We present the next-to-next-to-leading order (NNLO) calculation of quark quasiparton distribution functions (PDFs) in the large momentum effective theory. The nontrivial factorization at this order is established explicitly and the full analytic matching coefficients between the quasidistribution and the light-cone distribution are derived. We demonstrate that the NNLO numerical contributions can improve the behavior of the extracted PDFs sizably. With the unprecedented precision study of nucleon tomography at the planned electron-ion collider, high precision lattice QCD simulations with our NNLO results implemented will enable to test the QCD theory and more precise results on the PDFs of nucleons will be obtained.

We present a next-to-next-to-leading order (NNLO) calculation of the quasiparton distribution functions (quasi-PDFs) in the large momentum effective theory (LaMET). We focus on the flavor nondiagonal quark-quark channel and demonstrate the LaMET factorization at the NNLO accuracy in the modified minimal subtraction scheme. The matching coefficient between the quasi-PDF and the light-cone PDF is derived. This provides a first step towards a complete NNLO analysis of quasi-PDFs and to better understand the nucleon structures from the first principle of QCD.

Photosynthetic terpene production represents one of the most carbon and energy-efficient routes for converting CO 2 into hydrocarbon. In photosynthetic organisms, metabolic engineering has led to limited success in enhancing terpene productivity, partially due to the low carbon partitioning. In this study, we employed systems biology analysis to reveal the strong competition for carbon substrates between primary metabolism (e.g., sucrose, glycogen, and protein synthesis) and terpene biosynthesis in Synechococcus elongatus PCC 7942. We then engineered key “source” and “sink” enzymes. The “source” limitation was overcome by knocking out either sucrose or glycogen biosynthesis to significantly enhance limonene production via altered carbon partitioning. Moreover, a fusion enzyme complex with geranyl diphosphate synthase (GPPS) and limonene synthase (LS) was designed to further improve pathway kinetics and substrate channeling. The synergy between “source” and “sink” achieved a limonene titer of 21.0 mg/L. Overall, the study demonstrates that balancing carbon flux between primary and secondary metabolism can be an effective approach to enhance terpene bioproduction in cyanobacteria. The design of “source” and “sink” synergy has significant potential in improving natural product yield in photosynthetic species.