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Edda Klipp, Humboldt-Universität zu Berlin Modeling of Gene expression. : Gene mRNA Proteins Cell processes Central Dogma of Molecular Biology Transcription.

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Präsentation zum Thema: "Edda Klipp, Humboldt-Universität zu Berlin Modeling of Gene expression. : Gene mRNA Proteins Cell processes Central Dogma of Molecular Biology Transcription."—  Präsentation transkript:

1 Edda Klipp, Humboldt-Universität zu Berlin Modeling of Gene expression. : Gene mRNA Proteins Cell processes Central Dogma of Molecular Biology Transcription factors

2 Edda Klipp, Humboldt-Universität zu Berlin Modeling of Gene Expression Modeling of Expression of one/few genes - Binding of transcription factors/RNAPolymerasen,... to DNA - Effect of inhibitors/activators - Production of mRNA, proteins - Feedback or regulation by products or external regulators Discovery of genetic networks - Cause of gene expression patterns or -profils - Modeling of the dynamics of artifical networks - Reverse Engineering - Search for Motifs and Clustern Basis: Data Basis: Processes and interactions

3 Edda Klipp, Humboldt-Universität zu Berlin Direction of Investigation knownto be predicted StructureFunction Protein interactionsExpression of genes TF bindiungRegulation Impact of perturbations Dynamic behavior, Bifurcations,... : FunctionStructure Expression patternMutual influence of genes Time courses of Regulation network concentrations, activities,…. :

4 Edda Klipp, Humboldt-Universität zu Berlin Concept of state The state of a system is a snapshot of the system at a given time that contains enough information to predict the behaviour of the system for all future times. The state of the system is described by the set of variables that must kept track of in a model. Different models of gene regulation have different representations of the state: Boolean model: a state is a list containing for each gene involved, of whether it is expressed (1) or not expressed (0) Each model defines what it means by the state of a system. Given the current state the model predicts what state/s can occur next. Differential equation model: a list of concentrations of each chemical entity Probabilistic model: a current probability distribution and/or a list of actual numbers of molecules of a type

5 Edda Klipp, Humboldt-Universität zu Berlin Kinetics – change of state A B k Deterministic, continuous time and state: e.g. ODE model concentration of A decreases and concentration of B increases. Concentration change in per time interval dt is given by Probabilistic, discrete time and state : transformation of a molecule of type A into a molecule of type Sorte B. The probability of this event in a time interval dt is given by a – number of molecules of type A Deterministic, discrete time and state : e.g. Boolean network model Presence (or activity) of B at time t+1 depends on presence (or activity) of A at time t

6 Edda Klipp, Humboldt-Universität zu Berlin One Network, Different Models gene agene bgene cgene d C A D B A B + + repression activation transcription translation gene protein A ab cd Directed graphs V = {a,b,c,d} E = {(a,c,+),(b,c,+), (c,b,-),(c,d,-),(d,b,+)} ab cd Boolean network a(t+1) = a(t) b(t+1) = (not c(t)) and d(t) c(t+1) = a(t) and b(t) d(t+1) = not c(t) ab cd Bayesian network p(xa)p(xa) p(xb)p(xb) p(x c |x a,x b ), p(x d |x c ),

7 Edda Klipp, Humboldt-Universität zu Berlin Directed Graphs ab cd Directed graphs V = {a,b,c,d} E = {(a,c,+),(b,c,+), (c,b,-),(c,d,-),(d,b,+)} A directed graph G is a tuple, with V - Set of vertices E – Set of edges Vertices are related to Genes (or other components of the system) and edges correspond to their regulatory interactions. An edge is a tuple of vertices. It is directed, if i and j can be associated with head and tail of the edge. Label of edges and vertices can be enlarged to store information about genes or interactions. Then in general, an edge is a tuple properties: e.g: j activates i (+) or j inhibits i (-), properties e.g. List of regulators and their effects on a specific egde Usually not suited for presenting dynamics

