Hepatocellular carcinoma (HCC) has a poor prognosis due to widespread intrahepatic and extrahepatic metastases. There is an urgent need to understand signaling cascades that promote disease progression. Aspartyl-(Asparaginyl)-β-hydroxylase (ASPH) is a cell surface enzyme that generates enhanced cell motility, migration, invasion and metastatic spread in HCC. We hypothesize that inhibition of its enzymatic activity could have antitumor effects. Small molecule inhibitors (SMIs) were developed based on the crystal structure of the ASPH catalytic site followed by computer assisted drug design. Candidate compounds were tested for inhibition of β-hydroxylase activity and selected for their capability to modulate cell proliferation, migration, invasion and colony formation in vitro and to inhibit HCC tumor growth in vivo using orthotopic and subcutaneous murine models. The biologic effects of SMIs on the Notch signaling cascade were evaluated. The SMI inhibitor MO-I-1100 was selected since it reduced ASPH enzymatic activity by 80% and suppressed HCC cell migration, invasion and anchorage independent growth. Furthermore, substantial inhibition of HCC tumor growth and progression was observed in both animal models. The mechanism(s) for this antitumor effect was associated with reduced activation of Notch signaling both in vitro and in vivo. Conclusions These studies suggest that the enzymatic activity of ASPH was important for hepatic oncogenesis. Reduced β-hydroxylase activity generated by the SMI MO-I-1100 led to antitumor effects through inhibiting Notch signaling cascade in HCC. ASPH promotes the generation of an HCC malignant phenotype and represents an attractive molecular target for therapy of this fatal disease.

The AlkB protein is a repair enzyme that uses an α-ketoglutarate/Fe(II)-dependent mechanism to repair alkyl DNA adducts. AlkB has been reported to repair highly susceptible substrates, such as 1-methyladenine and 3-methylcytosine, more efficiently in ss-DNA than in ds-DNA. Here, we tested the repair of weaker AlkB substrates 1-methylguanine and 3-methylthymine, and found that AlkB prefers to repair them in ds-DNA. We also discovered AlkB and its human homologs, ABH2 and ABH3, are able to repair the aforementioned adducts when the adduct is present in a mismatched base pair. These observations demonstrate the strong adaptability of AlkB on repairing various adducts in different environments.

Pancreatic cancer (PC) is one of the leading causes of cancer related deaths due to aggressive progression and metastatic spread. Aspartate β-hydroxylase (ASPH), a cell surface protein that catalyzes the hydroxylation of epidermal growth factor (EGF)-like repeats in Notch receptors and ligands, is highly overexpressed in PC. ASPH upregulation confers a malignant phenotype characterized by enhanced cell proliferation, migration, invasion and colony formation in vitro as well as PC tumor growth in vivo. The transforming properties of ASPH depend on enzymatic activity. ASPH links PC growth factor signaling cascades to Notch activation. A small molecule inhibitor of β-hydroxylase activity was developed and found to reduce PC growth by downregulating the Notch signaling pathway. These findings demonstrate the critical involvement of ASPH in PC growth and progression, provide new insight into the molecular mechanisms leading to tumor development and growth and have important therapeutic implications.

This paper constitutes our initial effort in developing sparse grid discontinuous Galerkin (DG) methods for high-dimensional partial differential equations (PDEs). Over the past few decades, DG methods have gained popularity in many applications due to their distinctive features. However, they are often deemed too costly because of the large number of degrees of freedom of the approximation space, which are the main bottleneck for simulations in high dimensions. In this paper, we develop sparse grid DG methods for elliptic equations with the aim of breaking the curse of dimensionality. Using a hierarchical basis representation, we construct a sparse finite element approximation space, reducing the degrees of freedom from the standardproblems, where h is the uniform mesh size in each dimension. Our method, based on the interior penalty (IP) DG framework, can achieve accuracy of O(h k | log 2 h| d−1 ) in the energy norm, where k is the degree of polynomials used. Error estimates are provided and confirmed by numerical tests in multi-dimensions.

