Dynamic structure factor of vibrating fractals: proteins as a case study.

Area of Science:

• Biophysics
• Soft Matter Physics
• Computational Biology

Background:

• Proteins exhibit complex internal dynamics crucial for their function.
• Understanding these dynamics, particularly vibrational motions, is key to protein folding and interactions.
• Previous studies often simplified protein dynamics, necessitating more sophisticated models.

Purpose of the Study:

• To analytically calculate the dynamic structure factor S(k,t) for proteins at large wave numbers.
• To investigate the role of vibrational dynamics in folded proteins using fractal analogies.
• To evaluate the influence of rotational and translational diffusion on protein dynamics.

Main Methods:

• Developed an analytical model based on the analogy between proteins and fractals.
• Utilized the Gaussian Network Model (GNM) and Protein Data Bank (PDB) structures for numerical evaluations.
• Calculated displacement two-point correlation functions and the dynamic structure factor S(k,t).

Main Results:

• Showed that S(k,t) decay is dominated by the mean-square displacement of amino acids, exhibiting subdiffusive behavior.
• Derived a stretched exponential decay for S(k,t) (S(k,t)≃S(k)e(-(Γ(k)t)(β))) with β≃ν, where ν is the anomalous diffusion exponent.
• Found that while vibrational dynamics follow anomalous diffusion, rotational and translational diffusion significantly impact finite-size proteins.

Conclusions:

• The fractal nature of protein folds governs the static structure factor.
• Internal vibrational dynamics manifest as a stretched exponential decay in S(k,t) under specific conditions.
• Arresting rotational and translational motion is crucial for experimentally detecting internal protein vibrational dynamics.