An introduction to biochemical reaction networks

Transcription

1 Chapter 1 An introduction to biochemical reaction networks (This part is discussed in the slides). Biochemical reaction network distinguish themselves from general chemical reaction networks in that the carbon-based compounds involved in the chemical reactions that make up Life use only a tiny fraction of the total possible carbonbased molecules 1. We distinguish three main types of biochemical reaction networks that one encounters in any living organism: Metabolic networks. It may be split into two subtypes: primary metabolism and secondary metabolism. Primary metablism is split in catabolism and anabolism. The lectures consider various subnetworks in primary metabolism of prokaryotes. Signalling networks. Gene regulatory networks. The three types are intimately linked. 1 According to Ch.M. Dobson (2004) Chemical space and biology, Nature 432, , Nature uses approximately 10 4 different carbon-based molecules out of the ca possible molecules. 5

2 Chapter 2 Metabolic networks (This part is discussed in the slides). In metabolism almost all reactions that occur are catalysed by enzymes. Moreover, so-called co-enzymes may be involved. The latter bind a metabolite and one or more resulting complexes, also with different metabolites and coenzymes, can subsequently bind the enzyme that makes the ultimate conversion, yielding the product metabolite(s) and releasing the co-enzymes. In most reactions only two, three or four metabolites are involved (apart from the enzyme and co-enzymes) as substrate or product. Moreover, the molecular numbers of metabolites in the cell are relatively high. Metabolic networks are built from essentially three types of building blocks, called elementary reactions. 2.1 Elementary metabolic reactions (This part is discussed in the slides). We shall now discuss the three main types of elementary metabolic reactions, following [4] Subgroup reorganisation The substrate and product have the same elemental composition, i.e. molecular formula, but different structural fomrula. Subgroups of the metabolite ( moiteies ) are relocated or rearranged. Enzymes involved in such reactions are calles isomerases. Example: In glycolysis, the reaction that turns glucose-6-phosphate (G6P) into fructose-6-phosphate (F6P) is such a reaction. 6

3 2.1. ELEMENTARY METABOLIC REACTIONS Bimolecular association or dissociation Two metabolites are bound together or a single metabolite is split into two. Dimerisation or polymerisatin reactions are of this type Cofactor-coupled reactions (Also called a carrier-mediated reaction ). A moiety of the metabolite is removed and transferred to a carrier molecule, or the other way round, the moiety, bound to the carrier, is donated by the carrier molecule to the metabolite. For example, a phosphate group may be removed from or transferred onto a metabolite. Typical carriers in this case are are ATP and ADP. A kinase is an enzyme that catalyzes a phosphorylation reaction, i.e. the transfer of a phosphate group onto a compound. A phosphates is an enzyme that catalyses the removal of a phosphate group. A loosely coupled cofactor is called a co-enzyme.

4 Chapter 3 Graph representations of chemical reaction networks 3.1 Representation in Chemical Reaction Network Theory The most precise, unambiguous, representation of chemical reaction networks by means of graphs is the description used in the branch of mathematics / theoretical chemistry that is called Chemical Reaction Network Theory (CRNT). There one defines: Definition A chemical reaction network is a triple (S,C,R) of finite sets: i.) S := {X 1,X 2,...,X m } is the set of basic species. or molecules, that undergo chemical transitions. ii.) C N m 0 is the set of all complexes, i.e. all combinations of specicies (togethers with their specific multiplicities) that are either substrate or product of a reaction. iii.) R = {R 1,R 2,...R r } C C is the set of all reactions, i.e. all transitions between complexes: R i = (y i,y i) : m y ij X j j=1 m j=1 y ijx j This allows one to model unambiguously enzyme-catalysed reactions, or more generally: reactions that have the same compound both as substrate and product. 8

5 3.2. NET REACTION REPRESENTATION 9 The graph representation associated to a chemical reaction network is a directed graph that has the complexes as nodes and the reactions as arrows. The reaction R = (y,y ) would be the arrow pointing from the note representing complex y to the node representing complex y. The graph representation of a chemical reaction network is hard to interpret immediately in terms of flow of metabolites through the network. However, its graph structure can indicate particular dynamical properties of the newtork it represents ( Feinberg s deficiency-one theorem ). 3.2 Net reaction representation In the graphical representation of metabolic networks that we shall use it is customary to represent net reactions only. This introduces some ambiguities for reactions in which a compound is both used and produced, e.g. an enzyme catalysed reaction. For examplem, the isomerisation reaction A+E B+E is reduced to A B. Similarly, a reaction A+2B C+B would be replaced by the net reaction A+B C. For the consideration of net changes in metabolites this does not matter. It does matter logically: one needs to realize that a net reaction can occur only if the required number of compounds in substrate complex of the original reaction is present in the system. However, the molecular number of specific metabolite is typically large if it is present. The number of specific enzyme is (much) lower, but still not so low that one should think about its presence or not. So we work with a net-reaction representation of metabolic networks. There are two types of nodes in the network (to start with; more type of nodes appear later): metabolites and reactions. These are connected by arrows. One draws an arrow from a metabolite to a reaction if this metabolites is used as substrate in this reaction. An arrow points from a reaction to a metabolite if the latter is produced in this reaction. Thus one obtains a bi-partite graph. Arrows are weighted according to the multiplicity of the metabolite as substrate or product in the reaction (Note that one uses net reactions! So a metabolite cannot be both substrate and product of the same reaction). For analytical purposes it is important to distinguish between reversible and irreversible reactions. In principle, any chemical reaction is reversible. However, for some, the expected time for a reverse reaction to take place can be so large that it can be easily ignored on the time scale of the life time of the organism that is considered. If this is the case, reactions are considered irreversible (or unidirectional). Convention: Metabolites are denoted by circular nodes. Irreversible reactions are denoted by squares.

6 10CHAPTER 3. GRAPH REPRESENTATIONS OF CHEMICAL REACTION NETWORKS Reversible reactions are denoted by diamonds. For reversible reaction arrows indicate the direction of the reaction that is considered as forward or positive. The other direction is then the backward or negative direction. Enzymes are not included in a metabolic network Currency metabolites (like ATP/ADP, NAD + / NADH) are repeatedly displayed as (circular) nodes, in order to simplify the many arrows that would otherwise point to or from a single node and thus improve readibility of the graph. 3.3 Modularisation Modularisation leads to two additional classes of reaction: internal reactions and exchange reactions. This relates to whether the reaction is inside a module (internal) or realizes the input and/or output of metabolites from a module (exchange). Both internal and exchange reactions can be either reversible or irreversible. Example: Glucose uptake in E. coli. 3.4 Derived graph representations From a net-reaction graph representation as bi-partite graph one obtains directed and undirected derived graphs: the substrate and reaction graphs. The directed substrate graph has the metabolites as nodes. An arrow is drawn from one metabolite to another for each reaction that uses the former as substrate to produce the latter. The undirected substrate graph is obtained form the directed one, by replacing each arrow by an (undirected) edge. The directed reaction graph has all reactions as nodes. An arrow is drawn from one reaction to another if the latter uses a product of the former as substrate. The undirected reaction graph is obtained from the directed reaction graph by replacing each arrow by an edge. Realize that substrate and reaction graphs (either directed or undirected) can give a substantial loss of information concerning the structure of the network. It creates much ambiguity.

7 Chapter 4 Network statistics 11