Estimating Reaction Rate Parameters in Cell Signaling Pathways Using Extreme Decomposition and Belief Propagation Tailored for Data-Rich Cases

TL;DR

This paper introduces BPPE, a novel method for estimating reaction rate parameters in cell signaling pathways by decomposing the optimization problem and using belief propagation, especially effective with data-rich measurements.

Contribution

The paper presents a new spline-based approach combined with loopy belief propagation for parameter estimation in ODE models of signaling networks, improving over traditional methods.

Findings

BPPE fits observed concentration data exactly and matches ODE derivatives.

The method provides systematic search coverage and asymptotic guarantees.

Demonstrated on Akt activation dynamics with redox effects.

Abstract

Motivation: Modeling biological signaling networks using ordinary differential equations (ODEs) has proven to be a powerful technique for generating insight into cellular dynamics, but it typically requires estimating rate parameters based on experimentally observed concentrations. New measurement methods can measure concentrations for all molecular species in a pathway, which creates a new opportunity to decompose the optimization of rate parameters. Results: In contrast with conventional methods that minimize the disagreement between simulated and observed concentrations, the BPPE method fits a spline curve through the observed concentration points, and then matches the derivatives of the spline-curve to the production and consumption of each species. Whereas traditional methods follow the ODEs exactly and then attempt to match the data, BPPE follows the data exactly and then attempts to match the ODEs. The new objective function is an extreme decomposition of the problem because each factor in the function is enforcing the equality of one ODE at one timeslice. A "loopy belief propagation" algorithm solves this factorized approximation of the parameter estimation problem providing systematic coverage of the search space and unique asymptotic behavior; the run time is polynomial in the number of molecules and timepoints, but exponential in the degree of the biochemical network. The implementation is a global-local hybrid optimization, and we compare with the performance of local, global, and hybrid methods. BPPE is demonstrated for a novel model of Akt activation dynamics including redox-mediated inactivation of PTEN. Availability: Software and supplementary information are available at http://webbppe.nus.edu.sg:8080/opal2/WebBPPE . Contact: LisaTK@nus.edu.sg . Keywords: probabilistic graphical models, physico-chemical modeling, systems biology, signal transduction.