Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition

In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer formulation, we derive its linear counterparts and show that they could be stronger than existing linear formulations. We also develop a variant of Jensen's inequality that extends the one for stochastic program. To solve this challenging problem, we present a variant of Benders decomposition method in bilinear form, which actually provides an easy-to-use algorithm framework for further improvements, along with a few enhancement strategies based on structural properties or Jensen's inequality. Computational study shows that the presented Benders decomposition method, jointly with appropriate enhancement techniques, outperforms a commercial solver by an order of magnitude on solving chance constrained program or detecting its infeasibility

Pharmacological regulation and function of store-operated calcium channels

Store-operated Ca²⁺ entry (SOCE) is an important Ca²⁺ influx pathway existing in almost all types of mammalian cell. STIM1, ORAI and TRPC have been regarded as the molecular basis of SOCE. Once the endoplasmic reticulum (ER) Ca²⁺ store is depleted, STIM1 proteins move to the plasma membrane and activate ORAI and TRPC channels to allow Ca²⁺ influx. In this thesis, the pharmacological aspects andregulatory mechanisms of SOCE were investigated using HEK293 cells overexpressing STIM1, ORAI or TRPC genes. The expression and function of TRPC channels and their spliced variants in native cells were also examined.Using live-cell imaging, the cytosolic clustering of STIM1-EYFP was observed after challenging with the compounds including 2-APB, flufenamic acid, 4-chloro-3-ethylphenol, U73122 and FCCP. The aggregation of STIM1 in the cytosol could be a novel mechanism for the inhibition of SOCE, and the process did not rely on the depletion of ER Ca²⁺ store. The ryanodine receptor agonist 4-chloro-3-ethylphenol not only caused Ca²⁺ release and cytosolic STIM1 clustering, but also nonselectively inhibited ORAI1/2/3 and TRPC3/4/5/6 channels.The sensitivity of TRP channels to metal ions was also investigated using patch clamp. Micromolar Cu²⁺ significantly increased the currents of TRPC3/4/5/6 channels. The glutamic acid (E542/E543) and cysteine (C554) residues in the extracellular pore region of TRPC4 were involved in the channel opening by Cu²⁺. Moreover, Cu²⁺ showed inhibitory effect on TRPM2 channel.TRPC1/3/4/6 and multiple alternatively spliced variants were detected in the human ovarian adenocarcinoma-derived SKOV3 cells. Blockade of TRPC channel activity by 2-APB, SKF-96365, TRPC pore-blocking antibodies or transfection with TRPC siRNA significantly inhibited SKOV3 cell proliferation. Overexpression of TRPC genes promoted colony growth of SKOV3 cells.It is concluded that cytosolic STIM1 movement could be a new pharmacological target for SOCE. 4-Chloro-3-ethylphenol and Cu²⁺ are new modulators of ORAI and TRP channels. TRPC channels and their spliced variants are important for cancer cell growth. These findings provide novel insights into the pharmacology and pathophysiology of store-operated channels