Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices

We derive exact analytic expressions for the distributions of eigenvalues and singular values for the product of an arbitrary number of independent rectangular Gaussian random matrices in the limit of large matrix dimensions. We show that they both have power-law behavior at zero and determine the corresponding powers. We also propose a heuristic form of finite size corrections to these expressions which very well approximates the distributions for matrices of finite dimensions.Comment: 13 pages, 3 figure

Universal microscopic correlation functions for products of independent Ginibre matrices

We consider the product of n complex non-Hermitian, independent random matrices, each of size NxN with independent identically distributed Gaussian entries (Ginibre matrices). The joint probability distribution of the complex eigenvalues of the product matrix is found to be given by a determinantal point process as in the case of a single Ginibre matrix, but with a more complicated weight given by a Meijer G-function depending on n. Using the method of orthogonal polynomials we compute all eigenvalue density correlation functions exactly for finite N and fixed n. They are given by the determinant of the corresponding kernel which we construct explicitly. In the large-N limit at fixed n we first determine the microscopic correlation functions in the bulk and at the edge of the spectrum. After unfolding they are identical to that of the Ginibre ensemble with n=1 and thus universal. In contrast the microscopic correlations we find at the origin differ for each n>1 and generalise the known Bessel-law in the complex plane for n=2 to a new hypergeometric kernel 0_F_n-1.Comment: 20 pages, v2 published version: typos corrected and references adde

Water-based fractionation of a commercial humic acid. Solid-state and colloidal characterization of the solubility fractions

Background and hypothesis: Humic acid (HA) is of considerable environmental significance, being a major component of soil, as well as being considered for application in other technological areas. However, its structure and colloidal properties continue to be the subject of debate, largely owing to its molecular complexity and association with other humic substances and mineral matter. As a class, HA is considered to comprise supramolecular assemblies of heterogeneous species, and herein we consider a simple route for the separation of some HA sub-fractions. Experiments: A commercial HA sample from Sigma-Aldrich has been fractionated into two soluble (S1, S2) and two insoluble (I1, I2) fractions by successive dissolution in deionized water at near-neutral pH. These sub-fractions have been characterized by solution and solid-state approaches. Findings: Using this simple approach, the HA has been shown to contain non-covalently bonded species with different polarity and water solubility. The soluble and insoluble fractions have very different chemical structures, as revealed particularly by their solid-state properties (13C NMR and IR spectroscopy, and TGA); in particular, S1 and S2 are characterized by higher carbonyl and aromatic contents, compared with I1 and I2. As shown by solution SAXS measurements and AFM, the soluble fractions behave as hydrophilic colloidal aggregates of at least 50 nm diameter

