1. Determining basal profiles for a healthy human subject
1.1. Targeting experimental plasma concentrations of VEGF and sVEGFR1 as functions of their secretion rates from the “normal” and “calf” compartments
In our stepwise search for the set of secretion rates that could computationally replicate the interstitial and plasma concentrations of VEGF and sVEGFR1 expected from experimental data in our healthy control model, we first established the VEGF concentrations in absence of sVEGFR1, and then introduced sVEGFR1 at modified secretion rates.
In the absence of sVEGFR1 expressions (qsR1
0), the steady-state plasma and interstitial free VEGF concentrations ([V]pl
) were mapped out as functions of total VEGF-secretion rates from the normal tissue and calf compartments (qTotalVEGF,Normal
), where the individual isoforms VEGF121
were secreted at a ratio of 1
10 ( top row, ‘-sR1’). Where [V]pl
was within the experimental ranges of 1–2 pM, [V]IS
were predicted to be ~10-fold higher, in contradiction of microdialysis measurements of [V]IS
at around 1 pM. Therefore, in the absence of sVEGFR1 expression, the control VEGF-secretion rates necessary to achieve the targeted [V]pl
of 1.5 pM, as well as symmetric [V]IS
(i.e., 15 pM in both “calf” and “normal” interstitia), would have been qV,-Ctrl
(0.264, 0.154) molecules/MD/s.
Targeting Control VEGF-Secretion Rates (qTotalVEGF) for Basal Profile of Healthy Subject.
However, the incorporation of sVEGFR1 expression into the system ( ‘+sR1’) was found to shift the VEGF profile upwards in the plasma – i.e., if VEGF-secretion rates were fixed at qV,-Ctrl
became 2.1 pM once sVEGFR1-secretion rates were high enough to attain a target [sR1]pl
of 100 pM. Hence in seeking our control sVEGFR1-secretion rates, we redefined the control VEGF-secretion rates to qV,+Ctrl
(0.1925, 0.1155) molecule/MD/s
tissue)/s, so that [V]pl
would start off at the lower bound of the target range (1 pM) in the absence of sVEGFR1. The steady-state plasma and interstitial free sVEGFR1 concentrations ([sR1]pl
) were then plotted over a range of sVEGFR1-secretion rates from the normal tissue and calf compartments (qsR1,Normal
) in , while VEGF-secretion was fixed at qV,+Ctrl
. The control sVEGFR1-secretion rates that could attain a [sR1]pl
of 100 pM, as well as symmetric [sR1]IS
(i.e, 36 pM in both “calf” and “normal” interstitia), were determined to be qsR1,Ctrl
tissue)/s. At this qsR1,Ctrl
became exactly the targeted 1.5 pM, with [V]IS
now at 10 pM ( middle row). Although the control secretion rates needed to reach a target set of [V]pl
were not unique – i.e., higher sVEGFR1-secretion rates could theoretically also have elevated [V]pl
from below 1 pM in absence of sVEGFR1 to 1.5 pM in presence of sVEGFR1 – we settled on this set of qV,+Ctrl
() such that [V]pl
remained within experimental range, with or without sVEGFR1 expression in the simulation.
Targeting Control sVEGFR1-Secretion Rates (qsR1) for Basal Profile of Healthy Subject.
VEGF- and sVEGFR1-Secretion Rates (Fitted Kinetic Parameters).
1.2. Basal distribution profiles
Using the aforementioned control secretion rates, the following molecular distributions and occupancy profiles were achieved at steady state. (See “Healthy Ctrl” in Supplemental Fig. S1
i. VEGF distribution
The ratio of free VEGF121
in plasma and interstitial concentrations were 1
10.8 and 1
10.6 respectively (Fig. S1-A
), just slightly lower than the original isoform ratio of the VEGF-secretion rate (1
10). In the blood, both VEGF121
were 23% free and 77% bound to sVEGFR1 (Fig. S1-C,D
). This predicted complexed fraction of VEGF was much higher than that experimentally measured by Belgore et al.
