Synthetic Biology: Modelling and
                        Optimisation
                                                  Na...
Outline
   •Brief Introduction to Computational Modeling
   •Modeling for Top Down SB
    •Executable Biology
    •A pinch...
Outline
   •Brief Introduction to Computational Modeling
   •Modeling for Top Down SB
    •Executable Biology
    •A pinch...
Synthetic Biology
   • Aims at designing, constructing and developing artificial biological
   systems

   •Offers new rou...
Models and Reality
     •The use of models is intrinsic to any
     scientific activity.

     •Models are abstractions of...
What is modelling?
     • Is an attempt at describing in a
     precise way an understanding of the
     elements of a sys...
•“feature selection” is the first issue one
     must confront when building a model

     •One starts from a system of in...
The goals of Modelling
     •To capture the essential features of
     a biological entity/phenomenon
     •To disambiguat...
•There is potentially a distinction between modelling for Synthetic Biology
 and Systems Biology:
       •Systems Biology ...
•There is potentially a distinction between modelling for Synthetic Biology
 and Systems Biology:
       •Systems Biology ...
Thus, Multi-Scale Modelling in the 2 SBs seek
     to produce computable understanding
     integrating massive datasets a...
The Pragmalogical Problem of
            Modelling in XXI century Biology
        • XXI century Biology brings to the fore...
The Pragmalogical Problem of
            Modelling in XXI century Biology
        • XXI century Biology brings to the fore...
 Modelling relies on rigorous computational,
     engineering and mathematical tools &
     techniques
    However, the ...
Modelling as a constrained
                           scientific art
       Although modelling lies at the interface of a...
The Scale Separation Map
       The Scale Separation Map is an
        abstraction recently proposed by Hoekstra
        ...
The Scale Separation Map
     A Cellular Automata is defined as:
 C= < A(Δx, Δt,L,T), S, R, G, F >


 A is a spatial doma...
          A Scale Separation Map (SSM) is a two dimensional
                          map with horizontal axis representi...
          A Scale Separation Map (SSM) is a two dimensional
                          map with horizontal axis representi...
          A Scale Separation Map (SSM) is a two dimensional
                          map with horizontal axis representi...
          A Scale Separation Map (SSM) is a two dimensional
                          map with horizontal axis representi...
          A Scale Separation Map (SSM) is a two dimensional
                          map with horizontal axis representi...
          A Scale Separation Map (SSM) is a two dimensional
                          map with horizontal axis representi...
Even within a single cell the space & time
              scale separations are important
                                 ...
The Scale Separation Map
                                                      • With sufficient data each process can be
...
Modelling Approaches

      There exist many modelling approaches, each with its
      advantages and disadvantages.
     ...
Modelling Frameworks
     •Denotational Semantics Models:
     Set of equations showing relationships between molecular
  ...
Tools Suitability and Cost
       From [D.E Goldberg, 2002] (adapted):
        “Since science and math are in the descrip...
Tools Suitability and Cost
                              Low cost/                                                      Hi...
From [Di Ventura et al., Nature, 2006]
                             Low cost/                         High cost/
         ...
From [Di Ventura et al., Nature, 2006]
                             Low cost/                         High cost/
         ...
From [Di Ventura et al., Nature, 2006]
                             Low cost/                         High cost/
         ...
24 /203

Thursday, 9 July 2009
Stochasticity in Cellular Systems
         Most commonly recognised sources of noise in cellular system are low
         ...
Towards Executable Modells for SBs
        “Although the road ahead is long and winding, it leads to a
           future w...
There are good reasons to think that information
   processing is a key viewpoint to take when modeling

   Life as we kno...
    It thus makes sense to use methodologies
           designed to cope with complex,
           concurrent, interactive...
InfoBiotics
                                  www.infobiotic.net
     •The utilisation of cutting-edge information
     pr...
Modeling in Systems & Synthetic Biology

      Systems Biology                         Synthetic Biology
                 ...
Model Design in Systems/Synthetic Biology
   • It is a hard process to design suitable models in systems/
   synthetic bio...
How you select features, disambiguate and
quantify depends on the goals behind your
modelling enterprise.
                ...
Model Development
          From [E. Klipp et al, Systems Biology in Practice,
           2005]
         1.      Formulat...
Outline
   •Brief Introduction to Computational Modeling
   •Modeling for Top Down SB
    •Executable Biology
    •A pinch...
Executable Biology with P systems
       Field of membrane computing initiated by
        Gheorghe Păun in 2000
       I...
Functional Entities
                                      Container
        • A boundary defining self/non-self (symmetry ...
Distributed and parallel rewritting systems in
      compartmentalised hierarchical structures.


