Björn H. Junker

Motivation: In systems biology, kinetic models represent the biological system using a set of ordinary differential equations (ODEs). The correct values of the parameters within these ODEs are critical for a reliable study of the dynamic behaviour of such systems. Typically, it is only possible to experimentally measure a fraction of these parameter values. The rest must be indirectly determined from measurements of other quantities. In this article, we propose a novel statistical inference technique to computationally estimate these unknown parameter values. By characterizing the ODEs with non-linear state-space equations, this inference technique models the unknown parameters as hidden states, which can then be estimated from noisy measurement data. Results: Here we extended the square-root unscented Kalman filter SR-UKF proposed by Merwe and Wan to include constraints with the state estimation process. We developed the constrained square-root unscented Kalman filter (CSUKF) to estimate parameters of non-linear state-space models. This probabilistic inference technique was successfully used to estimate parameters of a glycolysis model in yeast and a gene regulatory network. We showed that our method is numerically stable and can reliably estimate parameters within a biologically meaningful parameter space from noisy observations. When compared with the two common non-linear extensions of Kalman filter in addition to four widely used global optimization algorithms, CSUKF is shown to be both accurate and computationally efficient. With CSUKF, statistical analysis is straightforward, as it directly provides the uncertainty on the estimation result. Availability and implementation: Matlab code available upon request from the author. Contact: baker@ipk-gatersleben.de Supplementary information: Supplementary data are available at Bioinformatics online.

Background: Metabolic flux analysis has become an established method in systems biology and functional genomics. The most common approach for determining intracellular metabolic fluxes is to utilize mass spectrometry in combination with stable isotope labeling experiments. However, before the mass spectrometric data can be used it has to be corrected for biases caused by naturally occurring stable isotopes, by the analytical technique(s) employed, or by the biological sample itself. Finally the MS data and the labeling information it contains have to be assembled into a data format usable by flux analysis software (of which several dedicated packages exist). Currently the processing of mass spectrometric data is time-consuming and error-prone requiring peak by peak cut-and-paste analysis and manual curation. In order to facilitate high-throughput metabolic flux analysis, the automation of multiple steps in the analytical workflow is necessary. Results: Here we describe iMS2Flux, software developed to automate, standardize and connect the data flow between mass spectrometric measurements and flux analysis programs. This tool streamlines the transfer of data from extraction via correction tools to ¹³C-Flux software by processing MS data from stable isotope labeling experiments. It allows the correction of large and heterogeneous MS datasets for the presence of naturally occurring stable isotopes, initial biomass and several mass spectrometry effects. Before and after data correction, several checks can be performed to ensure accurate data. The corrected data may be returned in a variety of formats including those used by metabolic flux analysis software such as 13CFLUX, OpenFLUX and 13CFLUX2. Conclusion: iMS2Flux is a versatile, easy to use tool for the automated processing of mass spectrometric data containing isotope labeling information. It represents the core framework for a standardized workflow and data processing. Due to its flexibility it facilitates the inclusion of different experimental datasets and thus can contribute to the expansion of flux analysis applications.

Research on plant metabolism is currently experiencing the common use of various omics methods creating valuable information on the concentrations of the cell's constituents. However, little is known about in vivo reaction rates, which can be determined by Metabolic Flux Analysis (MFA), a combination of isotope labeling experiments and computer modeling of the metabolic network. Large-scale applications of this method so far have been hampered by tedious procedures of tissue culture, analytics, modeling and simulation. By streamlining the workflow of MFA, the throughput of the method could be significantly increased. We propose strategies for these improvements on various sub-steps which will move flux analysis to the medium-throughput range and closer to established methods such as metabolite profiling. Furthermore, this may enable novel applications of MFA, for example screening plant populations for traits related to the flux phenotype.

The quantification of metabolic fluxes is gaining increasing importance in the analysis of the metabolic behavior of biological systems such as organisms, tissues or cells. Various methodologies (wetlab or drylab) result in sets of fluxes which require an appropriate visualization for interpretation by scientists. The visualization of flux distributions is a necessary prerequisite for intuitive flux data exploration in the context of metabolic networks.

Synthetic biology methods are routinely applied in the plant field as in other eukaryotic model systems. Several synthetic components have been developed in plants and an increasing number of studies report on the assembly into functional synthetic genetic circuits. This chapter gives an overview of the existing plant genetic networks and describes in detail the application of two systems for inducible gene expression. The ethanol-inducible system relies on the ethanol-responsive interaction of the AlcA transcriptional activator and the AlcR receptor resulting in the transcription of the gene of interest (GOI). In comparison, the translational fusion of GOI and the glucocorticoid receptor (GR) domain leads to the dexamethasone-dependent nuclear translocation of the GOI::GR protein. This chapter contains detailed protocols for the application of both systems in the model plants potato and Arabidopsis, respectively.

In systems biology, experimentally measured parameters are not always available, necessitating the use of computationally based parameter estimation. In order to rely on estimated parameters, it is critical to first determine which parameters can be estimated for a given model and measurement set. This is done with parameter identifiability analysis. A kinetic model of the sucrose accumulation in the sugar cane culm tissue developed by Rohwer et al. was taken as a test case model. What differentiates this approach is the integration of an orthogonal-based local identifiability method into the unscented Kalman filter (UKF), rather than using the more common observability-based method which has inherent limitations. It also introduces a variable step size based on the system uncertainty of the UKF during the sensitivity calculation. This method identified 10 out of 12 parameters as identifiable. These ten parameters were estimated using the UKF, which was run 97 times. Throughout the repetitions the UKF proved to be more consistent than the estimation algorithms used for comparison.