Essentiality Is an Emergent Property of Metabolic Network Wiring

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FEBS Letters 581 (2007) 2485–2489

Essentiality is an emergent property of metabolic network wiring

Maria Concetta Palumboa,d, Alfredo Colosimoa,d, Alessandro Giulianib,*, Lorenzo Farinac,d a Physiology and Pharmacology Department, University of Rome, ‘Sapienza’, Italy b Istituto Superiore di Sanita`, Environment and Health Department, Viale Regina Elena 299, 00161 Rome, Italy c Department of Computer and Systems Science ‘‘A. Ruberti’’, University of Rome, ‘Sapienza’, Italy d CISB Center’, University of Rome, ‘Sapienza’, Italy

Received 9 January 2007; revised 20 April 2007; accepted 20 April 2007

Available online 2 May 2007

Edited by Robert B. Russell

by now incomplete. Thus we used two approaches for deriving Abstract The topological bases of essentiality in the yeast metabolic network from the perspective of double mutations are the this information: the Segre` group theoretical approach [18] in subject of this study. A strong relationship between essentiality which the essentiality of double mutations is obtained from the and the ‘missing alternative’ topological property is shown in application of an FBA model, and a full text mining meta- terms of the presence of multiple genes synthesizing the same en- analysis approach based on the extensive mining of available zyme, supplementary enzymes participating in the same meta- literature on double mutants experiments. Both the ap- bolic reaction, and availability of other pathways in the graph proaches converged into the missing alternative explanation connecting the separated nodes after the knockouts. of the generation of essentiality from the concomitant presence We demonstrate that the ‘missing alternative’ paradigm is suf- of single non-essential mutations. ﬁcient to explain the generation of essentiality for double mutations in which each single deleted element is non-essential. Ó 2007 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved. 2. Materials and methods

Keywords: Systems biology; Phenotype/genotype relations; A gene is defined as ‘essential’ if its deletion has lethal effects for the Double mutants; Yeast organism under a given experimental condition. In the case of yeast, knockout data for single mutations are available genome wide. In our study we referred to both Jeong and colleagues’ collection [19] and the SGDP. We consider the same yeast metabolic network as in our previous study (see Ref. [17] for details), obtained from the KEGG database as revised according to Ma and Zeng [20,21]. Each node 1. Introduction (metabolite) is labelled by a number (see Supplementary Material 1 in [17]) according to the authors’ terminology [20,21]. The global yeast metabolic network (graph) obtained in this way has metabolites as Metabolic networks were investigated by means of many dif- nodes and reactions transforming a metabolite into another as arcs ferent approaches: flux balance analysis (FBA) [1–7], elemen- (edges). There is a complex and not univocal relationship between arcs, tary flux modes and extreme pathways (EFM, EP) [1,8–11], enzymes and genes since reactions can be catalyzed by one or more en- minimization of metabolic adjustments (MOMA) [12], meta- zymes and enzymes can be synthesized by one or more genes. In this study we use a minimal model for the construction of our bolic control analysis (MCA) [13–16]. metabolic network: every gene involved in a reaction is considered as In a previous work [17] we demonstrated how the essential an arc; the network has ‘multiple edges’ between nodes if more than character of Saccharomyces cerevisiae single knockouts can one gene participates in the same reaction (or reactions, since the same be simply stated in terms of ‘missing alternative’ (MA) in enzyme can catalyze several biochemical reactions) transforming a metabolite into another one. reaching one or more nodes in the network. In this paper, A single knockout can disconnect two nodes of the network if the we move one fundamental step further by demonstrating deleted gene (arc) is the sole responsible for the catalysis of a reaction how two single non-essential mutations give rise to an essential and no alternative enzyme can restore the missing link between the sep- double mutant when the deletion of the two arcs correspond- arated nodes, otherwise the link ‘survives’. ing to the two knocked out enzymes gives rise to a ‘missing We define a gene as ‘topologically essential’ if its knockout causes the erasing of one arc (or more) so that the connection between the alternative’ pattern providing a proof-of-concept of the exis- nodes is not anymore guaranteed by alternative pathways, genes or en- tence of the metabolic network wiring diagram as a specific zymes; otherwise it is considered as ‘topologically non-essential’. phenotype. As for the experimental side, a double mutation can be classified as Whereas single deletion knockouts data for S. cerevisiae are ‘essential’ if the double deletion causes the yeast death, or ‘non-essential’ if the yeast survives. available from Stanford University Saccharomyces Genome When focusing on double mutations, we refer to couples of non-per 1 Deletion Project (SGDP), the experimental analysis of double se lethal (experimentally non-essential) knockouts. The complete con- mutations by means of an exhaustive gene couples deletion is cordance between topological and experimental definition of essentiality for single mutations was already assessed in a previous paper [17]. The assessment of such concordance for double mutations made of *Corresponding author. Fax: +39 064 9902355. two per se non-essential elements is the theme of this work. E-mail addresses: [email protected] When double gene knockout occurs, the network topology was (M.C. Palumbo), [email protected] (A. Giuliani). checked by looking for connections between nodes, i.e. for the reachability of one or more nodes previously linked by a pathway. A couple 1http://www-sequence.stanford.edu/group/yeast_deletion_project/dele- of genes can be considered topologically essential, if the connection be- tions3. tween two nodes is no more guaranteed after their double deletion. The

