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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? -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 β -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.

The process-based model 4C (FORESEE) has been developed over the past twenty years. The objective of this paper is to give a comprehensive description of the main features of 4C and to present an evaluation of the model at four different forest sites across Europe. The evaluation was focused on growth parameters, carbon, water and heat fluxes. The main data source for the evaluation was the PROFOUND database. We applied different statistical metrics of evaluation and compared the inter-annual and inter-monthly variability of observed and simulated carbon and water fluxes. The ability to reproduce forest growth differs from site to site and is best for the pine stand site Peitz. The model's performance in simulating carbon and water fluxes was very satisfactory on daily and monthly time scales in contrast to the annual time scale. This underlines the conclusion that processes that are either not represented in dependence on on medium- to long-term dynamic influences such as allocation, or those that are not represented at all but may have a large impact at specific sites – such as the dynamics of non-structural carbohydrates (NSC) and ground vegetation growth – need to be elaborated for general forest growth investigations under climate change. On the other hand, 4C has shown a great potential for improvement since it emphasizes the representation of boundary conditions such as soil temperature at different depths. Therefore, more spatial differentiation of processes such as organ-specific respiration should easily be accomplished. Nonetheless, by using the PROFOUND database we were able to demonstrate the applicability and reliability of 4C.

Organisms have evolved motility organelles that allow them to move to favorable 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, we identify the starvation-induced Ser/Thr protein kinase ArnS (Saci_1181) which is located proximally to the archaellum operon. 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 we combine in vivo experiments and mathematical models to describe for the first time in archaea the dynamics of key regulators of archaellum expression. This article is protected by copyright. All rights reserved.

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.

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.

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.

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.

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. Electronic supplementary material The online version of this article (doi:10.1007/s00484-013-0650-2) contains supplementary material, which is available to authorized users.

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. Electronic supplementary material The online version of this article (doi:10.1186/s12918-016-0325-9) contains supplementary material, which is available to authorized users.

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.

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. This work was supported via several projects funded by the European Commission: QUASI (Contract No. 503230 to SH, EK, FP and MP), CELLCOMPUT (Contract No. 043310 to SH, EK and FP), UNICELLSYS (Contract No. 201142 to SH, EK, FP, MP and MG), SYSTEMSBIOLOGY (Contract No. 514169 to SH and EK), and AMPKIN (Contract No. 518181 to SH and MG). In addition work was funded by grants from the Swedish Foundation for Strategic Research SSF (Bio-X to MG), the Swedish Research Council (project grants to SH and MG), the Carl Trygger Foundation (to MG), the Science Faculty, University of Gothenburg (to SH and MG), and the Swiss systemsX.ch (to MP)

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. Electronic supplementary material The online version of this article (doi:10.1186/s12859-015-0816-5) contains supplementary material, which is available to authorized users.

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.

Analysis of observational phenological data has indicated that the length of the vegetation period (VP), here defined as the time between leaf onset and leaf colouring (LC), has increased in the last decades in the northern latitudes mainly due to an advancement of bud burst. Analysing the patterns of spring phenology over the last century (1880–1999) in Southern Germany showed that the strong advancement of spring phases, especially in the decade before 1999, is not a singular event in the course of the 20th century. Similar trends were also observed in earlier decades. Distinct periods of varying trend direction for important spring phases could be distinguished. Marked differences in trend direction between early and late spring phases were detected, which can be explained by different trends in March and April mean temperatures. The advancement of spring phenology in recent decades is part of the multi-decadal fluctuations over the 20th century that vary with the species and the relevant seasonal temperatures. However, for all Natural Regions in Germany, spring phases were advanced by about 5–20 days on average between 1951 and 1999, LC was delayed between 1951 and 1984, but advanced after 1984 for all considered tree species and the length of the VP increased between 1951 and 1999 for all considered tree species by an average of 10 days throughout Germany.

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. OA gold

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.

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.

