Jiapu Zhang
The problem of locating sensors in telecommunication networks is a distance geometry problem (DGP). In such a case, the positions of some sensors are known (which are called anchors) and some of the distances between sensors (which can or cannot be anchors) are known. The DGP is to locate the positions of all the sensors. Molecular DGP (MDGP) looks sensors as atoms and their telecommunication network as a molecule for the determination of its three-dimensional (3D) structure. This Chapter defines some sensor networks for determining molecular structures of PrP(113-120) AGAAAAGA amyloid fibrils, which are unstable, noncrystalline, insoluble and hard to be determined in NMR or X-ray experimental laboratories. The amyloid fibril structure is the common structure associated with some 20 neurodegenerative amyloid diseases (including Parkinson’s, Alzheimer’s, Huntington’s, and Prions’), and other diseases such as Type II diabetes, etc. The sensor networks established in this Chapter will benefit the study of 3D molecular structures of all these diseases and will be useful in the research areas such as structural materials, computer-aided or structure-based drug design, and the computational theory of molecular dynamics, and quantum mechanics/molecular mechanics.
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