A novel canonical dual computational approach for prion AGAAAAGA amyloid fibril molecular modeling

Abstract

Many experimental studies have shown that the prion AGAAAAGA palindrome hydrophobic region (113-120) has amyloid fibril forming properties and plays an important role in prion diseases. However, due to the unstable, noncrystalline and insoluble nature of the amyloid fibril, to date structural information on AGAAAAGA region (113-120) has been very limited. This region falls just within the N-terminal unstructured region PrP (1-123) of prion proteins. Traditional X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy experimental methods cannot be used to get its structural information. Under this background, this paper introduces a novel approach of the canonical dual theory to address the 3D atomic-resolution structure of prion AGAAAAGA amyloid fibrils. The novel and powerful canonical dual computational approach introduced in this paper is for the molecular modeling of prion AGAAAAGA amyloid fibrils, and that the optimal atomic-resolution structures of prion AGAAAAGA amyloid fibils presented in this paper are useful for the drive to find treatments for prion diseases in the field of medicinal chemistry. Overall, this paper presents an important method and provides useful information for treatments of prion diseases.

Canonical duality theory and triality for solving general global optimization problems in complex systems

“…, p} are two integer sets with m and p that are fixed integers; all the coefficients b j with j ∈ I p are positive constants, and α i , θ j ∈ ‫ޒ‬ for all i ∈ I m and j ∈ I p are given parameters; the matrices {B i } i∈I m and {C j } j∈I p are assumed to be symmetric, positive semidefinite such that the cone generated by them contains a positive-definite matrix. The nonconvex optimization problem (ᏼ) arises naturally in complex systems with a wide range of applications, including chaotic dynamical systems [Gao 2003a;Gao and Ogden 2008a;Gao and Ruan 2008], computational biology [Zhang et al 2011], chemical-database analysis [Xie and Schlick 2000], large-deformation computational mechanics [Gao 1996;Santos and Gao 2012], population growing [Ruan and Gao 2014a], location/allocation, network communication , and transitions of solids [Gao and Ogden 2008a;2008b;Gao and Yu 2008], etc.…”

“…The sensor-network-localization-type problems also appear in computational biology, Euclidean ball packing, molecular confirmation, recently wireless network communication, etc. [Ruan and Gao 2014b;Zhang et al 2011]. Due to the nonconvexity, the sensor-network localization problem is considered to be NP-hard even for the simplest case d = 1 [Moré and Wu 1997;Saxe 1979].…”

RETRACTED: A framework of canonical dual algorithms for global optimization

“…The main merit of this theory is that it can transform nonconvex/nonsmoonth/discrete optimization/variational problems into continuous concave maximization problems over convex domains, which can be solved easily, under certain conditions, by many well-developed algorithms and types of software. Therefore, the canonical duality theory has been successfully used to solve a large class of challenging problems in computational biology [9], engineering mechanics [10][11][12], information theory [13], network communications [14], nonlinear dynamical systems [15] and some non-deterministic polynomial (NP)-hard problems in global optimization [16][17][18][19]; however, it is realized that a canonical dual problem may have no critical point in the dual feasible space and, in this case, the primal problem could be NP-hard [20]. By introducing a linear perturbation term to the primal problem or a quadratic perturbation term to the dual problem, the issue can be partially tackled to some extent but is still an open problem [19].…”

Canonical duality for solving general nonconvex constrained problems

“…This means that x 1 is the global minimum of the original constrained problem, while x 4 is the biggest local maximum of the original constrained problem. This example Table 1: Critical points of the primal and dual problems for example (19) with q = 1, c = 1, d = 6, e = 15.…”

“…Canonical duality theory is potentially powerful methodological method, which was developed originally from nonconvex analysis/mechanics [3,4]. This theory has been used successfully for solving a large class of challenging problems in nonconvex/nonsmooth/discrete systems [5,18,19], recently in network communications [7,15] and radial basis neural networks [14]. It was shown in [10] that both the Lagrange multiplier method and KKT conditions can be unified within a framework of the canonical duality theory.…”