Biologically relevant finite-size effects in a driven lattice gas with particle pausing and dynamical defects

Area of Science:

• Statistical Mechanics
• Biophysics
• Computational Biology

Background:

• The totally asymmetric simple exclusion process with pausing particles (pTASEP) models biological processes like RNAP dynamics.
• Previous mean-field theories had limitations in fully describing pTASEP.

Purpose of the Study:

• To establish the equivalence between pTASEP and the exclusion process with dynamical defects (ddTASEP).
• To extend mean-field theory to open boundary conditions for pTASEP.
• To investigate and address finite-size effects in pTASEP simulations.

Main Methods:

• Equivalence demonstration between pTASEP and ddTASEP.
• Extension of mean-field theory to open boundary conditions.
• Development of a single-cluster approximation to account for finite-size effects.

Main Results:

• pTASEP is shown to be equivalent to ddTASEP, broadening its applicability.
• The phase diagram and critical values for open boundary conditions were determined.
• A significant discrepancy between theory and simulations due to finite-size effects was identified and addressed.

Conclusions:

• The single-cluster approximation accurately captures current-lattice size relationships.
• Finite-size effects are critical and often overlooked in modeling biological systems like transcription and translation.
• The developed approach is applicable to various scenarios under open boundary conditions.