Calibration curve

Last updated
A calibration curve plot showing limit of detection (LOD), limit of quantification (LOQ), dynamic range, and limit of linearity (LOL). Calibration curve.png
A calibration curve plot showing limit of detection (LOD), limit of quantification (LOQ), dynamic range, and limit of linearity (LOL).

In analytical chemistry, a calibration curve, also known as a standard curve, is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration. [1] A calibration curve is one approach to the problem of instrument calibration; other standard approaches may mix the standard into the unknown, giving an internal standard. The calibration curve is a plot of how the instrumental response, the so-called analytical signal, changes with the concentration of the analyte (the substance to be measured).

Contents

General use

In more general use, a calibration curve is a curve or table for a measuring instrument which measures some parameter indirectly, giving values for the desired quantity as a function of values of sensor output. For example, a calibration curve can be made for a particular pressure transducer to determine applied pressure from transducer output (a voltage). [2] Such a curve is typically used when an instrument uses a sensor whose calibration varies from one sample to another, or changes with time or use; if sensor output is consistent the instrument would be marked directly in terms of the measured unit.

Method

The operator prepares a series of standards across a range of concentrations near the expected concentration of analyte in the unknown. The concentrations of the standards must lie within the working range of the technique (instrumentation) they are using. [3] Analyzing each of these standards using the chosen technique will produce a series of measurements. For most analyses a plot of instrument response vs. concentration will show a linear relationship. The operator can measure the response of the unknown and, using the calibration curve, can interpolate to find the concentration of analyte.

An example of a standard curve showing the absorbance of different concentrations of protein (two trials for each measurement). The mass of protein in a different sample is determined by determining where on the standard curve it should go - in this case, 30 milligrams. Standard curve.png
An example of a standard curve showing the absorbance of different concentrations of protein (two trials for each measurement). The mass of protein in a different sample is determined by determining where on the standard curve it should go - in this case, 30 milligrams.

The data - the concentrations of the analyte and the instrument response for each standard - can be fit to a straight line, using linear regression analysis. This yields a model described by the equation y = mx + y0, where y is the instrument response, m represents the sensitivity, and y0 is a constant that describes the background. The analyte concentration (x) of unknown samples may be calculated from this equation.

Many different variables can be used as the analytical signal. For instance, chromium (III) might be measured using a chemiluminescence method, in an instrument that contains a photomultiplier tube (PMT) as the detector. The detector converts the light produced by the sample into a voltage, which increases with intensity of light. The amount of light measured is the analytical signal.

Example

Samples treated with the Bradford assay. The brown sample (lower absorbance) contains no protein, while the blue sample (higher absorbance) contains protein. The amount of protein in the second sample can be determined by comparison to a standard curve. Bradford assay.jpg
Samples treated with the Bradford assay. The brown sample (lower absorbance) contains no protein, while the blue sample (higher absorbance) contains protein. The amount of protein in the second sample can be determined by comparison to a standard curve.

The Bradford assay is a colorimetric assay that measures protein concentration. The reagent Coomassie brilliant blue turns blue when it binds to arginine and aromatic amino acids present in proteins, thus increasing the absorbance of the sample. The absorbance is measured using a spectrophotometer, at the maximum absorbance frequency (Amax) of the blue dye (which is 595 nm). In this case, the greater the absorbance, the higher the protein concentration.

Data for known concentrations of protein are used to make the standard curve, plotting concentration on the X axis, and the assay measurement on the Y axis. The same assay is then performed with samples of unknown concentration. To analyze the data, one locates the measurement on the Y-axis that corresponds to the assay measurement of the unknown substance and follows a line to intersect the standard curve. The corresponding value on the X-axis is the concentration of substance in the unknown sample. [4] [5]

Error calculation

As expected, the concentration of the unknown will have some error which can be calculated from the formula below. [6] [7] [8] This formula assumes that a linear relationship is observed for all the standards. It is important to note that the error in the concentration will be minimal if the signal from the unknown lies in the middle of the signals of all the standards (the term goes to zero if )

Advantages and disadvantages

Most analytical techniques use a calibration curve. There are a number of advantages to this approach. First, the calibration curve provides a reliable way to calculate the uncertainty of the concentration calculated from the calibration curve (using the statistics of the least squares line fit to the data). [9] [10]

Second, the calibration curve provides data on an empirical relationship. The mechanism for the instrument's response to the analyte may be predicted or understood according to some theoretical model, but most such models have limited value for real samples. (Instrumental response is usually highly dependent on the condition of the analyte, solvents used and impurities it may contain; it could also be affected by external factors such as pressure and temperature.)

