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The human extended mitochondrial metabolic network: New hubs from lipids
BioSystems 109 (2012) 151–158
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The human extended mitochondrial metabolic network: New hubs from lipids Luigi Leonardo Palese ∗ , Fabrizio Bossis Department of Basic Medical Sciences (SMB), University of Bari “Aldo Moro”, Piazza G. Cesare-Policlinico, 70124 Bari, Italy
a r t i c l e
i n f o
Article history: Received 13 December 2011 Received in revised form 21 February 2012 Accepted 2 April 2012 Keywords: Systems biology Power-law distribution Neurodegenerative diseases Mitochondria Lipid metabolism Evolution
a b s t r a c t Even if systems thinking is not new in biology, rationalizing the explosively growing amount of knowledge has been the compelling reason for the sudden rise and spreading of systems biology. Based on ‘omics’ data, several genome-scale metabolic networks have been reconstructed and validated. One of the most striking aspects of complex metabolic networks is the pervasive power-law appearance of metabolite connectivity. However, the combinatorial diversity of some classes of compounds, such as lipids, has been scarcely considered so far. In this work, a lipid-extended human mitochondrial metabolic network has been built and analyzed. It is shown that, considering combinatorial diversity of lipids and multipurpose enzymes, an intimate connection between membrane lipids and oxidative phosphorilation appears. This finding leads to some biomedical considerations on diseases involving mitochondrial enzymes. Moreover, the lipid-extended network still shows power-law features. Power-law distributions are intrinsic to metabolic network organization and evolution. Hubs in the lipid-extended mitochondrial network strongly suggest that the “RNA world” and the “lipid world” hypothesis are both correct. © 2012 Elsevier Ireland Ltd. All rights reserved.
1. Introduction Advances in high-throughput technologies and in bioinformatics have rapidly expanded the information availability in biological sciences. This huge amount of information has raised the need for organizing and understanding the part catalogs present in biological databases, giving birth to systems biology as a new discipline (Ideker et al., 2001; Kitano, 2002; Westerhoff and Palsson, 2004). Systems understanding requires a substantial shift in our approach to biological sciences (von Bertalanffy, 1967). While knowledge of proteins and genes as isolated entities continues to be crucial, the focus is now on systems as a whole. Because “more is different” (Anderson, 1972), a system cannot be fully understood by simply knowing the list of all components. System-level understanding requires insight into system structure, dynamics and control (Ruppin et al., 2010). The behavior of complex systems emerges from the orchestrated activity of many components mutually interacting. At a high abstract level, the components can be reduced to a set of nodes, and the interactions among components to links. Nodes and links together form a network, or, more formally, a graph. Introduction of network theory tools into the systems biology field has been a major advance in our system-level understanding of biology. Various types of cellular networks can be visualized. Smallmolecule substrates can be pictured as nodes in a metabolic
∗ Corresponding author. Tel.: +39 0805448524; fax: +39 0805448538. E-mail addresses: [email protected], [email protected] (L.L. Palese). 0303-2647/$ – see front matter © 2012 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.biosystems.2012.04.001
network and enzyme-catalyzed reactions, transforming one metabolite into another, as links. Various metabolic network reconstructions have been carried out for microorganisms, such as, for example, Haemophilus influenzae (Edwards and Palsson, 1999), Escherichia coli (Edwards and Palsson, 2000), Helicobacter pylori (Paley and Karp, 2002; Price et al., 2002), Streptomyces coelicolor A3(2) (Borodina et al., 2005). The metabolic network of Saccharomyces cerevisiae has been the first reconstructed eukaryotic metabolic network (Duarte et al., 2004), and significant advances through the human metabolic network reconstruction have been done (Duarte et al., 2007; Ma et al., 2007). Mitochondrial metabolic network has been also studied (Thiele et al., 2005; Vo et al., 2004). Mitochondria are semi-autonomous organelles. Due to their endosymbiotic origin, mitochondria maintain their genome, membranes, transcriptional and translational machineries, signaling activities and division ability. For these reasons, mitochondria are excellent subjects for systems biology studies (Vo and Palsson, 2007), particularly based on proteomic analysis (Alonso et al., 2005; Da Cruz et al., 2005; Liu et al., 2004; Taylor et al., 2003). Doubtless an important breakthrough in the field of biological networks was the finding that numerous cellular networks exhibit a long-tail (power-law) distribution in node connectivity. In all networks, each node is characterized by the node degree (or connectivity). This is a number telling us how many links the node has to other nodes. A popular model aiming to describe such node connectivity distribution, in biological networks, is the scale-free model (Albert, 2005; Barabási and Oltvai, 2004; Boccaletti et al., 2006), in which the probability that a node is highly connected is statistically more significant than in random graphs, and network
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uniqueness are determined by a small number of highly connected nodes, known as hubs. Such networks have been named scale-free because power-laws have the property of having the same functional form at all scales and remain unchanged, under rescaling the independent variable. On the other hand, it has been shown that the metabolites in a metabolic network are far from being fully connected (Boccaletti et al., 2006; Ma and Zeng, 2003). The largest fully connected part of metabolic networks represents the core of the network and has the features of scale-free networks. An intriguing result is that observed distributions in metabolic networks derive from the carrier metabolites (Tanaka, 2005). Carrier metabolites are densely connected to various functional modules, whereas other metabolites are densely connected inside the modules. In such a view, power-law distribution comes from high variability of nodes connectivity and metabolic networks appear to be scalerich instead of scale-free (Csete and Doyle, 2004; Li et al., 2005; Tanaka, 2005; Tanaka et al., 2005). These self-dissimilar and scalerich models can also be obtained from High Optimized Tolerances (HOT) models (Carlson and Doyle, 2002). Both the above reported models lead to power-law distribution, one because of, essentially, evolutionary motif (the scale-free model), one of functional optimization motif (scale rich and HOT models). Beside this intense work about power-law topology of metabolic network, it should be noted that considerable criticisms on the real significance and novelty of these findings have been raised (Keller, 2005), and various works raise doubts about the exact statistical distribution of node connectivity in the biological networks (Lima-Mendez and van Helden, 2009). Beside the intellectual challenges, an in depth insight of metabolic networks promises numerous applications, for example network-based drug design (Hornberg et al., 2006; Murabito et al., 2011). A key step towards this goal is the extensive and detailed description of the whole network. An enormous number of chemically distinct molecular species arise from the various combinations of different fatty acids with backbone structures, such as glycerol or sphingoid bases. Lipidomics is the systems-level analysis and characterization of lipids and their interacting moieties. Technical difficulties, also related to the extreme complexity of lipid molecules, still keep this field of systems biology in his infancy (Wenk, 2005). But the crucial role of lipids in cell and the involvement of lipid metabolic enzymes and pathways in many human diseases are the compelling reasons for an increasing interest in this promising area of research. Rather surprisingly, in metabolic network reconstruction, lipid molecules are often considered only from a ‘cumulative’ point of view. The combinatorial diversity of lipids is not explicitly considered, but entire classes of molecules are treated as a single chemical species. This approach leads to consider in the reconstructed metabolic network few species of lipids, whereas the real cellular networks contain thousands of chemically different lipids. In this work a topological analysis of human mitochondrial metabolic network is presented. A hand-validated reaction set has been used to reconstruct the mitochondrial stoichiometric matrix. In this network, lipid diversity and enzymes able to work on different substrates have been explicitly taken into account. 2. Methods 2.1. The Stoichiometric Matrix A set of biochemical reactions involving human mitochondria has been manually constructed using the online databases KEGG (Kanehisha and Goto, 2000), MitoDB (available at http://bioinfo.nist.gov/hmpd/index.html) and Brenda (Schomburg et al., 2002) as well as biochemistry textbooks (Devlin, 2002; Nelson and Cox, 2008). This biochemical reaction set is based on the metabolic network of the human cardiac mitochondrion reported in Vo et al. (2004) with expansions and modifications. Few reactions in Vo et al. (2004) have been changed in our network; for example, the enzyme synthesizing carbamoyl phosphate, which was carbamoyl phosphate
Fig. 1. The stoichiometric matrix of lipid-extended human mitochondrial metabolic network. The dimensions of this stoichiometric matrix are 509 rows and 675 columns. Rows correspond to metabolites, considering the presence in different compartments of transported ones; columns correspond to reactions, some of which are thermodynamically reversible in the cellular environment and are considered in both directions. This matrix contains 343,575 elements; of these 2695 (0.78%) are nonzero. Long dot lines represent the highly connected metabolites. The ordered list of metabolites and reactions are reported in Supplementary data 1.
