Sensitivity to switching rates in stochastically switched ODEs

We consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices where the individual matrices and the average of the two matrices are all Hurwitz (all eigenvalues have strictly negative real part), but nonetheless the process goes to infinity at large time for certain values of the switching rate. We further construct examples in higher dimensions where again the two individual matrices and their averages are all Hurwitz, but the process has arbitrarily many transitions between going to zero and going to infinity at large time as the switching rate varies. In order to construct these examples, we first prove in general that if each of the individual matrices is Hurwitz, then the process goes to zero at large time for sufficiently slow switching rate and if the average matrix is Hurwitz, then the process goes to zero at large time for sufficiently fast switching rate. We also give simple conditions that ensure the process goes to zero at large time for all switching rates. © 2014 International Press.

Development of a Novel c-MET-Based CTC Detection Platform.

UNLABELLED: Amplification of the MET oncogene is associated with poor prognosis, metastatic dissemination, and drug resistance in many malignancies. We developed a method to capture and characterize circulating tumor cells (CTC) expressing c-MET using a ferromagnetic antibody. Immunofluorescence was used to characterize cells for c-MET, DAPI, and pan-CK, excluding CD45(+) leukocytes. The assay was validated using appropriate cell line controls spiked into peripheral blood collected from healthy volunteers (HV). In addition, peripheral blood was analyzed from patients with metastatic gastric, pancreatic, colorectal, bladder, renal, or prostate cancers. CTCs captured by c-MET were enumerated, and DNA FISH for MET amplification was performed. The approach was highly sensitive (80%) for MET-amplified cells, sensitive (40%-80%) for c-MET-overexpressed cells, and specific (100%) for both c-MET-negative cells and in 20 HVs. Of 52 patients with metastatic carcinomas tested, c-MET CTCs were captured in replicate samples from 3 patients [gastric, colorectal, and renal cell carcinoma (RCC)] with 6% prevalence. CTC FISH demonstrated that MET amplification in both gastric and colorectal cancer patients and trisomy 7 with gain of MET gene copies in the RCC patient. The c-MET CTC assay is a rapid, noninvasive, sensitive, and specific method for detecting MET-amplified tumor cells. CTCs with MET amplification can be detected in patients with gastric, colorectal, and renal cancers. IMPLICATIONS: This study developed a novel c-MET CTC assay for detecting c-MET CTCs in patients with MET amplification and warrants further investigation to determine its clinical applicability. Mol Cancer Res; 14(6); 539-47. ©2016 AACR.