in healthy human plasma (~4% mole fraction, based on 113 pg/mL free VEGF and 18 pg/mL complexed sVEGFR1) 
. In the normal interstitium, VEGF121
0.6% free, 0.8%
0.6% sVEGFR1-bound, 98.3%
63.0% surface receptor-bound, and 0%
35.8% matrix-bound (Fig. S1-C,D
). In the calf interstitium, VEGF121
1.4% free, 5.0%
1.5% sVEGFR1-bound, 90.2%
24.7% surface receptor-bound, and 0%
72.4% matrix-bound (Fig. S1-C,D
). In other words, while VEGF was mostly bound to sVEGFR1 in blood, almost all extracellular VEGF in muscle tissue was surface receptor- or matrix-bound. Compared to our previous single-compartment and multi-compartment results in the absence of sVEGFR1 
, the addition of sVEGFR1 into the VEGF system did not significantly alter the predicted total VEGF distribution in normal muscle tissue.
ii. sVEGFR1 distribution
In the blood, 95% of total sVEGFR1 were free, with only 5% complexed to VEGF (Fig. S1-B
). This predicted VEGF-occupancy of total plasma sVEGFR1 was again higher than that experimentally measured in healthy human plasma (~0.65% mole fraction, based on 21 ng/mL free sVEGFR1 vs. 18 pg/mL complexed sVEGFR1) 
. In the normal
calf interstitium, sVEGFR1 were 1.6%
1.9% free, 97.4% matrix-bound, 0.4%
0.6% VEGF-bound (with or without NRP1 coupling), and 0.6%
iii. Inter-compartmental distributions
Due to geometrical differences between histological cross-sections of vastus lateralis and gastrocnemius, our normal muscle was characterized with higher total receptor density (due to 11.3% higher myocyte volume fraction, ) than that in calf muscle, while our calf muscle was characterized with higher total matrix site density (due to 8% larger available interstitial fluid volume fraction, ) than that in normal muscle. Therefore the normal compartment had higher amount of total extracellular VEGF121
(mostly surface receptor-bound), but lower amounts of total extracellular VEGF165
and sVEGFR1 (mostly matrix-bound), per tissue volume than the calf compartment (Fig. S1-B,C,D
iv. Occupancy of matrix sites
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
). These fractional occupancies remained characteristically low (<0.6%) throughout sensitivity analyses.
v. Occupancy of VEGFRs and NRP1
The fractional occupancies of total surface receptors were also consistent between normal and calf compartments (differences <1%): (i) total VEGFR1 were 26% free, 66% NRP1-coupled but not VEGF-ligated, and 8% VEGF-ligated (Fig. S1-H
); (ii) total VEGFR2 were 80% free and 20% VEGF-ligated (Fig. S1-I
); (iii) total NRP1 were 16% free, 0.3% sVEGFR1-bound with or without VEGF121
, 0.1% VEGF165
-bound, 66% coupled to unactivated VEGFR1 (i.e., VEGFR1-NRP1), and 18% coupled to signaling VEGFRs (i.e., VEGF121
-VEGFR1-NRP1 or VEGFR2-VEGF165
-NRP1) (Fig. S1-J
1.3. Physiological variation in calf volume-of-interest
Within a threefold increase in volume of the “healthy calf muscle” compartment (up to 2,604 cm3), along with corresponding decreases in the “normal compartment” volume (down to 58,717 cm3), all control predictions of VEGF and sVEGFR1 distributions remained consistent (to within 1%), while receptor occupancy profiles remain unchanged. This implied that in cases that require modeling of bigger calf regions-of-interest, such as to include the tibialis anterior, or to study bilateral calves, the geometric differences between our calf vs. normal muscle parameterizations would not cause deviations in the overall baseline healthy profile attained by the stated set of control secretion rates.