synthase E.C. 2.7.2.2 in (Vo et al., 2004) here has been changed to carbamoyl phosphate synthase E.C. 6.3.4.16, because the latter enzyme is more appropriate in the human metabolic network. The reaction of cytochrome c oxidase, considered in Vo et al. (2004) as the reaction responsible for reactive oxygen species (ROS) production, has been revised. It should be noted that cytochrome c oxidase is a respiratory complex considered not involved in ROS production (Adam-Vizi and Chinopoulos, 2006). In this network, ROS production has been modeled as superoxide anion production by reduced coenzyme Q, and starting from this ROS molecule all different ROS have been obtained. The combinatorial features of lipids and enzymes involved in their metabolism have been considered in this work. Fatty acids oxidation reactions have been explicitly introduced in the metabolic network, instead of a cumulative global equation for -oxidation. Moreover, the combinatorial diversity of membrane lipids, has been (partially) taken into account, giving to an explosion in the number of reactions involving this class of molecules. Here, compounds such as, for example, phosphatidic acid have been considered not actually as ‘compounds’ but as ‘class of compounds’ and consequently expanded. Finally, the effect of including enzymes able to work on many different substrates has been evaluated. In the metabolic networks reported to date, an enzyme catalyzes usually no more than a single reaction. In the network used in this work, up to twenty different reactions could be catalyzed by the same low specificity enzyme. These are enzymes working on similar, but different, membrane lipids. The biochemical reaction set used in this work contains 331 metabolites, which grow to 509 if the same metabolite is counted as distinct when represented in different cellular compartments. The network contains 510 reactions, some of which must be considered reversible in the cell. Reactions are considered reversible only if this is stated in the sources used for the manual reconstruction of the network. The complete reaction set is reported as Supplementary data 1; the model is also provided in SBML format as Supplementary data 2. A metabolic reaction network without expansion of combinatorial metabolites, similar to what reported in (Vo et al., 2004), has been also reconstructed and analyzed. Biochemical reactions comprising the reconstructed metabolic network were represented by a stoichiometric matrix S (Palsson, 2006). The stoichiometric matrix was m × n where m is the number of metabolites and n is the number of reactions in the reconstructed network. Stoichiometric matrices are sparse (Palsson, 2006). A sparse matrix mainly contains zero elements. The stoichiometric matrix here obtained, after lipid expansion and considering forward and reverse reactions where appropriate, is also sparse (see Fig. 1): only 0.78% elements are nonzero. Considering as reaction participants both reactants and products, there are 219 reactions in which four compounds participate, the same number of reactions with five participating compounds, and much less reactions in which a larger number of reactants/products are observed (not shown). On average four compounds participate in a reaction in this network, and considering that this stoichiometric matrix contains 509 rows, one obtains the calculated number of nonzero elements. It should be noted that also the adjacency matrix A (see below) of this metabolic network is sparse (not shown), with 1.9% of nonzero elements. This is similar to values reported in Becker et al. (2006) for whole organisms genome-scale adjacency matrices, but well below the calculated value for
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human mitochondrial network in Vo et al. (2004; see also Becker et al., 2006). This finding confirms that the high density of mitochondrial network adjacency matrix previously reported is simply linked to network dimension, as suggested in Becker et al. (2006). 2.2. Metabolite Connectivity Analysis The fundamental topological features of the metabolic network are determined by the nonzero elements of S (Palsson, 2006). A binary form B of the stoichiometric matrix was thus constructed, whose elements are defined as bij = 0 if sij = 0 and bij = 1 / 0, with obvious meaning of symbols. Post-multiplication of the binary matrix if sij = A, the compound adjacency B by its transpose A = BBT leads to a symmetric matrix 2 matrix. The diagonal elements of A, (ax )ii = k (bik ) , represent the number of reactions in which the compound xi participates. These numbers are a measure of how connected a compound is in the biochemical network. Considering the network as a graph, these numbers could be called the node connectivity. Off-diagonal elements of A are (ax )ij = k bik bkj , that is the number of reactions in which both compounds xi and xj take part. This number shows how widely the two compounds are topologically associated in the metabolic network. Pre-multiplication of the binary matrix B by its transpose C = BT B leads to a symmetric matrix whose elements are the inner products of its columns. The diagonal elements of C are the participation number for a reaction. Off-diagonal elements of C count how many compounds two reactions share. For metabolite connectivity analysis different types of distributions have been considered. The power-law probability distribution (Clauset et al., 2009), in the continuous approximation, was in the form p(x) = [(˛ − 1)/xmin ][(x/xmin )−␣ ]. The lognormal probability distribution function was in the form p(x) = {c/[(2)1/2 x]} exp{−(1/2)[(ln x − )/]2 } with dispersion parameter , location parameter ≥ 0 and normalization constant c. Power-law distribution with exponential cut-off in the general form p(x) = cx˛ e−x and simple exponential distribution p(x) = ce−x with ≥ 0 and c a proper normalization constant have been also considered. Moreover, Poisson distribution has been evaluated. Cumulative distribution functions C(x) = Pr(X ≤ x) or in the complementary form C(x) = Pr(X > x) have been used for the Kolmogorov–Smirnov goodness of fit estimation by analyzing the parameter Dm = max |Cemp (x) − Ctheor (x)| with Cemp (x) and Ctheor (x) the empirical and theoretical cumulative distribution functions. 2.3. Systemic Reactions Analysis The dynamic mass balance of a biochemical system can be described using the stoichiometric matrix which maps the flux rates vector of enzymatic reactions vn×1 to time derivatives of concentrations vector xm×1 : dx/dt = Sv. Singular value decomposition (SVD) states that for a given matrix Sm×n of rank r, there are orthogonal matrices Um×m and Vn×n and a diagonal matrix r×r = diag( 1 , 2 , . . ., r ) with 1 ≥ 2 ≥ · · · ≥ r > 0 such that S = Um×n VT with m×n the zero padded diagonal matrix. Columns of U and V are, respectively, the left and right singular vectors of S. Combining the two above equations leads to UT (dx/dt) = VT v. This completely defines the S-matrix modes, or systemic reactions, as described in Famili and Palsson (2003). Dominant modes can be evaluated by calculating the singular value spectra (Palsson, 2006). The orthonormal basis vectors obtained from SVD give useful information about the overall chemical transformations at the whole network level. Elements of ui (i.e. of left singular vector of S) are equivalent to systemic stoichiometric coefficients. Elements of vi (i.e. of a right singular vector of S) are equivalent to systemic participation numbers; these last elements define the reactions driving the mode. All numerical manipulations were done with the Scilab software (The Scilab Consortium – DIGITEO; http://www.scilab.org).
Fig. 2. Node connectivity distribution in the human mitochondrial metabolic network. All the metabolites present in the network have been rank-ordered accordingly to the participation number on a log–log scale. Solid circles: plot of the rank vs participation number of metabolites in the lipid-extended network; dashed line: best fitting power-law curve, with exponent −1.17 (r2 = 0.9511). Open squares: plot of the rank vs participation number of metabolites in the network without lipid expansion; solid line: best fitting power-law curve, with exponent −1.16 (r2 = 0.9433).
is usually difficult. Fig. 3 reports our best result in comparing different theoretical distributions, as detailed in Section 2.2, showing that the cumulative probability distribution is best fitted by a power-law function. The second function, ranked according to the goodness of fit, is the lognormal distribution, followed by all the others assayed functions with very poor fitting (not shown). Poisson distribution, suggested by Lima-Mendez and van Helden (2009) as more appropriate to describe node degree distribution in biological networks, has been also tested but poor results have been obtained (data not shown). Incomplete sampling of real cellular networks prevents to get a definitive answer about meaning of these deviation from perfect fit. However, more sophisticated generative models leading to, possibly modified, power-law distribution cannot be ruled out. It should be noted that both networks, the starting one and the lipid-extended, show a good fitting with a simple power-law equation. This persistence of power-law distribution in metabolite connectivity after a large rearrangement of the network reported in Vo et al. (2004) is an interesting finding. It should be recalled that a number of new metabolites have been introduced, and, more importantly, multipurpose enzymes using up to twenty different substrates have been put in this metabolic network. This
3. Results 3.1. Metabolite Connectivity Distribution Fig. 2 represents the node connectivity distribution in the mitochondrial metabolic networks analyzed in this work. Accordingly to Tanaka (2005), all metabolites present in the network have been rank-ordered respect to the participation number. A straight line on a log–log plot gives a good data fitting, which is usually considered a strong evidence of an underlying power-law distribution. Small deviation from linearity in the log–log plot, and the fact that recent works have challenged the finding of true power-law distributions in biological networks (see, for example, Lima-Mendez and van Helden, 2009), induce to carefully consider if alternative distributions could better fit the data. This has been done by performing Kolmogorov–Smirnov analysis of connectivity distribution data (Clauset et al., 2009). It should be recalled that discriminating between lognormal and power-law distributions in empirical data
Fig. 3. Cumulative probability distribution in the lipid-extended human mitochondrial metabolic network. The connection number is reported on the horizontal axes (x) and the cumulative probability distribution as P(X > x) is reported on vertical axes. The empirical cumulative probability distribution values are indicated by open squares. The solid line represents the best fitting curve obtained by Kolmogorov–Smirnov analysis. This is a power-law curve with parameters ˛ = 2.036 and xmin = 0.918.
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Table 1 Topmost ranked metabolites in the extended mitochondrial network. Metabolite
Attributed compartment
Participation number
Hydrogen ion Water CMP Hydrogen ion Coenzyme A Phosphate ion Glycerol 3-phosphate Pyrophosphate ion ATP CDP-ethanolamine CTP ADP CO2 ATP CMP
Mitochondrion Mitochondrion Mitochondrion Cytosol Mitochondrion Mitochondrion Mitochondrion Mitochondrion Mitochondrion Mitochondrion Mitochondrion Mitochondrion Mitochondrion Cytosol Cytosol
247 101 82 81 72 58 50 44 42 42 42 38 35 32 23
indicates that power-law metabolites connectivity distribution is robust respect to these large rearrangements.
3.2. Hubs and Coupled Metabolites In the lipid-extended network presented here, it should be noted that, even if the rank ordering of most coupled metabolites is changed respect to the previously reported mitochondrial network (Thiele et al., 2005; Vo et al., 2004), carriers still are exceedingly represented among metabolites with the highest participation numbers (Table 1). Moreover, previously unrecognized molecular hubs appear in the network. Several of these participate to membrane lipids metabolism (for example CMP, CDP-ethanolamine, CTP and glycerol 3-phosphate), showing the importance of explicitly considering the combinatorial capacities of multi-substrate enzymes. It should be remarked that also the huge number of different molecules considered here separately, but usually clustered in classes of metabolites, play a role in the appearance of new molecular hubs. Since it is generally considered that hubs are important respect to the evolutionary history of the networks (Barabási and Oltvai, 2004), and considering their importance, for example as possible pharmacological targets, this work clearly demonstrates that care should be used in defining combinatorial metabolites, even if chemically similar, as single ones. The symmetric coupling matrix has been computed by multiplying the binary form of the S-matrix by its transpose, as detailed in the Methods section. Off-diagonal elements of this symmetric matrix represent the number of reactions in which two particular metabolites appear together in a stoichiometric equation. Fig. 4 reports the distribution of metabolite coupling in a log–log plot. Most pairs of metabolites never occur and they are obviously not reported in the figure. Most pairs of metabolites occur together only in one or few reactions and appear in the leftmost part of the data points. Pairs of metabolites occurring together in many reactions are illustrated by the rightmost data points in the figure. Again, significant differences respect to previously reported most coupled pairs are observed (Becker et al., 2006) (see Table 2), but the general appearance of data points shows that the overall topological features of the network are unchanged. In fact, the leftmost data points have been fitted by a power-law curve whose slope is close to the reported ones for genome-scale metabolic networks (Becker et al., 2006). Moreover, the most connected metabolites are also present in the highly coupled pairs (see Tables 1 and 2), as observed in previously reported genome-scale metabolic networks.
