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Logo of physiolgenomicsPublished ArticleArchivesSubscriptionsSubmissionsContact UsPhysiological GenomicsAmerican Physiological Society
Physiol Genomics. Jun 2009; 38(1): 29–41.
Published online Apr 7, 2009. doi:  10.1152/physiolgenomics.00031.2009
PMCID: PMC2696151

Computational kinetic model of VEGF trapping by soluble VEGF receptor-1: effects of transendothelial and lymphatic macromolecular transport

Abstract

Vascular endothelial growth factor (VEGF) signal transduction through the cell surface receptors VEGFR1 and VEGFR2 regulates angiogenesis—the growth of new capillaries from preexistent microvasculature. Soluble VEGF receptor-1 (sVEGFR1), a nonsignaling truncated variant of VEGFR1, has been postulated to inhibit angiogenic signaling via direct sequestration of VEGF ligands or dominant-negative heterodimerization with surface VEGFRs. The relative contributions of these two mechanisms to sVEGFR1's purported antiangiogenic effects in vivo are currently unknown. We previously developed a computational model for predicting the compartmental distributions of VEGF and sVEGFR1 throughout the healthy human body by simulating the molecular interaction networks of the VEGF ligand-receptor system as well as intercompartmental macromolecular biotransport processes. In this study, we decipher the dynamic processes that led to our prior prediction that sVEGFR1, through its ligand trapping mechanism alone, does not demonstrate significant steady-state antiangiogenic effects. We show that sVEGFR1-facilitated tissue-to-blood shuttling of VEGF accounts for a counterintuitive and drastic elevation in plasma free VEGF concentrations after both intramuscular and intravascular sVEGFR1 infusion. While increasing intramuscular VEGF production reduces free sVEGFR1 levels through increased VEGF-sVEGFR1 complex formation, we demonstrate a competing and opposite effect in which increased VEGF occupancy of neuropilin-1 (NRP1) and the corresponding reduction in NRP1 availability for internalization of sVEGFR1 unexpectedly increases free sVEGFR1 levels. In conclusion, dynamic intercompartmental transport processes give rise to our surprising prediction that VEGF trapping alone does not account for sVEGFR1's antiangiogenic potential. sVEGFR1's interactions with cell surface receptors such as NRP1 are also expected to affect its molecular interplay with VEGF.

Keywords: angiogenesis, vascular endothelial growth factor, soluble fms-like tyrosine kinase 1, molecular systems biology, mathematical modeling

angiogenesis, the growth of new capillaries from preexistent microvasculature, is regulated in vivo by a myriad of cytokines, including a key protein family called vascular endothelial growth factor (VEGF). VEGF121 and VEGF165 are two of the most prevalent endogenous isoforms of the VEGF ligand family member VEGF-A (29). Among their major endothelial cell surface receptor targets are the signaling receptor tyrosine kinases VEGFR1 (Flt-1) and VEGFR2 (mouse Flk-1; human KDR) and the nonsignaling coreceptor neuropilin-1 (NRP1) (30). Besides angiogenic processes [e.g., endothelial cell (EC) survival, proliferation, and migration], the VEGF·VEGFR signaling pathways also regulate other biological processes such as vascular permeability and inflammatory/immune responses (e.g., monocyte recruitment) (30).

Soluble VEGF receptor-1 (sVEGFR1 or sFlt-1) is an endogenous truncated version of VEGFR1 that lacks the transmembrane and intracellular signaling domains generated predominantly through alternative mRNA splicing (17) and possibly through proteolytic cleavage of VEGFR1 (6, 9, 32). One of the few known physiological roles of sVEGFR1 is its antiangiogenic participation in the maintenance of corneal avascularity (2). In contrast, the pathological involvement of sVEGFR1 is being discovered in a growing list of VEGF-dependent disease conditions, from preeclampsia (1, 25, 39) to cancers (3, 4, 8, 23) to liver cirrhosis (18), sepsis (35), and possibly peripheral arterial disease (16).

However, the exact biophysical or molecular mechanisms by which sVEGFR1 exerts its physiological and pathological effects are not yet known (26). It has been postulated that sVEGFR1 interferes with VEGF signaling via two mechanisms: 1) direct ligand trapping, i.e., effectively lowering free ligand concentrations available for receptor activation, and 2) dominant-negative heterodimerization with cell surface receptor tyrosine kinase monomers, i.e., effectively lowering the surface density of functional receptor tyrosine kinase dimers. Specifically, as illustrated in Fig. 1A, sVEGFR1's antiangiogenic potential theoretically arises from the nonsignaling sVEGFR1 complexes' (i.e., diffusible sVEGFR1 monomers/homodimers or cell surface sVEGFR1·VEGFR heterodimers) competition for VEGF ligand with the functional proangiogenic receptor species (i.e., VEGF-activated VEGFR2 complexes). While there is ex vivo evidence [in pooled amniotic fluids (17)] and limited in vivo evidence [in the avascular cornea (2)] that sVEGFR1 has significant capacity as a direct sink for VEGF, it is uncertain how much this molecular mechanism generally accounts for sVEGFR1's observed antiangiogenic effects in vivo (17) relative to the contribution from sVEGFR1 heterodimerization with transmembrane receptors.

Fig. 1.
Mechanistic study of vascular endothelial growth factor (VEGF) trapping by soluble VEGF receptor-1 (sVEGFR1). A: how sVEGFR1 inhibits angiogenic signaling at the cell surface: 2 postulated mechanisms. The 6 possible ligand-receptor complexes in the absence ...

