Characteristic Motions in Proteins
Molecular dynamics is concerned with time dependent processes in molecular systems.
- Each dynamic process (i.e., motion) has a characteristic time-scale, amplitude and energy range
- Macromolecules in general, and proteins in particular, display a broad range of characteristic motions
- motions that are very fast and very localized, such as atomic fluctuations
- slow motions that occur on the scale of the whole molecule, such as the folding transition
- Many of these motions have an important role in the biochemical function of the protein
- Furthermore, the various protein motions are coupled to one another
- the large-scale dynamic transitions involve many medium-scale motions, which naturally involve localized motions as well
The following table surveys the different types of motions in a protein. These motions span almost 20 orders-of-magnitude in characteristic time (from picoseconds to hours).
| Type of Motion
| Functionality Examples
| Time and Amplitude
Scales |
Local Motions:
- Atomic fluctuation
- Side chain motion
|
- Ligand docking flexibility
- Temporal diffusion pathways
|
- fs - ps
- (10-15 - 10-12 s)
- less than 1 A
|
Medium Scale Motions:
- Loop motion
- Terminal-arm motion
- Rigid-body motion (helices)
|
- Active site conformation adaptation
- Binding specificity
|
- ns - micro s
- (10-9 - 10-6 s)
- 1 - 5 A
|
Large Scale Motions:
- Domain motion
- Subunit motion
|
- Hinge bending motion
- Allosteric transitions
|
- micro s - ms
- (10-6 - 10-3 s)
- 5 - 10 A
|
Global Motions:
- Helix-coil transition
- Folding/unfolding
- Subunit association
|
- Hormone activation
- Protein functionality
|
- ms - h
- (10-3 - 104 s)
- more than 5 A
|
The equation that describes the temporal evolution of a physical system is called an equation of motion. There are several different equations of motion, which characterize the motion in different ways:
| Equation of Motion |
Kind of System |
| Time-dependent Schroedinger Equation |
A quantum-mechanical system |
| Newton's Equations |
A classical-mechanical system |
| Langevin's Equation |
A stochastic system |
Molecules are quantum-mechanical systems the motion of which should be described by the Schroedinger Equation. However, limits on computational power make the application of Schroedinger's Equation for large systems impractical. Hence, the motion of a molecule is usually approximated by the laws of classical mechanics and by Newton's
equation of Motion.
Some important properties of Newton's equation of motion are:
- Conservation of energy
- Conservation of linear momentum
- Conservation of angular momentum
- Time reversibility
These properties are used to test whether the numerical solution of the equation (i.e., the molecular dynamics simulation) is stable and reliable.
This page last modified 8:48 AM on Sunday October 22nd, 2006.
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