Fig. 4. Metabolite coupling in the lipid-extended human mitochondrial metabolic network. The number of metabolite pairs sharing a given number of reactions are log–log plotted. Solid line corresponds to the best fitting power-law curve of the leftmost data-points, corresponding to metabolites couples sharing 12 or less reactions. This power-law curve has a slope, in log–log plot, of −2.93 (r2 = 0.907).
3.3. Systemic Reactions Stoichiometric matrices of metabolic networks can be analyzed by SVD. SVD is usually used in data analysis to obtain dimensionality reduction or noise removal, but stoichiometric matrices are perfect matrices so SVD cannot be used for such purposes in this case. However, SVD of stoichiometric matrices can be employed to obtain a global description of systemic reactions (or modes) of the metabolic network under analysis. The singular value spectrum of genome-scale stoichiometric matrices is triphasic (Famili and Palsson, 2003). The first phase corresponds to the dominant modes, followed by a gradual steady decline in a large number of singular values. The third phase of the singular value spectra is composed of a small set of rapidly declining singular values. The mitochondrial network here analyzed shows such triphasic shape, as reported in Fig. 5. This shape is observed for the lipid expanded metabolic network, as well as for the network obtained without considering the combinatorial expansion of lipids. Randomly generated networks, in general, do not show such triphasic shape, usually lacking of clear and extended first and third phases (Famili and Palsson, 2003). This strongly indicates that metabolic networks are represented by rather peculiar sparse matrices, exhibiting dominant characteristics as well as distinct properties at the higher modes. These peculiarities of metabolic networks are not affected by the presence of combinatorial metabolites, or by explicitly considering them.
Table 2 Most coupled metabolites pairs.a Metabolite #1
Metabolite #2
Observed couples number
Hydrogen ion Phosphate ion Pyrophosphate ion Hydrogen ion Pyrophosphate ion Hydrogen ion Hydrogen ion CMP Glycerol 3-phosphate Water ATP Hydrogen ion Hydrogen ion Hydrogen ion (mitochondrion) Hydrogen ion
CMP Water Hydrogen ion Glycerol 3-phosphate CTP CDP-ethanolamine CTP CDP-ethanolamine CMP Hydrogen ion ADP ADP ATP Hydrogen ion (cytosol) CO2
82 45 44 43 42 42 42 42 40 39 36 28 28 24 24
a All the most coupled metabolites but one belong to the mitochondrial compartment.
Table 3 Topmost ranked metabolites respect to the systemic stoichiometric coefficients.a Lipid complexity not considered
Lipid complexity considered
First eigenreaction
Second eigenreaction
Third eigenreaction
First eigenreaction
Second eigenreaction
Third eigenreaction
Acetyl-CoA (m)
Hydrogen ion (c)
Hydrogen ion (c)
Hydrogen ion (m)
Hydrogen ion (m)
Hydrogen ion (m)
Arachidonyl-carnitine (c) 1,2-Diacylglycerol (C20:4–C20:4) (c)
Arachidonyl-carnitine (c) Phosphatidilcholine (C16:0–C20:4) (m)
Water (m)
Acetyl-CoA (m)
Water (m)
Docosahexaenoic acid (c)
NAD (m)
Water (m)
Cytochrome c ferric (m)
NADH (m)
Coenzyme A (m)
Cytochrome c ferrous (m)
Coenzyme A (m)
Cytochrome c ferric (m)
Coenzyme A (m)
FAD (m)
Cytochrome c ferrous (m)
Carbon dioxide (c)
3-(4Hydroxyphenyl)pyruvate (m) Docosahexaenoylcarnitine (c) Docosahexaenoylcarnitine (m) l-Aspartate (m)
2-Methyl-3oxopropanoate (m) 3-(4Hydroxyphenyl)pyruvate (m) 1,2-Diacylglycerol (C20:4–C20:4) (c)
Phosphatidilcholine (C16:0–C20:4) (m) 2-Methyl-3oxopropanoate (m) Docosahexaenoic acid (c)
FADH2 (m)
NAD (m)
Acetyl-CoA (m)
ATP (c)
Hydrogen ion (c)
NADH (m)
Water (c)
Docosahexaenoyl-CoA (m)
FAD (m)
Oxygen (m)
Arachidonyl-CoA (m)
FADH2 (m)
FAD (m)
Phosphatidilcholine (C16:0–C20:4) (m) 2-Methyl-3oxopropanoate (m) Fumarate (c)
Octadecynoyl-CoA (m)
Carbon dioxide (c)
FADH2 (m)
Palmitoyl-CoA (m)
Water (c)
ADP (m)
Cytochrome c ferric (m)
Hydrogen ion (e)
NAD (m)
Cytochrome c ferrous (m)
Phosphate ion (c)
NADH (m)
Oxygen (m)
ATP (c)
ATP (c)
Protoporphyrin (m)
l-Ornithine (m)
ATP (m)
Protoporphyrinogen IX (m)
ADP (c)
ADP (c)
Phosphate ion (m)
NAD (c)
Hydrogen ion (e)
Ubiquinone-10 (m)
NADH (c)
Carbon dioxide (m)
1,2-Diacylglycerol (C18:0–C18:0) (c) Phosphatidylserine (C20:4–C20:4) (m) Butanoyl-CoA (m)
ATP (c) Docosahexaenoic acid (c) 1,2-Diacylglycerol (C20:4–C20:4) (e) 1,2-Diacylglycerol (C18:2–C20:4) (e) Butanoyl-CoA (m)
Arachidonic acid (C20:4) (c) d-Glycerate-2phosphate (c) 1,2-Diacylglycerol (C18:0–C18:0) (c)
Phosphatidylserine (C18:1–C20:4) (c) 1,2-Diacylglycerol (C18:0–C18:0) (m) Fumarate (c) Phosphatidylserine (C18:1–C20:4) (e) 3-(4Hydroxyphenyl)pyruvate (m) Arachidonyl-carnitine (c) 1,2-Diacylglycerol (C20:4–C20:4) (e) 1,2-Diacylglycerol (C18:2–C20:4) (e) 1,2-Diacylglycerol (C22:6–C20:4) (c) Hydrogen peroxide (m) Phosphatidilcholine (C16:0–C20:4) (c) (S)-3-Hydroxydodecanoyl-CoA (m) Phosphatidic acid (C18:0–C18:0) (m) Docosahexaenoylcarnitine (c) Docosahexaenoylcarnitine (m)
155
Attributed compartments: m mitochondrial; c cytosolic; e external.
(S)-3-Hydroxydodecanoyl-CoA (m) CDP-diacylglycerol (C18:0–C20:4) (m)
(S)-3-Hydroxydodecanoyl-CoA (m) l-Aspartate (m)
Phosphatidylethanolamine (C18:1–C20:4) (m) L.L. Palese, F. Bossis / BioSystems 109 (2012) 151–158
a
1,2-Diacylglycerol (C18:1–C22:6) (c) 1,2-Diacylglycerol (C18:0–C18:0) (m) 1,2-Diacylglycerol (C18:2–C22:6) (c) Hydrogen peroxide (m)
Docosahexaenoylcarnitine (c) Docosahexaenoylcarnitine (m) Phosphatidylserine (C20:4–C20:4) (m) 1,2-Diacylglycerol (C18:0–C18:0) (c) Hydrogen peroxide (m)
Phosphatidylserine (C20:4–C20:4) (m)
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enzymes simply based on the systemic stoichiometric relations in the metabolic network. 4. Discussion
Fig. 5. Singular values spectra of the metabolic networks stoichiometric matrices. The singular values of the metabolic network with (black line) or without (gray line) considering the combinatorial diversity of lipids and enzymes acting on are reported. Both spectra show the triphasic shape observed in the genome-scale stoichiometric matrices.
The analysis of dominant modes in the mitochondrial stoichiometric matrix reveals interesting differences between the matrices with or without explicit expansion of lipids metabolic network. Table 3 reports the compound composition of the first three modes. For each mode, reported compounds are rank ordered respect to squared coefficients of the U matrix u2ij (i = 1, 2, 3), in order to make them all positive. Only the first twenty compounds are reported, i.e. those with the highest systemic stoichiometric coefficients in the particular eigen-reaction (or mode) under consideration. It should be noted that cofactors participating in energy, redox and phosphate metabolism emerge with the most significant values in the first eigen-reaction of all genome-scale networks analyzed by SVD so far. This is also true for the mitochondrial metabolic network without explicit consideration of combinatorial metabolites. Redox cofactors, phosphate carriers and well known hubs of energy metabolism are prevailing in the first three dominant modes of this network. But if combinatorial capacity of lipids is explicitly taken into account, systemic stoichiometric coefficients change dramatically. Beside ATP, the most significant values in the dominant eigen-reactions are observed for lipid metabolism intermediates, including species directly involved in the membrane lipid metabolism. Fumarate, aspartate and hydrogen peroxide also appear with high systemic stoichiometric coefficients in the dominant eigen-reactions of the lipid-extended metabolic network. Fig. 6 reports the reactions driving the conversion described by the first three dominant modes in the lipid-extended metabolic network. It comes out that the highest coefficients belong to the oxidative phosphorilation system. This finding shows a strong correlation relating lipids (including membrane components) as well as reactive oxygen species, and the oxidative phosphorilation
Lipids, and particularly membrane lipids, are extremely different and crucial molecules. The chemical composition of membrane lipids dictates physical and chemical properties of membranes and the recent blossoming interest for lipidomics witnesses the importance and the attention for this class of molecules (van Meer et al., 2008; Wenk, 2005). Moreover, to adequately describe the biochemical network avoiding biasing tailored assumptions, all the chemical components of it must be taken into account. This leads us to consider the combinatorial capacity of the enzymes involved in lipid metabolism. Here we show, using Kolmogorov–Smirnov statistical analysis, that the best mathematical model to describe the cumulative probability distribution function of metabolite connectivity is the power-law model. Other tested heavy-tail distributions, as well as the Poisson distribution (Lima-Mendez and van Helden, 2009), cannot be considered with our empirical data. This finding is important because, for example, lognormal and power-law distributions, although similar in shape, have distinct theoretical generative models (Mitzenmacher, 2004). The fact that the overall topological features of a complex biochemical network still obey to powerlaw distribution even in presence of combinatorial substrates and enzymes forces us to consider that no special mechanisms are required for their appearance, at least in biochemical networks. Such distribution (or, better, the long-tail distributions) must be considered “more normal than normal” from a statistical point of view (Keller, 2005; Li et al., 2005; Tanaka, 2005; Tanaka et al., 2005). Moreover, it has been shown that some random networks exhibit features usually considered peculiar to evolutionary shaped or functional adapted networks, such as small or ultra-small world appearance (Chung and Lu, 2004). Nevertheless, the fact that lognormal distribution and alternative ones (including the truncated power-law) have been ruled out leads to consider the theoretical generative model underlying such (pervasive) power-law distribution in metabolic networks. It should be noted that, in this work, some highly connected carrier molecules have been introduced, so preserving the overall statistical features of the metabolic network (see Figs. 2–5). It is conceivable that the presence of carrier metabolites is just the only responsible for the overall topological characteristics of complex metabolic networks. Considering the presence of highly connected carriers (as expected in real metabolic networks) beside low or poorly connected (at the whole network level) metabolites, power-law distributions emerge unavoidably in complex biochemical reactions networks. Spectral analysis shows that considering combinatorial metabolites explicitly does not affect the (peculiar) large-scale
Fig. 6. Dominant modes in lipid-extended metabolic matrix. Reactions driving the conversion in the first three dominant modes are reported. The ten enzymes with highest in mode vij 2 value are indicated by their E.C. number; vij 2 values are from the V matrix obtained by SVD. E.C. numbers – enzymes correspondence: 1.2.4.1 – pyruvate dehydrogenase; 1.3.3.3 – coproporphyrinogen oxidase; 1.3.3.4 – protoporphyrinogen oxidase; 1.3.99.3 – acyl-CoA dehydrogenase; 1.6.99.3 – NADH dehydrogenase (Complex I); 1.9.3.1 – cytochrome c oxidase (Complex IV); 1.10.2.2 – ubiquinone-cytochrome c reductase (Complex III); 1.15.1.1 – superoxide dismutase; 2.7.8.2 – CDP choline:1,2-diacylglycerol cholinephosphotransferase; 3.6.3.14 – ATP synthase (Complex V); 4.1.1.37 – uroporphyrinogen decarboxylase; 4.99.1.1 – ferrochelatase; 6.3.4.16 – carbamoyl-phosphate synthase.
