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.

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.

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.

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.

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.

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.

The Effect of Lithium on the Budding Yeast Saccharomyces cerevisiae upon Stress Adaptation.

Lithium salts are used in the treatment of mood disorders, cancer, and Alzheimer's disease. It has been shown to prolong life span in several phyla; however, not yet in budding yeast. In our study, we investigate the influence of lithium on yeast cells' viability by characterizing protein aggregate formation, cell volume, and molecular crowding in the context of stress adaptation. While our data suggest a concentration-dependent growth inhibition caused by LiCl, we show an extended long-term survival rate as an effect of lithium addition upon glucose deprivation. We show that caloric restriction mitigates the negative impact of LiCl on cellular survival. Therefore, we suggest that lithium could affect glucose metabolism upon caloric restriction, which could explain the extended long-term survival observed in our study. We find furthermore that lithium chloride did not affect an immediate salt-induced Hsp104-dependent aggregate formation but cellular adaptation to H2O2 and acute glucose starvation. We presume that different salt types and concentrations interfere with effective Hsp104 recruitment or its ATP-dependent disaggregase activity as a response to salt stress. This work provides novel details of Li+ effect on live eukaryotic cells which may also be applicable in further research on the treatment of cancer, Alzheimer's, or other age-related diseases in humans.

Second-generation TNFα turnover model for improved analysis of test compound interventions in LPS challenge studies.

This study presents a non-linear mixed effects model describing tumour necrosis factor alpha (TNFα) release after lipopolysaccharide (LPS) provocations in absence or presence of anti-inflammatory test compounds. Inter-occasion variability and the pharmacokinetics of two test compounds have been added to this second-generation model, and the goal is to produce a framework of how to model TNFα response in LPS challenge studies in vivo and demonstrate its general applicability regardless of occasion or type of test compound. Model improvements based on experimental data were successfully implemented and provided a robust model for TNFα response after LPS provocation, as well as reliable estimates of the median pharmacodynamic parameters. The two test compounds, Test Compound A and roflumilast, showed 81.1% and 74.9% partial reduction of TNFα response, respectively, and the potency of Test Compound A was estimated to 0.166 µmol/L. Comparing this study with previously published work reveals that our model leads to biologically reasonable output, handles complex data pooled from different studies, and highlights the importance of accurately distinguishing the stimulatory effect of LPS from the inhibitory effect of the test compound.

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.

A novel stepwise integrative analysis pipeline reveals distinct microbiota-host interactions and link to symptoms in irritable bowel syndrome.

Although incompletely understood, microbiota-host interactions are assumed to be altered in irritable bowel syndrome (IBS). We, therefore, aimed to develop a novel analysis pipeline tailored for the integrative analysis of microbiota-host interactions and association to symptoms and prove its utility in a pilot cohort. A multilayer stepwise integrative analysis pipeline was developed to visualize complex variable associations. Application of the pipeline was demonstrated on a dataset of IBS patients and healthy controls (HC), using the R software package to analyze colonic host mRNA and mucosal microbiota (16S rRNA gene sequencing), as well as gastrointestinal (GI) and psychological symptoms. In total, 42 IBS patients (57% female, mean age 33.6 (range 18-58)) and 20 HC (60% female, mean age 26.8 (range 23-41)) were included. Only in IBS patients, mRNA expression of Toll-like receptor 4 and genes associated with barrier function (PAR2, OCLN, TJP1) intercorrelated closely, suggesting potential functional relationships. This host genes-based "permeability cluster" was associated to mucosa-adjacent Chlamydiae and Lentisphaerae, and furthermore associated to satiety as well as to anxiety, depression and fatigue. In both IBS patients and HC, chromogranins, secretogranins and TLRs clustered together. In IBS patients, this host genes-based "immune-enteroendocrine cluster" was associated to specific members of Firmicutes, and to depression and fatigue, whereas in HC no significant association to microbiota was identified. We have developed a stepwise integrative analysis pipeline that allowed identification of unique host-microbiota intercorrelation patterns and association to symptoms in IBS patients. This analysis pipeline may aid in advancing the understanding of complex variable associations in health and disease.

Cell polarisation in a bulk-surface model can be driven by both classic and non-classic Turing instability.

The GTPase Cdc42 is the master regulator of eukaryotic cell polarisation. During this process, the active form of Cdc42 is accumulated at a particular site on the cell membrane called the pole. It is believed that the accumulation of the active Cdc42 resulting in a pole is driven by a combination of activation-inactivation reactions and diffusion. It has been proposed using mathematical modelling that this is the result of diffusion-driven instability, originally proposed by Alan Turing. In this study, we developed, analysed and validated a 3D bulk-surface model of the dynamics of Cdc42. We show that the model can undergo both classic and non-classic Turing instability by deriving necessary conditions for which this occurs and conclude that the non-classic case can be viewed as a limit case of the classic case of diffusion-driven instability. Using three-dimensional Spatio-temporal simulation we predicted pole size and time to polarisation, suggesting that cell polarisation is mainly driven by the reaction strength parameter and that the size of the pole is determined by the relative diffusion.

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.

Fine-Tuning of Energy Levels Regulates SUC2 via a SNF1-Dependent Feedback Loop.

