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Cortical actomyosin flows, among other mechanisms, scale up spontaneous symmetry breaking and thus play pivotal roles in cell differentiation, division, and motility. According to many model systems, myosin motor-induced local contractions of initially isotropic actomyosin cortices are nucleation points for generating cortical flows. However, the positive feedback mechanisms by which spontaneous contractions can be amplified towards large-scale directed flows remain mostly speculative. To investigate such a process on spherical surfaces, we reconstituted and confined initially isotropic minimal actomyosin cortices to the interfaces of emulsion droplets. The presence of ATP leads to myosin-induced local contractions that self-organize and amplify into directed large-scale actomyosin flows. By combining our experiments with theory, we found that the feedback mechanism leading to a coordinated directional motion of actomyosin clusters can be described as asymmetric cluster vibrations, caused by intrinsic non-isotropic ATP consumption with spatial confinement. We identified fingerprints of vibrational states as the basis of directed motions by tracking individual actomyosin clusters. These vibrations may represent a generic key driver of directed actomyosin flows under spatial confinement in vitro and in living systems.

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.

The ability of designing biosynthetic systems with well-defined functional biomodules from scratch is an ambitious and revolutionary goal to deliver innovative, engineered solutions to future challenges in biotechnology and process systems engineering. In this work, several key challenges including modularization, functional biomodule identification, and assembly are discussed. In addition, an in silico protocell modeling approach is presented as a foundation for a computational model-based toolkit for rational analysis and modular design of biomimetic systems., (© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

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., Competing Interests: The authors have declared that no competing interests exist.

Imaging flow cytometry is a powerful experimental technique combining the strength of microscopy and flow cytometry to enable high-throughput characterization of cell populations on a detailed microscopic scale. This approach has an increasing importance for distinguishing between different cellular phenotypes such as proliferation, cell division and cell death. In the course of undergoing these different pathways, each cell is characterized by a high amount of properties. This makes it hard to filter the most relevant information for cell state discrimination. The traditional methods for cell state discrimination rely on dye based two-dimensional gating strategies ignoring information that is hidden in the high-dimensional property space. In order to make use of the information ignored by the traditional methods, we present a simple and efficient approach to distinguish biological states within a cell population based on machine learning techniques. We demonstrate the advantages and drawbacks of filter techniques combined with different classification schemes. These techniques are illustrated with two case studies of apoptosis detection in HeLa cells. Thereby we highlight (i) the aptitude of imaging flow cytometry regarding automated, label-free cell state discrimination and (ii) pitfalls that are frequently encountered. Additionally a MATLAB script is provided, which gives further insight regarding the computational work presented in this study.

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: flassig@mpi-magdeburg.mpg.de., Supplementary Information: Supplementary data are available at Bioinformatics online., (© The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com)

Background: Photosynthetic organisms can be used for renewable and sustainable production of fuels and high-value compounds from natural resources. Costs for design and operation of large-scale algae cultivation systems can be reduced if data from laboratory scale cultivations are combined with detailed mathematical models to evaluate and optimize the process., Results: In this work we present a flexible modeling formulation for accumulation of high-value storage molecules in microalgae that provides quantitative predictions under various light and nutrient conditions. The modeling approach is based on dynamic flux balance analysis (DFBA) and includes regulatory models to predict the accumulation of pigment molecules. The accuracy of the model predictions is validated through independent experimental data followed by a subsequent model-based fed-batch optimization. In our experimentally validated fed-batch optimization study we increase biomass and [Formula: see text]-carotene density by factors of about 2.5 and 2.1, respectively., Conclusions: The analysis shows that a model-based approach can be used to develop and significantly improve biotechnological processes for biofuels and pigments.

A 1-D mathematical model of a porous enzymatic electrode exhibiting the mediated electron transfer (MET) mechanism has been developed. As a model system, glucose oxidation catalyzed by immobilized glucose oxidase (GOx) in the presence of a co-immobilized tetrathiafulvalene (TTF) mediator in the porous electrode matrix has been selected. The balance equations for potential fields in the electron- and ion-conducting phases as well as concentration field have been formulated, solved numerically and validated experimentally under steady state conditions. The relevant kinetic parameters of the lumped reaction kinetics have been obtained by global optimization. The confidence intervals (CIs) of each parameter have been extracted from the respective likelihood. The parameter study has shown that the parameters related to mediator consumption/regeneration steps can be responsible for the shift of the reaction onset potential. Additionally, the model has shown that diffusion of the oxidized mediator out of the catalyst layer (CL) plays a significant role only at more positive potentials and low glucose concentrations. Only concentration profiles in different layers influence the electrode performance while other state fields like potential distributions in different phases have no impact on the performance. The concentration profiles reveal that all electrodes work through; the observed limiting currents are diffusion-reaction limiting. The normalized electrode activity decreases with an increase of enzyme loading. According to the model, the reason for this observation is glucose depletion along the CL at higher enzyme loadings. Comparison with experiments advices a decrease of enzyme utilization at higher enzyme loadings., (Copyright © 2015 Elsevier B.V. All rights reserved.)

