High density lipoproteins (HDL) mediate cholesterol transport and protection from cardiovascular disease. Although synthetic HDLs have been studied for 30 years, the structure of human plasma-derived HDL, and its major protein apolipoprotein (apo)A-I, is unknown. We separated normal human HDL into 5 density subfractions and then further isolated those containing predominantly apoA-I (LpA-I). Using cross-linking chemistry and mass spectrometry, we found that apoA-I adopts a structural framework in these particles that closely mirrors that in synthetic HDL. We adapted established structural models for synthetic HDL to generate the first detailed models of authentic human plasma HDL in which apoA-I adopts a symmetrical cage-like structure. The models suggest that HDL particle size is modulated via a twisting motion of the resident apoA-I molecules. This understanding offers insights into how apoA-I structure modulates HDL function and its interactions with other apolipoproteins.

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Abstract. In this paper, we present and prove the first closed formula bounding the degree of regularity of an HFE system over an arbitrary finite field. Though these bounds are not necessarily optimal, they can be used to deduce if D, the degree of the corresponding HFE polynomial, and q, the size of the corresponding finite field, are fixed, inverting HFE system is polynomial for all fields; 2. if D is of the scale O(n α ) where n is the number of variables in an HFE system, and q is fixed, inverting HFE systems is quasipolynomial for all fields.We generalize and prove rigorously similar results by Granboulan, Joux and Stern in the case when q = 2 that were communicated at Crypto 2006.

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