The impetus for unraveling sVEGFR1's molecular mechanisms lies in the important implications for understanding diseases and designing therapies. As an example of its importance in understanding disease pathogenesis, a current hypothesis suggests that placental overproduction of sVEGFR1 causes the pregnancy disorder preeclampsia by lowering circulating levels of free VEGF [both VEGF-A and placental growth factor (PlGF)], which in turn leads to endothelial dysfunction in the pathogenesis of multiorgan disease (1, 25). Here, an implicit assumption that needs to be validated is that sVEGFR1 acts predominantly as a VEGF sink, thus mechanistically correlating the inverse changes in circulating levels of sVEGFR1 (increased) and free VEGF (decreased) observed in preeclampsia (39). As an example in aiding therapeutic design, the molecular optimization of exogenous soluble variants of VEGFR1 as antiangiogenic therapeutic agents requires identification of the most functionally important structural domains of endogenous sVEGFR1 proteins. The second and third extracellular Ig-like domains of the VEGFR1 protein are generally believed to confer its ligand-binding capacity (5, 12), while the fourth Ig-like domain was found responsible for receptor dimerization (5, 7). Several in vitro and in vivo studies have suggested that gene delivery of solely the first three Ig-like domains of VEGFR1 (ECD1–3) was effective in inhibiting VEGF-mediated corporal tissue vasoreactivity in rabbits (41), as well as in inhibiting human umbilical vein endothelial cell (HUVEC) proliferation and tumor angiogenesis in mice (24, 42, 44). This may suggest that VEGF binding through ECD1–3 alone is sufficient to simulate sVEGFR1's antiangiogenic effects. However, this did not rule out whether the natural sVEGFR1—which typically contains the first six Ig-like domains of VEGFR1, including the domains for receptor dimerization—could have additional antiangiogenic potency via dominant-negative heterodimerization with cell surface VEGFR1s. Therefore, quantitative comparison of sVEGFR1 vs. ECD1–3 gene therapy would be needed to rule out synergistic antiangiogenic effects from the cell surface heterodimerization mechanism before the comparative efficacy of these two agents can be accurately assessed.

In this computational study, we used a systems biology approach (26) to assess the antiangiogenic potential of sVEGFR1's direct VEGF-trapping mechanism, to contribute to the basic understanding of the molecular mechanisms that give rise to sVEGFR1's biological functions.

METHODS

Compartmental model of VEGF system for a healthy subject.

We previously developed (40) a multitissue compartmental model of systemic VEGF and sVEGFR1 distributions across three body compartments (calf muscle, blood, and the rest of the body) of a healthy human subject (Fig. 1B). Full mathematical equations, as well as details of the parameterization of healthy tissue geometries, binding kinetics, transport kinetics, and protein expression levels are presented in the supplemental material for this article.1 The “calf compartment” was modeled to have the typical combined volume of human unilateral gastrocnemius and soleus muscles (868 cm3), as well as a tissue geometry characterized from human gastrocnemius skeletal muscle histology. The 5-liter “blood compartment” was modeled to contain 3 liters of plasma. The “body (normal) compartment” was modeled to be 60,453 cm3 in volume to make up the rest of the 70-kg human and was first-approximated with homogeneous tissue geometry characteristic of healthy (normal) human vastus lateralis skeletal muscle.

Parenchymal cells (e.g., myocytes) of the muscle tissue compartments were modeled as the sole production source of interstitial free VEGF (isoforms VEGF121 and VEGF165). Free sVEGFR1 was secreted abluminally from the endothelium into the interstitial fluid; luminal secretion of sVEGFR1 was neglected, for consistency with the model assumptions neglecting luminal insertion of surface VEGFRs (36, 40). Once in the extracellular space, VEGF can be sequestered at interstitial matrix binding sites or form complexes with sVEGFR1 (sVEGFR1·VEGF121, sVEGFR1·VEGF165), VEGFR1 (VEGF121·VEGFR1, VEGF165·VEGFR1), VEGFR2 (VEGF121·VEGFR2, VEGF165·VEGFR2), neuropilin-1 (NRP1) (VEGF165·NRP1), or a combination thereof (VEGF121·VEGFR1·NRP1, VEGFR2·VEGF165·NRP1, VEGF121·sVEGFR1·NRP1). sVEGFR1 can also be sequestered at interstitial matrix binding sites or form internalizable cell surface complexes with NRP1. VEGFR1, VEGFR2, and NRP1 each had total plasma membrane expression levels conserved at 10,000 per EC by balancing constant free receptor insertion rates with constant and uniform internalization rates for all free and complexed receptors (27).

The soluble species—free VEGF (VEGF121 and VEGF165), free sVEGFR1, and sVEGFR1·VEGF complexes (sVEGFR1·VEGF121 and sVEGFR1·VEGF165)—were subjected to three types of intercompartmental transport flows: 1) lymphatic drainage from the available interstitial fluid of muscle tissue compartments into the plasma of the blood compartment (40), which occurs unidirectionally in normal physiology (15) but can be obstructed in pathological conditions such as lymphedema (13); 2) bidirectional vascular permeability between the tissue interstitia and plasma (36); and 3) direct clearance out of the plasma via nonspecific elimination processes (e.g., kidney filtration and protein degradation) (36).

Mathematically, a coupled system of 59 ordinary differential equations (ODEs) represented concentrational changes over time for each molecular species, as a function of production, destruction, molecular binding interaction, and transport processes. Within each muscle tissue compartment (calf compartment and normal compartment) 9 equations represented the unbound, VEGF165-occupied, and sVEGFR1-occupied interstitial matrix binding sites in the endothelial basement membrane, extracellular matrix, and parenchymal basement membranes (MEBM, MECM, MPBM), respectively, and 13 equations represented the abluminal endothelial cell surface-tethered species, including the free receptors VEGFR1, VEGFR2, and NRP1 (R1, R2, N1), their VEGF-bound counterparts (V121·R1, V165·R1, V121·R2, V165·R2, V165·N1), their NRP1-coupled forms (R1·N1, V121·R1·N1, R2·V165·N1), and sVEGFR1-bound NRP1 complexes (sR1·N1, V121·sR1·N1). An additional 15 equations defined the soluble species—free VEGF (V121 and V165), free sVEGFR1 (sR1), and sVEGFR1-VEGF complexes (sR1·V121 and sR1·V165)—within the plasma of the blood compartment and the accessible interstitial fluid of both muscle tissue compartments.

