Parameter estimation and uncertainty quantification for systems biology models

Abstract

Mathematical models can provide quantitative insight into immunoreceptor signaling, but require parameterization and uncertainty quantification before making reliable predictions. We review currently available methods and software tools to address these problems. We consider gradient-based and gradient-free methods for point estimation of parameter values, and methods of profile likelihood, bootstrapping, and Bayesian inference for uncertainty quantification. We consider recent and potential future applications of these methods to systems-level modeling of immune-related phenomena. Highlights• Models of immunoreceptor signaling often contain parameters that must be fit to data.• New tools including PyBioNetFit and AMICI support automated parameter estimation.• Optimization algorithms can be used to obtain point estimates of parameter values.• Parameter estimation can incorporate both quantitative and qualitative data.• Uncertainty quantification assesses confidence in parameter values and model predictions.

Programmatic modeling for biological systems

“…Model calibration is the process of adjusting model parameters to match experimental data, also known as parameter estimation/optimization when applied to parametric models. The most common form of model calibration involves a process of running many simulations (thousands to millions or more) and checking the distance between model and experimental data error using an objective function, which gives a measure of the model’s simulation “error” versus experiment; for a review see [39]. Since dynamic data for signaling models are hard to come by, the modeler often only has data for a few species, and thus model calibration often leaves a model underdetermined - multiple parameter sets fit the data equally well [40].…”

An Optimal Control Approach for Enhancing Natural Killer Cells’ Secretion of Cytolytic Molecules

“…Parameter estimation. The model parameters were estimated using a Bayesian framework; namely, the Metropolis-Hastings (MH) algorithm [52][53][54][55] , as we did previously 19 . We provide an extensive description of this approach in the published work.…”

Emergent signal execution modes in biochemical reaction networks calibrated to experimental data

“…These analyses typically entail building a network, either from prior knowledge or through network inference, developing a mathematical model of the network interactions, and subsequently calibrating the model to experimental data (Jaqaman and Danuser, 2006;Raue et al, 2011;Shockley, Vrugt and Lopez, 2018). Although small networks have been studied with great success, the fact remains that for large networks many parameters remain difficult to ascertain and optimization routines yield multiple parameter sets that reproduce the protein concentration trajectories equally well (Ryan N. Eydgahi et al, 2013;Mitra and Hlavacek, 2019). This has led to a common practice whereby one or a few parameter vectors are chosen to make mechanistic predictions which can be validated by experiments with varying degrees of success (Janes et al, 2005;Albeck et al, 2008;Becker et al, 2010).…”