Effect of Spatial Inhomogeneities on the Membrane Surface on Receptor Dimerization and Signal Initiation

Modeling the Cluster Size Distribution of Vascular Endothelial Growth Factor (VEGF) Receptors

We previously developed a method of defining receptor clusters in the membrane based on mutual distance and applied it to a set of transmission microscopy images of vascular endothelial growth factor receptors. An optimal length parameter was identified, resulting in cluster identification and a procedure that assigned a geometric shape to each cluster. We showed that the observed particle distribution results were consistent with the random placement of receptors within the clusters and, to a lesser extent, the random placement of the clusters on the cell membrane. Here, we develop and validate a stochastic model of clustering, based on a hypothesis of preexisting domains that have a high affinity for receptors. The proximate objective is to clarify the mechanism behind cluster formation and to estimate the effect on signaling. Receptor-enriched domains may significantly impact signaling pathways that rely on ligand-induced dimerization of receptors. We define a simple statistical model, based on the preexisting domain hypothesis, to predict the probability distribution of cluster sizes. The process yielded sets of parameter values that can readily be used in dynamical calculations as the estimates of the quantitative characteristics of the clustering domains.

Parameter Estimation and Uncertainty Quantification for Systems Biology Models

Mathematical models can provide quantitative insights into immunoreceptor signaling, and other biological processes, but require parameterization and uncertainty quantification before reliable predictions become possible. We review currently available methods and software tools to address these problems. We consider gradient-based and gradient-free methods for point estimation of parameter values, and methods of profile likelihood, bootstrapping, and Bayesian inference for uncertainty quantification. We consider recent and potential future applications of these methods to systems-level modeling of immune-related phenomena.

Surface reaction-diffusion kinetics on lattice at the microscopic scale

Microscopic models of reaction-diffusion processes on the cell membrane can link local spatiotemporal effects to macroscopic self-organized patterns often observed on the membrane. Simulation schemes based on the microscopic lattice method (MLM) can model these processes at the microscopic scale by tracking individual molecules, represented as hard spheres, on fine lattice voxels. Although MLM is simple to implement and is generally less computationally demanding than off-lattice approaches, its accuracy and consistency in modeling surface reactions have not been fully verified. Using the Spatiocyte scheme, we study the accuracy of MLM in diffusion-influenced surface reactions. We derive the lattice-based bimolecular association rates for two-dimensional (2D) surface-surface reaction and one-dimensional (1D) volume-surface adsorption according to the Smoluchowski-Collins-Kimball model and random walk theory. We match the time-dependent rates on lattice with off-lattice counterparts to obtain the correct expressions for MLM parameters in terms of physical constants. The expressions indicate that the voxel size needs to be at least 0.6% larger than the molecule to accurately simulate surface reactions on triangular lattice. On square lattice, the minimum voxel size should be even larger, at 5%. We also demonstrate the ability of MLM-based schemes such as Spatiocyte to simulate a reaction-diffusion model that involves all dimensions: three-dimensional (3D) diffusion in the cytoplasm, 2D diffusion on the cell membrane, and 1D cytoplasm-membrane adsorption. With the model, we examine the contribution of the 2D reaction pathway to the overall reaction rate at different reactant diffusivity, reactivity, and concentrations.

Single molecule localization microscopy coupled with touch preparation for the quantification of trastuzumab-bound HER2

All breast cancers are assessed for levels of human epidermal growth factor receptor 2 (HER2). Fluorescence in situ hybridization (FISH) and immunohistochemistry are currently used to determine if a patient is eligible for anti-HER2 therapy. Limitations of both tests include variability and relatively long processing times. Additionally, neither test determines whether HER2 contains the extracellular domain. While truncated in some tumors, this domain is required for binding of the therapeutic antibody trastuzumab. Here, trastuzumab was used to directly detect HER2 with quantitative single molecule localization microscopy (qSMLM). In proof of concept studies, our new method rapidly quantified both HER2 density and features of nano-organization. In cultured cells, the method was sensitive to subtle variations in HER2 expression. To assess patient samples, we combined qSMLM with tissue touch preparation (touch prep-qSMLM) and examined large areas of intact membranes. For cell lines and patient samples, HER2 copy numbers from FISH showed a significant positive correlation with detected densities from qSMLM and trended with HER2 cluster occupancy.