MIT OpenCourseWare http://ocw.mit.edu 6.047 / 6.878 Computational Biology: Genomes, Networks, EvolutionFall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.Lecture 21: Introduction to Steady State Metabolic Modeling November 18, 2008 1 Introduction Metabolic modeling allows us to use mathematical models to represent complex biological systems. This lecture discusses the role that modeling biological sys-tems at the steady state plays in understanding the metabolic capabilities of interesting organisms and how well steady state models are able to replicate in vitro experiments. 1.1 What is Metabolism? According to Matthews and van Holde, metabolism is “the totality of all chem-ical reactions that occur in living matter”. This includes catabolic reactions, which are reactions that lead the break down of molecules into smaller com-ponents and anabolic reactions, which are responsible for the creation of more complex molecules (e.g. proteins, lipids, carbohydrates, and nucleic acids) from smaller components. These reactions are responsible for the release of energy from chemical bonds and the storage of energy respectively. Metabolic reactions are also responsible for the transduction and transmission of information (for example, via the generation of cGMP as a secondary messenger or mRNA as a substrate for protein translation). 1.2 Why Model Metabolism? An important application of metabolic modeling is in the prediction of drug effects. An important subject of modeling is the organism Mycobacterium tu-berculosis [1]. The disruption of the mycolic acid synthesis pathways of this organism would help control TB infection. Computational modeling gives us a platform for identifying the best drug targets in this system. Gene knock-out studies in Escherichia coli have allowed scientists to determine which genes and gene combinations affect the growth of that important model organism [2]. Both agreements and disagreements between models and experimental data can help us assess our knowledge of biological systems and help us improve our 1predictions about metabolic capabilities. In the next lecture, we will learn the importance of incorporating expression data into metabolic models. 2 Model building 2.1 Chemical reactions In metabolic models, we are concerned with modeling chemical reactions that are catalyzed by enzymes. Enzymes work by facilitating a transition state of the enzyme-substrate complex that lowers the activation energy of a chemical reaction. The diagram on slide 5 of page 1 of the lecture slides demonstrates this phenomenon. A typical rate equation (which describes the conversion of the substrates of the enzyme reaction into its products S=P) can be described by a Michaelis-Menten rate law: V = [S] , where V is the rate of the Vmax Km+[S] equation as a function of substrate concentration. Km and Vmax are the two parameters necessary to characterize the equation. The inclusion of multiple substrates, products, and regulatory relationships quickly increases the number of parameters necessary to characterize enzyme function. The figures on slides 1, 2, and 3 of page 2 of the lecture notes demon-strate the complexity of biochemical pathways. Kinetic modeling quickly be-comes infeasible because the necessary parameters are difficult to measure and also vary across organisms [3]. Thus, we are interested in a modeling method that would allow us to avoid the use of large numbers of poorly-determined parameters. 2.2 Steady-state assumption The steady state assumption allows us to represent reactions entirely in terms of their chemistry (the stoichiometric relationships between the components of the enzymatic reaction) by assuming that there is not accumulation of any metabolite in the system. This does not mean that there is not flux through any of the reactions, simply that accumulation does not occur. An analogy is to a series of waterfalls that contribute water to pools. As the water falls from one pool to another, the water levels do not change even though water continues to flow (see page 2 slide 5). This framework prevents us from seeing transient kinetics that can result from perturbations of the system, but if we are interested in long-term metabolic capabilities (functions on a scale longer than milliseconds or seconds) then steady state dynamics may give us all the information that we need. An important aspect of the steady-state assumption is that reaction sto-chiometries are conserved across species, whereas the biology of enzyme catal-ysis (and the parameters that characterize it) are not conserved across species. This makes the ability to generalize across species and reuse conserved pathways in models much more feasible. 2� 2.3 Reconstructing Metabolic Pathways There are several databases that can provide the information necessary to re-construct metabolic pathways in silico. These databases allow reaction stoi-chiometry to be accessed using Enzyme Commission numbers, which are the same in each organism that uses that particular enzyme. Among the databases of interest are ExPASy [4], MetaCyc [5], and KEGG [6]. These databases often contain pathways organized by function that can be downloaded in a format such as SBML, often making pathway reconstruction very easy for well-characterized pathways. ExPASy [4], MetaCyc [5], and KEGG [6]. These databases often con-tain pathways organized by function that can be downloaded in a format such as SBML, often making pathway reconstruction very easy for well-characterized pathways. 3 Metabolic Flux Analysis Metabolic flux analysis (MFA) is a way of computing the distribution of reaction fluxes that is possible in a given metabolic network at steady state. We can place constraints on certain fluxes in order to limit the space described by the distribution of possible fluxes. 3.1 Mathematical representation We can represent the flux of each substrate xi, we can represent the rate of change of that substrate as dxi = S • v, where S is a vector that describes the dt stoichiometric coefficients of that metabolite in each reaction in which it is a substrate or product. With this steady state