A simple, all-purpose nonlinear algorithm for univariate calibration

Tellinghuisen, Joel

doi:10.1039/b002171g

Cited by 17 publications

(31 citation statements)

References 14 publications

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“…The 'lsqnonlin' function (optimization toolbox) was used to fit the model in equation 1 to the P CO2 -pH data. The uncertainty in the calculation of P CO2 , given the pH and the calibration buffer curve, was determined by a nonlinear algorithm [ 142 , 143 ]. The 'rlowess' function (curve-fitting toolbox) was applied for the smoothing of spectra.…”

Section: Methodsmentioning

confidence: 99%

Physiological responses of Daphnia pulex to acid stress

Weber

Pirow

2009

BMC Physiology

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BackgroundAcidity exerts a determining influence on the composition and diversity of freshwater faunas. While the physiological implications of freshwater acidification have been intensively studied in teleost fish and crayfish, much less is known about the acid-stress physiology of ecologically important groups such as cladoceran zooplankton. This study analyzed the extracellular acid-base state and CO2 partial pressure (PCO2), circulation and ventilation, as well as the respiration rate of Daphnia pulex acclimated to acidic (pH 5.5 and 6.0) and circumneutral (pH 7.8) conditions.ResultsD. pulex had a remarkably high extracellular pH of 8.33 and extracellular PCO2 of 0.56 kPa under normal ambient conditions (pH 7.8 and normocapnia). The hemolymph had a high bicarbonate concentration of 20.9 mM and a total buffer value of 51.5 meq L-1 pH-1. Bicarbonate covered 93% of the total buffer value. Acidic conditions induced a slight acidosis (ΔpH = 0.16–0.23), a 30–65% bicarbonate loss, and elevated systemic activities (tachycardia, hyperventilation, hypermetabolism). pH 6.0 animals partly compensated the bicarbonate loss by increasing the non-bicarbonate buffer value from 2.0 to 5.1 meq L-1 pH-1. The extracellular PCO2 of pH 5.5 animals was significantly reduced to 0.33 kPa, and these animals showed the highest tolerance to a short-term exposure to severe acid stress.ConclusionChronic exposure to acidic conditions had a pervasive impact on Daphnia's physiology including acid-base balance, extracellular PCO2, circulation and ventilation, and energy metabolism. Compensatory changes in extracellular non-bicarbonate buffering capacity and the improved tolerance to severe acid stress indicated the activation of defense mechanisms which may result from gene-expression mediated adjustments in hemolymph buffer proteins and in epithelial properties. Mechanistic analyses of the interdependence between extracellular acid-base balance and CO2 transport raised the question of whether a carbonic anhydrase (CA) is involved in the catalysis of the reaction, which led to the discovery of 31 CA-genes in the genome of D. pulex.

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Section: Methodsmentioning

confidence: 99%

Physiological responses of Daphnia pulex to acid stress

Weber

Pirow

2009

BMC Physiology

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“…Standard errors in a and b, written as σ a and σ b , respectively, may be found from the diagonal of the covariance matrix, V, given by [8],…”

Section: Fit Of Linear Equation To Datamentioning

confidence: 99%

Comparison of linear and non-linear equations for univariate calibration

Kirkup

Mulholland

2004

Journal of Chromatography A

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“…Estimation of the unknown x 0 and its uncertainty is the main goal of calibration. The essence of the new one-step (OS) algorithm 14 is the inclusion of x 0 among the adjustable parameters in a nonlinear least-squares (NLS) fit of the calibration data and y 0 , so that x 0 and its statistical error are obtained directly from the fit. The procedures for accomplishing this were spelled out in the initial Communication, 14 where it was also demonstrated that the algorithm gives eqn.…”

Section: Theorymentioning

confidence: 99%

“…In a sense, the algorithm is just a novel way to get the fit itself to solve for x 0 [from y 0 5 f(x 0 )], and to correctly perform the statistical error propagation needed to estimate s x0 . Since these points have already been demonstrated in some detail, 14 they will be reviewed only briefly here.…”

Section: Theorymentioning

confidence: 99%

Simple algorithms for nonlinear calibration by the classical and standard additions methods

Tellinghuisen

2005

Analyst

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In univariate calibration by both the classical method and the standard additions method, calibration data are fitted to a response function y=f(x), from which the amount of an unknown x(0) is estimated by solving an equation of form y(0)=f(x(0)). Most such calibrations are limited to linear response functions f, for which the uncertainty in x(0) can be estimated from well-known expressions. The present work describes and illustrates one-step algorithms, in which x(0) is treated as an adjustable parameter in a nonlinear fit of the calibration data, with its standard error thus obtained numerically as a direct outcome of the fit. The computations are easily implemented with a number of data analysis programs and are illustrated here for a representative one, KaleidaGraph. The methods handle heteroscedastic data as easily as homoscedastic and nonlinear functions as easily as linear, permitting the analyst to experiment with different response functions in the quest for an optimum calibration. The estimates of sigma (x0) are obtained from the variance-covariance matrix V for the fit, so for weighted fitting with commercial programs, it is important to know which V--a priori or a posteriori--is being used.

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A simple, all-purpose nonlinear algorithm for univariate calibration

Cited by 17 publications

References 14 publications

Physiological responses of Daphnia pulex to acid stress

Physiological responses of Daphnia pulex to acid stress

Comparison of linear and non-linear equations for univariate calibration

Simple algorithms for nonlinear calibration by the classical and standard additions methods

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