here - iGEM
Contents
1. gt x t v e v is vector of N integers and represents state change caused by the firing of R 22 SSA initialize time and system state tsim 0 X 2 Xo simulation up to time T while t im lt T do evaluate a x 1 lt j lt M and aj x t sample time step from density of Eq 1 j sample reaction index from distribution of Eq 2 tmi Uim t X X Vj end 11 07 2013 232. 11 07 2013 16 Subtilin system Modelling Not possible to model a population in BioNetGen But there is a way to get around it A set of rules to mimic the effects of the changes in population can be created Set of logical functions is introduced Example 11 07 2013 17 Single Cell vs Hybrid Models 2 begin parameters k1 1e6 kir 1e 4 kp1 1e6 k3 5e4 k4 1e4 k5 0 25e4 9 k6 1e4 10 kdp1 1e1 11 kdeg 0 1 12 kdeg1 0 1 13 end parameters 14 15 16 begin molecule types 17 SigH a 18 PspaRK a 19 SpaRK a ps U P 20 SpaBTC a 21 SpaIGEF a 22 SpaS a 23 Subtilin a 24 end molecule types 25 26 begin seed species 27 SigH a 2e 6 28 PspaRK a 2e 10 29 Subtilin a 2e 7 30 end seed species 31 32 33 the actual reactions 34 begin reaction rules 35 Synthesis of Spa RK 36 SigH a PspaRK a gt SpaRK a ps U SigH a PspaRK a ki 37 Detection of external Subtilin 38 Subtilin a SpaRK a ps U gt SpaRK a ps P Subtilin a kp1 39 Activation of Spa 40 SpaRK ps P gt SpaS a SpaRK ps P k3 41 SpaRK ps P gt SpaBTC a SpaRK ps P k4 42 SpaRK ps P SpalGEF a SpaRK ps P k5 43 SpaRK ps P SpaRK ps U kdp1 44 Conversion into subtilin 1 A model of subtilin biosynthesis hybrid 2egin parameters 3 k1 1e6 kir 1e 4 kp1 1e6 k3 5e4 k4 1e4 k5 0 25e4 k6 1e3 kdp1 12 kdeg 0 00001 kdeg1 0 001 nd parameters 7egin molecule types 3 SigH a PspaRK
3. Complex Stochastic Modelling ODE only accurate at high concentrations Otherwise use stochastic modelling Quantities expressed as numbers of molecules Reactions only occur with certain probability Because reactions occur when molecules collide randomly Uses stochastic simulation algorithm SSA 11 07 2013 Stochastic Modelling We now deal with integer quantities of chemical species instead of continuous quantities X X X one molecule of X plus one molecule of X are transformed into one molecule of X Let s simulate one step X 5 X 4 X 5 n X24 X 0 X 1 Note You should avoid using more than 2 reagents in a reaction e g X X X3 gt X ODE vs SSA When the number of molecules is high SSA behaves like ODE 10 11 07 2013 ODE vs SSA Deterministic simulation of MM at high concentrations E 2 10 S 5 10 MM gdat 5 00E 05 4 4 00E 05 3 00E 05 4 2006 08 1 00E 05 A 0 00 E00 0 00E00 1 00E01 2 00E01 3 00E01 4 00E01 5 00E01 6 00E01 7 00E01 8 00E01 9 00E01 1 00E02 time Concentration Enzyme Substrate Product Complex ODE vs SSA e Stochastic simulation of MM at high molecule numbers start with E 12 000 S 36 000 MM ssa gdat time 11 11 07 2013 ODE vs SSA Stochastic simulation of MM at low molecule numbers E 100 S 300 MM gdat 3 00E02 2 50E02 2 00E02 1 50E02 amp 100E02 5 00E01 e an 0
4. 00 EOD rr 0 00E00 1 00ED 2 00601 3 00E0 1 4 00601 5 00E01 6 00E01 7 00E01 8 00E01 9 00E01 1 00EO2 time oncentration Enzyme Substrate Product Complex Which Type of Model to Use e At low molecule numbers use Stochastic model At high molecule numbers Both types of simulation can be used But SSA might require more computing power than the ODE simulation 12 11 07 2013 NFsim Complex pathways are 10 f ore i 8 amp Network generation time consuming to 10 4 ODEs P f SSA A simulate have to keep wv ts 4 track of every FO e state interaction NFsim a BioNetGen add on runs network free simulations only tracks 123456789 TM sites n the existing system Runtime CPU seconds