Massachusetts General Hospital Department of Anesthesia, Critical Care and Pain Medicine - Pain and Neurosciences Research
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Kinetic Models

Among the more powerful tools for understanding how ligand-gated ion channels work are kinetic models. These are essentially chemical reaction schemes which specify the interaction of agonists and other ligands (e.g. anesthetics) with receptor protein sites, as well as the functional consequences of ligand binding.

When agonists are applied to ligand-gated ion channel receptors, binding occurs and channels open, resulting in a transmembrane flow of ions, which can be measured using electrophysiological techniques (voltage-clamp). If agonists remain bound to receptors, usually the channels will start to close again, a process called desensitization. Thus, kinetic models often consist of three different functionally distinct receptor types: Resting inactive receptors (R), Open active receptors (O), and Desensitized inactive receptors (D).

Binding of agonists is usually depicted as a step that precedes ion channel opening and desensitization in sequential models:

Scheme 1
Scheme 1

In Scheme 1, agonist (A) binding is characterized by an off-rate and an on-rate. The ratio of these two rates determines microscopic equilibrium binding constants. The equilibrium dissociation constant is koff/kon = KD, while the association constant is its inverse. In the sequential scheme, once agonist is bound, receptors open with a unimolecular rate b and open receptors close with a unimolecular rate a. The ratio a/b = f. Scheme 1 also depicts desensitization from open channels, with forward rate kdes and backward (resensitization) rate kres. At infinitely high agonist concentration (all receptors bound to agonist), the fraction of open receptors is the efficacy of the agonist, which is dependent on both f and desensitization.

Linear sequential schemes like Scheme 1 (and related linear branched schemes) are simple and useful for conceptualizing how ligand-gated ion channels behave. Nonetheless, as with all models, simplest is not necessarily best or most insightful, especially when evaluating the impact of adding additional allosteric ligands, changing the channel structure, etc. With these perturbations to the experimental system, simple models may represent un-helpful constraints on how we think about the system.

The principles underlying our kinetic models are based on Monot-Wyman-Changeux allosterism. These ideas were originally proposed for equilibrium models, but with additional data and/or constraints, they may also be translated into kinetic models. Our kinetic models look more like Scheme 2, where receptors can exist in three different conformations: resting (R), open (O), and desensitized (D). In addition, all of these conformations bind agonist (although not equally) and there are no imposed constraints on conformational interchanges. Even in the absence of agonists, this model allows receptors to transition to open or desensitized states, although these are low probability transitions. When agonist binds (G represents GABA, the agonist), the equilibria between these three states shifts from resting towards open and desensitized. This model can also be understood thermodynamically, with various energy barriers between states. Because of all the cycles in the model, there are many constraints and few free parameters

Scheme 2
Scheme 2

When we incorporate two agonist binding sites and additional desensitized states, these models can closely model both the equilibrium and kinetic behavior of ligand-gated ion channels like GABAA receptors (compare data in Figure 1 with model data in Figure 2).

Figure 1

Figure 2

We have used the same model to simulate the impact of two GABAA receptor mutations that alter gating and desensitization in different ways. This modeling suggests that the mutations change the major states that the channels go through, presumably because the mutations stabilize different functional states.

The impact of adding anesthetics can also be interpreted using our kinetic model and we are developing larger models that will eventually enable us to simulate the effects of both agonists and anesthetics on receptor kinetics, and to globally fit these models to data sets.

 

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