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People can identify the number of objects in sets of four or fewer items with near-perfect accuracy but exhibit linearly increasing error for larger sets. Some researchers have taken this discontinuity as evidence of two distinct representational systems. Here, we present a mathematical derivation showing that this behaviour is an optimal representation of cardinalities under a limited informational capacity, indicating that this behaviour can emerge from a single system. Our derivation predicts how the amount of information accessible to viewers should influence the perception of quantity for both large and small sets. In a series of four preregistered experiments (N = 100 each), we varied the amount of information accessible to participants in number estimation. We find tight alignment between the model and human performance for both small and large quantities, implicating efficient representation as the common origin behind key phenomena of human and animal numerical cognition.Membraneless organelles or condensates form through liquid-liquid phase separation1-4, which is thought to underlie gene transcription through condensation of the large-scale nucleolus5-7 or in smaller assemblies known as transcriptional condensates8-11. Transcriptional condensates have been hypothesized to phase separate at particular genomic loci and locally promote the biomolecular interactions underlying gene expression. However, there have been few quantitative biophysical tests of this model in living cells, and phase separation has not yet been directly linked with dynamic transcriptional outputs12,13. Here, we apply an optogenetic approach to show that FET-family transcriptional regulators exhibit a strong tendency to phase separate within living cells, a process that can drive localized RNA transcription. We find that TAF15 has a unique charge distribution among the FET family members that enhances its interactions with the C-terminal domain of RNA polymerase II. Nascent C-terminal domain clusters at primed genomic loci lower the energetic barrier for nucleation of TAF15 condensates, which in turn further recruit RNA polymerase II to drive transcriptional output. These results suggest that positive feedback between interacting transcriptional components drives localized phase separation to amplify gene expression.Although pyroptosis is critical for macrophages against pathogen infection, its role and mechanism in cancer cells remains unclear. PD-L1 has been detected in the nucleus, with unknown function. Here we show that PD-L1 switches TNFα-induced apoptosis to pyroptosis in cancer cells, resulting in tumour necrosis. Under hypoxia, p-Stat3 physically interacts with PD-L1 and facilitates its nuclear translocation, enhancing the transcription of the gasdermin C (GSDMC) gene. GSDMC is specifically cleaved by caspase-8 with TNFα treatment, generating a GSDMC N-terminal domain that forms pores on the cell membrane and induces pyroptosis. Nuclear PD-L1, caspase-8 and GSDMC are required for macrophage-derived TNFα-induced tumour necrosis in vivo. Moreover, high expression of GSDMC correlates with poor survival. Antibiotic chemotherapy drugs induce pyroptosis in breast cancer. These findings identify a non-immune checkpoint function of PD-L1 and provide an unexpected concept that GSDMC/caspase-8 mediates a non-canonical pyroptosis pathway in cancer cells, causing tumour necrosis.Ribulose-1,5-bisphosphate carboxylase-oxygenase (Rubisco) catalyses the first step in carbon fixation and is a strategic target for improving photosynthetic efficiency. In plants, Rubisco is composed of eight large and eight small subunits, and its biogenesis requires multiple chaperones. Here, we optimized a system to produce tobacco Rubisco in Escherichia coli by coexpressing chaperones in autoinduction medium. We successfully assembled tobacco Rubisco in E. coli with each small subunit that is normally encoded by the nuclear genome. Selleck BAY-218 Even though each enzyme carries only a single type of small subunit in E. coli, the enzymes exhibit carboxylation kinetics that are very similar to the carboxylation kinetics of the native Rubisco. Tobacco Rubisco assembled with a recently discovered trichome small subunit has a higher catalytic rate and a lower CO2 affinity compared with Rubisco complexes that are assembled with other small subunits. Our E. coli expression system will enable the analysis of features of both subunits of Rubisco that affect its kinetic properties.

Low circulating vitamin D levels are associated with poor colorectal cancer (CRC) survival. We assess whether vitamin D supplementation improves CRC survival outcomes.

PubMed and Web of Science were searched. Randomised controlled trial (RCTs) of vitamin D supplementation reporting CRC mortality were included. RCTs with high risk of bias were excluded from analysis. Random-effects meta-analysis models calculated estimates of survival benefit with supplementation. The review is registered on PROSPERO, registration number CRD42020173397.

Seven RCTs (n = 957 CRC cases) were identified three trials included patients with CRC at outset, and four population trials reported survival in incident cases. Two RCTs were excluded from meta-analysis (high risk of bias; no hazard ratio (HR)). While trials varied in inclusion criteria, intervention dose and outcomes, meta-analysis found a 30% reduction in adverse CRC outcomes with supplementation (n = 815, HR = 0.70; 95% confidence interval (CI) 0.48-0.93). A beneficial effect was seen in trials of CRC patients (progression-free survival, HR = 0.65; 95% CI 0.36-0.94), with suggestive effect in incident CRC cases from population trials (CRC-specific survival, HR = 0.76; 95% CI 0.39-1.13). No heterogeneity or publication bias was noted.

Meta-analysis demonstrates a clinically meaningful benefit of vitamin D supplementation on CRC survival outcomes. Further well-designed, adequately powered RCTs are needed to fully evaluate benefit of supplementation in augmenting ‘real-life’ follow-up and adjuvant chemotherapy regimens, as well as determining optimal dosing.

Meta-analysis demonstrates a clinically meaningful benefit of vitamin D supplementation on CRC survival outcomes. Further well-designed, adequately powered RCTs are needed to fully evaluate benefit of supplementation in augmenting ‘real-life’ follow-up and adjuvant chemotherapy regimens, as well as determining optimal dosing.