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.

In this work, a photoautotrophic growth model incorporating light and nutrient effects on growth and pigmentation of Dunaliella salina was formulated. The model equations were taken from literature and modified according to the experimental setup with special emphasis on model reduction. The proposed model has been evaluated with experimental data of D. salina cultivated in a flat-plate photobioreactor under stressed and non-stressed conditions. Simulation results show that the model can represent the experimental data accurately. The identifiability of the model parameters was studied using the profile likelihood method. This analysis revealed that three model parameters are practically non-identifiable. However, some of these non-identifiabilities can be resolved by model reduction and additional measurements. As a conclusion, our results suggest that the proposed model equations result in a predictive growth model for D. salina., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

Reliable and efficient detection of DNA damage constitutes a vital capability of human cells to maintain genome stability. Following DNA damage, the histone variant H2AX becomes rapidly phosphorylated by the DNA damage response kinases DNA-PKcs and ATM. H2AX phosphorylation plays a central role in signal amplification leading to chromatin remodeling and DNA repair initiation. The contribution of DNA-PKcs and ATM to H2AX phosphorylation is however puzzling. Although ATM is required, DNA-PKcs can substitute for it. Here we analyze the interplay between DNA-PKcs and ATM with a computational model derived by an iterative workflow: switching between experimental design, experiment and model analysis, we generated an extensive set of time-resolved data and identified a conclusive dynamic signaling model out of several alternatives. Our work shows that DNA-PKcs and ATM enforce a biphasic H2AX phosphorylation. DNA-PKcs can be associated to the initial, and ATM to the succeeding phosphorylation phase of H2AX resulting into a signal persistence detection function for reliable damage sensing. Further, our model predictions emphasize that DNA-PKcs inhibition significantly delays H2AX phosphorylation and associated DNA repair initiation.

Background: The data-driven inference of intracellular networks is one of the key challenges of computational and systems biology. As suggested by recent works, a simple yet effective approach for reconstructing regulatory networks comprises the following two steps. First, the observed effects induced by directed perturbations are collected in a signed and directed perturbation graph (PG). In a second step, Transitive Reduction (TR) is used to identify and eliminate those edges in the PG that can be explained by paths and are therefore likely to reflect indirect effects., Results: In this work we introduce novel variants for PG generation and TR, leading to significantly improved performances. The key modifications concern: (i) use of novel statistical criteria for deriving a high-quality PG from experimental data; (ii) the application of local TR which allows only short paths to explain (and remove) a given edge; and (iii) a novel strategy to rank the edges with respect to their confidence. To compare the new methods with existing ones we not only apply them to a recent DREAM network inference challenge but also to a novel and unprecedented synthetic compendium consisting of 30,5000-gene networks simulated with varying biological and measurement error variances resulting in a total of 270 datasets. The benchmarks clearly demonstrate the superior reconstruction performance of the novel PG and TR variants compared to existing approaches. Moreover, the benchmark enabled us to draw some general conclusions. For example, it turns out that local TR restricted to paths with a length of only two is often sufficient or even favorable. We also demonstrate that considering edge weights is highly beneficial for TR whereas consideration of edge signs is of minor importance. We explain these observations from a graph-theoretical perspective and discuss the consequences with respect to a greatly reduced computational demand to conduct TR. Finally, as a realistic application scenario, we use our framework for inferring gene interactions in yeast based on a library of gene expression data measured in mutants with single knockouts of transcription factors. The reconstructed network shows a significant enrichment of known interactions, especially within the 100 most confident (and for experimental validation most relevant) edges., Conclusions: This paper presents several major achievements. The novel methods introduced herein can be seen as state of the art for inference techniques relying on perturbation graphs and transitive reduction. Another key result of the study is the generation of a new and unprecedented large-scale in silico benchmark dataset accounting for different noise levels and providing a solid basis for unbiased testing of network inference methodologies. Finally, applying our approach to Saccharomyces cerevisiae suggested several new gene interactions with high confidence awaiting experimental validation.

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: klamt@mpi-magdeburg.mpg.de.

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: flassig@mpi-magdeburg.mpg.de, 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.