Runtime increases exponentially with Much lower runtime complexity except for NFsim Diagram taken from NFsim user manual Examples Before going any further into examples do You have any questions 13 11 07 2013 Fundamental Operations BioNetGen Script is split into blocks each defining a different part of the model Parameters reaction rate constants and values for initial concentrations of species in the biological system Molecule types The molecules the model contains including their components and allowed component states e g phosphorylation sites Seed species The initial state of system ini
5. CH cH coo Malate CH HO CH coo L I Eo Krebs Cycle i M co Ou CH uL en HC Succinyl CoA CH Be GGriete lc COO n coo c 0 LS coo i CoA SH rhe COO CH l GD e n CH B i NAD FAD f ope T Source http www npr org blogs krulwich 2011 09 14 140428189 lord save me from the krebs cycle Diagrammatic Model Useful to visualise the reactions taking place Can t predict what will happen if you change the reaction conditions e g add more of one reactant Can t predict how the concentration of molecules will change with time 11 07 2013 Mathematical Model Predict changes in a system as time progresses e What can change Concentrations of Reactants Products Enzymes Which might lead to a change in the rate of reactions Mathematical Model e Often simulated as Ordinary differential equation ODE Deterministic e Stochastic Non deterministic Random process which evolves in time 11 07 2013 Introduction to SBML Systems Biology Markup Language Often used to write models in synthetic biology Difficult to write from scratch A common language for communication between software packages What is Rule Based Modelling Each molecule contains domains that can link to other molecules Complexes are built up by assembly of binding molecules Rules specify which reactions can occur and at what rate 11 07 2013 Why R
6. a SpaRK a ps U P SpaBTC a SpaIGEF a SpaS a Subtilin a Food 26nd molecule types 28egin seed species 29 SigH a 30 PspaRK a 31 Subtilin a 32 Food 33nd seed species 34 35egin observables Molecules SigH SigH a Molecules Promoter PspaRK a Molecules SpaRK SpaRK a ps U Molecules SpaRK1 SpaRK a ps P Molecules SpaBTC SpaBTC a Molecules SpalGEF SpaIGEF a Molecules SpaS SpaS a Molecules Subtilin Subtilin a Molecules f obs Food Single Cell vs Hybrid Models 25 26 begin seed species 27 SigHCa 2e 6 28 PspaRK a 2e 10 29 Subtilin a 2e 7 30 end seed species 31 32 3343 the actual reactions 34 begin reaction rules 35 Synthesis of Spa RK 36 SigH a PspaRK a gt SpaRK a ps U SigH a PspaRK a k1 37 Detection of external Subtilin 38 Subtilin a SpaRK a ps U SpaRK a ps P Subtilin a kp1 39 Activation of Spa 40 SpaRK ps P SpaS a SpaRK ps P k3 41 SpaRK ps P SpaBTC a SpaRK ps P k4 42 SpaRK ps P SpalGEF a SpaRK ps P k5 43 SpaRK ps P SpaRK ps U kdp1 44 Conversion into subtilin 45 SpaS a SpaBTC a Subtilin a SpaBTC a k6 46 SpaRK gt 0 kdeg1 47 SpaBTC gt 0 kdeg1 48 SpaIGEF gt kdegi 49 Subtilin a 0 kdeg 50 end reaction rules 51 52 53 begin observables 54 Molecules SigH SigH a 55 Molecules Promoter PspaRK a 56 Molecules SpaRK SpaRK a ps U 57 Molecules SpaRK1 SpaRK a ps P 58 Molecules SpaBTC SpaBTC a 5
