Transforming signals into quantitative values and mathematical treatment of data

Identification of line-specific strategies for improving carotenoid production in synthetic maize through data-driven mathematical modeling

Plant synthetic biology is still in its infancy. However, synthetic biology approaches have been used to manipulate and improve the nutritional and health value of staple food crops such as rice, potato and maize. With current technologies, production yields of the synthetic nutrients are a result of trial and error, and systematic rational strategies to optimize those yields are still lacking. Here, we present a workflow that combines gene expression and quantitative metabolomics with mathematical modeling to identify strategies for increasing production yields of nutritionally important carotenoids in the seed endosperm synthesized through alternative biosynthetic pathways in synthetic lines of white maize, which is normally devoid of carotenoids. Quantitative metabolomics and gene expression data are used to create and fit parameters of mathematical models that are specific to four independent maize lines. Sensitivity analysis and simulation of each model is used to predict which gene activities should be further engineered in order to increase production yields for carotenoid accumulation in each line. Some of these predictions (e.g. increasing Zmlycb/Gllycb will increase accumulated β-carotenes) are valid across the four maize lines and consistent with experimental observations in other systems. Other predictions are line specific. The workflow is adaptable to any other biological system for which appropriate quantitative information is available. Furthermore, we validate some of the predictions using experimental data from additional synthetic maize lines for which no models were developed.

Time course of systolic and diastolic blood pressure decreases during the preintubation period of anesthesia induction: modeling with a logistic function

STUDY OBJECTIVE

To investigate whether systolic (SBP) and diastolic blood pressure (DBP) decreases during the preintubation period could be expressed as 4-parameter logistic and cubic functions giving S-shaped curves.

DESIGN

Prospective, clinical study.

SETTING

Operating room of a metropolitan general hospital.

PATIENTS

Seven ASA physical status I and II patients scheduled for elective spinal surgery during general anesthesia.

INTERVENTIONS

Anesthesia was induced with fentanyl, propofol, and vecuronium injection followed by inhalation of sevoflurane.

MEASUREMENTS

The SBP and DBP data were recorded at all beats from fentanyl injection to direct laryngoscopy. The respective changes were analyzed using a logistic function: P(t) = p(L) + (q(L) - p(L))/(1 + exp{[4 m(L)/(q(L) - p(L))][k(L) - t]}) and a cubic function: P(t) = at(3) + bt(2) + ct + d, where parameter p(L) is the upper asymptote, q(L) is the lower asymptote, m(L) is the slope at the inflection point, and k(L) is the time to the inflection point and where a, b, and c are coefficients, and d are constants. Goodness of fit of the two functions was compared using a correlation coefficient and residual mean squares. Each parameter was compared with the corresponding observed data.

MAIN RESULTS

Logistic correlation coefficient values for SBP and DBP decreases were larger than the cubic correlation coefficient values (0.990 [Z transformation: 2.64 +/- 0.32] vs 0.981 [Z: 2.32 +/- 0.37] and 0.977 [Z: 2.22 +/- 0.33] vs 0.967 [Z: 2.05 +/- 0.34], respectively; P < 0.05). Logistic residual mean squares values for SBP and DBP decreases were smaller than cubic residual mean squares values (20.6 vs 41.0 and 9.2 vs 13.7 mmHg(2), respectively; P < 0.05). There were significant correlations between p(L) and SBP or DBP after anesthesia induction, between q(L) and SBP or DBP before endotracheal intubation, and between k(L) and time to maximal rate of the SBP or DBP decrease (dP/dt(min)), but no significant correlation between m(L) and dP/dt(min) for SBP or DBP.

CONCLUSIONS

Time courses of SBP and DBP decreases during the preintubation period of anesthesia induction are modeled effectively by a logistic function.

Multianalytical system (MAS): software for enzyme-linked immunosorbent assay (ELISA) data processing with applications to screening and diagnostic tests

A microcomputer software package for determining the concentration of either the antibody or antigen from ELISA data for IBM PC compatible is presented. In the program optical densities (OD) and fluorescence obtained from 96-well ELISA plate can be input either directly, by interfacing with different brands of microplate reader such as Multiskan II Plus and Organon Teknika to the computer or manually. This software utilizes some mathematical and statistical models to fit the standard curve of each assay and interpolate analyte concentration using data from OD or fluorescence measurements. Cubic spline (Guardabasso et al., 1988), bezier and polynomial (Rodbard, 1979; Baud et al., 1991) interpolation formulas can be used to fit the data over the entire range for estimating the antibody or antigen concentration of the unknown samples whose OD or fluorescence is beyond the entire range. This software package, based on the concentration values of the analyte determined in different fluids (Núnez et al., 1994; Morales et al., 1994) and with some rules and algorithms, is used to calculate the parameters of screening and diagnostic tests such as sensitivity, specificity and predictive values (Coughlin et al., 1992). With the construction of the Receiver Operating Characteristic (ROC) curve it is possible to analyse different values of the sensitivity and specificity of the screening and diagnostic tests. A comparative statistical test for two populations that are non-normally distributed using a non-parametric Mann-Whitney test is provided. This software is an expandable tool designed for general use in clinical and experimental applications, including diagnostic and screening tests.

A computer program for quantification of SH groups generated after reduction of monoclonal antibodies

Reduction of disulfide bonds to sulfhydryl (SH) groups for direct radiolabeling of antibodies for immunoscintigraphic studies of colorectal and other cancers continues to be of considerable research interest. We have developed a general strategy and a versatile computer program for the quantification of the number of SH per molecule of antibody (Ab) generated after the treatment of monoclonal antibodies (MAbs) with reducing agents such as 2-mercaptoethanol (2-ME), stannous chloride (SnCl2), dithiothreitol (DTT), dithioerythritol (DTE), ascorbic acid (AA), and the like. The program we describe here performs an unweighted least-squares regression analysis of the cysteine standard curve and interpolates the cysteine concentration of the samples. The number of SH groups per molecule of antibody in the 2-mercaptoethanol and in the other reducing agents was calculated from the cysteine standard curve using Ellman's reagent to develop the yellow color. The linear least-squares method fit the standard data with a high degree of accuracy and with the correlation coefficient r of 0.999. A program has been written for the IBM PC compatible computer utilizing a friendly menu to interact with the users. The package allows the user to change parameters of the assay, to calculate regression coefficients slope, intercept and its standard errors, to perform statistical analysis, together with detailed analysis of variance, and to produce an output of the results in a printed format.

An enzyme-linked immunosorbent assay for the quantitative determination of anti-D in plasma samples and immunoglobulin preparations

Here we present an enzyme-linked immunosorbent assay (ELISA) on microtiter plates for the quantitative determination of anti-D. This method is based on the solubilization of red blood cells sensitized with anti-D and the subsequent measurement of immunoglobulin G by ELISA. The measuring range of the assay is 40-5,000 IU/ml and the lowest quantifiable concentration in plasma is 0.5 IU/ml. The interassay relative standard deviation for concentrations above 130 IU/ml ranges from 3.2 to 8.1% and below 50 IU/ml from 10.5 to 19.7%. Comparison of ELISA with automated hemagglutination shows that the results of the two assays correlate well: r = 0.992, n = 26. The assay was validated for donor plasma samples and anti-D immunoglobulin preparations and it can also be used in assessing the severity of Rh (D) hemolytic disease during pregnancy.