Parameterization 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.

Efficient gradient-based parameter estimation for dynamic models using qualitative data

“…In this study, we build upon the optimal scaling approach for parameter estimation using qualitative data [Pargett et al, 2014, Schmiester et al, 2020]. The optimal scaling approach introduces surrogate data , which are the best quantitative representations of the qualitative measurements .Therefore, for some parameter vector θ , the surrogate data aim to describe the model simulation y ( t i , θ ) optimally, while fulfilling the ordering of the qualitative categories (Figure 1A).…”

“… in which k ( i ) is the index of the category of the surrogate datapoint and w i are datapoint-specific weights. The weights are usually chosen such that the objective function value is independent on the scale of the simulation [Pargett et al, 2014, Schmiester et al, 2020]. The first inequality constraint of (2) guarantees that the surrogate datapoints are placed inside the respective interval, and the second inequality constraint assures that the ordering of the categories is fulfilled.…”

“…To estimate the unknown model parameters θ , the surrogate data optimization (2) can be nested into the model parameter optimization (Figure 1B), yielding the hierarchical optimization problem Therefore, in each iteration of the outer optimization (of the model parameters θ ), the inner constrained optimization problem (2) (for the surrogate data and category bounds) has to be solved. We have previously shown that the inner optimization problem can be simplified to improve efficiency and robustness by only estimating upper bounds u and determining l and analytically [Schmiester et al, 2020]. However, for the derivation of the gradient computation algorithm introduced in the next section we will consider the full optimization problem (2).…”

“…Calculate optimal surrogate data and category bounds l, u by solving (2) or a reformulation of this problem [Schmiester et al, 2020].…”

PEtab—Interoperable specification of parameter estimation problems in systems biology

“…Additionally, other formats like SBtab [17] or Antimony [23] provide converters to SBML and can therefore also indirectly be used together with PEtab. Recently, new methods have been developed to estimate parameters in a hierarchical manner [18], including from qualitative data [24,25]. PEtab could be extended to also allow for these types of measurements.…”