                        ...
Cell-like P systems
  Intuitive Visual representation
  as a Venn diagram with a
  unique superset and without
  intersect...
Cell-like P systems
  Intuitive Visual representation
  as a Venn diagram with a
  unique superset and without
  intersect...
Cell-like P systems
  Intuitive Visual representation
  as a Venn diagram with a
  unique superset and without
  intersect...
P-Systems: Modelling Principles
       Molecules                  Objects
       Structured Molecules       Strings
      ...
Stochastic P Systems




                        40 /203

Thursday, 9 July 2009
Rewriting Rules




    used by Multi-volume Gillespie’s algorithm
                        41 /203

Thursday, 9 July 2009
Molecular Species
                                 A molecular species can be represented using
                         ...
Molecular Interactions
                                     Comprehensive and relevant rule-based schema
                ...
Compartments / Cells
                                     Compartments and regions are explicitly
                       ...
Colonies / Tissues
                                     Colonies and tissues are representing as
                        ...
Molecular Interactions
                        Inside Compartments




                        46 /203

Thursday, 9 July 2...
Passive Diffusion of Molecules




                        47 /203

Thursday, 9 July 2009
48 /203

Thursday, 9 July 2009
a                 b       Transport Modalities


                                                    a       b    Antiport...
Transport Modalities



                                   5         2
                                                   ...
Transport Modalities




                                              Highly specific:
                                  ...
Signal Sensing and
                             Active Transport




                        52 /203

Thursday, 9 July 2009
Specification of Transcriptional
                  Regulatory Networks




                        53 /203

Thursday, 9 Ju...
Transcription as Rewriting Rules on
     Multisets of Objects and Strings




                        54 /203

Thursday, 9...
Translation as Rewriting Rules on
        Multisets of Objects and Strings




                        55 /203

Thursday, ...
Post-Transcriptional Processes
         For each protein in the system, post-transcriptional processes like
          tra...
Scalability through Modularity

          Cellular functions arise from orchestrated
           interactions between moti...
Basic P System Modules Used




                        58 /203

Thursday, 9 July 2009
Modularity in Gene Regulatory
                        Networks
   Cis-regulatory modules
    are nonrandom clusters of
  ...
Modularity in Gene Regulatory
                        Networks                   AHL
                                     ...
Modularity in Gene Regulatory
                        Networks                   AHL
                                     ...
Representing transcriptional
                      fusions
       Objects Variables can be instantiated with the name of ...
Representing transcriptional
                      fusions
       Objects Variables can be instantiated with the name of ...
Representing transcriptional
                      fusions
       Objects Variables can be instantiated with the name of ...
Representing transcriptional
                      fusions
       Objects Variables can be instantiated with the name of ...
Representing transcriptional
                      fusions
       Objects Variables can be instantiated with the name of ...
Representing transcriptional
                      fusions
       Objects Variables can be instantiated with the name of ...
Representing transcriptional
                      fusions
       Objects Variables can be instantiated with the name of ...
Representing Directed Evolution
       Variables for stochastic constants can be instantiated
        with specific value...
Representing Directed Evolution
       Variables for stochastic constants can be instantiated
        with specific value...
Representing Directed Evolution
       Variables for stochastic constants can be instantiated
        with specific value...
Representing Directed Evolution
       Variables for stochastic constants can be instantiated
        with specific value...
Representing synthetic
                        transcriptional networks
       The genes used to instantiate variables in...
Representing synthetic
                        transcriptional networks
       The genes used to instantiate variables in...
Stochastic P Systems
       Gillespie Algorithm (SSA) generates trajectories of a stochastic
        system consisting of...
Multicompartmental Gillespie
               Algorithm




                        64 /203

Thursday, 9 July 2009
Multicompartmental Gillespie
               Algorithm
                                          1
                        ...
Multicompartmental Gillespie
               Algorithm
                                                    1
              ...
Multicompartmental Gillespie
               Algorithm
                                                    1
              ...
Multicompartmental Gillespie
               Algorithm
                                                    1
              ...
Multicompartmental Gillespie
               Algorithm
                                                    1
              ...
Multicompartmental Gillespie
               Algorithm
                                                    1
              ...
Multicompartmental Gillespie
               Algorithm
                                                    1
              ...
Multicompartmental Gillespie
               Algorithm
                                                    1
              ...
Multicompartmental Gillespie
               Algorithm
                                                    1
              ...
Multicompartmental Gillespie
               Algorithm
                                                    1
              ...
Multicompartmental Gillespie
               Algorithm
                                                    1
              ...
Multicompartmental Gillespie
               Algorithm
                                                      1
            ...
Multicompartmental Gillespie
               Algorithm
                                                        1
          ...
   Using P systems modules one can model a large variety of
       commonly occurring BRN:

            Gene Regulatory ...
InfoBiotics
                                   Pipeline




                        66 /203

Thursday, 9 July 2009
SBML from CellDesigner




                        67 /203

Thursday, 9 July 2009
Runs simulations and extract data




                        68 /203

Thursday, 9 July 2009
Plot Timeseries




                        69 /203

Thursday, 9 July 2009
in time and space




                        70 /203

Thursday, 9 July 2009
Synthetic Biology Examples




                        71 /203

Thursday, 9 July 2009
Multi-component negative-
                  feedback oscillator




            Oscillations caused by time-delayed negati...
Multi-component negative-
                     feedback oscillator
          Mathematical model
             −   Xc = [mR...
Single protein represses gene
                  p=1




                        74 /203

Thursday, 9 July 2009
When repression is weak
                   (dissociation rate = 10)




             No obvious oscillatory behaviour in s...
When repression is weak
                         (dissociation rate = 10)




             Mean of 100 runs shows converge...
When repression is strong
                  (dissociation rate = 0.1)




                           Oscillations evident ...
When repression is strong
                         (dissociation rate = 0.1)




         Averging 100 runs dampens oscill...
Repressor binding sequence
      When p=2 there are two possible scenarios:
        – First protein binds to second prote...
1. Protein represses as dimer