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organization of the metabolic network (see Fig. 5). Remarkably, systemic reaction analysis in the lipid-extended network shows that an intimate relation exists connecting lipid metabolism intermediates and oxidative phosphorilation enzymes. In the first three modes, also an enzyme of the urea cycle, metabolically important dehydrogenases (pyruvate dehydrogenase and enzymes of fatty acids -oxidation pathway), the superoxide dismutase and numerous heme biosynthetic enzymes (see Fig. 6 and Table 3) appear involved at high extent. This finding could help to rationalize the relation existing between some pathological conditions involving alterations of membrane lipids and oxidative phosphorilation system failures. In some important diseases, lipids, including membrane ones, are directly involved (Abibhatla and Hatcher, 2008), and frequently mitochondria are involved also (Swerdlow, 2009). For example, in Parkinson’s disease, deficit of respiratory chain enzymes (particularly the Complex I) and membrane lipids abnormality have been shown (Winklhofer and Haass, 2010; Ellis et al., 2005; Pacelli et al., 2011). Abnormal mitochondrial dynamics, including membrane fusion and fission, have been suggested to mediate or amplify mitochondrial dysfunction and neural dysfunction during the course of neurodegenerative diseases (Su et al., 2010). Our results show that a direct link exists relating membranes, lipids in general, and respiratory chain enzymes. This link derives directly from stoichiometric organization of the whole metabolic network when the combinatorial diversity of lipids is explicitly considered. Systemic reactions suggest that changes, or failures, in mitochondrial respiratory enzymes could immediately affect intermediates of lipid, including membranes, metabolism. On the other hand, interactions among apparently nonrelated metabolites become evident, as for example the presence of hydrogen peroxide together with a number of lipid metabolism intermediates in the topmost ranked metabolites of first three eigenreactions. Closer examination of metabolic hubs obtained from the lipid extended mitochondrial network leads also to some evolutionary considerations. Scale-free model predicts that nodes appearing early in the history of the network are the most connected ones (Barabási and Albert, 1999). Inspection of metabolic hubs usually suggests that they are remnants of the RNA world (such as coenzyme A, NAD+ , ATP) or they are elements of the most ancient metabolic pathways (glycolysis and the tricarboxylic acid cycle) as reported in (Wagner and Fell, 2001; Jeong et al., 2000). Looking at metabolic hubs in the extended mitochondrial network here reported (see Tables 1 and 2) suggests that they are not only remnants of the ancient RNA world (Gilbert, 1986), but also molecules coming from an equally ancient “lipid world” (Segré et al., 2001). Beside water and hydrogen ion, our results show that no other metabolites out of RNA world, lipid world and the phosphate/pyrophosphate couple (Kornberg et al., 1999) could be considered hubs. At the best of our knowledge, this is the first time that such close correlation (of evolutionary origin, assuming scale free model) connecting these ancient pre-biotic world, can be observed. Finally, it should be recalled that theoretical studies aiming to exactly and formally defining what life is have shown that a crucial requirement for living systems is the metabolic circularity or, more formally, the closure to efficient causation in (M, R) systems (Cornish-Bowden and Cárdenas, 2007, 2008; Rosen, 1991). In these studies it has been shown that the circle of efficient causation can only be closed if some (or, better, many) of the catalysts used by organisms fulfill multiple functions. A suggested solution for the efficient causation closure is multi-functionality, such as the presence of “moonlighting” proteins, or the fact that a small number of nucleic acid molecules encode an enormous number of proteins (Cornish-Bowden and Cárdenas, 2008). Here we suggest that lipid metabolism offers another possible solution to the closure to
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efficient causation, and it is particularly suggestive here also to recall that lipids are important to the spatial closure if we consider a cell an autopoietic system (Maturana and Varela, 1980). The lipid-extended metabolic network shows that multi-functionality is deeply embedded in the metabolism of lipids, suggesting a more profound role for such class of molecules in defining what life is. Acknowledgements The authors thank Prof. Sergio Papa for his continuous encouragement and for his example of a life dedicated to science. The authors would also thank the three anonymous reviewers for insightful and helpful comments. This work is part of PRIN “Mitochondrial Bioenergetics: Redox Mechanisms, ROS Production, Redox Control of Cell Differentiation”. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.biosystems.2012. 04.001. References Abibhatla, R.M., Hatcher, J.F., 2008. Altered lipid metabolism in brain injury and disorders. Subcell Biochem. 49, 241–268. Adam-Vizi, V., Chinopoulos, C., 2006. Bioenergetics and the formation of mitochondrial reactive oxygen species. Trends Pharmacol. 27, 639–645. Albert, R., 2005. Scale-free networks in cell biology. J. Cell Sci. 118, 4947–4957. Alonso, J., Rodriguez, J.M., Baena-Lopez, L.A., Santaren, J.F., 2005. Characterization of the Drosophila melanogaster mitochondrial proteome. J. Proteome Res. 4, 1636–1645. Anderson, P.W., 1972. More is different. Science 177, 393–396. Barabási, A.L., Albert, R., 1999. Emergence of scaling in random networks. Science 286, 509–512. Barabási, A.L., Oltvai, Z.N., 2004. Network biology: understanding the cell’s functional organization. Nat. Rev. Genet. 5, 101–113. Becker, S.A., Price, N.D., Palsson, B.O., 2006. Metabolite coupling in genome-scale metabolic networks. BMC Bioinform. 7, 111, http://dx.doi.org/10.1186/14712105-7-111. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U., 2006. Complex networks: structure and dynamics. Phys. Rep. 424, 175–308. Borodina, I., Krabben, P., Nielsen, J., 2005. Genome-scale analysis of Streptomyces coelicolor A3(2) metabolism. Genome Res. 15, 820–829. Carlson, J.M., Doyle, J., 2002. Complexity and robustness. Proc. Natl. Acad. Sci. U. S. A. 99 (Suppl. 1), 2538–2545. Chung, F., Lu, L., 2004. The average distance in a random graph with given expected degree. Internet Math. 1, 91–114. Clauset, A., Shalizi, C.R., Newman, M.E.J., 2009. Power-law distributions in empirical data. SIAM Rev. 51, 661–703. Cornish-Bowden, A., Cárdenas, M.L., 2008. Self-organization at the origin of life. J. Theor. Biol. 252, 411–418. Cornish-Bowden, A., Cárdenas, M.L., 2007. Organizational invariance in (M, R) systems. Chem. Biodivers. 4, 2396–2406. Csete, M., Doyle, J., 2004. Bow ties, metabolism and disease. Trends Biotechnol. 22, 446–450. Da Cruz, S., Parone, P.A., Martinou, J.C., 2005. Building the mitochondrial proteome. Expert Rev. Proteomics 2, 541–551. Devlin, T.M. (Ed.), 2002. Textbook of Biochemistry with Clinical Correlations. , fifth ed. Wiley-Liss, New York. Duarte, N.C., Becker, S.A., Jamshidi, N., Thiele, I., Mo, M.L., Vo, T.D., Srivas, R., Palsson, B.O., 2007. Global reconstruction of the human metabolic network based on genomic and bibliomic data. Proc. Natl. Acad. Sci. U. S. A. 104, 1777–1782. Duarte, N.C., Herrgard, M.J., Palsson, B.O., 2004. Reconstruction and validation of Saccharomyces cerevisiae iND750, a fully compartmentalized genome-scale metabolic model. Genome Res. 14, 1289–1309. Edwards, J.S., Palsson, B.O., 1999. Systems properties of the Haemophilus influenzae Rd metabolic genotype. J. Biol. Chem. 274, 17410–17416. Edwards, J.S., Palsson, B.O., 2000. The Escherichia coli MG1655 in silico metabolic genotype; its definition, characteristics, and capabilities. Proc. Natl. Acad. Sci. U. S. A. 97, 5528–5533. Ellis, C.E., Murphy, E.J., Mitchell, D.C., Golovko, M.Y., Scaglia, F., Barcelo-Coblijn, G.C., Nussbaum, R.L., 2005. Mitochondrial lipid abnormality and electron chain impairment in mice lacking alpha-synuclein. Mol. Cell Biol. 25, 10190–10201. Famili, I., Palsson, B.O., 2003. Systemic metabolic reactions are obtained by singular value decomposition of genome-scale stoichiometric matrices. J. Theor. Biol. 224, 87–96. Gilbert, W., 1986. The RNA world. Nature 319, 618.
