The power series expansion of certain infinite products q r ∏ n = 1 ∞ ( 1 − q n ) a 1 ( 1 − q 2 n ) a 2 ⋯ ( 1 − q m n ) a m $q^{r}\prod_{n=1}^{\infty}(1-q^{n})^{a_{1}}(1-q^{2n})^{a_{2}}\cdots(1-q^{mn})^{a_{m}}$

Abstract

In this paper, we derive some new identities satisfied by the series ∞ m,n=−∞ q m 2 +mn+2n 2 using Ramanujan's identities for L(q), M (q) and N(q). Our work is motivated by an attempt to develop a theory of elliptic functions to the septic base.

RAPIDASH: A tag-free enrichment of ribosome-associated proteins reveals compositional dynamics in embryonic tissues and stimulated macrophages

“…The N-terminus of LLPH is highly conserved and forms a helix, while the remainder of the protein is disordered. Recently, cryo-electron microscopy (cryo-EM) structures of the pre-60S particle in yeast 40 and humans 41 have captured the N-terminus of LLPH binding to the ribosome at the base of sarcin-ricin loop (Figure 3A). This binding site is suggestive of LLPH's potential role in regulating translation, as the sarcin-ricin loop is a highly conserved sequence critical for GTP hydrolysis of EF1A and EEF2, which enables proper translocation during protein synthesis 42,43 .…”

The tumour-derived extracellular vesicle proteome varies by endometrial cancer histology and is confounded by an obesogenic environment

“…In order to yield enough material for analysis, we also had to pool patient samples into groups, which could remove significant outliers; however, clustering showed similarities between biological replicates. Our SEC method combined broad fractions of the secretome, and further subfractionation would better define the association of identified proteins with true EVs or with co-isolated particle components such as exomeres [71] and supermeres [72]. To date, direct EV isolation from the interstitial fluid of tumours has only been reported for metastatic melanoma [73], colorectal [74] and renal carcinomas [75,76].…”