Bootstrapping least-squares estimates in biochemical reaction networks

Area of Science:

• Computational biology
• Biochemical kinetics
• Stochastic modeling

Background:

• Estimating rate constants in biochemical networks is crucial for understanding cellular processes.
• Current methods using ordinary differential equations (ODEs) for large-volume limits can be numerically unstable.
• Accurate confidence bounds for these estimates are essential for reliable model interpretation.

Purpose of the Study:

• To develop new computational techniques for computing confidence bounds of least-squares estimates (LSEs) for rate constants.
• To address the challenges posed by ill-conditioned and unstable ODEs in covariance structure calculations.
• To provide robust estimation methods for mass action biochemical reaction networks and stochastic epidemic models.

Main Methods:

• Utilizing two bootstrap Monte Carlo procedures based on diffusion and linear noise approximations.
• Applying these methods to pure jump Markov processes, avoiding direct solution of limiting covariance ODEs.
• Fitting deterministic ODEs to partially observed trajectories of biochemical reaction networks.

Main Results:

• The proposed bootstrap methods successfully compute confidence bounds for LSEs without solving complex ODEs.
• Demonstrated effectiveness using both in-silico simulations and real data from the LINE 1 gene retrotranscription model.
• Showcased improved or comparable performance against existing estimation techniques.

Conclusions:

• The novel bootstrap approaches offer a computationally stable and efficient alternative for estimating rate constants and their confidence bounds.
• These methods enhance the reliability of parameter estimation in complex biological systems modeled by ODEs.
• The study provides valuable tools for analyzing biochemical reaction networks and epidemic models with partially observed data.