Power-to-X processes convert excess renewable energy into storable fuels such as methane, addressing critical energy storage and transportation challenges. However, implementing these processes presents operational difficulties, particularly in managing fluctuating energy inputs. Digital Twins, or virtual replicas of physical systems, offer a promising solution by enabling model-based strategies for optimization and control. However, traditional mechanistic models are computationally intensive, limiting their application in real-time scenarios. This highlights the need for surrogate models that are computationally efficient and capable of accurately capturing the essential dynamics of complex systems. In this study, we evaluate and compare advanced techniques for modeling spatio-temporal processes, including a graph attention network (GAT), operator inference (OpInf) with stability guarantees, and sparse identification with greedy sampling (GN-SINDy). These methods are evaluated for their ability to model the dynamic operation and control of a catalytic CO2 methanation reactor. By evaluating their accuracy and computational efficiency, we aim to identify surrogate models tailored to spatio-temporal systems, advance the development of Digital Twins, and improve renewable energy conversion.

BACKGROUND: The green microalga Dunaliella salina accumulates a high proportion of β-carotene during abiotic stress conditions. To better understand the intracellular flux distribution leading to carotenoid accumulation, this work aimed at reconstructing a carbon core metabolic network for D. salina CCAP 19/18 based on the recently published nuclear genome and its validation with experimental observations and literature data. RESULTS: The reconstruction resulted in a network model with 221 reactions and 212 metabolites within three compartments: cytosol, chloroplast and mitochondrion. The network was implemented in the MATLAB toolbox CellNetAnalyzer and checked for feasibility. Furthermore, a flux balance analysis was carried out for different light and nutrient uptake rates. The comparison of the experimental knowledge with the model prediction revealed that the results of the stoichiometric network analysis are plausible and in good agreement with the observed behavior. Accordingly, our model provides an excellent tool for investigating the carbon core metabolism of D. salina. CONCLUSIONS: The reconstructed metabolic network of D. salina presented in this work is able to predict the biological behavior under light and nutrient stress and will lead to an improved process understanding for the optimized production of high-value products in microalgae.

CD95/Fas/APO-1 is a member of the death receptor family that triggers apoptotic and anti-apoptotic responses in particular, NF-κB. These responses are characterized by a strong heterogeneity within a population of cells. To determine how the cell decides between life and death we developed a computational model supported by imaging flow cytometry analysis of CD95 signaling. Here we show that CD95 stimulation leads to the induction of caspase and NF-κB pathways simultaneously in one cell. The related life/death decision strictly depends on cell-to-cell variability in the formation of the death-inducing complex (DISC) on one side (extrinsic noise) vs. stochastic gene expression of the NF-κB pathway on the other side (intrinsic noise). Moreover, our analysis has uncovered that the stochasticity in apoptosis and NF-kB pathways leads not only to survival or death of a cell, but also causes a third type of response to CD95 stimulation that we termed ambivalent response. Cells in the ambivalent state can undergo cell death or survive which was subsequently validated by experiments. Taken together, we have uncovered how these two competing pathways control the fate of a cell, which in turn plays an important role for development of anti-cancer therapies.

MOTIVATION: Biological cells operate in a noisy regime influenced by intrinsic, extrinsic and external noise, which leads to large differences of individual cell states. Stochastic effects must be taken into account to characterize biochemical kinetics accurately. Since the exact solution of the chemical master equation, which governs the underlying stochastic process, cannot be derived for most biochemical systems, approximate methods are used to obtain a solution. RESULTS: In this study, a method to efficiently simulate the various sources of noise simultaneously is proposed and benchmarked on several examples. The method relies on the combination of the sigma point approach to describe extrinsic and external variability and the τ -leaping algorithm to account for the stochasticity due to probabilistic reactions. The comparison of our method to extensive Monte Carlo calculations demonstrates an immense computational advantage while losing an acceptable amount of accuracy. Additionally, the application to parameter optimization problems in stochastic biochemical reaction networks is shown, which is rarely applied due to its huge computational burden. To give further insight, a MATLAB script is provided including the proposed method applied to a simple toy example of gene expression. AVAILABILITY AND IMPLEMENTATION: MATLAB code is available at Bioinformatics online. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Understanding the dynamics of biological processes can substantially be supported by computational models in the form of nonlinear ordinary differential equations (ODE). Typically, this model class contains many unknown parameters, which are estimated from inadequate and noisy data. Depending on the ODE structure, predictions based on unmeasured states and associated parameters are highly uncertain, even undetermined. For given data, profile likelihood analysis has been proven to be one of the most practically relevant approaches for analyzing the identifiability of an ODE structure, and thus model predictions. In case of highly uncertain or non-identifiable parameters, rational experimental design based on various approaches has shown to significantly reduce parameter uncertainties with minimal amount of effort. RESULTS: In this work we illustrate how to use profile likelihood samples for quantifying the individual contribution of parameter uncertainty to prediction uncertainty. For the uncertainty quantification we introduce the profile likelihood sensitivity (PLS) index. Additionally, for the case of several uncertain parameters, we introduce the PLS entropy to quantify individual contributions to the overall prediction uncertainty. We show how to use these two criteria as an experimental design objective for selecting new, informative readouts in combination with intervention site identification. The characteristics of the proposed multi-criterion objective are illustrated with an in silico example. We further illustrate how an existing practically non-identifiable model for the chlorophyll fluorescence induction in a photosynthetic organism, D. salina, can be rendered identifiable by additional experiments with new readouts. CONCLUSIONS: Having data and profile likelihood samples at hand, the here proposed uncertainty quantification based on prediction samples from the profile likelihood provides a simple way for determining individual contributions of parameter uncertainties to uncertainties in model predictions. The uncertainty quantification of specific model predictions allows identifying regions, where model predictions have to be considered with care. Such uncertain regions can be used for a rational experimental design to render initially highly uncertain model predictions into certainty. Finally, our uncertainty quantification directly accounts for parameter interdependencies and parameter sensitivities of the specific prediction.