1.4. Basal concentration gradients & flow profiles
summarizes the inter- and intra-compartmental flow balance of soluble species at basal secretion rates; as will be shown in subsequent sections, the net directions and relative magnitudes of these mass flows dictated how the system responded to parameter perturbations. A key difference was noted between the VEGF and sVEGFR1 flows at steady state: most interstitial VEGF was internalized locally, via complex formation with abluminal VEGFRs, before it had a chance to permeate into the plasma, contributing to its lower plasma concentrations; whereas interstitial sVEGFR1, apart from its abluminal internalization, had an equally significant route of escape via lymph flow which contributed to its higher plasma concentration. Consequently, the transendothelial (plasma vs. interstitial) concentration gradients were differentially established, such that free VEGF and sVEGFR1-VEGF complexes experienced net intravastion (IS to plasma) at control, while free sVEGFR1 had an overall tendency to extravasate (plasma to IS) at control. Integral to the flow balances were the net mass transfers between the three soluble species: interstitially, the steady-state inflows for both free VEGF and sVEGFR1 outweighed their respective outflows, signifying a net tendency for them to associate and form sVEGFR1-VEGF complexes; in the plasma, the steady-state inflows for VEGF and sVEGFR1 were less than their respective outflows, indicative of an additional source from net dissociation of sVEGFR1-VEGF complexes.
Basal Steady-State Flow Profiles of Free VEGF (left), sVEGFR1-VEGF Complexes (middle), Free sVEGFR1 (right).
2. Increasing VEGF- or sVEGFR1-secretion rates did not systemically lower free sVEGFR1 or free VEGF concentrations respectively
2.1. System sensitivity to VEGF-secretion rates
First we examined the VEGF response to increasing VEGF-secretion rates as illustrated in . [V]IS,Normal and [V]IS,Calf were essentially determined by their respective local VEGF secretion rates, qTotalVEGF,Normal and qTotalVEGF,Calf. This was expected with [V]IS, since the intracompartmental flows (secretion and internalization) of VEGF dominated over its intercompartmental flows (vascular permeability and lymphatic drainage) in magnitude (). Thus [V]IS was greatly sensitive to local changes in qTotalVEGF, but relatively insensitive to qTotalVEGF of the other compartment due to weak intercompartmental communication. Similarly, [V]pl was increasingly dependent on qTotalVEGF,Normal but largely insensitive to qTotalVEGF,Calf, following the much larger intravasation flow from the normal compartment relative to that from the calf ().
On the other hand, sVEGFR1 concentrations were affected by VEGF-secretion rates in two asymmetrical ways. Firstly, the response to increasing qTotalVEGF,Calf
was expected from previous flow analysis (): a surge in [V]IS,Calf
was compensated by increased complex formation, lowering [sR1]IS,Calf
in the process of association (). Subsequent intravasation of sVEGFR1-VEGF complexes and their dissociation in plasma was too modest to affect [sR1]pl
. A second mode of response occurred with increasing qTotalVEGF,Normal
, beginning with an elevated [V]IS,Normal
which promoted VEGFR2-VEGF165
-NRP1 formation, thereby diminishing the availability of free NRP1 to bind free sVEGFR1. As a result of decreased sVEGFR1-internalization via NRP1-complexes, interstitial free sVEGFR1 actually increased globally (in both [sR1]IS,Normal
) via [sR1]pl
(). The asymmetry was a consequence of the calf compartment having less endothelial surface area per volume and thus lower total surface receptor densities than the normal muscle compartment (supplemental Fig. S1
), such that the second mechanism involving NRP1-VEGFR2 coupling was not sizeable enough to override the first mechanism involving sVEGFR1-VEGF association.
Lastly, the density of VEGF-ligated signaling complexes on the abluminal surface of the endothelium positively correlated with [V]IS. Consequently, increasing qTotalVEGF intensified both VEGFR1 and VEGFR2 signaling profiles ().
