At the established control settings, a detailed molecular characterization of the healthy model is then given: the steady-state compartmental distributions of total VEGF and sVEGFR1; the tissue-specific profiles of matrix site occupancies and receptor signaling; and the balance of mass flows.
Whereas these effects culminated into several-fold changes in total VEGF165 and sVEGFR1 in muscle tissues, the fractional occupancy of total matrix sites remained very low (at a consistent 0.19% irrespective of matrix site densities) and changing minutely with varying VEGF165-affinity (up to 0.55% at 10× control Kd(M,V165).
To the extent that the present study focuses on sVEGFR1's effect on the formation of surface VEGF signaling complexes, the uncertainties in the characterization of matrix sites are not of concern.
In contrast, the quantities of matrix-bound VEGF165 and sVEGFR1 increased drastically with increasing matrix site densities (Fig. 7A,B); while the matrix-bound reservoir of VEGF165 also grew drastically with higher VEGF165-affinity of matrix sites (Fig. 7A).
Release of VEGF165 from interstitial matrix sites through plasmin/MMP degradation of matrix core proteins was also neglected.
Although the compartmental model did not include the spatial resolution needed to examine interstitial VEGF gradients, the in vivo distribution of matrix sites between the ECM and BMs could affect spatial morphogenic gradients that guide sprouting angiogenesis.
Steady-state analyses showed that fluctuations in the VEGF-binding affinity and densities of interstitial matrix sites had no detectable effects on the concentrations of all soluble species (in both plasma and interstitial fluid), nor on surface receptor occupancies (Fig. 7).
Such characterization proved useful in explaining VEGF/sVEGFR1 system responses observed in subsequent parameter sensitivity analyses of: the secretion rates of VEGF and sVEGFR1 (Results section 2); surface receptor densities (section 3); VEGF-affinities of surface receptors (section 4); VEGF-affinities of interstitial matrix sites (section 5); and transport parameters (section 6).
The fractional occupancies of total matrix sites were uniformly minute across ECM, EBM and PBM, as well as between normal and calf compartments (differences <0.001%) – only 0.04% VEGF165-occupied and 0.15% sVEGFR1-occupied – leaving 99.81% unoccupied (Fig. S1-E,F,G).
Lastly, we explored lower VEGF-binding affinities for matrix sites, considering that our control value of VEGF165's Kd for matrix sites was estimated from that of FGF-2 [107], in light of indication that VEGF165's Kd for modified heparin could be ∼6 7 times higher than that of FGF-2 [109], [109].
