0.1 Representing proteins in silico and protein forward kinematics

Topics in this module

• Modeling Proteins on a Computer
  • Cartesian Representation of Protein Conformations
  • The Internal Degrees of Freedom of a Protein
  • Dihedral Representation of Protein Conformations
• Protein Forward Kinematics
  • Mathematical Background: Matrices and Transformations
  • Forward Kinematics
    • A simple approach
    • Denavit-Hartenberg Local Frames

Modeling proteins on a computer

In order to construct efficient, maintainable software to deal with and manipulate protein structures, a suitable way to store these structures has to be adopted. Depending on the ultimate application, different representations may have advantages and disadvantages from a software perspective. For example, when designing a simple visualization software, the Cartesian (x,y,z) coordinates of each atom are useful and simple to render on the screen. However, if the program is to manipulate bond angles and bond lengths for example, a representation based on the internal degrees of freedom (see below) may be more appropriate. Some applications may even need to store more than one representation at a time; for example a simulation program that needs to compute a protein's Potential Energy, which is a function of both Cartesian and Internal coordinates, would benefit from keeping both representations at the same time.

The structure of a protein is the set of atoms it contains, and the bonds that join them, that is, its inherent connectivity. A particular geometric shape of a protein (that is, the spatial arrangement of the atoms in the molecule) is called its conformation . Thus, a given protein structure can have many different conformations. Next, we discuss the two most common ways to model protein structures and conformations for software applications: Cartesian and Dihedral representations.

Cartesian representation of protein conformations

The most essential information for modeling a protein structure is the relative position of each atom, given as (x,y,z) Cartesian coordinates. Popular imaging methods such as X-Ray Crystallography, Nuclear Magnetic Resonance (NMR) and Cryogenic Electron Microscopy (Cryo-EM) are used to experimentally obtain relative atom positions from protein crystals and solutions. This is precisely the information provided by Protein Databank (PDB) format coordinate files: