Dynamic transition states of ErbB1 phosphorylation predicted by spatial stochastic modeling

Abstract

ErbB1 overexpression is strongly linked to carcinogenesis, motivating better understanding of erbB1 dimerization and activation. Recent single-particle-tracking data have provided improved measures of dimer lifetimes and strong evidence that transient receptor coconfinement promotes repeated interactions between erbB1 monomers. Here, spatial stochastic simulations explore the potential impact of these parameters on erbB1 phosphorylation kinetics. This rule-based mathematical model incorporates structural evidence for conformational flux of the erbB1 extracellular domains, as well as asymmetrical orientation of erbB1 cytoplasmic kinase domains during dimerization. The asymmetric dimer model considers the theoretical consequences of restricted transactivation of erbB1 receptors within a dimer, where the N-lobe of one monomer docks with the C-lobe of the second monomer and triggers its catalytic activity. The dynamic nature of the erbB1 phosphorylation state is shown by monitoring activation states of individual monomers as they diffuse, bind, and rebind after ligand addition. The model reveals the complex interplay between interacting liganded and nonliganded species and the influence of their distribution and abundance within features of the membrane landscape.

Figure 1

ErbB1 species, simulation space, diffusion, and off-rate validation. (A) Monomer and dimer species accounted for in the spatial stochastic model. R is a resting monomer with no ligand bound. Resting receptors spend 99% of simulation time in a tethered conformation, with 1% probability of flux to the extended conformation. LR is a ligand-bound monomer and is stabilized in the open conformation. RR is a preformed dimer, formed by encounters between two monomers in the open conformation. LRR is comprised of one unliganded monomer and one liganded monomer. The LRLR dimer is comprised of two ligand-bound monomers. (B) TEM image used to initialize the starting positions of erbB1 receptors and estimate size and density of confinement zones. (C) Simulation interpretation of the TEM image, including static confinement zones in black boxes. (D) Sample trajectory of three different receptors over a 4 min simulation. (E) Monomer diffusion coefficient calculated from simulation data. Simulation diffusion coefficients match the diffusion coefficients from SPT experiments. (F) Histograms of dimer lifetimes for 2:2 dimers. Each histogram is fit to determine the specific dimer off rate. The red line is the simulation data fit and the blue line is the experimental data fit (17).

Figure 2

Membrane domains influence repeat interactions between receptors. (A) Separation distance over time between two QD-labeled receptors during an SPT experiment. The receptors, initially in a dimer state, dissociate and redimerize several times, as indicated by the state line overlay. (B) Separation distance over time between two ligand-bound receptors during a simulation demonstrating the same pattern of repeat interactions. (C) Summary of repeated interactions over an entire simulation for all possible receptor pairs. A few individual receptors interact with one another >100 times during a single 4 min simulation. (D) Times between rebinding interactions of two receptors are shown for LRLR dimers. Many rebinding interactions occur below the frame rate, 20 frames/s, used in SPT experiments (17) (arrow). Although most rebinding incidents occur within 50 s, time to rebinding can occur >150 s later.

Figure 3

Impact of asymmetric receptor phosphorylation. (A) A model for receptor phosphorylation shuffle. When a dimer forms, due to the configuration of the N and C lobes, only one tail of the dimer can be phosphorylated. For a dually phosphorylated dimer to occur, a phosphorylated receptor and an unphosphorylated receptor must dimerize in the correct configuration such that the unphosphorylated receptor is phosphorylated. (B) Example of a ligand-bound receptor state over a 4 min simulation (upper) and the average percentage of time spent in each state for all of the ligand-bound receptors during the simulation (lower). Ligand-bound receptors spend the majority of time in the dimer state. (C) Sample receptor state of a nonligand-bound receptor (upper) and the average percentage of time spent in each state for all of the nonligand-bound receptors during the simulation (lower). Nonligand-bound receptors also spend a large fraction of time in the dimer state, but they are also found to be in the monomer state much more often than are ligand-bound receptors. (D) Phosphorylation state of nonliganded and liganded species, independent of receptor state. Fewer than 40% of nonliganded species are phosphorylated, on average, compared to the almost 60% of phosphoylated liganded species. (E) Percentage of LRLR dimers in different phosphorylation states. LRLR is an unphosphorylated dimer (blue), LRPLR is a singly phosphorylated dimer (green), and LRPLRP is a dually phosphorylated dimer (red). A quasi-steady state is reached in the first minute of the simulation.

Figure 4

Ratio of liganded (LRP) to unliganded (RP) phosphorylated receptors. (A) Percentage of phosphorylated LR and R for increasing amounts of receptor ligand occupancy for A431 cells. Initially, at low levels of ligand-bound receptor, the percentage of phosphorylated nonligand-bound receptors increases. As liganded receptor percentage increases, unliganded receptor phosphorylation decreases. (B) Percentage of phosphorylated LR and R for increasing amounts of receptor ligand occupancy for HEC50 cells. A similar trend of LRP and RP is seen for HEC50, although the sparseness of the receptors on the membrane creates a larger deviation between simulations.

Figure 5

Membrane landscape impacts receptor state. (A–D) Receptor density and distribution for simulations. (A) Initial simulation space imported from an immunogold-labeled EM image of an A431 cell. Static confinement zones based on receptor cluster size are included. (B) Randomized distribution of the same number of receptors as in A after diffusion simulations in the absence of confinement zones. (C) Initial simulation space imported from an immunogold-labeled EM image of an HEC50 cell. Static confinement zones based on receptor cluster size are included. (D) Randomized distribution of the same number of receptors as in C after diffusion simulations in the absence of confinement zones. (E) Receptor state for simulation conditions represented in the matching simulation space and 0% ligand-bound receptors. The presence of domains impacts how often receptors will encounter one another. The simulations with domains present have a higher rate of dimer occurrence, as well as a large number of phosphorylated receptor species. (F) Receptor state for simulation conditions of 10% ligand-bound receptors and corresponding simulation space. Similar to the 0%-ligand-bound simulations, the occurrence of dimers and phosphorylated species is increased in the presence of domains. The presence of ligand also allows for the formation of species not present in 0%-ligand-bound receptor simulations. (G and H) Number of phosphorylated species present on average during a simulation, scaled to whole-cell values, for A431 cells (G) and HEC50 cells (H). The presence of domains has a clear impact on the number of phosphorylated species. (I) Repeated interactions of receptors on HEC50 cells with 10% ligand-bound receptors present. Simulations with domains and without domains were performed.