Systems biology of the modified branched Entner-Doudoroff pathway in Sulfolobus solfataricus.

Sulfolobus solfataricus is a thermoacidophilic Archaeon that thrives in terrestrial hot springs (solfatares) with optimal growth at 80°C and pH 2-4. It catabolizes specific carbon sources, such as D-glucose, to pyruvate via the modified Entner-Doudoroff (ED) pathway. This pathway has two parallel branches, the semi-phosphorylative and the non-phosphorylative. However, the strategy of S.solfataricus to endure in such an extreme environment in terms of robustness and adaptation is not yet completely understood. Here, we present the first dynamic mathematical model of the ED pathway parameterized with quantitative experimental data. These data consist of enzyme activities of the branched pathway at 70°C and 80°C and of metabolomics data at the same temperatures for the wild type and for a metabolic engineered knockout of the semi-phosphorylative branch. We use the validated model to address two questions: 1. Is this system more robust to perturbations at its optimal growth temperature? 2. Is the ED robust to deletion and perturbations? We employed a systems biology approach to answer these questions and to gain further knowledge on the emergent properties of this biological system. Specifically, we applied deterministic and stochastic approaches to study the sensitivity and robustness of the system, respectively. The mathematical model we present here, shows that: 1. Steady state metabolite concentrations of the ED pathway are consistently more robust to stochastic internal perturbations at 80°C than at 70°C; 2. These metabolite concentrations are highly robust when faced with the knockout of either branch. Connected with this observation, these two branches show different properties at the level of metabolite production and flux control. These new results reveal how enzyme kinetics and metabolomics synergizes with mathematical modelling to unveil new systemic properties of the ED pathway in S.solfataricus in terms of its adaptation and robustness.

Senoptosis: non-lethal DNA cleavage as a route to deep senescence.

DNA-damage-induced apoptosis and cellular senescence are perceived as two distinct cell fates. We found that after ionizing radiation (IR)-induced DNA damage the majority (up to 70 %) of senescent human diploid fibroblasts (HDFs) were subjected to controlled cleavage of DNA, resulting in the establishment of a viable and stable sub-G1 population, i.e. deeply senescent cells. We show that in senescent HDFs this DNA cleavage is triggered by modest loss of the mitochondrial membrane potential, which is not sufficient to activate caspases, but strong enough to release mitochondrial endonuclease G (EndoG). We demonstrate that upon γ-irradiation in HDFs EndoG translocates into the nucleus playing an essential role in the non-lethal cleavage of damaged DNA. Notably, the established sub-G1 cell population does not contribute to the senescence-associated secretory phenotype (SASP), however, it exhibits increased senescence-associated ß-galactosidase activity. We show that EndoG knockdown causes an increase in DNA damage, indicating a role of this enzyme in DNA repair. Thus, we conclude that IR-induced deep senescence of HDFs exhibits features of both senescence, such as cell cycle arrest and viability, and apoptosis like reduced DNA content and no SASP, and, resembles uncomplete or stalled apoptosis, a phenomenon we term senoptosis.

ArnS, a kinase involved in starvation-induced archaellum expression.

Organisms have evolved motility organelles that allow them to move to favourable habitats. Cells integrate environmental stimuli into intracellular signals to motility machineries to direct this migration. Many motility organelles are complex surface appendages that have evolved a tight, hierarchical regulation of expression. In the crenearchaeon Sulfolobus acidocaldarius, biosynthesis of the archaellum is regulated by regulatory network proteins that control expression of archaellum components in a phosphorylation-dependent manner. A major trigger for archaellum expression is nutrient starvation, but although some components are known, the regulatory cascade triggered by starvation is poorly understood. In this work, the starvation-induced Ser/Thr protein kinase ArnS (Saci_1181) which is located proximally to the archaellum operon was identified. Deletion of arnS results in reduced motility, though the archaellum is properly assembled. Therefore, our experimental and modelling results indicate that ArnS plays an essential role in the precisely controlled expression of archaellum components during starvation-induced motility in Sulfolobus acidocaldarius. Furthermore they combined in vivo experiments and mathematical models to describe for the first time in archaea the dynamics of key regulators of archaellum expression.

