Missing links as a source of seemingly variable constants in complex reaction networks

TL;DR

This paper investigates how missing information in complex chemical reaction networks can cause significant variability in estimated rate constants, even without experimental errors, challenging the reliability of iterative model expansion.

Contribution

It demonstrates that unaccounted network links can lead to large apparent parameter variations, highlighting limitations in current parameter estimation methods for complex networks.

Findings

Missing links can cause order-of-magnitude variations in rate constants.

Correlation between estimation errors and neglected sensitivities is weak (<0.5).

Iterative model expansion may not reliably improve parameter estimates.

Abstract

A major challenge in network science is to determine parameters governing complex network dynamics from experimental observations and theoretical models. In complex chemical reaction networks, for example, such as those describing processes in internal combustion engines and power generators, rate constant estimates vary significantly across studies despite substantial experimental efforts. Here, we examine the possibility that variability in measured constants can be largely attributed to the impact of missing network information on parameter estimation. Through the numerical simulation of measurements in incomplete chemical reaction networks, we show that unaccountability of network links presumed unimportant (with local sensitivity amounting to less than two percent of that of a measured link) can create apparent rate constant variations as large as one order of magnitude even if no experimental errors are present in the data. Furthermore, the correlation coefficient between the logarithmic deviation of the rate constant estimate and the cumulative relative sensitivity of the neglected reactions was less than $0.5$ in all cases. Thus, for dynamical processes on complex networks, iteratively expanding a model by determining new parameters from data collected under specific conditions is unlikely to produce reliable results.