Nutrient sensing pathways are playing an important role in cellular response to different energy levels. In budding yeast, Saccharomyces cerevisiae, the sucrose non-fermenting protein kinase complex SNF1 is a master regulator of energy homeostasis. It is affected by multiple inputs, among which energy levels is the most prominent. Cells which are exposed to a switch in carbon source availability display a change in the gene expression machinery. It has been shown that the magnitude of the change varies from cell to cell. In a glucose rich environment Snf1/Mig1 pathway represses the expression of its downstream target, such as SUC2. However, upon glucose depletion SNF1 is activated which leads to an increase in SUC2 expression. Our single cell experiments indicate that upon starvation, gene expression pattern of SUC2 shows rapid increase followed by a decrease to initial state with high cell-to-cell variability. The mechanism behind this behavior is currently unknown. In this work we study the long-term behavior of the Snf1/Mig1 pathway upon glucose starvation with a microfluidics and non-linear mixed effect modeling approach. We show a negative feedback mechanism, involving Snf1 and Reg1, which reduces SUC2 expression after the initial strong activation. Snf1 kinase activity plays a key role in this feedback mechanism. Our systems biology approach proposes a negative feedback mechanism that works through the SNF1 complex and is controlled by energy levels. We further show that Reg1 likely is involved in the negative feedback mechanism.

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.

Symmetry structures in dynamic models of biochemical systems.

Understanding the complex interactions of biochemical processes underlying human disease represents the holy grail of systems biology. When processes are modelled in ordinary differential equation (ODE) fashion, the most common tool for their analysis is linear stability analysis where the long-term behaviour of the model is determined by linearizing the system around its steady states. However, this asymptotic behaviour is often insufficient for completely determining the structure of the underlying system. A complementary technique for analysing a system of ODEs is to consider the set of symmetries of its solutions. Symmetries provide a powerful concept for the development of mechanistic models by describing structures corresponding to the underlying dynamics of biological systems. To demonstrate their capability, we consider symmetries of the nonlinear Hill model describing enzymatic reaction kinetics and derive a class of symmetry transformations for each order of the model. We consider a minimal example consisting of the application of symmetry-based methods to a model selection problem, where we are able to demonstrate superior performance compared to ordinary residual-based model selection. Moreover, we demonstrate that symmetries reveal the intrinsic properties of a system of interest based on a single time series. Finally, we show and propose that symmetry-based methodology should be considered as the first step in a systematic model building and in the case when multiple time series are available it should complement the commonly used statistical methodologies.

Synergistic effects of repair, resilience and retention of damage determine the conditions for replicative ageing.

Accumulation of damaged proteins is a hallmark of ageing, occurring in organisms ranging from bacteria and yeast to mammalian cells. During cell division in Saccharomyces cerevisiae, damaged proteins are retained within the mother cell, resulting in an ageing mother while a new daughter cell exhibits full replicative potential. The cell-specific features determining the ageing remain elusive. It has been suggested that the replicative ageing is dependent on the ability of the cell to repair and retain pre-existing damage. To deepen the understanding of how these factors influence the life of individual cells, we developed and experimentally validated a dynamic model of damage accumulation accounting for replicative ageing on the single cell level. The model includes five essential properties: cell growth, damage formation, damage repair, cell division and cell death, represented in a theoretical framework describing the conditions allowing for replicative ageing, starvation, immortality or clonal senescence. We introduce the resilience to damage, which can be interpreted as the difference in volume between an old and a young cell. We show that the capacity to retain damage deteriorates with high age, that asymmetric division allows for retention of damage, and that there is a trade-off between retention and the resilience property. Finally, we derive the maximal degree of asymmetry as a function of resilience, proposing that asymmetric cell division is beneficial with respect to replicative ageing as it increases the lifespan of a given organism. The proposed model contributes to a deeper understanding of the ageing process in eukaryotic organisms.

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.

Cardiac troponin T concentrations and patient-specific risk of myocardial infarction using the novel PALfx parameter.

BACKGROUND: Myocardial infarction (MI) is more likely if the heart damage biomarker cardiac troponin T (cTnT) is elevated in a blood sample from a patient with chest pain. There is no conventional method to estimate the risk of MI at a specific cTnT concentration. The purpose of this study was to evaluate the performance of a novel method that converts cTnT concentrations to patient-specific risks of MI. METHODS: Admission cTnT measurements in 15,425 ED patients from three hospitals with a primary complaint of chest pain, with or without a clinical diagnosis of MI, were Box-Cox-transformed to normality density functions to calculate the percentage with MI among patients with a given cTnT concentration, the parametric predictive value among lookalikes (PALfx). The ability of the PALfx to generate stable risk estimates of MI was examined by bootstrapping and expressed as the coefficient of variation (CV). RESULTS: Four age and sex-specific subgroups above or below 60 years of age with distinct cTnT distributions were identified among patients without MI. The cTnT distributions across subgroups with MI were similar, allowing us to use all admissions with MI to calculate the PALfx in the four subgroups. For instance, at a baseline cTnT concentration of 7 ng/L, a female patient <60 years would have a 0.5% risk of MI whereas a male patient >60 years would have a 1.9% risk of MI. To assess the stability of the PALfx method we bootstrapped smaller and smaller subsets of the 15,422 ED visits. We found that 1950 patients without MI and 50 patients with MI were sufficient to limit the variation of the PALfx with a CV of 0.8-5.4%, close to the CV using the entire dataset. The MI risk estimates were similar when data from the three hospitals were used separately to derive the PALfx equations. CONCLUSIONS: The PALfx can be used to estimate the risk of MI at patient-specific cTnT concentrations with acceptable margins of error. The patient-specific risk of disease using the PALfx could complement decision limits.