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Bisubmodularity-a natural generalization of submodularity-applies to set functions with two arguments and appears in a broad range of applications, including coupled sensor placement in infrastructure, coupled feature selection in machine learning, and drug-drug interaction detection in healthcare. In this paper, we study maximization problems with bisubmodular objective functions. We propose valid linear inequalities, namely the bisubmodular inequalities, for the hypograph of any bisubmodular function. We show that maximizing a bisubmodular function is equivalent to solving a mixed-integer linear program with exponentially many bisubmodular inequalities. Using this representation in a delayed constraint generation framework, we design the first exact algorithm to solve general bisubmodular maximization problems. Our computational experiments on the coupled sensor placement problem demonstrate the efficacy of our algorithm in constrained nonlinear bisubmodular maximization problems for which no existing exact methods are available.

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Novel 2-arylmethoxy-4-(2,2′-dihalogen-substituted biphenyl-3-ylmethoxy) benzylamine derivatives were designed, synthesized, and evaluated in vitro and in vivo against cancers as PD-1/PD-L1 inhibitors. Through the computer-aided structural optimization and the homogeneous time-resolved fluorescence (HTRF) assay, compound A56 was found to most strongly block the PD-1/PD-L1 interaction with an IC50 value of 2.4 ± 0.8 nM and showed the most potent activity. 1H NMR titration results indicated that A56 can tightly bind to the PD-L1 protein with K D < 1 μM. The X-ray diffraction data for the cocrystal structure of the A56/PD-L1 complex (3.5 Å) deciphered a novel binding mode in detail, which can account for its most potent inhibitory activity. Cell-based assays further demonstrated the strong ability of A56 as an hPD-1/hPD-L1 blocker. Especially in an hPD-L1 MC38 humanized mouse model, A56 significantly inhibited tumor growth without obvious toxicity, with a TGI rate of 55.20% (50 mg/kg, i.g.). In conclusion, A56 is a promising clinical candidate worthy of further development.