Clustering Algorithms to Analyze Molecular Dynamics Simulation Trajectories for Complex Chemical and Biological Systems

Molecular dynamics （MD） simulation has become a powerful tool to investigate the structure- function relationship of proteins and other biological macromolecules at atomic resolution and biologically relevant timescales. MD simulations often produce massive datasets con- taining millions of snapshots describing proteins in motion. Therefore, clustering algorithms have been in high demand to be developed and applied to classify these MD snapshots and gain biological insights. There mainly exist two categories of clustering algorithms that aim to group protein conformations into clusters based on the similarity of their shape （geometric clustering） and kinetics （kinetic clustering）. In this paper, we review a series of frequently used clustering algorithms applied in MD simulations, including divisive algorithms, ag- glomerative algorithms （single-linkage, complete-linkage, average-linkage, centroid-linkage and ward-linkage）, center-based algorithms （K-Means, K-Medoids, K-Centers, and APM）, density-based algorithms （neighbor-based, DBSCAN, density-peaks, and Robust-DB）, and spectral-based algorithms （PCCA and PCCA＋）. In particular, differences between geomet- ric and kinetic clustering metrics will be discussed along with the performances of diflhrent clustering algorithms. We note that there does not exist a one-size-fits-all algorithm in the classification of MD datasets. For a specific application, the right choice of clustering algo- rithm should be based on the purpose of clustering, and the intrinsic properties of the MD conformational ensembles. Therefore, a main focus of our review is to describe the merits and limitations of each clustering algorithm. We expect that this review would be helpful to guide researchers to choose appropriate clustering algorithms for their own MD datasets.

Analysis of Higher Order System with Impulse Exciting Functions in Z-Domain

This paper deals with mathematical modelling of impulse waveforms and impulse switching functions used in electrical engineering. Impulse switching functions are later investigated using direct and inverse z-transformation. The results make possible to present those functions as infinite series expressed in pure numerical, exponential or trigonometric forms. The main advantage of used approach is the possibility to calculate investigated variables directly in any instant of time;dynamic state can be solved with the step of sequences (T/6, T/12) that means very fast. Theoretically derived waveforms are compared with simulation worked-out results as well as results of circuit emulator LT spice which are given in the paper.