The system of ODEs was solved numerically in MATLAB, using its “ode15s” stiff problem solver routine (default numerical differentiation formulas scheme; relative error tolerance of 10−6; initial step size of 10−4), to predict dynamic and steady-state compartmental protein concentrations. A typical in silico experiment, such as the 35-wk simulations shown in Figs. 4 and 5, takes on average 30 s of computational time for parameter retrieval and numerical solution (excluding plot generation) when running MATLAB 7.3 (R2006b) software on a 3 GHz Pentium 4 CPU with 1 GB of RAM.

All model parameters are presented in the supplemental material: the control values for the VEGF and sVEGFR1 secretion rates, fitted to achieve the baseline concentrations of 1.5 pM of VEGF and 100 pM of sVEGFR1 in the plasma (40), are tabulated in Supplemental Table S5.

Background: lack of antiangiogenic effects of sVEGFR1 via VEGF-trapping.

Through its capacity as a diffusible decoy receptor for VEGF, sVEGFR1 was expected to exert antiangiogenic effects by 1) reducing systemic levels of free VEGF and 2) reducing tissue-level proangiogenic signaling complex formation (Fig. 1A). However, as quantified by these two metrics, antiangiogenic effects were not observed upon introduction of sVEGFR1 into our in silico model (40). In particular, increasing the intramuscular production of sVEGFR1 (i.e., the abluminal endothelial secretion rates of sVEGFR1) led to modest reductions in interstitial free VEGF levels and striking elevations in plasma free VEGF concentration (40). Second, intramuscular production of VEGF (i.e., increasing the parenchymal secretion rate of VEGF) from the normal compartment led to striking elevations in free sVEGFR1 levels globally (in the normal interstitium, plasma, and calf interstitium) (40). This latter observation contradicted the intuitive expectation that systemic sVEGFR1 levels should decrease in the presence of higher VEGF production because of VEGF·sVEGFR1 complex formation.

These prior computational predictions indicating that sVEGFR1 does not exert significant antiangiogenic effects via ligand trapping raise several questions of biological significance: Does sVEGFR1's antiangiogenic potential instead depend on sVEGFR1's ability to heterodimerize and impede the functionality of endothelial cell surface VEGFRs? Are there alternative conditions (e.g., different intercompartmental transport rates, different protein expression levels) under which sVEGFR1 can modulate VEGF signaling through ligand trapping alone? The objective of the computational experiments presented below was to address the latter question, i.e., to fully explore the underlying conditions or molecular mechanisms that contributed to the apparent lack of antiangiogenic effects during introduction of homodimerized sVEGFR1.

Intramuscular secretion of sVEGFR1.

To test our hypothesis that sVEGFR1-facilitated transport of VEGF from the interstitial space into the blood is responsible for the counterintuitive rise in plasma VEGF in response to elevated intramuscular production of sVEGFR1, we selectively blocked intercompartmental biotransport processes in our model as follows: Experiment 1 (E1) explored the blockade of lymphatic and bidirectional vascular permeability transport of the VEGF·sVEGFR1 complex, i.e., kL(sR1·V) = 0 and kP(sR1·V) = 0 [kL(X) and kP(X) are defined as the lymphatic transport rate and vascular permeability rate of soluble species X, respectively]. Experiment 2 (E2) simulated zero lymphatic transport rates for all soluble species (VEGF, sVEGFR1, and VEGF·sVEGFR1 complexes), i.e., kL(V) = kL(sR1) = kL(sR1·V) = 0. Experiment 3 (E3) investigated the blockade of lymphatic transport of all soluble species and bidirectional vascular permeability transport of the VEGF·sVEGFR1 complex, i.e., kL(V) = kL(sR1) = kL(sR1·V) = 0 and kP(sR1·V) = 0. These scenarios were chosen to illuminate elements of VEGF and sVEGFR1 transport discussed in results.

Intramuscular secretion of VEGF.

To test our hypothesis that VEGF-induced reduction in free NRP1 available for binding and internalizing sVEGFR1 is responsible for the counterintuitive rises in global free sVEGFR1 subsequent to elevated intramuscular VEGF production, we removed from the model NRP1's affinity for free or VEGF121-bound sVEGFR1, i.e., kon(N1,sR1) = kon(N1,sR1·V) = 0 (where kon is binding rate), in experiment 4 (E4).

Intravascular infusion of sVEGFR1: dose dependence.

We further explored whether the direct infusion of sVEGFR1 into the blood compartment would circumvent the counterintuitive sVEGFR1-facilitated interstitium-to-blood transport of VEGF as hypothesized above, and be able to produce reductions in plasma VEGF as expected from sVEGFR1's VEGF-trapping capacity. For the purposes of this study, IV refers to “intravascular” or “intravenous”; in the context of our model, these terms are interchangeable. Continuous IV infusion of sVEGFR1 was modeled at 1, 2, 5, and 10 times an arbitrary dosage unit of 8.05 fmol/s (Table 1), defined such that an equivalent single dosage infused intramuscularly or interstitially would raise the steady-state plasma VEGF concentration to ~2 pM (also an arbitrary benchmark concentration).

Table 1.
Defining a single-dosage unit for intravascular (1× dosage) infusion of sVEGFR1

Intravascular infusion of sVEGFR1: biotransport dependence.

Upon observing that direct IV infusion of sVEGFR1 was also predicted to elevate steady-state plasma VEGF concentration, we investigated the recurrence of sVEGFR1-facilitated VEGF transport by selective blockade of intercompartmental biotransport processes through attenuated bidirectional vascular permeability flow of VEGF·sVEGFR1, i.e., kP(sR1·V) at 0%, 25%, 50%, 75% and 100% of its control value (Supplemental Fig. S1); attenuated bidirectional vascular permeability transport of both free sVEGFR1 and VEGF·sVEGFR1, i.e., kP(sR1) and kP(sR1·V) at 0%, 25%, 50%, 75% and 100% of their control values (Supplemental Fig. S2); as well as all of the above plus superimposed blockade of lymphatic drainage of the complex, i.e., kL(sR1·V) = 0 (Supplemental Figs. S3 and S4).

Sensitivity analysis of isoform ratio in VEGF secretion rate.