                        80 /203

Thursday, 9 July 2009
1. Protein represses as dimer




                                           target




        mRNA levels oscillate read...
2. Proteins repress cooperatively




                        82 /203

Thursday, 9 July 2009
2. Proteins repress cooperatively




                                                          target




         Oscill...
An example: Ron Weiss' Pulse Generator

       Two different bacterial strains carrying specific synthetic
        gene r...
Sending Cells




                        85 /203

Thursday, 9 July 2009
Sending Cells




                        85 /203

Thursday, 9 July 2009
Sending Cells




  Pconst




                        85 /203

Thursday, 9 July 2009
Sending Cells




  Pconst
               luxI




                        85 /203

Thursday, 9 July 2009
Sending Cells

                                      Pconst({X = luxI },…)



  Pconst
               luxI




           ...
Sending Cells
                                  AHL


                                        Pconst({X = luxI },…)
      ...
Pulse Generating Cells




                        86 /203

Thursday, 9 July 2009
Pulse Generating Cells




                        86 /203

Thursday, 9 July 2009
Pulse Generating Cells

                   LuxR



  Pconst
                luxR




                        86 /203

Thur...
Pulse Generating Cells
                          AHL


                       AHL
                   LuxR



  Pconst
    ...
Pulse Generating Cells
                          AHL


                       AHL
                   LuxR                 ...
Pulse Generating Cells
                          AHL


                       AHL
                   LuxR                 ...
Pulse Generating Cells
                          AHL


                       AHL
                   LuxR                 ...
Pulse Generating Cells
                          AHL


                       AHL                              Pconst({X=l...
Spatial Distribution of Senders
                                         and Pulse Generators
                   AHL
     ...
AHL
                                    Spatial Distribution of Senders
                                         and Pulse...
Wave propagation
                                    simulation I




                                    SIMULATION I



...
Pulse Generating Cells
                            AHLWith Relay
                            AHL
                        L...
Pulse Generating Cells
                            AHLWith Relay
                            AHL
                        L...
Pulse Generating Cells
                            AHLWith Relay
                            AHL                          ...
Pulse Generating Cells
                            AHLWith Relay
                            AHL                          ...
Pulse Generating Cells
                            AHLWith Relay
                            AHL                          ...
Pulse Generating Cells
                            AHLWith Relay
                            AHL                          ...
Pulse Generating Cells
                            AHLWith Relay
                            AHL                          ...
Pulse Generating Cells
                            AHLWith Relay
                            AHL                          ...
Pulse Generating Cells
                            AHLWith Relay
                            AHL                          ...
Wave propagation
                                   simulation II



                                   SIMULATION II




...
AHL
                                                  Spatial Distribution of
                                            ...
Wave propagation with
                                  Four Droplets of Signal



                                      S...
Pulse Generating Cells
                            AHLWith Relay
                        LuxR
                            ...
Combining Complex Modules
                            AHL


                            AHL                     Inverter(X...
Combining Complex Modules
                            AHL


                            AHL                        Inverte...
Inversion Through a
                                   Propagating Wave



                                   SIMULATION I...
Outline
   •Brief Introduction to Computational Modeling
   •Modeling for Top Down SB
    •Executable Biology
    •A pinch...
Probabilistic Model Checking
      A precise computational/mathematical model allows
       us to perform formal verifica...
P Systems and PRISM
                        P System Component           PRISM Component
                                 ...
Post-transcriptional Regulation



                                              Post-transcriptional
                    ...
Post-transcriptional Regulation
                                           R = ? [ I = 240 ]




                         ...
Positive Regulation




   [ TF + gene ] b  [ TF.gene ] b   con

   [ TF.gene ] b  [ TF + gene ] b   coff

   [ gene ]b ...
Positive Regulation
                 R = ? [ C <= 100 ]                           R = ? [ C <= 100 ]




                 ...
Model Checking on the Pulse
               Generator
       The simulation of the Pulse Generator show some interesting
 ...
Model Checking on the Pulse
                Generator
          The simulations show that although the number of signals
...
   We studied the expected number of GFP molecules produced over time for
     different increase rates of AHL.

        ...
   In order to get a clearer idea, the probability distribution of the number of
       GFP molecules at 60 minutes was c...
     Finally, assuming that for a cell to be fluorescence it needs to have a given
       number of GFP for an appreciabl...
Outline
   •Brief Introduction to Computational Modeling
   •Modeling for Top Down SB
    •Executable Biology
    •A pinch...
A (Proto)Cell as an Information
                    Processing Device




                   LeDuc et al. Towards an in vi...
Towards a synthetic cell from
                   the bottom up
         Biocompatible vesicles as long-circulating carrie...
Vesicle Biorecognition




                             Pasparakis, G. et al, Angew Chem Int Ed. 2008 47 (26), 4847-4850

...
‘Talking’ to cell-vesicle aggregates




                              Pasparakis, G. Angew Chem Int Ed. 2008 47 (26), 484...
Outline
   •Brief Introduction to Computational Modeling
   •Modeling for Top Down SB
    •Executable Biology
    •A pinch...
Dissipative Particle Dynamics
   Simulate movement of particles which represent several
    atoms / molecules
   Calcula...
Dissipative Particle Dynamics
     First introduced by Hoogerbrugge and Koelmann in 1992.
     Statistical mechanics of ...
Dissipative Particle Dynamics
        Conservative Force

                                   i W
                         ...
Dissipative Particle Dynamics
          Polymers
          A number of simulation beads are tied together to
           ...
Liposome Formation in DPD