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The human extended mitochondrial metabolic network: New hubs from lipids Luigi Leonardo Palese ∗ , Fabrizio Bossis Department of Basic Medical Sciences (SMB), University of Bari “Aldo Moro”, Piazza G. Cesare-Policlinico, 70124 Bari, Italy
a r t i c l e
i n f o
Article history: Received 13 December 2011 Received in revised form 21 February 2012 Accepted 2 April 2012 Keywords: Systems biology Power-law distribution Neurodegenerative diseases Mitochondria Lipid metabolism Evolution
a b s t r a c t Even if systems thinking is not new in biology, rationalizing the explosively growing amount of knowledge has been the compelling reason for the sudden rise and spreading of systems biology. Based on ‘omics’ data, several genome-scale metabolic networks have been reconstructed and validated. One of the most striking aspects of complex metabolic networks is the pervasive power-law appearance of metabolite connectivity. However, the combinatorial diversity of some classes of compounds, such as lipids, has been scarcely considered so far. In this work, a lipid-extended human mitochondrial metabolic network has been built and analyzed. It is shown that, considering combinatorial diversity of lipids and multipurpose enzymes, an intimate connection between membrane lipids and oxidative phosphorilation appears. This finding leads to some biomedical considerations on diseases involving mitochondrial enzymes. Moreover, the lipid-extended network still shows power-law features. Power-law distributions are intrinsic to metabolic network organization and evolution. Hubs in the lipid-extended mitochondrial network strongly suggest that the “RNA world” and the “lipid world” hypothesis are both correct. © 2012 Elsevier Ireland Ltd. All rights reserved.
1. Introduction Advances in high-throughput technologies and in bioinformatics have rapidly expanded the information availability in biological sciences. This huge amount of information has raised the need for organizing and understanding the part catalogs present in biological databases, giving birth to systems biology as a new discipline (Ideker et al., 2001; Kitano, 2002; Westerhoff and Palsson, 2004). Systems understanding requires a substantial shift in our approach to biological sciences (von Bertalanffy, 1967). While knowledge of proteins and genes as isolated entities continues to be crucial, the focus is now on systems as a whole. Because “more is different” (Anderson, 1972), a system cannot be fully understood by simply knowing the list of all components. System-level understanding requires insight into system structure, dynamics and control (Ruppin et al., 2010). The behavior of complex systems emerges from the orchestrated activity of many components mutually interacting. At a high abstract level, the components can be reduced to a set of nodes, and the interactions among components to links. Nodes and links together form a network, or, more formally, a graph. Introduction of network theory tools into the systems biology field has been a major advance in our system-level understanding of biology. Various types of cellular networks can be visualized. Smallmolecule substrates can be pictured as nodes in a metabolic
∗ Corresponding author. Tel.: +39 0805448524; fax: +39 0805448538. E-mail addresses: [email protected], [email protected] (L.L. Palese). 0303-2647/$ – see front matter © 2012 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.biosystems.2012.04.001
network and enzyme-catalyzed reactions, transforming one metabolite into another, as links. Various metabolic network reconstructions have been carried out for microorganisms, such as, for example, Haemophilus influenzae (Edwards and Palsson, 1999), Escherichia coli (Edwards and Palsson, 2000), Helicobacter pylori (Paley and Karp, 2002; Price et al., 2002), Streptomyces coelicolor A3(2) (Borodina et al., 2005). The metabolic network of Saccharomyces cerevisiae has been the first reconstructed eukaryotic metabolic network (Duarte et al., 2004), and significant advances through the human metabolic network reconstruction have been done (Duarte et al., 2007; Ma et al., 2007). Mitochondrial metabolic network has been also studied (Thiele et al., 2005; Vo et al., 2004). Mitochondria are semi-autonomous organelles. Due to their endosymbiotic origin, mitochondria maintain their genome, membranes, transcriptional and translational machineries, signaling activities and division ability. For these reasons, mitochondria are excellent subjects for systems biology studies (Vo and Palsson, 2007), particularly based on proteomic analysis (Alonso et al., 2005; Da Cruz et al., 2005; Liu et al., 2004; Taylor et al., 2003). Doubtless an important breakthrough in the field of biological networks was the finding that numerous cellular networks exhibit a long-tail (power-law) distribution in node connectivity. In all networks, each node is characterized by the node degree (or connectivity). This is a number telling us how many links the node has to other nodes. A popular model aiming to describe such node connectivity distribution, in biological networks, is the scale-free model (Albert, 2005; Barabási and Oltvai, 2004; Boccaletti et al., 2006), in which the probability that a node is highly connected is statistically more significant than in random graphs, and network
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uniqueness are determined by a small number of highly connected nodes, known as hubs. Such networks have been named scale-free because power-laws have the property of having the same functional form at all scales and remain unchanged, under rescaling the independent variable. On the other hand, it has been shown that the metabolites in a metabolic network are far from being fully connected (Boccaletti et al., 2006; Ma and Zeng, 2003). The largest fully connected part of metabolic networks represents the core of the network and has the features of scale-free networks. An intriguing result is that observed distributions in metabolic networks derive from the carrier metabolites (Tanaka, 2005). Carrier metabolites are densely connected to various functional modules, whereas other metabolites are densely connected inside the modules. In such a view, power-law distribution comes from high variability of nodes connectivity and metabolic networks appear to be scalerich instead of scale-free (Csete and Doyle, 2004; Li et al., 2005; Tanaka, 2005; Tanaka et al., 2005). These self-dissimilar and scalerich models can also be obtained from High Optimized Tolerances (HOT) models (Carlson and Doyle, 2002). Both the above reported models lead to power-law distribution, one because of, essentially, evolutionary motif (the scale-free model), one of functional optimization motif (scale rich and HOT models). Beside this intense work about power-law topology of metabolic network, it should be noted that considerable criticisms on the real significance and novelty of these findings have been raised (Keller, 2005), and various works raise doubts about the exact statistical distribution of node connectivity in the biological networks (Lima-Mendez and van Helden, 2009). Beside the intellectual challenges, an in depth insight of metabolic networks promises numerous applications, for example network-based drug design (Hornberg et al., 2006; Murabito et al., 2011). A key step towards this goal is the extensive and detailed description of the whole network. An enormous number of chemically distinct molecular species arise from the various combinations of different fatty acids with backbone structures, such as glycerol or sphingoid bases. Lipidomics is the systems-level analysis and characterization of lipids and their interacting moieties. Technical difficulties, also related to the extreme complexity of lipid molecules, still keep this field of systems biology in his infancy (Wenk, 2005). But the crucial role of lipids in cell and the involvement of lipid metabolic enzymes and pathways in many human diseases are the compelling reasons for an increasing interest in this promising area of research. Rather surprisingly, in metabolic network reconstruction, lipid molecules are often considered only from a ‘cumulative’ point of view. The combinatorial diversity of lipids is not explicitly considered, but entire classes of molecules are treated as a single chemical species. This approach leads to consider in the reconstructed metabolic network few species of lipids, whereas the real cellular networks contain thousands of chemically different lipids. In this work a topological analysis of human mitochondrial metabolic network is presented. A hand-validated reaction set has been used to reconstruct the mitochondrial stoichiometric matrix. In this network, lipid diversity and enzymes able to work on different substrates have been explicitly taken into account. 2. Methods 2.1. The Stoichiometric Matrix A set of biochemical reactions involving human mitochondria has been manually constructed using the online databases KEGG (Kanehisha and Goto, 2000), MitoDB (available at http://bioinfo.nist.gov/hmpd/index.html) and Brenda (Schomburg et al., 2002) as well as biochemistry textbooks (Devlin, 2002; Nelson and Cox, 2008). This biochemical reaction set is based on the metabolic network of the human cardiac mitochondrion reported in Vo et al. (2004) with expansions and modifications. Few reactions in Vo et al. (2004) have been changed in our network; for example, the enzyme synthesizing carbamoyl phosphate, which was carbamoyl phosphate
Fig. 1. The stoichiometric matrix of lipid-extended human mitochondrial metabolic network. The dimensions of this stoichiometric matrix are 509 rows and 675 columns. Rows correspond to metabolites, considering the presence in different compartments of transported ones; columns correspond to reactions, some of which are thermodynamically reversible in the cellular environment and are considered in both directions. This matrix contains 343,575 elements; of these 2695 (0.78%) are nonzero. Long dot lines represent the highly connected metabolites. The ordered list of metabolites and reactions are reported in Supplementary data 1.
