Modelling non-Markovian dynamics in biochemical reactions

Area of Science:

• Biochemistry
• Computational Biology
• Biophysics

Background:

• Biochemical reactions are typically modeled as memoryless Markov processes.
• However, some biochemical systems exhibit non-Markovian dynamics, requiring more precise modeling techniques.

Purpose of the Study:

• To develop a methodology for stochastic simulation algorithms that accurately model non-Markovian processes.
• To enable more precise modeling of biochemical systems, particularly enzyme reactions.

Main Methods:

• Utilizing Constraint Programming and the Gecode framework for constraint solving.
• Developing algorithms to randomly sample waiting times from non-exponential probability density functions.

Main Results:

• The methodology allows sampling waiting times from arbitrary probability density functions, not limited to exponential distributions.
• A case study demonstrated inferring probability density functions from single-molecule experiments for enzyme reaction time intervals.
• This enables the modeling of certain enzyme reactions as non-Markovian processes.

Conclusions:

• The proposed methodology yields accurate models for enzymatic reactions.
• In specific cases, these non-Markovian models demonstrate a better fit to experimental data compared to traditional Markovian models.