Recursive Alterations of the Relationship between Simple Membrane Geometry and Insertion of Amphiphilic Motifs

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Abstract
The shape and composition of a membrane directly regulate the localization, activity, and signaling properties of membrane associated proteins. Proteins that both sense and generate membrane curvature, e.g., through amphiphilic insertion motifs, potentially engage in recursive binding dynamics, where the recruitment of the protein itself changes the properties of the membrane substrate. Simple geometric models of membrane curvature interactions already provide prediction tools for experimental observations, however these models are treating curvature sensing and generation as separated phenomena. Here, we outline a model that applies both geometric and basic thermodynamic considerations. This model allows us to predict the consequences of recursive properties in such interaction schemes and thereby integrate the membrane as a dynamic substrate. We use this combined model to hypothesize the origin and properties of tubular carrier systems observed in cells. Furthermore, we pinpoint the coupling to a membrane reservoir as a factor that influences the membrane curvature sensing and generation properties of local curvatures in the cell in line with classic determinants such as lipid composition and membrane geometry.

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