Many theoretical relationships, such as fluorescence, require the determination of an instrumental constant anyway, by analysis of one or more reference standards; a calibration curve is a convenient extension of this approach. The calibration curve for a particular analyte in a particular (type of) sample provides the empirical relationship needed for those particular measurements.

The chief disadvantages are (1) that the standards require a supply of the analyte material, preferably of high purity and in known concentration, and (2) that the standards and the unknown are in the same matrix. Some analytes - e.g., particular proteins - are extremely difficult to obtain pure in sufficient quantity. Other analytes are often in complex matrices, e.g., heavy metals in pond water. In this case, the matrix may interfere with or attenuate the signal of the analyte. Therefore, a comparison between the standards (which contain no interfering compounds) and the unknown is not possible. The method of standard addition is a way to handle such a situation.

Applications

See also

Related Research Articles

<span class="mw-page-title-main">Analytical chemistry</span> Study of the separation, identification, and quantification of matter

Analytical chemistry studies and uses instruments and methods to separate, identify, and quantify matter. In practice, separation, identification or quantification may constitute the entire analysis or be combined with another method. Separation isolates analytes. Qualitative analysis identifies analytes, while quantitative analysis determines the numerical amount or concentration.

<span class="mw-page-title-main">Titration</span> Laboratory method for determining the concentration of an analyte

Titration is a common laboratory method of quantitative chemical analysis to determine the concentration of an identified analyte. A reagent, termed the titrant or titrator, is prepared as a standard solution of known concentration and volume. The titrant reacts with a solution of analyte to determine the analyte's concentration. The volume of titrant that reacted with the analyte is termed the titration volume.

<span class="mw-page-title-main">Ultraviolet–visible spectroscopy</span> Range of spectroscopic analysis

Ultraviolet (UV) spectroscopy or ultraviolet–visible (UV-VIS) spectrophotometry refers to absorption spectroscopy or reflectance spectroscopy in part of the ultraviolet and the full, adjacent visible regions of the electromagnetic spectrum. Being relatively inexpensive and easily implemented, this methodology is widely used in diverse applied and fundamental applications. The only requirement is that the sample absorb in the UV-Vis region, i.e. be a chromophore. Absorption spectroscopy is complementary to fluorescence spectroscopy. Parameters of interest, besides the wavelength of measurement, are absorbance (A) or transmittance (%T) or reflectance (%R), and its change with time.

<span class="mw-page-title-main">ELISA</span> Method to detect an antigen using an antibody and enzyme

The enzyme-linked immunosorbent assay (ELISA) is a commonly used analytical biochemistry assay, first described by Eva Engvall and Peter Perlmann in 1971. The assay uses a solid-phase type of enzyme immunoassay (EIA) to detect the presence of a ligand in a liquid sample using antibodies directed against the protein to be measured. ELISA has been used as a diagnostic tool in medicine, plant pathology, and biotechnology, as well as a quality control check in various industries.

Chemometrics is the science of extracting information from chemical systems by data-driven means. Chemometrics is inherently interdisciplinary, using methods frequently employed in core data-analytic disciplines such as multivariate statistics, applied mathematics, and computer science, in order to address problems in chemistry, biochemistry, medicine, biology and chemical engineering. In this way, it mirrors other interdisciplinary fields, such as psychometrics and econometrics.

<span class="mw-page-title-main">Spectrophotometry</span> Branch of spectroscopy

Spectrophotometry is a branch of electromagnetic spectroscopy concerned with the quantitative measurement of the reflection or transmission properties of a material as a function of wavelength. Spectrophotometry uses photometers, known as spectrophotometers, that can measure the intensity of a light beam at different wavelengths. Although spectrophotometry is most commonly applied to ultraviolet, visible, and infrared radiation, modern spectrophotometers can interrogate wide swaths of the electromagnetic spectrum, including x-ray, ultraviolet, visible, infrared, and/or microwave wavelengths.

