Slow kinetics - Dianthus α
Slow Kinetics is a measurement mode that can be unlocked for Dianthus instruments equipped with Spectral Shift optics. NT.23 instruments are not capable of performing Slow Kinetics measurements, but can be physically upgraded to enable this functionality. The Slow Kinetics mode allows users to monitor binding interactions in real time as they progress towards equilibrium. This article explains the principles behind Slow Kinetics measurements and outlines the most suitable applications.
Many biologically relevant interactions do not reach equilibrium instantaneously. Some binding events occur over extended periods due to factors such as:
- Slow association rates (kon)
- Slow dissociation rates (koff)
- Covalent bond formation following initial binding
- Conformational changes upon binding
Standard equilibrium measurements may miss these interactions or provide incomplete information about the binding mechanism. Slow Kinetics measurements address this by tracking the binding process over time.
Measurement Principle
Slow Kinetics measurements repeatedly monitor the fluorescence signal of a binding interaction over a defined time scale. This experimental time scale can range from minutes to several hours and the measurement frequency can be adjusted by cycle time (minimum cycle time depends on number of scanned wells). Due to the Spectral Shift technology the measurement is non-invasive, meaning the fluorescence detection does not perturb the binding reaction allowing for wells to be scanned repeatedly over time. The ratio changes of each well over time can then be exponentially fitted to obtain the experimental rate constant kobs.The measurement principle is shown in Figure 1.
Types of Interactions Suitable for Slow Kinetics
Tight Binding Interactions
High affinity interactions (Kd < 1 nM) often exhibit slow binding kinetics. The time to reach equilibrium can be substantial, making real-time monitoring essential for accurate characterisation. These reactions follow the standard two-state binding model:
A reversible interaction is governed by two rate constants:
- kon: The association rate constant (M⁻¹s⁻¹), describing how fast the complex forms
- koff: The dissociation rate constant (s⁻¹), describing how fast the complex falls apart
Under reaction conditions where the target concentration is significantly smaller than the ligand concentration ([L]), also referred to as pseudo-first order conditions, the relationship between the observed rate constant kobs and the ligand concentration [L] simplifies to a linear equation. The association rate constant kon and dissociation rate constant koff can be calculated via following formula:
where [L] is the ligand concentration.
Covalent Inhibitors
In modern drug discovery covalently binding inhibitors have emerged as an important tool in the design of drug molecules with superior therapeutic properties over reversible binding inhibitors. Some of these advantages include higher potency, sustained target engagement and the ability to target previously undruggable binding sites. Covalent inhibitors typically follow a two-step mechanism:
1. Reversible binding: Formation of initial non-covalent complex (characterised by Ki)
2. Covalent bond formation: Irreversible reaction step (characterised by kinact)
Three parameters are of particular importance for describing a covalent reaction:
- kinact: the inactivation rate constant (s-1), describing the maximum rate of covalent bond formation, once the reversible complex has formed
- KI: Michaelis-like constant (M-1), referring to the ligand concentration at which the reaction occurs at half of the maximum rate (kobs = kinact/2)
- kinact / KI: kinact over KI is a second-order rate constant (M⁻¹s⁻¹) for covalent modification and often referred to as the efficiency of the covalent inhibitor.
The observed rate constant of covalent bond formation depends on both KI and kinact and follows the formula:
Slow Kinetics measurements can characterise interactions with kinact values up to 1.5 × 10⁻² s⁻¹ with no practical limitations on KI.
Lower panel: Hyperbolic plot of kobs versus ligand concentration. Non-linear fitting yields kinact = 3.73 × 10⁻³ s⁻¹, KI = 3.20 × 10⁻⁵ M, and the second-order rate constant kinact / KI = 116.49 M⁻¹s⁻¹, characteristic of a two-step covalent binding mechanism.
Slow Dissociation Events
Some compounds exhibit very slow dissociation from their targets, which can be therapeutically advantageous. In cases where the association rate can be monitored the dissociation rate can be simply calculated from koff = koff * kon, even when the dissociation is not measured directly.
A displacement experiment allows direct measurement of the dissociation rate in a single experiment. First, the target-ligand complex is pre-formed by incubating a 2-3 fold molar excess of ligand over labeled target for a sufficient amount of time. The pre-formed complex is then mixed with a large excess of unlabeled target, and the fluorescence ratio is monitored over time. As the complex dissociates, the free ligand will rebind a target molecule, but due to the excess of unlabeled target, it will nearly exclusively bind the unlabeled species. The observed rate constant is therefore governed solely by the dissociation rate constant, and if the excess of unlabeled target is sufficiently high the formula simplifies to: kobs = koff
What is the Time Resolution for Slow Kinetics Measurements?
The measurable range of the experimental rates kobs is approximately from 1 × 10⁻⁶ s⁻¹ (slowest) to 1 × 10⁻² s⁻¹ (fastest).
The range of kinact that can be determined is 5 × 10⁻⁶ s⁻¹ (slowest) to 1.5 × 10⁻² s⁻¹ (fastest).
For non-covalent kinetics, the fastest measurable reactions rate are:
- kon ≤ 10⁵ M⁻¹ s⁻¹
- koff ≤ 10⁻² s⁻¹