8 Edda Klipp, Humboldt-Universität zu Berlin Bayesian Network Representation of network as directed acyclic graph Nodes -- Genes Edges E -- regulatory interactions. Variables, belonging to nodes i = for regulation relevant properties, e.g. Gene expression leves or amount of active protein. A conditional probability distribution is defined for every, with parent variables belonging to direct regulators of i. Directed Graph G and conditional probability distribution together Yield the joint probability distribution, which defines the Bayesian network. The joint probability distribution can be decomposed to ab cd Bayesian network p(xa)p(xa) p(xb)p(xb) p(x c |x a,x b ), p(x d |x c ),

9 Edda Klipp, Humboldt-Universität zu Berlin Bayessche Netze Gerichteter Graph: Abhängigkeit von Wahrscheinlichkeiten: Genexpressionslevel eines Kindknotens ist abhängig von Expressionslevel der Eltern Daher auch: bedingte Unabhängigkeiten: Die bedeuten, dass unabhängig von Variablen y ist, wenn Variablen z gegeben sind. Zwei Graphen oder Bayessche Netzwerke sind äquivalent, wenn sie den gleichen Satz von Unabhängigkeiten bestimmen. Äquivalente Graphen sind durch Beobachtung der Variablen x nicht unterscheidbar. Für das Beispielnetz sind die bedingten Unabhängigkeiten Die gemeinsame Wahrscheinlichkeitsverteilung ist ab cd p(xa)p(xa) p(xb)p(xb) p(x c |x a,x b ), p(x d |x c ),

10 Edda Klipp, Humboldt-Universität zu Berlin Boolean Models (George Boole, ) Each gene can assume one of two states: expressed (1) or not expressed (0) Background: Not enough information for more detailed description Increasing complexity and computational effort for more specific models (discrete, deterministic) Replacement of continuous functions (e.g. Hill function) by step function

11 Edda Klipp, Humboldt-Universität zu Berlin Boolean Models Boolean network is characterized by - the number of nodes (genes): N - the number of inputs per node (regulatory interactions): k The dynamics are described by rules: if input value/s at time t is/are...., then output value at t+1 is.... Boolean network have always a finite number of possible states and, therefore, a finite number of state transitions. BC Linear chain Ring ABCD AB CD A B A

12 Edda Klipp, Humboldt-Universität zu Berlin Boolean Models gene agene bgene cgene d C A D B A B + + repression activation transcription translation gene protein ab cd Boolean network a(t+1) = a(t) b(t+1) = (not c(t)) and d(t) c(t+1) = a(t) and b(t) d(t+1) = not c(t) Steady state: Cycle:

13 Edda Klipp, Humboldt-Universität zu Berlin Beschreibung mit Differentialgleichungen Time Concentration a d b c Nur für mRNA: gene agene bgene cgene d C A D B A B + + repression activation transcription translation gene protein A

14 Edda Klipp, Humboldt-Universität zu Berlin Network motifs R. Milo, …, U. Alon, Network Motifs: Simple Building Blocks of Complex Networks, Science, 2002 Schematic view of network motif detection. Network motifs are patterns that recur much more frequently (A) in the real network than (B) in an ensemble of randomized networks. Each node in the randomized networks has the same number of incoming and outgoing edges as does the corresponding node in the real network. Red dashed lines indicate edges that participate in the feedforward loop motif, which occurs five times in the real network.

