Abstract
Membrane proteins are primary targets for most therapeutic indications in cancer and neurological diseases, binding over 50% of all known small molecule drugs. Understanding how such ligands impact membrane proteins requires knowledge on the molecular structure of ligand binding, a reasoning that has driven relentless efforts in drug discovery and translational research. Binding of small ligands appears however highly complex involving interaction to multiple transmembrane protein sites featuring single or multiple occupancy states. Within this scenario, looking for new developments in the field, we investigate the concentration-dependent binding of ligands to multiple saturable sites in membrane proteins. The study relying on docking and free-energy perturbation provides us with an extensive description of the probability density of protein-ligand states that allows for computation of thermodynamic properties of interest. It also provides one- and three-dimensional spatial descriptions for the ligand density across the protein-membrane system which can be of interest for structural purposes. Illustration and discussion of the results are shown for binding of the general anesthetic sevoflurane against Kv1.2, a mammalian ion channel for which experimental data are available.
Highlights
As a pre-requisite to solve this hierarchical problem, we investigate ligand binding to a specific protein conformation that features multiple sites occupied by one or more ligands in a concentration-dependent manner
In Theory and Methods, the equilibrium binding constant (see equation (6)) and following results are derived in the limit of a homogeneous diluted reservoir occupied by ligands at constant density ρ and excess chemical potential μ
We presented a theoretical approach based on docking and free-energy perturbation (FEP) to study concentration-dependent interactions of ligands to multiple saturable sites in membrane receptors
Summary
As a pre-requisite to solve this hierarchical problem, we investigate ligand binding to a specific protein conformation that features multiple sites occupied by one or more ligands in a concentration-dependent manner. The theory provides us with a complete description of the probability density of the protein-ligand bound states allowing for computation of any thermodynamic properties of interest. The system comprises of a single protein receptor fixed at the origin of the coordinate system and embedded in a large membrane-aqueous volume that contains N identical ligands under dilute conditions. We consider that ligands dissolve uniformly across the membrane-aqueous region of the system from where they can partition into the protein binding sites. We denote by O(n1, ..., ns) the specific state featuring exactly nj bound ligands at corresponding sites and by n = n1 + ... In which, ρ(n1, ..., ns) denotes the probability of finding the protein receptor at the ligand-bound state O(n1, ..., ns). Note that for dilute solutions, equation (1) is equivalent to its classical definition in terms of the concentration of each of the species in the process
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