Binding equations for the lipid composition dependence of peripheral membrane-binding proteins

The specific recognition of peripheral membrane-binding proteins for their target membranes is mediated by a complex constellation of various lipid contacts. Despite the inherent complexities of the heterogeneous protein-membrane interface, the binding dependence of such proteins is, surprisingly, often reliably described by simple models such as the Langmuir Adsorption Isotherm or the Hill equation. However, these models were not developed to describe associations with two-dimensional, highly concentrated heterogeneous ligands such as lipid membranes. In particular, these models fail to capture the dependence on the lipid composition, a significant determinant of binding that distinguishes target from non-target membranes. In this work, we present a model that describes the dependence of peripheral proteins on lipid composition through an analytic expression for their association. The resulting membrane-binding equation retains the features of these simple models but completely describes the binding dependence on multiple relevant variables in addition to the lipid composition, such as protein and vesicle concentration. Implicit in this lipid composition dependence is a new form of membrane-based cooperativity that significantly differs from traditional solution-based cooperativity. We introduce the Membrane-Hill number as a measure of this cooperativity and describe its unique properties. We illustrate the utility and interpretational power of our model by analyzing previously published data on two peripheral proteins that associate with phosphatidylserine-containing membranes: The transmembrane immunoglobulin and mucin domain-containing protein 3 (TIM3) that employs calcium in its association, and milk fat globulin epidermal growth factor VIII (MFG-E8) which is completely insensitive to calcium. We also provide binding equations for systems that exhibit more complexity in their membrane-binding.