A Bayesian approach to estimating hidden variables as well as missing and wrong molecular interactions in ordinary...

Area of Science:

• Systems Biology
• Computational Biology
• Bioinformatics

Background:

• Ordinary differential equations (ODEs) are widely used for quantitative modeling of molecular networks.
• Model discrepancies often arise from incomplete biological knowledge, including wrongly modeled mechanisms or unincluded external factors.
• Identifying the precise causes of these discrepancies in complex biological systems is challenging.

Purpose of the Study:

• To develop a Bayesian approach for estimating hidden influences in ODE-based models.
• To differentiate between exogenous (external) and endogenous (internal) hidden influences.
• To aid modelers in identifying sources of error and missed interactions in ODE models using experimental data.

Main Methods:

• A Bayesian dynamic elastic-net method was developed to estimate hidden influences.
• The method analyzes discrepancies between ODE model predictions and experimental data.
• It distinguishes between external and internal factors contributing to model errors.

Main Results:

• The Bayesian approach successfully identifies wrongly specified and missed molecular interactions.
• Performance was demonstrated across diverse ODE models, including signaling pathways (JAK-STAT), receptor dynamics, chemical reactions (α-Pinene isomerization), and gene regulation.
• The method proved effective in analyzing network motifs and a gene-regulatory network.

Conclusions:

• The proposed Bayesian method provides an algorithmic solution for detecting errors in ODE-based models.
• It enhances model accuracy by identifying hidden exogenous and endogenous influences.
• This approach supports modelers in refining biological network models based on experimental evidence.