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Mathematical modeling is the link between mathematics and practical problems and is the medium through which mathematics is widely used in related fields. This paper introduces the definitions of mathematical models in different disciplines and for different practical problems and gives the specific steps of mathematical modeling and the key problems to be solved in each step, the most important of which is nonlinear regression theory. The parameter estimation of the error variance of the nonlinear regression model is performed by the least squares method, and for the problem of poor numerical stability and computational complexity due to the pathological matrix in solving the least squares method, the least squares method is proposed based on adding the edge computing framework. The results show that the system efficiency of the nonlinear regression model based on edge computing is 92%, and the resource utilization is between 80% and 90% on average, which is higher than the two algorithms of RPP and RPA. The nonlinear regression model based on edge computing proposed in this paper organically combines mathematical modeling, which can make mathematical modeling play a greater role in the practical application process and solve more practical problems.

Hydrate-based gas separation (HBGS) has good potential in the separation of helium from helium-rich natural gas. HBGS should be carried out under a pressure higher than the thermodynamic equilibrium hydrate formation pressure (Peq) to ensure the formation of hydrate so that the accurate prediction of Peq is the basis of the determination of HBGS pressure. In this work, the Peq of the helium-rich natural gases with different helium contents (1 mol%, 10 mol%, and 50 mol%) in gas and different tetrahydrofuran (THF) contents (5 wt%, 10 wt%, and 19 wt%) in liquid at different temperatures were experimentally investigated through the isothermal pressure search method. A new thermodynamic model was proposed to predict the Peq of helium-rich natural gas. This model can quantitatively describe the effects of THF and helium on Peq, and it predicts the Peq of the helium-rich natural gases in this work accurately. The average relative deviation of the model is less than 3%. This model can guide the determination of the operating condition of the HBGS of helium-rich natural gas. [ABSTRACT FROM AUTHOR]

MTOR (mechanistic target of rapamycin kinase) complex 1 (MTORC1) orchestrates diverse environmental signals to facilitate cell growth and is frequently activated in cancer. Translocation of MTORC1 from the cytosol to the lysosomal surface by the RRAG GTPases is the key step in MTORC1 activation. Here, we demonstrated that transcription factors MEF2A and MEF2D synergistically regulated MTORC1 activation via modulating its cyto-lysosome shutting. Mechanically, MEF2A and MEF2D controlled the transcription of FNIP1 and FNIP2, the components of the FLCN-FNIP1 or FNIP2 complex that acts as a RRAGC-RRAGD GTPase-activating element to promote the recruitment of MTORC1 to lysosome and its activation. Furthermore, we determined that the pro-oncogenic protein kinase SRC/c-Src directly phosphorylated MEF2D at three conserved tyrosine residues. The tyrosine phosphorylation enhanced MEF2D transcriptional activity and was indispensable for MTORC1 activation. Finally, both the protein and tyrosine phosphorylation levels of MEF2D are elevated in human pancreatic cancers, positively correlating with MTORC1 activity. Depletion of both MEF2A and MEF2D or expressing the unphosphorylatable MEF2D mutant suppressed tumor cell growth. Thus, our study revealed a transcriptional regulatory mechanism of MTORC1 that promoted cell anabolism and proliferation and uncovered its critical role in pancreatic cancer progression. Abbreviation: ACTB: actin beta; ChIP: chromatin immunoprecipitation; EGF: epidermal growth factor; EIF4EBP1: eukaryotic translation initiation factor 4E binding protein 1; FLCN: folliculin; FNIP1: folliculin interacting protein 1; FNIP2: folliculin interacting protein 2; GAP: GTPase activator protein; GEF: guanine nucleotide exchange factors; GTPase: guanosine triphosphatase; LAMP2: lysosomal associated membrane protein 2; MAP1LC3B/LC3B: microtubule associated protein 1 light chain 3 beta; MEF2: myocyte enhancer factor 2; MEF2A: myocyte enhancer factor 2A; MEF2D: myocyte enhancer factor 2D; MEF2D-3YF: Y131F, Y333F, Y337F mutant; MTOR: mechanistic target of rapamycin kinase; MTORC1: MTOR complex 1; NR4A1: nuclear receptor subfamily 4 group A member 1; RPTOR: regulatory associated protein of MTOR complex 1; RHEB: Ras homolog, mTORC1 binding; RPS6KB1: ribosomal protein S6 kinase B1; RRAG: Ras related GTP binding; RT-qPCR: real time-quantitative PCR; SRC: SRC proto-oncogene, non-receptor tyrosine kinase; TMEM192: transmembrane protein 192; WT: wild-type. [ABSTRACT FROM AUTHOR]

Benzene exposure inhibits the hematopoietic system and leads to the occurrence of various types of leukemia. However, the mechanism underlying the hematotoxicity of benzene is still largely unclear. Emerging evidence has shown that exosomes are involved in toxic mechanisms of benzene. To understand the effect of 1,4‐benzoquinone (PBQ; an active metabolite of benzene in bone marrow) on the exosomal release characteristics and role of exosomal secretion in PBQ‐induced cytotoxicity. Exosomes were isolated from PBQ‐treated HL‐60 cells, purified by ultracentrifugation, and verified by transmission electron microscopy, nanoparticle tracking analysis and the presence of specific biomarkers. Our results showed that PBQ increased exosomal secretion in a dose‐dependent manner, reaching a peak in 3 h at 10 μM PBQ treatment and then slowly decreasing in HL‐60 cells. The exosomes contained miRNAs, which have been reported to be associated with benzene exposure or benzene poisoning. In particular, mir‐34a‐3p and mir‐34A‐5p were enriched in exosomes derived from PBQ‐treated cells. In addition, the inhibition of exosomal release by GW4869 (an inhibitor of exosomal release) exacerbated PBQ‐induced cytotoxicity, including increased intracellular reactive oxygen species levels, decreased mitochondrial membrane potential, and increased the apoptosis rate. Our findings illustrated that exosomes secretion plays an important role in antagonizing PBQ‐induced cytotoxicity and maintaining cell homeostasis. [ABSTRACT FROM AUTHOR]