0014-5793/$32.00 Ó 2007 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.febslet.2007.04.067 2486 M.C. Palumbo et al. / FEBS Letters 581 (2007) 2485–2489 use of singularly non-essential genes assures us that the arising of a tween essentiality/non-essentiality and the presence of topolog- double essential mutation is solely due to the interaction between the ical connection. It is also intuitive that the existence of many two mutants, thus essentiality can be considered as an ‘emergent’ glo- alternatives is synonymous of dispensability and robustness: bal property. In order to validate our method, both in silico and in vivo double duplicated genes as well as more than one pathway are the mutations data were used: the former is the Segre` group collection main mechanisms of metabolic flexibility conferring robustness [18] of double knockouts, while the latter are experimental results col- to the system [4,11,18,52–58]. lected from the literature. The literature was surveyed by both classical It is important to keep in mind that the MA condition must search engines as PubMed and dedicated databases such as the GRID2 [22]. We focused on genes whose per se non-essential character was be considered as a necessary but not sufficient prerequisite for consistent among the following three resources: our network, Segre` essentiality, since the corresponding missing metabolite may be group collection, and experimental data. This ended up with 25 cou- included in the culture medium, or its role played by another ples of genes singularly non-essential. one. Thus, only the presence of a non-empty cell at the ES/A intersection in Table 1 could falsify our topological hypothesis of essentiality. 3. Results Only one couple, TDH2–TDH3, does not satisfy our definition of essentiality as absence of alternative genes and en- Synthetic data from the Segre` group are available in many zymes. In fact, TDH1, TDH2 and TDH3 codify for the simulated different growth conditions and their synthetic- same enzyme (EC 1.2.1.12) and participate in the same reac- lethality range goes from 0 (essential couple) to 1 (non-essen- tions; in [42,44], however, the couple TDH2–TDH3 is not via- tial couple). Since many genes are relevant only under partic- ble and in [42–44] TDH1–TDH2 and TDH1–TDH3 are ular growth conditions, we analyzed literature studies in considered as not essential. which many conditions are tested or, as an alternative, we The above papers confirm that the three genes are expressed compared the lethality results of all the experimental works at different levels during cell growth and that the contribution available to us and considered a double deletion as ‘essential’ of each gene product to the total glyceraldehyde-3-phosphate if such deletion is lethal in at least one experimental condition. activity is different. Moreover, TDH3 encodes two forms of In Fig. 1 three examples of coincidence between experimental glyceraldehyde-3-phosphate dehydrogenase, which differ in and topological essentiality are shown. net charge. In [43] the authors suggest the presence of iso- In our study, we looked for agreements between Segre` group zymes, too. It is likely that the three structural genes do not en- simulated results, experimental data (see [23–51]) and our code functionally equivalent polypeptides, and Delgado and topological essentiality features. Table 1 reports the classifica- colleagues [44] suggest that TDH1 may carry out a function tion of the 25 pairs of genes common to the Segre` collection, that is different from glycolysis. In