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

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

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

yApoptosis: yeast apoptosis database

In the past few years, programmed cell death (PCD) has become a popular research area due to its fundamental aspects and its links to human diseases. Yeast has been used as a model for studying PCD, since the discovery of morphological markers of apoptotic cell death in yeast in 1997. Increasing knowledge in identification of components and molecular pathways created a need for organization of information. To meet the demands from the research community, we have developed a curated yeast apoptosis database, yApoptosis. The database structurally collects an extensively curated set of apoptosis, PCD and related genes, their genomic information, supporting literature and relevant external links. A web interface including necessary functions is provided to access and download the data. In addition, we included several networks where the apoptosis genes or proteins are involved, and present them graphically and interactively to facilitate rapid visualization. We also promote continuous inputs and curation by experts. yApoptosis is a highly specific resource for sharing information online, which supports researches and studies in the field of yeast apoptosis and cell death

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

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

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

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

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 \ub5mol/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