State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation

Area of Science:

• Computational biology
• Chemical kinetics
• Systems biology

Background:

• The discrete chemical master equation (dCME) is crucial for modeling stochasticity in mesoscopic reaction networks.
• Directly solving dCMEs is often intractable due to large state spaces, necessitating state space truncation.
• Assessing and minimizing errors from state space truncation is vital for accurate dCME solutions.

Purpose of the Study:

• To introduce a novel method for state space truncation in dCMEs.
• To develop a theoretical framework for analyzing truncation errors.
• To provide a rapid, a priori method for estimating truncation error bounds.

Main Methods:

• Partitioning reaction networks into molecular equivalence groups (MEGs).
• Truncating state space by limiting molecular copy numbers within each MEG.
• Analyzing truncation error using reflecting boundaries and aggregated Markov processes.
• Developing an a priori method to estimate truncation error bounds from reaction rates.

Main Results:

• Truncation error for a MEG can be bounded by the probability of states on its reflecting boundary.
• Truncating one MEG does not affect the error estimation of other MEGs.
• An overall error estimate for networks with multiple MEGs was established.
• A priori error estimates can be rapidly computed without trial dCME solutions.

Conclusions:

• The novel MEG-based truncation and error analysis methods ensure accurate dCME solutions for diverse stochastic networks.
• These methods provide a robust framework for quantifying and controlling errors in dCME simulations.
• The developed techniques are applicable to a wide range of biological and chemical systems.