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A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in studying numerous subgraph problems, on top of the ordinary graph problems. Many algorithms are proposed in studying subgraph problems, where one common approach is by extracting the patterns and structures of a given graph. Due to the complex structures of certain types of graphs and to improve overall performances of the existing frameworks, machine learning techniques have recently been employed in dealing with various subgraph problems. In this article, we present a comprehensive review on five well known subgraph problems that have been tackled by using machine learning methods. They are subgraph isomorphism (both counting and matching), maximum common subgraph, community detection and community search problems. We provide an outline of each proposed method, and examine its designs and performances. We also explore non-learning-based algorithms for each problem and a brief discussion is given. We then suggest some promising research directions in this area, hoping that relevant subgraph problems can be tackled by using a similar strategy. Since there is a huge growth in employing machine learning techniques in recent years, we believe that this survey will serve as a good reference point to relevant research communities., Comment: v1: 41 pages; v2: 40 pages ; v3: This version focuses on just subgraph problems (discussions on other classic graph problems can be found in the earlier versions)

In a pancreatic tumor microenvironment, activated pancreatic stellate cells (PSCs) produce extracellular matrix (ECM) to form a barrier to drug penetration. Moreover, the interaction between cancer cells and activated PSCs promotes the tumor growth. Vitamin D receptor (VDR), as a key regulator to promote the recovery of PSCs to the resting state, is an attractive therapeutic target for pancreatic cancer. Herein, we reported the design and synthesis of 57 nonsecosteroidal VDR modulators based on the skeleton of phenyl-pyrrolyl pentane. Among them, compounds C4, I5, and I8 exhibited excellent VDR affinity and effective inhibition of the activation of PSCs, as well as potent suppression of the interaction between cancer cells and PSCs in vitro. In vivo, compound I5 combined with gemcitabine achieved efficacious antitumor activity without causing hypercalcemia. In conclusion, the compounds designed in our study can remodel the tumor microenvironment and are expected to be candidates for the treatment of pancreatic cancer.

Modulating the vitamin D receptor (VDR) is an effective way to treat for cancer. We previously reported a potent non-secosteroidal VDR modulator (sw-22) with modest anti-tumor activity, which could be due to its undesirable physicochemical and pharmacokinetic properties. In this study, we investigated the structure-activity and structure-property relationships around the 2′-hydroxyl group of sw-22 to improve the physicochemical properties, pharmacokinetic properties and anti-tumor activity. Compounds 19a and 27b, the potent non-secosteroidal VDR modulators, were identified as the most effective molecules in inhibiting the proliferation of three cancer cell lines, particularly breast cancer cells, with a low IC50 via the distribution of cell cycle and induction of apoptosis by stimulating the expression of p21, p27 and Bax. Further investigation revealed that 19a and 27b possessed favorable rat microsomal metabolic stability (2.22 and 2.3 times, respectively, more stable than sw-22), solubility (43.9 and 50.2 times, respectively, more soluble than sw-22) and in vivo pharmacokinetic properties. In addition, 19a and 27b showed excellent in vivo anti-tumor activity without cause hypercalcemia, which is the main side effect of marketed VDR modulators. In summary, the favorable physicochemical properties, pharmacokinetic properties and anti-tumor activity of 19a and 27b highlight their potential therapeutic applications in cancer treatment.

Chronic pancreatitis (CP) is a serious disease that characterized by the progressive replacement of functional pancreas tissue by fibrotic tissue. Vitamin D receptor (VDR) plays a critical role in the development of CP, since it inhibits excessive deposition of extracellular matrix (ECM) in activated pancreatic stellate cells (PSCs). Herein, a novel series of non-secosteriodal VDR ligands were designed and synthesized, and their VDR affinity and anti-fibrosis activity were evaluated. The identification of the potent compound 9c was found over structural optimization, which inhibited ECM deposition and fibrotic gene expression in the western blot and qPCR assays, respectively. Further investigation revealed that compound 9c inhibited pancreatic fibrosis in vivo without increase on serum calcium, which could cause hypercalcemia. These results provide novel insight in possible drug discovery for the treatment of CP using non-secosteroidal VDR modulators.