Low-frequency collective motion in proteins and DNA
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Low-frequency collective motion in proteins and DNA refers to the application of statistical thermodynamics to understand low-frequency vibrations in biomolecules.
The concept of low-frequency phonons (or internal motion) in proteins was originally proposed by Professor Kuo-Chen Chou and Professor Nian-Yi Chen in order to solve a perplexing “free-energy deficit” problem in protein binding. In studying the binding interaction between proteins such as insulin and insulin receptor, it was noted that enumerating the known explanations for the free energy change, such as translational and rotational entropy, hydrogen bonds, van der Waals interactions, and hydrophobic interactions, did not fully account for the observed free energy change for the reaction. It was inferred that the deficit could be explained by the creation of extra vibrational modes with very low wave numbers in the range of 10–100 cm−1, corresponding to the range of terahertz frequency (3×1011 to 3×1012 Hz).
Subsequently, the aforementioned low-frequency modes have been indeed observed by Raman spectroscopy for a number of protein molecules and different types of DNA. These observed results have also been further confirmed by neutron scattering experiments.
Quasi-continuum model 
The quasi-continuum model is one model developed to identify and analyze this kind of low-frequency motions in protein and DNA molecules. This model operates on an intermediate level of complexity between the elastic global model, which treats the biomolecule as a continuous elastic sphere, and atomistic normal mode methods. It treats the biomolecule's backbone as a continuous mass distribution, with discrete interactions representing hydrogen bonds modeling the effects of internal conformation. This has the advantage of being simpler than explicit-atom methods, and providing a much more intuitive physical picture of the dynamics involved.
It has been successfully used to simulate various low-frequency collective motions in protein and DNA molecules, such as accordion-like motion, pulsation or breathing motion, as reflected by the fact that the low-frequency wave numbers thus derived were quite close to the experimental observations.
Application to biological functions and medical treatments 
Many biological functions and their profound dynamic mechanisms can be revealed through the low-frequency collective motion or resonance in protein and DNA molecules, such as cooperative effects, allosteric transition, and intercalation of drugs into DNA. In this regard, some phenomenological theories were established. Meanwhile, the solitary wave motion was also used to address the internal motion during microtubule growth. The relationship between solitons—a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed—and the low-frequency phonons in proteins have been discussed in a recent paper.
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