Optimality of broken extremals

In this paper we analyse the optimality of broken Pontryagin extremal for an n-dimensional affine control system with a control parameter, taking values in a k- dimensional closed ball. We prove the optimality of broken normal extremals when n = 3 and the controllable vector fields form a contact distribution, and when the Lie algebra of the controllable fields is locally orthogonal to the singular locus and the drift does not belong to it. Moreover, if k = 2, we show the optimality of any broken extremal even abnormal when the controllable fields do not form a contact distribution in the point of singularity.Comment: arXiv admin note: text overlap with arXiv:1610.0675

The androgen receptor controls expression of the cancer-associated sTn antigen and cell adhesion through induction of ST6GalNAc1 in prostate cancer

Patterns of glycosylation are important in cancer, but the molecular mechanisms that drive changes are often poorly understood. The androgen receptor drives prostate cancer (PCa) development and progression to lethal metastatic castration-resistant disease. Here we used RNA-Seq coupled with bioinformatic analyses of androgen-receptor (AR) binding sites and clinical PCa expression array data to identify ST6GalNAc1 as a direct and rapidly activated target gene of the AR in PCa cells. ST6GalNAc1 encodes a sialytransferase that catalyses formation of the cancer-associated sialyl-Tn antigen (sTn), which we find is also induced by androgen exposure. Androgens induce expression of a novel splice variant of the ST6GalNAc1 protein in PCa cells. This splice variant encodes a shorter protein isoform that is still fully functional as a sialyltransferase and able to induce expression of the sTn-antigen. Surprisingly, given its high expression in tumours, stable expression of ST6GalNAc1 in PCa cells reduced formation of stable tumours in mice, reduced cell adhesion and induced a switch towards a more mesenchymal-like cell phenotype in vitro. ST6GalNAc1 has a dynamic expression pattern in clinical datasets, beingsignificantly up-regulated in primary prostate carcinoma but relatively down-regulated in established metastatic tissue. ST6GalNAc1 is frequently upregulated concurrently with another important glycosylation enzyme GCNT1 previously associated with prostate cancer progression and implicated in Sialyl Lewis X antigen synthesis. Together our data establishes an androgen-dependent mechanism for sTn antigen expression in PCa, and are consistent with a general role for the androgen receptor in driving important coordinate changes to the glycoproteome during PCa progression

Mutational dynamics and immune evasion in diffuse large B-cell lymphoma explored in a relapse-enriched patient series

Peer reviewe

Collision tumors revealed by prospectively assessing subtype-defining molecular alterations in 904 individual prostate cancer foci.

BACKGROUNDProstate cancer is multifocal with distinct molecular subtypes. The utility of genomic subtyping has been challenged due to inter- and intrafocal heterogeneity. We sought to characterize the subtype-defining molecular alterations of primary prostate cancer across all tumor foci within radical prostatectomy (RP) specimens and determine the prevalence of collision tumors.METHODSFrom the Early Detection Research Network cohort, we identified 333 prospectively collected RPs from 2010 to 2014 and assessed ETS-related gene (ERG), serine peptidase inhibitor Kazal type 1 (SPINK1), phosphatase and tensin homolog (PTEN), and speckle type BTB/POZ protein (SPOP) molecular status. We utilized dual ERG/SPINK1 immunohistochemistry and fluorescence in situ hybridization to confirm ERG rearrangements and characterize PTEN deletion, as well as high-resolution melting curve analysis and Sanger sequencing to determine SPOP mutation status.RESULTSBased on index focus alone, ERG, SPINK1, PTEN, and SPOP alterations were identified in 47.5%, 10.8%, 14.3%, and 5.1% of RP specimens, respectively. In 233 multifocal RPs with ERG/SPINK1 status in all foci, 139 (59.7%) had discordant molecular alterations between foci. Collision tumors, as defined by discrepant ERG/SPINK1 status within a single focus, were identified in 29 (9.4%) RP specimens.CONCLUSIONInterfocal molecular heterogeneity was identified in about 60% of multifocal RP specimens, and collision tumors were present in about 10%. We present this phenomenon as a model for the intrafocal heterogeneity observed in previous studies and propose that future genomic studies screen for collision tumors to better characterize molecular heterogeneity.FUNDINGEarly Detection Research Network US National Cancer Institute (NCI) 5U01 CA111275-09, Center for Translational Pathology at Weill Cornell Medicine (WCM) Department of Pathology and Laboratory Medicine, US NCI (WCM SPORE in Prostate Cancer, P50CA211024-01), R37CA215040, Damon Runyon Cancer Research Foundation, US MetLife Foundation Family Clinical Investigator Award, Norwegian Cancer Society (grant 208197), and South-Eastern Norway Regional Health Authority (grant 2019016 and 2020063)

Multilevel genomics of colorectal cancers with microsatellite instability—clinical impact of JAK1 mutations and consensus molecular subtype 1

Background Approximately 15% of primary colorectal cancers have DNA mismatch repair deficiency, causing a complex genome with thousands of small mutations—the microsatellite instability (MSI) phenotype. We investigated molecular heterogeneity and tumor immunogenicity in relation to clinical endpoints within this distinct subtype of colorectal cancers. Methods A total of 333 primary MSI+ colorectal tumors from multiple cohorts were analyzed by multilevel genomics and computational modeling—including mutation profiling, clonality modeling, and neoantigen prediction in a subset of the tumors, as well as gene expression profiling for consensus molecular subtypes (CMS) and immune cell infiltration. Results Novel, frequent frameshift mutations in four cancer-critical genes were identified by deep exome sequencing, including in CRTC1, BCL9, JAK1, and PTCH1. JAK1 loss-of-function mutations were validated with an overall frequency of 20% in Norwegian and British patients, and mutated tumors had up-regulation of transcriptional signatures associated with resistance to anti-PD-1 treatment. Clonality analyses revealed a high level of intra-tumor heterogeneity; however, this was not associated with disease progression. Among the MSI+ tumors, the total mutation load correlated with the number of predicted neoantigens (P = 4 × 10−5), but not with immune cell infiltration—this was dependent on the CMS class; MSI+ tumors in CMS1 were highly immunogenic compared to MSI+ tumors in CMS2-4. Both JAK1 mutations and CMS1 were favorable prognostic factors (hazard ratios 0.2 [0.05–0.9] and 0.4 [0.2–0.9], respectively, P = 0.03 and 0.02). Conclusions Multilevel genomic analyses of MSI+ colorectal cancer revealed molecular heterogeneity with clinical relevance, including tumor immunogenicity and a favorable patient outcome associated with JAK1 mutations and the transcriptomic subgroup CMS1, emphasizing the potential for prognostic stratification of this clinically important subtype. See related research highlight by Samstein and Chan 10.1186/s13073-017-0438-