Transient-state fluctuationlike relation for the driving force on a biomolecule.

Area of Science:

• Biophysics
• Computational Biology
• Statistical Mechanics

Background:

• Single biomolecular systems exhibit fluctuating forces when subjected to constant velocity driving.
• Understanding these fluctuations is crucial for characterizing nonequilibrium processes.

Purpose of the Study:

• To investigate if force fluctuations in single biomolecular systems satisfy a transient state fluctuation-like relation.
• To analyze the behavior of these fluctuations under varying velocities during protein unfolding.

Main Methods:

• Steered molecular dynamics simulations were employed to study protein unfolding.
• Constant velocity pulling was used to drive the system out of equilibrium.
• Probabilities of positive and negative force values were analyzed to derive the fluctuation relation.

Main Results:

• Force fluctuations were confirmed to satisfy a transient-state fluctuation-like relation: 1/γ(T,v) ln[P(v)(+f)/P(v)(-f)] = f.
• Decreasing velocity in the nonequilibrium region led to substantial negative force fluctuations, potentially indicating refolding.
• The factor γ(T,v) and relaxation time τ(T,v) were found to scale with temperature (T) and velocity (v) as γ(T,v) ~ T(-δ)v(α) and τ(T,v) ~ T(δ)v(-(1+α)).

Conclusions:

• The study validates a transient fluctuation relation for force fluctuations in driven biomolecular systems.
• Negative force fluctuations suggest the possibility of transient refolding during protein unfolding.
• The derived scaling exponents provide quantitative insights into the system's relaxation dynamics under nonequilibrium conditions.