the absence of other infor- 3 our data, and experiments. Two different properties were mation to be encoded in our metabolic network in terms of taken into consideration in order to classify these couples: connections or nodes, we deduce that some essential data are experimental essentiality/non-essentiality coded as ES/NES still missing. Thus, it seems fair to conclude that the location and presence/missing of alternatives (A/MA) to maintain of TDH2–TDH3 in Table 1 is not completely reliable. network connectivity in our topological analysis. Such alterna- In some cases predictions of double essentiality deduced by tives can be: (i) other pathways, (ii) multiple genes synthesizing the Segre` group [18] do not agree with both our topological the same enzyme, (iii) supplementary enzymes participating in analysis and experimental data. For example, FBA predicts the reaction. yeast survival after deletion of both URA5 and URA10, while As clearly shown by Table 1, our conjecture (namely that both our analysis (Fig. 1) and De Montigny experimental essentiality arises from the lack of alternative ways to link study [29] say the opposite. The same considerations apply two or more nodes) is consistent with the obtained results, gi- when taking into account the couples SER3–SER33 (isozymes, ven that only one couple out of 25 goes into the ‘forbidden whose essentiality is found in Albers et al. [32]), and LYS20– class’ (namely essential even if in presence of alternatives). LYS21, whose lethality estimated by Segre` is 0.96 (thus consid- Moreover, such inconsistency seems to be due to a lack of ered non-essential), but whose essentiality is experimentally information (see Section 4 section for details). It is worth proved by Feller and colleagues [30] (Fig. 1). remembering that the elements of all the considered couples Our network approach provides useful information at a very are non-essential, if considered one by one, and therefore we low computational cost; in Fig. 2 (Supplementary Material) are allowed to conclude that the essential character of double the complete list of analyzed double mutants is reported with mutations is an emergent property of the interaction. the only exception to our paradigm bolded. The proposed paradigm is not new: it has a very long history [59]. The original contribute of our work is in the recognition that practically no 4. Discussion lethal mutation preserving the continuity of the network does exist. This ‘descriptive formal metaphor’ is endowed with obvi- The aim of our study is to show: (i) that experimental and ous limitations. In fact, a very simple tool such as network topological essentiality are strictly linked, and (ii) that in order analysis cannot capture some very important aspects and to make predictions of gene essentiality in metabolic networks mechanisms of living organisms, for example epistasis. Epista- topological considerations are of basic importance. Looking at sis refers to those non-essential gene pairs made of at least one Table 1, one can argue the existence of a close relationship be- per se essential element. This kind of interaction cannot by definition deal with our paradigm, because the erasing of another arc cannot in any case rebuild a deleted path in the graph. As 2http://www.thebiogrid.org. an example in Neurospora crassa, Barthelmess [60] discovered 3For more information, see http://www.dis.uniroma1.it/~farina/Yeast/. a conditionally lethal mutant in the allele cpc-1 that becomes M.C. Palumbo et al. / FEBS Letters 581 (2007) 2485–2489 2487

