The plasma membrane is the initiation site for signaling pathways that govern cell differentiation, proliferation and survival (Groves and Kuriyan, 2010; Radhakrishnan et al., 2012). The membrane provides a platform for the reversible binding of ligands to receptors, initiating critical processes such as dimerization, activation of catalytic activity and recruitment of binding partners (Groves and Kuriyan, 2010). Given its importance in cell signaling, the structure and composition of membranes have been probed by many different groups. Singer and Nicholson, in their landmark paper of the fluid mosaic model, proposed membranes to be largely homogenous with randomly distributed mixtures of integral membrane proteins and lipids (Singer and Nicolson, 1972). However, the authors also showed electron microscopy images of major histocompatibility antigen “patches,” providing early evidence for membrane organization. Since then, considerable evidence has accumulated showing that membrane proteins and lipids can be transiently confined in specific domains (Kaizuka et al., 2007; Chung et al., 2010; Treanor et al., 2010; Radhakrishnan et al., 2012; Goñi, 2014). The anomalous diffusion of membrane constituents, observed through single molecule tracking methods (Fujiwara et al., 2002), is likely due, at least in part, to their transient entrapments within heterogeneous domains (Marguet et al., 2006). Multiple theories exist to explain the richness of the plasma membrane topography, including lipid rafts which are enriched in unsaturated fatty acids and cholesterol (Pike, 2003), corrals formed by the actin cortical cytoskeleton network (Jaqaman et al., 2011; Kalay, 2012; Cambi and Lidke, 2015) and protein islands (Lillemeier et al., 2006). Even very short periods of confinement within domains give rise to lateral heterogeneity and an uneven distribution of proteins on the membrane surface that can be captured in “snap-shot” images by electron microscopy of membrane rip-flips (Wilson et al., 2000; Prior et al., 2001; Andrews et al., 2009). More recently, super-resolution microscopy methods have also been employed to document the clustering of membrane proteins (van den Dries et al., 2013; Itano et al., 2014). The exchange of proteins between domains is highly variable, ranging from very low exchange rates observed in yeast membranes (Spira et al., 2012) to very rapid exchanges described for the EGFR in mammalian cell membranes (Low-Nam et al., 2011).

Many important receptors exhibit varying degrees of clustering prior to ligand engagement, including members of the EGFR/ErbB family (Nagy et al., 2002; Yang et al., 2007) and the ITAM-bearing immunoreceptors (FcεRI, BCR, TCR) (Pike, 2003; Lillemeier et al., 2006; Andrews et al., 2009; Tolar et al., 2009; Treanor et al., 2010; Dinic et al., 2015). Experimental evidence has suggested that membrane domains can both enhance and inhibit signaling in different settings (Marmor and Julius, 2001; Miura et al., 2001; Douglass and Vale, 2005; Allen et al., 2007; Bénéteau et al., 2008; Ganguly et al., 2008). Computational studies have also supported the concept that membrane organization has cell and receptor-specific outcomes (Lim and Yin, 2005; Hsieh et al., 2008; Costa et al., 2011; Abel et al., 2012; Kalay et al., 2012). For example, the formation of different signaling clusters has been proposed to support distinct TCR signaling patterns (Singleton et al., 2009). Vale and colleagues recently demonstrated in model membranes that phase separation of signaling partners can create distinct signaling compartments (Su et al., 2016). Members of the ErbB family of receptor tyrosine kinases have been shown to have distinct distribution patterns on cancer cell membranes (Yang et al., 2007; Steinkamp et al., 2014), leading to computational studies from our group that predict the impact of critical variables such as receptor co-expression, density and dimer off-rates (Hsieh et al., 2008; Pryor et al., 2013, 2015).