Systems Level Analysis of the Yeast Osmo-Stat.

Adaptation is an important property of living organisms enabling them to cope with environmental stress and maintaining homeostasis. Adaptation is mediated by signaling pathways responding to different stimuli. Those signaling pathways might communicate in order to orchestrate the cellular response to multiple simultaneous stimuli, a phenomenon called crosstalk. Here, we investigate possible mechanisms of crosstalk between the High Osmolarity Glycerol (HOG) and the Cell Wall Integrity (CWI) pathways in yeast, which mediate adaptation to hyper- and hypo-osmotic challenges, respectively. We combine ensemble modeling with experimental investigations to test in quantitative terms different hypotheses about the crosstalk of the HOG and the CWI pathways. Our analyses indicate that for the conditions studied i) the CWI pathway activation employs an adaptive mechanism with a variable volume-dependent threshold, in contrast to the HOG pathway, whose activation relies on a fixed volume-dependent threshold, ii) there is no or little direct crosstalk between the HOG and CWI pathways, and iii) its mainly the HOG alone mediating adaptation of cellular osmotic pressure for both hyper- as well as hypo-osmotic stress. Thus, by iteratively combining mathematical modeling with experimentation we achieved a better understanding of regulatory mechanisms of yeast osmo-homeostasis and formulated new hypotheses about osmo-sensing.

How time delay and network design shape response patterns in biochemical negative feedback systems.

BACKGROUND: Negative feedback in combination with time delay can bring about both sustained oscillations and adaptive behaviour in cellular networks. Here, we study which design features of systems with delayed negative feedback shape characteristic response patterns with special emphasis on the role of time delay. To this end, we analyse generic two-dimensional delay differential equations describing the dynamics of biochemical signal-response networks. RESULTS: We investigate the influence of several design features on the stability of the model equilibrium, i.e., presence of auto-inhibition and/or mass conservation and the kind and/or strength of the delayed negative feedback. We show that auto-inhibition and mass conservation have a stabilizing effect, whereas increasing abruptness and decreasing feedback threshold have a de-stabilizing effect on the model equilibrium. Moreover, applying our theoretical analysis to the mammalian p53 system we show that an auto-inhibitory feedback can decouple period and amplitude of an oscillatory response, whereas the delayed feedback can not. CONCLUSIONS: Our theoretical framework provides insight into how time delay and design features of biochemical networks act together to elicit specific characteristic response patterns. Such insight is useful for constructing synthetic networks and controlling their behaviour in response to external stimulation.

Simulation of forest tree species' bud burst dates for different climate scenarios: chilling requirements and photo-period may limit bud burst advancement.

This study investigates whether the assumed increase of winter and spring temperatures is depicted by phenological models in correspondingly earlier bud burst (BB) dates. Some studies assume that rising temperatures lead to an earlier BB, but even later BB has been detected. The phenological model PIM (promoter-inhibitor-model) fitted to the extensive phenological database of the German Weather Service was driven by several climate scenarios. This model accounts for the complicated mechanistic interactions between chilling requirements, temperature and photo-period. It predicts BB with a r 2 between 0.41 and 0.62 and a RMSE of around 1 week, depending on species. Parameter sensitivities depict species dependent interactions between growth and chilling requirements as well as photo-period. A mean trend to earlier BB was revealed for the period 2002- 2100, varying between -0.05 and -0.11 days per year, depending on species. These trends are lower than for the period 1951- 2009. Within climate scenario period, trends are decreasing for beech and chestnut, stagnating for birch and increasing for oak. Results suggest that not fulfilled chilling requirements accompanied by an increasing dependency on photo-period potentially limit future BB advancement. The combination of a powerful phenological model, a large scale phenological database and several climate scenarios, offers new insights into the mechanistic comprehension of spring phenology.

The role of time delay in adaptive cellular negative feedback systems.

