# A Comprehensive Suite of Online Tools

AAT Bioquest offers a suite of online tools to aid researchers in post-experimental data analysis. These tools are free to use for all researchers and complement our extensive catalog of assays and kits. Here, we provide a rough description of these web-tools, which can be broken down into three main categories: regression analysis, spectral analysis and protein analysis.

As always, all tools and related products can be found online at aatbio.com.

As always, all tools and related products can be found online at aatbio.com.

## Regression analysis

Regression analysis is a statistical technique for modeling data and analyzing the relationship between variables (e.g. independent and dependent). This relationship is expressed as a best-fit line, or an equation that best represents the experimental data set. Depending on the type of experiment and data, different regression models can be chosen. For biochemical assays, such as ELISAs, regression analysis typically consists of one of three different types: linear analysis, logarithmic analysis and four parameter logistical analysis.

Linear analysis, or linear regression, is used when there is a simple scalar relationship between the independent variable (x) and the dependent variable (y). The equation for linear regression is that of a straight line, which follows the form:

The linear analysis of Amplite

^{®}Fluorimetric Peroxidase (HRP) Assay Kit (Cat# 11552) using Linear Analysis Tooly is the dependent variable (i.e. response)

x is the independent variable (i.e. treatment)

m is the scalar or slope

b is the y-intercept (i.e. y when x = 0)

Linear regression typically uses a least squares method to determine the slope and intercept for a given dataset. The degree of fitness for a given regression line is expressed as R-squared (R2), where R2 > 0.95 or R2 > 0.98 is considered good.

Logarithmic analysis (also known as log-log analysis or power law analysis) is used when the relationship between the independent variable (x) and the dependent variable (y) is exponential rather than linear. This type of analysis is often used when modeling standard curves for experiments. This is because standard curves are generated in a non-linear fashion (i.e. using serial dilutions). While the relationship between the independent and dependent variables is exponential, the graphed line is still linear (i.e. straight line) if both the x-axis and y-axis are set to logarithmic scale. In Microsoft Excel, this type of regression is called Power Regression. Logarithmic analysis generates an equation of the form:

y = ax

^{k}y is the dependent variable (i.e. response)

x is the independent variable (i.e. treatment)

a is the scalar for the function

k is the exponent denoting the proportionality between x and y

Like linear analysis, logarithmic analysis can utilize an R-squared value to represent the fitness of a given best-fit line, where again R2 > 0.95 or R2 > 0.98 is considered good.

Lastly, we have a tool for four parameter logistical (4PL) analysis, which is a type of logistic regression (not to be confused with logarithmic). Four parameter logistical plots are often expressed as sigmoidal, or s-shaped, curves. This type of modeling is useful when a dataset approaches limits on either end (i.e. the minimum and maximum) while having a non-linear function in the middle. This type of modeling is commonly used to analyze inhibition assays (e.g. drug potency experiments) and is particularly useful for determining various half-max response values such as IC

_{50}, EC

_{50}, LD

_{50}and LC

_{50}. A term often related to this type of regression is probit, or logit, models, which can be determined using similar methodology. In 4PL analysis, the equation takes the form:

y is the dependent variable (i.e. response)

x is the independent variable (i.e. treatment)

A is the lower limit of the dataset (i.e. minimum)

B is the upper limit of the dataset (i.e. maximum)

C is the x value of the inflection point (i.e. IC

_{50}, EC

_{50}, LD

_{50}or LC

_{50})

D is the slope at the inflection point (i.e. Hill slope)

A few important things should be kept in mind when using 4PL analysis.

- The inflection point is the point at which the first derivative of the function changes signs (either from positive to negative or negative to positive). It is also the point wherein the response value is halfway between the minimum and the maximum limits of the function. The actual slope at the inflection point, known as the Hill slope, will be positive in an overall downward curve (i.e. inhibition assay) or negative in an overall upward curve (ie. dose-response assay).
- The curve of the function will be mirrored symmetrically before and after the inflection point. If the dataset is not symmetrical around the inflection point, then five parameter logistical (5PL) analysis must be used. This is also called Richards' curve or generalized logistic function.
- 4PL analysis is not well represented by an R-squared value. This is because R-squared values are suitable for linear models due to the way they are calculated and have little meaning when applied to non-linear models. That is, a high R-squared value does not necessarily equate to a good best-fit line in non-linear models. For a more detailed discussion on the topic, see here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2892436/.
- The inflection point generated by the 4PL model is typically thought of as the relative inflection point. This means that the response value at the inflection point (i.e. the half-max response) is calculated such that:

The other way to interpret half-max response is to understand it as the absolute inflection point. This interpretation is represented by the equation:

Care should be taken in interpreting our online calculator results as the half-max response values given are relative half-max response values and not absolute half-max response values.