synthase E.C. 2.7.2.2 in (Vo et al., 2004) here has been changed to carbamoyl phosphate synthase E.C. 6.3.4.16, because the latter enzyme is more appropriate in the human metabolic network. The reaction of cytochrome c oxidase, considered in Vo et al. (2004) as the reaction responsible for reactive oxygen species (ROS) production, has been revised. It should be noted that cytochrome c oxidase is a respiratory complex considered not involved in ROS production (Adam-Vizi and Chinopoulos, 2006). In this network, ROS production has been modeled as superoxide anion production by reduced coenzyme Q, and starting from this ROS molecule all different ROS have been obtained. The combinatorial features of lipids and enzymes involved in their metabolism have been considered in this work. Fatty acids oxidation reactions have been explicitly introduced in the metabolic network, instead of a cumulative global equation for -oxidation. Moreover, the combinatorial diversity of membrane lipids, has been (partially) taken into account, giving to an explosion in the number of reactions involving this class of molecules. Here, compounds such as, for example, phosphatidic acid have been considered not actually as ‘compounds’ but as ‘class of compounds’ and consequently expanded. Finally, the effect of including enzymes able to work on many different substrates has been evaluated. In the metabolic networks reported to date, an enzyme catalyzes usually no more than a single reaction. In the network used in this work, up to twenty different reactions could be catalyzed by the same low specificity enzyme. These are enzymes working on similar, but different, membrane lipids. The biochemical reaction set used in this work contains 331 metabolites, which grow to 509 if the same metabolite is counted as distinct when represented in different cellular compartments. The network contains 510 reactions, some of which must be considered reversible in the cell. Reactions are considered reversible only if this is stated in the sources used for the manual reconstruction of the network. The complete reaction set is reported as Supplementary data 1; the model is also provided in SBML format as Supplementary data 2. A metabolic reaction network without expansion of combinatorial metabolites, similar to what reported in (Vo et al., 2004), has been also reconstructed and analyzed. Biochemical reactions comprising the reconstructed metabolic network were represented by a stoichiometric matrix S (Palsson, 2006). The stoichiometric matrix was m × n where m is the number of metabolites and n is the number of reactions in the reconstructed network. Stoichiometric matrices are sparse (Palsson, 2006). A sparse matrix mainly contains zero elements. The stoichiometric matrix here obtained, after lipid expansion and considering forward and reverse reactions where appropriate, is also sparse (see Fig. 1): only 0.78% elements are nonzero. Considering as reaction participants both reactants and products, there are 219 reactions in which four compounds participate, the same number of reactions with five participating compounds, and much less reactions in which a larger number of reactants/products are observed (not shown). On average four compounds participate in a reaction in this network, and considering that this stoichiometric matrix contains 509 rows, one obtains the calculated number of nonzero elements. It should be noted that also the adjacency matrix A (see below) of this metabolic network is sparse (not shown), with 1.9% of nonzero elements. This is similar to values reported in Becker et al. (2006) for whole organisms genome-scale adjacency matrices, but well below the calculated value for
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human mitochondrial network in Vo et al. (2004; see also Becker et al., 2006). This finding confirms that the high density of mitochondrial network adjacency matrix previously reported is simply linked to network dimension, as suggested in Becker et al. (2006). 2.2. Metabolite Connectivity Analysis The fundamental topological features of the metabolic network are determined by the nonzero elements of S (Palsson, 2006). A binary form B of the stoichiometric matrix was thus constructed, whose elements are defined as bij = 0 if sij = 0 and bij = 1 / 0, with obvious meaning of symbols. Post-multiplication of the binary matrix if sij = A, the compound adjacency B by its transpose A = BBT leads to a symmetric matrix 2 matrix. The diagonal elements of A, (ax )ii = k (bik ) , represent the number of reactions in which the compound xi participates. These numbers are a measure of how connected a compound is in the biochemical network. Considering the network as a graph, these numbers could be called the node connectivity. Off-diagonal elements of A are (ax )ij = k bik bkj , that is the number of reactions in which both compounds xi and xj take part. This number shows how widely the two compounds are topologically associated in the metabolic network. Pre-multiplication of the binary matrix B by its transpose C = BT B leads to a symmetric matrix whose elements are the inner products of its columns. The diagonal elements of C are the participation number for a reaction. Off-diagonal elements of C count how many compounds two reactions share. For metabolite connectivity analysis different types of distributions have been considered. The power-law probability distribution (Clauset et al., 2009), in the continuous approximation, was in the form p(x) = [(˛ − 1)/xmin ][(x/xmin )−␣ ]. The lognormal probability distribution function was in the form p(x) = {c/[(2)1/2 x]} exp{−(1/2)[(ln x − )/]2 } with dispersion parameter , location parameter ≥ 0 and normalization constant c. Power-law distribution with exponential cut-off in the general form p(x) = cx˛ e−x and simple exponential distribution p(x) = ce−x with ≥ 0 and c a proper normalization constant have been also considered. Moreover, Poisson distribution has been evaluated. Cumulative distribution functions C(x) = Pr(X ≤ x) or in the complementary form C(x) = Pr(X > x) have been used for the Kolmogorov–Smirnov goodness of fit estimation by analyzing the parameter Dm = max |Cemp (x) − Ctheor (x)| with Cemp (x) and Ctheor (x) the empirical and theoretical cumulative distribution functions. 2.3. Systemic Reactions Analysis The dynamic mass balance of a biochemical system can be described using the stoichiometric matrix which maps the flux rates vector of enzymatic reactions vn×1 to time derivatives of concentrations vector xm×1 : dx/dt = Sv. Singular value decomposition (SVD) states that for a given matrix Sm×n of rank r, there are orthogonal matrices Um×m and Vn×n and a diagonal matrix r×r = diag( 1 , 2 , . . ., r ) with 1 ≥ 2 ≥ · · · ≥ r > 0 such that S = Um×n VT with m×n the zero padded diagonal matrix. Columns of U and V are, respectively, the left and right singular vectors of S. Combining the two above equations leads to UT (dx/dt) = VT v. This completely defines the S-matrix modes, or systemic reactions, as described in Famili and Palsson (2003). Dominant modes can be evaluated by calculating the singular value spectra (Palsson, 2006). The orthonormal basis vectors obtained from SVD give useful information about the overall chemical transformations at the whole network level. Elements of ui (i.e. of left singular vector of S) are equivalent to systemic stoichiometric coefficients. Elements of vi (i.e. of a right singular vector of S) are equivalent to systemic participation numbers; these last elements define the reactions driving the mode. All numerical manipulations were done with the Scilab software (The Scilab Consortium – DIGITEO; http://www.scilab.org).
Fig. 2. Node connectivity distribution in the human mitochondrial metabolic network. All the metabolites present in the network have been rank-ordered accordingly to the participation number on a log–log scale. Solid circles: plot of the rank vs participation number of metabolites in the lipid-extended network; dashed line: best fitting power-law curve, with exponent −1.17 (r2 = 0.9511). Open squares: plot of the rank vs participation number of metabolites in the network without lipid expansion; solid line: best fitting power-law curve, with exponent −1.16 (r2 = 0.9433).
is usually difficult. Fig. 3 reports our best result in comparing different theoretical distributions, as detailed in Section 2.2, showing that the cumulative probability distribution is best fitted by a power-law function. The second function, ranked according to the goodness of fit, is the lognormal distribution, followed by all the others assayed functions with very poor fitting (not shown). Poisson distribution, suggested by Lima-Mendez and van Helden (2009) as more appropriate to describe node degree distribution in biological networks, has been also tested but poor results have been obtained (data not shown). Incomplete sampling of real cellular networks prevents to get a definitive answer about meaning of these deviation from perfect fit. However, more sophisticated generative models leading to, possibly modified, power-law distribution cannot be ruled out. It should be noted that both networks, the starting one and the lipid-extended, show a good fitting with a simple power-law equation. This persistence of power-law distribution in metabolite connectivity after a large rearrangement of the network reported in Vo et al. (2004) is an interesting finding. It should be recalled that a number of new metabolites have been introduced, and, more importantly, multipurpose enzymes using up to twenty different substrates have been put in this metabolic network. This
3. Results 3.1. Metabolite Connectivity Distribution Fig. 2 represents the node connectivity distribution in the mitochondrial metabolic networks analyzed in this work. Accordingly to Tanaka (2005), all metabolites present in the network have been rank-ordered respect to the participation number. A straight line on a log–log plot gives a good data fitting, which is usually considered a strong evidence of an underlying power-law distribution. Small deviation from linearity in the log–log plot, and the fact that recent works have challenged the finding of true power-law distributions in biological networks (see, for example, Lima-Mendez and van Helden, 2009), induce to carefully consider if alternative distributions could better fit the data. This has been done by performing Kolmogorov–Smirnov analysis of connectivity distribution data (Clauset et al., 2009). It should be recalled that discriminating between lognormal and power-law distributions in empirical data
Fig. 3. Cumulative probability distribution in the lipid-extended human mitochondrial metabolic network. The connection number is reported on the horizontal axes (x) and the cumulative probability distribution as P(X > x) is reported on vertical axes. The empirical cumulative probability distribution values are indicated by open squares. The solid line represents the best fitting curve obtained by Kolmogorov–Smirnov analysis. This is a power-law curve with parameters ˛ = 2.036 and xmin = 0.918.
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Table 1 Topmost ranked metabolites in the extended mitochondrial network. Metabolite
Attributed compartment
Participation number
Hydrogen ion Water CMP Hydrogen ion Coenzyme A Phosphate ion Glycerol 3-phosphate Pyrophosphate ion ATP CDP-ethanolamine CTP ADP CO2 ATP CMP
Mitochondrion Mitochondrion Mitochondrion Cytosol Mitochondrion Mitochondrion Mitochondrion Mitochondrion Mitochondrion Mitochondrion Mitochondrion Mitochondrion Mitochondrion Cytosol Cytosol
247 101 82 81 72 58 50 44 42 42 42 38 35 32 23
indicates that power-law metabolites connectivity distribution is robust respect to these large rearrangements.
3.2. Hubs and Coupled Metabolites In the lipid-extended network presented here, it should be noted that, even if the rank ordering of most coupled metabolites is changed respect to the previously reported mitochondrial network (Thiele et al., 2005; Vo et al., 2004), carriers still are exceedingly represented among metabolites with the highest participation numbers (Table 1). Moreover, previously unrecognized molecular hubs appear in the network. Several of these participate to membrane lipids metabolism (for example CMP, CDP-ethanolamine, CTP and glycerol 3-phosphate), showing the importance of explicitly considering the combinatorial capacities of multi-substrate enzymes. It should be remarked that also the huge number of different molecules considered here separately, but usually clustered in classes of metabolites, play a role in the appearance of new molecular hubs. Since it is generally considered that hubs are important respect to the evolutionary history of the networks (Barabási and Oltvai, 2004), and considering their importance, for example as possible pharmacological targets, this work clearly demonstrates that care should be used in defining combinatorial metabolites, even if chemically similar, as single ones. The symmetric coupling matrix has been computed by multiplying the binary form of the S-matrix by its transpose, as detailed in the Methods section. Off-diagonal elements of this symmetric matrix represent the number of reactions in which two particular metabolites appear together in a stoichiometric equation. Fig. 4 reports the distribution of metabolite coupling in a log–log plot. Most pairs of metabolites never occur and they are obviously not reported in the figure. Most pairs of metabolites occur together only in one or few reactions and appear in the leftmost part of the data points. Pairs of metabolites occurring together in many reactions are illustrated by the rightmost data points in the figure. Again, significant differences respect to previously reported most coupled pairs are observed (Becker et al., 2006) (see Table 2), but the general appearance of data points shows that the overall topological features of the network are unchanged. In fact, the leftmost data points have been fitted by a power-law curve whose slope is close to the reported ones for genome-scale metabolic networks (Becker et al., 2006). Moreover, the most connected metabolites are also present in the highly coupled pairs (see Tables 1 and 2), as observed in previously reported genome-scale metabolic networks.