VEGF121, VEGF165, and VEGF189 are considered the predominant proangiogenic isoforms in vivo. Our previous studies have consistently assumed a VEGF secretion rate isoform ratio of qV121:qV165 = 1:10 in correspondence with the mRNA expression ratio of freely diffusible isoforms (VEGF120) vs. heparin-binding isoforms (VEGF164+VEGF188) in mice (29). However, another study found the mRNA expression levels of VEGF121, VEGF165, and VEGF189 to be 3:4:3 in humans (14). Here we performed sensitivity analysis of a range of isoform ratios—1:10, 3:7, 3:4, 1:1, 4:3, 7:2, 10:1—for qV121:qV165 (Supplemental Fig. S5) to explore whether the fractional availability of freely diffusible VEGF may influence the extent of VEGF trapping by sVEGFR1. Because VEGF189 shares similar heparin-binding and neuropilin-binding properties with VEGF165 [both expressing exons 7 and 8, differing only by VEGF189's additional partial expression of exon 6 (22, 37)], our computational studies make an approximation in modeling VEGF189 as VEGF165. The present model can be extended in the future to reflect VEGF189-specific molecular interactions, when quantitative experimental data are available.

Sensitivity analysis of sVEGFR1's binding affinities for VEGF, interstitial matrix sites, and NRP1.

Sensitivity analysis was also performed on the binding kinetic rates for molecular interactions involving sVEGFR1. First, we had assumed a Kd of 33 pM for VEGF-sVEGFR1 binding at control, the same as that previously used for VEGF-VEGFR1 binding (27), and so we tested the higher VEGF-binding affinities of Kd ~ 20 and 10 pM, respectively, characterized for baculovirus-expressed and HUVEC-derived human sFlt-1 in vitro (20, 21). Second, sVEGFR1-binding affinities of various heparan sulfate proteoglycans (HSPGs) have not been characterized; thus we tested an order of magnitude higher and lower than the Kd = 23.8 nM we had assumed from VEGF/FGF-2 binding to HSPGs at control. Third, we previously modeled sVEGFR1's affinity to NRP1 with a Kd of 1.8 nM, based on BIAcore analysis of binding between VEGFR1 extracellular domains and immobilized NRP1 (12) and then calculated the kon based on the same unbinding rate (koff) as full-length VEGFR1's dissociation from NRP1 (27). Here we tested the values of kon (2.5 × 105 M−1s−1) and koff (4.5 × 10−4 s−1) as directly quantified by Fuh et al. (12).

RESULTS

Increasing intramuscular sVEGFR1 secretion rates elevates plasma VEGF through “shuttling mechanism.”

In response to increased local tissue (intramuscular, IM) production of sVEGFR1, the minor declines in interstitial free VEGF and the significant rise in plasma free VEGF, which were predicted at control rates of biotransport (Fig. 2, A and B, Ctrl), did not occur when lymphatic and vascular permeability flows of sVEGFR1·VEGF were blocked (Fig. 2, A and B, E1). This showed that the rise in steady-state plasma free VEGF was dependent on interstitium-to-blood transport of the complex. Additionally blocking lymphatic transport of free VEGF and free sVEGFR1 did not drastically alter the slope of the plasma free VEGF surface (Fig. 2, A and B, E3), suggesting that the control elevations in plasma free VEGF originated not from the lymphatic drainage of interstitial free VEGF but from dissociation of intravasated sVEGFR1·VEGF complexes. Total blockade of lymphatic transport showed that vascular permeability flow of soluble species alone contributed significantly to the control elevations in plasma VEGF (Fig. 2, A and B, E2). This was mirrored in the calf for calf-only increases in VEGF secretion (Fig. 2C), although little effect was observed on plasma concentrations in this case because of the small size of the calf tissue. These results lent support to our hypothesis that at control biotransport rates sVEGFR1-facilitated VEGF shuttling (Fig. 2J)—i.e., interstitial sVEGFR1·VEGF complex formation followed by interstitium-to-blood transport of the complex (with vascular permeability being a significant route) and intravascular dissociation of the complex—was responsible for the counterintuitive rise in steady-state plasma free VEGF levels in response to increased tissue production of sVEGFR1. As transport was blocked, both free sVEGFR1 and sVEGFR1-VEGF complexes increased in interstitia and decreased in plasma (Fig. 2, D–I, Ctrl vs. E1, E2, E3).

Fig. 2.
Increasing intramuscular (interstitial; abluminal endothelial) secretion of sVEGFR1 from the normal (body) and calf compartments. A–I: steady-state analysis under varying biotransport conditions. +Ctrl, control rates of macromolecular ...

Increasing intramuscular VEGF secretion rates elevates interstitial and plasma sVEGFR1 through a “NRP1 redistribution mechanism.”

In response to increased tissue (IM) production of VEGF from the normal compartment, the elevations in plasma and interstitial levels of free sVEGFR1 that were observed at control (Fig. 3, G–I, Ctrl), did not occur when the binding affinity between sVEGFR1 (free or VEGF121 bound) and NRP1 was set to zero (Fig. 3, G–I, E4). This supported our hypothesis that in the presence of significant sVEGFR1-NRP1 binding at control, elevated production and abundance of interstitial VEGF led to redistribution of total surface NRP1s (Fig. 3J), such that a larger fraction was involved in ligated complexes (especially VEGFR2·VEGF165·NRP1) and a smaller fraction was left available for the binding and internalization of free sVEGFR1. Thus in the absence of NRP1-sVEGFR1 affinity, free sVEGFR1 (Fig. 3, G–I, E4) was always higher than in the control case because of a lack of internalization by NRP1 and was attenuated by sVEGFR1-VEGF formation (Fig. 3, D–F) as VEGF secretion rates increased. The sVEGFR1-NRP1 coupling did not appear to impact tissue VEGF levels (Fig. 3, A and C) but did decrease plasma VEGF slightly (Fig. 3B) because of reduced interstitium-to-blood shuttling of VEGF by sVEGFR1 (i.e., less interstitial sVEGFR1-VEGF complexes at Ctrl of Fig. 3, D and F).

