University of Groningen Thermodynamic principles governing metabolic operation : inference, analysis, and prediction Niebel, Bastian IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2015 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Niebel, B. (2015). Thermodynamic principles governing metabolic operation : inference, analysis, and prediction. [S.l.]: [S.n.]. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date: 12-04-2019
Chapter 1 Thermodynamic constraints on metabolic operations Bastian Niebel 9
Chapter 1 General overview Metabolism converts nutrients into energy and biomass precursors. These conversions (or metabolic processes) are the enzyme-catalyzed chemical transformations and the transports of metabolites across cellular membranes. But metabolic operations are not solely a consequence of the individual enzyme mechanisms. Instead, concerted action of metabolic processes are important for the functioning of metabolism. To unravel the complex system behavior of metabolic processes operating in an orchestrated manner, systems biology approaches have been successfully applied and generated new insights into the operation of metabolism (1-4). In systems biology, mathematical models of metabolism or other cellular processes are developed, and the formal analysis of these models typically leads to new insights into the operation of these processes (2). Given the fact that metabolic networks contain about thousand different metabolic processes, it is difficult to develop models that describe the mechanism of every metabolic process in great detail, i.e. with kinetics of the enzymatically catalyzed reactions. Thus, constraint-based models have been used, circumventing the need for detailed kinetic information on every metabolic process (4-6). In constraint-based models, metabolism is defined by a set of constraints, where the solution space of these constraints describes the different possible metabolic operations. Generally, the basis for these constraints are steady-state mass balances for the metabolites, which state that for every metabolite in the metabolic network the consumption rate equals the production rate, and thereby ensuring the conservation of mass. Adding besides steady-state mass balances more constraints to the model reduces the solution space and thereby can influence the quality of the predictions made with the model (6). During the last decades, numerous additional constraints have been identified ranging from constraints based on physical principles, e.g. thermodynamic constraints applied to the metabolic operations, or heuristically motivated constraints such as enzyme solvent capacity or transcriptional regulation (5, 6). Thermodynamic constraints have the advantage of a physical foundation. Also, because thermodynamic principles need to apply irrespective of the cellular growth conditions, these constraints are independent of the conditions. Therefore, thermodynamic constraints do not require readjustments when the model is applied to different conditions, unlike for most heuristic constraints, where for every new condition the constraint has to be reevaluated. Because of the physical foundations and condition-independence of thermodynamic constraints, they are being thought of as major constraints on the evolution of metabolism (7-13). Constraint-based models can be analyzed using a multitude of different analysis techniques (6). The tool of flux balance analysis (FBA) uses a cellular objective functions, e.g. growth rate, to predict metabolic fluxes (14). This approach has been extended to explore possible cellular objectives using multi-objective optimization (15). Further, the shape of the solution space has been explored using flux variability analysis (16) and sampling based approaches (6, 15, 17, 18), while the topology of the metabolic network has been studied using extreme pathways (19) and elementary mode analysis (20). All these analyses depend on the quality of the constraint-based model. Thus, this calls for carefully curated and assembled models supplemented with a maximum number of hard physical constraints, but with a minimal number of heuristic ad-hoc constraints. Here, thermodynamics could offer such physical constraints. 10
Background Background Thermodynamic principles Thermodynamic data Previous work Thermodynamic analysis of metabolic networks Analysis of metabolic networks with the loop-law Thermodynamic analysis of growth processes Connections between kinetics and thermodynamics This work Research question and outline In the following sections (cf. Fig. 1), we briefly review the background of thermodynamic principles used in biochemistry and methods to determine thermodynamic data. Then, we discuss how these principles and data were used in previous work to get new insights in metabolic operations. Specifically, we review the topics thermodynamic analysis of metabolic networks, thermodynamic analysis of growth processes, analysis of metabolic networks with the loop-law, and connections between kinetics and thermodynamics. We conclude this introduction with deriving the research question underlying this thesis, and provide an