cytoplasmic bundles of microfilaments accumulate in the Neurospora crassa morphological mutant snowflake. We have performed ultrastructural, immunoelectron, and immunofluorescence microscope studies of snowflake strains and we show here that these bundles of cytoplasmic microfilaments contain 8- to 10-nm-diameter filaments and the 59-kDa polypeptide (P59Nc) described in wild-type N. crassa strains. The immunofluorescence studies showed that almost all of the snowflake bundles are abnormal in size and morphology. Polyacrylamide gel electrophoresis of proteins from total extracts, subcellular fractions, and partially purified P59Nc from snowflake strains showed that the subcellular distribution and relative amount of P59Nc are normal in the mutants. In vitro disassembly of P59Nc bundles obtained from snowflake strains appears to occur identically to that of bundles purified from wild-type N. crassa. A polypeptide of 48 kDa enriched in a subcellular fraction of the wild-type strain was not detected in the corresponding fraction of the snowflake mutants. No significant differences in the presence or relative amounts of other polypeptides were detected between the wild-type and the snowflake strains. The results are compatible with the possibility that sn is the genetic locus either of P59Nc or of the polypeptide of 48 kDa and/or of a modifier of the P59Nc properties for in vivo supramolecular assembly in bundles of 8- to 10-nm-diameter filaments.     

A PC program for performing multigroup longitudinal comparisons using the Potthoff-Roy analysis and orthogonal polynomials

A PC-program performing the Potthoff-Roy (PR) multigroup (G-sample) analysis of longitudinal data is described and illustrated. This program and the underlying statistical model are useful in the comparison of several longitudinal samples. Applications include the study of growth, development, adaptation, aging, and treatment effects (in short, any phenomenon in which the passage of time is important) for which serial data are available. Specifically, this method fits polynomials to the average growth curves in the samples, and tests hypotheses concerning the curves themselves and the individual coefficients of the polynomials. The program features the utilization of orthogonal polynomial regression coefficients (OPRCs) and is written in GAUSS, a relatively inexpensive yet comprehensive matrix programming language. It is documented that using OPRCs to comprise the within-individual or time design matrix has several advantages over the more usual choice of the successive-powers-of-t form of this matrix and an example of one important such advantage is provided. GAUSS was employed to make the program readily-accessible (i.e., executable code) to biomedical investigators. The GAUSS compiler is not required to run this program. Information regarding the availability of the program is provided in the Appendix.     

LILLY—A linear least squares curve fitting program for one independent variable

A program was written to perform a linear least squares curve fitting on data. It includes facilities to report the usual statistics and digital plotter output. Seven types of curves are available for fitting the data. Other features of LILLY include provision of facilities for the selection of subsets in different symbols and separate curve fitting for these subsets. The program also provides a confidence region about the fitted line and the prediction interval for data points. Examples of the use of the program are described.     

Les faunes d'ammonites du Carixien inférieur et moyen du gisement des Cottards (Cher)

The study of the traditional Cottard layer forthe first time allows the exact succession of lower and middle Carixian ammonites to be established.The most striking fact is the evolution of the Tropidoceras-Acanthopleuroceras lineage, a regular modification of the ribbing density and L¹ structure, an iterative variation of section and tuberculization.Precisions are given on Polymorphites and Beaniceras and three new species are described: Polymorphites evolutus, Beaniceras cottardiense, Acanthopleuroceras alisiense.     

Assembly of subunit d (Vma6p) and G (Vma10p) and the NMR solution structure of subunit G (G1-59) of the Saccharomyces cerevisiae V1VO ATPase

Understanding the structural traits of subunit G is essential, as it is needed for V₁V_O assembly and function. Here solution NMR of the recombinant N- (G_1-59) and C-terminal segment (G_61-114) of subunit G, has been performed in the absence and presence of subunit d of the yeast V-ATPase. The data show that G does bind to subunit d via its N-terminal part, G_1-59 only. The residues of G_1-59 involved in d binding are Gly7 to Lys34. The structure of G_1-59 has been solved, revealing an α-helix between residues 10 and 56, whereby the first nine- and the last three residues of G_1-59 are flexible. The surface charge distribution of G_1-59 reveals an amphiphilic character at the N-terminus due to positive and negative charge distribution at one side and a hydrophobic surface on the opposite side of the structure. The C-terminus exhibits a strip of negative residues. The data imply that G_1-59-d assembly is accomplished by hydrophobic interactions and salt-bridges of the polar residues. Based on the recently determined NMR structure of segment E_18-38 of subunit E of yeast V-ATPase and the presently solved structure of G_1-59, both proteins have been docked and binding epitopes have been analyzed.     

