Analysis of Membrane Translocation Simulations using Dimensionality Reduction

Abstract

In understanding biological processes and biosystems, molecular motion at the atomic level plays a critical role. Computational studies on molecular motion are commonly based on simulations of molecular models, which give a huge number of conformations in the form of Cartesian coordinates for each of the atoms as output (Plaku, Stamati, Clementi, & Kavraki, 2007; Stamati, Clementi, & Kavraki, 2010). In order to quantitatively characterize a computer simulation and extract the important information of the motion of the system, a low-dimensional embedding such that the properties of the underlying manifold is preserved should be defined. Mathematically, finding a set of coordinates in which very few of them show significant variation and the others may said to be inconsiderable is called dimensionality reduction problem. The commonly used dimensionality reduction techniques, principal component analysis (PCA) and multidimensional scaling (MDS) are simple and easy to apply, affordable in the means of computing time and resource and efficiently determine the true structure of data in the high-dimensional input space (Tenenbaum, de Silva, & Langford, 2000). In an effort to characterize the translocation of the 18-residue long cell-penetrating peptide pVEC (LLIILRRRIRKQAHAHSK) through a lipid bilayer, we performed steered molecular dynamic (SMD) simulations, in which force is applied on the peptide to move it from one side of the membrane to the other. We examined the simulation trajectories using linear and nonlinear dimensionality reduction techniques to obtain a description of the underlying energy landscape for the nonlinear process of membrane uptake.