2.2. System sensitivity to sVEGFR1-secretion rates
illustrates the VEGF and sVEGFR1 responses to increasing sVEGFR1-secretion rates. [sR1]IS,Normal and [sR1]IS,Calf were predicted to most significantly depend on their local sVEGFR1-secretion rates, qsR1,Normal and qsR1,Calf respectively, in a linear fashion. Flow analysis () suggested that the elevated interstitial free sVEGFR1 would then associate with free VEGF to form sVEGFR1-VEGF complexes, which accounted for the slight decreases in [V]IS in the direction of increasing local qsR1. Furthermore, the complexes formed in the interstitium were expected to intravasate and dissociate in the plasma, as confirmed by the rise in [V]pl and [sR1]pl in the direction of increasing qsR1,Normal. The cycle completes with part of the elevated [sR1]pl extravasating back into the interstitium, hence accounting for the increase in [sR1]IS,Calf in the direction of increasing qsR1,Normal. Thus unlike VEGF in the previous subsection, interstitial sVEGFR1 (e.g., [sR1]IS,Calf) was able to respond to distal changes (e.g., qsR1,Normal). The asymmetry where increasing qsR1,Calf did not elevate [sR1]IS,Normal was due to the fact that the intravasation flow of the complex from the calf was insufficient to elevate [sR1]pl on its own. Finally, the signaling profiles did not change significantly as a function of qsR1 (), reflective of the minute changes in [V]IS already described.
3. Receptor densities and ratios affected plasma and interstitial concentrations of VEGF and sVEGFR1, as well as surface-bound VEGFR occupancy
Receptor densities and ratios were varied over two orders of magnitude about the healthy control values, while keeping VEGF- and sVEGFR1-secretion rates fixed, in a steady-state sensitivity analysis to predict system response to physiological/pathological regulation of receptor expression levels. Interstitial and plasma concentrations of free VEGF and free sVEGFR1 were found to be sensitive over most of the tested ranges (), as described in further mechanistic detail below. Overall, increasing NRP1 density, increasing VEGFR2
VEGFR1 ratio (denoted as [R2]/[R1]), and decreasing total VEGFR density all steepened plasma vs. interstitium gradients (i.e., farther from 1
1) for VEGF concentrations; while increases in all three parameters reduced sVEGFR1 gradients (i.e., closer to 1
1). In addition, higher NRP1 density or [R2]/[R1] favored a net shift towards pro-angiogenic signaling; while total VEGFR densities within the same order of magnitude as NRP1 density were predicted to be optimal for overall pro-angiogenic signaling ().
Steady-State Sensitivity to Receptor Density.
3.1. Sensitivity to neuropilin-1 density
Higher NRP1 densities were generally associated with lower concentrations of all soluble species, since NRP1 was a vehicle for internalizing VEGF and sVEGFR1 via endothelial VEGF121-NRP1, VEGF165-NRP1, sVEGFR1-NRP1, VEGF121-VEGFR1-NRP1 complexes. For free VEGF, this was most evident at low total VEGFR density (), when the alternative internalization route for VEGF via VEGFR was minimized. For free sVEGFR1, this was most evident at high total VEGFR density (), when free VEGF remained low to reduce the secondary effects of sVEGFR1-VEGF complex formation. Secondarily, declines in sVEGFR1-VEGF complex concentrations followed increases in NRP1 density (), as NRP1 competed with sVEGFR1 for binding with free VEGF.
Moreover, increasing NRP1 density shifted the VEGF-signaling profiles as shown in . The overall drop in “anti-angiogenic potential”, as represented by ligated VEGFR1 complexes, can be explained by NRP1's high affinity for VEGFR1. At 105
NRP1/EC, almost all (97%) VEGFR1 became part of unligated VEGFR1-NRP1 complexes – a shift that dramatically reduced the availability of VEGFR1 for VEGF165
-ligation (). On the other hand, the overall rise in “pro-angiogenic potential”, as represented by ligated VEGFR2 complexes, can be explained by NRP1's role as a co-receptor in presenting NRP1-bound VEGF165
to VEGFR2, as well as in stabilizing VEGF165
-VEGFR2 through their triplet configuration. All together, these synergistic functions of NRP1 in reducing anti-angiogenic complexes and promoting pro-angiogenic complexes, were in tune with computational predictions from our previous studies in the absence of sVEGFR1 
3.2. Sensitivity to VEGFR2
VEGFR1 density ratio ([R2]/[R1])
Although higher NRP1 density in general lowered free VEGF concentrations predominantly through enhanced internalization of VEGF-bound NRP1, exceptions were noted in the region of low [R2]/[R1] (<1), roughly between 10,000 to 20,000 total VEGFR/EC, where free VEGF concentrations were apparently higher at 10,000 NRP1/EC than at 1,000 NRP1/EC (). In this region, the greater abundance of VEGFR1 gave more prominence to NRP1's tendency to competitively shift the distribution of total VEGFR1 towards formation of unligated VEGFR1-NRP1 complexes, in the process freeing VEGF that had been bound to uncoupled VEGFR1, hence elevating free VEGF concentrations.
