Study Notes on Dilutions and Titers
Introduction to Dilutions and Titers
This section of the lab math lectures covers chapter four focusing on dilutions and titers.
Overview of Dilutions
Definition of Key Terms
Sample Volume: The volume of the specific material being diluted (the solute).
Diluent Volume: The volume of solvent added to perform the dilution.
Total Volume: The sum of sample volume and diluent volume.
Importance of Understanding Dilutions
Dilutions are commonly performed in laboratories to achieve concentrations suitable for analysis.
Chemistry Laboratory: A sample concentration may exceed the linear range of analytical methods (e.g., glucose concentration of 1,800 exceeding an analyzer's range of 1,000).
Microbiology Laboratory: Used to determine the minimum inhibitory concentration (MIC) of antibiotics necessary to inhibit bacterial growth.
Immunology Laboratory: Serial dilutions are performed to determine antibody titers.
Hematology: Dilutions help analyze samples with high cell counts or interference, such as in cases of lipemia.
Practical Aspects of Dilutions
Many analyzers include automatic dilution features for samples exceeding linearity, although manual dilutions may still be required in some instances.
Components of a Dilution
Parts of the Dilution
Solute/Sample: The substance being diluted (e.g., ethyl alcohol).
Diluent/Solvent: The substance used to dilute (commonly water).
Example
For a dilution of ethyl alcohol in water:
Solute: Ethyl alcohol.
Diluent: Water.
Calculation of Total Volume: If 5 mL of solute is mixed with 20 mL of diluent, the total volume is 25 mL.
Simple Dilutions
Formula for Simple Dilutions
The dilution can be calculated using the formula:
ext{Dilution} = rac{ ext{Sample Volume}}{ ext{Sample Volume} + ext{Diluent Volume}}
This equation represents the proportion of the sample within the final solution.
Example of Simple Dilution Calculation
A one to ten (1:10) dilution of serum:
Total volume: 100 microliters.
Sample Volume Calculation: Set up the equation reflecting the ratio, where 1 part sample equates to 10 parts total.
Using proportions:
1 imes 100 = 10 imes x
Solving for x results in: Sample volume (x) = 10 microliters and Diluent volume = 90 microliters.
Additional Example
A dilution of 0.5 parts sample to 9.5 parts diluent can be simplified:
Equate this to a total dilution of one to twenty (1:20).
Reporting Dilution Results
Results from diluted samples must be corrected to reflect the undiluted concentration using the dilution factor:
E.g., in a one to two dilution yielding a result of 725, the reported value becomes:
725 imes 2 = 1450
Remember the dilution factor is the reciprocal of the dilution ratio.
Differences Between Dilutions and Ratios
Defining Ratios vs. Dilutions
A dilution expresses the ratio of sample to total volume, whereas a ratio is simply parts of sample to parts of diluent:
Dilution Example: A 1:4 dilution means 1 part sample to 3 parts diluent.
Ratio Example: A 1:4 ratio (which represents total of 5 parts including diluent).
Practice Problem
Given 20 microliters sample and 180 microliters of diluent:
Ratio: 1:9.
Dilution: 1:10.
Types of Complex or Multi-Step Dilutions
Serial Dilutions
Sequential dilutions where the same ratio is applied across multiple tubes.
Allows preparation of large dilutions from minimal sample volume.
Example of Performing a Serial Dilution
To create a one to 1,000 dilution:
Start with a one to ten dilution repeatedly, adjusting the relationships through successive tubes.
Each tube dilutes the previous tube, ultimately reaching the desired dilution.
Tube Dilutions
Involve separate dilutions in each tube, where each tube has a different dilution factor.
Importance of mixing tubes before transferring samples to ensure accurate dilution results.
Example Problems in Tube Dilution
Starting with a sample concentration of 1650 mg:
Calculate expected concentrations across tubes after performing varying dilutions.
Each dilution reduces concentration based on the factor of the dilution applied.
Understanding Titers in Immunology
Definition of Titer
Titer: The inverse of the dilution at which a reaction occurs, particularly antibody-antigen reactions.
A low titer signals lower antibodies present, indicating weaker immune status.
Performing Titer Tests
Serial dilutions of patient serum followed by antigen addition in individual wells/tubes until a positive reaction is no longer observed. The last dilution showing a positive result marks the titer.
Example Titer Calculation
If last positive reaction appears in a one to 640 dilution, the patient’s titer is 640.
Another Example with Specific Titers
For West Nile virus, calculating titers can similarly involve listing observations across different dilutions, while maintaining reciprocal definitions.