[Paper Review] Discrete breathers in protein secondary structure

A.E. Sitnitsky|ArXiv.org|Jun 5, 2003

Nonlinear Photonic Systems25 references3 citations

TL;DR

This paper proposes that discrete breathers (DBs)—highly localized, long-lived vibrational modes—can exist in protein secondary structures due to weak coupling interactions and nonlinear potentials. Using a realistic microscopic model, it shows that DBs in α-helices, with a frequency of ~115 cm⁻¹, can explain long-lived far-infrared absorption observed in myoglobin and bacteriorhodopsin, suggesting a functional role in energy localization for enzymatic catalysis.

ABSTRACT

The role of the rigidity of a peptide chain in its equilibrium dynamics is investigated within a realistic model with stringent microscopically derived coupling interaction potential and effective on-site potential. The coupling interaction characterizing the chain rigidity and the effective on-site potentials are calculated for three main types of protein secondary structure. The coupling interaction is found to be surprisingly weak for all of them but different in character: repulsive for alpha-helix and anti-parallel beta-sheet structures and attractive for parallel beta-sheet structure. The effective on-site potential is found to be a hard one for alpha-helix and anti-parallel beta-sheet and a soft one for parallel beta-sheet. In all three types of protein secondary structures a stable zig-zag shape discrete breather (DB) associated with the oscillations of torsional (dihedral) angles can exist due to weakness of the coupling interaction. However, since the absorption of far infrared radiation (IR) by proteins is known to require the existence of rather long chains of hydrogen bonds that takes place only in alpha-helicies, then one can conclude that the excitation of a DB in such a way is possible in alpha-helix and seems to be hardly possible in beta-sheet structures. The interpretation of the recent experiments of Xie et al. on far IR laser pulse spectroscopy of proteins is suggested. The frequency of a DB in an the alpha-helix is obtained in the region of 115 cm^{-1} in accordance with these experiments.

Motivation & Objective

• To investigate the role of peptide chain rigidity in protein equilibrium dynamics using a realistic microscopic model.
• To determine whether discrete breathers (DBs) can exist in protein secondary structures due to weak coupling and nonlinear potentials.
• To interpret recent far-infrared laser spectroscopy experiments showing long-lived oscillations in α-helices but not β-sheets.
• To explore the potential functional role of DBs in enzymatic catalysis through localized energy storage.
• To establish a link between the observed 115 cm⁻¹ DB frequency and experimental data from Xie et al.

Proposed method

• Developed a realistic model of the polypeptide chain with microscopically derived coupling interaction and effective on-site potentials.
• Calculated the coupling interaction and on-site potential for α-helices, anti-parallel, and parallel β-sheets using detailed physical constraints.
• Modeled the dynamics of torsional (dihedral) angles using a nonlinear lattice equation with anharmonic terms.
• Analyzed the existence and stability of discrete breathers (DBs) via numerical and analytical solutions of the equation of motion.
• Assessed dissipation mechanisms via phenomenological damping terms and considered acoustic/phonon-mediated energy loss.
• Used fluctuation-dissipation theorems to relate noise and friction, though the microscopic origin of γ remains speculative.

Experimental results

Research questions

• RQ1 Can discrete breathers exist in protein secondary structures due to weak coupling and nonlinear potentials?
• RQ2 Why are long-lived far-infrared oscillations observed in α-helices but not in β-sheets?
• RQ3 What is the frequency of a discrete breather in an α-helix, and does it match experimental observations?
• RQ4 How does the effective on-site potential (hard vs. soft) influence DB formation in different secondary structures?
• RQ5 Could discrete breathers serve as localized energy storage mechanisms in enzymes, particularly in relation to rate-promoting vibrations?

Key findings

• The coupling interaction is surprisingly weak in all three secondary structures, with repulsive character in α-helices and anti-parallel β-sheets, and attractive in parallel β-sheets.
• The effective on-site potential is hard for α-helices and anti-parallel β-sheets, but soft for parallel β-sheets.
• A stable zig-zag shaped discrete breather (DB) can exist in all three secondary structures due to weak coupling interactions.
• The DB frequency in α-helices is calculated to be approximately 115 cm⁻¹, in excellent agreement with experimental observations from Xie et al.
• The long-lived oscillations in myoglobin and bacteriorhodopsin are interpreted as DBs arising from torsional angle oscillations, not solitons or phonons.
• The DB energy (~40kB T at room temperature) is comparable to typical enzymatic activation energies, suggesting a potential functional role in energy localization for catalysis.