Fig. 3.
Increasing intramuscular (interstitial; parenchymal) secretion of VEGF from the normal (body) and calf compartments. A–I: steady-state analysis with vs. without sVEGFR1-NRP1 affinity. +Ctrl, control binding kinetic rates; E4, zero affinity ...

Increasing dosage intensifies but does not prolong “initial trapping phase” of plasma VEGF during IV infusion of sVEGFR1.

We simulated continuous IV infusion of sVEGFR1 to see whether direct delivery of sVEGFR1 into the blood would circumvent the interstitium-to-blood shuttling of VEGF that was observed in our previous simulations of upregulated interstitial secretion of sVEGFR1 and instead lower plasma free VEGF, as would be intuitively expected from the VEGF-trapping behavior of sVEGFR1. However, as shown in the dynamic results of Fig. 4, an “initial VEGF-trapping phase” during which free VEGF in plasma dipped (presumably because of local sequestration by sVEGFR1) eventually gave way to a “compensation phase” (Fig. 4B, ,1,1, ,2,2, ,5,5, 10× dosage IV). We hypothesized that extravasated free sVEGFR1 once again bound and shuttled interstitial VEGF into the blood, resulting in an overall increase in plasma VEGF at steady state. Why did the compensation phase show a VEGF level higher than that before sVEGFR1 delivery? As before, increased interstitial sVEGFR1 (following extravasation) resulted in increased plasma VEGF (Fig. 2B, Ctrl).

Fig. 4.
Dynamic analysis of continuous intravascular (IV) infusion of sVEGFR1: dose dependence. Dosage units were defined such that an equivalent single dosage infused intramuscularly (IM) or interstitially (IS; dashed line) would raise the steady-state plasma ...
Fig. 5.
Dynamic analysis of continuous IV infusion of sVEGFR1: dependence on macromolecular biotransport. CTRL, control biotransport rates; kL, lymphatic drainage rate; kP, vascular permeability rate; sR1, free sVEGFR1; sR1·V, sVEGFR1·VEGF complex. ...

Closer examination of the initial dynamics of interstitial free VEGF concentrations (Fig. 4, A and C, insets) showed evidence of a temporarily reversed shuttling mechanism: before their reduced steady-state levels, interstitial free VEGF increased minutely, presumably from dissociation of extravasating sVEGFR1·VEGF complexes formed during the “initial trapping phase” of plasma free VEGF.

Comparing the steady-state free VEGF concentrations attained with a single dosage of sVEGFR1 infused IV vs. IM, the counterintuitive elevation in plasma free VEGF was reduced through IV infusion, but the desired depression in interstitial free VEGF (which correlates with reduction of IM VEGFR signaling) was also lessened during IV infusion (Fig. 4; Table 1), although neither was large [0.3% (IV) vs. 0.4% (IM) reductions in the calf interstitium; 0.4% (IV) vs. 0.8% (IM) reductions in the normal interstitium].

Increasing the dosage of IV-infused sVEGFR1 intensified the temporary dip in plasma free VEGF but did not prolong the “initial trapping phase” beyond ~2 days (Fig. 4B, inset). Increasing dosage also achieved lower steady-state interstitial free VEGF levels (Fig. 4, A and C), but at the cost of drastically higher steady-state systemic levels of free VEGF (Fig. 4B), sVEGFR1·VEGF (Fig. 4, D–F), and free sVEGFR1 (Fig. 4, G–I).

Extravasation of free sVEGFR1 and lymphatic drainage of sVEGFR1·VEGF drive “compensation phase” of plasma VEGF during IV sVEGFR1 infusion.

To confirm our hypotheses above regarding the molecular underpinnings of the VEGF response to IV infusion of sVEGFR1, we tested in various degrees and combinations the selective attenuation of these biotransport rates: lymphatic drainage rate of sVEGFR1·VEGF, kL(sR1·V); vascular permeability flow rate of sVEGFR1·VEGF, kP(sR1·V); and vascular permeability flow rate of free sVEGFR1, kP(sR1). Selected results are summarized in Fig. 5; full results can be found in Supplemental Figs. S1–S4.

First, independently turning off lymphatic or vascular permeability transport of the sVEGFR1·VEGF complex did not obliterate the “compensation phase” of plasma free VEGF. In Fig. 5B, the plasma free VEGF curves labeled “CTRL,” “kP(sR1·V) = 0,” and “kL(sR1·V) = 0” had steady-state “compensated” concentrations that were 0.286 pM (20%), 0.313 pM (22%), and 0.058 pM (5%) higher, respectively, than their initial steady-state concentrations before IV infusion at 15 wk. This indicated that the compensatory increase in plasma free VEGF was lymphatically driven—i.e., the unidirectional lymphatic drainage of sVEGFR1·VEGF complexes [kP(sR1·V) = 0] contributed more to the overall sVEGFR1-facilitated VEGF shuttling mechanism at control than did the bidirectional vascular permeability flow of sVEGFR1·VEGF [kL(sR1·V) = 0]. In fact, the compensatory increase in plasma free VEGF during independent unidirectional lymphatic drainage of sVEGFR1·VEGF complexes [kP(sR1·V) = 0] was slightly larger than that attained through combined lymphatic and permeability transport of the complex (CTRL), suggesting that the extravasation of sVEGFR1·VEGF (blood-to-interstitium permeability flow) actually dampened the compensatory increase in plasma free VEGF at control. The interstitial free VEGF curves in Fig. 5, A and C, corroborated the above conclusions: Lymphatic drainage of sVEGFR1·VEGF left a relatively deeper depression [kP(sR1·V) = 0: −0.025 pM; −0.24%] than did vascular permeability flow of sVEGFR1-VEGF [kL(sR1·V) = 0: −0.005 pM; −0.05%], even slightly more than their combined effects (CTRL: −0.022 pM; −0.2%). The latter result was again due to blocked sVEGFR1·VEGF extravasation during “kP(sR1·V) = 0,” which also eliminated the small peak in interstitial free VEGF that would have resulted from dissociation of extravasated complexes during the “initial phase.”

