We present a generalization of Krylov-Rozovskii's result on the existence and uniqueness of solutions to monotone stochastic differential equations. As an application, the stochastic generalized porous media and fast diffusion equations are studied for σ -finite reference measures, where the drift term is given by a negative definite operator acting on a time-dependent function, which belongs to a large class of functions comparable with the so-called N -functions in the theory of Orlicz spaces.

The NSD family histone methyltransferases, including NSD1, NSD2 and NSD3, play crucial roles in chromatin regulation and are implicated in oncogenesis 1 , 2 . NSD enzymes exhibit an auto-inhibitory state that is relieved by nucleosome engagement, allowing for H3K36 di-methylation catalysis 3 – 7 . However, the molecular basis underlying this mechanism is largely unknown. Here, we have solved the cryo-EM structures of NSD2 and NSD3 bound to mononucleosomes at atomic resolution. We find that NSD2/3 mononucleosome engagement causes DNA near the linker region to unwrap, which facilitates insertion of their catalytic core in-between the histone octamer and the unwrapped segment of DNA. A network of DNA- and histone-specific contacts between the nucleosome and NSD2/3 precisely define the enzymes’ position on the nucleosome, explaining the methylation specificity for H3K36. Further, NSD-nucleosome intermolecular contacts are altered by several recurrent cancer-associated NSD2/3 mutations. NSDs harboring these mutations are catalytically hyperactive in vitro and in cells, and their ectopic expression promotes cancer cell proliferation and xenograft tumor growth. Together, our research provides molecular insights into the nucleosome-based recognition and modification mechanisms of NSD2 and NSD3, which should uncover strategies for therapeutic targeting of the NSD family of proteins.

Most eukaryotic mRNAs contain a 5' cap (m7GppX) and a 3' poly(A) tail to increase synergistically the translational efficiency. Recently, the poly(A) binding protein (PABP) and cap-binding protein, eIF-4F, were found to interact [Le et al. (1997) J. Biol. Chem. 272, 16247-16255; Tarun and Sachs (1996) EMBO J. 15, 7168-7177]. These data suggest that PABP may exert its effect on translational efficiency either by increasing the formation of initiation factor-mRNA complex or by enhancing ribosome recycling. To investigate the functional consequences of these interactions, the fluorescent cap analogue, ant-m7GTP, which is an environmentally sensitive fluorescent probe [Ren and Goss (1996) Nucleic Acids Res. 24, 3629-3634] was used to investigate the cap-binding affinity. Our data show that the binding of eIF-(iso)4F or eIF-4F to cap analogue enhanced their binding affinity toward PABP approximately 40-fold. Similarly, the eIF-4F/PABP or eIF-(iso)4F/PABP complexes show a 40-fold enhancement of cap analogue binding as compared to eIF-4F or eIF-(iso)4F alone. At least part of the enhancement of the translational initiation by PABP can be accounted for by direct changes in cap-binding affinity. The interactions of these components also suggest a mechanism whereby the poly(A) tail is brought into close proximity with m7G cap. This effect was examined by fluorescence energy transfer, and it was determined that the PABP/eIF-4F complex could bind both poly(A) and 5' cap simultaneously.

Fused in sarcoma (FUS) is involved in many processes of RNA metabolism. FUS and another RNA binding protein, TDP-43, are implicated in amyotrophic lateral sclerosis (ALS). It is significant to characterize the RNA recognition motif (RRM) of FUS as its nucleic acid binding properties are unclear. More importantly, abolishing the RNA binding ability of the RRM domain of TDP43 was reported to suppress the neurotoxicity of TDP-43 in Drosophila. The sequence of FUS-RRM varies significantly from canonical RRMs, but the solution structure of FUS-RRM determined by NMR showed a similar overall folding as other RRMs. We found that FUS-RRM directly bound to RNA and DNA and the binding affinity was in the micromolar range as measured by surface plasmon resonance and NMR titration. The nucleic acid binding pocket in FUS-RRM is significantly distorted since several critical aromatic residues are missing. An exceptionally positively charged loop in FUS-RRM, which is not found in other RRMs, is directly involved in the RNA/DNA binding. Substituting the lysine residues in the unique KK loop impaired the nucleic acid binding and altered FUS subcellular localization. The results provide insights into the nucleic acid binding properties of FUS-RRM and its potential relevance to ALS.