MOTIVATION: Systems Genetics approaches, in particular those relying on genetical genomics data, put forward a new paradigm of large-scale genome and network analysis. These methods use naturally occurring multi-factorial perturbations (e.g. polymorphisms) in properly controlled and screened genetic crosses to elucidate causal relationships in biological networks. However, although genetical genomics data contain rich information, a clear dissection of causes and effects as required for reconstructing gene regulatory networks is not easily possible. RESULTS: We present a framework for reconstructing gene regulatory networks from genetical genomics data where genotype and phenotype correlation measures are used to derive an initial graph which is subsequently reduced by pruning strategies to minimize false positive predictions. Applied to realistic simulated genetic data from a recent DREAM challenge, we demonstrate that our approach is simple yet effective and outperforms more complex methods (including the best performer) with respect to (i) reconstruction quality (especially for small sample sizes) and (ii) applicability to large data sets due to relatively low computational costs. We also present reconstruction results from real genetical genomics data of yeast. AVAILABILITY: A MATLAB implementation (script) of the reconstruction framework is available at www.mpi-magdeburg.mpg.de/projects/cna/etcdownloads.html CONTACT: [email protected].

MOTIVATION: Biochemical reaction networks in the form of coupled ordinary differential equations (ODEs) provide a powerful modeling tool for understanding the dynamics of biochemical processes. During the early phase of modeling, scientists have to deal with a large pool of competing nonlinear models. At this point, discrimination experiments can be designed and conducted to obtain optimal data for selecting the most plausible model. Since biological ODE models have widely distributed parameters due to, e.g. biologic variability or experimental variations, model responses become distributed. Therefore, a robust optimal experimental design (OED) for model discrimination can be used to discriminate models based on their response probability distribution functions (PDFs). RESULTS: In this work, we present an optimal control-based methodology for designing optimal stimulus experiments aimed at robust model discrimination. For estimating the time-varying model response PDF, which results from the nonlinear propagation of the parameter PDF under the ODE dynamics, we suggest using the sigma-point approach. Using the model overlap (expected likelihood) as a robust discrimination criterion to measure dissimilarities between expected model response PDFs, we benchmark the proposed nonlinear design approach against linearization with respect to prediction accuracy and design quality for two nonlinear biological reaction networks. As shown, the sigma-point outperforms the linearization approach in the case of widely distributed parameter sets and/or existing multiple steady states. Since the sigma-point approach scales linearly with the number of model parameter, it can be applied to large systems for robust experimental planning. AVAILABILITY: An implementation of the method in MATLAB/AMPL is available at http://www.uni-magdeburg.de/ivt/svt/person/rf/roed.html. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are are available at Bioinformatics online.

MOTIVATION: Distinguishing direct from indirect influences is a central issue in reverse engineering of biological networks because it facilitates detection and removal of false positive edges. Transitive reduction is one approach for eliminating edges reflecting indirect effects but its use in reconstructing cyclic interaction graphs with true redundant structures is problematic. RESULTS: We present TRANSWESD, an elaborated variant of TRANSitive reduction for WEighted Signed Digraphs that overcomes conceptual problems of existing versions. Major changes and improvements concern: (i) new statistical approaches for generating high-quality perturbation graphs from systematic perturbation experiments; (ii) the use of edge weights (association strengths) for recognizing true redundant structures; (iii) causal interpretation of cycles; (iv) relaxed definition of transitive reduction; and (v) approximation algorithms for large networks. Using standardized benchmark tests, we demonstrate that our method outperforms existing variants of transitive reduction and is, despite its conceptual simplicity, highly competitive with other reverse engineering methods.