When the optimal is not the best: parameter estimation in complex biological models

TL;DR

This paper explores the challenges of parameter estimation in complex biological models, highlighting that optimal data fit does not always equate to biologically meaningful parameters, and proposes alternative selection criteria.

Contribution

It demonstrates the ruggedness of the cost function landscape in tumor growth models and advocates for selecting parameters based on biological plausibility rather than just optimal fit.

Findings

Cost function landscape is highly rugged with many local minima.

Optimal fit parameters may not be biologically plausible.

Alternative criteria are needed for parameter selection.

Abstract

Background: The vast computational resources that became available during the past decade enabled the development and simulation of increasingly complex mathematical models of cancer growth. These models typically involve many free parameters whose determination is a substantial obstacle to model development. Direct measurement of biochemical parameters in vivo is often difficult and sometimes impracticable, while fitting them under data-poor conditions may result in biologically implausible values. Results: We discuss different methodological approaches to estimate parameters in complex biological models. We make use of the high computational power of the Blue Gene technology to perform an extensive study of the parameter space in a model of avascular tumor growth. We explicitly show that the landscape of the cost function used to optimize the model to the data has a very rugged surface in parameter space. This cost function has many local minima with unrealistic solutions, including the global minimum corresponding to the best fit. Conclusions: The case studied in this paper shows one example in which model parameters that optimally fit the data are not necessarily the best ones from a biological point of view. To avoid force-fitting a model to a dataset, we propose that the best model parameters should be found by choosing, among suboptimal parameters, those that match criteria other than the ones used to fit the model. We also conclude that the model, data and optimization approach form a new complex system, and point to the need of a theory that addresses this problem more generally.