Effect of disrupted SOX18 transcription factor function on tumor growth, vascularization, and endothelial development

Background. The growth of solid tumors depends on establishing blood supply; thus, inhibiting tumor angiogenesis has been a long-term goal in cancer therapy. The SOX18 transcription factor is a key regulator of murine and human blood vessel formation. Methods: We established allograft melanoma tumors in wild-type mice, Sox18-null mice, and mice expressing a dominant-negative form of Sox18 (Sox18RaOp) (n = 4 per group) and measured tumor growth and microvessel density by immunohistochemical analysis with antibodies to the endothelial marker CD31 and the pericyte marker NG2. We also assessed the affects of disrupted SOX18 function on MCF-7 human breast cancer and human umbilical vein endothelial cell (HUVEC) proliferation by measuring BrdU incorporation and by MTS assay, cell migration using Boyden chamber assay, and capillary tube formation in vitro. All statistical tests were two-sided. Results: Allograft tumors in Sox18-null and Sox18RaOp mice grew more slowly than those in wild-type mice (tumor volume at day 14, Sox18 null, mean = 486 mm(3), 95% confidence interval [CI] = 345 mm(3) to 627 mm(3), p = .004; Sox18RaOp, mean = 233 mm(3), 95% CI = 73 mm(3) to 119 mm(3), p < .001; versus wild-type, mean = 817 mm(3), 95% CI = 643 mm(3) to 1001 mm(3)) and had fewer CD31- and NG2-expressing vessels. Expression of dominant-negative Sox18 reduced the proliferation of MCF-7 cells (BrdU incorporation: MCF-7(Ra) = 20%, 95% CI = 15% to 25% versus MCF-7 = 41%, 95% CI = 35% to 45%; P = .013) and HUVECs (optical density at 490 nm, empty vector, mean = 0.46 versus SOX18 mean = 0.29; difference = 0.17, 95% CI = 0.14 to 0.19; P = .001) compared with control subjects. Overexpression of wild-type SOX18 promoted capillary tube formation of HUVECs in vitro, whereas expression of dominant-negative SOX18 impaired tube formation of HUVECs and the migration of MCF-7 cells via the disruption of the actin cytoskeleton. Conclusions: SOX18 is a potential target for antiangiogenic therapy of human cancers.

Lower bounds on the complexity of simulating quantum gates

We give a simple proof of a formula for the minimal time required to simulate a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with fast local unitaries. We also note that a related lower bound holds for arbitrary n-qubit gates.

Practicality of time-optimal two-qubit Hamiltonian simulation

What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer, and Cirac [Phys. Rev. Lett. 88, 237902 (2002)] have obtained a set of powerful results characterizing the time-optimal simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian and fast local control over the individual qubits. How practically useful are these results? We prove that there are two-qubit Hamiltonians such that time-optimal simulation requires infinitely many steps of evolution, each infinitesimally small, and thus is physically impractical. A procedure is given to determine which two-qubit Hamiltonians have this property, and we show that almost all Hamiltonians do. Finally, we determine some bounds on the penalty that must be paid in the simulation time if the number of steps is fixed at a finite number, and show that the cost in simulation time is not too great.

Correlations, integration and Hansen-Jagannathan Bounds

Recent studies have documented the growing economic and financial integration between countries. Among other things, this has led to the argument that greater integration results in higher bilateral correlations between returns on national stock markets. This study endeavours to link the two issues by utilizing the assumption that if countries are integrated, they would have to display a minimum level of correlation. This is achieved by constructing a bound on the level of the bilateral correlation, as originally developed by Kasa (1995). In contrast to Kasa, the present studies demonstrate that the correlation bound may not be downward sloping in all cases and careful interpretation of the results is required.