Next-Generation Sequencing of Connective Tissue Genes in Patients with Classical Ehlers-Danlos Syndrome

Background: Ehlers-Danlos syndrome (EDS) is a common non-inflammatory, congenital connective tissue disorder. Classical type (cEDS) EDS is one of the more common forms, typically caused by mutations in the COL5A1 and COL5A2 genes, though causative mutations in the COL1A1 gene have also been described. Material and methods: The study group included 59 patients of Polish origin, diagnosed with cEDS. The analysis was performed on genomic DNA (gDNA) with NGS technology, using an Illumina sequencer. Thirty-five genes related to connective tissue were investigated. The pathogenicity of the detected variants was assessed by VarSome. Results: The NGS of 35 genes revealed variants within the COL5A1, COL5A2, COL1A1, and COL1A2 genes for 30 of the 59 patients investigated. Our panel detected no sequence variations for the remaining 29 patients. Discussion: Next-generation sequencing, with an appropriate multigene panel, showed great potential to assist in the diagnosis of EDS and other connective tissue disorders. Our data also show that not all causative genes giving rise to cEDS have been elucidated yet.     

Quantitative quality control in microarray image processing and data acquisition

A new integrated image analysis package with quantitative quality control schemes is described for cDNA microarray technology. The package employs an iterative algorithm that utilizes both intensity characteristics and spatial information of the spots on a microarray image for signal–background segmentation and defines five quality scores for each spot to record irregularities in spot intensity, size and background noise levels. A composite score q_com is defined based on these individual scores to give an overall assessment of spot quality. Using q_com we demonstrate that the inherent variability in intensity ratio measurements is closely correlated with spot quality, namely spots with higher quality give less variable measurements and vice versa. In addition, gauging data by q_com can improve data reliability dramatically and efficiently. We further show that the variability in ratio measurements drops exponentially with increasing q_com and, for the majority of spots at the high quality end, this improvement is mainly due to an improvement in correlation between the two dyes. Based on these studies, we discuss the potential of quantitative quality control for microarray data and the possibility of filtering and normalizing microarray data using a quality metrics-dependent scheme.     

Evidence concerning a possible steady state rate equation for E. coli alkaline phosphatase

• 1.1. Steady state data was obtained for alkaline phosphatase over a wide range of experimental conditions using two substrates, four inhibitors, two modifiers and several pH, ionic strength and temperatures values.
• 2.2. The data was fitted by rational functions of degree 1:1, 2:2 and 3:3 using a non-linear regression program and then the F-test was used to assess the goodness of fit.
• 3.3. A proportion of the curves could only be fitted by 2:2 functions but many of them could be adequately fitted by 1:1 functions.
• 4.4. No statistically significant improvement in fit occurred with 3:3 functions.
• 5.5. Data was simulated using a computer program to see what sort of curves could be generated by a two sites mechanism proposed for alkaline phosphatase and this study showed that it is difficult to detect cubic terms in this rate equation.
• 6.6. It was concluded that alkaline phosphatase does not obey Michaelis-Menten kinetics. Rather, the steady state data require a mechanism of at least second degree but do not exclude a rate equation of third degree.

     

Improved Assessment of Denitrifying, N2-Fixing, and Total-Community Bacteria by Terminal Restriction Fragment Length Polymorphism Analysis Using Multiple Restriction Enzymes

A database of terminal restriction fragments (tRFs) of the 16S rRNA gene was set up utilizing 13 restriction enzymes and 17,327 GenBank sequences. A computer program, termed TReFID, was developed to allow identification of any of these 17,327 sequences by means of polygons generated from the specific tRFs of each bacterium. The TReFID program complements and exceeds in its data content the Web-based phylogenetic assignment tool recently described by A. D. Kent, D. J. Smith, B. J. Benson, and E. W. Triplett (Appl. Environ. Microb. 69:6768-6766, 2003). The method to identify bacteria is different, as is the region of the 16S rRNA gene employed in the present program. For the present communication the software of the tRF profiles has also been extended to allow screening for genes coding for N₂ fixation (nifH) and denitrification (nosZ) in any bacterium or environmental sample. A number of controls were performed to test the reliability of the TReFID program. Furthermore, the TReFID program has been shown to permit the analysis of the bacterial population structure of bacteria by means of their 16S rRNA, nifH, and nosZ gene content in an environmental habitat, as exemplified for a sample from a forest soil. The use of the TReFID program reveals that noncultured denitrifying and dinitrogen-fixing bacteria might play a more dominant role in soils than believed hitherto.