Fig 1.
Schematic of molecular interactions of the computational model.
Cellular biophysical and biochemical reactions between VEGFR1, VEGFR2 and NRP1 receptors. The receptors can homodimerize (at a lower level than that induced by ligands), and unlike VEGFR2, VEGFR1 can form a complex with NRP1 in the absence of ligands [26]. All molecular complexes are listed in S2 Table. During trafficking, surface protein complexes (monomeric, dimeric, or higher order) can be internalized (rate constants denoted kint). Early endosomal (“Rab4a/5a”) receptors can be degraded (rate constant kdeg), recycled (rate constant krec4), or transferred to the Rab11a compartment (rate constant k4to11) which leads to an additional recycling pathway (rate constant krec11). New surface receptors (monomers) are produced at rate kprod. Model reactions are listed in S1 Table. Each of the rate constant values can be different for the different receptors. Reaction rate constants and species concentrations are detailed in S3, S4, S5 and S6 Tables.
Fig 2.
Experimental measures of VEGFR1, VEGFR2, and NRP1: whole-cell and surface levels in HUVEC.
Western blot of total HUVEC lysates treated as indicated for 1–24 hours with 50 μg/ml cycloheximide (CHX) and stained for VEGFR1, VEGFR2 and NRP1. Representative of n = 3 replicates. B, Western blot of biotin labeling assay to measure surface and internal VEGFR1, VEGFR2, and NRP1 levels in HUVEC. Representative of n = 3 replicates. C, Western blot showing the effect of depletion by siRNA knockdown of both Rab4a and Rab11a on whole-cell VEGFR1, VEGFR2, and NRP1 levels.
Fig 3.
Previous estimates of VEGFR trafficking parameters are not consistent with HUVEC observations.
A, VEGFR2 and NRP1 trafficking parameters as previously estimated using a computational model and published experimental data from porcine aortic endothelial cells overexpressing human VEGFR2 and NRP1 [16]; and VEGFR1 parameters as then assumed based on VEGFR2 parameters for computational models incorporating all three receptors [33]. B, Model-predicted levels (“Sim”) of VEGFR1, VEGFR2 and NRP1 at steady state on the cell surface and in intracellular endosomes (Rab4a/5a and Rab11a) using the 2015–2017 trafficking parameters based mainly on PAEC data. Experimental data comparisons (“Exp”) for surface receptor levels are for HUVECs from this study. C, Simulations (lines) and experimental data (dots) for whole-cell VEGFR1, VEGFR2, and NRP1 over time following CHX treatment. The schematic shows how CHX inhibition of protein synthesis is represented in the model.
Fig 4.
Estimates of parameter values for VEGFR1, VEGFR2, and NRP1 based on optimization to experimental data from HUVEC.
The trafficking and degradation rate constants (A) represent first-order processes, and the production rates of the receptors (B) are zeroth-order. While there is not one single unique optimization solution, the optimized parameter sets are well constrained; for most, the majority of estimates are constrained within an order of magnitude. For each parameter, we used the median of the 100 optimizations (S6 Table), refitting the production rates to obtain the observed surface receptor levels, to create a standard parameter set for use through the rest of the manuscript (Fig 5A).
Fig 5.
Computational model predictions and model validation with trafficking parameters.
A, Updated trafficking parameters for VEGFR1, VEGFR2, and NRP1 based on geometric means of optimized parameter distributions. B, Surface, Rab4a/5a and Rab11a distributions of VEGFR1, VEGFR2 and NRP1 at steady state with the 2022 trafficking parameters. Simulations (“Sim”) and experimental data (“Exp”) of surface VEGFR1, VEGFR2 and NRP1 levels. C, Simulations (lines) and experimental data (dots) for whole-cell VEGFR1, VEGFR2, and NRP1 over time following CHX treatment. D, The schematics show how perturbations–cycloheximide (CHX) and the siRNA Rab knockdowns–are represented in the model. E-F, Changes in surface levels (E) and whole cell levels (F) of VEGFR1, VEGFR2, and NRP1 after Rab4a knockdown, Rab11a knockdown, and double Rab4a/Rab11a knockdown, compared to control (–, no siRNA treatment). The dots in panel F represent experimental results (no change in whole cell VEGFR1, VEGFR2, NRP1 following knockdown treatment) (Fig 2C).
Fig 6.
Sensitivity of model outputs to VEGFR1, VEGFR2 and NRP1 trafficking parameters.
Local sensitivity analysis was performed by examining the sensitivity of model outputs (total receptor, surface receptor, internal receptor, and the percentage of receptors on the surface) to small changes in each of the receptor trafficking, degradation, and production parameters. Sensitivity values are the ratio of percent change in key model outputs (x-axis) to percent change in the parameter values (y-axis). The gray values represent higher than linear sensitivity that negatively (production of VEGFR1) or positively (production of NRP1) affect NRP1 levels due to the nonlinearity of VEGFR1-NRP1 interactions.
Fig 7.
Transport rate analysis on differential transport of VEGFR1, VEGFR2 and NRP1.
A, Receptor expression levels on the cell surface and intracellularly at steady state in our model simulations without perturbation. The surface levels match those previously measured experimentally [25] and the internal, endosomal, and total levels are those predicted by the simulations for the median parameter set (Fig 5A). Using all 100 optimized parameter sets (Fig 4), the 5th-95th percentile range of values for these internal receptor levels are 907, 610, and 13,655 receptors for VEGFR1, VEGFR2, and NRP1 respectively, so the relative receptor levels are consistent across the many simulations. B, Mechanistic insights from trafficking parameters, informed by key ratios of rate constants. C, The overall transport rates (rate constant multiplied by concentration) for VEGFR1, VEGFR2, and NRP1 in each subcellular location. A rate constant may be high, but if the corresponding concentration is low (and we know that the receptors are not uniformly distributed across cellular compartments), then the rate of movement will be low. At steady state, these overall rates in and out are balanced, so the ’net’ rates are close to zero. For Rab11a: receptors arriving from Rab4a are balanced out by recycling; for Rab4a: receptors internalized to Rab4a are balanced out the sum of degraded and recycling; for surface: receptor internalization balances the sum of new synthesis and recycling. Degr. = degradation; prodn. = production.
Fig 8.
Impact of inhibiting lysosomal degradation on whole cell and surface VEGFR1, VEGFR2, and NRP1 trafficking.
Chloroquine (CHQ) treatment inhibits lysosomal degradation. A, Western blot of total (whole-cell) VEGFR1, VEGFR2, NRP1 levels after indicated times of CHQ treatment. B, Comparison of simulation result (line) and quantification of Western blot (dot) for whole cell VEGFR1 levels after indicated times of CHQ treatment. C, Western blot of total (whole-cell), surface fraction, and internal fraction receptors for VEGFR1, VEGFR2, NRP1 levels after indicated times of CHQ treatment. D, Comparison of simulation results (Sim) and quantification of Western blots for biotin labeling experiments (Exp) on VEGFR1 surface and internal levels after four hours and 18 hours of CHQ treatment.