CRISPR-Cas9 Knockin Mice for Genome Editing and Cancer Modeling

CRISPR-Cas9 is a versatile genome editing technology for studying the functions of genetic elements. To broadly enable the application of Cas9 in vivo, we established a Cre-dependent Cas9 knockin mouse. We demonstrated in vivo as well as ex vivo genome editing using adeno-associated virus (AAV)-, lentivirus-, or particle-mediated delivery of guide RNA in neurons, immune cells, and endothelial cells. Using these mice, we simultaneously modeled the dynamics of KRAS, p53, and LKB1, the top three significantly mutated genes in lung adenocarcinoma. Delivery of a single AAV vector in the lung generated loss-of-function mutations in p53 and Lkb1, as well as homology-directed repair-mediated Kras[superscript G12D] mutations, leading to macroscopic tumors of adenocarcinoma pathology. Together, these results suggest that Cas9 mice empower a wide range of biological and disease modeling applications.National Science Foundation (U.S.). Graduate Research Fellowship (Grant 1122374)Damon Runyon Cancer Research Foundation (Fellowship DRG-2117-12)Massachusetts Institute of Technology. Simons Center for the Social Brain (Postdoctoral Fellowship)European Molecular Biology Organization (Fellowship)Foundation for Polish Science (Fellowship)American Society for Engineering Education. National Defense Science and Engineering Graduate FellowshipNational Science Foundation (U.S.). Graduate Research FellowshipMassachusetts Institute of Technology (Presidential Graduate Fellowship)Human Frontier Science Program (Strasbourg, France) (Postdoctoral Fellowship)National Human Genome Research Institute (U.S.) (CEGS P50 HG006193)Howard Hughes Medical InstituteKlarman Cell ObservatoryNational Cancer Institute (U.S.) (Center of Cancer Nanotechnology Excellence Grant U54CA151884)National Institutes of Health (U.S.) (Controlled Release Grant EB000244)National Heart, Lung, and Blood Institute (Program of Excellence in Nanotechnology (PEN) Award Contract HHSN268201000045C)Massachusetts Institute of Technology (Poitras Gift 1631119)Stanley CenterSimons Foundation (6927482)Nancy Lurie Marks Family Foundation (6928117)United States. Public Health Service (National Institutes of Health (U.S.) R01-CA133404)David H. Koch Institute for Integrative Cancer Research at MIT (Marie D. and Pierre Casimir-Lambert Fund)MIT Skoltech InitiativeNational Cancer Institute (U.S.) (Koch Institute Support (Core) Grant P30-CA14051)National Institute of Mental Health (U.S.) (Director’s Pioneer Award DP1-MH100706)National Institute of Neurological Disorders and Stroke (U.S.) (Transformative R01 Grant R01-NS 07312401)National Science Foundation (U.S.) (Waterman Award)W. M. Keck FoundationKinship Foundation. Searle Scholars ProgramKlingenstein FoundationVallee FoundationMerkin Foundatio

Effects of rapamycin and curcumin on inflammation and oxidative stress in vitro and in vivo - in search of potential anti-epileptogenic strategies for temporal lobe epilepsy

Background: Previous studies in various rodent epilepsy models have suggested that mammalian target of rapamycin (mTOR) inhibition with rapamycin has anti-epileptogenic potential. Since treatment with rapamycin produces unwanted side effects, there is growing interest to study alternatives to rapamycin as anti-epileptogenic drugs. Therefore, we investigated curcumin, the main component of the natural spice turmeric. Curcumin is known to have anti-inflammatory and anti-oxidant effects and has been reported to inhibit the mTOR pathway. These properties make it a potential anti-epileptogenic compound and an alternative for rapamycin.Methods: To study the anti-epileptogenic potential of curcumin compared to rapamycin, we first studied the effects of both compounds on mTOR activation, inflammation, and oxidative stress in vitro, using cell cultures of human fetal astrocytes and the neuronal cell line SH-SY5Y. Next, we investigated the effects of rapamycin and intracerebrally applied curcumin on status epilepticus (SE)—induced inflammation and oxidative stress in hippocampal tissue, during early stages of epileptogenesis in the post-electrical SE rat model for temporal lobe epilepsy (TLE).Results: Rapamycin, but not curcumin, suppressed mTOR activation in cultured astrocytes. Instead, curcumin suppressed the mitogen-activated protein kinase (MAPK) pathway. Quantitative real-time PCR analysis revealed that curcumin, but not rapamycin, reduced the levels of inflammatory markers IL-6 and COX-2 in cultured astrocytes that were challenged with IL-1β. In SH-SY5Y cells, curcumin reduced reactive oxygen species (ROS) levels, suggesting anti-oxidant effects. In the post-SE rat model, however, treatment with rapamycin or curcumin did not suppress the expression of inflammatory and oxidative stress markers 1 week after SE.Conclusions: These results indicate anti-inflammatory and anti-oxidant properties of curcumin, but not rapamycin, in vitro. Intracerebrally applied curcumin modified the MAPK pathway in vivo at 1 week after SE but failed to produce anti-inflammatory or anti-oxidant effects. Future studies should be directed to increasing the bioavailability of curcumin (or related compounds) in the brain to assess its anti-epileptogenic potential in vivo

Diet and Energy-Sensing Inputs Affect TorC1-Mediated Axon Misrouting but Not TorC2-Directed Synapse Growth in a Drosophila Model of Tuberous Sclerosis