Fig. 4. Metabolite coupling in the lipid-extended human mitochondrial metabolic network. The number of metabolite pairs sharing a given number of reactions are log–log plotted. Solid line corresponds to the best fitting power-law curve of the leftmost data-points, corresponding to metabolites couples sharing 12 or less reactions. This power-law curve has a slope, in log–log plot, of −2.93 (r2 = 0.907).
3.3. Systemic Reactions Stoichiometric matrices of metabolic networks can be analyzed by SVD. SVD is usually used in data analysis to obtain dimensionality reduction or noise removal, but stoichiometric matrices are perfect matrices so SVD cannot be used for such purposes in this case. However, SVD of stoichiometric matrices can be employed to obtain a global description of systemic reactions (or modes) of the metabolic network under analysis. The singular value spectrum of genome-scale stoichiometric matrices is triphasic (Famili and Palsson, 2003). The first phase corresponds to the dominant modes, followed by a gradual steady decline in a large number of singular values. The third phase of the singular value spectra is composed of a small set of rapidly declining singular values. The mitochondrial network here analyzed shows such triphasic shape, as reported in Fig. 5. This shape is observed for the lipid expanded metabolic network, as well as for the network obtained without considering the combinatorial expansion of lipids. Randomly generated networks, in general, do not show such triphasic shape, usually lacking of clear and extended first and third phases (Famili and Palsson, 2003). This strongly indicates that metabolic networks are represented by rather peculiar sparse matrices, exhibiting dominant characteristics as well as distinct properties at the higher modes. These peculiarities of metabolic networks are not affected by the presence of combinatorial metabolites, or by explicitly considering them.
Table 2 Most coupled metabolites pairs.a Metabolite #1
Metabolite #2
Observed couples number
Hydrogen ion Phosphate ion Pyrophosphate ion Hydrogen ion Pyrophosphate ion Hydrogen ion Hydrogen ion CMP Glycerol 3-phosphate Water ATP Hydrogen ion Hydrogen ion Hydrogen ion (mitochondrion) Hydrogen ion
CMP Water Hydrogen ion Glycerol 3-phosphate CTP CDP-ethanolamine CTP CDP-ethanolamine CMP Hydrogen ion ADP ADP ATP Hydrogen ion (cytosol) CO2
82 45 44 43 42 42 42 42 40 39 36 28 28 24 24
a All the most coupled metabolites but one belong to the mitochondrial compartment.
Table 3 Topmost ranked metabolites respect to the systemic stoichiometric coefficients.a Lipid complexity not considered
Lipid complexity considered
First eigenreaction
Second eigenreaction
Third eigenreaction
First eigenreaction
Second eigenreaction
Third eigenreaction
Acetyl-CoA (m)
Hydrogen ion (c)
Hydrogen ion (c)
Hydrogen ion (m)
Hydrogen ion (m)
Hydrogen ion (m)
Arachidonyl-carnitine (c) 1,2-Diacylglycerol (C20:4–C20:4) (c)
Arachidonyl-carnitine (c) Phosphatidilcholine (C16:0–C20:4) (m)
Water (m)
Acetyl-CoA (m)
Water (m)
Docosahexaenoic acid (c)
NAD (m)
Water (m)
Cytochrome c ferric (m)
NADH (m)
Coenzyme A (m)
Cytochrome c ferrous (m)
Coenzyme A (m)
Cytochrome c ferric (m)
Coenzyme A (m)
FAD (m)
Cytochrome c ferrous (m)
Carbon dioxide (c)
3-(4Hydroxyphenyl)pyruvate (m) Docosahexaenoylcarnitine (c) Docosahexaenoylcarnitine (m) l-Aspartate (m)
2-Methyl-3oxopropanoate (m) 3-(4Hydroxyphenyl)pyruvate (m) 1,2-Diacylglycerol (C20:4–C20:4) (c)
Phosphatidilcholine (C16:0–C20:4) (m) 2-Methyl-3oxopropanoate (m) Docosahexaenoic acid (c)
FADH2 (m)
NAD (m)
Acetyl-CoA (m)
ATP (c)
Hydrogen ion (c)
NADH (m)
Water (c)
Docosahexaenoyl-CoA (m)
FAD (m)
Oxygen (m)
Arachidonyl-CoA (m)
FADH2 (m)
FAD (m)
Phosphatidilcholine (C16:0–C20:4) (m) 2-Methyl-3oxopropanoate (m) Fumarate (c)
Octadecynoyl-CoA (m)
Carbon dioxide (c)
FADH2 (m)
Palmitoyl-CoA (m)
Water (c)
ADP (m)
Cytochrome c ferric (m)
Hydrogen ion (e)
NAD (m)
Cytochrome c ferrous (m)
Phosphate ion (c)
NADH (m)
Oxygen (m)
ATP (c)
ATP (c)
Protoporphyrin (m)
l-Ornithine (m)
ATP (m)
Protoporphyrinogen IX (m)
ADP (c)
ADP (c)
Phosphate ion (m)
NAD (c)
Hydrogen ion (e)
Ubiquinone-10 (m)
NADH (c)
Carbon dioxide (m)
1,2-Diacylglycerol (C18:0–C18:0) (c) Phosphatidylserine (C20:4–C20:4) (m) Butanoyl-CoA (m)
ATP (c) Docosahexaenoic acid (c) 1,2-Diacylglycerol (C20:4–C20:4) (e) 1,2-Diacylglycerol (C18:2–C20:4) (e) Butanoyl-CoA (m)
Arachidonic acid (C20:4) (c) d-Glycerate-2phosphate (c) 1,2-Diacylglycerol (C18:0–C18:0) (c)
Phosphatidylserine (C18:1–C20:4) (c) 1,2-Diacylglycerol (C18:0–C18:0) (m) Fumarate (c) Phosphatidylserine (C18:1–C20:4) (e) 3-(4Hydroxyphenyl)pyruvate (m) Arachidonyl-carnitine (c) 1,2-Diacylglycerol (C20:4–C20:4) (e) 1,2-Diacylglycerol (C18:2–C20:4) (e) 1,2-Diacylglycerol (C22:6–C20:4) (c) Hydrogen peroxide (m) Phosphatidilcholine (C16:0–C20:4) (c) (S)-3-Hydroxydodecanoyl-CoA (m) Phosphatidic acid (C18:0–C18:0) (m) Docosahexaenoylcarnitine (c) Docosahexaenoylcarnitine (m)
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Attributed compartments: m mitochondrial; c cytosolic; e external.
(S)-3-Hydroxydodecanoyl-CoA (m) CDP-diacylglycerol (C18:0–C20:4) (m)
(S)-3-Hydroxydodecanoyl-CoA (m) l-Aspartate (m)
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a
1,2-Diacylglycerol (C18:1–C22:6) (c) 1,2-Diacylglycerol (C18:0–C18:0) (m) 1,2-Diacylglycerol (C18:2–C22:6) (c) Hydrogen peroxide (m)
Docosahexaenoylcarnitine (c) Docosahexaenoylcarnitine (m) Phosphatidylserine (C20:4–C20:4) (m) 1,2-Diacylglycerol (C18:0–C18:0) (c) Hydrogen peroxide (m)
Phosphatidylserine (C20:4–C20:4) (m)
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enzymes simply based on the systemic stoichiometric relations in the metabolic network. 4. Discussion
Fig. 5. Singular values spectra of the metabolic networks stoichiometric matrices. The singular values of the metabolic network with (black line) or without (gray line) considering the combinatorial diversity of lipids and enzymes acting on are reported. Both spectra show the triphasic shape observed in the genome-scale stoichiometric matrices.
The analysis of dominant modes in the mitochondrial stoichiometric matrix reveals interesting differences between the matrices with or without explicit expansion of lipids metabolic network. Table 3 reports the compound composition of the first three modes. For each mode, reported compounds are rank ordered respect to squared coefficients of the U matrix u2ij (i = 1, 2, 3), in order to make them all positive. Only the first twenty compounds are reported, i.e. those with the highest systemic stoichiometric coefficients in the particular eigen-reaction (or mode) under consideration. It should be noted that cofactors participating in energy, redox and phosphate metabolism emerge with the most significant values in the first eigen-reaction of all genome-scale networks analyzed by SVD so far. This is also true for the mitochondrial metabolic network without explicit consideration of combinatorial metabolites. Redox cofactors, phosphate carriers and well known hubs of energy metabolism are prevailing in the first three dominant modes of this network. But if combinatorial capacity of lipids is explicitly taken into account, systemic stoichiometric coefficients change dramatically. Beside ATP, the most significant values in the dominant eigen-reactions are observed for lipid metabolism intermediates, including species directly involved in the membrane lipid metabolism. Fumarate, aspartate and hydrogen peroxide also appear with high systemic stoichiometric coefficients in the dominant eigen-reactions of the lipid-extended metabolic network. Fig. 6 reports the reactions driving the conversion described by the first three dominant modes in the lipid-extended metabolic network. It comes out that the highest coefficients belong to the oxidative phosphorilation system. This finding shows a strong correlation relating lipids (including membrane components) as well as reactive oxygen species, and the oxidative phosphorilation
Lipids, and particularly membrane lipids, are extremely different and crucial molecules. The chemical composition of membrane lipids dictates physical and chemical properties of membranes and the recent blossoming interest for lipidomics witnesses the importance and the attention for this class of molecules (van Meer et al., 2008; Wenk, 2005). Moreover, to adequately describe the biochemical network avoiding biasing tailored assumptions, all the chemical components of it must be taken into account. This leads us to consider the combinatorial capacity of the enzymes involved in lipid metabolism. Here we show, using Kolmogorov–Smirnov statistical analysis, that the best mathematical model to describe the cumulative probability distribution function of metabolite connectivity is the power-law model. Other tested heavy-tail distributions, as well as the Poisson distribution (Lima-Mendez and van Helden, 2009), cannot be considered with our empirical data. This finding is important because, for example, lognormal and power-law distributions, although similar in shape, have distinct theoretical generative models (Mitzenmacher, 2004). The fact that the overall topological features of a complex biochemical network still obey to powerlaw distribution even in presence of combinatorial substrates and enzymes forces us to consider that no special mechanisms are required for their appearance, at least in biochemical networks. Such distribution (or, better, the long-tail distributions) must be considered “more normal than normal” from a statistical point of view (Keller, 2005; Li et al., 2005; Tanaka, 2005; Tanaka et al., 2005). Moreover, it has been shown that some random networks exhibit features usually considered peculiar to evolutionary shaped or functional adapted networks, such as small or ultra-small world appearance (Chung and Lu, 2004). Nevertheless, the fact that lognormal distribution and alternative ones (including the truncated power-law) have been ruled out leads to consider the theoretical generative model underlying such (pervasive) power-law distribution in metabolic networks. It should be noted that, in this work, some highly connected carrier molecules have been introduced, so preserving the overall statistical features of the metabolic network (see Figs. 2–5). It is conceivable that the presence of carrier metabolites is just the only responsible for the overall topological characteristics of complex metabolic networks. Considering the presence of highly connected carriers (as expected in real metabolic networks) beside low or poorly connected (at the whole network level) metabolites, power-law distributions emerge unavoidably in complex biochemical reactions networks. Spectral analysis shows that considering combinatorial metabolites explicitly does not affect the (peculiar) large-scale
Fig. 6. Dominant modes in lipid-extended metabolic matrix. Reactions driving the conversion in the first three dominant modes are reported. The ten enzymes with highest in mode vij 2 value are indicated by their E.C. number; vij 2 values are from the V matrix obtained by SVD. E.C. numbers – enzymes correspondence: 1.2.4.1 – pyruvate dehydrogenase; 1.3.3.3 – coproporphyrinogen oxidase; 1.3.3.4 – protoporphyrinogen oxidase; 1.3.99.3 – acyl-CoA dehydrogenase; 1.6.99.3 – NADH dehydrogenase (Complex I); 1.9.3.1 – cytochrome c oxidase (Complex IV); 1.10.2.2 – ubiquinone-cytochrome c reductase (Complex III); 1.15.1.1 – superoxide dismutase; 2.7.8.2 – CDP choline:1,2-diacylglycerol cholinephosphotransferase; 3.6.3.14 – ATP synthase (Complex V); 4.1.1.37 – uroporphyrinogen decarboxylase; 4.99.1.1 – ferrochelatase; 6.3.4.16 – carbamoyl-phosphate synthase.