For the independent increase of [R2]/[R1] while fixing total receptors at control densities, the following concentration changes were observed in all three fluid compartments (), originating from the tissues' interstitial fluids and propagated into the plasma: (i) free VEGF121
increased – due to a net decrease in internalization force (reduction in VEGF121
-VEGFR1 and VEGF121
-VEGFR1-NRP1 outweighed increase in VEGF121
-VEGFR2) (); (ii) free VEGF165
decreased – due to a net increase in internalization force (increase in VEGF165
-VEGFR2 and VEGFR2-VEGF165
-NRP1 overshadowed reduction in VEGF165
-VEGFR1) (); (iii) an overall decrease in free total VEGF – despite an increasing fraction of isoform 121 (up to VEGF121
3 at [R2]/[R1]
10); and (iv) free sVEGFR1 decreased – due to dissociation of NRP1 from VEGFR1-NRP1 complexes to become available for sVEGFR1-binding and internalization (data not shown).
3.3. Sensitivity to total VEGFR density ([R1]+[R2])
Our simulations presented several theoretical indications that the VEGF/sVEGFR1 system has optimal operating range around the VEGFR1
NRP1 receptor density ratio of 1
1. Firstly, in examining the free sVEGFR1 concentration surfaces shown in , the region of maximal or linear gain for each surface always spanned total VEGFR densities near the same order of magnitude as NRP1 density. In fact, the sVEGFR1 concentration surfaces for 10,000 NRP1/EC were not only sigmoidal over the examined total VEGFR density range, centered about [R1]+[R2]
20,000/EC, they were also sigmoidal in the direction of VEGFR ratio, centered about 1
1. Similarly, of the free VEGF concentration surfaces, the sigmoidal surface for 10,000 NRP/EC had the closest operating range over [R1]+[R2]
20,000/EC. A second indication was based on the observation that the formation of signaling VEGFR2 complexes was biphasic in the direction of total VEGFR density, allowing the most efficient net “pro-angiogenic potential” to be reached within the order of 10,000 total VEGFR/EC ().
Mechanistically, the dependence of signaling profiles on total VEGFR density as depicted in could be explained by two forces: (1) the direct effects of the sheer increase in number of VEGFRs available for VEGF ligation; (2) the indirect effects of VEGFR's density ratio relative to NRP1 which was fixed at 10,000/EC. The former effects increased quantities of non-NRP1-coupled VEGF-VEGFR complexes with increasing total VEGFR density, despite the diminishing fractional occupancies of VEGFRs (). The latter effects stemmed from an increasing proportion of total NRP1 being used up in formation of unligated VEGFR1-NRP1 complexes with increasing total VEGFR density (). This meant that the higher the total VEGFR density, the less free NRP1 were available to form VEGFR2-VEGF165-NRP1 and VEGF121-VEGFR1-NRP1, hence the generally decreasing contribution of these species in their respective signaling profiles (). The opposing trend in the biphasic nature of VEGFR2-VEGF165-NRP1 () came from the fact that at very low total VEGFR density, quantities of VEGFR2 were so limited that there was an unusual population of VEGF165-NRP1 left at steady state for 2,000 VEGFR/EC () with no VEGFR2 to present to. Thus explained the quick jump in VEGFR2-VEGF165-NRP1 as soon as VEGFR2 were available at 10,000 VEGFR/EC ().
