Computation by Synthetic Cell Signaling and Oscillating Processes - PowerPoint PPT Presentation

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Computation by Synthetic Cell Signaling and Oscillating Processes Modelled using Mass-Action Kinetics T.Hinze 1 R.Faßler 1 G.Escuela 2 B.Ibrahim 3 S.Schuster 1 {thomas.hinze,gabi.escuela,stefan.schu}@uni-jena.de, raf@minet.uni-jena.de, b.ibrahim@dkfz-heidelberg.de Friedrich Schiller University Jena 1 Department Bioinformatics at School of Biology/Pharmacy 2 Bio Systems Analysis Group 3 German Cancer Research Center Mol.Biol.of Centrosomes & Cilia Computability in Europe (CiE 2009) Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Outline Computation by Synthetic Cell Signaling 1. Motivation 2. Chemical information processing: Cell signaling 3. Mass-action kinetics 4. Deterministic register machine (RAM) 5. Chemical RAM representation • Clock # • Master-slave flip-flops • Registers • Program control time 1 0 0 1 1 0 0 6. Example 1: Integer addition 0 1 1 0 0 1 0 1 0 1 1 0 1 0 7. Example 2: Maximum of three nat. numbers 1 0 0 1 0 0 1 8. Outlook and acknowledgement Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Motivation • Chemical/Molecular computing • Potential high capacity and density of molecular data storage • Exploring similarities to biological information processing • Identification of computational units in biological systems [ A ] [ A ] (0) = 24 k A = 0,02 Stoffkonzentration R [ ] [ B ] (0) = 0 B B Stoffkonzentration • Artificial evolution of species concentration reaction networks towards specific tasks time Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Biological Principles of Cell Signaling external signal receptors ligands endocrine (dist.) hormones, factors, ... enzyme−linked paracrine (near) autocrine (same cell) ion−channel G−protein−linked GDP GTP activation cascade cell membrane cell response phospholipid bilayer phosphorylation ATP activation by protein kinases ADP gene expression signal transduction, transformation, amplification via pathways cytosol nucleus inner membrane genomic dna Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Typical Information Flow in Cell Signaling signal/stimulus K reception P A B information flow via P activation cascades (pathways) P C D P P E F P transduction: signal amplification, transformation, combination • Motif: stepwise protein activation by phosphorylation • Cascadization of motifs for signal transduction, amplification, transformation, combination Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Typical Information Flow in Metabolic Networks K1 K2 K3 A B C D A2 B’ B2 C’ C2 D’ • Sequence of catalyzed reactions • Reactants and products usually not acting as catalysts Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Mass-Action Kinetics: Background Modeling Temporal Behavior of Chemical Reaction Networks Assumption: number of effective reactant collisions Z proportional to reactant concentrations (Guldberg 1867) k ˆ A + B → C . . . . Z C ∼ [ A ] and Z C ∼ [ B ] , so − Z C ∼ [ A ] · [ B ] Production rate generating C : v prod ([ C ]) = ˆ k · [ A ] · [ B ] Consumption rate of C : . . . . . . v cons ([ C ]) = 0 d [ C ] = v prod ([ C ]) − v cons ([ C ]) d t d [ C ] k · [ A ] · [ B ] = ˆ d t Initial conditions: [ C ]( 0 ) , [ A ]( 0 ) , [ B ]( 0 ) to be set Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Mass-Action Kinetics: Background Modeling Temporal Behavior of Chemical Reaction Networks Assumption: number of effective reactant collisions Z proportional to reactant concentrations (Guldberg 1867) k ˆ A + B → C . . . . Z C ∼ [ A ] and Z C ∼ [ B ] , so − Z C ∼ [ A ] · [ B ] Production rate generating C : v prod ([ C ]) = ˆ k · [ A ] · [ B ] Consumption rate of C : . . . . . . v cons ([ C ]) = 0 d [ C ] = v prod ([ C ]) − v cons ([ C ]) d t d [ C ] k · [ A ] · [ B ] = ˆ d t Initial conditions: [ C ]( 0 ) , [ A ]( 0 ) , [ B ]( 0 ) to be set Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Mass-Action Kinetics: Background Modeling Temporal Behavior of Chemical Reaction Networks Assumption: number of effective reactant collisions Z proportional to reactant concentrations (Guldberg 1867) k ˆ A + B → C . . . . Z C ∼ [ A ] and Z C ∼ [ B ] , so − Z C ∼ [ A ] · [ B ] Production rate generating C : v prod ([ C ]) = ˆ k · [ A ] · [ B ] Consumption rate of C : . . . . . . v cons ([ C ]) = 0 d [ C ] = v prod ([ C ]) − v cons ([ C ]) d t d [ C ] k · [ A ] · [ B ] = ˆ d t Initial conditions: [ C ]( 0 ) , [ A ]( 0 ) , [ B ]( 0 ) to be set Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Mass-Action Kinetics: Background Modeling Temporal Behavior of Chemical Reaction Networks Assumption: number of effective reactant collisions Z proportional to reactant concentrations (Guldberg 1867) k ˆ A + B → C . . . . Z C ∼ [ A ] and Z C ∼ [ B ] , so − Z C ∼ [ A ] · [ B ] Production rate generating C : v prod ([ C ]) = ˆ k · [ A ] · [ B ] Consumption rate of C : . . . . . . v cons ([ C ]) = 0 d [ C ] = v prod ([ C ]) − v cons ([ C ]) d t d [ C ] k · [ A ] · [ B ] = ˆ d t Initial conditions: [ C ]( 0 ) , [ A ]( 0 ) , [ B ]( 0 ) to be set Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Mass-Action Kinetics: Background Modeling Temporal Behavior of Chemical Reaction Networks Assumption: number of effective reactant collisions Z proportional to reactant concentrations (Guldberg 1867) k ˆ A + B → C . . . . Z C ∼ [ A ] and Z C ∼ [ B ] , so − Z C ∼ [ A ] · [ B ] Production rate generating C : v prod ([ C ]) = ˆ k · [ A ] · [ B ] Consumption rate of C : . . . . . . v cons ([ C ]) = 0 d [ C ] = v prod ([ C ]) − v cons ([ C ]) d t d [ C ] k · [ A ] · [ B ] = ˆ d t Initial conditions: [ C ]( 0 ) , [ A ]( 0 ) , [ B ]( 0 ) to be set Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Mass-Action Kinetics: Background Modeling Temporal Behavior of Chemical Reaction Networks Assumption: number of effective reactant collisions Z proportional to reactant concentrations (Guldberg 1867) k ˆ A + B → C . . . . Z C ∼ [ A ] and Z C ∼ [ B ] , so − Z C ∼ [ A ] · [ B ] Production rate generating C : v prod ([ C ]) = ˆ k · [ A ] · [ B ] Consumption rate of C : . . . . . . v cons ([ C ]) = 0 d [ C ] = v prod ([ C ]) − v cons ([ C ]) d t d [ C ] k · [ A ] · [ B ] = ˆ d t Initial conditions: [ C ]( 0 ) , [ A ]( 0 ) , [ B ]( 0 ) to be set Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Mass-Action Kinetics: General ODE Model Chemical reaction system k 1 ˆ a 1 , 1 S 1 + a 2 , 1 S 2 + . . . + a n , 1 S n b 1 , 1 S 1 + b 2 , 1 S 2 + . . . + b n , 1 S n − → k 2 ˆ a 1 , 2 S 1 + a 2 , 2 S 2 + . . . + a n , 2 S n b 1 , 2 S 1 + b 2 , 2 S 2 + . . . + b n , 2 S n − → . . . k h ˆ a 1 , h S 1 + a 2 , h S 2 + . . . + a n , h S n b 1 , h S 1 + b 2 , h S 2 + . . . + b n , h S n , − → results in ordinary differential equations h n d [ S i ] � � [ S l ] a l ,ν k ν · ( b i ,ν − a i ,ν ) · ˆ i = 1 , . . . , n . � � = with d t l = 1 ν = 1 Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster

Motivation Cell Signaling Mass-Action Kinetics Chemical RAM Examples Outlook Mass-Action Kinetics: A Simple Example k 1 ˆ 2 A + 0 B 0 A + 1 B [ A ] [ A ] (0) = 24 − → k A = 0,02 Stoffkonzentration R B [ B ] [ B ] (0) = 0 Stoffkonzentration ODE system species concentration d [ A ] k 1 · [ A ] 2 − 2 · ˆ = d t d [ B ] k 1 · [ A ] 2 ˆ = d t Analytic solution time � − 1 � 1 [ A ]( t ) 2 ˆ k 1 t + [ A ]( 0 ) > 0 [ A ]( t ) = 0 = iff else [ A ]( 0 ) + [ A ]( 0 ) �� − 1 � � 1 [ B ]( t ) k 1 t + + [ B ]( 0 ) 2 ˆ = − 2 [ A ]( 0 ) 2 T. Hinze, M. Sturm. Rechnen mit DNA. ISBN 978-3-486-27530-5, Oldenbourg Wissenschaftsverlag, 2004 Computation by Synthetic Cell Signaling T. Hinze, R. Faßler, G. Escuela, B. Ibrahim, S. Schuster