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organization of the metabolic network (see Fig. 5). Remarkably, systemic reaction analysis in the lipid-extended network shows that an intimate relation exists connecting lipid metabolism intermediates and oxidative phosphorilation enzymes. In the first three modes, also an enzyme of the urea cycle, metabolically important dehydrogenases (pyruvate dehydrogenase and enzymes of fatty acids -oxidation pathway), the superoxide dismutase and numerous heme biosynthetic enzymes (see Fig. 6 and Table 3) appear involved at high extent. This finding could help to rationalize the relation existing between some pathological conditions involving alterations of membrane lipids and oxidative phosphorilation system failures. In some important diseases, lipids, including membrane ones, are directly involved (Abibhatla and Hatcher, 2008), and frequently mitochondria are involved also (Swerdlow, 2009). For example, in Parkinson’s disease, deficit of respiratory chain enzymes (particularly the Complex I) and membrane lipids abnormality have been shown (Winklhofer and Haass, 2010; Ellis et al., 2005; Pacelli et al., 2011). Abnormal mitochondrial dynamics, including membrane fusion and fission, have been suggested to mediate or amplify mitochondrial dysfunction and neural dysfunction during the course of neurodegenerative diseases (Su et al., 2010). Our results show that a direct link exists relating membranes, lipids in general, and respiratory chain enzymes. This link derives directly from stoichiometric organization of the whole metabolic network when the combinatorial diversity of lipids is explicitly considered. Systemic reactions suggest that changes, or failures, in mitochondrial respiratory enzymes could immediately affect intermediates of lipid, including membranes, metabolism. On the other hand, interactions among apparently nonrelated metabolites become evident, as for example the presence of hydrogen peroxide together with a number of lipid metabolism intermediates in the topmost ranked metabolites of first three eigenreactions. Closer examination of metabolic hubs obtained from the lipid extended mitochondrial network leads also to some evolutionary considerations. Scale-free model predicts that nodes appearing early in the history of the network are the most connected ones (Barabási and Albert, 1999). Inspection of metabolic hubs usually suggests that they are remnants of the RNA world (such as coenzyme A, NAD+ , ATP) or they are elements of the most ancient metabolic pathways (glycolysis and the tricarboxylic acid cycle) as reported in (Wagner and Fell, 2001; Jeong et al., 2000). Looking at metabolic hubs in the extended mitochondrial network here reported (see Tables 1 and 2) suggests that they are not only remnants of the ancient RNA world (Gilbert, 1986), but also molecules coming from an equally ancient “lipid world” (Segré et al., 2001). Beside water and hydrogen ion, our results show that no other metabolites out of RNA world, lipid world and the phosphate/pyrophosphate couple (Kornberg et al., 1999) could be considered hubs. At the best of our knowledge, this is the first time that such close correlation (of evolutionary origin, assuming scale free model) connecting these ancient pre-biotic world, can be observed. Finally, it should be recalled that theoretical studies aiming to exactly and formally defining what life is have shown that a crucial requirement for living systems is the metabolic circularity or, more formally, the closure to efficient causation in (M, R) systems (Cornish-Bowden and Cárdenas, 2007, 2008; Rosen, 1991). In these studies it has been shown that the circle of efficient causation can only be closed if some (or, better, many) of the catalysts used by organisms fulfill multiple functions. A suggested solution for the efficient causation closure is multi-functionality, such as the presence of “moonlighting” proteins, or the fact that a small number of nucleic acid molecules encode an enormous number of proteins (Cornish-Bowden and Cárdenas, 2008). Here we suggest that lipid metabolism offers another possible solution to the closure to
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efficient causation, and it is particularly suggestive here also to recall that lipids are important to the spatial closure if we consider a cell an autopoietic system (Maturana and Varela, 1980). The lipid-extended metabolic network shows that multi-functionality is deeply embedded in the metabolism of lipids, suggesting a more profound role for such class of molecules in defining what life is. Acknowledgements The authors thank Prof. Sergio Papa for his continuous encouragement and for his example of a life dedicated to science. The authors would also thank the three anonymous reviewers for insightful and helpful comments. This work is part of PRIN “Mitochondrial Bioenergetics: Redox Mechanisms, ROS Production, Redox Control of Cell Differentiation”. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.biosystems.2012. 04.001. References Abibhatla, R.M., Hatcher, J.F., 2008. Altered lipid metabolism in brain injury and disorders. Subcell Biochem. 49, 241–268. Adam-Vizi, V., Chinopoulos, C., 2006. Bioenergetics and the formation of mitochondrial reactive oxygen species. Trends Pharmacol. 27, 639–645. Albert, R., 2005. Scale-free networks in cell biology. J. Cell Sci. 118, 4947–4957. Alonso, J., Rodriguez, J.M., Baena-Lopez, L.A., Santaren, J.F., 2005. Characterization of the Drosophila melanogaster mitochondrial proteome. J. Proteome Res. 4, 1636–1645. Anderson, P.W., 1972. More is different. Science 177, 393–396. Barabási, A.L., Albert, R., 1999. Emergence of scaling in random networks. Science 286, 509–512. Barabási, A.L., Oltvai, Z.N., 2004. Network biology: understanding the cell’s functional organization. Nat. Rev. Genet. 5, 101–113. Becker, S.A., Price, N.D., Palsson, B.O., 2006. Metabolite coupling in genome-scale metabolic networks. BMC Bioinform. 7, 111, http://dx.doi.org/10.1186/14712105-7-111. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U., 2006. Complex networks: structure and dynamics. Phys. Rep. 424, 175–308. Borodina, I., Krabben, P., Nielsen, J., 2005. Genome-scale analysis of Streptomyces coelicolor A3(2) metabolism. Genome Res. 15, 820–829. Carlson, J.M., Doyle, J., 2002. Complexity and robustness. Proc. Natl. Acad. Sci. U. S. A. 99 (Suppl. 1), 2538–2545. Chung, F., Lu, L., 2004. The average distance in a random graph with given expected degree. Internet Math. 1, 91–114. Clauset, A., Shalizi, C.R., Newman, M.E.J., 2009. Power-law distributions in empirical data. SIAM Rev. 51, 661–703. Cornish-Bowden, A., Cárdenas, M.L., 2008. Self-organization at the origin of life. J. Theor. Biol. 252, 411–418. Cornish-Bowden, A., Cárdenas, M.L., 2007. Organizational invariance in (M, R) systems. Chem. Biodivers. 4, 2396–2406. Csete, M., Doyle, J., 2004. Bow ties, metabolism and disease. Trends Biotechnol. 22, 446–450. Da Cruz, S., Parone, P.A., Martinou, J.C., 2005. Building the mitochondrial proteome. Expert Rev. Proteomics 2, 541–551. Devlin, T.M. (Ed.), 2002. Textbook of Biochemistry with Clinical Correlations. , fifth ed. Wiley-Liss, New York. Duarte, N.C., Becker, S.A., Jamshidi, N., Thiele, I., Mo, M.L., Vo, T.D., Srivas, R., Palsson, B.O., 2007. Global reconstruction of the human metabolic network based on genomic and bibliomic data. Proc. Natl. Acad. Sci. U. S. A. 104, 1777–1782. Duarte, N.C., Herrgard, M.J., Palsson, B.O., 2004. Reconstruction and validation of Saccharomyces cerevisiae iND750, a fully compartmentalized genome-scale metabolic model. Genome Res. 14, 1289–1309. Edwards, J.S., Palsson, B.O., 1999. Systems properties of the Haemophilus influenzae Rd metabolic genotype. J. Biol. Chem. 274, 17410–17416. Edwards, J.S., Palsson, B.O., 2000. The Escherichia coli MG1655 in silico metabolic genotype; its definition, characteristics, and capabilities. Proc. Natl. Acad. Sci. U. S. A. 97, 5528–5533. Ellis, C.E., Murphy, E.J., Mitchell, D.C., Golovko, M.Y., Scaglia, F., Barcelo-Coblijn, G.C., Nussbaum, R.L., 2005. Mitochondrial lipid abnormality and electron chain impairment in mice lacking alpha-synuclein. Mol. Cell Biol. 25, 10190–10201. Famili, I., Palsson, B.O., 2003. Systemic metabolic reactions are obtained by singular value decomposition of genome-scale stoichiometric matrices. J. Theor. Biol. 224, 87–96. Gilbert, W., 1986. The RNA world. Nature 319, 618.
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