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Set-oriented dimension reduction: Localizing principal component analysis via hidden Markov models
(2006)
BACKGROUND: Presurgical planning of the correction angle plays a
decisive role in a high tibial osteotomy, affecting the loading situation in
the knee affected by osteoarthritis. The planning approach by Fujisawa et
al. aims to adjust the weight-bearing line to achieve an optimal knee joint
load distribution. While this method is accessible, it may not fully
consider the complexity of individual dynamic knee-loading profiles. This
review aims to disclose existing alternative HTO planning methods that
do not follow Fujisawa’s standard.
METHODS: PubMed, Web of Science and CENTRAL databases were
screened, focusing on HTO research in combination with alternative
planning approaches.
RESULTS: Eight out of 828 studies were included, with seven simulation
studies based on finite element analysis and multi-body dynamics. The
planning approaches incorporated gradual degrees of realignment
parameters (weight-bearing line shift, medial proximal tibial angle, hip-
knee-ankle, knee joint line orientation), simulating their effect on knee
kinematics, contact force/stress, Von Mises and shear stress. Two studies
proposed implementing individual correction magnitudes derived from
preoperatively predicted knee adduction moments.
CONCLUSION: Most planning methods depend on static alignment
assessments, neglecting an adequate loading-depending profile. They are
confined to their conceptual phases, making the associated planning
methods unviable for current clinical use.
Decomposition of the high dimensional conformational space of bio-molecules into metastable subsets is used for data reduction of long molecular trajectories in order to facilitate chemical analysis and to improve convergence of simulations within these subsets. The metastability is identified by the Perron-cluster cluster analysis of a Markov process that generates the thermodynamic distribution. A necessary prerequisite of this analysis is the discretization of the conformational space. A combinatorial approach via discretization of each degree of freedom will end in the so called ''curse of dimension''. In the following paper we analyze Hybrid Monte Carlo simulations of small, drug-like biomolecules and focus on the dihedral degrees of freedom as indicators of conformational changes. To avoid the ''curse of dimension'', the projection of the underlying Markov operator on each dihedral is analyzed according to its metastability. In each decomposition step of a recursive procedure, those significant dihedrals, which indicate high metastability, are used for further decomposition. The procedure is introduced as part of a hierarchical protocol of simulations at different temperatures. The convergence of simulations within metastable subsets is used as an ''a posteriori'' criterion for a successful identification of metastability. All results are presented with the visualization program AmiraMol.
A recently developed algorithm allows Rigid Body Docking of ligands to proteins, regardless of the accessibility and location of the binding site. The Docking procedure is divided into three subsequent optimization phases, two of which utilize rigid body dynamics. The last one is applied with the ligand already positioned inside the binding pocket and accounts for full flexibility. Initially, a combination of geometrical and force-field based methods is used as a Coarse Docking strategy, considering only Lennard-Jones interactions between the target and pharmaceutically relevant atoms or functional groups. The protein is subjected to a Hot Spot Analysis, which reveals points of high affinity in the protein environment towards these groups. The hot spots are distributed into different subsets according to their group affiliation. The ligand is described as a complementary point set, consisting of the same subsets. Both sets are matched in $\mathrm{I\!R}^{3}$, by superimposing members of the same subsets. In the first instance, steric inhibition is nearly neglected, preventing the system's trajectory from trapping in local minima and thus from finding false positive solutions. Hence the exact location of the binding site can be determined fast and reliably without any additional information. Subsequently, errors resulting from approximations are minimized via finetuning, this time considering both Lennard-Jones and Coulomb forces. Finally, the potential energy of the whole complex is minimized. In a first evaluation, results are rated by a reduced scoring function considering only noncovalent interaction energies. Exemplary Screening results will be given for specific ligands.
In this paper we discuss several ways to visualize stationary and non-stationary quantum mechanical systems. We demonstrate an approach for the quantitative interpretation of probability density isovalues which yields a reasonable correlation between isosurfaces for different timesteps. As an intuitive quantity for visualizing the momentum of a quantum system we propose the probability flow density which can be treated by vector field visualization techniques. Finally, we discuss the visualization of non-stationary systems by a sequence of single timestep images.