• Corpus ID: 116981530

# The Lennard-Jones Potential Minimization Problem for Prion AGAAAAGA Amyloid Fibril Molecular Modeling

@article{Zhang2011TheLP,
title={The Lennard-Jones Potential Minimization Problem for Prion AGAAAAGA Amyloid Fibril Molecular Modeling},
author={Jiapu Zhang},
journal={arXiv: Mathematical Physics},
year={2011}
}
• Jiapu Zhang
• Published 8 June 2011
• Chemistry
• arXiv: Mathematical Physics
The simplified Lennard-Jones (LJ) potential minimization problem is minimize f(x)=4\sum_{i=1}^N \sum_{j=1,j<i}^N (\tau_{ij}^{-6} -\tau_{ij}^{-3}) subject to x\in \mathbb{R}^n, where $\tau_{ij}=(x_{3i-2}-x_{3j-2})^2 +(x_{3i-1}-x_{3j-1})^2+(x_{3i} -x_{3j})^2$, $(x_{3i-2},x_{3i-1},x_{3i})$ is the coordinates of atom $i$ in $\mathbb{R}^3$, $i,j=1,2,...,N(\geq 2 \quad \text{integer})$, $n=3N$ and $N$ is the whole number of atoms. The nonconvexity of the objective function and the huge number of…
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## Figures from this paper

• Chemistry
• 2012
A new theoretical computational method is presented—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.

## References

SHOWING 1-7 OF 7 REFERENCES

• Biology, Chemistry
Nature
• 2007
Structures of 13 of these microcrystals all reveal steric zippers, but with variations that expand the range of atomic architectures for amyloid-like fibrils and offer an atomic-level hypothesis for the basis of prion strains.
• Computer Science
J. Glob. Optim.
• 1997
The proposed global optimization method is related to the previous stochastic/perturbation global optimization methods for finding minimum energy configurations, but has several key differences that are important to its success.
• Biology
Biochemistry
• 2011
Three X-ray atomic structures from human, mouse, and hamster PrP reveal that different sequences encode different steric zippers and suggest that the degree of dissimilarity of these zipper structures gives rise to transmission barriers in prion disease, such as those that protect humans from acquiring bovine spongiform encephalopathy and chronic wasting disease.
• Computer Science
Comput. Optim. Appl.
• 2009
Three distinct approaches to global optimization algorithms based on multiple local searches for the Molecular Distance Geometry Problem (MDGP) are presented and for each of them a computational analysis is performed.
• Mathematics
SIAM J. Optim.
• 1997
Distance geometry problems arise in the determination of protein structure. We consider the case where only a subset of the distances between atoms is given and formulate this distance geometry
• Geology
• 2008
This is the first issue of 2008 and it is a very dense one with a Scientific contribution on computational biology, some announcements, reports of conferences and events, the MPS Chairs Column. Thus,
• Biology, Chemistry
Nature
• 2007
Structures of 13 of these microcrystals all reveal steric zippers, but with variations that expand the range of atomic architectures for amyloid-like fibrils and offer an atomic-level hypothesis for the basis of prion strains.