Development of hypoxic regions is an indicator of poor prognosis in many tumors. Here, we demonstrate that HIF1alpha, the direct effector of hypoxia, partly through increases in SDF1alpha, induces recruitment of bone marrow-derived CD45+ myeloid cells containing Tie2+, VEGFR1+, CD11b+, and F4/80+ subpopulations, as well as endothelial and pericyte progenitor cells to promote neovascularization in glioblastoma. MMP-9 activity of bone marrow-derived CD45+ cells is essential and sufficient to initiate angiogenesis by increasing VEGF bioavailability. In the absence of HIF1alpha, SDF1alpha levels decrease, and fewer BM-derived cells are recruited to the tumors, decreasing MMP-9 and mobilization of VEGF. VEGF also directly regulates tumor cell invasiveness. When VEGF activity is impaired, tumor cells invade deep into the brain in the perivascular compartment.

To understand the kinetics of protein folding, we introduce the concept of a “transition coordinate” which is defined to be the coordinate along which the system progresses most slowly. As a practical implementation of this concept, we define the transmission coefficient for any conformation to be the probability for a chain with the given conformation to fold before it unfolds. Since the transmission coefficient can serve as the best possible measure of kinetic distance for a system, we present two methods by which we can determine how closely any parameter of the system approximates the transmission coefficient. As we determine that the transmission coefficient for a short-chain heteropolymer system is dominated by entropic factors, we have chosen to illustrate the methods mentioned by applying them to geometrical properties of the system such as the number of native contacts and the looplength distribution. We find that these coordinates are not good approximations of the transmission coefficient and therefore, cannot adequately describe the kinetics of protein folding.