Multi-scale model suggests the trade-off between protein and ATP demand as a driver of metabolic changes during yeast replicative ageing.

The accumulation of protein damage is one of the major drivers of replicative ageing, describing a cell's reduced ability to reproduce over time even under optimal conditions. Reactive oxygen and nitrogen species are precursors of protein damage and therefore tightly linked to ageing. At the same time, they are an inevitable by-product of the cell's metabolism. Cells are able to sense high levels of reactive oxygen and nitrogen species and can subsequently adapt their metabolism through gene regulation to slow down damage accumulation. However, the older or damaged a cell is the less flexibility it has to allocate enzymes across the metabolic network, forcing further adaptions in the metabolism. To investigate changes in the metabolism during replicative ageing, we developed an multi-scale mathematical model using budding yeast as a model organism. The model consists of three interconnected modules: a Boolean model of the signalling network, an enzyme-constrained flux balance model of the central carbon metabolism and a dynamic model of growth and protein damage accumulation with discrete cell divisions. The model can explain known features of replicative ageing, like average lifespan and increase in generation time during successive division, in yeast wildtype cells by a decreasing pool of functional enzymes and an increasing energy demand for maintenance. We further used the model to identify three consecutive metabolic phases, that a cell can undergo during its life, and their influence on the replicative potential, and proposed an intervention span for lifespan control.

Scalable and flexible inference framework for stochastic dynamic single-cell models.

Understanding the inherited nature of how biological processes dynamically change over time and exhibit intra- and inter-individual variability, due to the different responses to environmental stimuli and when interacting with other processes, has been a major focus of systems biology. The rise of single-cell fluorescent microscopy has enabled the study of those phenomena. The analysis of single-cell data with mechanistic models offers an invaluable tool to describe dynamic cellular processes and to rationalise cell-to-cell variability within the population. However, extracting mechanistic information from single-cell data has proven difficult. This requires statistical methods to infer unknown model parameters from dynamic, multi-individual data accounting for heterogeneity caused by both intrinsic (e.g. variations in chemical reactions) and extrinsic (e.g. variability in protein concentrations) noise. Although several inference methods exist, the availability of efficient, general and accessible methods that facilitate modelling of single-cell data, remains lacking. Here we present a scalable and flexible framework for Bayesian inference in state-space mixed-effects single-cell models with stochastic dynamic. Our approach infers model parameters when intrinsic noise is modelled by either exact or approximate stochastic simulators, and when extrinsic noise is modelled by either time-varying, or time-constant parameters that vary between cells. We demonstrate the relevance of our approach by studying how cell-to-cell variation in carbon source utilisation affects heterogeneity in the budding yeast Saccharomyces cerevisiae SNF1 nutrient sensing pathway. We identify hexokinase activity as a source of extrinsic noise and deduce that sugar availability dictates cell-to-cell variability.

Modelling of glucose repression signalling in yeast Saccharomyces cerevisiae.

Saccharomyces cerevisiae has a sophisticated signalling system that plays a crucial role in cellular adaptation to changing environments. The SNF1 pathway regulates energy homeostasis upon glucose derepression; hence, it plays an important role in various processes, such as metabolism, cell cycle and autophagy. To unravel its behaviour, SNF1 signalling has been extensively studied. However, the pathway components are strongly interconnected and inconstant; therefore, elucidating its dynamic behaviour based on experimental data only is challenging. To tackle this complexity, systems biology approaches have been successfully employed. This review summarizes the progress, advantages and disadvantages of the available mathematical modelling frameworks covering Boolean, dynamic kinetic, single-cell models, which have been used to study processes and phenomena ranging from crosstalks to sources of cell-to-cell variability in the context of SNF1 signalling. Based on the lessons from existing models, we further discuss how to develop a consensus dynamic mechanistic model of the entire SNF1 pathway that can provide novel insights into the dynamics of nutrient signalling.

A novel yeast hybrid modeling framework integrating Boolean and enzyme-constrained networks enables exploration of the interplay between signaling and metabolism.