7. 11 07 2013 Newcastle University Rule based modelling with BioNetGen INE veg ye AES oss cel 14 tes NUS Kw ua NM Ae a D te E X EM EBEA a M Bt Hor Se DINEM PREY See Le gt UE a a n A I Ses uv x AN MU E EE NE CES iGEM 2013 a l P e n TOY EN t e wh ies S Se i Ec D 2 Workshop Overview What is modelling e Why rule based modelling P Deterministic and Stochastic modelling Michaelis Menten model BioNetGen practice 11 07 2013 What is a Model Taken from the Oxford dictionary A three dimensional representation of a person or thing or of a proposed structure typically on a smaller scale than the original A thing used as an example to follow or imitate A simplified description especially a mathematical one of a system or process to assist calculations and predictions A person employed to display clothes by wearing them p ploy play y g a 999 Source http oxforddictionaries com definition english model http commons wikimedia org Modelling in Synthetic Biology Modelling traditionally used in biology to understand and imitate systems e Synthetic Biology utilizes modelling as a design to follow e g Predicting the effect of adding a BioBrick into our bacteria 11 07 2013 Modelling Biological Pathways coo ALIE H Na pia o c yY c coo NAD JY cu J cn n COO 5820 T coo Coo Y a CIID Isocitrate HO
8. 9 Molecules SpaIGEF SpaIGEF a 60 Molecules SpaS SpaS a Molecules Subtilin Subtilin a end observables 64 24 actions 65 generate network overwrite 1 66 67 Equilibratior simulate ode t end 100 n steps 1000 atol 1e 10 rtol 1e 8 sparse 1 B X subtilinhybrid gdat zh 47 Functions which relate single cell model to the change in the population 48 49 begin functions 50 Spark trnscr if f obs 1e 4 0 k1 51 52 f_decriQ if Subtilin lt 1 5e 4 amp amp f obs gt 9e 5 90 01 0 001 53 54 f incr if Subtilin gt 8e 4 Subtilin 0 005 0 55 Subt decr if f obs 3e 4 0 01 0 005 56 end functions 57 58 the actual reactions 59 begin reaction rules 60 Synthesis of Spa RK 61 SigH a PspaRK a gt SpaRK a ps U SigH a Spark trnscr 62 Detection of external Subtilin 63 Subtilin a SpaRK a ps U gt SpaRK a ps P Subtilin a kp1 64 Activation of SpaRK 65 SpaRK ps P SpaS a SpaRK ps P k3 66 SpaRK ps P SpaBTC a SpaRK ps P k4 67 SpaRK ps P gt SpalGEF a SpaRK ps P k5 68 SpaRK ps P gt SpaRK ps U kdp1 69 70 Degradati on of made products 71 SpaRK ps U gt 0 01 72 SpaBTC a gt 0 0 01 73 SpalGEF a gt 0 01 74 75 Decrease in subtilin as production stops and it diffu 76 Subtilin a gt 0 Subt decr es away degraded by IGEF 78 Conversion of SpaS into subtilin 79 SpaS a SpaBTC a g
9. S3 gt lt listOfProducts gt sn Ne S p e C l e S m u st b e lt apply gt Ae contained within the lt apply gt Bia model lt kineticLaw gt lt reaction gt lt listOfReactions gt lt model gt sbml Example of a Michaelis Menten ODE ing aaa Parameters which define j E ooo the rate of reaction 4 kir ie 4 S k2 0 1 6 end rameter 7 aaa List of the molecules d involved in the reaction 8begin molecule types 9 S a 10 E a NA P Starting concentrations of i2end molecule types molecules 13 begin seed species 14 S a 5e 5 15 E a 2e 5 16 P 0 17 end seed species Reactions that are 19 begin reaction rules going to be simulated 21 S a E a lt gt S a 1 E a 1 ki kir hc r 1 a u J FEN F EIB E Declaration of names of species 25 en r tion ru P r E which will be measured in the graph 25begin observables 26 Molecules Enzyme E a 27 Molecules Substrate S a 28 Molecules Product P 29 Molecules Complex S a 1 E a 1 30 end observables 32generate network ioverwrite 1 34 simulate ode t end 100 n steps 1000 atol 1e 10 rtol 1e 8 sparse 51 Concentration 11 07 2013 Michaelis Menten Simulation MM gdat 5 00E 05 4 00E 05 3 00E 05 200E05 1 00E 05 A 0 00 E00 0 00 EDD 1 00E01 2 00E01 3 00E01 4 00E01 5 00E01 6 00E01 7 00E01 8 00E01 9 00E01 1 00E02 time Enzyme Substrate Product
