The LBFGS quasi-Newtonian method for molecular modeling prion AGAAAAGA amyloid fibrils

Abstract

<p> Experimental X-ray crystallography, NMR (Nuclear Magnetic Resonance) spectroscopy, dual polarization interferometry, etc. are indeed very powerful tools to determine the 3-Dimensional structure of a protein (including the membrane protein); theoretical mathematical and physical computational approaches can also allow us to obtain a description of the protein 3D structure at a submicroscopic level for some unstable, noncrystalline and insoluble proteins. X-ray crystallography finds the X-ray final structure of a protein, which usually need refinements using theoretical protocols in order to produce a better structure. This means theoretical methods are also important in determinations of protein structures. Optimization is always needed in the computer-aided drug design, structure-based drug design, molecular dynamics, and quantum and molecular mechanics. This paper introduces some optimization algorithms used in these research fields and presents a new theoretical computational method—an improved LBFGS Quasi-Newtonian mathematical optimization method—to produce 3D structures of prion AGAAAAGA amyloid fibrils (which are unstable, noncrystalline and insoluble), from the potential energy minimization point of view. Because the NMR or X-ray structure of the hydrophobic region AGAAAAGA of prion proteins has not yet been determined, the model constructed by this paper can be used as a reference for experimental studies on this region, and may be useful in furthering the goals of medicinal chemistry in this field. </p&gt

The Hybrid Idea of (Energy Minimization) Optimization Methods Applied to Study PrionProtein Structures Focusing on the beta2-alpha2 Loop

“…Currently, there is no structural information about prion AGAAAAGA amyloid fibrils because of unstable, noncrystalline and insoluble nature of this region, though numerous laboratory experimental results have confirmed this region owning an amyloid fibril forming property (initially described in 1992 by Stanley B. Prusiner's group). We also did accurate computer calculations on this region and confirmed the amyloid fibril property in this palindrome region [67,73].…”

Molecular dynamics studies on 3D structures of the hydrophobic region PrP(109-136)

“…Computer simulations of amyloid fibril formation by the Syrian hamster prion protein (SHaPrP) residues AGAAAAGA, the mouse prion protein (MoPrP) residues VA- GAAAAGAV, and their variations GA 6 G (a longer uninterrupted Alanine stretch flanked by Glycine), (AG) 4 (a complete disruption of hydrophobic residues), A 8 , GAAAGAAA (a mimic of Aβ (29)(30)(31)(32)(33)(34)(35)(36)), A 10 , V 10 , GAVAAAAVAG (uninterrupted hydrophobic sequence), VAVAAAAVAV (less flexible than MoPrP(111-120)) are studied in [10]. The first two peptides are thought to act as the velcro that holds the parent prion proteins together in amyloid structures and can form fibrils themselves [10].…”

“…In all these models, there is about 5 angstroms between the two closest adjacent β-sheets, maintained by hydrophobic bonds, and about 4.5 angstroms between the two closest adjacent β-strands, which are linked by hydrogen bonds. Illuminated by PDB templates 3FVA, 3NHC/D, 3NVF/G/H/E, 3MD4/5, 2OMP, computational approaches of global optimization, local search energy minimization (EM), simulated annealing (SA) and structural bioinformatics etc or introducing novel mathematical formulations and physical concepts into molecular biology may allow us to obtain a description of the protein 3D structure at a submicroscopic level for prion AGAAAAGA amyloid fibrils [24,26,27,28,29,30].…”

The Sensor Network in Molecular Structures of PrP(113-120) AGAAAAGA Amyloid Fibrils

“…Solving the ten MDGPs in the above section by any Optimization Solver (which will remove the bad vdW/HB contacts) [9][10][11][12][13][14][15][16] and then refining all the models by the Optimization program of Amber 11 [9,17]. At last we got the optimized prion 113-120 GAAAAGA amyloid fibril models, which are illuminated in Figures 8-14.…”