## Spectral data

AAT Bioquest offers a Spectrum Viewer tool that allows users to display and compare spectral curves for an extensive library of fluorophores. This tool is particularly useful during the initial planning phases of an experiment as it allows researchers to find fluorophores which match their application as well as their instrumentation. For example, researchers can display fluorophores with excitation sources (e.g. lasers) and filter sets to determine if a particular fluorophore is suitable with a given instrument setup. Researchers can also use the Spectrum Viewer tool to find alternatives for fluorophores. This is easily accomplished through filtering of fluorophores by excitation, emission and Stokes' shift properties. Finally, our Spectrum Viewer tool is uniquely able to export a given setup as either an image or a sharable link. This allows for easy and seamless collaboration amongst researchers (See Figure 3).

Absorption and emission spectrum of PE (Cat#2556). Exciations at 488 nm (Blue laser line) and 568 nm (Green laser line). PE read with emission filter Cy3

^{®}/TRITC (Yellow band).For more comprehensive experimental planning, the spectrum viewer tool can also be combined with our Extinction Coefficient Finder tool. This tool is a queryable database of extinction coefficients for all common fluorophores. Researchers are typically interested in this value as it provides a rough estimate of a fluorophore's brightness. It is important to note, of course, that the actual brightness of a fluorophore and its performance in a particular application greatly varies depending on the actual experimental conditions. But as a first-pass metric, the extinction coefficient is a valid quantity for narrowing down potentially desirable fluorophore.

## Protein calculators

AAT Bioquest offers two extremely useful tools for protein analysis.

The first tool is our protein concentration calculator. In order to use this tool, a user simply has to select their protein and enter the OD at max absorbance (λmax). For most proteins and antibodies, λmax is at 280 nm. Thus, users simply need to enter the absorbance value at 280 nm as measured by a spectrophotometer. Optionally, users may also choose to include a dilution factor and an adjusted path length in their calculations. The path length of a standard quartz cuvette is 1 cm (default).

In choosing the protein, users have the option of picking from a pre-selected set of common proteins such as IgG and BSA. Alternatively, users can enter the amino acid sequence of a custom protein. The UniProt ID can also be used. If a custom sequence is used, the calculator will also supply the molecular weight and the extinction coefficient of the sequence for use in calculations.

This calculator works by utilizing the well-established Beer-Lambert law, which defines the relationship between concentration and absorbance of a given substance. The equation can be simplified to the following form:

A = a

_{λ}x b x c

A is the absorbance

aλ is the molar absorption coefficient or extinction coefficient

b is the path length

c is the concentration

Re-written for concentration, the equation is as follows:

*c = A/a*

_{λ}bThe equation can also be adjusted for a dilution factor and for conversion between molarity (M) and mass/volume (g/L). The revised equation is as follows:

*c = A/a*

_{λ}b x MW x DFMW is the molecular Weight

DF is the dilution factor

A second tool for protein analysis is our degree of labeling (DOL) calculator. The DOL (sometimes called degree of substitution, DOS) is the average ratio of labels bound per target macromolecule (e.g. protein). This value is especially important when determining the success of bioconjugation reactions. A DOL that is too low often represents low conjugation efficiency. Additionally, if the DOL is too low, the signal generated from the bioconjugate (e.g. colorimetric or fluorimetric) may be too weak to detect. On the other hand, if the DOL is too high, the conjugation product may suffer steric issues (such as blocking of active sites) or poor solubility in aqueous solutions.

For antibody conjugates, the optimal DOL usually falls in-between two to ten, that is, two to ten labels per antibody. However, the exact DOL should always be determined experimentally depending on the label-antibody pair. An alternative to testing the DOL is to use a pre-tested conjugation system, such as our antibody labeling kits. These kits provide optimized labeling ratios for precision biological applications. A list of these products can be found here: https://www.aatbio.com/search?narrow=0&query=antibody+labeling+kit.

The DOL is calculated by essentially applying the Beer-Lambert law twice, once for the label and once for the target, and then dividing the two resulting concentrations. Two important things must be kept in mind, however, when calculating the DOL.

- A correction factor is required (CF
_{280}) for every given label-target pair to account for any spectral overlaps. This value must be experimentally determined or, in the case of our antibody labeling kits, provided in the product specifications. - The bioconjugate must be purified before using a spectrophotometer to measure the absorbances. If not, excess label or target substrates will bias the concentration values.

### AAT Bioquest's Online Interactive Tools:

- Buffer Preparation and Recipes
- Degree of Labeling Calculator
- DNA Molecular Weight Calculator
- Extinction Coefficient Finder
- EC
_{50}Calculator - ED
_{50}Calculator - IC
_{50}Calculator - LC
_{50}Calculator - LD
_{50}Calculator - Interactive Spectrum Viewer
- Peptide and Protein Molecular Weight Calculator
- 4PL Calculator
- Protein Concentration Calculator
- RNA Molecular Weight Calculator
- Serial Dilution Calculator