Statistical inference of mechanistic models from qualitative data using an efficient optimal scaling approach

Abstract

Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. These models usually comprise unknown parameters, which have to be inferred from experimental data. For quantitative experimental data, there are several methods and software tools available. However, for qualitative data the available approaches are limited and computationally demanding. Here, we consider the optimal scaling method which has been developed in statistics for categorical data and has been applied to dynamical systems. This approach turns qualitative variables into quantitative ones, accounting for constraints on their relation. We derive a reduced formulation for the optimization problem defining the optimal scaling. The reduced formulation possesses the same optimal points as the established formulation but requires less degrees of freedom. Parameter estimation for dynamical models of cellular pathways revealed that the reduced formulation improves the robustness and convergence of optimizers. This resulted in substantially reduced computation times. We implemented the proposed approach in the open-source Python Parameter EStimation TOolbox (pyPESTO) to facilitate reuse and extension. The proposed approach enables efficient parameterization of quantitative dynamical models using qualitative data.

PEtab -- interoperable specification of parameter estimation problems in systems biology

“…While at the time of writing, PEtab only allows for models defined in the SBML format, the format is general enough to be integrated with other model specification formats like CellML and rule-based formats (Harris et al, 2016) in the future. Recently, new methods have been developed to estimate parameters from qualitative data (Mitra et al, 2018;Mitra and Hlavacek, 2020;Schmiester et al, 2019b). PEtab could be extended to also allow for these types of measurements.…”

Combining Quantitative Data with Logic-Based Specifications for Parameter Inference

“…Several recent papers present work on parameter fitting for non-stochastic models of dynamics from qualitative data [12,14,13]. All of these consider deterministic ordinary differential equation models.…”

“…In [13] this work is extended to give a Bayesian formulation of parameter inference from qualitative data. The authors of [14] take an alternative approach where the best quantitative representation of the qualitative observations in the form of categorical data is found via optimal scaling methods. The found quantitative representation is referred to as surrogate data.…”

“…Outside of formal methods, the inference problems are generally based on fitting the model parameters using existing observed data. The observed data can come in the form of quantitative data, like measured time trajectories, or qualitative data [14].…”