We consider the Anderson tight binding model H = -A + V acting in l 2 (Z d ) and its restriction H Λ to finite hypercubes A C Z d . Here V = {V x ; x G Z d } is a random potential consisting of independent identically distributed random variables. Let {Ej(Λ)}j be the eigenvalues of H Λ , and let ξj(Λ 9 E) = \Λ\(Ej(A) -E), j ^ 1, be its rescaled eigenvalues. Then assuming that the exponential decay of the fractional moment of the Green function holds for complex energies near E and that the density of states n(E) exists at E, we shall prove that the random sequence {ξj(A,E)}j 9 considered as a point process on R 1 , converges weakly to the stationary Poisson point process with intensity measure n(E)dx as A gets large, thus extending the result of Molchanov proved for a one-dimensional continuum random Schrόdinger operator. On the other hand, the exponential decay of the fractional moment of the Green function was established recently by Aizenman, Molchanov and Graf as a technical lemma for proving Anderson localization at large disorder or at extreme energy. Thus our result in this paper can be summarized as follows: near the energy E where Anderson localization is expected, there is no correlation between eigenvalues of H Λ if A is large.

In many cancers, high proliferation rates correlate with elevation of rRNA and tRNA levels, and nucleolar hypertrophy. However, the underlying mechanisms linking increased nucleolar transcription and tumorigenesis are only minimally understood. Here we show that IMP dehydrogenase-2 (IMPDH2), the rate-limiting enzyme for de novo guanine nucleotide biosynthesis, is overexpressed in the highly lethal brain cancer, glioblastoma (GBM). This leads to increased rRNA and tRNA synthesis, stabilization of the nucleolar GTP-binding protein, Nucleostemin, and enlarged, malformed nucleoli. Pharmacological or genetic inactivation of IMPDH2 in GBM reverses these effects and inhibits cell proliferation, whereas untransformed glia cells are unaffected by similar IMPDH2 perturbations. Impairment of IMPDH2 activity triggers nucleolar stress and growth arrest of GBM cells even in the absence of functional p53. Our results reveal that upregulation of IMPDH2 is a prerequisite for aberrant nucleolar function and increased anabolic processes in GBM, which constitutes a primary event in gliomagenesis.

Histopathologically, clustering hypertrophic neurons and vacuolation with slight gliosis or without gliosis were considered to be pathological characteristics of AE. Amygdalohippocampectomy or hippocampal transection with amygdalotomy is effective for seizure control in patients with AE.

Both glycolytic and mitochondrial-type energy production can sustain tumor propagation by isogenic GSCs. Whereas both phenotypes can be independent and stable, cells that rely on oxidative phosphorylation can also switch to a more glycolytic phenotype in response to metabolic stress, suggesting that plasticity is a further characteristic of GSC metabolism.

Achieving robust cancer-specific lethality is the ultimate clinical goal. Here, we identify a compound with dual-inhibitory properties, named a131, that selectively kills cancer cells, while protecting normal cells. Through an unbiased CETSA screen, we identify the PIP4K lipid kinases as the target of a131. Ablation of the PIP4Ks generates a phenocopy of the pharmacological effects of PIP4K inhibition by a131. Notably, PIP4Ks inhibition by a131 causes reversible growth arrest in normal cells by transcriptionally upregulating PIK3IP1, a suppressor of the PI3K/Akt/mTOR pathway. Strikingly, Ras activation overrides a131-induced PIK3IP1 upregulation and activates the PI3K/Akt/mTOR pathway. Consequently, Ras-transformed cells override a131-induced growth arrest and enter mitosis where a131’s ability to de-cluster supernumerary centrosomes in cancer cells eliminates Ras-activated cells through mitotic catastrophe. Our discovery of drugs with a dual-inhibitory mechanism provides a unique pharmacological strategy against cancer and evidence of cross-activation between the Ras/Raf/MEK/ERK and PI3K/AKT/mTOR pathways via a Ras˧PIK3IP1˧PI3K signaling network.