BayFlux: A Bayesian Method to Quantify Metabolic Fluxes and their Uncertainty at the Genome Scale.

Metabolic fluxes, the number of metabolites traversing each biochemical reaction in a cell per unit time, are crucial for assessing and understanding cell function. 13C Metabolic Flux Analysis (13C MFA) is considered to be the gold standard for measuring metabolic fluxes. 13C MFA typically works by leveraging extracellular exchange fluxes as well as data from 13C labeling experiments to calculate the flux profile which best fit the data for a small, central carbon, metabolic model. However, the nonlinear nature of the 13C MFA fitting procedure means that several flux profiles fit the experimental data within the experimental error, and traditional optimization methods offer only a partial or skewed picture, especially in “non-gaussian” situations where multiple very distinct flux regions fit the data equally well. Here, we present a method for flux space sampling through Bayesian inference (BayFlux), that identifies the full distribution of fluxes compatible with experimental data for a comprehensive genome-scale model. This Bayesian approach allows us to accurately quantify uncertainty in calculated fluxes. We also find that, surprisingly, the genome-scale model of metabolism produces narrower flux distributions (reduced uncertainty) than the small core metabolic models traditionally used in 13C MFA. The different results for some reactions when using genome-scale models vs core metabolic models advise caution in assuming strong inferences from 13C MFA since the results may depend significantly on the completeness of the model used. Based on BayFlux, we developed and evaluated novel methods (P-13C MOMA and P-13C ROOM) to predict the biological results of a gene knockout, that improve on the traditional MOMA and ROOM methods by quantifying prediction uncertainty

Metabolic diversity in cell populations: probability densities over the flux polytope

Even in clonal populations, cells appear to be strongly heterogeneous in terms of, e.g., protein levels, RNA levels, sizes at birth or division, interdivision times and elongation rates. Part of this variability is likely due to the inherent stochasticity of gene expression at the level of single cells. It is however known that heterogeneous populations may possess an evolutionary advantage, for instance in variable environments or under stress. Despite appearing to be at odds with the idea of optimality presented in the previous chapters, metabolic diversity can be described and modeled within the constraint-based framework introduced in the previous chapters. Specifically, a statistical representation of heterogeneous populations can be obtained by defining suitable probability distributions on the flux polytope. This chapter addresses • the different sources of variation that affect microbial metabolism along with the mechanisms that may favor higher variability, • the methods devised to represent heterogeneous microbial populations within the framework of constraint- based models, and • how these approaches connect to the optimality scenario presented in the previous chapters

An introduction to the maximum entropy approach and its application to inference problems in biology

A cornerstone of statistical inference, the maximum entropy framework is being increasingly applied to construct descriptive and predictive models of biological systems, especially complex biological networks, from large experimental data sets. Both its broad applicability and the success it obtained in different contexts hinge upon its conceptual simplicity and mathematical soundness. Here we try to concisely review the basic elements of the maximum entropy principle, starting from the notion of ‘entropy’, and describe its usefulness for the analysis of biological systems. As examples, we focus specifically on the problem of reconstructing gene interaction networks from expression data and on recent work attempting to expand our system-level understanding of bacterial metabolism. Finally, we highlight some extensions and potential limitations of the maximum entropy approach, and point to more recent developments that are likely to play a key role in the upcoming challenges of extracting structures and information from increasingly rich, high-throughput biological data

Relationship between fitness and heterogeneity in exponentially growing microbial populations

Despite major environmental and genetic differences, microbial metabolic networks are known to generate consistent physiological outcomes across vastly different organisms. This remarkable robustness suggests that, at least in bacteria, metabolic activity may be guided by universal principles. The constrained optimization of evolutionarily motivated objective functions, such as the growth rate, has emerged as the key theoretical assumption for the study of bacterial metabolism. While conceptually and practically useful in many situations, the idea that certain functions are optimized is hard to validate in data. Moreover, it is not always clear how optimality can be reconciled with the high degree of single-cell variability observed in experiments within microbial populations. To shed light on these issues, we develop an inverse modeling framework that connects the fitness of a population of cells (represented by the mean single-cell growth rate) to the underlying metabolic variability through the maximum entropy inference of the distribution of metabolic phenotypes from data. While no clear objective function emerges, we find that, as the medium gets richer, the fitness and inferred variability for Escherichia coli populations follow and slowly approach the theoretically optimal bound defined by minimal reduction of variability at given fitness. These results suggest that bacterial metabolism may be crucially shaped by a population-level trade-off between growth and heterogeneity