Recruitment algorithms in forest gap models are examined with particular regard to their suitability for simulating forest ecosystem responses to a changing climate. The traditional formu- lation of recruitment is found limiting in three areas. First, the aggregation of different regeneration stages (seed production, dispersal, storage, germination and seedling establishment) is likely to result in less accurate predictions of responses as compared to treating each stage separately. Second, the related assumptions that seeds of all species are uniformly available and that environmental conditions are homogeneous, are likely to cause overestimates of future species diversity and for- est migration rates. Third, interactions between herbivores (ungulates and insect pests) and forest vegetation are a big unknown with potentially serious impacts in many regions. Possible strategies for developing better gap model representations for the climate-sensitive aspects of each of these key areas are discussed. A working example of a relatively new model that addresses some of these limitations is also presented for each case. We conclude that better models of regeneration processes are desirable for predicting effects of climate change, but that it is presently impossible to determine what improvements can be expected without carrying out rigorous tests for each new formulation.

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., Author Summary Osmotic changes are common environmental challenges for cells, even in multi-cellular organisms, having led to sophisticated adaptation mechanisms. In order to adapt to hyperosmotic stress, yeast cells accumulate glycerol. This is achieved by short-term responses involving metabolic and transmembrane transport changes as well as long-term transcriptional responses. By integrating experimentation and simulation of a mathematical model we resolve the quantitative and temporal characteristics of different processes contributing to glycerol accumulation. We show that osmoadaptation prioritizes the redox and energy balance in glycolysis while rerouting flux from biomass to glycerol production. We further show that the glycerol accumulation network provides osmoadaptation with robustness by compensating for the loss of certain nodes and with the flexibility necessary for responding to different stress situations. Finally we provide novel insight into the roles of transport processes in glycerol accumulation and evidence that trehalose may play a role in yeast osmoadaptation. The present work provides for the first time an integrated dynamic view on a eukaryotic osmolyte system and links signaling with regulation of gene expression and metabolic control.

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 .

Ensemble modelling is used to study the yeast high osmolarity glycerol (HOG) pathway, a prototype for eukaryotic mitogen-activated kinase signalling systems. The best fit model provides new insights into the function of this system, some of which are then experimentally validated., The main mechanism for osmo-adaptation is a fast and transient non-transcriptional Hog1-mediated activation of glycerol production. The transcriptional response rather serves to maintain an increased steady-state glycerol production with low steady-state Hog1 activity after adaptation. A fast negative feedback of activated Hog1 on the upstream signalling branches serves to stabilise the adaptation response by preventing oscillatory behaviour. Two parallel redundant signalling branches elicit a more robust and swifter adaptation than a single branch alone, at least for low osmotic shock. This notion could be corroborated by dedicated measurements of single-cell volume recovery for the wild-type and single-branch mutants., 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.

Errors in the labels of panels C and D of Fig. 7 and incorrect text callouts to Figs. 7E and 7F are corrected.

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.

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 G 1 by direct phosphorylation of the cyclin-dependent kinase (CDK) inhibitor Sic1 and by inhibition of the transcription of the genes encoding the G 1 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 G 1 -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 G 1 arrest upon hyperosmotic stress.

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.

We describe a method for combining phenological time series and outlier detection based on linear models as presented in Schaber and Badeck (Tree Physiol, 22, 973–982, 2002). We extend the outlier detection method based on Gaussian Mixture Models as proposed by Doktor et al. (Geostatistics for environmental applications, Springer, Berlin, 2005) in order to take into account year-location interactions. We quantify the effect of the extension of the outlier detection algorithm using Gaussian Mixture Models. The proposed methods are adequate for the analysis of messy time series with heterogeneous distribution in time and space as well as frequent gaps in the time series. We illustrate the use of combined time series for the generation of geographical maps of phenological phases using station effects. The algorithms discussed in the current paper are publicly available in the updated R – package “pheno”.

