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

Colorectal Cancer Consensus Molecular Subtypes Translated to Preclinical Models Uncover Potentially Targetable Cancer Cell Dependencies

Purpose: Response to standard oncologic treatment is limited in colorectal cancer. The gene expression-based consensus molecular subtypes (CMS) provide a new paradigm for stratified treatment and drug repurposing; however, drug discovery is currently limited by the lack of translation of CMS to preclinical models. Experimental Design: We analyzed CMS in primary colorectal cancers, cell lines, and patient-derived xenografts (PDX). For classification of preclinical models, we developed an optimized classifier enriched for cancer cell-intrinsic gene expression signals, and performed high-throughput in vitro drug screening (n = 459 drugs) to analyze subtype-specific drug sensitivities. Results: The distinct molecular and clinicopathologic characteristics of each CMS group were validated in a single-hospital series of 409 primary colorectal cancers. The new, cancer cell-adapted classifier was found to perform well in primary tumors, and applied to a panel of 148 cell lines and 32 PDXs, these colorectal cancer models were shown to recapitulate the biology of the CMS groups. Drug screening of 33 cell lines demonstrated subtype-dependent response profiles, confirming strong response to EGFR and HER2 inhibitors in the CMS2 epithelial/canonical group, and revealing strong sensitivity to HSP90 inhibitors in cells with the CMS1 microsatellite instability/immune and CMS4 mesenchymal phenotypes. This association was validated in vitro in additional CMS-predicted cell lines. Combination treatment with 5-fluorouracil and luminespib showed potential to alleviate chemoresistance in a CMS4 PDX model, an effect not seen in a chemosensitive CMS2 PDX model. Conclusions: We provide translation of CMS classification to preclinical models and uncover a potential for targeted treatment repurposing in the chemoresistant CMS4 group. (C) 2017 AACR.Peer reviewe

Patient-Derived Organoids from Multiple Colorectal Cancer Liver Metastases Reveal Moderate Intra-patient Pharmacotranscriptomic Heterogeneity

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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-

Long noncoding RNA MIR31HG is a bona fide prognostic marker with colorectal cancer cell-intrinsic properties

Elevated miR‐31 expression is associated with poor outcome in colorectal cancer (CRC). Whether the prognostic information is independent of known molecular subgroups and gene expression‐based consensus molecular subtypes (CMS) is currently unknown. To investigate this, we analyzed nearly 2000 CRC biopsies and preclinical models. The expression of miR‐31‐5p and its host transcript, long noncoding RNA MIR31HG, was strongly correlated (Spearman's ρ > 0.80). MIR31HG outlier expression was observed in 158/1265 (12%) of pCRCs and was associated with depletion of CMS2‐canonical subgroup (odds ratio = 0.21 [0.11–0.35]) and shorter relapse‐free survival (RFS) in multivariable analysis (adjusted hazard ratio = 2.2 [1.6–3.0]). For stage II disease, 5‐year RFS for patients with MIR31HG outlier status was 49% compared to 77% for those with normal‐like expression. MIR31HG outlier status was associated with inferior outcome also within clinical high risk groups and within the poor prognostic CMS4‐mesenchymal gene expression subtype specifically. Preclinical models with MIR31HG outlier expression were characterized by reduced expression of MYC targets as well as elevated epithelial‐mesenchymal transition, TNF‐α/NFκB, TGF‐β, and IFN‐α/γ gene expression signatures, indicating cancer cell‐intrinsic properties resembling the CMS4 subgroup—associations which were recapitulated in patient biopsies. Moreover, the prognostic value of MIR31HG outlier status was independent of cytotoxic T lymphocyte and fibroblast infiltration. We here present evidence that MIR31HG expression provides clinical stratification beyond major gene expression phenotypes and tumor immune and stromal cell infiltration and propose a model where increased expression is an indicator of a cellular state conferring intrinsic invasive and/or immuno‐evasive capabilities

Alternative splicing expands the prognostic impact of KRAS in microsatellite stable primary colorectal cancer