4. VEGFRs' affinities for VEGF affected free sVEGFR1 concentrations via NRP1 availability; NRP1's affinity for VEGF121 was inconsequential
This section explores system sensitivity to the effective (microenvironment-dependent) dissociation constants of VEGF from its receptors over the wide ranges reported in literature.
4.1. Sensitivity to VEGF-binding affinity of VEGFR1 and VEGFR2
The shifts in signaling profiles were as expected from the competitive binding of VEGF between VEGFRs: increasing one VEGFR's VEGF-affinity boosted formation of its signaling complexes to the detriment of the other VEGFR's complex formation (). As for the soluble species, total free VEGF in all compartments decreased with increasing VEGF-binding affinity of either VEGFR1 or VEGFR2 – presumably through enhanced internalization of complexed VEGF (). Free sVEGFR1 concentrations, however, changed in opposite directions: lowered with increasing VEGF-VEGFR1 affinity but rose with increasing VEGF-VEGFR2 affinity. The directional change in free sVEGFR1 thus followed that of VEGFR2-VEGF165-NRP1 complexes () – i.e., the more VEGFR2-VEGF165-NRP1 complexes formed, the less unbound NRP1 available for binding and internalization of free sVEGFR1 ().
Steady-State Sensitivity to VEGF-Binding Affinities of Cell Surface Receptors: VEGFR1, VEGFR2 and NRP1.
4.2. Sensitivity to VEGF-binding affinity of NRP1
Lowering NRP1's affinity for VEGF165 over two orders of magnitude – Kd(V165,N) from 200 pM to 25 nM –caused only opposing changes of up to 0.3% in the VEGF-bound fractional occupancies of VEGFR1 and VEGFR2 (). The minute attenuation of pro-angiogenic potential reflected a declining availability of VEGF165-bound NRP1s for coupling with VEGFR2, hence the diminishing quantities of VEGFR2-VEGF165-NRP1 (). Simultaneously in all fluid volumes, free VEGF121 levels remained consistent while free VEGF165, presumably released from NRP1s, elevated slightly (plasma data shown in ). This in turn increased availability of free VEGF165 for direct VEGFR1-binding ().
Our simulations also predicted inconsequential effects from incorporating the newly purported binding interaction between NRP1 and VEGF121
. Specifically, when modeling both VEGF121
- and VEGF165
-affinities of NRP1 at the low affinities cited by Pan et al.
(220 nM and 120 nM respectively 
), there were no remarkable changes in signaling profiles () nor concentrations of free soluble species () compared to simulation results with no VEGF121
-NRP1 binding but weak VEGF165
-NRP1 binding. Furthermore, when keeping VEGF165
-NRP1 affinity at control (320 pM) and introducing VEGF121
-NRP1 binding at an affinity 1.83× higher than that (in accordance with the ratio reported by Pan et al.
), all system distributions were almost identical to those at control – because even then, the steady-state population of VEGF121
-NRP1 only represented an insignificant 0.7% of total VEGF121
in muscle tissues.
Thus, as long as VEGF had a lower affinity to NRP1 than to VEGFRs, the system was largely insensitive to variations in the VEGF-binding affinities of NRP1. This suggested that mechanistically, the significance of NRP1 as a co-receptor in the VEGF system could be largely attributed to NRP1's strength in coupling VEGFRs rather than its direct affinity for VEGF.
5. Densities and VEGF-affinity of interstitial matrix sites affected only matrix-bound reservoirs of VEGF165 and sVEGFR1
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 (). In contrast, the quantities of matrix-bound VEGF165 and sVEGFR1 increased drastically with increasing matrix site densities (); while the matrix-bound reservoir of VEGF165 also grew drastically with higher VEGF165-affinity of matrix sites (). 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).
Sensitivity to Density & VEGF-Binding Affinity of Interstitial Matrix Sites for VEGF165 & sVEGFR1.