10. ath MathML apply plus cn 0 cn ci S4 ci lt apply gt lt math gt lt assignmentRule gt lt Global functions gt lt listOfRules gt lt listOfReactions gt lt reaction id R1 reversible false gt lt listOfReactants gt lt speciesReference species S1 gt lt speciesReference species S2 gt lt listOfReactants gt lt listOfProducts gt lt speciesReference species S4 gt lt listOfProducts gt kineticLaw math xmlnsz http www w3 org 1998 Math MathML apply times ci c1 ci ci S1 ci ci S2 ci lt apply gt 10 11 07 2013 11 07 2013 Simple Michaelis Menten Reaction lt math gt Writing models by lt reaction id R2 reversible false gt lt listOfReactants gt lt speciesReference species S4 gt lt listOfReactants gt h a N d l n S B M L l S lt listOfProducts gt lt speciesReference species S1 gt lt speciesReference species S2 gt Pere clearly difficult kineticLaw math xmlnsz http www w3 org 1998 Math MathML apply times s Written for the computer ci S4 ci s not the user lt reaction gt lt reaction id R3 reversible false gt posed species S4 gt ES Eve ry p ote nt l a lt listOfReactants gt lt listOfProducts gt lt speciesReference species S2 gt i n t e ra ct i O n b etwe e n speciesReference species
11. centrations Convert M moles per litre into molecule numbers 20 11 07 2013 Concentrations and molecules example For example let s try to convert M of the enzyme RibA to molecules number e RibA 25 107 M Volume of the cell is V 10 litres e Number of moles in the RibA enzyme is RibA V 5 10 22 To get number of molecules we need to multiply moles with Avogadro number n4 n RibA V n 5 107 Ordinary Differential Equation ODE e t works under three assumptions 1 Reactions always in well stirred homogenous media mass action kinetics 2 Quasi steady state assumption and substrate enzyme Michaelis Menten rate law 3 Concentrations are not small so we can use ODE s 21 11 07 2013 Stochastic modelling The state space of a stochastic model is thus a set of tuples E g the state of a 6 species model is a tuple X X2 X3 X4 Xs where each x is a natural number n theory the state space can be infinite the number of tuples not the length of each tuple Stochastic simulation algorithm SSA nitially developed to analyse and better understand various chemical reactions which include large number of species e Suppose system includes M chemical reactions R Ra f and N chemical species e x t x t x t is the state vector number of molecules of species of the system at a time t e When reaction R fires the system changes as x t
12. t Subtilin a SpaBTC a k6 80 81 Change in food do to population increase decrease 82 0 gt Food f incrO p decr 83 Food 0 f decr1Q 84 end reaction rules 86 87 8834 actions generate network overwrites 1 11 07 2013 18 Concentration Hybrid Model X Axis linear a Y Axis linear 0 Subtilin synthesis model gdat 2 00E 03 M 1 75E 03 1 50E 03 1 25E 03 1 00E 03 7 50E 04 5 00E 04 2 50E 04 0 00E00 0 00E00 2 50E01 5 00E01 7 50E01 1 00E02 time SigH Promoter SpaRK X SpaRK1 SpaBTC SpalGEF SpaS Subtilin Subtilin hybrid gdat 23 X Axis linear Y Axis linear ra Concentration Subtilin hybrid gdat 4 00E 04 3 50E 04 3 00E 04 2 50E 04 2 00E 04 1 50E 04 1 00E 04 5 00E 05 0 00E00 0 00E00 1 00E02 2 00E02 3 00E02 4 00E02 5 00E02 6 00E02 7 00E02 8 00E02 9 00E02 1 00E03 time SigH Promoter SpaRK SpaRK1 SpaBTC SpalGEF SpaS Subtilin f obs 11 07 2013 19 11 07 2013 A discrete time Markov chain Example of Markov chain All outgoing Rate parameter conversion Most of the papers use deterministic models e We might want to convert deterministic model ODE into non deterministic Stochastic We would need to convert deterministic rate constants the k s into stochastic rate constants the c s e First thing to do would be to deal with con