Strategies for engineering microbial communities

Understanding how microbes assemble into communities is a fundamental open question in biology, with applications to human health, environmental sustainability, and metabolic engineering. Although it is known that the competition and exchange of nutrients (i.e., metabolic interactions) shape microbial community structure and dynamics, the ability to reliably predict the metabolic interactions and their effect on microbial communities is still being studied. This dissertation investigates how metabolism and environment shape microbial communities through the use of mathematical models, based on linear programming (LP) and mixed integer linear programming (MILP) methods. The first system I studied is a synthetic microbial consortium composed of two species, Cellulomonas fimi and Yarrowia lipolytica, hypothesized to be able to jointly transform cellulose into biofuel precursors. I combined experimental data and flux balance analysis (FBA) to test our capacity to predict metabolic interactions between the two organisms, and explored a proof-of-concept method to monitor the growth dynamics of this coculture. I next explored the possibility of generalizing the design of synthetic communities through the implementation of a computational method that can design division of labor strategies. The algorithm finds consortia of engineered bacterial strains that can survive by exchanging with each other specific nutrients. By distributing functions, microbial consortia can perform tasks that are impossible for individual species to accomplish alone. In addition to highlighting the trade-off between metabolic self-reliance and mutualistic exchange, this approach suggests how division of labor may arise in Escherichia coli monocultures. While mechanistic models are helpful for studying metabolism in microbes and microbial communities, it is interesting to ask whether increasingly cheaper high-throughput phenotypic data, can help achieve similar goals. To address this question, I developed a computational approach to investigate the relationship between growth profiles and microbial species, based on the identification of growth conditions that can best represent the whole dataset. This approach can help engineer microbial communities by identifying microbes that are more likely to engage in cross-feeding, rather than competition, based on their phenotypic profiles. In general, this dissertation demonstrates how different types of metabolic modeling approaches, both mechanism-based and data-driven, can be used to predict metabolic interactions between members of microbial consortia, and to help engineer novel synthetic communities

Metabolic modelling and 13C flux analysis : application to biotechnologically important yeasts and a fungus

All bioconversions in cells derive from metabolism. Microbial metabolisms contain potential for bioconversions from simple source molecules to unlimited number of biochemicals and for degradation of even detrimental compounds. Metabolic fluxes are rates of consumption and production of compounds in metabolic reactions. Fluxes emerge as an ultimate phenotype of an organism from an integrated regulatory function of the underlying networks of complex and dynamic biochemical interactions. Since the fluxes are time-dependent, they have to be inferred from other, measurable, quantities by modelling and computational analysis. 13C-labelling is crucial for quantitative analysis of fluxes through intracellular alternative pathways. Local flux ratio analysis utilises uniform 13C-labelling experiments, where the carbon source contains a fraction of uniformly 13C-labelled molecules. Carbon-carbon bonds are cleaved and formed in metabolic reactions depending on the in vivo fluxes. 13C-labelling patterns of metabolites or macromolecule components can be detected by mass spectrometry (MS) or nuclear magnetic resonance (NMR) spectroscopy. Local flux ratio analysis utilises directly the 13C-labelling data and metabolic network models to solve ratios of converging fluxes. In this thesis the local flux ratio analysis has been extended and applied to analysis of phenotypes of biotechnologically important yeasts Saccharomyces cerevisiae and Pichia pastoris, and a fungus Trichoderma reesei. Oxygen dependence of in vivo net flux distribution of S. cerevisiae was quantified by using local flux ratios as additional constraints to the stoichiometric model of the central carbon metabolism. The distribution of fluxes in the pyruvate branching point turned out to be most responsive to different oxygen availabilities. The distribution of fluxes was observed to vary not only between the fully respiratory, respiro-fermentative and fermentative metabolic states but also between different respiro-fermentative states. The local flux ratio analysis was extended to the case of two-carbon source of glycerol and methanol co-utilisation by P. pastoris. The fraction of methanol in the carbon source did not have as profound effect on the distribution of fluxes as the growth rate. The effect of carbon catabolite repression (CCR) on fluxes of T. reesei was studied by reconstructing amino acid biosynthetic pathways and by performing local flux ratio analysis. T. reesei was observed to primarily utilise respiratory metabolism also in conditions of CCR. T. reesei metabolism was further studied and L-threo-3-deoxy-hexulosonate was identified as L-galactonate dehydratase reaction product by using NMR spectroscopy. L-galactonate dehydratase reaction is part of the fungal pathway for D-galacturonic acid catabolism

Dynamic modelling of biochemical reaction networks and sampling methods for constraint-based models

This dissertation is a partial fulfillment of the requirements for the degree of Doctor of Philosophy (PhD). This study is carried out at the Department of Mathematics, University of Bergen. The subject of the thesis is dynamic Modelling of biochemical reaction networks and sampling methods for constraint-based models.Doktorgradsavhandlin