                        118 /203

Thursday, 9 July 2009
119 /203

Thursday, 9 July 2009
Case Study One: Vesicle Diffusion
  Polar heads


  Non polar tails


        Pores




           J. Smaldon, J. Blake, D...
Case Study One: Vesicle
                          Diffusion
          The regions were formed by allowing vesicles to sel...
122 /203

Thursday, 9 July 2009
Case Study One: Vesicle Diffusion
   Tagged solvent particles were placed within the liposome inner
   volume, the change ...
Case Study Two: Liposome
                        Logic
          The behaviour of some prokaryotic RNA
           transcr...
125 /203

Thursday, 9 July 2009
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
Synthetic Biology -  Modeling and Optimisation
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Synthetic Biology - Modeling and Optimisation

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This tutorial was given at GECCO 2009. It updates and extends the slideshow "Executable Biology Tutorial"

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Synthetic Biology - Modeling and Optimisation

  1. 1. Synthetic Biology: Modelling and Optimisation Natalio Krasnogor ASAP - Interdisciplinary Optimisation Laboratory School of Computer Science Centre for Integrative Systems Biology School of Biology Centre for Healthcare Associated Infections Institute of Infection, Immunity & Inflammation University of Nottingham Copyright is held by the author/owner(s). GECCO’09, July 8–12, 2009, Montréal Québec, Canada. ACM 978-1-60558-505-5/09/07. 1 /203 Thursday, 9 July 2009
  2. 2. Outline •Brief Introduction to Computational Modeling •Modeling for Top Down SB •Executable Biology •A pinch of Model Checking •Modeling for the Bottom Up SB •Dissipative Particle Dynamics •Automated Model Synthesis and Optimisation •Conclusions 2 /203 Thursday, 9 July 2009
  3. 3. Outline •Brief Introduction to Computational Modeling •Modeling for Top Down SB •Executable Biology •A pinch of Model Checking •Modeling for the Bottom Up SB •Dissipative Particle Dynamics •Automated Model Synthesis and Optimisation •Conclusions 3 /203 Thursday, 9 July 2009
  4. 4. Synthetic Biology • Aims at designing, constructing and developing artificial biological systems •Offers new routes to ‘genetically modified’ organisms, synthetic living entities, smart drugs and hybrid computational-biological devices. • Potentially enormous societal impact, e.g., healthcare, environmental protection and remediation, etc • Synthetic Biology's basic assumption: • Methods commonly used to build non-biological systems could also be use to specify, design, implement, verify, test and deploy novel synthetic biosystems. • These method come from computer science, engineering and maths. • Modelling and optimisation run through all of the above. 4 /203 Thursday, 9 July 2009
  5. 5. Models and Reality •The use of models is intrinsic to any scientific activity. •Models are abstractions of the real-world that highlight some key features while ignoring others that are assumed to be not relevant. •A model should not be seen or presented as representations of the truth, but instead as a statement of our current knowledge. 5 /203 Thursday, 9 July 2009
  6. 6. What is modelling? • Is an attempt at describing in a precise way an understanding of the elements of a system of interest, their states and interactions • A model should be operational, i.e. it should be formal, detailed and “runnable” or “executable”. 6 /203 Thursday, 9 July 2009
  7. 7. •“feature selection” is the first issue one must confront when building a model •One starts from a system of interest and then a decision should be taken as to what will the model include/leave out •That is, at what level the model will be built 7 /203 Thursday, 9 July 2009
  8. 8. The goals of Modelling •To capture the essential features of a biological entity/phenomenon •To disambiguate the understanding behind those features and their interactions •To move from qualitative knowledge towards quantitative knowledge 8 /203 Thursday, 9 July 2009
  9. 9. •There is potentially a distinction between modelling for Synthetic Biology and Systems Biology: •Systems Biology is concerned with Biology as it is •Synthetic Biology is concerned with Biology as it could be “Our view of engineering biology focuses on the abstraction and standardization of biological components” by R. Rettberg @ MIT newsbite August 2006. “Well-characterized components help lower the barriers to modelling. The use of control elements (such as temperature for a temperature-sensitive protein, or an exogenous small molecule affecting a reaction) helps model validation” by Di Ventura et al, Nature, 2006 9 /203 Thursday, 9 July 2009
  10. 10. •There is potentially a distinction between modelling for Synthetic Biology and Systems Biology: •Systems Biology is concerned with Biology as it is •Synthetic Biology is concerned with Biology as it could be “Our view of engineering biology focuses on the abstraction and standardization of biological components” by R. Rettberg @ MIT newsbite August 2006. “Well-characterized components help lower the barriers to modelling. The use of control elements (such as temperature for a temperature-sensitive protein, or an exogenous small molecule affecting a reaction) helps model validation” by Di Ventura et al, Nature, 2006 Co-design of parts and their models hence improving and making both more reliable 9 /203 Thursday, 9 July 2009