15 Edda Klipp, Humboldt-Universität zu Berlin Network motifs X Y X Y Z X Z 1 Z 2 Z 3 Z n X 1 X 2 X 3 X m Z 1 Z 2 Z 3 Z n Single input High Density Feedforward loop Feedback loop Activation Inhibition R. Milo, …, U. Alon, Network Motifs: Simple Building Blocks of Complex Networks, Science, 2002 X Y Z

16 Edda Klipp, Humboldt-Universität zu Berlin Transcription

17 Edda Klipp, Humboldt-Universität zu Berlin Structure of Eukaryotic Promoter (a) Figure 6.1 TATA INRDPE TFIIA TBP TFIIF TFIIB RNAPII/GTF complex TF binding sites Distal promoter module TF binding sites Proximal promoter module TATA boxTranscription start Downstream promoter element (b) TCCCTGAACGG TCCGAGAACCT TTGCTCCGCA_ TTCCTGAGCTG TTCGTAAGGAG A C G T Aligned TFBSs TYCSTGARCNG Positional Weight Matrix Consensus

18 Edda Klipp, Humboldt-Universität zu Berlin Transcription...

19 Edda Klipp, Humboldt-Universität zu Berlin Time delay in Transcription TF-RE TF-A P P P P tf-a Delay, translocation of mRNA Delay, translocation of protein + k f /min Log 10 TF-A Region of multistability Transkriptionsfaktor TF-A aktiviert seine eigene Transkription als phosphorylierter Homodimer, der an Enhancer TF-RE bindet. Modell nach Smolen mit time delay: - schnelles Gleichgewicht von Monomer und Dimer - Sättigungskinetik für Transkription - Abbau von TF mit k d, basale Produktion mit R bas t – delay time

20 Edda Klipp, Humboldt-Universität zu Berlin Protein Biosynthesis

21 Edda Klipp, Humboldt-Universität zu Berlin Model for Elongation of a Peptid chain Heyd A & Drew DA, Bulletin of Mathematical Biology (2003) 65, 1095–1109 [mRNA] - concentration of messenger RNA, [ mRNA 0 ] - concentration of the mRNA–ribosome complex [ mRNA j ] - concentration of the mRNA–ribosome complex with a nascent peptide chain of length j attached. reaction rate – k R [ R ][ mRNA ] - rate at which the mRNA–ribosome complex is formed (rate of binding of the mRNA to the ribosome) reaction rate j [ a j ][ mRNA j - 1 ] is the elongation rate (rate constant times the concentrations of the amino acid to be attached, and the mRNA–ribosome complex with the nascent chain)

22 Edda Klipp, Humboldt-Universität zu Berlin Modell for Elongation of a Peptid chain AEF-Tu:aa-tRNA complex. A1 - correct complex, and A2 - wrong complex. Bopen A-site on ribosome. In this configuration, the ribosome is available to any amino acid. Cinitial binding. Dcodon recognition. EGTPase activation and GTP hydrolysis. FEF-Tu released after EF-Tu conformation change. Gaccommodation and peptide transfer. A ready ribosome [ B ] initially binds (reversibly) with EF-Tu:aa-tRNA complex [ A ]. This is followed by codon recognition [ D ]. After codon recognition, GTPase activation and GTP hydrolysis follow successively [ E ]. EF-Tu then undergoes a conformation change allowing EF-Tu to be released [ F ]. At this point proofreading occurs. If the wrong aa-tRNA is present, it is rejected, and the A-site is open again [ B ]. If the correct aa-tRNA is present, it is accommodated and the peptide bond forms almost immediately [ G ]. The ribosome then resets back to its open position [ B ]. k 52 =0 incorrect aa-tRNA [ A 2 ] correct aa-tRNA [ A 1 ]

23 Edda Klipp, Humboldt-Universität zu Berlin Elongation model correct aa-tRNA [ A 1 ]

24 Edda Klipp, Humboldt-Universität zu Berlin Jacob-Monod-Modell Jacob, F. & Monod, J. (1961) On the Regulation of Gene Activity, Cold Spring Harb. Symp. Quant. Biol., 26, Modell of Griffith Griffith, J.S. (1971) Mathematical Neurobiology, Academic Press, London. Keener, J. & Sneyd, J. (1998) Mathematical Physiology, Springer-Verlag, New York. Nicolis-Prigogine-Modell Nicolis, G. & Prigogine, I. (1977) Self-Organization in Non-Equilibrium Systems, John Wiley & Sons, New York. Regulation der Genexpression am Beispiel des Lac-Operons