An assay is an investigative (analytic) procedure in laboratory medicine, mining, pharmacology, environmental biology and molecular biology for qualitatively assessing or quantitatively measuring the presence, amount, or functional activity of a target entity. The measured entity is often called the analyte, the measurand, or the target of the assay. The analyte can be a drug, biochemical substance, chemical element or compound, or cell in an organism or organic sample. An assay usually aims to measure an analyte's intensive property and express it in the relevant measurement unit.

<span class="mw-page-title-main">Regression analysis</span> Set of statistical processes for estimating the relationships among variables

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables. The most common form of regression analysis is linear regression, in which one finds the line that most closely fits the data according to a specific mathematical criterion. For example, the method of ordinary least squares computes the unique line that minimizes the sum of squared differences between the true data and that line. For specific mathematical reasons, this allows the researcher to estimate the conditional expectation of the dependent variable when the independent variables take on a given set of values. Less common forms of regression use slightly different procedures to estimate alternative location parameters or estimate the conditional expectation across a broader collection of non-linear models.

Cavity ring-down spectroscopy (CRDS) is a highly sensitive optical spectroscopic technique that enables measurement of absolute optical extinction by samples that scatter and absorb light. It has been widely used to study gaseous samples which absorb light at specific wavelengths, and in turn to determine mole fractions down to the parts per trillion level. The technique is also known as cavity ring-down laser absorption spectroscopy (CRLAS).

The Bradford protein assay was developed by Marion M. Bradford in 1976. It is a quick and accurate spectroscopic analytical procedure used to measure the concentration of protein in a solution. The reaction is dependent on the amino acid composition of the measured proteins.

<span class="mw-page-title-main">Immunoassay</span> Biochemical test for a protein or other molecule using an antibody

An immunoassay (IA) is a biochemical test that measures the presence or concentration of a macromolecule or a small molecule in a solution through the use of an antibody (usually) or an antigen (sometimes). The molecule detected by the immunoassay is often referred to as an "analyte" and is in many cases a protein, although it may be other kinds of molecules, of different sizes and types, as long as the proper antibodies that have the required properties for the assay are developed. Analytes in biological liquids such as serum or urine are frequently measured using immunoassays for medical and research purposes.

<span class="mw-page-title-main">Regression dilution</span> Statistical bias in linear regressions

Regression dilution, also known as regression attenuation, is the biasing of the linear regression slope towards zero, caused by errors in the independent variable.

The limit of detection is the lowest signal, or the lowest corresponding quantity to be determined from the signal, that can be observed with a sufficient degree of confidence or statistical significance. However, the exact threshold used to decide when a signal significantly emerges above the continuously fluctuating background noise remains arbitrary and is a matter of policy and often of debate among scientists, statisticians and regulators depending on the stakes in different fields.

<span class="mw-page-title-main">Isotope dilution</span>

Isotope dilution analysis is a method of determining the quantity of chemical substances. In its most simple conception, the method of isotope dilution comprises the addition of known amounts of isotopically enriched substance to the analyzed sample. Mixing of the isotopic standard with the sample effectively "dilutes" the isotopic enrichment of the standard and this forms the basis for the isotope dilution method. Isotope dilution is classified as a method of internal standardisation, because the standard is added directly to the sample. In addition, unlike traditional analytical methods which rely on signal intensity, isotope dilution employs signal ratios. Owing to both of these advantages, the method of isotope dilution is regarded among chemistry measurement methods of the highest metrological standing.

<span class="mw-page-title-main">Dose–response relationship</span> Measure of organism response to stimulus

The dose–response relationship, or exposure–response relationship, describes the magnitude of the response of an organism, as a function of exposure to a stimulus or stressor after a certain exposure time. Dose–response relationships can be described by dose–response curves. This is explained further in the following sections. A stimulus response function or stimulus response curve is defined more broadly as the response from any type of stimulus, not limited to chemicals.