  11. 11. Thus, Multi-Scale Modelling in the 2 SBs seek to produce computable understanding integrating massive datasets at various levels of details simultaneously Progress Organ Individual Cell colony Cells Regulatory Networks Proteins DNA/RNA Time 10 /203 Thursday, 9 July 2009
  12. 12. The Pragmalogical Problem of Modelling in XXI century Biology • XXI century Biology brings to the fore the ubiquitous philosophical questions in complex systems, that of emergent behavior and the tension between reductionism and holistic approaches to science. • Synthetic Biology (and SysBio) has, however, a very pragmatic agenda: the engineering and control of novel biological systems • The pragmalogical problem: If each subcomponent of a living system (and processes/components therein) are understood… Can we say that the system is understood? That is, can we assume that the system = ∑parts ? • More importantly: can we control that biosystem? 11 /203 Thursday, 9 July 2009
  13. 13. The Pragmalogical Problem of Modelling in XXI century Biology • XXI century Biology brings to the fore the ubiquitous philosophical questions in complex systems, that of emergent behavior and the tension between reductionism and holistic approaches to science. & Integrative • Synthetic Biology (and SysBio) has, however, a very pragmatic agenda: the engineering and control of novel biological systems • The pragmalogical problem: If each subcomponent of a living system (and processes/components therein) are understood… Can we say that the system is understood? That is, can we assume that the system = ∑parts ? • More importantly: can we control that biosystem? 11 /203 Thursday, 9 July 2009
  14. 14.  Modelling relies on rigorous computational, engineering and mathematical tools & techniques  However, the act of modelling remains at the interface between art and science  Undoubtedly, a multidisciplinary endeavour 12 /203 Thursday, 9 July 2009
  15. 15. Modelling as a constrained scientific art  Although modelling lies at the interface of art and science there are guidelines we can follow  Some examples:  The scale separation map [Hoekstra et al, LNCS 4487, 2007]  Tools suitability & cost [Goldberg, 2002] 13 /203 Thursday, 9 July 2009
  16. 16. The Scale Separation Map  The Scale Separation Map is an abstraction recently proposed by Hoekstra and co-workers [Hoekstra et al, LNCS 4487, 2007]  Introduced in the context of Multi-scale modelling with cellular automata but the core concepts still valid for other modelling techniques 14 /203 Thursday, 9 July 2009
  17. 17. The Scale Separation Map  A Cellular Automata is defined as: C= < A(Δx, Δt,L,T), S, R, G, F > A is a spatial domain made of cells of size Δx with a total size of L The simulation clock ticks every Δt units for a total of T units T We can simulate processes: Δt  as fast as Δt for as long as T units  ranging from Δx to L sizes. Δx L L 15 /203 Thursday, 9 July 2009
  18. 18.  A Scale Separation Map (SSM) is a two dimensional map with horizontal axis representing time and vertical axis representing space 1 0 B ξB A ξA τB Spatial scale (log) τA 3.1 2 3.2 Temporal scale (log) 16 /203 Thursday, 9 July 2009
  19. 19.  A Scale Separation Map (SSM) is a two dimensional map with horizontal axis representing time and vertical axis representing space • Region 0: A and B overlap  single scale multi-science 1 0 model A ξA • Region 1: ξA ≈ ξB ^ τA > τB B ξB  temporal scale separation Spatial scale (log) τA • Region 2: ξA > ξB ^ τB ≈ τA τB  coarse and fine structures 3.1 2 3.2 in similar timescales • Region 3.1: ξA > ξB ^ τB < τA  familiar micro-macro models • Region 3.2: ξA > ξB ^ τB > τA  small and slow process linked to a fast and Temporal scale (log) large process (e.g. Blood flood and artery repair) 16 /203 Thursday, 9 July 2009
  20. 20.  A Scale Separation Map (SSM) is a two dimensional map with horizontal axis representing time and vertical axis representing space • Region 0: A and B overlap  single scale multi-science 1 0 model A ξA • Region 1: ξA ≈ ξB ^ τA > τB B ξB  temporal scale separation Spatial scale (log) τA • Region 2: ξA > ξB ^ τB ≈ τA τB  coarse and fine structures 3.1 2 3.2 in similar timescales • Region 3.1: ξA > ξB ^ τB < τA  familiar micro-macro models • Region 3.2: ξA > ξB ^ τB > τA  small and slow process linked to a fast and Temporal scale (log) large process (e.g. Blood flood and artery repair) 16 /203 Thursday, 9 July 2009
  21. 21.  A Scale Separation Map (SSM) is a two dimensional map with horizontal axis representing time and vertical axis representing space • Region 0: A and B overlap  single scale multi-science 1 0 model A ξA • Region 1: ξA ≈ ξB ^ τA > τB  temporal scale separation Spatial scale (log) τA • Region 2: ξA > ξB ^ τB ≈ τA  coarse and fine structures 3.1 2 3.2 in similar timescales • Region 3.1: ξA > ξB ^ τB < τA  familiar micro-macro models B ξB • Region 3.2: ξA > ξB ^ τB > τB τA  small and slow process linked to a fast and Temporal scale (log) large process (e.g. Blood flood and artery repair) 16 /203 Thursday, 9 July 2009
  22. 22.  A Scale Separation Map (SSM) is a two dimensional map with horizontal axis representing time and vertical axis representing space • Region 0: A and B overlap  single scale multi-science 1 0 model A ξA • Region 1: ξA ≈ ξB ^ τA > τB  temporal scale separation Spatial scale (log) τA • Region 2: ξA > ξB ^ τB ≈ τA  coarse and fine structures 3.1 2 3.2 in similar timescales • Region 3.1: ξA > ξB ^ τB < τA  familiar micro-macro models • Region 3.2: ξA > ξB ^ τB > B ξB τA  small and slow τB process linked to a fast and Temporal scale (log) large process (e.g. Blood flood and artery repair) 16 /203 Thursday, 9 July 2009
