Unveiling the hidden structure of complex stochastic biochemical networks

Area of Science:

• Biochemistry
• Computational Biology
• Chemical Kinetics

Background:

• Complex Markov models are essential for analyzing stochastic biochemical processes.
• Estimating network states and transition rates from data is crucial when the system's structure is unknown.

Purpose of the Study:

• To derive the complete Taylor expansion of first-passage time distributions for general Markov models.
• To establish a method for analyzing unknown Markov model states and estimating rates.

Main Methods:

• Utilized algebraic methods combined with graph theory.
• Derived the Taylor expansion for first-passage time distributions between arbitrary states.

Main Results:

• The first term of the Taylor expansion is dictated by the shortest path between states.
• When the shortest path is unique, its coefficient is the product of transition rates along that path.

Conclusions:

• The derived Taylor expansion provides insights into the short-time behavior of Markov models.
• This approach can aid in estimating transition rates and their dependence on external parameters using experimental data.