Dimensional Dependence of Binding Kinetics

by Megan Dixon & James Keener 

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Experimentally, the strength of protein-protein interactions is typically measured in solution, and dissociation constants are traditionally reported in units of volume concentration. It is often assumed that these three-dimensional dissociation constants give direct insight into how tightly the same proteins bind when they are membrane-associated. In this article, we explore and counter this notion. We demonstrate mathematically that dissociation constants are highly dependent on dimension. In both discrete and continuous space, we present and analyze stochastic models of binding kinetics in one, two, and three dimensions. Not only do dissociation constants in two dimensions have different units and forms than dissociation constants in three dimensions, the conversion between them is quite complex and requires detailed information. We present a novel formula to convert three-dimensional dissociation constants to two-dimensional dissociation constants. This conversion allows for better understanding of protein interactions on membranes and how to appropriately model them.