Khovanov Homology, Lee Homology and a Rasmussen Invariant for Virtual Knots

The paper contains an essentially self-contained treatment of Khovanov homology, Khovanov-Lee homology as well as the Rasmussen invariant for virtual knots and virtual knot cobordisms which directly applies to classical knot and classical knot cobordisms. To do so, we give an alternate formulation for the Manturov definition of Khovanov homology for virtual knots and links with arbitrary coefficients. This approach uses cut loci on the knot diagram to induce a conjugation operator in the Frobenius algebra. We then discuss the implications of the maps induced in the aforementioned theory to the universal Frobenius algebra for virtual knots. Next we show how one can apply the Karoubi envelope approach of Bar-Natan and Morrison on abstract link diagrams with cross cuts to construct the canonical generators of the Khovanov-Lee homology. Using these canonical generators we derive a generalization of the Rasmussen invariant for virtual knot cobordisms and furthermore generalize Rasmussen's result on the slice genus for positive knots to the case of positive virtual knots. It should also be noted that this generalization of the Rasmussen invariant provides an easy to compute obstruction to knot cobordisms in $S_g \times I \times I$ in the sense of Turaev

Patient-derived xenograft (PDX) models in basic and translational breast cancer research

Patient-derived xenograft (PDX) models of a growing spectrum of cancers are rapidly supplanting long-established traditional cell lines as preferred models for conducting basic and translational preclinical research. In breast cancer, to complement the now curated collection of approximately 45 long-established human breast cancer cell lines, a newly formed consortium of academic laboratories, currently from Europe, Australia, and North America, herein summarizes data on over 500 stably transplantable PDX models representing all three clinical subtypes of breast cancer (ER+, HER2+, and "Triple-negative" (TNBC)). Many of these models are well-characterized with respect to genomic, transcriptomic, and proteomic features, metastatic behavior, and treatment response to a variety of standard-of-care and experimental therapeutics. These stably transplantable PDX lines are generally available for dissemination to laboratories conducting translational research, and contact information for each collection is provided. This review summarizes current experiences related to PDX generation across participating groups, efforts to develop data standards for annotation and dissemination of patient clinical information that does not compromise patient privacy, efforts to develop complementary data standards for annotation of PDX characteristics and biology, and progress toward "credentialing" of PDX models as surrogates to represent individual patients for use in preclinical and co-clinical translational research. In addition, this review highlights important unresolved questions, as well as current limitations, that have hampered more efficient generation of PDX lines and more rapid adoption of PDX use in translational breast cancer research

Molecular mechanisms of cell death: recommendations of the Nomenclature Committee on Cell Death 2018.

Over the past decade, the Nomenclature Committee on Cell Death (NCCD) has formulated guidelines for the definition and interpretation of cell death from morphological, biochemical, and functional perspectives. Since the field continues to expand and novel mechanisms that orchestrate multiple cell death pathways are unveiled, we propose an updated classification of cell death subroutines focusing on mechanistic and essential (as opposed to correlative and dispensable) aspects of the process. As we provide molecularly oriented definitions of terms including intrinsic apoptosis, extrinsic apoptosis, mitochondrial permeability transition (MPT)-driven necrosis, necroptosis, ferroptosis, pyroptosis, parthanatos, entotic cell death, NETotic cell death, lysosome-dependent cell death, autophagy-dependent cell death, immunogenic cell death, cellular senescence, and mitotic catastrophe, we discuss the utility of neologisms that refer to highly specialized instances of these processes. The mission of the NCCD is to provide a widely accepted nomenclature on cell death in support of the continued development of the field