The simultaneous blockade of lymphatic and vascular permeability transport of the sVEGFR1·VEGF complex [kL(sR1·V) = 0, kP(sR1·V) = 0] was also not able to completely obliterate the compensation phase of plasma free VEGF—a very slight depression in plasma free VEGF (−0.019 pM; −2%) was left after compensation (Fig. 5B). It turned out that confining the exogenous pool of free sVEGFR1 within the plasma was key to uncompensated and sustained intravascular “VEGF trapping,” as demonstrated through additional blockade of vascular permeability flow of free sVEGFR1 [kL(sR1·V) = 0, kP(sR1,sR1·V) = 0], which lowered the steady-state plasma free VEGF concentration by 0.06 pM (6%). In fact, the blockade of lymphatic transport of the complex was unnecessary, as long as the other two requirements were intact [i.e., the impermeability of sVEGFR1 and sVEGFR1·VEGF, kP(sR1,sR1·V) = 0], contributing no further benefits in terms of percent reduction of plasma free VEGF (−0.074 pM; −6%).

Figure 6 summarizes the biotransport processes underlying the initial dip and the steady-state compensatory elevation of plasma free VEGF in response to continuous intravascular infusion of sVEGFR1.

Fig. 6.
System response to continuous intravascular infusion of sVEGFR1. A: immediately after the onset of IV infusion of sVEGFR1, sVEGFR1-facilitated shuttling of VEGF reversed direction (complex extravasation) during the initial intravascular “VEGF-trapping ...

Sensitivity analysis of isoform ratio in VEGF secretion rate.

Altering the secreted VEGF isoform ratio led to small changes in plasma VEGF level but significantly changed the plasma sVEGFR1 concentration at steady state (Supplemental Fig. S5A). The change was not caused by the small variation in sVEGFR1-bound fraction of total VEGF (<8% change in plasma and <1% change in the interstitial fluids; Supplemental Fig. S5, C and D) but presumably resulted from increased VEGF occupation of NRP1 and the associated reduction in free NRP1 molecules available to bind and internalize free sVEGFR1 (Supplemental Fig. S5J). Additionally, altering the secreted VEGF isoform ratio dramatically changed steady-state signaling profiles (Supplemental Fig. S5K): the higher the ratio of secreted VEGF165 to secreted VEGF121, the more proangiogenic VEGF·VEGFR2 existed at steady state (as 2 of 3 VEGF·VEGFR2 complex subtypes involve VEGF165), and the less antiangiogenic VEGF·VEGFR1 complex existed at steady state (as 2 of 3 VEGF·VEGFR1 complex subtypes involve VEGF121).

Sensitivity analysis of sVEGFR1's binding affinities for VEGF, interstitial matrix sites, and NRP1.

The complexed fractions of total plasma VEGF and total plasma sVEGFR1 increased to 92% and 18%, respectively, at the in vitro value of Kd(sR1,V) = 10 pM, up from 77% and 5% at control Kd(sR1,V) = 33 pM. This could imply that the VEGF trapping capacity of sVEGFR1 may be stronger in vivo than simulated here.

Throughout the tested 100-fold range of matrix site affinities for sVEGFR1, the total occupancy of interstitial matrix sites remained very low (<2%). Only increases in the binding affinity between matrix sites and sVEGFR1 produced observable effects on the system—mostly lowering global levels of free sVEGFR1, but without significant effects on free VEGF.

Free sVEGFR1 levels were also sensitive to the individual binding (kon) and unbinding (koff) rates (despite fixed dissociation constant, Kd = koff/kon) between sVEGFR1 and NRP1 (data not shown), but interstitial free VEGF and signaling VEGF·VEGFR complex formation were unaffected (<1% change) throughout all sensitivity analyses of dissociation constants involving sVEGFR1 in our model.

DISCUSSION

Antiangiogenic potential of sVEGFR1.

In our computational model, in which components were assumed to be free of disease, we predicted minimal antiangiogenic capacity for sVEGFR1, whether introduced intramuscularly (Fig. 2) or intravascularly (Fig. 4). Endogenous intramuscular (interstitial) production of sVEGFR1, through abluminal endothelial secretion, was simulated in Fig. 2, but the analysis could equally have represented the scenario of exogenous intramuscular delivery of sVEGFR1. Exogenous intravascular infusion of sVEGFR1 was simulated in Fig. 4, but the dynamic results could equally apply to the scenario of endogenous luminal endothelial production of sVEGFR1. In both cases, the achieved steady-state reductions in interstitial free VEGF—which directly correlated with surface VEGF·VEGFR complex formation or VEGF-signaling potential—were minuscule, especially compared with the inadvertent increases in plasma free VEGF. Therefore, our simulations did not demonstrate sVEGFR1's antiangiogenic potential by either metric: 1) upregulated sVEGFR1 expression did not systemically lower free VEGF levels, despite the ability of free sVEGFR1 to travel between compartments via vascular permeability and lymphatic drainage; and 2) upregulated sVEGFR1 expression was inefficient in dampening intramuscular VEGF signaling potential.

Intercompartmental shuttling of VEGF by sVEGFR1.

The key to the unexpected results described above was intercompartmental transport of the sVEGFR1·VEGF complex. Rather than traveling in its free form into all accessible compartments and acting as a VEGF sink in its destination compartment, our model allowed sVEGFR1 to carry VEGF (in their complexed form) between compartments. Instead of lowering free VEGF concentrations statically where sVEGFR1 was first introduced, the dynamic effects of sVEGFR1 continued after local “VEGF trapping,” followed by intercompartmental flow of the associated complex, and often dissociation at their destination compartment, effectively increasing free VEGF concentrations there. The concentration gradients and transport rates of our healthy control model were such that VEGF shuttling by sVEGFR1 occurred in the net direction of interstitium to blood at the reestablished steady state after upregulated IV or IM expression of sVEGFR1 (Figs. 2 and and44).

Insights for sVEGFR1 delivery as antiangiogenic therapy.

