### Stoichiometry Experiment

The stoichiometry of an interaction is the molecular ratio at which the binding partners interact. Most biologically relevant interactions exhibit a 1:1 stoichiometry. If the molecular stoichiometry of an interaction is of interest, a stoichiometry analysis can be performed using Monolith

**Prerequisites**

The exact concentrations of target and ligand as well as the K_{d} of their interaction need to be determined in order to design the stoichiometry experiment. As a rule of thumb, the concentration of your target should be **at least 20-fold higher** than the K_{d} of the interaction (e.g. if the K_{d} is 100 nM, use at least 2 µM of fluorescent molecule). At target concentrations **below the K _{d}**, the titration experiment yields a sigmoid binding curve (Figure 1, left). In this case, the MST signal at each ligand concentration is determined by the ratio of bound to unbound ligand, and can thus be used to calculate the dissociation constant. However, a binding curve cannot be used to determine the stoichiometry of the interaction. At target concentrations

**above the K**, the titration experiment yields a saturation curve (Figure 1, right). Added ligand is completely bound to the target molecules until they are saturated. Once saturation is reached, a characteristic “kink” appears, and further addition of ligand does not affect the signal. Saturation curves cannot be used to determine the K

_{d}_{d}, but yield the stoichiometry of the interaction, which is represented by the ratio of ligand concentration at the “kink” and the target concentration.

*Figure 1: Simulations of a typical binding curve (target concentration < K _{d}) and a typical saturation curve (target concentration ≫ K_{d}) using the simulation tool implemented within the MO.Control software on the Plan page. The saturation curve displays a characteristic “kink” (red arrow) at the ligand concentration at which the target is saturated. In the shown example, saturation of 10 µM target occurs with 10 µM ligand (black line), which corresponds to a 1:1 interaction. Please note that exact stoichiometry information cannot be directly extracted from the curves in this figure but requires more detailed experiments and analysis as described below.*

**Approach**

The best practice for determining the stoichiometry of a molecular interaction using MST will be illustrated through the example of binding of biotin to streptavidin. The K_{d} of this interaction is extremely low (in the pico- to femto-molar range). Streptavidin is a stable tetramer, and each subunit is known to bind one biotin molecule.

**1. Determine concentration range for stoichiometry experiment (Figure 2, left):**

In an initial experiment, a standard setup using 25 nM fluorescently labeled streptavidin and titrating biotin at concentrations ranging from 10 µM to 0.3 nM using a 1:1 dilution series is performed. Note that the streptavidin concentration is well above the K_{d}. This initial experiment already gives a first hint about the potential stoichiometry, as the saturation “kink” occurs around ligand concentrations of ~100 nM. However, since a 1:1 dilution series is used, it is necessary to narrow down the ligand concentration range in order to obtain sufficient data points for a precise determination of the interaction's stoichiometry.

**2. Stoichiometry experiment using a narrow concentration range (Figure 2, right):**

In a second experiment, the same streptavidin concentration is used while biotin concentrations in the range of the saturation point determined in the first experiment (in this case from 10-160 nM) are titrated. A 1:1 dilution series is no longer used in this case, and different ligand concentrations should be pipetted separately. Ideally, there are fewer data points in the saturated part of the curve (5-6 points) and most data points in the non-saturated part (10-11 points).

Note that the data in the example below are plotted on a logarithmic x-axis for the initial experiment (left), and on a linear x-axis for the second experiment (right).

*Figure 2: Determination of the binding stoichiometry of biotin and streptavidin. (Left) A wide range of biotin is titrated against 25 nM labeled streptavidin. The K _{d} fit yields a saturation curve (red line) with a “kink” at a biotin concentration of ~100 nM (red arrow). (Right) In a follow-up experiment, biotin is titrated in a narrow concentration range from 10-160 nM against 25 nM labeled streptavidin. Linear regression of the saturated and non-saturated parts of the data points reveals a saturation of streptavidin at 94.35 nM biotin, yielding a binding stoichiometry of ~ 4:1.*

The stoichiometry of the interaction can now be analyzed. For this, the exact position of the saturation “kink” should be determined. It is recommended to plot the data on a linear x-axis to identify the linear sections of the saturated and non-saturated parts of the curve. After linear regression of the respective data points, calculate the x-position of the intersection (corresponding to the ligand concentration at which saturation occurs) of the two linear regressions using:

x = (b_{2}-b_{1})/(m_{1}-m_{2})

where m is the slope, and b the y-intercept (according to the general equation y = mx + b)

For this particular example, the saturation concentration was determined to be 94.35 nM. Given a concentration of 25 nM streptavidin, this means that each streptavidin tetramer binds to 3.78 biotin molecules, which is in good agreement with the known 4:1 stoichiometry.

Notes

- Determination of interaction stoichiometry requires rather high affinities. For low affinity interactions with Kds in the intermediate or high µM range, stoichiometry experiments are difficult since high concentrations are required for both target and ligand. In the case of high target concentrations, if the Monolith detector is saturated due to too high fluorescence, a mixture of labeled and unlabeled target may be used.
- We recommend using the simulation tool to determine suitable concentrations of target and ligand. This tool is implemented within the MO.Control software on the Plan page and can be found under “Highest concentration in this assay”.
- A stoichiometry < 1 can be caused by partially unfolded or inactive protein. In this case use a new protein batch or different buffer conditions.