Adaptation in cellular systems is often mediated by negative feedbacks, which usually come with certain time delays causing several characteristic response patterns including an overdamped response, damped or sustained oscillations. Here, we analyse generic two-dimensional delay differential equations with delayed negative feedback describing the dynamics of biochemical adaptive signal-response networks. We derive explicit thresholds and boundaries showing how time delay determines characteristic response patterns of these networks. Applying our theoretical analyses to concrete data we show that adaptation to osmotic stress in yeast is optimal in the sense of minimizing adaptation time without causing oscillatory behaviour, i.e., a critically damped response. In addition, our framework demonstrates that a slight increase of time delay in the NF-κB system might induce a switch from damped to sustained oscillatory behaviour. Thus, we demonstrate how delay differential equations can be used to explicitly study the delay in biochemical negative feedback systems. Our analysis also provides insight into how time delay may tune biological signal-response patterns and control the systems behaviour.

To senesce or not to senesce: how primary human fibroblasts decide their cell fate after DNA damage.

Excessive DNA damage can induce an irreversible cell cycle arrest, called senescence, which is generally perceived as an important tumour-suppressor mechanism. However, it is unclear how cells decide whether to senesce or not after DNA damage. By combining experimental data with a parameterized mathematical model we elucidate this cell fate decision at the G1-S transition. Our model provides a quantitative and conceptually new understanding of how human fibroblasts decide whether DNA damage is beyond repair and senesce. Model and data imply that the G1-S transition is regulated by a bistable hysteresis switch with respect to Cdk2 activity, which in turn is controlled by the Cdk2/p21 ratio rather than cyclin abundance. We experimentally confirm the resulting predictions that to induce senescence i) in healthy cells both high initial and elevated background DNA damage are necessary and sufficient, and ii) in already damaged cells much lower additional DNA damage is sufficient. Our study provides a mechanistic explanation of a) how noise in protein abundances allows cells to overcome the G1-S arrest even with substantial DNA damage, potentially leading to neoplasia, and b) how accumulating DNA damage with age increasingly sensitizes cells for senescence.

FoCo: a simple and robust quantification algorithm of nuclear foci.

BACKGROUND: The number of γH2AX foci per nucleus is an accepted measure of the number of DNA double-strand breaks in single cells. One of the experimental techniques for γH2AX detection in cultured cells is immunofluorescent labelling of γH2AX and nuclei followed by microscopy imaging and analysis. RESULTS: In this study, we present the algorithm FoCo for reliable and robust automatic nuclear foci counting in single cell images. FoCo has the following advantages with respect to other software packages: i) the ability to reliably quantify even densely distributed foci, e.g., on images of cells subjected to radiation doses up to 10 Gy, ii) robustness of foci quantification in the sense of suppressing out-of-focus background signal, and iii) its simplicity. FoCo requires only 5 parameters that have to be adjusted by the user. CONCLUSIONS: FoCo is an open-source user-friendly software with GUI for individual foci counting, which is able to produce reliable and robust foci quantifications even for low signal/noise ratios and densely distributed foci.

Development of a robust DNA damage model including persistent telomere-associated damage with application to secondary cancer risk assessment.

Mathematical modelling has been instrumental to understand kinetics of radiation-induced DNA damage repair and associated secondary cancer risk. The widely accepted two-lesion kinetic (TLK) model assumes two kinds of double strand breaks, simple and complex ones, with different repair rates. Recently, persistent DNA damage associated with telomeres was reported as a new kind of DNA damage. We therefore extended existing versions of the TLK model by new categories of DNA damage and re-evaluated those models using extensive data. We subjected different versions of the TLK model to a rigorous model discrimination approach. This enabled us to robustly select a best approximating parsimonious model that can both recapitulate and predict transient and persistent DNA damage after ionizing radiation. Models and data argue for i) nonlinear dose-damage relationships, and ii) negligible saturation of repair kinetics even for high doses. Additionally, we show that simulated radiation-induced persistent telomere-associated DNA damage foci (TAF) can be used to predict excess relative risk (ERR) of developing secondary leukemia after fractionated radiotherapy. We suggest that TAF may serve as an additional measure to predict cancer risk after radiotherapy using high dose rates. This may improve predicting risk-dose dependency of ionizing radiation especially for long-term therapies.

