This question landed on my desk recently. “We have a Zetasizer in our lab. We have taken the size and zeta potential of a mixture of two particle types. I am wondering to what extent the zeta potential and size would change upon binding?

In more general terms, is it possible to use Dynamic Light Scattering (DLS) or zeta potential to assess binding? Either of two particle types, or two different molecules, or a ligand to a molecule.

In principle this is can be quite complicated to answer. But let’s try to see how we can possibly make sense of this experiment.

#### The starting compounds

Before we can look at whether binding happens we need to check the components first. We can consider two starting components A and B that we intend to mix. They each have a respective intensity or derived count rate, size, and zeta.

• Sample A with intensity_a, size_a and zeta_a
• Sample B with intensity_b, size_b and zeta_b

So each sample has measured with a certain count rate that is due to the concentration and the size. And the zeta potential is the overall effective mean zeta potential of that sample.

#### Mixing two samples – prediction

When we mix sample A and B we have to take into account their relative volume ratios. Typically we have α of A and β of B, such that α + β = 1 (or 100%). When we now mix the two components and they are NOT interacting, we expect an intensity averaged size and an intensity averaged zeta:

• intensity_AB = α · intensity_a + β · intensity_b
• size_AB = (α · intensity_a · size_a + β · intensity_b · size_b)/intensity_AB
• zeta_AB = (α · intensity_a · zeta_a + β · intensity_b · zeta_b)/intensity_AB

By comparing the actual scattering intensity of the mixture with the theoretical prediction intensity_AB we can confirm that binding may have taken place. However this is under the assumption that the buffer or dispersion condition has not significantly changed. For example, this would certainly not hold true if one was a sample prepared at pH 9  and the other a sample prepared at pH 6. In that case, aggregation could be the reason for an increased scattering intensity.

This can be expressed in these equations:

#### Mixing two samples – reality

What do you experimentally get when you mix the two components? If the measured intensity is larger, it would support the formation of a complex. This would also hold, if the measured size of the mixture is larger than the predicted size_AB. It is quite possible that your zeta potential is also going to be different from the expectation of no interaction. However this can all be quite tricky if your data are polydisperse or of less-than-ideal data quality.

Under the best circumstances, estimating the number of charges per particle as well as finding the most prevalent size by number may be possible. Hope the above can help in some studies where particle-particle interactions or binding are suspected.

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