Fig. 1. Experimental and topological essentiality. The ﬁgure reports three examples of double deletion. On the left panel, yellow bars indicate ARO3 and ARO4 genes (EC 2.5.1.54), involved both in two reactions; on the panel in the middle, the yellow bar refers to URA5 and URA10 (EC 2.4.2.10); on the right one LYS20 and LYS21 (EC 2.3.3.14) are shown. In all of the examples the double mutation causes the yeast death, there are no alternative enzymes or genes and a pathway is isolated.

Table 1 Couples are classiﬁed by rows as ‘essential’ (ES) or ‘not essential’ (NES) if experimental data proof the yeast survival or death, and by column if they have topological ‘alternatives’ (A) or not (MA) to arcs deletions. These alternatives can be: other pathways (P), multiple genes synthesizing the same enzyme (G) or supplementary enzymes involved in the reaction (E) AMA ES TDH2 (YJR009C)–TDH3 (YGR192C) (E,G) ADE16 (YLR028C)–ADE17 (YMR120C) ARO3 (YDR035W)–ARO4 (YBR249C) PGM1 (YKL127W)–PGM2 (YMR105C) URA5 (YML106W)–URA10 (YMR271C) LYS20 (YDL182W)–LYS21 (YDL131W) GSY1 (YFR015C)–GSY2 (YLR258W) SER3 (YER081W)–SER33 (YIL074C) TKL1 (YPR074C)–TKL2 (YBR117C) ASN1 (YPR145W)–ASN2 (YGR124W)

NES DAL7 (YIR031C)–MLS1 (YNL117W) (G,P) FUR1 (YHR128W)–URA5 (YML106W) ADH1 (YOL086C)–ADH2 (YMR303C) (G) ALD2 (YMR170C)–ALD3 (YMR169C) GDH1 (YOR375C)–GDH3 (YAL062W) (E) APT1 (YML022W)–APT2 (YDR441C) GLT1 (YDL171C)–GDH3 (YAL062W) (E) AAH1 (YNL141W)–APT2 (YDR441C) GLT1 (YDL171C)–GDH1 (YOR375C) (E) SHM1 (YBR263W)–SHM2 (YLR058C) TDH1 (YJL052W)–TDH2 (YJR009C) (E,G) SHM1 (YBR263W)–GCV1 (YDR019C) TDH1 (YJL052W)–TDH3 (YGR192C) (E,G) GCV1 (YDR019C)–SHM2 (YLR058C) MIS1 (YBR084W)–SHM1 (YBR263W) (E,G)

viable in the presence of another mutation. In yeast such con- mation on the presence/absence of a pathway between metab- ditions are, however, very rare, as stated by Szafraniec et al. olites, becomes crucial. By contrast, when considering [61]. mutations leading to a living but non-fully functional pheno- It is worth stating that the ‘essentiality-by-reachability’ par- type, one should expect that also the dynamical features of adigm is particularly effective when dealing with metabolic fluxes distribution in the metabolic network come into play. pathways. In the case of more complex and poorly defined net- When the environmental pressure becomes very stringent, the works as regulatory and signalling pathways the things become consequence is a drastic simplification of the system behaviour much more fuzzy and difficult to systematize. Other obvious which, in turn, makes realistic a crude metaphor such as the limitations come from problems in gene annotation and to interaction network. subtle effects like enzyme underground activity, low specific- ity,substrate promiscuity. More refined methods such as flux balance analysis [18] can be profitably used to complement 5. Conclusions the simple topological approach in these cases. Recently, an important methodological work by Pan et al. In this study, we confirm that the conjecture of ‘essential- [62,63] opened the way to a more systematic analysis of double ity = non-reachability’, proposed in our previous analysis [17] mutants in yeast that can provide a much wider experimental and commonly used in genetics [59] , extends now up to a more material for modeling purposes. general ‘missing alternative’ property. We demonstrate the As a final remark, it is worth noting that the concept of arising of essentiality from non-essential elements, simply essentiality is related to an extreme biological situation in looking at their position in the network. Our conjecture re- which the only possible outcomes are ‘‘to live’’ or ‘‘to die’’. mains almost always valid for the analyzed double mutants. In this case one may expect that topology, i.e. the basic infor- This implies that the relevance of a specific enzyme can be only 2488 M.C. Palumbo et al. / FEBS Letters 581 (2007) 2485–2489 defined in the context of the pattern of relations with other ele- [9] Schuster, S., Dandekar, T. and Fell, D.A. (1999) Detection of ments in the network. In fact, when talking about topological elementary flux modes in biochemical networks: a promising tool essentiality, we do not focus on specific functions of the en- for pathway analysis and metabolic engineering. 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