The interplay between nutrient-induced signaling and metabolism plays an important role in maintaining homeostasis and its malfunction has been implicated in many different human diseases such as obesity, type 2 diabetes, cancer, and neurological disorders. Therefore, unraveling the role of nutrients as signaling molecules and metabolites together with their interconnectivity may provide a deeper understanding of how these conditions occur. Both signaling and metabolism have been extensively studied using various systems biology approaches. However, they are mainly studied individually and in addition, current models lack both the complexity of the dynamics and the effects of the crosstalk in the signaling system. To gain a better understanding of the interconnectivity between nutrient signaling and metabolism in yeast cells, we developed a hybrid model, combining a Boolean module, describing the main pathways of glucose and nitrogen signaling, and an enzyme-constrained model accounting for the central carbon metabolism of Saccharomyces cerevisiae, using a regulatory network as a link. The resulting hybrid model was able to capture a diverse utalization of isoenzymes and to our knowledge outperforms constraint-based models in the prediction of individual enzymes for both respiratory and mixed metabolism. The model showed that during fermentation, enzyme utilization has a major contribution in governing protein allocation, while in low glucose conditions robustness and control are prioritized. In addition, the model was capable of reproducing the regulatory effects that are associated with the Crabtree effect and glucose repression, as well as regulatory effects associated with lifespan increase during caloric restriction. Overall, we show that our hybrid model provides a comprehensive framework for the study of the non-trivial effects of the interplay between signaling and metabolism, suggesting connections between the Snf1 signaling pathways and processes that have been related to chronological lifespan of yeast cells.

The synergy of damage repair and retention promotes rejuvenation and prolongs healthy lifespans in cell lineages.

Damaged proteins are inherited asymmetrically during cell division in the yeast Saccharomyces cerevisiae, such that most damage is retained within the mother cell. The consequence is an ageing mother and a rejuvenated daughter cell with full replicative potential. Daughters of old and damaged mothers are however born with increasing levels of damage resulting in lowered replicative lifespans. Remarkably, these prematurely old daughters can give rise to rejuvenated cells with low damage levels and recovered lifespans, called second-degree rejuvenation. We aimed to investigate how damage repair and retention together can promote rejuvenation and at the same time ensure low damage levels in mother cells, reflected in longer health spans. We developed a dynamic model for damage accumulation over successive divisions in individual cells as part of a dynamically growing cell lineage. With detailed knowledge about single-cell dynamics and relationships between all cells in the lineage, we can infer how individual damage repair and retention strategies affect the propagation of damage in the population. We show that damage retention lowers damage levels in the population by reducing the variability across the lineage, and results in larger population sizes. Repairing damage efficiently in early life, as opposed to investing in repair when damage has already accumulated, counteracts accelerated ageing caused by damage retention. It prolongs the health span of individual cells which are moreover less prone to stress. In combination, damage retention and early investment in repair are beneficial for healthy ageing in yeast cell populations.

Mig1 localization exhibits biphasic behavior which is controlled by both metabolic and regulatory roles of the sugar kinases.

Glucose, fructose and mannose are the preferred carbon/energy sources for the yeast Saccharomyces cerevisiae. Absence of preferred energy sources activates glucose derepression, which is regulated by the kinase Snf1. Snf1 phosphorylates the transcriptional repressor Mig1, which results in its exit from the nucleus and subsequent derepression of genes. In contrast, Snf1 is inactive when preferred carbon sources are available, which leads to dephosphorylation of Mig1 and its translocation to the nucleus where Mig1 acts as a transcription repressor. Here we revisit the role of the three hexose kinases, Hxk1, Hxk2 and Glk1, in glucose de/repression. We demonstrate that all three sugar kinases initially affect Mig1 nuclear localization upon addition of glucose, fructose and mannose. This initial import of Mig1 into the nucleus was temporary; for continuous nucleocytoplasmic shuttling of Mig1, Hxk2 is required in the presence of glucose and mannose and in the presence of fructose Hxk2 or Hxk1 is required. Our data suggest that Mig1 import following exposure to preferred energy sources is controlled via two different pathways, where (1) the initial import is regulated by signals derived from metabolism and (2) continuous shuttling is regulated by the Hxk2 and Hxk1 proteins. Mig1 nucleocytoplasmic shuttling appears to be important for the maintenance of the repressed state in which Hxk1/2 seems to play an essential role.

Adaptive damage retention mechanism enables healthier yeast population.