Therapeutic implications for exogenous sVEGFR1 delivery can be drawn from our simulations; however, it is important to consider whether the site for targeting VEGF for antiangiogenic action is in the tissue interstitia or blood. For example, VEGFRs expressed on hematopoietic stem cells, blood cells, and endothelial progenitor cells are known to be involved in autocrine and paracrine signaling pathways that regulate the survival and growth of several hematologic malignancies, including acute leukemia and multiple myeloma (31, 33), and contribute to angiogenesis in solid tumors. Thus it may be possible to arrest the recruitment and survival of circulating tumor or progenitor cells through therapeutic reduction of free VEGF in plasma. On the other hand, upon recruitment of these cells into the tissue, the VEGF receptors on abluminal endothelial cell surfaces (e.g., for tumor angiogenesis) (11) or tumor cell surfaces (e.g., for tumor cell survival) (38) would be expected to respond to interstitial free VEGF levels, while VEGF receptors on the luminal surface of endothelia would be expected to respond to circulating free VEGF. Our model considered only abluminal endothelial VEGF receptors, but it remains to be determined whether significant luminal populations of endothelial VEGF receptors exist in vivo.

If the treatment goal is to lower circulating free VEGF, our results in Fig. 4 predict that continuous IV infusion of sVEGFR1 protein will have a window of efficacy of ~2 days, during which unintended effects are restricted to minimal elevations in interstitial free VEGF. Continued delivery beyond ~2 days is expected to cause adverse countereffects, drastically elevating plasma free VEGF and systemic free sVEGFR1. Both the efficacy within the first 2 days of administration and the adverse effects beyond 2 days directly correlate with infusion dosage. These model predictions were dependent on the intercompartmental transport properties of sVEGFR1, as demonstrated in Fig. 5, suggesting that the molecular size dependence of permeability rates can be exploited in designing nonextravasating anti-VEGF agents of persistent efficacy. For instance, protein conjugation with polyethylene glycol (PEG) can increase the size and lower the theoretical vascular permeability of delivered sVEGFR1 proteins. However, to the best of our knowledge, PEG-linked sVEGFR1 had only been tested via intraperitoneal delivery in a mouse model of rheumatoid arthritis (28), and its therapeutic advantage through direct intravenous infusion is unknown.

If the treatment goal is to lower interstitial free VEGF, our results in Fig. 4 suggest that direct IM or interstitial delivery of sVEGFR1 is preferable to IV infusion, because it avoids an initial rise in interstitial free VEGF. Additionally, Fig. 2 suggests that interstitial delivery of sVEGFR1 would allow localization of effects within the targeted tissue, e.g., increasing sVEGFR1 production from the calf lowered interstitial free VEGF in the calf but not in the normal compartment. However, as confirmed in both Fig. 2 and Fig. 4, the steady-state interstitial efficacy achieved through IM sVEGFR1 delivery is expected to be minimal, with significant elevation of plasma free VEGF, which may be detrimental for antiangiogenic therapy.

sVEGFR1 in ischemic diseases and proangiogenic therapy.

For ischemic muscle diseases, such as peripheral arterial disease (PAD), proangiogenic treatment strategies have thus far sought to promote muscle angiogenesis through delivery of exogenous VEGF genes or proteins (43). Our control simulation in Fig. 2 suggests that additional inhibition of intramuscular production of sVEGFR1, e.g., through RNA interference, may work synergistically (albeit slightly) to increase interstitial free VEGF levels, through sVEGFR1-facilitated redistribution of free VEGF from plasma to tissue interstitia. This approach is further supported by an experimental finding in mice that increased muscle production of sVEGFR1 contributed to the impaired muscle angiogenesis in PAD (16). However, the precise prediction of systemic effects from inhibition of sVEGFR1 expression as a treatment for PAD requires a more comprehensive model of a PAD patient, as it is likely that there are other molecular maladaptations in ischemic muscles in addition to increased sVEGFR1 production. In particular, our simulation of an independent increase in muscular production of sVEGFR1 predicted the simultaneous increase in circulating free sVEGFR1 (Fig. 2H), yet a recent study found that plasma levels of sVEGFR1 did not significantly vary between PAD patients and control subjects (10), suggesting other pathological alterations in VEGF ligand and receptor expressions as well.

Regulation of free sVEGFR1 levels by VEGF-dependent NRP1 redistribution.

Figure 3 demonstrates that the involvement of the surface coreceptor NRP1 can further complicate the molecular interplay between VEGF and sVEGFR1. Upregulated parenchymal production of VEGF from the normal compartment—rather than reducing free sVEGFR1 levels as one might expect from increased VEGF occupancy of total sVEGFR1—led to increased systemic levels of free sVEGFR1 in our healthy control model. As it turned out, increased interstitial free VEGF led to an increased number of VEGF·VEGFR complexes competing for free NRP1 coupling, effectively reducing NRP1-facilitated internalization of sVEGFR1. The reason that calf production of VEGF did not similarly lower calf interstitial sVEGFR1 was that the calf muscle compartment had a lower total surface receptor density than the normal body muscle compartment, such that NRP1 involvement was not sufficient to override the more intuitive response of lowering free sVEGFR1 through increased VEGF occupancy (40). The binding affinity between NRP1 and sVEGFR1 also determines the significance of NRP1's involvement in the interdependence between VEGF and sVEGFR1 levels. Our present value for NRP1·sVEGFR1 binding affinity came from cell-free BIAcore measurements; if cell-based measurements are available in the future, we expect the affinity to be even higher because of optimized cell surface spatial configurations. Finally, the internalization rates of NRP1 complexes have not been quantified and may have been overestimated in our model by assuming the same internalization rates as VEGFR complexes.

Experimental validation.