outline of the following chapters. Background Figure 1. Overview of topics covered in this introduction. Thermodynamic principles Thermodynamics of metabolic processes can be described by changes in the Gibbs energies, r G (Fig. 2). r G describes the difference in the Gibbs energy stored in the substrates and products of a metabolic processes (the so-called Gibbs formation energy). For a metabolic process to obey the second law of thermodynamics, r G has to be negative (21). Strictly spoken, for a metabolic processes to proceed according to the second law of thermodynamics, entropy has to be produced. However, at the conditions, at which the metabolic process take place (i.e. constant pressure and temperature), the production of entropy is proportional to r G. Metabolic processes consist of chemical transformations and metabolite transport. Knowing Gibbs formation energies for the substrates and products of a process, it is possible to determine the metabolic processes changes in the Gibbs energies, r G. For chemical transformations (superscript c), e.g. A B, r G c is defined by r G c A B = f G B - f G A, where f G is the Gibbs energies of formation of the chemical compounds, i.e. substrates and products of the transformations. f G of a compound X is calculated by, f G = f G o + RT ln a X, where f G o is the compound s standard Gibbs energy of formation, a the compound s chemical activity, R the Gas constant, and T the temperature. f G o of a compound describes its change in Gibbs energy with respect to a common reference state, which is indicated by the superscript o. Note: The standard Gibbs energies of formations for a chemical conversion can be combined in the standard Gibbs energy of reaction r G o, e.g. r G o A B = f G o B - f G o A, therefore the r G c 11
Chapter 1 Gibbs energy A B G Progress of metabolic process A A A G < 0 G = 0 G > 0 B B B Figure 2. Second law of thermodynamics for metabolic processes. A metabolic process consisting of a chemical transformation of the metabolite A to B can happen when the change in the Gibbs energy G is negative. G describes the difference in the Gibbs energy between the initial (A) and the final state (B) of the process. becomes, r G c A B = r G o A B + RT (ln a B - ln a A ). Metabolic networks not only consist of chemical transformations, but they also involve transport of metabolites across membranes. The change of Gibbs energy r G t of a metabolite transport (superscript t), e.g. the transport of a compound X from the outside (superscript out) to the inside (superscript in) of a cellular compartment, X out X in, is defined by, r G t Xout Xin = RT (ln a Xout - ln a Xin ) + F z X φ, where z is the charge of X, φ is the electrical membrane potential, and F is the Faraday constant. One feature of many metabolic processes is that different mechanisms are mechanistically and thermodynamically coupled (22), e.g. the coupling of a chemical transformation, A B, to the transport of a compound, X out X in. The change of Gibbs energy, r G, of this coupled metabolic process is then defined by the sum of the change in Gibbs energy of the chemical transformation, r G c, and the transport process, r G t, r G = r G c A B + r G t Xout Xin. Thermodynamic data In order to specify the Gibbs energy changes of metabolic processes, we need standard Gibbs energies of formation (or of reactions). These standard Gibbs energies can be inferred from the experimental equilibrium constant of chemical conversions (21, 23-27) also referred as reactant-contribution method (RC) (27) or predicted using a group contribution method (GC) (26-30). Both methods rely on collections of experimentally determined equilibrium constants for a set of about 400 of enzymatic reactions, which has been collected and curated from 1000 different articles into a database (31). These two approaches deliver different coverages: With the RC method, one can obtain standard energies Gibbs energies of reactions for 11 % (~600) of all relevant reactions (full chemical description and chemically balanced) in the KEGG database, and 88 % (~4800) with GC (27). The median root mean square error of the estimated standard Gibbs energies of reactions has been determined to 1 KJ mol -1 with RC and 5.5 KJ mol -1 with GC (27). Another approach has been developed, which infers Gibbs energy changes based on similarities in the reactions (32), but the high average root mean square error of 10 KJ mol -1 and the ability to only infer the standard Gibbs energies of 106 reactions, renders this approach not practical. Recently, different approaches to combine both the RC and GC methods have been developed (26, 27, 33, 34). When combining both methods, one is faced with the challenge of different reference states that were used for the estimated (RC) or predicted (GC) Gibbs energies of formations. If Gibbs energies are used in the thermodynamic constraints within a metabolic network model, then different reference states would lead to a violation of the first law of thermodynamics, and thus all used standard Gibbs energies of formations must have the same thermodynamic reference state (27). This problem has been solved by the component contribution method (CC) by ensuring that all standard Gibbs energies of formations are within 12