Mathematical modelling of arsenic transport, distribution and detoxification processes in yeast.

Arsenic has a dual role as causative and curative agent of human disease. Therefore, there is considerable interest in elucidating arsenic toxicity and detoxification mechanisms. By an ensemble modelling approach, we identified a best parsimonious mathematical model which recapitulates and predicts intracellular arsenic dynamics for different conditions and mutants, thereby providing novel insights into arsenic toxicity and detoxification mechanisms in yeast, which could partly be confirmed experimentally by dedicated experiments. Specifically, our analyses suggest that: (i) arsenic is mainly protein-bound during short-term (acute) exposure, whereas glutathione-conjugated arsenic dominates during long-term (chronic) exposure, (ii) arsenic is not stably retained, but can leave the vacuole via an export mechanism, and (iii) Fps1 is controlled by Hog1-dependent and Hog1-independent mechanisms during arsenite stress. Our results challenge glutathione depletion as a key mechanism for arsenic toxicity and instead suggest that (iv) increased glutathione biosynthesis protects the proteome against the damaging effects of arsenic and that (v) widespread protein inactivation contributes to the toxicity of this metalloid. Our work in yeast may prove useful to elucidate similar mechanisms in higher eukaryotes and have implications for the use of arsenic in medical therapy.

Nested autoinhibitory feedbacks alter the resistance of homeostatic adaptive biochemical networks.

Negative feedback control is a ubiquitous feature of biochemical systems, as is time delay between a signal and its response. Negative feedback in conjunction with time delay can lead to oscillations. In a cellular context, it might be beneficial to mitigate oscillatory behaviour to avoid recurring stress situations. This can be achieved by increasing the distance between the parameters of the system and certain thresholds, beyond which oscillations occur. This distance has been termed resistance. Here, we prove that in a generic three-dimensional negative feedback system the resistance of the system is modified by nested autoinhibitory feedbacks. Our system features negative feedbacks through both input-inhibition as well as output-activation, a signalling component with mass conservation and perfect adaptation. We show that these features render the system applicable to biological data, exemplified by the high osmolarity glycerol system in yeast and the mammalian p53 system. Output-activation is better supported by data than input-inhibition and also shows distinguished properties with respect to the system's stimulus. Our general approach might be useful in designing synthetic systems in which oscillations can be tuned by synthetic autoinhibitory feedbacks.

Quantitative analysis of glycerol accumulation, glycolysis and growth under hyper osmotic stress.

We provide an integrated dynamic view on a eukaryotic osmolyte system, linking signaling with regulation of gene expression, metabolic control and growth. Adaptation to osmotic changes enables cells to adjust cellular activity and turgor pressure to an altered environment. The yeast Saccharomyces cerevisiae adapts to hyperosmotic stress by activating the HOG signaling cascade, which controls glycerol accumulation. The Hog1 kinase stimulates transcription of genes encoding enzymes required for glycerol production (Gpd1, Gpp2) and glycerol import (Stl1) and activates a regulatory enzyme in glycolysis (Pfk26/27). In addition, glycerol outflow is prevented by closure of the Fps1 glycerol facilitator. In order to better understand the contributions to glycerol accumulation of these different mechanisms and how redox and energy metabolism as well as biomass production are maintained under such conditions we collected an extensive dataset. Over a period of 180 min after hyperosmotic shock we monitored in wild type and different mutant cells the concentrations of key metabolites and proteins relevant for osmoadaptation. The dataset was used to parameterize an ODE model that reproduces the generated data very well. A detailed computational analysis using time-dependent response coefficients showed that Pfk26/27 contributes to rerouting glycolytic flux towards lower glycolysis. The transient growth arrest following hyperosmotic shock further adds to redirecting almost all glycolytic flux from biomass towards glycerol production. Osmoadaptation is robust to loss of individual adaptation pathways because of the existence and upregulation of alternative routes of glycerol accumulation. For instance, the Stl1 glycerol importer contributes to glycerol accumulation in a mutant with diminished glycerol production capacity. In addition, our observations suggest a role for trehalose accumulation in osmoadaptation and that Hog1 probably directly contributes to the regulation of the Fps1 glycerol facilitator. Taken together, we elucidated how different metabolic adaptation mechanisms cooperate and provide hypotheses for further experimental studies.