  23. 23.  A Scale Separation Map (SSM) is a two dimensional map with horizontal axis representing time and vertical axis representing space • Region 0: A and B overlap  single scale multi-science 1 0 model A ξA • Region 1: ξA ≈ ξB ^ τA > τB  temporal scale separation Spatial scale (log) τA • Region 2: ξA > ξB ^ τB ≈ τA  coarse and fine structures 3.1 2 3.2 in similar timescales • Region 3.1: ξA > ξB ^ τB < τA  familiar micro-macro models B ξB • Region 3.2: ξA > ξB ^ τB > τB τA  small and slow process linked to a fast and Temporal scale (log) large process (e.g. Blood flood and artery repair) 16 /203 Thursday, 9 July 2009
  24. 24. Even within a single cell the space & time scale separations are important E.g.: • Within a cell the dissociation constants of DNA/ transcription factor binding to specific/non- specific sites differ by 4-6 orders of magnitude • DNA protein binding occurs at 1-10s time scale very fast in comparison to a cell’s life cycle. [F.J. Romero Campero, 2007] 17 /203 Thursday, 9 July 2009
  25. 25. The Scale Separation Map • With sufficient data each process can be assigned its space-time region unambiguously Couplings, e.g. F • A given process may well have its Δx (respectively Δt) > than another’s ξA (respectively τA) Spatial scale (log) • Hence different processes in the SSM might require different modelling techniques Temporal scale (log) 18 /203 Thursday, 9 July 2009
  26. 26. Modelling Approaches There exist many modelling approaches, each with its advantages and disadvantages. Macroscopic, Microscopic and Mesoscopic Quantitative and qualitative Discrete and Continuous Deterministic and Stochastic Top-down or Bottom-up 19 /203 Thursday, 9 July 2009
  27. 27. Modelling Frameworks •Denotational Semantics Models: Set of equations showing relationships between molecular quantities and how they change over time. They are approximated numerically. (I.e. Ordinary Differential Equations, PDEs, etc) •Operational Semantics Models: Algorithm (list of instructions) executable by an abstract machine whose computation resembles the behaviour of the system under study. (i.e. Finite State Machine) Jasmin Fisher and Thomas Henzinger. Executable cell biology. Nature Biotechnology, 25, 11, 1239-1249 (2008) 20 /203 Thursday, 9 July 2009
  28. 28. Tools Suitability and Cost  From [D.E Goldberg, 2002] (adapted): “Since science and math are in the description business, the model is the thing…The engineer or inventor has much different motives. The engineered object is the thing” ε, error Synthetic Biologist Computer Scientist/Mathematician C, cost of modelling 21 /203 Thursday, 9 July 2009
  29. 29. Tools Suitability and Cost Low cost/ High cost/ High error Low error Adapted from [Goldberg 2002] Unarticulated Articulated Dimensional Facetwise Equations wisdom Qualitative models models Of motion models Chemical Bioinformatic Biopolimer Microarrays and G.E. Markup Language Sequence Markup Markup Language Markup Language (CML) Language (BSML) (BioML) (MAGEML) Cell Systems Biology Mathematics Markup Language Markup Language Markup Language (MathML) (SBML) (MathML) 22 /203 Thursday, 9 July 2009
  30. 30. From [Di Ventura et al., Nature, 2006] Low cost/ High cost/ High error Low error Unarticulated Dimensional Facetwise Equations wisdom models models Of motion  Formalism-independent errors  Formalism-dependent errors 23 /203 Thursday, 9 July 2009
  31. 31. From [Di Ventura et al., Nature, 2006] Low cost/ High cost/ High error Low error Unarticulated Dimensional Facetwise Equations wisdom models models Of motion  Formalism-independent errors  Formalism-dependent errors 23 /203 Thursday, 9 July 2009
  32. 32. From [Di Ventura et al., Nature, 2006] Low cost/ High cost/ High error Low error Unarticulated Dimensional Facetwise Equations wisdom models models Of motion  Formalism-independent errors  Formalism-dependent errors 23 /203 Thursday, 9 July 2009
  33. 33. 24 /203 Thursday, 9 July 2009
  34. 34. Stochasticity in Cellular Systems  Most commonly recognised sources of noise in cellular system are low number of molecules and slow molecular interactions.  Over 80% of genes in E. coli express fewer than a hundred proteins per cell.  Mesoscopic, discrete and stochastic approaches are more suitable:  Only relevant molecules are taken into account.  Focus on the statistics of the molecular interactions and how often they take place. Mads Karn et al. Stochasticity in Gene Expression: From Theories to Phenotypes. Nature Reviews, 6, 451-464 (2005) Purnananda Guptasarma. Does replication-induced transcription regulate synthesis of the myriad low copy number poteins of E. Coli. BioEssays, 17, 11, 987-997 25 /203 Thursday, 9 July 2009
  35. 35. Towards Executable Modells for SBs “Although the road ahead is long and winding, it leads to a future where biology and medicine are transformed into precision engineering.” - Hiroaki Kitano.  Synthetic Biology and Systems biology promise more than integrated understanding: it promises systematic control of biological systems: 1. From an experimental viewpoint: Improved data acquisition 2. From a bioinformatics viewpoint: Improved data analysis tools 3. From a conceptual viewpoint: move from a science of mass-action/ energy-conversion to a science of information processing through multiple heterogeneous medium 26 /203 Thursday, 9 July 2009