13. tial species and their concentrations Observables The model outputs Fundamental Operations BioNetGen Script is split into blocks each defining a different part of the model Functions Define global and or local functions of observables for use in rate laws Not essential Reaction rules Rules that describe how molecules interact Actions Network generation and simulation Each block must be enclosed with begin x and close x where x is the block in question e g begin parameters and end parameters 14 11 07 2013 Fundamental Operations BioNetGen To define a molecule a with 2 binding sites a b c Where the names of the binding sites are unimportant To define a phosphorylation site ps on molecule a a ps U P Where U represents one state unphosphorylated and P represents the other state phosphorylated Fundamental Operations BioNetGen To bind molecules a and b with binding sites b and a a b b a a b 1 b a 1 For the phosphorylation at site ps on molecule a a ps U gt a ps P Where molecule a has previously been defined as a ps U P 15 Thank you for your attention Subtilin production Natural antibiotic secreted by B subtilis in response to excessive growth Lack of food activates Subtilin production Immunity of cells e This system can be modeled using BioNetGen
14. tionz 30099 name P gt species id S4 compartment cell initialConcentrationz 1 name E a 1 S a 1 gt lt listOfSpecies gt lt listOfParameters gt lt Independent variables gt lt parameter id c1 value 0 00166 gt parameter id cir value 0 0001 gt lt parameter id c2 value 0 1 gt lt Dependent variables gt lt Observables gt lt parameter id Enzyme constant false gt lt parameter id Substrate constant false gt lt parameter id Product constant false gt lt parameter id Complex constant false gt lt Global functions gt lt listOfParameters gt lt listOfRules gt lt Dependent variables gt lt Observables gt lt assignmentRule variable Enzyme gt math xmlIns http www w3 org 1998 Math MathML gt lt apply gt lt plus gt lt cn gt 0 lt cn gt ci S2 ci lt apply gt lt math gt lt assignmentRule gt lt assignmentRule variable Substrate gt math xmlnsz http www w3 org 1998 Math MathML apply plus cn 0 cn ci S1 ci lt apply gt lt math gt lt assignmentRule gt lt assignmentRule variable Product gt math xmIns http www w3 org 1998 Math MathML gt lt apply gt lt plus gt cn 0 lt cn gt ci S3 lt ci gt lt apply gt lt math gt lt assignmentRule gt lt assignmentRule variable Complex gt math xmlnsz http www w3 org 1998 M
15. ule Based Modelling e In modelling each different State is usually treated as a 108 separate species B Reactions Molecular species Rules 10 But with rule based 10 modelling you can define a 103 molecule with multiple states 10 This saves time and effort 10 123456789 Sites n Sneddon MW Faeder JR and Emonet T Efficient modeling simulation and coarse graining of biological complexity with NFsim Nature Methods 2011 8 2 177 83 Michaelis Menten MM Rate Law e Enzyme Substrate amp Enzyme Substrate Complex e Enzyme Substrate Complex gt Product Enzyme e The M M rate law Vinax 5 Vmax Ky E ES Michaelis Menten Rate Law concentration time Figure 8 3 A First Course in Systems Biology Garland Science 2013 10 reaction speed 0 O Ky 5 concentration of S B 1 Vmax Simple Michaelis Menten Reaction lt xml versionz 1 0 encoding UTF 8 gt lt Created by BioNetGen 2 2 4 gt sbml xmlnsz http www sbml org sbml level2 level 2 version 1 gt model id MM ssa gt lt listOfCompartments gt compartment id cell sizez 1 lt listOfCompartments gt lt listOfSpecies gt species id S1 compartment cell initialConcentration 0 name S a gt species id S2 compartment cell initialConcentration 11999 name E a gt species id S3 compartment cell initialConcentra
Download Pdf Manuals
Related Search