Deterministic models based upon Ordinary Differential Equations (ODEs) are not well suited to explore spatial aspects of signaling, since they assume molecules in a system are well mixed. Stochastic modeling approaches offer greater flexibility to consider effects of membrane topography, receptor clustering and diffusion dynamics on signaling events (Mayawala et al., 2006; Nicolau et al., 2006; Hsieh et al., 2008; Costa et al., 2009; Chaudhuri et al., 2011). These versatile mathematical models provide a platform for rapid exploration of key factors that are difficult to vary (and measure) experimentally. In this study, we take advantage of this powerful approach to consider the effect of two parameters, membrane domain overlap and domain retention, on ErbB3 and ErbB2 homo- and heterodimerization. Our group previously evaluated the domain occupancy and distribution of ErbB2 and ErbB3 stably expressed as recombinant proteins in Chinese Hamster Ovary (CHO) cells (Steinkamp et al., 2014; Pryor et al., 2015). Analysis of dual-color single particle tracking data, which permitted independent observations of each species, indicated that domains confining the two ErbB receptors were only partially overlapping in the CHO cell membrane (Pryor et al., 2015). We then built a spatial stochastic model based upon this distribution, as well as experimentally measured values for dimer off-rates, kinase/phosphatase activity and receptor diffusion (Pryor et al., 2015). However, we speculate that the degree to which there is differential segregation of these two closely related receptors will vary widely as a property of cell type, because of dissimilar receptor ratios, density, cytoskeletal features, membrane composition and on-going signal transduction from other cell surface receptors triggered by circulating or local ligands. In this paper, we focus on two specific parameters that affect the degree to which ErbB2 and ErbB3 experience periods of co-confinement: domain overlap and retention, where the latter is expressed as a function of escape probability.

ErbB2 and ErbB3 are members of the ErbB family of receptor tyrosine kinases that are often co-expressed in cells. Under physiological conditions, neither receptor is active on its own. However, through heterointeractions these receptors activate two key pro-survival pathways. ErbB3 primarily activates the PI3K/Akt pathway and ErbB2 favors the MAP kinase pathway (Yarden and Sliwkowski, 2001). Activation of the ErbB2/ErbB3 signaling unit via overexpression of the receptors, gain-of-function oncogenic mutations, or autocrine release of the ErbB3 ligand, heregulin, have been identified in many types of cancer (Holbro et al., 2003; Wolf-Yadlin et al., 2006; Sheng et al., 2010; Jaiswal et al., 2013; Capparelli et al., 2015). Given the potency of this interaction, normal cells must maintain tight control over ErbB2/ErbB3 interactions. In the absence of ligand, dimerization is limited by the constant fluxing of the ErbB3 extracellular domain from a tethered, inactive conformation to an upright, active conformation with the active conformation stabilized by ligand binding (Dawson et al., 2007). Another way to control ErbB2/ErbB3 interactions may be through dynamic reorganization of membrane domains. Sequestration of ErbB2 and ErbB3 in separate domains could prevent spurious signaling in the absence of ligand, while reorganization into overlapping domains upon ligand binding could encourage the formation of signaling clusters (Vámosi et al., 2006). Evidence for reorganization can be seen in electron microscopy studies of SKBR3 breast cancer cell membranes. ErbB2 and ErbB3 are dispersed in the absence of ligand, but in the presence of ligand, ErbB3 forms large clusters with areas of co-localized ErbB2 and ErbB3 (Yang et al., 2007). It has also been shown that ErbB2 clusters within lipid rafts and that disruption of these rafts reduces both ErbB2 clustering and the association of ErbB2 and ErbB3 (Nagy et al., 2002). The remodeling of domains during active signaling has not yet been explored by simulation, in part due to difficulties in accurately measuring the dynamics of these changes. Here, we have examined how domain remodeling, represented in our model by varying domain overlap and domain retention, will effect heterodimer formation and signaling.

Our spatial stochastic model of ErbB2/ErbB3 interactions provides a useful system in which to explore how changes in domain configuration might affect receptor activation. We began with a model parameterized based on single particle tracking data acquired under low (nanomolar) ligand conditions. We then explored how changes in domain characteristics, as well as ligand occupancy, influences dimerization and phosphorylation in this system. The sensitivity of the model to these parameters illustrates that variations in domain characteristics amongst different cell and tissue types are likely unappreciated modulators of signaling by these (and other) receptors.

