Symmetry and stochastic gene regulation

Area of Science:

• Theoretical Physics
• Biophysics
• Systems Biology

Background:

• Gene expression is a complex process influenced by stochasticity.
• Understanding regulatory protein-gene interactions is crucial for deciphering gene expression dynamics.
• Lie symmetries offer a powerful mathematical framework for analyzing complex systems.

Purpose of the Study:

• To identify and characterize novel symmetries in stochastic gene expression models.
• To explore the relationship between Lie symmetries and the dynamics of gene expression.
• To provide a group-theoretical framework for classifying noise regimes in gene expression.

Main Methods:

• Application of Lorentz-like noncompact Lie symmetry SO(2,1) to a spin-boson stochastic model of gene expression.
• Analysis of the algebra's invariant to characterize decay to equilibrium.
• Construction of raising and lowering operators to study affinity parameter changes.
• Utilizing group-theoretical numbers for noise regime classification.

Main Results:

• The SO(2,1) symmetry was successfully identified in the gene expression model.
• The algebra's invariant was found to characterize the decay rate towards equilibrium.
• Azimuthal eigenvalues were shown to represent the affinity between regulatory proteins and gene operator sites.
• Raising and lowering operators were demonstrated to modulate this affinity.
• A classification of gene noise regimes was established based on group-theoretical numbers.

Conclusions:

• The SO(2,1) symmetry provides a new mathematical lens for understanding gene expression dynamics.
• This framework elucidates the relationship between symmetry properties and biological parameters like protein-gene affinity.
• The study offers a group-theoretical approach to classifying and understanding noise in gene regulatory systems.