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Volume-to-Volume Dilutions

Volume-to-volume dilutions describe the ratio of a solute to the final volume of the diluted solution. A majority of the time, antibody manufacturers suggest a certain starting dilution of antibody to use for a specific application.
So if the manufacturer suggests a 1:2000 dilution of antibody for a western blot, this would mean 1 part of the stock antibody to 1999 parts of diluent (blocking buffer). The dilution factor is equal to the final volume divided by the initial volume. So for a 1:2000 dilution:

\[{2000 \over 1} = 2000 = dilution factor\]

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If you need a final volume of 10 ml or 10,000 µl of antibody diluted 1:2000 for your blot:

\[{final \ volume \ you \ want \over dilution \ factor} = volume \ of \ stock \ antibody \ to \ at \ to \ diluent\]

\[{10,000 \ µl \over 2000} = 5 \ µl\]

Then you would need to add 5 µl of antibody to 9,995 µl of diluent for a final volume of 10,000 μl or 10 ml of diluted antibody.

C1 x V1 = C2 x V2

The formula \(C1 \times V1 = C2 \times V2\) is useful for determining how to dilute an antibody or stock solution of a known concentration to a desired final concentration and desired volume.

In this formula \(C1\) is the concentration of the starting solution and \(V1\) is the volume of the starting solution, and \(C2\) is the concentration of the new solution and \(V2\) is the volume of the new solution.

So let’s say you have an antibody stock at a concentration of \({0.2 \ mg \over ml}\) OR \({200 \ µg \over ml}\)* and you need \(20 \ ml\) of antibody diluted to a concentration of \({0.04 \ µg \over ml}\)*.

*When performing these calculations it is important to keep the units the same throughout the equation.

You know the starting concentration ( \(C1\) ) of the antibody stock provided in the vial and you know both the final concentration ( \(C1\) ) and final volume ( \(V2\) ) of solution that you want (in the case of diluting antibodies, the final solution would be in a diluent of blocking or staining buffer). We need to find \(V1\) which represents how much of the starting solution we need to add to the final volume of diluent ( \(V2\) ).

Rearranging the formula \(C1 \times V1 = C2 \times V2\) to solve for \(V1\):

\[V1 = {{V2 \times C2} \over C1}\]

\[V1 = {{0.04 {μg \over ml} \times 20 \ ml} \over 200 {μg \over ml}}\]

\[V1 = 0.004 \ ml\]

Converting \(0.004 \ ml\) to μl \(= 0.004 \ ml \times {1000 \ μl \over ml} = 4.0 μl\)

So you need to take \(4.0 \ μl\) of the original \({200 \ μg} \over ml\) antibody solution and add it to \(19,996 μl (19.996 ml)\) of diluent. The final \(20 \ ml\) solution will represent a solution of \({0.04 \ μg} \over ml\) of antibody.

Now that we have diluted the antibody we can calculate what volume-to-volume dilution we actually performed (the dilution factor) because of the relationship \({C1 \over C2} = {V2 \over V1}\):

\[{V1 \over V2} = dilution \ factor\]

\[{20,000 \over 2} = {5,000 \over 1} = 5,000 \ dilution \ factor \ \text{or} \ 1:5,000 \ dilution\]

The dilution factor can also be calculated by dividing the concentration of the starting stock solution by the concentration of the new solution:

\[{C1 \over C2} = \ dilution \ factor\]

\[{{200 \ μg/ml} \over {0.04 \ μg/ml}} = 5,000 \ dilution \ factor \ \text{or} \ 1:5,000 \ dilution\]