This module introduces concepts on dimensionality reduction, including Principal Components Analysis (PCA) and Isomap. It also shows how to apply them to molecular motion data, and how to interpret the resulting coordinates.
Topics in this module
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Introduction
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Dimensionality Reduction
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Principal Components Analysis
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PCA of conformational data
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Non-Linear Methods
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Isometric Feature Mapping (Isomap)
Introduction
The study of many biological processes at the molecular level involves understanding how biological molecules (especially proteins) behave dynamically. The three-dimensional shape of these molecules, which we call a
conformation , usually determines the chemical action they perform. Both the stable (also called
native ) shape of a biomolecule and dynamical deviations from it are important to understand how it interacts with other molecules such as pharmaceutical drugs or other complexes. For these reasons, understanding the main shapes and motions of these molecules is of utmost importance.
Current structural biology experimental methods are restricted in the amount of information they can provide regarding protein motions because they were designed mainly to determine the three-dimensional static representation of a molecule. For this reason,
in silico methods (i.e., run in a computer) are used to extensively sample protein conformations. As a summary, the most popular methods to gather protein conformations are:
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X-Ray Crystallography. The most established and accurate method of determining the three-dimensional structure of a protein is
X-ray crystallography . This technique is based on the collection of diffraction data generated by exposing a protein crystal to an X-ray beam. The main limitation of this experimental technique is that it is necessary to obtain protein crystals in order to collect experimental data. Unfortunately, creating protein crystals is a very lengthy and laborious process which is not always successful.
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Nuclear Magnetic Resonance (NMR). The second most common method of determining the structure of a protein is
NMR {Wuthrich, 1986 #184}. This method uses a spectroscopy approach to collect the experimental data necessary for structure determination. This method is in general not as accurate as X-ray crystallography and its use is limited to small and medium-sized proteins. However, it provides useful information about protein dynamics directly and avoids some of the problems of X-ray crystallography such as protein crystallization.
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In silico sampling. An alternative to using experimental methods to derive structural data is using computational methods such as Molecular Dynamics (MD) or Monte Carlo (MC) simulations, or other forms of computational sampling. In fact, computational methods are used to augment existing experimental data since MD simulations typically start from a three-dimensional protein structure determined by X-ray crystallography or NMR. MD uses an empirical
force field to approximate the potential energy of a protein shape. Once a force field model has been chosen, the time evolution of the system is determined by numerically solving the resulting equations of motion. One of the main disadvantages of MD is that it is very computationally expensive, making it impossible (with current technology) to run all-atom simulations of big proteins for time-scales relevant to the majority of biological processes. Nevertheless, simulations can provide us with invaluable data since they are the only method of observing proteins in “real time”. Recently, the development of so-called
coarse-grained models (which model a group of atoms as a single entity) has allowed the sampling of longer times. MD is a good data source for sampling purposes because it can provide a large number of conformations of a molecule. For an introduction to Molecular Dynamics simulations, please refer to
[6] .