6. Transport parameters affected concentrations of plasma VEGF, plasma sVEGFR1 and interstitial sVEGFR1, but not surface-bound VEGFR occupancy
Transport parameters were independently varied over two orders of magnitude about control for sensitivity analysis. In plasma, steady-state concentrations of all soluble species were strongly dependent on transport rates, whereas in the interstitium, sVEGFR1 concentration was much more sensitive than VEGF to transport parameters. In general: increasing kP
reduced plasma vs. interstitium gradients (i.e., closer to 1
1) for both VEGF and sVEGFR1 concentrations (); increasing kL
lessened VEGF gradients but steepened sVEGFR1 gradients (); while decreasing kCL
reduced VEGF gradients without much effect on sVEGFR1 gradients (). Additionally, the current model showed that physiological fluctuations in transport parameters were ineffective in altering endothelial VEGFR occupancy, given their minute effect on interstitial free VEGF levels.
Steady-State Effects of Permeability Rate (kP) on VEGF and sVEGFR1 Concentrations (A) & Flows (B).
Steady-State and Dynamic Effects of Lymphatic Drainage Rates (kL).
Steady-state Effects of Plasma Clearance Rate (kCL) on VEGF and sVEGFR1 Concentrations.
6.1. Steady-state effects of vascular permeability rates (kP)
The effect of kP on free VEGF and sVEGFR1 concentrations () could be explained by their associated flow changes (). Firstly, since the transendothelial VEGF gradient at control favored net intravasation, increasing kP resulted in significantly higher plasma concentrations of free VEGF. Interstitially, the corresponding decreases in free VEGF were insignificant, as the change in VEGF's transvascular flow was still overshadowed in magnitude by its secretion and internalization flows. Secondly, the transendothelial gradient of sVEGFR1 at control favored net extravasation, hence increasing kP resulted in: lower plasma concentrations of free sVEGFR1; as well as increased free sVEGFR1 in the interstitium facing the endothelium where kP was upregulated, at the expense of a decrease in interstitial free sVEGFR1 in the other tissue compartment (e.g., “Control” vs. “Fenestration” in ).
VEGF and sVEGFR1 distribution changes were also more drastic in blood than in interstitia. In the blood, the number of complexed sVEGFR1-VEGF increased slightly (e.g., 1.5× from control) with increasing global kP (e.g., 10× from control). This was sufficient to elevate the fractional occupancy of total sVEGFR1 (e.g., +9%) despite decreasing free sVEGFR1; yet not enough to prevent overall reductions in bound fraction of total VEGF (e.g., -14%) because of the greater increase in free VEGF. In the interstitium, the fractional occupancies of VEGFR1 and VEGFR2 by VEGF decreased <0.5% within the 100-fold increase in kP tested.
6.2. Steady-state effects of lymph flow rates (kL)
Similarly, kL-driven changes in steady-state concentrations of free VEGF and sVEGFR1 () could be explained by their associated flow changes (). Since lymph flow represented a unidirectional flushing of VEGF and sVEGFR1 from the interstitium into blood, increasing kL resulted in higher plasma and lower interstitial concentrations of free VEGF and sVEGFR1. All resulting differences were significant except for interstitial free VEGF, as lymphatic flow was also dwarfed by the secretion and internalization flows in the net balancing of VEGF entering and leaving the interstitia. It was noted that when increasing kL in one tissue compartment only (e.g., increasing kL,N only from “Calf Peak Exercise” to “Peak Exercise” in ), the interstitial concentration of free sVEGFR1 only decreased locally (e.g., normal), while slightly increased in the other tissue compartment (e.g., calf). This was due to a secondary “spill-over” of the elevated plasma free sVEGFR1 through increased extravasation into the distal compartment. This may suggest that if increasing kL were to be explored as a therapeutic means to alleviate calf tissue accumulation of sVEGFR1, local lymphatic flushing as induced by leg exercise may be more productive than whole-body exercise ().
