Leptin has not evolved as a therapeutic modality for the treatment of obesity due to the prevalence of leptin resistance in a majority of the obese population. Nevertheless, the molecular mechanisms of leptin resistance remain poorly understood. Here, we show that increased endoplasmic reticulum (ER) stress and activation of the unfolded protein response (UPR) in the hypothalamus of obese mice inhibits leptin receptor signaling. The genetic imposition of reduced ER capacity in mice results in severe leptin resistance and leads to a significant augmentation of obesity on a high-fat diet. Moreover, we show that chemical chaperones, 4-phenyl butyric acid (PBA), and tauroursodeoxycholic acid (TUDCA), which have the ability to decrease ER stress, act as leptin-sensitizing agents. Taken together, our results may provide the basis for a novel treatment of obesity.

Despite the fact that X-box binding protein-1 (XBP-1) is one of the main regulators of the unfolded protein response (UPR), the modulators of XBP-1 are poorly understood. Here, we show that the regulatory subunits of phosphotidyl inositol 3-kinase (PI3K), p85α (encoded by Pik3r1) and p85β (encoded by Pik3r2) form heterodimers that are disrupted by insulin treatment. This disruption of heterodimerization allows the resulting monomers of p85 to interact with, and increase the nuclear translocation of, the spliced form of XBP-1 (XBP-1s). The interaction between p85 and XBP-1s is lost in ob/ob mice, resulting in a severe defect in XBP-1s translocation to the nucleus and thus in the resolution of endoplasmic reticulum (ER) stress. These defects are ameliorated when p85α and p85β are overexpressed in the liver of ob/ob mice. Our results define a previously unknown insulin receptor signaling pathway and provide new mechanistic insight into the development of ER stress during obesity.The ER is a large membrane-enclosed cellular organelle in which secretory and membranebound proteins are folded into their final three-dimensional structures, lipids and sterols are synthesized, and free calcium is stored 1,2 . Conditions that interfere with proper functioning of the ER create a state defined as ER stress and lead to activation of the UPR3-5.The UPR is conveyed to the cell through three main signaling pathways. The first two pathways are initiated by type I transmembrane kinases, PKR-like endoplasmic reticulum kinase (PERK) and inositol requiring enzyme-1 (IRE1), and the third pathway launches with activation of a type II transmembrane protein called activating transcription factor-6 (ATF6) [1][2][3][4][5] . Activation of PERK during ER stress leads to phosphorylation of eukaryotic translation initiation factor-2α at Ser51 and consequently results in global translational attenuation 6,7 . IRE1, on the other hand, has both kinase and endoRNase activity [8][9][10][11] . The endoRNase domain of IRE1 splices the mRNA of a transcription factor called X-boxbinding protein-1 (XBP-1), removing a 26-bp segment from the full-length XBP-1 messenger RNA that creates a translational frame shift leading to the expression of a highermolecular-weight protein, XBP-1s 12-14 .

Maps of local tissue compression or expansion are often computed by comparing magnetic resonance imaging (MRI) scans using nonlinear image registration. The resulting changes are commonly analyzed using tensor-based morphometry to make inferences about anatomical differences, often based on the Jacobian map, which estimates local tissue gain or loss. Here, we provide rigorous mathematical analyses of the Jacobian maps, and use themto motivate a new numerical method to construct unbiased nonlinear image registration. First, we argue that logarithmic transformation is crucial for analyzing Jacobian values representing morphometric differences. We then examine the statistical distributions of log-Jacobian maps by defining the Kullback-Leibler (KL) distance on material density functions arising in continuum-mechanical models. With this framework, unbiased image registration can be constructed by quantifying the symmetric KL-distance between the identity map and the resulting deformation. Implementation details, addressing the proposed unbiased registration as well as the minimization of symmetric image matching functionals, are then discussed and shown to be applicable to other registration methods, such as inverse consistent registration. In the results section, we test the proposed framework, as well as present an illustrative application mapping detailed 3-D brain changes in sequential magnetic resonance imaging scans of a patient diagnosed with semantic dementia. Using permutation tests, we show that the symmetrization of image registration statistically reduces skewness in the log-Jacobian map.