Markov Random Field Modeling of the Spatial Distribution of Proteins on Cell Membranes

Abstract

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.

Mapping ErbB receptors on breast cancer cell membranes during signal transduction

“…Fig. S1C shows results of applying Hidden Markov Random Field modeling (Zhang et al, 2007) to simulate the complete distribution of EGFR on the surface of transfected CHO EGFR-GFP cells. This image corrects mathematically and spatially for underlabeling.…”

“…The Ripley's K bivariate function was used to evaluate co-clustering (Haase, 1995;Wilson et al, 2004;Zhang et al, 2005). Markov random field simulations were used to account for hidden receptors (Zhang et al, 2007). This work was supported by NIH grants R01 CA119232 (B.W.) and P20 GM067594 (J.M.O.)…”

Stochastic simulations of ErbB homo and heterodimerisation: potential impacts of receptor conformational state and spatial segregation

“…EGFR, ErbB2 and ErbB3 clusters are generally segregated, with only about 14% of EGFR co-clustered with ErbB2 and only about 1.3% ErbB2 are co-clustered with ErbB3. These estimates were based upon Markov random field simulations that account for underlabelling in the EM approach [42]. Even after SKBR3 cells were stimulated with EGF, only 30% of the images passed the Ripley's statistical test for co-clustering between EGFR and ErbB2.…”

Using Hierarchical Clustering and Dendrograms to Quantify the Clustering of Membrane Proteins

“…The membrane sheets were labeled for 20 minutes using 5 nm gold particles functionalized to recognize the cytoplasmic tails of the FcεRI β subunit. Labeling conditions were adjusted so that 70 to 90% of the receptors were labeled (Zhang et al 2008; Zhang 2010). Specimens were subsequently strongly fixed, processed for TEM and digital images representing a 2266 nm by 2266 nm part of the membrane were collected using an Hitachi H7500 electron microscope.…”