The plant phenological online database (PPODB): an online database for long-term phenological data.

We present an online database that provides unrestricted and free access to over 16 million plant phenological observations from over 8,000 stations in Central Europe between the years 1880 and 2009. Unique features are (1) a flexible and unrestricted access to a full-fledged database, allowing for a wide range of individual queries and data retrieval, (2) historical data for Germany before 1951 ranging back to 1880, and (3) more than 480 curated long-term time series covering more than 100 years for individual phenological phases and plants combined over Natural Regions in Germany. Time series for single stations or Natural Regions can be accessed through a user-friendly graphical geo-referenced interface. The joint databases made available with the plant phenological database PPODB render accessible an important data source for further analyses of long-term changes in phenology. The database can be accessed via www.ppodb.de .

Modelling reveals novel roles of two parallel signalling pathways and homeostatic feedbacks in yeast.

The high osmolarity glycerol (HOG) pathway in yeast serves as a prototype signalling system for eukaryotes. We used an unprecedented amount of data to parameterise 192 models capturing different hypotheses about molecular mechanisms underlying osmo-adaptation and selected a best approximating model. This model implied novel mechanisms regulating osmo-adaptation in yeast. The model suggested that (i) the main mechanism for osmo-adaptation is a fast and transient non-transcriptional Hog1-mediated activation of glycerol production, (ii) the transcriptional response serves to maintain an increased steady-state glycerol production with low steady-state Hog1 activity, and (iii) fast negative feedbacks of activated Hog1 on upstream signalling branches serves to stabilise adaptation response. The best approximating model also indicated that homoeostatic adaptive systems with two parallel redundant signalling branches show a more robust and faster response than single-branch systems. We corroborated this notion to a large extent by dedicated measurements of volume recovery in single cells. Our study also demonstrates that systematically testing a model ensemble against data has the potential to achieve a better and unbiased understanding of molecular mechanisms.

Easy parameter identifiability analysis with COPASI.

BACKGROUND AND SCOPE: Differential equation systems modeling biochemical reaction networks can only give quantitative predictions, when they are in accordance with experimental data. However, even if a model can well recapitulate given data, it is often the case that some of its kinetic parameters can be arbitrarily chosen without significantly affecting the simulation results. This indicates a lack of appropriate data to determine those parameters. In this case, the parameter is called to be practically non-identifiable. Well-identified parameters are paramount for reliable quantitative predictions and, therefore, identifiability analysis is an important topic in modeling of biochemical reaction networks. Here, we describe a hidden feature of the free modeling software COPASI, which can be exploited to easily and quickly conduct a parameter identifiability analysis of differential equation systems by calculating likelihood profiles. The proposed combination of an established method for parameter identifiability analysis with the user-friendly features of COPASI offers an easy and rapid access to parameter identifiability analysis even for non-experts. AVAILABILITY: COPASI is freely available for academic use at http://www.copasi.org.

Time-dependent quantitative multicomponent control of the G1-S network by the stress-activated protein kinase Hog1 upon osmostress.

