# Measuring analyte concentration using serial dilutions and standard curve

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### Introduction

When working with immunoassays, measuring the analyte’s concentration is vital. Usually this is done by comparing the results obtained to a sample with known concentration, often diluted in series.

By processing the sample and standard in the same way and then measuring the absorbance using a spectrophotometer, we can ensure that the results obtained are true and minimise human error.

### What is absorbance and how does it relate to concentration:

Spectrophotometers, as the name suggests, are a piece of equipment that measures the light absorption of a sample by using a focused beam of light going through the sample at a specific wavelength.

As this beam passes through, the different compounds in the sample absorb some of the light and once it exits the sample and hits the detector, the machine gives us a number representing how much of the initial light beam has been absorbed by the sample.

One of the major factors that determine the amount of absorbance a sample has is the concentration (c) of analyte inside.

As the concentration of compounds inside the sample increases, the space for light to pass through uninterrupted decreases, leading to higher absorption.

The other factor is path length (b), which means the longer the light beam has to travel through a sample, the higher the chance of it encountering a compound and being absorbed.

Usually, spectrometry cuvettes are standardised, and the path is 1 cm, which simplifies future calculations.

The last factor that should be considered is molar absorptivity, also known as extinction coefficient (ε).

This coefficient is a way to measure how good the analyte of interest absorbs light from the specific wavelength that has been shined on them.

This factor is also directly proportional to the absorbance.

As these three factors are directly proportional to the absorbance, the Beer-Lambert law can be used:

A= εbc

This equation is for a straight line, which has a y-intercept at 0.

### Using standard dilutions for a standard curve:

Serial dilutions are done in a way that the dilution factor stays the same for each step. They are used to find out the relative concentration of a target molecule that can be later quantified. To create the standard curve, the serial dilution samples have their absorbance measured in duplicates or triplicates, alongside a blank cuvette, for background corrections.

After the readings have been averaged, the reading from the blank sample (background) is subtracted from all of them.

The background-corrected values then can be plotted against the serial dilution concentrations in Excel, using a scatter plot.

As the dots get displayed on the graph, you should be able to draw an imaginary straight line through them if all went to plan.

This can be better visualised by adding a linear trendline to the graph and the graph equation and R-squared value will get displayed as well.

R2 is a coefficient that represents how close the dots are to the straight trendline, the closer the number to 1 (i.e. 100%) the better, meaning the data fits completely.

The equation displayed on the graph is the key step to determining the unknown concentration of the target samples.

It includes the relation between the slope of the line and its intercept of the y-axis.

After rearranging the equation for x, you can mathematically work out the concentration of the unknown sample. 