# Affinity determination using Gyrolab systems

Experimental considerations and assay guidelines are described in the documents:

Assay Guideline: Affinity in solution adapted for evaluation in Gyrolab systems:** ****Download PDFThe user guide chapter describing software functionality: **

**Download PDF**

## Introduction

Interactions between biomolecules are one of the fundamental events in biology. The strength of an interaction is described by the *affinity*. Characterizing interactions between interactants is often a prerequisite for efficient decision-making, particularly in the development of biotherapeutics. For example, therapeutic antibodies with high affinity have higher efficacy, and high affinity may improve safety and also reduce the dosage and cost of treatment. Determining affinity therefore plays a key role throughout the development of biotherapeutics, from discovery to product release.

A simple bimolecular interaction is defined by the equilibrium equation that describes two interactants, A and B that form a reversible AB complex – Fig 1 (click to enlarge). The equilibrium equation can be rearranged to derive an equilibrium dissociation constant (K_{D}) that defines the binding strength or affinity. K_{D} can also be calculated from the association rate constant k_{on} and the dissociation rate constant k_{off}. These two rate constants describe the intrinsic binding properties of the interaction.

When the binding between two interacting partners is tight and stable, the affinity is high and, at equilibrium, the concentration of complex is high, typically driven by a fast association rate and slow dissociation rate – Fig 2 (click to enlarge). The K_{D} for a high affinity interaction is low, reflecting a low concentration of free or unbound interactants. The analysis of high affinity interactions requires methods that can accurately determine affinity in the low- or sub-picomolar range.

When the binding between the two interacting partners is weak and less stable, the affinity is low. At equilibrium, the concentration of free interactants is high, driven by fast dissociation rates, and the K_{D} is correspondingly high – Fig 3 (click to enlarge).

Affinity is commonly determined using real-time, surface-based methods that measure kinetic rate constants for the association and dissociation phases, from which the equilibrium dissociation constant (K_{D}) is calculated as (k_{off}/k_{on}= K_{D} = 1/K_{A}), where K_{A} is the affinity or equilibrium association constant. However, these methods often have difficulty in measuring the slow dissociation kinetics associated with high-affinity K_{D}’s. Surface-based measurements also require immobilization of one of the interactants to a surface, which may affect the determination of K_{D}.

A classic method for determining high affinity constants is to measure affinity in solution. In this approach, the concentrations of free, unbound interactants are measured at equilibrium in solution using a sensitive immunoassay. The affinity (K_{D}) is then determined after curve fitting. The advantages of the in-solution approach are that both interactants are unmodified and in solution, thus mimicking the biological system, and that affinity to receptors on cell surfaces can be measured.

Gyrolab systems have a number of advantages that make them suitable for determining affinity in solution: high sensitivity, rapid measurement in the flow-through affinity column format that minimizes equilibrium shifts, and automation. Gyrolab systems can be used to perform in-solution affinity measurements of up to 14 interacting pairs per CD per hour and the determination of K_{D}’s as low as picomolar.

The procedure for measuring affinity using Gyrolab systems is briefly as follows:

- Mix interactants in solution, one at a fixed concentration and one at variable concentrations to form an affinity series. These solutions are allowed to form complexes that reach equilibrium. The time required to reach equilibrium depends on the properties and concentrations of the interactants.
- Determine the free, unbound fixed interactant in the equilibrium solution using a suitable immunoassay in Gyrolab system.
- Analyze data using curve-fitting models to calculate the K
_{D}.

F_{tot} is an additional fitting parameter in the curve fitting models. Under conditions limited by stoichiometry, this parameter can be useful in establishing the active concentration of one of the interactants:

**Deriving the affinity equation**

The basic affinity model is obtained by combining the equilibrium equation (1) defining the K_{D, }the mass conservation equation (2) for both the total amount of fixed and variable interactants, and the proportional relationship between the Gyrolab response and the concentration of unbound fixed interactant (3).

The affinity data is fitted using a third party numerical library for mathematical and statistical computing. The curve fitting algoritm is based on nonlinear regression using the Levenberg-Marquardt algorithm. The standard deviation gives an estimate of the accuracy of parameter values given for a curve fit from of a set of sample data. Confidence limits are the lower and upper boundaries of a confidence interval calculated from the standard deviation of the fitted parameter.

**Gyrolab Affinity Software **

### Step by Step Procedure

**A. Set up an affinity run with Affinity Design type in Gyrolab Control Software**

- The Affinity Design Type is a wizard that helps you create an Affinity Run, selecting
**Method**, defining**Reagents**and interacting molecules. - The interacting molecules are defined as Fixed and Variable Interactants.
- The
**Fixed**and**Variable interactants**, number of different concentrations and the concentration or dilution values used are defined. **Affinity series**is formed by combing a fixed interactant and its concentration/dilution properties and a Variable dilution series.**Experiments**are formed by combining Affinity series with Capture and Detection Reagents.- Save the created Affinity Run and it is ready to start when incubation is completed.
- A
**Loading list**containing microplate loading information defining how to prepare your affinity samples and reagents is created.

**B. Data Evaluation with Gyrolab Affinity Software**

**Add Runs**to be analyzed.- To start Affinity Evaluation select
**Affinity Analysis**wizard.

**Affinity Analysis setup page**:

- Select a Run and Fit Models for Affinity Analysis including suitable Fit Weight.
- When the concentration of the variable interactant is known the Basic model is recommended.
- If the Variable concentration is unknown the Unknown V
_{tot}model is recommended.

- Customize your Chart and table settings if changes to default setting is necessary.
- Click next.

**Affinity Analysis page**:

- Evaluate if the fitted curve is K
_{D}controlled or stoichiometrically controlled and verify that it is a good curve fit.- Check the shape of the curve in linear-log and linear-linear formats to see the characteristics of the curve.
- Check the standard deviations and/or confidence intervals of the parameters.
- Check the ratio between F
_{tot}and K_{D}to determine the accuracy of the determined parameter. - Calculate confidence values for determinations from repeated experiments.

- Confirm the result of the data points and the curve fit. Check the quality of the data and exclude obvious outliers to obtain a good fit (use the viewer functionality).
- Change fit settings to obtain a relevant and good fit.
- Mark the checkbox for the curves in Data Selection that you want to analyze further and compare.
- Click next.

**Affinity Summary page:**

- Analyze the results from selected curves graphically and in the Summary Table.
- Look at the K
_{D}and F_{tot}values and relationship and check if the calculated values are accurately determined. Correlate this with your graphical interpretation of the curves. Use the curve shapes in linear-log and linear-linear formats to see the difference between stoichiometrically- and K_{D}controlled curves. - Compare different affinity series and extract the information according to the analytical question.
- Click
**Create Report**to generate a report with the evaluated data. **Save project**in the Evaluation database.

Experimental considerations and assay guidelines are described in the documents:

**Assay Guideline: Affinity in solution adapted for evaluation in Gyrolab systems: ****Download PDF**

T**he user guide chapter describing software functionality: ****Download PDF**