Introduction to Bioinformatics
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1 Systems biology Introduction to Bioinformatics Systems biology: modeling biological p Study of whole biological systems p Wholeness : Organization of dynamic interactions Different behaviour of the individual parts when isolated or when combined together Systems cannot be fully understood by of their components in isolation -- Ludwig von Bertalanffy, 934 (according to Zvelebil & Baum) Outline p. Systems biology and biological Transcriptional regulation Metabolism Signalling Protein interactions p 2. Modeling frameworks and discrete Static and dynamic p 3. Identification of from data. Systems biology p Systems biology biology of Shift from component-centered biology to systems of interacting components Prokaryotic cell Eukaryotic cell Mariana Ruiz, Magnus Manske Interactions within the cell Paradigm shift from study of individual components to systems p Density of biomolecules in the cell is high: plenty of interactions! p Figure shows a crosssection of an Escherichia coli cell Green: cell wall Blue, purple: cytoplasmic area Yellow: nucleoid region White: mrna Number of different systems? System2 System Interaction Component David S. Goodsell System size
2 Paradigm shift from study of individual components to systems Biological systems of Number of different systems Level of model detail System size Transcriptional regulation Metabolism metabolite Gene product (protein) enzyme regulatory region microarray experiments gene co-operative regulation transcription factor Signal transduction signal molecule & receptor activated relay molecule inactive signaling protein active signaling protein end product of the signaling cascade (activated enzyme) Protein interaction p Protein interaction is the unifying theme of all regulation at the cellular level p Protein interaction occurs in every cellular system including systems introduced earlier p Data on protein interaction reveals associations both within a system and between systems 2
3 Protein interaction 2. Graphs as of biological p A graph is a natural model for biological systems of p Nodes of a graph represent biomolecules, edges interactions between the molecules p Graph can be undirected or directed p To address questions beyond simple connectivity (node degree, paths), one can enrich the graph with information relevant to the modeling task at hand Enriching examples: transcriptional regulation p Regulatory effects can be (roughly) divided into activation inhibition p We can encode this distinction by labeling the edges by + and -, for example p Graph of transcriptional regulation are called gene(tic) regulatory gene 2 3 gene 3 gene 2 Activator Activation Repressor Inhibition Enriching examples: more transcriptional regulation A gene regulatory network might be enriched further: In this diagram, proteins working cooperatively as regulators are marked with a black circle. This network is a simplified part of cell cycle regulation. Frameworks for biological network modeling Static Dynamic p A variety of information can be encoded in graphs p Modeling frameworks can be categorised based on what sort of information they include and/or discrete? Static or dynamic model? (take time into account?) Spatial features? (consider the physical location molecules in the cell?) p Choice of framework depends on what we want to do with the model: Data exploration Explanation of observed behaviour Prediction 3
4 Static Dynamic Static Dynamic Boolean Boolean Bayesian Bayesian Dynamic : differential equations p In a differential equation model x i correspond to the concentrations of biological molecules; change of over time is governed by rate equations, dx i /d t = f i (x), i n p In general, f i (x) is an arbitrary function (not necessarily linear) p Note that the graph structure is encoded by parameters to functions f i (x) Properties of a differential equation model p The crucial step in specifying the model is to choose functions f i (x) to balance model complexity (number of parameters) level of detail p Overly complex model may need more data than is available to specify Example of a differential equation model of transcriptional regulation p Let x be the concentration of the target gene product p A simple kinetic (i.e., derived from reaction mechanics) model could take into account multiple regulators of target gene and degradation of gene products and assume that regulation effects are independent of each other Example of a differential equation model of transcriptional regulation p Rate equation for change of x could then be wherek is the maximal rate of transcription of the gene, k 2 is the rate constant of target gene degradation, w j is the regulatory weight of regulator j and y j is the concentration of regulatorj Number of parameters? 4