The Target of Rapamycin (TOR) growth regulatory system is influenced by a number of different inputs, including growth factor signaling, nutrient availability, and cellular energy levels. While the effects of TOR on cell and organismal growth have been well characterized, this pathway also has profound effects on neural development and behavior. Hyperactivation of the TOR pathway by mutations in the upstream TOR inhibitors TSC1 (tuberous sclerosis complex 1) or TSC2 promotes benign tumors and neurological and behavioral deficits, a syndrome known as tuberous sclerosis (TS). In Drosophila, neuron-specific overexpression of Rheb, the direct downstream target inhibited by Tsc1/Tsc2, produced significant synapse overgrowth, axon misrouting, and phototaxis deficits. To understand how misregulation of Tor signaling affects neural and behavioral development, we examined the influence of growth factor, nutrient, and energy sensing inputs on these neurodevelopmental phenotypes. Neural expression of Pi3K, a principal mediator of growth factor inputs to Tor, caused synapse overgrowth similar to Rheb, but did not disrupt axon guidance or phototaxis. Dietary restriction rescued Rheb-mediated behavioral and axon guidance deficits, as did overexpression of AMPK, a component of the cellular energy sensing pathway, but neither was able to rescue synapse overgrowth. While axon guidance and behavioral phenotypes were affected by altering the function of a Tor complex 1 (TorC1) component, Raptor, or a TORC1 downstream element (S6k), synapse overgrowth was only suppressed by reducing the function of Tor complex 2 (TorC2) components (Rictor, Sin1). These findings demonstrate that different inputs to Tor signaling have distinct activities in nervous system development, and that Tor provides an important connection between nutrient-energy sensing systems and patterning of the nervous system

Mapping the Spatio-Temporal Pattern of the Mammalian Target of Rapamycin (mTOR) Activation in Temporal Lobe Epilepsy

Growing evidence from rodent models of temporal lobe epilepsy (TLE) indicates that dysregulation of the mammalian target of rapamycin (mTOR) pathway is involved in seizures and epileptogenesis. However, the role of the mTOR pathway in the epileptogenic process remains poorly understood. Here, we used an animal model of TLE and sclerotic hippocampus from patients with refractory TLE to determine whether cell-type specific activation of mTOR signaling occurs during each stage of epileptogenesis. In the TLE mouse model, we found that hyperactivation of the mTOR pathway is present in distinct hippocampal subfields at three different stages after kainate-induced seizures, and occurs in neurons of the granular and pyramidal cell layers, in reactive astrocytes, and in dispersed granule cells, respectively. In agreement with the findings in TLE mice, upregulated mTOR was observed in the sclerotic hippocampus of TLE patients. All sclerotic hippocampus (n = 13) exhibited widespread reactive astrocytes with overactivated mTOR, some of which invaded the dispersed granular layer. Moreover, two sclerotic hippocampus exhibited mTOR activation in some of the granule cells, which was accompanied by cell body hypertrophy. Taken together, our results indicate that mTOR activation is most prominent in reactive astrocytes in both an animal model of TLE and the sclerotic hippocampus from patients with drug resistant TLE

Tuberous sclerosis complex neuropathology requires glutamate-cysteine ligase

Introduction: Tuberous sclerosis complex (TSC) is a genetic disease resulting from mutation in TSC1 or TSC2 and subsequent hyperactivation of mammalian Target of Rapamycin (mTOR). Common TSC features include brain lesions, such as cortical tubers and subependymal giant cell astrocytomas (SEGAs). However, the current treatment with mTOR inhibitors has critical limitations. We aimed to identify new targets for TSC pharmacotherapy. Results: The results of our shRNA screen point to glutamate-cysteine ligase catalytic subunit (GCLC), a key enzyme in glutathione synthesis, as a contributor to TSC-related phenotype. GCLC inhibition increased cellular stress and reduced mTOR hyperactivity in TSC2-depleted neurons and SEGA-derived cells. Moreover, patients’ brain tubers showed elevated GCLC and stress markers expression. Finally, GCLC inhibition led to growth arrest and death of SEGA-derived cells. Conclusions: We describe GCLC as a part of redox adaptation in TSC, needed for overgrowth and survival of mutant cells, and provide a potential novel target for SEGA treatment. Electronic supplementary material The online version of this article (doi:10.1186/s40478-015-0225-z) contains supplementary material, which is available to authorized users