Dynamic hysteresis in a one-dimensional Ising model: application to allosteric proteins

Area of Science:

• Statistical Mechanics
• Biophysics
• Computational Biology

Background:

• Dynamic hysteresis is crucial for understanding systems with feedback.
• Allosteric proteins, like hemoglobin, exhibit switch-like behavior relevant to biological signaling.
• Nonequilibrium conditions are common in biological systems due to active processes.

Purpose of the Study:

• To analyze dynamic hysteresis in a finite one-dimensional Ising model at low temperatures.
• To determine the relationship between hysteresis loop area and field frequency.
• To predict the switching dynamics of allosteric proteins under time-varying ligand concentrations.

Main Methods:

• Utilizing a finite one-dimensional Ising model.
• Analyzing the system's response to a periodically varied magnetic field.
• Investigating scaling laws for hysteresis loop area as a function of field frequency.

Main Results:

• Hysteresis loop area scales as the square root of field frequency over a broad range.
• A critical frequency exists below which a linear relationship between hysteresis area and frequency is observed.
• The findings provide insights into the dynamic behavior of switch-like biological systems.

Conclusions:

• The one-dimensional Ising model effectively captures dynamic hysteresis relevant to allosteric proteins.
• The study predicts how allosteric proteins respond to fluctuating ligand concentrations.
• Analysis informs understanding of allosteric protein sensitivity to signals versus intrinsic fluctuations.