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Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov
Yen Ting Lin1,2, Nicolas E Buchler3,4,5
1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA yentingl@lanl.gov.
Journal of the Royal Society, Interface
|February 2, 2018
Summary
This study introduces a piecewise deterministic Markov process (PDMP) to model gene expression stochasticity in the non-adiabatic binding regime. The PDMP accurately captures bursty gene expression and oscillations in titration-based systems.
Area of Science:
- Systems Biology
- Molecular Biology
- Biophysics
Background:
- Single-cell gene expression is characterized by stochasticity and bursting.
- This behavior can arise from slow promoter state switching, influenced by chromatin dynamics or transcription factor binding kinetics (non-adiabatic regime).
Purpose of the Study:
- To develop an analytical framework describing stochastic gene expression in the non-adiabatic regime.
- To apply this framework to analyze titration-based gene expression oscillators.
Main Methods:
- Introduced a piecewise deterministic Markov process (PDMP) analytical framework.
- Transformed the chemical master equation into a PDMP for systems with slow promoter transitions and fast transcription factor dynamics.
- Analyzed properties of activator and repressor-based titration oscillators.
Main Results:
- The PDMP accurately models stochastic gene expression dynamics in the non-adiabatic limit.
- PDMP analysis explains observed stochastic cycles in titration oscillators.
- Demonstrated how multiple binding sites lengthen oscillation periods and improve coherence.
- Linked noise-induced oscillations to non-adiabatic and discrete binding events.
Conclusions:
- The PDMP provides an effective model for gene expression stochasticity in the non-adiabatic regime.
- This framework elucidates the mechanisms behind oscillations and coherence in titration-based systems.
- Non-adiabatic binding and discrete events are crucial for noise-induced oscillations.
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