Our computational predictions that sVEGFR1 infusion in our healthy control model elevated plasma free VEGF concentration do not contradict the experimental studies in which changes in free sVEGFR1 and free VEGF concentrations were inversely correlated, e.g., an ex vivo study demonstrating sVEGFR1's capacity as a direct sink for VEGF in pooled amniotic fluid (17) and an in vivo study demonstrating increased VEGF and corneal neovascularization in sVEGFR1 knockouts (2). A key result of Fig. 5 was that the extravasation permeability rates of the infused sVEGFR1 and the complexes it forms with plasma VEGF determined whether intravascular sVEGFR1 infusion led to steady-state elevations or reductions in plasma free VEGF concentration. In the situation in which the plasma compartment resembled a closed system for free and ligand-bound sVEGFR1 [e.g., kP(sR1) = 0 and kP(sR1·V) = 0 in Fig. 5], sVEGFR1 infusion led to persistent reductions in plasma free VEGF. Pooled amniotic fluids, and possibly the cornea because of its minimal vascularity, may behave more akin to single-compartment (closed) systems than our multitissue compartmental model of healthy human skeletal muscle. Alternatively, there may be significant physiological intravascular sources of sVEGFR1 [e.g., luminal secretion from EC, further discussed below; release from activated monocytes (19)] that the present model neglected. Introducing these blood sources of sVEGFR1 may lead to effects resembling those predicted for intravascular infusion of sVEGFR1, i.e., transient inversely correlated decreases in plasma free VEGF. Furthermore, if the extravasation permeability rates of free and ligand-bound sVEGFR1 are much lower in vivo than our model estimations, it is plausible that endogenous intravascular sources of sVEGFR1 can inversely regulate free VEGF in plasma as predicted in Fig. 5.

Here we propose crucial experiments that would be necessary to validate our computational predictions. Measurements are needed for interstitial (extracellular) concentrations of free VEGF and free sVEGFR1 in human skeletal muscle, in addition to the commonly measured plasma concentrations, in order to verify the accuracy of our predicted transendothelial gradients and thus the feasibility of sVEGFR1-facilitated interstitium-to-blood transport of VEGF as we have predicted. IM or IV infusion of exogenous sVEGFR1 tagged with donor fluorophores into transgenic animals expressing VEGF fused to acceptor fluorophores and subsequent in vivo fluorescence resonance energy transfer (FRET) imaging to trace the intercompartmental movements of exogenous sVEGFR1 in free vs. VEGF-bound forms could directly confirm or disprove our computational results. Further experiments are also needed to determine the presence and significance of intravascular sources of sVEGFR1, as well as the in vivo extravasation rates of plasma sVEGFR1, for reasons described above.

Implications of model assumptions on sVEGFR1 sources.

In our present model, endogenous production of sVEGFR1 occurred only through abluminal endothelial production of sVEGFR1—an assumption that was made to parallel another assumption in our model of abluminal-only endothelial surface expression of VEGFRs. These assumptions were based on the fact that the in vivo significance of luminal surface receptor expression remains to be experimentally determined. It is unknown whether the exocytotic secretion of alternatively spliced sVEGFR1 is mediated by cell membrane-targeting processes that differ from those that mediate plasma membrane expression of VEGFR1; it is plausible that luminal secretion of sVEGFR1 may still be significant in vivo even if the luminal surface expression of VEGFR1 proves insignificant. Model incorporation of luminal secretion of sVEGFR1 would effectively introduce a direct blood source of sVEGFR1. We expect this would further exaggerate the transendothelial gradient of free sVEGFR1 established in the healthy control (Supplemental Table S6 and Ref. 40), i.e., <36 pM interstitial free sVEGFR1 is expected to be necessary to target the same 100 pM of plasma free sVEGFR1. Thus we anticipate that the net directions of transendothelial gradients and flow profiles, which governed the sVEGFR1-facilitated shuttling of VEGF from tissues into the plasma as observed in this study, would be intact upon the introduction of luminal secretion of sVEGFR1.

Recently, a new soluble splice variant of the VEGFR1 gene was discovered and named sFlt1-14, which retains exon 14, unlike the originally described sFlt-1, which terminates with exon 13 (34). Crucially, sFlt1-14 was found to be produced by vascular smooth muscle cells (VSMC) in the blood vessel wall but not the EC of human saphenous vein (34). There was also preliminary evidence suggesting that the antiangiogenic involvement of sVEGFR1 in preeclampsia and corneal avascularity may in fact be attributable to this newly discovered VSMC-produced sFlt1-14 rather than the original EC-produced sFlt-1 (34). Luminal secretion of VSMC-produced sFlt1-14 from larger blood vessels can potentially contribute a significant direct blood source of endogenous sVEGFR1. Given the emerging in vivo significance of sFlt1-14's antiangiogenic role in human physiology, direct intravascular sources of sVEGFR1 need to be computationally investigated.

Conclusions.

This study showed that a systems biology perspective is needed to predict how free VEGF levels respond to changes in free sVEGFR1 levels, and vice versa—intercompartmental biotransport rates, NRP1 density, and NRP1's affinity for sVEGFR1 were all examples of factors that could critically alter the molecular interplay between VEGF and sVEGFR1. In summary, VEGF trapping alone could not account for sVEGFR1's antiangiogenic potential in the context of our multicompartmental model with dynamic intercompartmental transport processes that favored sVEGFR1-facilitated interstitium-to-blood transport of free VEGF. Heterodimerization with surface VEGFRs remains to be investigated as a potential antiangiogenic mechanism for sVEGFR1.

GRANTS

This work was supported by National Heart, Lung, and Blood Institute (NHLBI) Grants R33-HL-087351 and R01-HL-079653, a Natural Sciences and Engineering Research Council of Canada postgraduate PGS-M scholarship (F. T. H. Wu), and NHLBI Training Grant T32-HL-7284 (F. Mac Gabhann).

Supplementary Material

[Supplemental Figures and Tables]

Acknowledgments

The authors thank Dr. Amina A. Qutub, David Noren, Prakash Vempati, and all members of the Popel Lab for their helpful discussions.

Notes

Address for reprint requests and other correspondence: F. T. H. Wu, Dept. of Biomedical Engineering, Johns Hopkins Univ. School of Medicine, 720 Rutland Ave., 613 Traylor Research Bldg., Baltimore, MD, 21205 (e-mail: ude.uhj@uw.ecnerolf).

Footnotes

1The online version of this article contains supplemental material.

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