Unformatted text preview: D.J.M. analyzed data; and W.W.Y. and D.J.M. wrote
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
1 To whom correspondence should be addressed. E-mail: [email protected] This article contains supporting information online at www.pnas.org/lookup/suppl/
doi:10.1073/pnas.1001192107/-/DCSupplemental. PNAS ∣ October 19, 2010 ∣ vol. 107 ∣ no. 42 ∣ 17933–17938 APPLIED BIOLOGICAL
SCIENCES Nature frequently utilizes opposing factors to create a stable activator gradient to robustly control pattern formation. This study
employs a biomimicry approach, by delivery of both angiogenic
and antiangiogenic factors from spatially restricted zones of a
synthetic polymer to achieve temporally stable and spatially
restricted angiogenic zones in vivo. The simultaneous release of
the two spatially separated agents leads to a spatially sharp angiogenic region that is sustained over 3 wk. Further, the contradictory
action of the two agents leads to a stable level of proangiogenic
stimulation in this region, in spite of significant variations in the
individual release rates over time. The resulting spatially restrictive
and temporally sustained profiles of active signaling allow the
creation of a spatially heterogeneous and functional vasculature. radioactivity of each scaffold layer (n ¼ 5) was measured with a WIZARD
Automatic Gamma Counter (PerkinElmer) prior to incubation at 37 °C in
2 mL of PBS. At specific measurement time points, release solutions
were measured using the Gamma counter and the scaffolds were placed
in fresh release solutions. The cumulative protein release from the scaffolds
at each time point was normalized as a percentage of total protein
Mathematical Model. A computational model was generated to depict the
concentration profiles of free VEGF, anti-VEGF, and VEGF complexed with
anti-VEGF. This model accounted for diffusion, release from scaffolds,
binding kinetics, and protein degradation. The governing equations of
the VEGF and anti-VEGF concentrations inside the scaffold and underlying
muscle were ∂c1
¼ D1 ∇2 c1 − k1 c1 þ f 1 − kon c1 c2 þ koff c3 ;
¼ D2 ∇2 c2 − k2 c2 þ f 2 − kon c1 c2 þ koff c3 ;
¼ D3 ∇2 c3 þ kon c1 c2 − koff c3 ;
where ci ¼ concentration
fi ¼ ci ðx;y;z;t ¼ 0Þ ¼ 0; release function;
0; ∀i;x;y;z inside scaffold
inside muscle 1 free VEGF
i ¼ 2 free anti-VEGF
3 VEGF-anti-VEGF complex
−7 D1 ¼ 7 × 10 scm ¼ Effective interstitial diffusion coefficient of VEGF165
D2 ¼ 3.2 × 10 scm ¼ Effective interstitial diffusion coefficient of IgG Ab
D3 ¼ 2.9 × 10 scm ¼ Effective interstitial diffusion coefficient of complex (25).
k1 ¼ 2.31 × 10−4 s−1 ¼ Degradation rate of VEGF (20).
k2 ¼ k3 ¼ 1.34 × 10−6 s−1 ¼ Degradation rate of free anti-VEGF and VEGFanti-VEGF complex (26, 27).
kon ¼ 5.5 × 104 M−1 s−1 ¼ VEGF-anti-VEGF complex formation r...
View Full Document
- Spring '13