Dynamic modelling of biochemical reaction networks has to cope with the inherent uncertainty about biological processes, concerning not only data and parameters but also kinetics and structure. These different types of uncertainty are nested within each other: uncertain network structures contain uncertain reaction kinetics, which in turn are governed by uncertain parameters. Here, the authors review some issues arising from such uncertainties and sketch methods, solutions and future directions to deal with them.

Volume is a highly regulated property of cells, because it critically affects intracellular concentration. In the present chapter, we focus on the short-term volume regulation in yeast as a consequence of a shift in extracellular osmotic conditions. We review a basic thermodynamic framework to model volume and solute flows. In addition, we try to select a model for turgor, which is an important hydrodynamic property, especially in walled cells. Finally, we demonstrate the validity of the presented approach by fitting the dynamic model to a time course of volume change upon osmotic shock in yeast.

Experimental research has revealed components and mechanisms of cellular stress sensing, signaling, and adaptation. In addition, mathematical modeling has proven to foster the understanding of basic principles of signal transduction and signal processing. In the following, we will give an outline of the modeling process and introduce basic concepts for dynamic model analysis. We briefly review basic dynamic properties of stress activated protein (SAP) or mitogen activated protein (MAP) kinase (K) cascades that demonstrate why this type of signaling pathways is so abundantly used in cellular information processing and response.

Cells must be able to process multiple information in parallel and, moreover, they must also be able to combine this information in order to trigger the appropriate response. This is achieved by wiring signalling pathways such that they can interact with each other, a phenomenon often called crosstalk. In this study, we employ mathematical modelling techniques to analyse dynamic mechanisms and measures of crosstalk. We present a dynamic mathematical model that compiles current knowledge about the wiring of the pheromone pathway and the filamentous growth pathway in yeast. We consider the main dynamic features and the interconnections between the two pathways in order to study dynamic crosstalk between these two pathways in haploid cells. We introduce two new measures of dynamic crosstalk, the intrinsic specificity and the extrinsic specificity. These two measures incorporate the combined signal of several stimuli being present simultaneously and seem to be more stable than previous measures. When both pathways are responsive and stimulated, the model predicts that (a) the filamentous growth pathway amplifies the response of the pheromone pathway, and (b) the pheromone pathway inhibits the response of filamentous growth pathway in terms of mitogen activated protein kinase activity and transcriptional activity, respectively. Among several mechanisms we identified leakage of activated Ste11 as the most influential source of crosstalk. Moreover, we propose new experiments and predict their outcomes in order to test hypotheses about the mechanisms of crosstalk between the two pathways. Studying signals that are transmitted in parallel gives us new insights about how pathways and signals interact in a dynamical way, e.g., whether they amplify, inhibit, delay or accelerate each other.

International audience; Most endosymbiotic bacteria have extremely reduced genomes, accelerated evolutionary rates, and strong AT base compositional bias thought to reflect reduced efficacy of selection and increased mutational pressure. Here, we present a comparative study of evolutionary forces shaping five fully sequenced bacterial endosymbionts of insects. The results of this study were three-fold: (i) Stronger conservation of high expression genes at not just nonsynonymous, but also synonymous, sites. (ii) Variation in amino acid usage strongly correlates with GC content and expression level of genes. This pattern is largely explained by greater conservation of high expression genes, leading to their higher GC content. However, we also found indication of selection favoring GC-rich amino acids that contrasts with former studies. (iii) Although the specific nutritional requirements of the insect host are known to affect gene content of endosymbionts, we found no detectable influence on substitu! tion rates, amino acid usage, or codon usage of bacterial genes involved in host nutrition.

Summary Climate change effects on seasonal activity in terrestrial ecosystems are significant and well documented, especially in the middle and higher latitudes. Temperature is a main driver of many plant developmental processes, and in many cases higher temperatures have been shown to speed up plant development and lead to earlier switching to the next ontogenetic stage. Qualitatively consistent advancement of vegetation activity in spring has been documented using three independent methods, based on ground observations, remote sensing, and analysis of the atmospheric CO2 signal. However, estimates of the trends for advancement obtained using the same method differ substantially. We propose that a high fraction of this uncertainty is related to the time frame analysed and changes in trends at decadal time scales. Furthermore, the correlation between estimates of the initiation of spring activity derived from ground observations and remote sensing at interannual time scales is often weak. We propose that this is caused by qualitative differences in the traits observed using the two methods, as well as the mixture of different ecosystems and species within the satellite scenes.

