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Recent experimental evidence strongly supports that three-dimensional (3D) long-range enhancer-promoter (E-P) interactions have important influences on gene-expression dynamics, but it is unclear how the interaction information is translated into gene expression over time (4D). To address this question, we developed a general theoretical framework (named as a 4D nucleome equation), which integrates E-P interactions on chromatin and biochemical reactions of gene transcription. With this equation, we first present the distribution of mRNA counts as a function of the E-P genomic distance and then reveal a power-law scaling of the expression level in this distance. Interestingly, we find that long-range E-P interactions can induce bimodal and trimodal mRNA distributions. The 4D nucleome equation also allows for model selection and parameter inference. When this equation is applied to the mouse embryonic stem cell smRNA-FISH data and the E-P genomic-distance data, the predicted E-P contact probability and mRNA distribution are in good agreement with experimental results. Further statistical inference indicates that the E-P interactions prefer to modulate the mRNA level by controlling promoter activation and transcription initiation rates. Our model and results provide quantitative insight into both spatiotemporal gene-expression determinants (i.e., long-range E-P interactions) and cellular fates during development. Author summary: Gene expression is an essential biological process in all organisms. Numerous experimental studies have reported that the long-range enhancer-promoter (E-P) interaction on three-dimensional (3D) chromatin architecture plays important roles in regulating gene expression and cell functions, but the quantitative and qualitative impact of E-P interaction on gene expression over time is unclear. We develop a theoretically and numerically efficient model (called the 4D nucleome equation) to couple E-P interaction with gene expression and use this equation to characterize dynamic behavior. Then, we obtain the theoretical distribution of mRNAs and predict the gene expression profiles under E-P regulations. Interestingly, we find that E-P interactions can induce bimodal and trimodal shapes of mRNA distribution. When applying this framework to mouse embryonic stem cell data to investigate the dynamical behaviors of E-P interaction and gene expression, we reproduce the experimentally measured E-P contact frequencies and mRNA distribution under different E-P interactions. Our results support the picture of an essential mechanism for explaining phenotypic diversity and cellular decision-making. [ABSTRACT FROM AUTHOR]

Zirconium-based porphyrin metal organic frameworks (Zr-PMOFs) had attracted attention in the field of photocatalysis in recent years. However, the recombination of photogenerated carriers of monomer PMOF limits its performance of photocatalytic organic pollutants degradation. Metal sulfide has a suitable visible band gap, which can form a heterojunction with MOF materials to enhance the photocatalytic efficiency of MOF. Therefore, a typical metal sulfide semiconductor ZnIn2S4 (ZIS) was introduced into a Zr-MOF (MOF-525) by solvothermal method to prepare a series of ZIS/MOF-525 (ZIS/MOF-525–1, ZIS/MOF-525–2, ZIS/MOF-525–3 and ZIS/MOF-525–4) composite photocatalysts in this work. The results of characterization analysis, optical analysis and electrochemical analysis showed that the interface of ZIS/MOF-525 formed a typical type-II heterojunction, which accelerated the electron transport rate and effectively inhibited the recombination of photogenerated e− and h+ in MOF-525. The optimal removal efficiency of tetracycline (TC) by ZIS/MOF-525–3 (the mass of MOF-525 is 30 mg) reached 93.8% under 60 min visible light illumination, which was greater than that of pure MOF-525 (37.2%) and ZnIn2S4 (70.0%), and it still maintained good stability after five cycles reusing experiment. This work provides feasible insight for the preparation of novel and efficient PMOF-based photocatalysts in the future. [ABSTRACT FROM AUTHOR]

Gene-expression bimodality, as a potential mechanism generating phenotypic cell diversity, can enhance the survival of cells in a fluctuating environment. Previous studies have shown that intrinsic or extrinsic regulations could induce bimodal gene expressions, but it is unclear whether this bimodality can occur without regulation. Here we develop an interpretable and tractable model, namely a generalized telegraph model (GTM), which considers silent transcription intervals and translational bursting, each being characterized by a general distribution. Using the queuing theory, we derive the analytical expressions of protein distributions, and show that non-exponential inactive times and translational bursting can lead to two peaks of the protein distribution away from the origin, which are different from those occurring in classical telegraph models. We also find that both silent-interval noise and translational burst-size noise can amplify gene-expression noise and induce diverse dynamic expression patterns. Our results not only provide an alternative mechanism of phenotypic switching but also could be used in explaining the bimodal phenomenon in experimental observations. [ABSTRACT FROM AUTHOR]

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