  36. 36. There are good reasons to think that information processing is a key viewpoint to take when modeling Life as we know is: • coded in discrete units (DNA, RNA, Proteins) • combinatorially assembles interactions (DNA-RNA, DNA- Proteins,RNA-Proteins , etc) through evolution and self-organisation • Life emerges from these interacting parts • Information is: • transported in time (heredity, memory e.g. neural, immune system, etc) • transported in space (molecular transport processes, channels, pumps, etc) • Transport in time = storage/memory  a computational process • Transport in space = communication  a computational process • Signal Transduction = processing  a computational process 27 /203 Thursday, 9 July 2009
  37. 37.  It thus makes sense to use methodologies designed to cope with complex, concurrent, interactive systems of parts as found in computer sciences (e.g.):  Petri Nets  Process Calculi  P-Systems 28 /203 Thursday, 9 July 2009
  38. 38. InfoBiotics www.infobiotic.net •The utilisation of cutting-edge information processing techniques for biological modelling and synthesis •The understanding of life itself as multi-scale (Spatial/Temporal) information processing systems •Composed of 3 key components: •Executable Biology (or other modeling techniques) •Automated Model and Parameter Estimation •Model Checking (and other formal analysis) 29 /203 Thursday, 9 July 2009
  39. 39. Modeling in Systems & Synthetic Biology Systems Biology Synthetic Biology Colonies • Understanding •Control • Integration • Design • Prediction • Engineering • Life as it is •Life as it could be Cells Computational modelling to Computational modelling to elucidate and characterise engineer and evaluate modular patterns exhibiting possible cellular designs robustness, signal filtering, exhibiting a desired amplification, adaption, behaviour by combining well error correction, etc. studied and characterised Networks cellular modules 30 /203 Thursday, 9 July 2009
  40. 40. Model Design in Systems/Synthetic Biology • It is a hard process to design suitable models in systems/ synthetic biology where one has to consider the choice of the model structure and model parameters at different points repeatedly. • Some use of computer simulation has been mainly focused on the computation of the corresponding dynamics for a given model structure and model parameters. • Ultimate goal: for a new biological system (spec) one would like to estimate the model structure and model parameters (that match reality/constructible) simultaneously and automatically. • Models should be clear & understandable to the biologist 31 /203 Thursday, 9 July 2009
  41. 41. How you select features, disambiguate and quantify depends on the goals behind your modelling enterprise. Basic goal: to clarify current understandings by formalising what the constitutive elements of a system Systems Biology are and how they interact Intermediate goal: to test current understandings Synthetic Biology against experimental data Advanced goal: to predict beyond current understanding and available data Dream goal: (1) to combinatorially combine in silico well-understood components/models for the design and generation of novel experiments and hypothesis and ultimately (2) to design, program, optimise & control (new) biological systems 32 /203 Thursday, 9 July 2009
  42. 42. Model Development  From [E. Klipp et al, Systems Biology in Practice, 2005] 1. Formulation of the problem 2. Verification of available information 3. Selection of model structure 4. Establishing a simple model 5. Sensitivity analysis 6. Experimental tests of the model predictions 7. Stating the agreements and divergences between experimental and modelling results 8. Iterative refinement of model 33 /203 Thursday, 9 July 2009
  43. 43. Outline •Brief Introduction to Computational Modeling •Modeling for Top Down SB •Executable Biology •A pinch of Model Checking •Modeling for the Bottom Up SB •Dissipative Particle Dynamics •Automated Model Synthesis and Optimisation •Conclusions 34 /203 Thursday, 9 July 2009
  44. 44. Executable Biology with P systems  Field of membrane computing initiated by Gheorghe Păun in 2000  Inspired by the hierarchical membrane structure of eukaryotic cells  A formal language: precisely defined and machine processable  An executable biology methodology 35 /203 Thursday, 9 July 2009
  45. 45. Functional Entities Container • A boundary defining self/non-self (symmetry breaking). • Maintain concentration gradients and avoid environmental damage. Metabolism • Confining raw materials to be processed. • Maintenance of internal structures (autopoiesis). Information • Sensing environmental signals / release of signals. • Genetic information 36 /203 Thursday, 9 July 2009
  46. 46. Distributed and parallel rewritting systems in compartmentalised hierarchical structures. Objects Compartments Rewriting Rules • Computational universality and efficiency. • Modelling Framework 37 /203 Thursday, 9 July 2009
  47. 47. Cell-like P systems Intuitive Visual representation as a Venn diagram with a unique superset and without intersected sets. the classic P system diagram appearing in most papers (Păun) 38 /203 Thursday, 9 July 2009
  48. 48. Cell-like P systems Intuitive Visual representation as a Venn diagram with a unique superset and without intersected sets. formally equivalent to a tree: 1 2 4 3 7 5 6 the classic P system diagram appearing in most papers (Păun) 8 9 38 /203 Thursday, 9 July 2009
