Markov random field modeling of the spatial distribution of proteins on cell membranes

Cell membranes display a range of receptors that bind ligands and activate signaling pathways. Signaling is characterized by dramatic changes in membrane molecular topography, including the co-clustering of receptors with signaling molecules and the segregation of other signaling molecules away from receptors. Electron microscopy of immunogold-labeled membranes is a critical technique to generate topographical information at the 5-10 nm resolution needed to understand how signaling complexes assemble and function. However, due to experimental limitations, only two molecular species can usually be labeled at a time. A formidable challenge is to integrate experimental data across multiple experiments where there are from 10 to 100 different proteins and lipids of interest and only the positions of two species can be observed simultaneously. As a solution, we propose the use of Markov random field (MRF) modeling to reconstruct the distribution of multiple cell membrane constituents from pair-wise data sets. MRFs are a powerful mathematical formalism for modeling correlations between states associated with neighboring sites in spatial lattices. The presence or absence of a protein of a specific type at a point on the cell membrane is a state. Since only two protein types can be observed, i.e., those bound to particles, and the rest cannot be observed, the problem is one of deducing the conditional distribution of a MRF with unobservable (hidden) states. Here, we develop a multiscale MRF model and use mathematical programming techniques to infer the conditional distribution of a MRF for proteins of three types from observations showing the spatial relationships between only two types. Application to synthesized data shows that the spatial distributions of three proteins can be reliably estimated. Application to experimental data provides the first maps of the spatial relationship between groups of three different signaling molecules. The work is an important step toward a more complete understanding of membrane spatial organization and dynamics during signaling.