Background the null space of the stoichiometric network, i.e. fulfill the loop-law (27). To this end, CC also allows the exact determination of the estimation errors of the standard Gibbs energies. Because the chemical conditions at which metabolic processes take place within the cellular compartments can be approximated by a dilute mixture of compounds in an electrolyte solution with constant ionic strength, I, and constant ph, we can transform the standard Gibbs energies to take into account theses chemical conditions. The assumption of a dilute electrolyte solution allows to approximate the chemical activity, a, by the molar concentration, C, using the extended Debye-Hückel theory (21), i.e. a = γ(i)c, where γ is the activity coefficient determined as a function of I. Often, the activity coefficients are included in the standard Gibbs energy of formations, f G o (I) = f G o + RT ln γ(i), and thereby f G o becomes a function of the ionic strength I. In aqueous solutions, in which biochemical processes take place, metabolites (i.e. the reactants) are typically present as different chemical species (i.e. differently protonated). The distribution between the abundance of these species is often ph-dependent. As handling of individual species would be cumbersome, we only consider reactants in biochemical thermodynamics. In order to determine the ph-dependent Gibbs energy of a reactant, we first make the standard Gibbs energy of formation of the species ι, f G o ι(i), ph-dependent using the Legendre transformation (21), f G o ι = f G o ι(i) N H ( f G o H+(I)- RT ph ln 10), where N H is the number of hydrogen atoms of the species, and f G o H+(I) the standard Gibbs energy of formation of hydrogen ions (protons, H + ). This Legendre transformation transforms the standard Gibbs energy of the species to the biochemical reference state (indicated by the apostrophe ), and thereby making f G o ι(i) a function of the ph and the ionic strength I. The standard Gibbs energy of formation of a reactant is then determined from all its chemical species ι, using the relationship (21) f G o = -RT ln[ ι exp(- f G o ι/rt)], where we assume an equilibrium between the differently protonated species. Note, that while this concept is very practical, it complicates things once it comes to the thermodynamic description of transport processes, where we still also need to consider, for instance, the charge of individual species. For a detailed treatment of thermodynamics of transport processes, however, the reader is referred to the work of Jol et al. (35). Gibbs energy changes of metabolic processes are also dependent on the processes reactant concentrations. In microorganisms and mammalian cells, metabolite concentrations typically ranges between 1 um to 10 mm (36-39). When using thermodynamic constraints on metabolic network operation, one can constrain metabolite concentrations to such generic physiological bounds. Notably, in some studies wider concentration ranges were used (34, 40, 41). Likely, metabolite concentration bounds had to be relaxed, because of inconsistencies in the reference state of the Gibbs energies of formation or missing adjustments of the thermodynamic data to ph or ionic strength (42, 43). Such inconsistencies in the thermodynamic data are regretful in the first place, because they might lead to wrong conclusions. But, furthermore, these inconsistencies then typically required researchers to apply large metabolite concentration ranges to get the network feasible at all. Consequently the constraints imposed by the Gibbs energies are relaxed significantly and might not be active after all. Therefore, it is key to use standard Gibbs energies estimated by methods which ensure the same thermodynamic reference state, such as component contribution (27). Then, narrow 13
Chapter 1 concentration ranges between 1 um and 10 mm can be used and consequently thermodynamic constraints are more active. Previous work Thermodynamic analysis of metabolic networks The second law of thermodynamics together with detailed information of the Gibbs energies of reactions and concentration ranges have been used to determine the feasibility of metabolic pathways (9-13, 42-46) and metabolic networks (33, 34, 38, 40, 41, 47-54). Early studies focused on the thermodynamic feasibilities of metabolic pathways, where especially reactions were identified that serve as thermodynamic bottlenecks in glycolysis for different concentration ranges of the substrates and products of the glycolytic pathway (44, 45). Also the sensitivity of the thermodynamic bottlenecks with respect to ph, ionic strength, and magnesium has been studied (42, 43). More recent thermodynamic feasibility studies have been carried out to unravel the biochemical logic behind the glycolytic pathway (11, 13) and other pathways in central metabolism (13). Thermodynamic feasibility statements have been also applied for industrial applications. Here, feasibility of thermodynamic pathways have been used to optimize the penicillin production of Penicillium