Diagnostics of Data-Driven Models: Uncertainty Quantification of PM7 Semi-Empirical Quantum Chemical Method.

We report an evaluation of a semi-empirical quantum chemical method PM7 from the perspective of uncertainty quantification. Specifically, we apply Bound-to-Bound Data Collaboration, an uncertainty quantification framework, to characterize (a) variability of PM7 model parameter values consistent with the uncertainty in the training data and (b) uncertainty propagation from the training data to the model predictions. Experimental heats of formation of a homologous series of linear alkanes are used as the property of interest. The training data are chemically accurate, i.e., they have very low uncertainty by the standards of computational chemistry. The analysis does not find evidence of PM7 consistency with the entire data set considered as no single set of parameter values is found that captures the experimental uncertainties of all training data. A set of parameter values for PM7 was able to capture the training data within ±1 kcal/mol, but not to the smaller level of uncertainty in the reported data. Nevertheless, PM7 was found to be consistent for subsets of the training data. In such cases, uncertainty propagation from the chemically accurate training data to the predicted values preserves error within bounds of chemical accuracy if predictions are made for the molecules of comparable size. Otherwise, the error grows linearly with the relative size of the molecules.

Tracking transience: a method for dynamic monitoring of biological events in Arabidopsis thaliana biosensors.

MAIN CONCLUSION: The activation and level of expression of an endogenous, stress-responsive biosensor (bioreporter) can be visualized in real-time and non-destructively using highly accessible equipment (fluorometer). Biosensor output can be linked to computer-controlled systems to enable feedback-based control of a greenhouse environment. Today's agriculture requires an ability to precisely and rapidly assess the physiological stress status of plants in order to optimize crop yield. Here we describe the implementation and utility of a detection system based on a simple fluorometer design for real-time, continuous, and non-destructive monitoring of a genetically engineered biosensor plant. We report the responses to heat stress of Arabidopsis thaliana plants expressing a Yellow Fluorescent Protein bioreporter under the control of the DREB2A temperature-sensing promoter. Use of this bioreporter provides the ability to identify transient and steady-state behavior of gene activation in response to stress, and serves as an interface for novel experimental protocols. Models identified through such experiments inform the development of computer-based feedback control systems for the greenhouse environment, based on in situ monitoring of mature plants. More broadly, the work here provides a basis for informing biologists and engineers about the kinetics of bioreporter constructs, and also about ways in which other fluorescent protein constructs could be integrated into automated control systems.

Interval prediction of molecular properties in parametrized quantum chemistry.

The accurate evaluation of molecular properties lies at the core of predictive physical models. Most reliable quantum-chemical calculations are limited to smaller molecular systems while purely empirical approaches are limited in accuracy and reliability. A promising approach is to employ a quantum-mechanical formalism with simplifications and to compensate for the latter with parametrization. We propose a strategy of directly predicting the uncertainty interval for a property of interest, based on training-data uncertainties, which sidesteps the need for an optimum set of parameters.

Sensitivity analysis of uncertainty in model prediction.

Data Collaboration is a framework designed to make inferences from experimental observations in the context of an underlying model. In the prior studies, the methodology was applied to prediction on chemical kinetics models, consistency of a reaction system, and discrimination among competing reaction models. The present work advances Data Collaboration by developing sensitivity analysis of uncertainty in model prediction with respect to uncertainty in experimental observations and model parameters. Evaluation of sensitivity coefficients is performed alongside the solution of the general optimization ansatz of Data Collaboration. The obtained sensitivity coefficients allow one to determine which experiment/parameter uncertainty contributes the most to the uncertainty in model prediction, rank such effects, consider new or even hypothetical experiments to perform, and combine the uncertainty analysis with the cost of uncertainty reduction, thereby providing guidance in selecting an experimental/theoretical strategy for community action.

Model discrimination using data collaboration.

This paper introduces a practical data-driven method to discriminate among large-scale kinetic reaction models. The approach centers around a computable measure of model/data mismatch. We introduce two provably convergent algorithms that were developed to accommodate large ranges of uncertainty in the model parameters. The algorithms are demonstrated on a simple toy example and a methane combustion model with more than 100 uncertain parameters. They are subsequently used to discriminate between two models for a contemporarily studied biological signaling network.