During cytokinesis in budding yeast (Saccharomyces cerevisiae) damaged proteins are distributed asymmetrically between the daughter and the mother cell. Retention of damaged proteins is a crucial mechanism ensuring a healthy daughter cell with full replicative potential and an ageing mother cell. However, the protein quality control (PQC) system is tuned for optimal reproduction success which suggests optimal health and size of the population, rather than long-term survival of the mother cell. Modelling retention of damage as an adaptable mechanism, we propose two damage retention strategies to find an optimal way of decreasing damage retention efficiency to maximize population size and minimize the damage in the individual yeast cell. A pedigree model is used to investigate the impact of small variations in the strategies over the whole population. These impacts are based on the altruistic effects of damage retention mechanism and are measured by a cost function whose minimum value provides the optimal health and size of the population. We showed that fluctuations in the cost function allow yeast cell to continuously vary its strategy, suggesting that optimal reproduction success is a local minimum of the cost function. Our results suggest that a rapid decrease in the efficiency of damage retention, at the time when the mother cell is almost exhausted, produces fewer daughters with high levels of damaged proteins. In addition, retaining more damage during the early divisions increases the number of healthy daughters in the population.

Challenge model of TNFα turnover at varying LPS and drug provocations.

A mechanism-based biomarker model of TNFα-response, including different external provocations of LPS challenge and test compound intervention, was developed. The model contained system properties (such as kt, kout), challenge characteristics (such as ks, kLPS, Km, LPS, Smax, SC50) and test-compound-related parameters (Imax, IC50). The exposure to test compound was modelled by means of first-order input and Michaelis-Menten type of nonlinear elimination. Test compound potency was estimated to 20 nM with a 70% partial reduction in TNFα-response at the highest dose of 30 mg·kg-1. Future selection of drug candidates may focus the estimation on potency and efficacy by applying the selected structure consisting of TNFα system and LPS challenge characteristics. A related aim was to demonstrate how an exploratory (graphical) analysis may guide us to a tentative model structure, which enables us to better understand target biology. The analysis demonstrated how to tackle a biomarker with a baseline below the limit of detection. Repeated LPS-challenges may also reveal how the rate and extent of replenishment of TNFα pools occur. Lack of LPS exposure-time courses was solved by including a biophase model, with the underlying assumption that TNFα-response time courses, as such, contain kinetic information. A transduction type of model with non-linear stimulation of TNFα release was finally selected. Typical features of a challenge experiment were shown by means of model simulations. Experimental shortcomings of present and published designs are identified and discussed. The final model coupled to suggested guidance rules may serve as a general basis for the collection and analysis of pharmacological challenge data of future studies.

Modelling of oscillatory cortisol response in horses using a Bayesian population approach for evaluation of dexamethasone suppression test protocols.

Cortisol is a steroid hormone relevant to immune function in horses and other species and shows a circadian rhythm. The glucocorticoid dexamethasone suppresses cortisol in horses. Pituitary pars intermedia dysfunction (PPID) is a disease in which the cortisol suppression mechanism through dexamethasone is challenged. Overnight dexamethasone suppression test (DST) protocols are used to test the functioning of this mechanism and to establish a diagnosis for PPID. However, existing DST protocols have been recognized to perform poorly in previous experimental studies, often indicating presence of PPID in healthy horses. This study uses a pharmacokinetic/pharmacodynamic (PK/PD) modelling approach to analyse the oscillatory cortisol response and its interaction with dexamethasone. Two existing DST protocols were then scrutinized using model simulations with particular focus on their ability to avoid false positive outcomes. Using a Bayesian population approach allowed for quantification of uncertainty and enabled predictions for a broader population of horses than the underlying sample. Dose selection and sampling time point were both determined to have large influence on the number of false positives. Advice on pitfalls in test protocols and directions for possible improvement of DST protocols were given. The presented methodology is also easily extended to other clinical test protocols.

Stress granule-defective mutants deregulate stress responsive transcripts.