Control of cell cycle progression by stress-activated protein kinases (SAPKs) is essential for cell adaptation to extracellular stimuli. Exposure of yeast to hyperosmotic stress activates the SAPK Hog1, which delays cell cycle progression through G1 by direct phosphorylation of the cyclin-dependent kinase (CDK) inhibitor Sic1 and by inhibition of the transcription of the genes encoding the G1 cyclins Cln1 and 2. Additional targets of Hog1 may also play a role in this response. We used mathematical modeling and quantitative in vivo experiments to define the contributions of individual components of the G1-S network downstream of Hog1 to this stress-induced delay in the cell cycle. The length of the arrest depended on the degree of stress and the temporal proximity of the onset of the stress to the commitment to cell division, called "Start." Hog1-induced inhibition of the transcription of the gene encoding cyclin Clb5, rather than that of the gene encoding Cln2, prevented entry into S phase upon osmostress. By controlling the accumulation of specific cyclins, Hog1 delayed bud morphogenesis (through Clns) and delayed DNA replication (through Clb5). Hog1-mediated phosphorylation and degradation of Sic1 at Start prevented residual activity of the cyclin/CDK complex Clb5/Cdc28 from initiating DNA replication before adaptation to the stress. Thus, our work defines distinct temporal roles for the actions of Hog1 on Sic1 and cyclins in mediating G1 arrest upon hyperosmotic stress.

Automated ensemble modeling with modelMaGe: analyzing feedback mechanisms in the Sho1 branch of the HOG pathway.

In systems biology uncertainty about biological processes translates into alternative mathematical model candidates. Here, the goal is to generate, fit and discriminate several candidate models that represent different hypotheses for feedback mechanisms responsible for downregulating the response of the Sho1 branch of the yeast high osmolarity glycerol (HOG) signaling pathway after initial stimulation. Implementing and testing these candidate models by hand is a tedious and error-prone task. Therefore, we automatically generated a set of candidate models of the Sho1 branch with the tool modelMaGe. These candidate models are automatically documented, can readily be simulated and fitted automatically to data. A ranking of the models with respect to parsimonious data representation is provided, enabling discrimination between candidate models and the biological hypotheses underlying them. We conclude that a previously published model fitted spurious effects in the data. Moreover, the discrimination analysis suggests that the reported data does not support the conclusion that a desensitization mechanism leads to the rapid attenuation of Hog1 signaling in the Sho1 branch of the HOG pathway. The data rather supports a model where an integrator feedback shuts down the pathway. This conclusion is also supported by dedicated experiments that can exclusively be predicted by those models including an integrator feedback.modelMaGe is an open source project and is distributed under the Gnu General Public License (GPL) and is available from http://modelmage.org.

Model-based inference of biochemical parameters and dynamic properties of microbial signal transduction networks.

Because of the inherent uncertainty about quantitative aspects of signalling networks it is of substantial interest to use computational methods that allow inferring non-measurable quantities such as rate constants, from measurable quantities such as changes in protein abundances. We argue that true biochemical parameters like rate constants can generally not be inferred using models due to their non-identifiability. Recent advances, however, facilitate the analysis of parameter identifiability of a given model and automated discrimination of candidate models, both being important techniques to still extract quantitative biological information from experimental data.

Biophysical properties of Saccharomyces cerevisiae and their relationship with HOG pathway activation.

Parameterized models of biophysical and mechanical cell properties are important for predictive mathematical modeling of cellular processes. The concepts of turgor, cell wall elasticity, osmotically active volume, and intracellular osmolarity have been investigated for decades, but a consistent rigorous parameterization of these concepts is lacking. Here, we subjected several data sets of minimum volume measurements in yeast obtained after hyper-osmotic shock to a thermodynamic modeling framework. We estimated parameters for several relevant biophysical cell properties and tested alternative hypotheses about these concepts using a model discrimination approach. In accordance with previous reports, we estimated an average initial turgor of 0.6 ± 0.2 MPa and found that turgor becomes negligible at a relative volume of 93.3 ± 6.3% corresponding to an osmotic shock of 0.4 ± 0.2 Osm/l. At high stress levels (4 Osm/l), plasmolysis may occur. We found that the volumetric elastic modulus, a measure of cell wall elasticity, is 14.3 ± 10.4 MPa. Our model discrimination analysis suggests that other thermodynamic quantities affecting the intracellular water potential, for example the matrix potential, can be neglected under physiological conditions. The parameterized turgor models showed that activation of the osmosensing high osmolarity glycerol (HOG) signaling pathway correlates with turgor loss in a 1:1 relationship. This finding suggests that mechanical properties of the membrane trigger HOG pathway activation, which can be represented and quantitatively modeled by turgor.