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Dynamic states of ErbB1 phosphorylation predicted by spatial-stochastic modeling


The major achievements of this work include the development of a novel stochastic simulation framework with successful integration of single molecule experimental data and observations. A revealing investigation into said single molecule observations and their impact on important biological processes. Finally, this work highlights the importance of membrane landscape and how the landscape critically impacts cell signaling.

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 co-confinement 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 domains during dimerization.

The conformational states of erbB1 structure are specifically represented by dimerization rules in the model, as illustrated schematically in Figure 1A. An important feature of the model is the introduction of membrane domains that transiently confine receptors. Figure 1B-C illustrates how the area and distribution of domains are initialized based upon immunogold-labeling of erbB1 decorating the membrane of A431 breast cancer cells. Both domain location and receptor density are imported directly from EM images. The model captures the essential features of anomalous diffusion, as well as the stochastic nature of dimer dissociation, observed for erbB1 receptors in living membranes. Membrane Domains Promote Repeated Interactions between Monomer Pairs. Figure 2A illustrates the reproducible observation that pairs of erbB1 monomers, tracked with 2 colors of QD-EGF, can bind and rebind multiple times during live cell imaging. This characteristic behavior has been attributed to co-confinement, based upon the unlikely probability of repeat encounters if dissociated monomers diffuse rapidly away from their original contact site, as seen by the UNM team during SPT experiments. We tested this notion by examining the trajectories and binding events between receptors in the spatial stochastic model, using a simulation space with membrane domains and 50% ligand-bound receptors. Representative results are shown in Figure 2B, where two receptors interact multiple times during a 50 simulation. Repeated interactions implications on the asymmetric model for receptor transphosphorylation.

We next consider the implications of asymmetric kinase orientation within erbB1 dimers. The cartoon in Figure 3a illustrates the basic scheme used to create rules for trans-phosphorylation when kinase activation is restricted to only one monomer in a given pair. Here, the N-lobe of the “activator” monomer is in contact with the C-lobe of the “receiver” monomer. We make the theoretical assumption that the now active “receiver” then trans-phosphorylates its partner; the probability of this enzymatic modification is a function of the dimer lifetime for the pair. This fundamental premise leads to a novel and interesting prediction: As dimers dissociate and rebind in a stochastic process, it improves the likelihood that each erbB1 monomer has the opportunity to be both receiver and activator. The predicted outcome of this receptor “shuffle” process is illustrated in Figure 3B, in the context of a simulation with 50% of receptors bound to ligand at the onset. The graph traces the transition states of a single ligand-bound erbB1 receptor in the simulation space over 250 seconds. Collectively, the ligand-bound receptors in this simulation achieved the dimer state approximately 90% of the time. They cycle rapidly through all possible dimerization and phosphorylation states, spending 58% of the time as a phosphorylated species. In contrast, Figure 3C tracks the transition states of an unliganded receptor in the same simulation. The unliganded receptors in this simulation participated in dimer events frequently, spending only 9% of the simulation period as free monomers. However, due to the short dimer lifetimes for RR and LRR, only 35% of unliganded receptors are phosphorylated on average. The Membrane Landscape Impacts Receptor State.

Our next goal was to evaluate the impact of membrane domains upon phosphorylation efficiency, integrating both the improved dimer lifetime measurements and the asymmetric model. We chose to compare the high receptor density scenario represented by A431 cells (~4 million receptors/cell) to the normal expression levels of Hec50 cells (~30,000 receptors/cell). Results in Figure 4A-B illustrate the relative impact of domains and receptor density on signaling output, represented by the number of receptors predicted to be phosphorylated at steady state. In the case of high receptor density (Fig. 4A), up to 3% (~150,000) of receptors are phosphorylated in the absence of ligand on A431 membranes with domains. At 10% ligand occupancy, this value rises dramatically to an estimated 1 million phosphorylated receptors. In the absence of domains, these estimates drop to 18,000 and 587,000 phosphorylated receptors respectively. For the case of Hec50 cells with normal erbB1 receptor density (Fig. 4B), predicted values of phosphorylation attributed to pre-formed dimers is modest even in the presence of domains, at only 1400 phosphorylated receptors. Without domains, receptor phosphorylation of ligand-less receptors is exquisitely low (17 total). Values in the case of 10% ligand occupancy are also reported in Fig. 4B, with 8,500 phosphorylated receptors in the domain landscape and only 1,200 in the absence of domains.

Address Goals

The primary and secondary goals this work addresses are discovery and research infrastructure, respectively. This work tackles these goals in a very efficient, integrative manner. Establishing this stochastic simulation framework, then utilizing the simulations to investigate ErbB receptors allows for a versatile tool to be developed, validated, and applied. ErbB receptors are directly implicated in cancers due to their signaling pathways, which suppress apoptosis, among other cellular functions. We address this critical process, working to understand how the kinetics and dynamics of the ErbB receptors initiate these signaling pathways. Although we have chosen to investigate repeated interactions of ErbB receptors and the impact of membrane landscape here, the established model can be used continuously as a key research tool in the future. While developing this simulator, care was taken to create a user-friendly environment, allowing not only programmers but also experimentalists to be comfortable using the tool. Creating a user-friendly tool is essential to integrating the workspace between programmers and experimentalists.

One of the major extended goals of this work is to be able to suggest novel experimental setups and procedures directly from the predictions of the model. The current work highlights the models capability of investigating beyond the current experimental limits through the exploration of the asymmetric phosphorylation mechanism. This model can also be used as a tool on the experimental workbench by allowing experimentalists to quickly investigate new observations and conclusions from experiments. Predictions from the model will give the experimentalist an indication of the outcome of further research, without the extra time and money. Utilizing tools like this simulator will allow for faster, more efficient research and development to occur through an experimental-modeling handshake and development cycle. As new data is available, this simulator can be updated and validated, the new model predictions can then be used to suggest novel experiments. The cycle continues with the new data from the novel experiments being used to further validate/update the model.