Distribution changes were again more evident in the blood: the simultaneous elevations in free VEGF and sVEGFR1, due to increasing global kL (e.g., 10× from control), in turn synergistically increased sVEGFR1-VEGF complex formation (e.g., 88× from control), which elevated the complexed fractions of both VEGF (e.g., +13%) and sVEGFR1 (e.g., +8.7%). In addition, a reversal in permeability flow of sVEGFR1-VEGF complex, from net intravasation to net extravasation, was also observed upon increasing kL from control to steady exercise rate (). In the interstitium, the fractional VEGF-occupancies of VEGFR1 and VEGFR2 decreased <1% within the 100-fold increase in kL tested.
While steady-state analyses showed that plasma concentrations of sVEGFR1 and VEGF could vary up to 164 pM and 2.4 pM respectively (>150% about controls) over the physiological range of kL, we further examined whether concentration ranges of these magnitudes were attainable within physiological time-course.
6.3. Dynamic effects of lymph flow rates (kL)
A dynamic simulation of the diurnal changes of kL over a combination of “bed-rest days” and “active days”, as illustrated in , suggested that physiological variation of kL over the course of a day can still account for significant variation in plasma concentrations of VEGF and sVEGFR1. In blood, dynamic fluctuations in free sVEGFR1 always eclipsed that of free VEGF in amplitude, at up to 76 vs. 1.65 pM (~76% vs. 110% about controls). In the interstitia, diurnal ranges of VEGF and sVEGFR1 were much subdued compared to steady-state ranges: free VEGF varied up to 0.2 pM (~2% about controls), with negligible effects on VEGF-VEGFR complex formation; while free sVEGFR1 varied up to 2.5 pM (~7% about controls).
It was noted that sVEGFR1 equilibrated slower than VEGF, such that sVEGFR1 never fully re-established its steady state within the day, while VEGF reached its new steady state within hours. This differential characteristic time between VEGF and sVEGFR1 accounts for the unique responses of the three soluble species to activity-dependent changes in kL during “active days”. From the waking hour (e.g., 48th h in ), plasma concentration of free sVEGFR1 followed a steady rise over the next 15 h before the onset of sleep. On the other hand, plasma free VEGF experienced a much steeper initial rise to a transient peak that closely accompanied the kL peak of early exercise, but soon falls into a lower plateau as kL also settled to its own steady state of normal activity. As for the sVEGFR1-VEGF complex in plasma, its steep initial peak and dip followed those of free VEGF, while a latter steady rise was driven by the persistent net influx of free sVEGFR1. In fact, plasma sVEGFR1-VEGF overtook interstitial sVEGFR1-VEGF at some point near the latter active hours of wakefulness, whereupon the permeability flow of the complex reversed in direction to become a net extravasation until the onset of sleep ().
In summary, a 15-h period of daytime activity could elevate plasma concentrations to 42 pM and 1.1 pM above control for free sVEGFR1 and VEGF respectively. However, 9 h of sleep was adequate for plasma free sVEGFR1 to fall back to below control levels regardless of whether the subject was active or inactive during waking hours (−32 pM after bed-rest vs. −16 pM after activity). Hence, consecutive “active days” negligibly enhanced the peak sVEGFR1 level attainable in subsequent “active days” (+44 pM sVEGFR1; +1.0 pM VEGF relative to control).
6.4. Steady-state effects of plasma clearance rates (kCL)
Increasing direct clearance from blood (kCL) drastically lowered free VEGF and sVEGFR1 concentrations in plasma (). These primary effects in blood in turn were propagated into the interstitium through permeability, i.e., via reduced net sVEGFR1 extravasation and upregulated net VEGF intravasation. Consequently, interstitial concentrations of free sVEGFR1 were significantly lowered as well; though decreases in interstitial free VEGF were negligible, again because changes in intercompartmental flows were masked by the predominant secretion and internalization flows of VEGF.
Distribution analysis in the blood showed that the number of sVEGFR1-VEGF complexes reduced proportionally to free VEGF (sVEGFR1-complexed fraction of total VEGF was consistent within 2%) while the fractional occupancy of sVEGFR1 dropped from 19% to 2% over the 100-fold variation in kCL. In the interstitium, the fractional VEGF-occupancies of VEGFRs decreased <0.2% for the kCL range tested.