25 Edda Klipp, Humboldt-Universität zu Berlin Experimentelle Fakten Organismus: E.coli Bildung von Tryptophansynthase ist reguliert durch ein Strukturgen. In Abwesenheit von Tryptophan wird dieses Enzym synthetisiert. In Anwesenheit von Tryptophan wird seine Synthese gestoppt. Repression der Enzymsynthese: spezifisch für Enzyme des Trp-Syntheseweges Bildung des Enzyms -Galactosidase ist unter Kontrolle eines Strukturgens. In Abwesenheit eines Galactosides wird kaum -Galactosidase synthetisiert. Sobald Galactosid da ist, wird die Syntheserate um das fache gesteigert. Induktion der Enzymsynthese, ebenfalls sehr spezifisch

26 Edda Klipp, Humboldt-Universität zu Berlin

27 Jacob-Monod-Model

28 Edda Klipp, Humboldt-Universität zu Berlin Genaktivierung Durchschnittliche Produktion von mRNA Konzentrationsänderungen von Permease (E 1 ) und ß-Galactosidase (E 2 ) Laktose Aufnahme Interne Laktose (Aufnahme, Umwandlung zu Allolaktose) Allolaktose (von Laktose, to Glukose und Galaktose) Modell von Griffith Expressionsrate

29 Edda Klipp, Humboldt-Universität zu Berlin VereinfachungenQuasi-steady state für mRNA Gleiche Enzymkonzentrationen Keine Verzögerung in der Umwandlung von Laktose in Allolaktose Dimensionlose Variablen Gleichungssystem Modell von Griffith

30 Edda Klipp, Humboldt-Universität zu Berlin Lösung der Differentialgleichungen Parameter Anfangsbedingungen Modell von Griffith

31 Edda Klipp, Humboldt-Universität zu Berlin Catabolite Repression CAP = Catabolite Activator Protein CRP = cyclic AMP Receptor Protein positive regulation factor Aktives CAP bindet an die CAP Bindungsregion. Glukose reguliert die Catabolitrepression durch Senkung der freien cAMP-Konzentration.

32 Edda Klipp, Humboldt-Universität zu Berlin Lac-Operon, Gene regulation and CAP protein

33 Edda Klipp, Humboldt-Universität zu Berlin

34 Lac-Operon, Model of Nicolis and Prigogine R – Repressor I – Inducer E, M – Enzyme G – Glukose O – Operator

35 Edda Klipp, Humboldt-Universität zu Berlin Mathematical formulation of the Nicolis-Prigogine-Model

36 Edda Klipp, Humboldt-Universität zu Berlin

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42 Bakterielle Genexpression mit Reportergen gusA Quantifizierung der Regulation der Genexpression durch ein externes Signal, O 2 Operon cytNOQP von A. brasilense codiert eine Cytochrome cbb3 Oxidase, die bei Wachstum und Atmung eine Rolle spielt. Die Expression ist abhängig vom Sauerstoffgehalt. Die Expression von cytN wurde mittels der Fusion von cytN-gusA gemessen. Modell X – Biomasse-Konzentration S – Konzentration der Kohlenhydratquelle S in – Konz. der zugefütterten Kohlenhydrate P – Konzentration des Fusionsproteins D – Verdünnungsrate µ - spezifische Wachstumsrate – spezifische Kohlenstoffverbrauchsrate – spezifische Expressionsrate des Fusionsproteins k – Abbaurate des Fusionsproteins

43 Edda Klipp, Humboldt-Universität zu Berlin Bakterielle Genexpression mit Reportergen gusA Vorgegebenes Sauerstoffprofil Kohlenstoffquelle, Hier: Malat Verdünnungsrate Gus Aktivität ß-Glucuronidase als Maß für cytN-Expression


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