The Standard addition method, often used in analytical chemistry, quantifies the analyte present in an unknown. This method is useful for analyzing complex samples where a matrix effect interferes with the analyte signal. In comparison to the calibration curve method, the standard addition method has the advantage of the matrices of the unknown and standards being nearly identical. This minimizes the potential bias arising from the matrix effect when determining the concentration.

Total ionic strength adjustment buffer (TISAB) is a buffer solution which increases the ionic strength of a solution to a relatively high level. This is important for potentiometric measurements, including ion selective electrodes, because they measure the activity of the analyte rather than its concentration. TISAB essentially masks minor changes made in the ionic strength of the solution and hence increases the accuracy of the reading.

In a chemical analysis, the internal standard method involves adding the same amount of a chemical substance to each sample and calibration solution. The internal standard responds proportionally to changes in the analyte and provides a similar, but not identical, measurement signal. It must also be absent from the sample matrix to ensure there is no other source of the internal standard present. Taking the ratio of analyte signal to internal standard signal and plotting it against the analyte concentrations in the calibration solutions will result in a calibration curve. The calibration curve can then be used to calculate the analyte concentration in an unknown sample.

In chemical analysis, matrix refers to the components of a sample other than the analyte of interest. The matrix can have a considerable effect on the way the analysis is conducted and the quality of the results are obtained; such effects are called matrix effects. For example, the ionic strength of the solution can have an effect on the activity coefficients of the analytes. The most common approach for accounting for matrix effects is to build a calibration curve using standard samples with known analyte concentration and which try to approximate the matrix of the sample as much as possible. This is especially important for solid samples where there is a strong matrix influence. In cases with complex or unknown matrices, the standard addition method can be used. In this technique, the response of the sample is measured and recorded, for example, using an electrode selective for the analyte. Then, a small volume of standard solution is added and the response is measured again. Ideally, the standard addition should increase the analyte concentration by a factor of 1.5 to 3, and several additions should be averaged. The volume of standard solution should be small enough to disturb the matrix as little as possible.

Ion suppression in LC-MS and LC-MS/MS refers to reduced detector response, or signal:noise as a manifested effect of competition for ionisation efficiency in the ionisation source, between the analyte(s) of interest and other endogenous or exogenous species which have not been removed from the sample matrix during sample preparation. Ion suppression is not strictly a problem unless interfering compounds elute at the same time as the analyte of interest. In cases where ion suppressing species do co-elute with an analyte, the effects on the important analytical parameters including precision, accuracy and limit of detection can be extensive, severely limiting the validity of an assay's results.

References

  1. "Worksheet for analytical calibration curve". umd.edu.
  2. ASTM: Static Calibration of Electronic Transducer-Based Pressure Measurement Systems Archived 2016-03-04 at the Wayback Machine Example of calibration curve for instrumentation.
  3. "Bioanalytical Method Validation Guidance for Industry". fda.gov. Center for Drug Evaluation and Research. May 2018. Archived from the original on 1 September 2022. Retrieved 5 November 2022.
  4. Bio-Rad, Quick Start™ Bradford Protein Assay Instruction Manual (PDF), retrieved 2022-08-27
  5. "Bradford Assay Background". HistoSoft. Archived from the original on 2006-03-01.
  6. "Statistics in Analytical Chemistry - Regression (6)". utoronto.ca. 4 September 2008. Archived from the original on 26 July 2015. Retrieved 5 November 2009.
  7. Salter, Carl (September 2000). Gammon, Steven D. (ed.). "Error Analysis Using the Variance-Covariance Matrix" (PDF). Journal of Chemical Education. 77 (9): 1239. Bibcode:2000JChEd..77.1239S. doi:10.1021/ed077p1239 . Retrieved 5 November 2022.
  8. Larsen, Ingvar (1975). "Linear Instrument Calibration with Statistical Application". Journal of Chemical Education. ACS. 52 (4): 215. Bibcode:1975JChEd..52..215L. doi:10.1021/ed052p215 . Retrieved 27 December 2020.
  9. The details for this procedure may be found in D. A. Skoog; et al. (2006). Principles of Instrumental Analysis., as well as many other textbooks.
  10. "Caliberation guides". Wednesday, 11 September 2019

Bibliography