Uniqueness and Stability of Optimizers for a Membrane Problem

We investigate a PDE-constrained optimization problem, with an intuitive interpretation in terms of the design of robust membranes made out of an arbitrary number of different materials. We prove existence and uniqueness of solutions for general smooth bounded domains, and derive a symmetry result for radial ones. We strengthen our analysis by proving that, for this particular problem, there are no non-global local optima. When the membrane is made out of two materials, the problem reduces to a shape optimization problem. We lay the preliminary foundation for computable analysis of this type of problem by proving stability of solutions with respect to some of the parameters involved.Comment: 19 pages, 1 figur

Deciphering The Tetrad Of Epigenetic Cytosine Modifications

A tetrad of epigenetic cytosine modifications imbues the DNA code with complex, dynamic meaning. DNA methyltransferase enzymes deposit methyl marks on the 5-carbon of cytosine, forming 5-methylcytosine (mC), which generally mediates long-term, locus-specific transcriptional repression during development and reprogramming. Ten-eleven translocation (TET) family enzymes oxidize the methyl group in three steps, forming predominantly 5-hydroxymethylcytosine (hmC) but also low levels of 5-formylcytosine (fC) and 5-carboxylcytosine (caC). These additional bases likely provide pathways for erasing methylation, but they may also harbor epigenetic functions in their own right. Questions regarding how each base forms and functions drive at the fundamental biology of the epigenome. In this thesis, I chronicle our lab’s efforts to probe the epigenome at its source—by deciphering and manipulating TET enzyme mechanisms. In particular, we aim to understand how and why TET enzymes generate rare fC and caC bases rather than hmC alone. Following a review of the field, I describe in Chapter 2 the methods that we developed to study rare cytosine modifications with high sensitivity. In Chapter 3, we applied these techniques to a rigorous kinetic study of how mouse Tet2 establishes and maintains oxidized cytosines. We found that Tet2 is capable of iterative oxidation, staying on a DNA strand to catalyze multiple rounds of oxidation and thereby enabling efficient generation of fC and caC under certain circumstances. In Chapter 4, we asked what structure-function determinants could allow for the generation of fC and caC. We discovered a conserved active site scaffold in human TET2 that specifically supports the formation of all three oxidized bases, not just hmC. By mutating the active site, we could alter the interactions between key residues to achieve stalling of oxidation at hmC. These mutants have now paved the way for applications in model systems to examine the function of hmC independently of fC and caC, which will allow us to dissect whether the rare, highly oxidized bases are truly critical for epigenetic processes. I describe our progress to date in Chapter 5, along with further mechanistic explorations of the dynamic epigenome

International Competitive Strategy Choices: Comparing Firms in China and India

The international business literature has yet to adequately explore international competitive strategy choices made by firms in developing countries. This study aims to address this gap by investigating the types of international competitive strategies followed by Chinese and Indian firms. Using firm-level primary data, the study analyzes factors that affect strategy choices and whether these factors differ between the two countries. The empirical results indicate that besides cost leadership strategies, firms have already developed international differentiation strategies and strategies combining cost and differentiation advantages (hybrid strategies). This confirms that firms from China and India are moving to international markets not only because of their low cost advantage but also because they are upgrading their capabilities to compete in the global market. The study highlights the fact that firms’ resources and capabilities influence firms’ propensity to choose a specific international competitive strategy and that the strategies can also differ in relation to the destination market. In general, the pursuit of well-articulated international competitive strategies (in particular differentiation strategy) is more common among Indian firms than among Chinese firms.

AMPK Activation by A-769662 Controls IL-6 Expression in Inflammatory Arthritis

International audienceAMP-activated protein kinase (AMPK) is a serine/threonine protein kinase critically involved in the regulation of cellular energy homeostasis. It is a central regulator of both lipid and glucose metabolism. Many studies have suggested that AMPK activation exert significant anti-inflammatory and immunosuppressive effects. In this study, we assessed whether targeted activation of AMPK inhibits inflammatory arthritis in vivo.METHODS:We tested the effect of A-769662, a specific AMPK agonist (60mg/kg/bid) in mouse models of antigen-induced arthritis (AIA) and passive K/BxN serum-induced arthritis. The passive K/BxN serum-induced arthritis model was also applied to AMPKα1-deficient mice. Joints were harvested and subjected to histological analysis. IL-6 expression was measured in both joint tissues and sera by ELISA. The effect of A-769662 on bone marrow derived macrophage (BMDM) response to stimulation with TLR2 and TLR4 agonists was tested in vitro.RESULTS:AMPK activation by A-769662 reduced inflammatory infiltration and joint damage in both mouse models. IL-6 expression in serum and arthritic joints was significantly decreased in A-769662-treated mice. AMPKα1 deficient mice mildly elicited an increase of clinical arthritis. IL-6 expression at both mRNA and protein levels, phosphorylation of p65 NF-κB and MAPK phosphorylation were inhibited by A-769662 in BMDMs stimulated with either TLR2 or TLR4 agonists.CONCLUSIONS:AMPK activation by specific AMPK agonist A-769662 suppressed inflammatory arthritis in mice as well as IL-6 expression in serum and arthritic joints. These data suggest that targeted activation of AMPK has a potential to be an effective therapeutic strategy for IL-6 dependent inflammatory arthritis

Sensorimotor Integration Along the Neuraxis

Sensory feedback is a vital component of behavior. Oftentimes we use sensory feedback to learn new motor skills, such as riding a bike. Other times we passively consume sensory information for our own enjoyment or to support cognitive processes such as learning. We occasionally even move to acquire certain sensory experiences or achieve sensory states. When sensory feedback is impaired, movement is also impaired. However, deficiencies of sensory feedback do not necessarily prohibit movement---motor tasks can be accomplished with limited or noisy sensory feedback, even if slowly and with reduced accuracy. This suggests that there are interactions between sensory modalities as well as interactions between sensation and movement at every level of the nervous system and raises the question of how sensory feedback interacts with motor commands along the neuraxis, from the periphery to the cerebral cortex. Here we studied the neural mechanisms of interactions and integration between sensation and movement in the periphery, in spinal circuits, and finally in volitional control of a brain-computer interface using signals extracted from motor cortex. We found that contact force influences the neural encoding of tactile stimuli in primary afferents, that spinal circuits encode sterotyped motor output to sensory stimulation, and that sensory feedback interacts with movement intent in motor cortex. Together, these studies suggest that sensation and movement are intertwined at every level of the nervous system, and that sensory signals must be demultiplexed and contextualized in terms of the movements used to acquire them, and motor commands must take into account the evolving sensory state