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Binary relation plays a prominent role in the study of mathematics in particular applied mathematics. Recently, some authors generated closure spaces through relation and made a comparative study of topological properties in the space by varying the property on the relation. In this paper, we have studied closure spaces generated from a tree through binary relation and observed that under certain situation the space generated from a tree is normal.

Background: Activating mutations in KRAS, NRAS, and BRAF are known to cause resistance to anti-EGFR therapy. However, only ~40% of colorectal cancer (CRC) patients with RASWT tumors respond to that treatment. We aim to leverage tumor transcriptomes to predict response to anti-EGFR antibody (e.g., cetuximab) treatment and understand intrinsic resistance mechanisms in CRC. Experimental Design: Transcriptomic profiles with RAS mutation status from two clinical (Okita et al., n = 135; Khambata-Ford et al., n = 68), and preclinical cohorts of CRC cell lines (Medico et al., n = 146) and PDX models (Bertotti et al., n = 216) treated with cetuximab were downloaded from Gene Expression Omnibus (GEO). Each cohort was divided into RASWT and RASMut groups, and transcriptomic profiles were used to assign consensus molecular subtypes (CMS) to each sample. Gene Set Enrichment Analysis (GSEA) was performed to identify resistant pathways in each CMS RASWT group. Results: Restricting to RASWT patients (n = 80) in Okita et al. cohort, we observed that CMS2 tumors had significantly higher disease control rates (DCR) [92% (33/36); chi-square p = 0.03] with cetuximab in combination with doublet chemotherapy relative to CMS1 [50% (2/4)], CMS3 [59% (13/22)], and CMS4 [83% (15/18)] tumors. RASWT CMS2 tumors (n = 43) also showed significantly higher DCR [68% (15/22); chi-square p = 0.03] with single-agent cetuximab compared to CMS1 [0% (0/4)], and CMS4 [29% (5/17)] tumors in Khambata-Ford et al. cohort. In multivariate analysis including both CMS and tumor sidedness, only CMS2 (HR = 0.62, p = 0.03) was significant predictor of cetuximab response in Okita et al. cohort. CMS1 tumors showed worst treatment response irrespective of tumor sidedness [DCR, left: 50% (1/2) vs right: 50% (1/2)]. In contrast both left and right-sided CMS2 tumors responded well [DCR, left: 91% (31/34) vs 100% (2/2)] to cetuximab plus chemotherapy [PFS, 7.9 vs 7 months; log-rank test p = 0.7]. In microsatellite stable (MSS) RASWT cell lines (n = 27), CMS2 cells lines were most sensitive [59% (7/17)] relative to CMS4 [0% (0/10)]. In MSS RASWT PDX models (n = 60), CMS2 had highest DCR [75% (18/24)] than CMS1 [36% (4/11)], CMS3 [55% (5/9)], CMS4 [62% (10/16)]. We found Myc, E2F, and mTOR gene sets/pathways were consistently enriched in resistant patients, cell lines, and PDX models (Normalized enrichment score > 1, FDR < 0.25). Small molecule inhibitors of Myc (JQ1), E2F (AZD7762 & MK-8776), and mTOR (Everolimus) pathways in resistant CRC cell line (HT55) exhibited additive, but not synergistic, effects with cetuximab. Conclusions: These data suggest that tumor transcriptional profiles are a better predictor of anti-EGFR response than tumor-sidedness. Use of CMS to predict anti-EGFR response should be validated in a larger, prospective study. Activation of Myc, E2F, and mTOR pathways are associated with cetuximab resistance in colorectal cancer cells. Citation Format: Saikat Chowdhury, Ria Gupta, Valsala Haridas, Mohammad A. Zeineddine, Scott Kopetz, John Paul Shen. Consensus molecular subtypes (CMS) of colorectal cancer predict anti-EGFR response irrespective of tumor sidedness [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 1246.

PURPOSE Activating mutations in KRAS, NRAS, and BRAF are known to cause resistance to anti–epidermal growth factor receptor (EGFR) therapy; however, only approximately 40% of patients with colorectal cancer (CRC) with RAS WT tumors respond to anti-EGFR treatment. We sought to discover novel biomarkers to predict response to anti-EGFR antibody treatment in CRC and to understand mechanisms of resistance to anti-EGFR therapy. MATERIALS AND METHODS Transcriptomic profiles from three clinical and two preclinical cohorts treated with cetuximab were used to assign consensus molecular subtypes (CMS) to each sample and correlated with outcomes. RESULTS Restricting to RAS WT patients, we observed that CMS2 tumors (canonical subtype) had significantly higher response rates relative to other CMS when treated with cetuximab combination with doublet chemotherapy (Okita et al cohort: 92% disease control rate (DCR) for CMS2, chi-square P = .04; CALGB/SWOG 80405 cohort: 90% objective response rate (ORR) for CMS2, chi-square P < .001) and with single-agent cetuximab (68%, chi-square P = .01). CMS2 tumors showed best response among right-sided (ORR = 80%) and left-sided (ORR = 92%) tumors in the CALGB/SWOG 80405 cohort. CMS2 cells lines were most likely to be sensitive to cetuximab (60%) and CMS2 patient-derived xenograft had the highest DCR (84%). We found Myc, E2F, and mammalian target of rapamycin pathways were consistently upregulated in resistant samples (enrichment score >1, false discovery rate <0.25). Inhibitors of these pathways in resistant cell lines exhibited additive effects with cetuximab. CONCLUSION These data suggest that CRC transcriptional profiles, when used to assign CMS, provide additional ability to predict response to anti-EGFR therapy relative to using tumor sidedness alone. Notably both right-sided and left-sided CMS2 tumors had excellent response, suggesting that anti-EGFR therapy be included as a treatment option for right-sided CMS2 tumors.