KRAS mutation is a well‐known marker for poor response to targeted treatment and patient prognosis in microsatellite stable (MSS) colorectal cancer (CRC). However, variation in clinical outcomes among patients wild‐type for KRAS underlines that this is not a homogeneous population. Here, we evaluated the prognostic impact of KRAS alternative splicing in relation to mutation status in a single‐hospital series of primary MSS CRCs (N = 258). Using splicing‐sensitive microarrays and RNA sequencing, the relative expression of KRAS‐4A versus KRAS‐4B transcript variants was confirmed to be down‐regulated in CRC compared to normal colonic mucosa (N = 41; p ≤ 0.001). This was independent of mutation status, however, gene set enrichment analysis revealed that the effect of splicing on KRAS signaling was specific to the KRAS wild‐type subgroup, in which low relative KRAS‐4A expression was associated with a higher level of KRAS signaling (p = 0.005). In concordance, the prognostic value of KRAS splicing was also dependent on mutation status, and for patients with Stage I–III KRAS wild‐type MSS CRC, low relative KRAS‐4A expression was associated with inferior overall survival (HR: 2.36, 95% CI: 1.07–5.18, p = 0.033), a result not found in mutant cases (pinteraction = 0.026). The prognostic association in the wild‐type subgroup was independent of clinicopathological factors, including cancer stage in multivariable analysis (HR: 2.68, 95% CI: 1.18–6.09, p = 0.018). This suggests that KRAS has prognostic value beyond mutation status in MSS CRC, and highlights the importance of molecular heterogeneity in the clinically relevant KRAS wild‐type subgroup

Technical differences between sequencing and microarray platforms impact transcriptomic subtyping of colorectal cancer

Gene expression profiling has increasing relevance in the molecular screening of patients with colorectal cancer (CRC). We investigated potential platform-specific effects on transcriptomic subtyping according to established frameworks by comparisons of expression profiles from RNA sequencing and exon-resolution microarrays in 126 primary microsatellite stable CRCs. There was a strong platform correspondence in global gene expression levels, albeit with systematic technical bias likely attributed to few sequencing reads covering short (<2000 nucleotides) and/or lowly expressed genes (<1 FPKM), as well as over-saturation of highly expressed genes on microarrays. Classification concordances according to both the consensus molecular subtypes and CRC intrinsic subtypes (CRIS) were also strong, but with disproportionate subtype distributions between platforms caused by frequent disagreements in adherence to sample classification thresholds. Subtypes defined largely by genes expressed at low levels, including the CRIS-D subtype and the estimated level of tumor-infiltrating cytotoxic lymphocytes, had a weaker correspondence in classification metrics between platforms. In conclusion, even subtle differences between platforms suggest that clinical translation of transcriptomic CRC subtyping frameworks is dependent on assay standardization, and systematic technical biases reinforce the need for careful selection of classifier genes

Prognostic, predictive, and pharmacogenomic assessments of CDX2 refine stratification of colorectal cancer

We aimed to refine the value of CDX2 as an independent prognostic and predictive biomarker in colorectal cancer (CRC) according to disease stage and chemotherapy sensitivity in preclinical models. CDX2 expression was evaluated in 1045 stage I-IV primary CRCs by gene expression (n = 403) or immunohistochemistry (n = 642) and in relation to 5-year relapse-free survival (RFS), overall survival (OS), and chemotherapy. Pharmacogenomic associations between CDX2 expression and 69 chemotherapeutics were assessed by drug screening of 35 CRC cell lines. CDX2 expression was lost in 11.6% of cases and showed independent poor prognostic value in multivariable models. For individual stages, CDX2 was prognostic only in stage IV, independent of chemotherapy. Among stage I-III patients not treated in an adjuvant setting, CDX2 loss was associated with a particularly poor survival in the BRAF-mutated subgroup, but prognostic value was independent of microsatellite instability status and the consensus molecular subtypes. In stage III, the 5-year RFS rate was higher among patients with loss of CDX2 who received adjuvant chemotherapy than among patients who did not. The CDX2-negative cell lines were significantly more sensitive to chemotherapeutics than CDX2-positive cells, and the multidrug resistance genes MDR1 and CFTR were significantly downregulated both in CDX2-negative cells and in patient tumors. Loss of CDX2 in CRC is an adverse prognostic biomarker only in stage IV disease and appears to be associated with benefit from adjuvant chemotherapy in stage III. Early-stage patients not qualifying for chemotherapy might be reconsidered for such treatment if their tumor has loss of CDX2 and mutated BRAF.Peer reviewe