In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high order weighted essentially non-oscillatory (WENO) methods for scalar hyperbolic conservation laws, to develop a class of high order positivity-preserving finite difference WENO method for the ideal magnetohydrodynamic (MHD) equations. Our scheme, under the constrained transport (CT) framework, can achieve high order accuracy, a discrete divergence-free condition and positivity of the numerical solution simultaneously. Numerical examples in 1D, 2D and 3D are provided to demonstrate the performance of the proposed method. literature [6,11,35]. To design divergence-free methods for solving the ideal MHD equations, the CT methodology arises as one important approach, see [1,5,9,10,11,12,15,25,26, 30, 32,33,35,34, 31] for references. Following [9,15,16, 30, 31], we propose to conduct our investigation within the CT framework in this paper.Another major focus of this paper is the design of high-order schemes that preserve the positivity of the density and pressure of the MHD system. Even with divergencefree methods, negative density or/and pressure can still be observed in numerical simulations, such as those for the low-β plasma. This can lead to a complex wave speed that breaks the hyperbolicity of the system and causes the numerical simulations to break down. A lot of efforts have been dedicated addressing this issue in the literature. For instance, Balsara and Spicer [4] proposed a strategy to maintain the positivity of pressure by switching the Riemann solvers based on different wave situations. Janhunen [18] designed a new Riemann solver for the modified ideal MHD equations and demonstrated its positivity-preserving property numerically. In [36], a conservative second-order MUSCL-Hancock scheme was shown to be positivity-preserving for the 1D ideal MHD equations and the extension to multi-dimensional (multi-D) cases was constructed based on similar ideas as Powell's 8-wave formulation [28,29]. Balsara [2] developed a high-order positivity-preserving scheme for ideal MHD through limiting high-order numerical solutions by a conservative bounded solution. Another class of important methods for the ideal MHD equations is discontinuous Galerkin (DG) methods [21,22,23, 31,41]. Recently, Cheng et al. proposed positivity-preserving DG and central DG methods for the ideal MHD equations [7], in which they generalized Zhang and Shu's positivity-preserving limiters for the compressible Euler equations [42]. In [7], it was proven that the first-order Lax-Fridrichs scheme is positivity-preserving for the 1D MHD under the restriction CFL≤ 0.5. This first-order scheme also serves as the building block for the positivity-preserving scheme in this paper.Besides the aforementioned work for MHD equations, several high-order positivitypreserving schemes have been developed recently for compressible Euler equations. Zhang and Shu developed arbitrary-order positivity-preserving finite volume WENO and DG methods by limiting ...

In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient high-order WENO spatial discretizations with high-order strong stability-preserving Runge-Kutta (SSP-RK) time-stepping schemes. Numerical results have shown that with such methods we are able to resolve solution structures that are only visible at much higher grid resolutions with lower-order schemes. The key challenge in applying such methods to ideal MHD is to control divergence errors in the magnetic field. We achieve this by augmenting the base scheme with a novel high-order constrained transport approach that updates the magnetic vector potential. The predicted magnetic field from the base scheme is replaced by a divergence-free magnetic field that is obtained from the curl of this magnetic potential. The non-conservative weakly hyperbolic system that the magnetic vector potential satisfies is solved using a version of FD-WENO developed for Hamilton-Jacobi equations. The resulting numerical method is endowed with several important properties: (1) all quantities, including all components of the magnetic field and magnetic potential, are treated as point values on the same mesh (i.e., there is no mesh staggering); (2) both the spatial and temporal orders of accuracy are fourth-order; (3) no spatial integration or multidimensional reconstructions are needed in any step; and (4) special limiters in the magnetic vector potential update are used to control unphysical oscillations in the magnetic field. Several 2D and 3D numerical examples are presented to verify the order of accuracy on smooth test problems and to show high-resolution on test problems that involve shocks.

Cancer-associated mutations often lead to perturbed cellular energy metabolism and accumulation of potentially harmful oncometabolites. One example is the chiral molecule 2-hydroxyglutarate (2HG); its two stereoisomers (D- and L-2HG) have been found with abnormally high concentrations in tumors featuring anomalous metabolic pathways. 2HG has been demonstrated to competitively inhibit several α-ketoglutarate (αKG)- and non-heme iron-dependent dioxygenases, including some of the AlkB family DNA repair enzymes, such as ALKBH2 and ALKBH3. However, previous studies have only provided the IC50 values of D-2HG on the enzymes and the results have not been correlated to physiologically relevant concentrations of 2HG and αKG in cancer cells. In this work, we carried out detailed kinetic analyses of DNA repair reactions catalyzed by ALKBH2, ALKBH3 and the bacterial AlkB in the presence of D- and L-2HG in both double and single stranded DNA contexts. We determined kinetic parameters of inhibition, including kcat, KM, and Ki. We also correlated the relative concentrations of 2HG and αKG previously measured in tumor cells with the inhibitory effect of 2HG on the AlkB family enzymes. Both D- and L-2HG significantly inhibited the human DNA repair enzymes ALKBH2 and ALKBH3 under pathologically relevant concentrations (73–88% for D-2HG and 31–58% for L-2HG inhibition). This work provides a new perspective that the elevation of either D- or L-2HG in cancer cells may contribute to an increased mutation rate by inhibiting the DNA repair carried out by the AlkB family enzymes and thus exacerbate the genesis and progression of tumors.

A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This added-mass partitioned (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous addeddamping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added-mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forces on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this first part of a two-part series, the properties of the AMP scheme are motivated and evaluated through the development and analysis of some model problems. The analysis shows when and why the traditional partitioned scheme becomes unstable due to either added-mass or added-damping effects. The analysis also identifies the proper form of the added-damping which depends on the discrete time-step and the grid-spacing normal to the rigid body. The results of the analysis are confirmed with numerical simulations that also demonstrate a second-order accurate implementation of the AMP scheme.