Previous spatial stochastic models have shed insight on the effect of domains on signaling (Hsieh et al., 2008; Costa et al., 2009, 2011; Chaudhuri et al., 2011; Kalay et al., 2012). Kalay et al. evaluated movement of tracer molecules within lattice-based domains and found that confinement increased reaction rates (Kalay et al., 2012). Addressing ErbB receptor family interactions with rectangular subdomains, Hsieh et al found that domains created local densities that favored EGFR interactions on the membrane surfaces (Hsieh et al., 2008). Our model increases the complexity by introducing two interacting receptor types with unique behaviors and overlapping, experimentally-defined domains. Thus, the model provides a mechanistic understanding of the interplay between domain overlaps and domain retention on the complex interactions of ErbB2 and ErbB3. The model relies on previously described characteristics of these receptors. For example, ErbB2 homodimers are not favored due to evidence for electrostatic repulsion (Garrett et al., 2003); this translates in the model to a low probability for ErbB2 homointeractions. In addition, ErbB3 has very low kinase activity unless activated by ErbB2 (Steinkamp et al., 2014). Thus, in cells where these are the two predominant ErbB species, they are predicted to be mutually dependent on each other for activation. It follows that differential preference of the two species for unique confinement zones or membrane domains should have a strong influence.

Accordingly, we found that phosphorylation of the two ErbB species was differentially affected by domain overlap. This was particularly evident in the case of 100% liganded ErbB3, where ErbB2 phosphorylation dropped by 50% between completely overlapping to non-overlapping domains (Figure 4D). At these physiological receptor levels, ErbB2 homo-encounters are largely unproductive due to the low on-rate. Simulations with more domain overlap had a larger number of heterodimer interactions than those with partial or no domain overlap. This was most notable when all ErbB3 were occupied with ligand (Figure 4). ErbB3 relies heavily on heterodimerization for activation. However, once ErbB3 receptors are activated by ErbB2, they can go on to homodimerize and activate other ErbB3 receptors. Therefore, steady state ErbB3 phosphorylation was less dependent on domain overlap.

It should be noted that the amount of hetero- and homodimers and phosphorylation levels were nearly the same between no domain spatial stochastic simulations and 100% domain overlapping conditions. This finding differs from our previous work with EGFR which showed that domains greatly improved phosphorylation of EGFR receptors, indicating that the introduction of multiple receptor types to these simulations further complicates outcome (Pryor et al., 2013). True domain overlaps are likely to fall somewhere between non-overlapping and completely overlapping configurations, indicating the need for spatial simulations that take this into account. Ligand binding to ErbB3 in SKBR3 breast cancer cell membranes leads to formation of large ErbB3 clusters with modest levels of co-localized ErbB2; this indicates that domain reorganization can occur during signaling (Yang et al., 2007). The remodeling of domains during active signaling has not yet been explored by simulation, in part due to difficulties in accurately measuring the dynamics of these changes.

SPT has revealed a range of non-brownian motion for proteins on the membrane plane. Anomalous diffusion is a term often used to explain the characteristic restricted movements of proteins that “hop” between membrane domains. There are also reports of specific membrane proteins that undergo directed (motor-driven) motion (Kusumi and Sako, 1996; Saxton and Jacobson, 1997; Schütz et al., 1997; Kusumi et al., 2005). These different modes of motion can have a profound impact on reaction kinetics on the membrane surface by perturbing reaction rates (Saxton and Jacobson, 1997; Melo and Martins, 2006). Thus, it is important to continue evaluating factors, such as diffusion coefficients, corral sizes and escape probability of proteins from their confined domains (Saxton and Jacobson, 1997), that are expected to impact signal initiation and propagation. In this work, we used a simulation approach to study the effect of escape probabilities on the reaction kinetics of the ErbB2/3 signaling pathway. We show that membrane segregation can influence signaling in non-intuitive ways that are linked to the individual characteristics of receptors. Given the technical challenges associated with measuring the dynamics of domain confinement, extent of mixing and escape rates in live cell membranes, simulation offers a powerful tool to explore these variables.

Conception and design: ÁH, JE. Development of computation framework: RK, ÁH. Acquisition and interpretation of data: RK, ÁH, MS, BW, JE. Writing, review, and/or revision of the manuscript: BW, RK, MS, ÁH, JE. Administrative support and study supervision: BW.

This study was supported by National Institutes of Health Grant P50GM085273 (BW), R01GM104973 (JE and ÁH), and R01HG006876 (JE).