Computational methods toward early detection of neuronal deterioration

In today's world, because of developments in medical sciences, people are living longer, particularly in the advanced countries. This increasing of the lifespan has caused the prevalence of age-related diseases like Alzheimer’s and dementia. Researches show that ion channel disruptions, especially the formation of permeable pores to cations by Aβ plaques, play an important role in the occurrence of these types of diseases. Therefore, early detection of such diseases, particularly using non-invasive tools can aid both patients and those scientists searching for a cure. To achieve the goal toward early detection, the computational analysis of ion channels, ion imbalances in the presence of Aβ pores in neurons and fault detection is done. Any disruption in the membrane of the neuron, like the formation of permeable pores to cations by Aβ plaques, causes ionic imbalance and, as a result, faults occur in the signalling of the neuron.The first part of this research concentrates on ion channels, ion imbalances and their impacts on the signalling behaviour of the neuron. This includes investigating the role of Aβ channels in the development of neurodegenerative diseases. Results revealed that these types of diseases can lead to ionic imbalances in the neuron. Ion imbalances can change the behaviour of neuronal signalling. Therefore, by identifying the pattern of these changes, the disease can be detected in the very early stages. Then the role of coupling and synchronisation effects in such diseases were studied. After that, a novel method to define minimum requirements for synchronicity between two coupled neurons is proposed. Further, a new computational model of Aβ channels is proposed and developed which mimics the behaviour of a neuron in the course of Alzheimer's disease. Finally, both fault computation and disease detection are carried out using a residual generation method, where the residuals from two observers are compared to assess their performance

Systems Modeling of Calcium Homeostasis and Mobilization in Platelets Mediated by Ip3 and Store-Operated Calcium Entry

Platelet aggregation is one of the body\u27s first responses to vascular damage to prevent blood loss; upon injury to the endothelium platelets react to the exposed extracellular matrix and undergo a host of intracellular biochemical changes enabling them to activate and form a plug at the site of injury. Internally, platelets respond to their environment by exhibiting a sharp rise in cytosolic calcium that triggers a series of chemical and morphological changes which are critical to platelet activation and subsequent clot propagation. This thesis develops a mechanistic, computational model of platelet calcium regulation using coupled sets of ordinary differential equations. This thesis extends previous work modeling calcium release mediated by inositol 1,4,5-trisphosphate (IP3) to engineer what is the first, to date, complete model of store-operated calcium entry (SOCE) integrated into a systems model for calcium signaling. SOCE is a ubiquitous extracellular calcium entry pathway which is activated by calcium store depletion, is seen in many cells types and is yet to be fully understood. Our model for SOCE regulation consists of diffusion-limited dimerization of the calcium sensor STIM1, followed by fast, cytosolic calcium-dependent association of STIM1 dimers with Orai1 channels in the plasma membrane resulting in graded store-operated channel activation. Appropriate model resting states were characterized using a dense Monte Carlo technique on an initial condition sampling space constrained by available data on species concentrations and protein copy numbers. From this set of resting configurations, following application of physiologic IP3 stimuli, we selected for resting states exhibiting calcium dynamics that are in agreement with experimental data. We also selected for states presenting significant SOCE current based on differences in cytosolic calcium between simulations run with and without extracellular calcium. Low resting levels of IP3 are required for system robustness and for simultaneous appropriate dynamic response to physiologic agonists. Platelets require a resting electrical potential across the membrane surrounding the calcium stores of greater than -70 mV in order to exhibit significant agonist-induced calcium release

Computational Design of Synthetic Microbial Communities

In naturally occurring microbial systems, species rarely exist in isolation. There is strong ecological evidence for a positive relationship between species diversity and the functional output of communities. The pervasiveness of these communities in nature highlights that there may be advantages for engineered strains to exist in cocultures as well. Building synthetic microbial communities allows us to create distributed systems that mitigate issues often found in engineering a monoculture, especially when functional complexity is increasing. The establishment of synthetic microbial communities is a major challenge we must overcome in order to implement coordinated multicellular systems. Here I present computational tools that help us design engineering strategies for establishing synthetic microbial communities. Using these tools I identify promising candidates for several design scenarios. This work highlights the importance of parameter inference and model selection to build robust communities. The findings highlight important interaction motifs that provide stability, and identify requirements for selecting genetic parts and tuning the community composition. Additionally, I show that fundamental interactions in small synthetic communities can produce chaotic behaviour that is unforecastable. Together these findings have important ramifications for how we build synthetic communities in the lab, and the considerations of interactions in microbiomes we manipulate