A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows

The effectiveness of sparse matrix techniques for directly solving large-scale linear least-squares problems is severely limited if the system matrix A has one or more nearly dense rows. In this paper, we partition the rows of A into sparse rows and dense rows (A s and A d ) and apply the Schur complement approach. A potential difficulty is that the reduced normal matrix AsTA s is often rank-deficient, even if A is of full rank. To overcome this, we propose explicitly removing null columns of A s and then employing a regularization parameter and using the resulting Cholesky factors as a preconditioner for an iterative solver applied to the symmetric indefinite reduced augmented system. We consider complete factorizations as well as incomplete Cholesky factorizations of the shifted reduced normal matrix. Numerical experiments are performed on a range of large least-squares problems arising from practical applications. These demonstrate the effectiveness of the proposed approach when combined with either a sparse parallel direct solver or a robust incomplete Cholesky factorization algorithm

Role of Plant-Specific N-Terminal Domain of Maize CK2β1 Subunit in CK2β Functions and Holoenzyme Regulation

Protein kinase CK2 is a highly pleiotropic Ser/Thr kinase ubiquituous in eukaryotic organisms. CK2 is organized as a heterotetrameric enzyme composed of two types of subunits: the catalytic (CK2α) and the regulatory (CK2β). The CK2β subunits enhance the stability, activity and specificity of the holoenzyme, but they can also perform functions independently of the CK2 tetramer. CK2β regulatory subunits in plants differ from their animal or yeast counterparts, since they present an additional specific N-terminal extension of about 90 aminoacids that shares no homology with any previously characterized functional domain. Sequence analysis of the N-terminal domain of land plant CK2β subunit sequences reveals its arrangement through short, conserved motifs, some of them including CK2 autophosphorylation sites. By using maize CK2β1 and a deleted version (ΔNCK2β1) lacking the N-terminal domain, we have demonstrated that CK2β1 is autophosphorylated within the N-terminal domain. Moreover, the holoenzyme composed with CK2α1/ΔNCK2β1 is able to phosphorylate different substrates more efficiently than CK2α1/CK2β1 or CK2α alone. Transient overexpression of CK2β1 and ΔNCK2β1 fused to GFP in different plant systems show that the presence of N-terminal domain enhances aggregation in nuclear speckles and stabilizes the protein against proteasome degradation. Finally, bimolecular fluorescence complementation (BiFC) assays show the nuclear and cytoplasmic location of the plant CK2 holoenzyme, in contrast to the individual CK2α/β subunits mainly observed in the nucleus. All together, our results support the hypothesis that the plant-specific N-terminal domain of CK2β subunits is involved in the down-regulation of the CK2 holoenzyme activity and in the stabilization of CK2β1 protein. In summary, the whole amount of data shown in this work suggests that this domain was acquired by plants for regulatory purposes

Modeling and Analysis of the Molecular Basis of Pain in Sensory Neurons

Intracellular calcium dynamics are critical to cellular functions like pain transmission. Extracellular ATP plays an important role in modulating intracellular calcium levels by interacting with the P2 family of surface receptors. In this study, we developed a mechanistic mathematical model of ATP-induced P2 mediated calcium signaling in archetype sensory neurons. The model architecture, which described 90 species connected by 162 interactions, was formulated by aggregating disparate molecular modules from literature. Unlike previous models, only mass action kinetics were used to describe the rate of molecular interactions. Thus, the majority of the 252 unknown model parameters were either association, dissociation or catalytic rate constants. Model parameters were estimated from nine independent data sets taken from multiple laboratories. The training data consisted of both dynamic and steady-state measurements. However, because of the complexity of the calcium network, we were unable to estimate unique model parameters. Instead, we estimated a family or ensemble of probable parameter sets using a multi-objective thermal ensemble method. Each member of the ensemble met an error criterion and was located along or near the optimal trade-off surface between the individual training data sets. The model quantitatively reproduced experimental measurements from dorsal root ganglion neurons as a function of extracellular ATP forcing. Hypothesized architecture linking phosphoinositide regulation with P2X receptor activity explained the inhibition of P2X-mediated current flow by activated metabotropic P2Y receptors. Sensitivity analysis using individual and the whole system outputs suggested which molecular subsystems were most important following P2 activation. Taken together, modeling and analysis of ATP-induced P2 mediated calcium signaling generated qualitative insight into the critical interactions controlling ATP induced calcium dynamics. Understanding these critical interactions may prove useful for the design of the next generation of molecular pain management strategies

Multifaceted roles of GSK-3 and Wnt/β-catenin in hematopoiesis and leukemogenesis: opportunities for therapeutic intervention

Glycogen synthase kinase-3 (GSK-3) is well documented to participate in a complex array of critical cellular processes. It was initially identified in rat skeletal muscle as a serine/threonine kinase that phosphorylated and inactivated glycogen synthase. This versatile protein is involved in numerous signaling pathways that influence metabolism, embryogenesis, differentiation, migration, cell cycle progression and survival. Recently, GSK-3 has been implicated in leukemia stem cell pathophysiology and may be an appropriate target for its eradication. In this review, we will discuss the roles that GSK-3 plays in hematopoiesis and leukemogenesis as how this pivotal kinase can interact with multiple signaling pathways such as: Wnt/β-catenin, phosphoinositide 3-kinase (PI3K)/phosphatase and tensin homolog (PTEN)/Akt/mammalian target of rapamycin (mTOR), Ras/Raf/MEK/extracellular signal-regulated kinase (ERK), Notch and others. Moreover, we will discuss how targeting GSK-3 and these other pathways can improve leukemia therapy and may overcome therapeutic resistance. In summary, GSK-3 is a crucial regulatory kinase interacting with multiple pathways to control various physiological processes, as well as leukemia stem cells, leukemia progression and therapeutic resistance. GSK-3 and Wnt are clearly intriguing therapeutic targets

Assessment of the feasibility of a rehabilitation intervention program for breast cancer survivors with cognitive complaints

To assess the feasibility of a cognitive rehabilitation program in breast cancer survivors (BCS) with persistent post-treatment cognitive complaints. BCS with cognitive complaints, 18-months to 5-years post-treatment, were recruited for a once-weekly, five-week, group cognitive training intervention. Outcome measures included self-reported mood and cognitive function, and neurocognitive tests administered at pre-intervention, immediate-, two-month and four-month post-intervention. A sub-study in eight participants evaluated resting state quantitative electroencephalography (qEEG) changes from pre- to immediate post-intervention in relationship to post-intervention changes in cognitive complaints. Twenty-seven BCS completed the protocol and tolerated the intervention well. We observed significant reductions in total and memory-specific cognitive complaints from pre-intervention to immediate post-intervention (p = 0.031 and p = 0.009, respectively) and at four-months post-intervention (p < 0.0001 and p < 0.001, respectively). Significant improvement in neurocognitive tests were found for Symbol Digit, Stroop, and Trails A tests (df = 26, all p's <0.05). Effect sizes for changes from pre-intervention to immediate and to four-month post intervention ranged from 0.429 to 0.607, and from 0.439 to 0.741, respectively. Increase in qEEG absolute alpha power over the course of the intervention was associated with reduced complaints at immediate post-intervention (r = -0.78, p = 0.021), two-months (r range = -0.76 to -0.82, p-value range 0.004 to 0.03), and four-months (r = -0.71, p = 0.048). A five-week group cognitive training intervention is feasible and well tolerated. Cognitive complaints and neurocognitive test performances showed positive changes. qEEG may serve as a potential biomarker for improvement in self-reported complaints. A randomized clinical trial is underway to test the efficacy of the intervention