Grammatical Immune System Evolution for Reverse Engineering Nonlinear Dynamic Bayesian Models

Abstract

An artificial immune system algorithm is introduced in which nonlinear dynamic models are evolved to fit time series of interacting biomolecules. This grammar-based machine learning method learns the structure and parameters of the underlying dynamic model. In silico immunogenetic mechanisms for the generation of model-structure diversity are implemented with the aid of a grammar, which also enforces semantic constraints of the evolved models. The grammar acts as a DNA repair polymerase that can identify recombination and hypermutation signals in the antibody (model) genome. These signals contain information interpretable by the grammar to maintain model context. Grammatical Immune System Evolution (GISE) is applied to a nonlinear system identification problem in which a generalized (nonlinear) dynamic Bayesian model is evolved to fit biologically motivated artificial time-series data. From experimental data, we use GISE to infer an improved kinetic model for the oxidative metabolism of 17β-estradiol (E2), the parent hormone of the estrogen metabolism pathway.

Biochemical Systems Theory: A Review

“…e group also tested ant colony optimization [284,285] and simulated annealing [286,287] (see also [288,289]) and provided a benchmark system for comparing different approaches [290]. McKinney and Tian proposed an arti�cial immune system for the same estimation purposes and compared various underlying models [291]. Lee and Yang used a clustering approach [292].…”

Informatics approaches for identifying biologic relationships in time‐series data

“…The enormity of the search space of possible model structures calls for heuristic search methods such as evolutionary algorithms. 17,18,26,27 When learning the structure of a model, it is often necessary to include parsimony constraints in the objective function. A typical choice for objective function involves some variant of least squares deviation of the model prediction from the time-series panel data.…”

“…A recursive approach using the UKF has been successful for parameter estimation of dynamic biologic models. 17,18 Figure 3 shows the results of this parameter estimation approach for data (filled circles) simulated based on the hypothetical model shown in Figure 2, disturbed by a large measurement noise and sparsely sampled (only five time points). The recursive steps are depicted as multiple lines for each variable shown in Figure 3 at the end of each UKF pass through the time series.…”

“…A true-positive detection of a dynamic model is not an all or nothing prospect; one can correctly identify parts of the model and misidentify others. 18 For stochastic system-identification algorithms, rather than taking the top-scoring system as the final model, a useful strategy to detect false-positive model components might be to inspect the set of top-scoring models to identify consensus model components and components that show more inter-model variation, and then run the algorithm again, this time focusing on the uncertain model components, which are more likely to be false. The best way to reduce false-positive models that all reasonably describe the available experimental data is to make computational predictions to design a new experiment that can discriminate between the hypothetical models.…”

“…The unscented Kalman filter (UKF) is an accurate and computationally efficient method for estimating parameters of nonlinear dynamic systems 15, 16. It has been used to model in vivo protein time‐series with noise and nonlinearities17, 18 and has the ability to model unobserved state components, yet computational limitations still must be overcome for high‐dimensional systems.…”