To reduce expression of gene products not required under stress conditions, eukaryotic cells form large and complex cytoplasmic aggregates of RNA and proteins (stress granules; SGs), where transcripts are kept translationally inert. The overall composition of SGs, as well as their assembly requirements and regulation through stress-activated signaling pathways remain largely unknown. We have performed a genome-wide screen of S. cerevisiae gene deletion mutants for defects in SG formation upon glucose starvation stress. The screen revealed numerous genes not previously implicated in SG formation. Most mutants with strong phenotypes are equally SG defective when challenged with other stresses, but a considerable fraction is stress-specific. Proteins associated with SG defects are enriched in low-complexity regions, indicating that multiple weak macromolecule interactions are responsible for the structural integrity of SGs. Certain SG-defective mutants, but not all, display an enhanced heat-induced mutation rate. We found several mutations affecting the Ran GTPase, regulating nucleocytoplasmic transport of RNA and proteins, to confer SG defects. Unexpectedly, we found stress-regulated transcripts to reach more extreme levels in mutants unable to form SGs: stress-induced mRNAs accumulate to higher levels than in the wild-type, whereas stress-repressed mRNAs are reduced further in such mutants. Our findings are consistent with the view that, not only are SGs being regulated by stress signaling pathways, but SGs also modulate the extent of stress responses. We speculate that nucleocytoplasmic shuttling of RNA-binding proteins is required for gene expression regulation during stress, and that SGs modulate this traffic. The absence of SGs thus leads the cell to excessive, and potentially deleterious, reactions to stress.

Essential genetic interactors of SIR2 required for spatial sequestration and asymmetrical inheritance of protein aggregates.

Sir2 is a central regulator of yeast aging and its deficiency increases daughter cell inheritance of stress- and aging-induced misfolded proteins deposited in aggregates and inclusion bodies. Here, by quantifying traits predicted to affect aggregate inheritance in a passive manner, we found that a passive diffusion model cannot explain Sir2-dependent failures in mother-biased segregation of either the small aggregates formed by the misfolded Huntingtin, Htt103Q, disease protein or heat-induced Hsp104-associated aggregates. Instead, we found that the genetic interaction network of SIR2 comprises specific essential genes required for mother-biased segregation including those encoding components of the actin cytoskeleton, the actin-associated myosin V motor protein Myo2, and the actin organization protein calmodulin, Cmd1. Co-staining with Hsp104-GFP demonstrated that misfolded Htt103Q is sequestered into small aggregates, akin to stress foci formed upon heat stress, that fail to coalesce into inclusion bodies. Importantly, these Htt103Q foci, as well as the ATPase-defective Hsp104Y662A-associated structures previously shown to be stable stress foci, co-localized with Cmd1 and Myo2-enriched structures and super-resolution 3-D microscopy demonstrated that they are associated with actin cables. Moreover, we found that Hsp42 is required for formation of heat-induced Hsp104Y662A foci but not Htt103Q foci suggesting that the routes employed for foci formation are not identical. In addition to genes involved in actin-dependent processes, SIR2-interactors required for asymmetrical inheritance of Htt103Q and heat-induced aggregates encode essential sec genes involved in ER-to-Golgi trafficking/ER homeostasis.

Yeast AMP-activated protein kinase monitors glucose concentration changes and absolute glucose levels.

Analysis of the time-dependent behavior of a signaling system can provide insight into its dynamic properties. We employed the nucleocytoplasmic shuttling of the transcriptional repressor Mig1 as readout to characterize Snf1-Mig1 dynamics in single yeast cells. Mig1 binds to promoters of target genes and mediates glucose repression. Mig1 is predominantly located in the nucleus when glucose is abundant. Upon glucose depletion, Mig1 is phosphorylated by the yeast AMP-activated kinase Snf1 and exported into the cytoplasm. We used a three-channel microfluidic device to establish a high degree of control over the glucose concentration exposed to cells. Following regimes of glucose up- and downshifts, we observed a very rapid response reaching a new steady state within less than 1 min, different glucose threshold concentrations depending on glucose up- or downshifts, a graded profile with increased cell-to-cell variation at threshold glucose concentrations, and biphasic behavior with a transient translocation of Mig1 upon the shift from high to intermediate glucose concentrations. Fluorescence loss in photobleaching and fluorescence recovery after photobleaching data demonstrate that Mig1 shuttles constantly between the nucleus and cytoplasm, although with different rates, depending on the presence of glucose. Taken together, our data suggest that the Snf1-Mig1 system has the ability to monitor glucose concentration changes as well as absolute glucose levels. The sensitivity over a wide range of glucose levels and different glucose concentration-dependent response profiles are likely determined by the close integration of signaling with the metabolism and may provide for a highly flexible and fast adaptation to an altered nutritional status.

Bridging the gaps in systems biology.