There are several applications of combined phenological time series; e.g., trend analysis with long continuous time series, obtaining a compound and representative time series around weather stations for model fitting, data gap filling and outlier detection. Various methods to combine phenological time series have been proposed. We show that all of these methods can be analyzed within the theory of linear models. This has the advantage that the underlying assumptions for each model become transparent providing a theoretical basis for selecting a model for a particular situation. Moreover, the common theoretical background provides a means of comparing methods by Monte-Carlo simulation and with real data. Additionally, we explored the influences of two outlier detection methods. We show that the error called the month-mistake, whose origin is known and which is one of the few mistakes that can be detected in phenological data because of its large deviation, is best detected by the distribution-free 30-day residual rule in combination with a robust estimation procedure based on the minimization of the sum of absolute residuals (L1-norm).

Models of phenology are needed for the projection of effects of a changing climate on, for example, forest production, species competition, vegetation-atmosphere feedback and public health. A new phenology model for deciduous tree bud burst is developed and parameters are determined for a wide geographical range (Germany) and several forest tree species. The new model is based on considerations of simple interactions between inhibitory and promotory agents that are assumed to control the developmental status of a plant. Several alternative model structures were formulated emphasizing different hypothetical physiological processes. The new models fitted the observations better than classical models. The bias of the classical models, i.e. overestimation of early observations and underestimation of late observations, could be reduced but not completely removed. Differences in the best-fitting model equations for each species indicated that, for the late spring phases (bud burst of Fagus sylvatica and Quercus robur), the photoperiod played a more dominant role than for early spring phases (bud burst of Betula pendula and Aesculus hippocastanum). Chilling only plays a subordinate role for spring bud burst compared to temperatures preceding this event in our data. The presented modeling approach allowed for a species-specific weighting of the dominant processes. The model results are in accordance with experimental findings that indicate an important role of day length in late spring BB. Potentials for model improvement are discussed.

Understanding evolutionary processes that drive genome reduction requires determining the tempo (rate) and the mode (size and types of deletions) of gene losses. In this study, we analysed five endosymbiotic genome sequences of the gamma-proteobacteria (three different Buchnera aphidicola strains, Wigglesworthia glossinidia, Blochmannia floridanus) to test if gene loss could be driven by the selective importance of genes. We used a parsimony method to reconstruct a minimal ancestral genome of insect endosymbionts and quantified gene loss along the branches of the phylogenetic tree. To evaluate the selective or functional importance of genes, we used a parameter that measures the level of adaptive codon bias in E. coli (i.e. codon adaptive index, or CAI), and also estimates of evolutionary rates (Ka) between pairs of orthologs either in free-living bacteria or in pairs of symbionts. Our results demonstrate that genes lost in the early stages of symbiosis were on average less selectively constrained than genes conserved in any of the extant symbiotic strains studied. These results also extend to more recent events of gene losses (i.e. among Buchnera strains) that still tend to concentrate on genes with low adaptive bias in E. coli and high evolutionary rates both in free-living and in symbiotic lineages. In addition, we analyzed the physical organization of gene losses for early steps of symbiosis acquisition under the hypothesis of a common origin of different symbioses. In contrast with previous findings we show that gene losses mostly occurred through loss of rather small blocks and mostly in syntenic regions between at least one of the symbionts and present-day E. coli. At both ancient and recent stages of symbiosis evolution, gene loss was at least partially influenced by selection, highly conserved genes being retained more readily than lowly conserved genes: although losses might result from drift due to the bottlenecking of endosymbiontic populations, we demonstrated that purifying selection also acted by retaining genes of greater selective importance.