An application of the Krylov-FSP-SSA method to parameter fitting with maximum likelihood

Area of Science:

• Systems Biology
• Computational Biology
• Biophysics

Background:

• Traditional gene regulation modeling relies on stochastic simulation algorithms (SSA).
• Solving the chemical master equation (CME) offers direct probability distribution insights but faces dimensionality challenges.
• Finite State Projection (FSP) and its variants aim to mitigate CME's curse of dimensionality.

Purpose of the Study:

• To apply the efficient Krylov-FSP-SSA method to a synthetic mutual inhibitory gene network in Saccharomyces cerevisiae.
• To demonstrate the method's capability in approximating transient probability distributions.
• To evaluate its utility for parameter fitting in systems biology models.

Main Methods:

• Utilized the Krylov-FSP-SSA variant, combining SSA with adaptive Krylov techniques for matrix exponential evaluation.
• Applied the method to a bimodal mutual inhibitory gene network.
• Compared five optimization schemes for parameter estimation using maximum likelihood on transient probability distributions.

Main Results:

• The Krylov-FSP-SSA method efficiently approximates transient probability distributions for the gene network.
• The approach is well-suited for parameter fitting, requiring fewer computations across multiple parameter sets.
• Numerical efficiency was demonstrated for a synthetically engineered gene network exhibiting bimodality.

Conclusions:

• The Krylov-FSP-SSA method provides an efficient computational tool for analyzing gene regulatory dynamics.
• This technique facilitates parameter estimation in systems biology, enhancing the calibration of complex models.
• The study highlights the method's potential for handling models with high dimensionality and stochastic behavior.