chrysogenum (46), and for the design of new carbon fixation pathways (9, 10, 12). The second law of thermodynamics, applied to the reactions of a metabolic network model, has been used in thermodynamic analysis of metabolic networks (38) to predict ranges for the Gibbs energies of reactions and concentrations in Escherichia coli (33, 38, 49-51, 54), Geobacter sulfurreducens (52), Saccharomyces cerevisiae (34, 38, 40, 41) and mammalian cells (34, 48, 51, 53) and to further check the thermodynamic consistency of metabolome data for E. coli and S. cerevisiae (38). Based on the predicted ranges of the Gibbs energies of reactions, potential regulatory reactions in metabolic networks have been identified (38, 41, 50, 52). By varying concentrations of toxic compounds, thermodynamic analysis of metabolic networks has been used to predict the responses of intracellular metabolite concentrations and Gibbs energies of reactions to different dosages of this toxic compounds (48). Also, the second law has been directly integrated as a mixed integer constraint allowing the computationally tractable integration of network thermodynamics and the second law of thermodynamics (49, 51). This mixed integer constraint has been used together with flux balance analysis to predict flux distributions based on measured intracellular and extracellular metabolic concentrations (51), and to study the effect of thermodynamic constraints on the feasible solution space of metabolic networks (54). Thermodynamic analysis of metabolic networks has further been used to define the directionality of reactions within the metabolic network. In constraint-based models reactions are either classified as irreversible or reversible, where typically the majority of the reactions are classified as irreversible. This irreversibility classifications have been incorrectly referred to as thermodynamic constraints (55, 56). Thermodynamic analysis of metabolic networks allowed to determine which reactions can be correctly classified as irreversible on the basis of thermodynamics. Therefore, we collected from different studies that classified the irreversibility of reactions using thermodynamic analysis, the fraction of reactions that were correctly classified as irreversible. With this literature summary, we found that for dif- 14
Previous work ferent genome scale metabolic reconstructions of E. coli, 28% (47), 29% (57), 34% (33), and mammalian reconstructions 39% (53), 29% (34), were correctly classified as irreversible on the basis of thermodynamics. In summary, on average 30% of the reactions classified as irreversible in this genome scale metabolic reconstructions are correctly classified on thermodynamic basis. Thermodynamic analysis of growth processes Thermodynamic principles not only apply to intracellular metabolic processes, but also to the overall growth process, i.e the conversion of substrates, S, e.g. glucose, phosphate, oxygen, into biomass, B, and by-products, P, e.g. carbon-dioxide, ethanol, acetate, lactate, by the growth process, S B + P. Similar to every metabolic process, the growth process has to fulfill the second law of thermodynamics, and thus, the change in Gibbs energy associated with the growth process needs to be negative, r G S B+P. To analyze these Gibbs energy changes of the growth process, black box models have been developed that determine r G S B+P on the basis of measured extracellular rates and Gibbs energies of formation of the different substrates, products and the biomass as input (8, 58-67). The Gibbs energy of formation of the biomass has been determined using low temperature calorimetry, statistical mechanics, or empirical relationships (67-69). Using these black box models that describe r G S B+P, the thermodynamic efficiency of different growth condition has been analyzed (59, 60, 62, 65, 67), and a number of different empirical relationships have been developed to predict the biomass yield based on measured r G S B+P (63, 65-67). Analysis of metabolic networks with the loop-law For metabolic networks, the first law of thermodynamics, i.e. conservation of energy, ensures that no energy can be produced or destroyed. Therefore, the first law is the energetic analogue to the mass conversation. For the operation of a metabolic network, this means that the Gibbs energy changes of a cyclic series of metabolic processes, e.g. loops of chemical conversions, A B C A, of the metabolites, A, B, and C, must be zero, e.g. r G A B + r G B C + r G C A = 0. Combining the first law with the second law of thermodynamics forbids a metabolic flux through a loop of metabolic processes (in the following, we refer to this as the loop-law (70)). These loops in the metabolic network are defined by the null space of the stoichiometric matrix, i.e. the mathematical representation of the metabolic network (70). Using the looplaw does not require any information about Gibbs energies of formation. It only requires the calculation of the null space of the stoichiometric matrix. The loop-law was used in a series of constraint-based models as constraints and was used to exclude loops from the flux distributions (18, 19, 71-74), to predict Gibbs energies of formations (73), and was included in flux variability analysis (75). It has been mathematically proven that using the loop-law only constrains thermodynamic infeasible loops and does not remove thermodynamically possible flux distributions (76). Connections between kinetics and thermodynamics For elemental reaction steps, the kinetics of these reactions are described by the law of mass action and therefore the Gibbs energy is proportional to the natural logarithm of the ratio of the forward, v +, and the backward rate, v -, of this elementary reaction step, i.e. r G = RT ln(v + /v - ) (77, 78). This relationship between r G and ln(v + /v - ) has been integrated in con- 15