Systems biology aims at creating mathematical models, i.e., computational reconstructions of biological systems and processes that will result in a new level of understanding-the elucidation of the basic and presumably conserved "design" and "engineering" principles of biomolecular systems. Thus, systems biology will move biology from a phenomenological to a predictive science. Mathematical modeling of biological networks and processes has already greatly improved our understanding of many cellular processes. However, given the massive amount of qualitative and quantitative data currently produced and number of burning questions in health care and biotechnology needed to be solved is still in its early phases. The field requires novel approaches for abstraction, for modeling bioprocesses that follow different biochemical and biophysical rules, and for combining different modules into larger models that still allow realistic simulation with the computational power available today. We have identified and discussed currently most prominent problems in systems biology: (1) how to bridge different scales of modeling abstraction, (2) how to bridge the gap between topological and mechanistic modeling, and (3) how to bridge the wet and dry laboratory gap. The future success of systems biology largely depends on bridging the recognized gaps.

Kinetic models in industrial biotechnology - Improving cell factory performance.

An increasing number of industrial bioprocesses capitalize on living cells by using them as cell factories that convert sugars into chemicals. These processes range from the production of bulk chemicals in yeasts and bacteria to the synthesis of therapeutic proteins in mammalian cell lines. One of the tools in the continuous search for improved performance of such production systems is the development and application of mathematical models. To be of value for industrial biotechnology, mathematical models should be able to assist in the rational design of cell factory properties or in the production processes in which they are utilized. Kinetic models are particularly suitable towards this end because they are capable of representing the complex biochemistry of cells in a more complete way compared to most other types of models. They can, at least in principle, be used to in detail understand, predict, and evaluate the effects of adding, removing, or modifying molecular components of a cell factory and for supporting the design of the bioreactor or fermentation process. However, several challenges still remain before kinetic modeling will reach the degree of maturity required for routine application in industry. Here we review the current status of kinetic cell factory modeling. Emphasis is on modeling methodology concepts, including model network structure, kinetic rate expressions, parameter estimation, optimization methods, identifiability analysis, model reduction, and model validation, but several applications of kinetic models for the improvement of cell factories are also discussed.

Exploring carbon source related localization and phosphorylation in the Snf1/Mig1 network using population and single cell-based approaches.

The AMPK/SNF1 pathway governs energy balance in eukaryotic cells, notably influencing glucose de-repression. In S. cerevisiae, Snf1 is phosphorylated and hence activated upon glucose depletion. This activation is required but is not sufficient for mediating glucose de-repression, indicating further glucose-dependent regulation mechanisms. Employing fluorescence recovery after photobleaching (FRAP) in conjunction with non-linear mixed effects modelling, we explore the spatial dynamics of Snf1 as well as the relationship between Snf1 phosphorylation and its target Mig1 controlled by hexose sugars. Our results suggest that inactivation of Snf1 modulates Mig1 localization and that the kinetic of Snf1 localization to the nucleus is modulated by the presence of non-fermentable carbon sources. Our data offer insight into the true complexity of regulation of this central signaling pathway in orchestrating cellular responses to fluctuating environmental cues. These insights not only expand our understanding of glucose homeostasis but also pave the way for further studies evaluating the importance of Snf1 localization in relation to its phosphorylation state and regulation of downstream targets.

Network medicine: facilitating a new view on complex diseases.

Complex diseases are prevalent medical conditions which are characterized by inter-patient heterogeneity with regards to symptom profiles, disease trajectory, comorbidities, and treatment response. Their pathophysiology involves a combination of genetic, environmental, and psychosocial factors. The intricacies of complex diseases, encompassing different levels of biological organization in the context of environmental and psychosocial factors, makes them difficult to study, understand, prevent, and treat. The field of network medicine has progressed our understanding of these complex mechanisms and highlighted mechanistic overlap between diagnoses as well as patterns of symptom co-occurrence. These observations call into question the traditional conception of complex diseases, where diagnoses are treated as distinct entities, and prompts us to reconceptualize our nosological models. Thus, this manuscript presents a novel model, in which the individual disease burden is determined as a function of molecular, physiological, and pathological factors simultaneously, and represented as a state vector. In this conceptualization the focus shifts from identifying the underlying pathophysiology of diagnosis cohorts towards identifying symptom-determining traits in individual patients. This conceptualization facilitates a multidimensional approach to understanding human physiology and pathophysiology in the context of complex diseases. This may provide a useful concept to address both the significant interindividual heterogeneity of diagnose cohorts as well as the lack of clear distinction between diagnoses, health, and disease, thus facilitating the progression towards personalized medicine.