5 Differential equation model for metabolism p Likewise, rate equations can be derived for differential equation for metabolism p For simple enzymes, two parameters might be enough p Realistic modeling of some enzyme requires knowledge of 0-20 parameters p Such data is usually not available in highthroughput manner Static Bayesian Boolean Dynamic theory (BST) p BST is a modeling framework, where differential rate equations are restricted to the following power-law form, Static Dynamic Interestingly, if we assume Stochastic that the simulation concentrations are constant over time (steady-state), an analytical solution can be found to a BST model. But then we Boolean throw away the dynamics of the system! where i is the rate constant for molecule i and g ij is a kinetic constant for molecule i and reaction j p BST approximates the kinetic system and requires less parameters than the genetic kinetic model Bayesian Steady-state modeling p Is the study of steady-states meaningful? p If we assume dx i /dt = 0, we restrict ourselves to systems, where the production of a molecule is balanced by its consumption metabolite enzyme In a metabolic steady-state, these two enzymes consume and produce the metabolite in the middle at the same rate Static Bayesian Boolean Dynamic 5
6 modeling p modeling is a linear framework, where the system is assumed to be in a steady-state p Model is represented byastoichiometric matrix S, where S ij gives the number of molecules of type i produced in reaction j in a time unit S ij = 0 if value omitted modeling p Since x i are constant, the questions asked now deal with reaction rates p For instance, we could characterise solutions to the linear steady-state condition, which can be written in matrix notation as Sv = 0 p Solutions v are reaction rate vectors, which for example reveal alternative pathways inside the network Static Bayesian Boolean Dynamic : Boolean p Boolean have been widely used in modeling gene regulation Switch-like behaviour of gene regulation resembles logic circuit behaviour Conceptually easy framework: easy to interpret Boolean extend naturally to dynamic modeling Boolean A Boolean network G(V, F) contains p Nodes V = {x,, x n }, x i = 0 orx i = p Boolean functions F = {f,, f n } p Boolean function f i is assigned to node x i Dynamics in Boolean p Dynamic behaviour can be simulated p State of a variable x i at time t+ is calculated by function f i with input at time t p Dynamics are deterministic: state of the network at any time depends only on the state at time 0. NOT AND Logic diagram for activity of Rb 6
7 Example of Boolean network dynamics p Consider a Boolean network with 3 x, x 2 and x 3 and functions given by x := x 2 and x 3 x 2 := notx 3 x 3 := x orx 2 t x x2 x Problems with Boolean p 0/ modeling is unrealistic in many cases p Deterministic Boolean network does not cope well with missing or noisy data p Many Boolean to choose from specifying the model requires a lot of data A Boolean function has n parameters, or inputs Each input is 0 or => 2 n possible input states The function is specified by input states for which f(x) = => 2^(2^n) possible Boolean functions Static Bayesian Boolean Dynamic 3. Model identification from data p We would like to learn a model from the data such that the learned model Explains the observed data Predicts the future data well p Generalization property: model has a good tradeoff between a good fit to the data and model simplicity Three steps in learning a model p Representation: choice of modeling framework, how to encode the data into the model Restricting : number of inputs to a Boolean function, for example p Optimization: choosing the best model from the framework Structure, parameters p Validation: how can one trust the inferred model? Conclusions p Graph are important tools in systems biology p Choice of modeling framework depends on the properties of the system under study p Particular care should be paid to dealing with missing and incomplete data - choice of the framework should take the quality of data into account 7
8 References and further reading p Florence d Alché-Buc and Vincent Schachter: Modeling and identification of biological. In Proc. Intl. Symposium on Applied Stochastic Models and Data Analysis, p Marketa Zvelebil and Jeremy O. Baum: Understanding bioinformatics. Garland Science, p Hiroaki Kitano: Systems Biology: A Brief Overview. Science 295, p Marie E. Csete and John C. Doyle: Reverse engineering of biological complexity. Science 295, p James M. Bower and Hamid Bolouri (eds): Computational Modeling of Genetic and Biochemical Networks. MIT Press,
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