Autocatalytic genetic networks modeled by piecewise-deterministic Markov processes

Area of Science:

• Systems biology
• Computational biology
• Biophysics

Background:

• Autocatalytic gene networks are crucial for cellular functions.
• Existing models often simplify gene state transitions.
• Understanding gene regulatory dynamics is key to cell behavior.

Purpose of the Study:

• To propose piecewise-deterministic Markov processes (PDMPs) as an alternative modeling approach for autocatalytic networks.
• To analyze the behavior of autoregulated networks with positive feedback loops using PDMPs.
• To investigate the emergence of binary versus graded cellular responses.

Main Methods:

• Modeling gene activity with random transitions between active/inactive states.
• Deterministic modeling of subsequent transcription and translation processes.
• Analytical derivation of stationary distributions for one-dimensional correlated random walks.
• Numerical analysis of distributions under varying simulation periods and initial concentrations.

Main Results:

• Stationary distributions were analytically determined as solutions to a system of equations for a correlated random walk.
• Numerical simulations confirmed these findings and explored parameter space.
• The study identified that network structure dictates observable responses, including both binary and graded outcomes.

Conclusions:

• Piecewise-deterministic Markov processes offer a robust framework for modeling complex gene regulatory networks.
• The model successfully captures the emergence of diverse cellular responses based on network architecture.
• This approach provides new insights into the stochastic and deterministic interplay in gene expression dynamics.