Chapter 1 straint-based models (72, 79-81) and been used to identify kinetically limited reactions in metabolic pathways (13). But since this relationship assumes mass action kinetics, the generality of this relationship is questionable, since enzymatic reactions are not described by a single elementary reactions but consist of a series of elementary reactions, which make up the enzymatic mechanism. To this end, several attempts have been made to extend this relationship and develop new kinetic relationships between the Gibbs energy and reaction and the enzymatic rates (82, 83). This work Research question Thermodynamic principles apply to every aspect of metabolic operations, although from previous work it remains unclear to what degree metabolic operations are constrained by thermodynamics beyond pure feasibility statements. Metabolic operations that generally occur in most organisms, e.g. bacteria (84), fungi (85), mammalian cells (86, 87), and even plants (88), are respiration and aerobic fermentation (89). While with respiration, ATP is generated at high yields, with aerobic fermentation ATP is only generated at low yields through substrate-level phosphorylation (90). Different research fields postulated numerous explanations why cells under aerobic conditions choose an ATP-inefficient fermentative metabolism over an ATP-efficient respiratory metabolism, amongst which are economics of enzyme production (89), make-accumulate-consume strategy (85), intracellular crowding (84), limited nutrient transport capacity (91), and adjustments to growth-dependent requirements (86, 87). These explanations have all the short coming that they do not give a detailed mechanistic reason, therefore they could not be quantified and validated by experimental data. We asked whether in contrast to the previously proposed explanations rather a common inevitable principle would underlie the specific choice of metabolic operation, with fermentation being seemingly connected with high, and respiration with low rates of glucose uptake and glycolysis (92). Specifically we investigated, using constraint-based modeling (4, 6), whether thermodynamic constraints could be the cause for the ubiquitously observed and obviously sugar uptake rate-dependent choice between respiration and aerobic fermentation. Here, we aimed to identify these constraints by integrating previous work of thermodynamic analysis of metabolic networks, thermodynamic analysis of cellular growth, and the use of the loop-law to formulate a new thermodynamic metabolic network model. Outline of this thesis In Chapter 2, we develop a constraint-based model for Saccharomyces cerevisiae, which combines mass and charge balances with comprehensive description of the biochemical thermodynamics governing metabolic operations. As the model does not use any heuristic irreversibility assignments of the intracellular rates, therefore all conclusions drawn from the model are based on thermodynamic principles. We use this model together with experimental physiological and metabolome data of S. cerevisiae and identify a global thermodynamic constraint, i.e. a limit in the cellular rate of entropy production. Using this constraint in a flux balance analysis together with a cellular objective of maximizing the growth rate, we correctly predict the intracellular and extracellular rates of S. cerevisiae for a wide range of different 16
This work glucose uptake rates. In Chapter 3, we present a computational workflow to develop thermodynamic metabolic network models similar to the one developed in Chapter 2. Here, we especially focus on the potential pitfalls, when gathering the necessary biochemical information from different sources. Further, we give advice on potential model reductions and how to gather the necessary data to train such a model. In Chapter 4, we use the thermodynamic metabolic model of S. cerevisiae and develop a statistical workflow to accurately quantify the metabolic operation based on experimental data, where we combine the thermodynamic metabolic model with isotopomer balancing. We use this workflow to infer intracellular metabolic fluxes and also backward fluxes from measured extracellular rates, metabolomics data, standard Gibbs energies of reactions, and measured isotopomer patterns. Lastly, we conclude this work by a short discussion of the impact of the here identified principles on metabolic operations and suggest potential following studies. 17