BioMet Toolbox: genome-wide analysis of metabolism.

The rapid progress of molecular biology tools for directed genetic modifications, accurate quantitative experimental approaches, high-throughput measurements, together with development of genome sequencing has made the foundation for a new area of metabolic engineering that is driven by metabolic models. Systematic analysis of biological processes by means of modelling and simulations has made the identification of metabolic networks and prediction of metabolic capabilities under different conditions possible. For facilitating such systemic analysis, we have developed the BioMet Toolbox, a web-based resource for stoichiometric analysis and for integration of transcriptome and interactome data, thereby exploiting the capabilities of genome-scale metabolic models. The BioMet Toolbox provides an effective user-friendly way to perform linear programming simulations towards maximized or minimized growth rates, substrate uptake rates and metabolic production rates by detecting relevant fluxes, simulate single and double gene deletions or detect metabolites around which major transcriptional changes are concentrated. These tools can be used for high-throughput in silico screening and allows fully standardized simulations. Model files for various model organisms (fungi and bacteria) are included. Overall, the BioMet Toolbox serves as a valuable resource for exploring the capabilities of these metabolic networks. BioMet Toolbox is freely available at www.sysbio.se/BioMet/.

The choice of the objective function in flux balance analysis is crucial for predicting replicative lifespans in yeast.

Flux balance analysis (FBA) is a powerful tool to study genome-scale models of the cellular metabolism, based on finding the optimal flux distributions over the network. While the objective function is crucial for the outcome, its choice, even though motivated by evolutionary arguments, has not been directly connected to related measures. Here, we used an available multi-scale mathematical model of yeast replicative ageing, integrating cellular metabolism, nutrient sensing and damage accumulation, to systematically test the effect of commonly used objective functions on features of replicative ageing in budding yeast, such as the number of cell divisions and the corresponding time between divisions. The simulations confirmed that assuming maximal growth is essential for reaching realistic lifespans. The usage of the parsimonious solution or the additional maximisation of a growth-independent energy cost can improve lifespan predictions, explained by either increased respiratory activity using resources otherwise allocated to cellular growth or by enhancing antioxidative activity, specifically in early life. Our work provides a new perspective on choosing the objective function in FBA by connecting it to replicative ageing.

Optimizing study design in LPS challenge studies for quantifying drug induced inhibition of TNFα response: Did we miss the prime time?

In this work we evaluate the study design of LPS challenge experiments used for quantification of drug induced inhibition of TNFα response and provide general guidelines of how to improve the study design. Analysis of model simulated data, using a recently published TNFα turnover model, as well as the optimal design tool PopED have been used to find the optimal values of three key study design variables - time delay between drug and LPS administration, LPS dose, and sampling time points - that in turn could make the resulting TNFα response data more informative. Our findings suggest that the current rule of thumb for choosing the time delay should be reconsidered, and that the placement of the measurements after maximal TNFα response are crucial for the quality of the experiment. Furthermore, a literature study summarizing a wide range of published LPS challenge studies is provided, giving a broader perspective of how LPS challenge studies are usually conducted both in a preclinical and clinical setting.

The effect of stress on biophysical characteristics of misfolded protein aggregates in living Saccharomyces cerevisiae cells.

Aggregation of misfolded or damaged proteins is often attributed to numerous metabolic and neurodegenerative disorders. To reveal underlying mechanisms and cellular responses, it is crucial to investigate protein aggregate dynamics in cells. Here, we used super-resolution single-molecule microscopy to obtain biophysical characteristics of individual aggregates of a model misfolded protein ∆ssCPY* labelled with GFP. We demonstrated that oxidative and hyperosmotic stress lead to increased aggregate stoichiometries but not necessarily the total number of aggregates. Moreover, our data suggest the importance of the thioredoxin peroxidase Tsa1 for the controlled sequestering and clearance of aggregates upon both conditions. Our work provides novel insights into the understanding of the cellular response to stress via revealing the dynamical properties of stress-induced protein aggregates.