  49. 49. Cell-like P systems Intuitive Visual representation as a Venn diagram with a unique superset and without intersected sets. formally equivalent to a tree: 1 2 4 3 7 5 6 the classic P system diagram appearing in most papers (Păun) 8 9 • a string of matching parentheses: [ 1 [2 ] 2 [ 3 ] 3 [4 [5 ] 5 [6 [ 8 ] 8 [9 ] 9 ]6 [7 ]7 ]4 ]1 38 /203 Thursday, 9 July 2009
  50. 50. P-Systems: Modelling Principles Molecules Objects Structured Molecules Strings Molecular Species Multisets of objects/ strings Membranes/organelles Membrane Biochemical activity rules Biochemical transport Communication rules 39 /203 Thursday, 9 July 2009
  51. 51. Stochastic P Systems 40 /203 Thursday, 9 July 2009
  52. 52. Rewriting Rules used by Multi-volume Gillespie’s algorithm 41 /203 Thursday, 9 July 2009
  53. 53. Molecular Species  A molecular species can be represented using individual objects.  A molecular species with relevant internal structure can be represented using a string. 42 /203 Thursday, 9 July 2009
  54. 54. Molecular Interactions  Comprehensive and relevant rule-based schema for the most common molecular interactions taking place in living cells. Transformation/Degradation Complex Formation and Dissociation Diffusion in / out Binding and Debinding Recruitment and Releasing Transcription Factor Binding/Debinding Transcription/Translation 43 /203 Thursday, 9 July 2009
  55. 55. Compartments / Cells  Compartments and regions are explicitly specified using membrane structures. 44 /203 Thursday, 9 July 2009
  56. 56. Colonies / Tissues  Colonies and tissues are representing as collection of P systems distributed over a lattice.  Objects can travel around the lattice through translocation rules. v 45 /203 Thursday, 9 July 2009
  57. 57. Molecular Interactions Inside Compartments 46 /203 Thursday, 9 July 2009
  58. 58. Passive Diffusion of Molecules 47 /203 Thursday, 9 July 2009
  59. 59. 48 /203 Thursday, 9 July 2009
  60. 60. a b Transport Modalities a b Antiport channel a b Symport channel a c b a b Promoted symport channel (trap) a b 49 /203 Thursday, 9 July 2009
  61. 61. Transport Modalities 5 2 1 4 3 Phagocitosys Endocitosys Pinocitosys Exocitosys 50 /203 Thursday, 9 July 2009
  62. 62. Transport Modalities Highly specific: cell specific & topology specific 51 /203 Thursday, 9 July 2009
  63. 63. Signal Sensing and Active Transport 52 /203 Thursday, 9 July 2009
  64. 64. Specification of Transcriptional Regulatory Networks 53 /203 Thursday, 9 July 2009
  65. 65. Transcription as Rewriting Rules on Multisets of Objects and Strings 54 /203 Thursday, 9 July 2009
  66. 66. Translation as Rewriting Rules on Multisets of Objects and Strings 55 /203 Thursday, 9 July 2009
  67. 67. Post-Transcriptional Processes  For each protein in the system, post-transcriptional processes like translational initiation, messenger and protein degradation, protein dimerisation, signal sensing, signal diffusion etc are represented using modules of rules.  Modules can have also as parameters the stochastic kinetic constants associated with the corresponding rules in order to allow us to explore possible mutations in the promoters and ribosome binding sites in order to optimise the behaviour of the system. 56 /203 Thursday, 9 July 2009
  68. 68. Scalability through Modularity  Cellular functions arise from orchestrated interactions between motifs consisting of many molecular interacting species.  A P System model is a set of rules representing molecular interactions motifs that appear in many cellular systems. 57 /203 Thursday, 9 July 2009
  69. 69. Basic P System Modules Used 58 /203 Thursday, 9 July 2009
  70. 70. Modularity in Gene Regulatory Networks  Cis-regulatory modules are nonrandom clusters of target binding sites for transcription factors regulating the same gene or operon.  A P system module is a set of rewriting rules containing variables that can be instantiated with specific objects, stochastic constants and membrane labels. E. Davidson (2006) The Regulatory Genome, Gene Regulation Networks in Development and Evolution, Elsevier 59 /203 Thursday, 9 July 2009
  71. 71. Modularity in Gene Regulatory Networks AHL LuxR CI  Cis-regulatory modules are nonrandom clusters of target binding sites for transcription factors regulating the same gene or operon.  A P system module is a set of rewriting rules containing variables that can be instantiated with specific objects, stochastic constants and membrane labels. E. Davidson (2006) The Regulatory Genome, Gene Regulation Networks in Development and Evolution, Elsevier 59 /203 Thursday, 9 July 2009
  72. 72. Modularity in Gene Regulatory Networks AHL LuxR CI  Cis-regulatory modules are nonrandom clusters of target binding sites for transcription factors regulating the same gene or operon.  A P system module is a set of rewriting rules containing variables that can be instantiated with specific objects, stochastic constants and membrane labels. E. Davidson (2006) The Regulatory Genome, Gene Regulation Networks in Development and Evolution, Elsevier 59 /203 Thursday, 9 July 2009
  73. 73. Representing transcriptional fusions  Objects Variables can be instantiated with the name of specific genes to represent a construct where the gene is fused to the promoter or cluster of TF binding sites specified by the module. 60 /203 Thursday, 9 July 2009
  74. 74. Representing transcriptional fusions  Objects Variables can be instantiated with the name of specific genes to represent a construct where the gene is fused to the promoter or cluster of TF binding sites specified by the module. 60 /203 Thursday, 9 July 2009
  75. 75. Representing transcriptional fusions  Objects Variables can be instantiated with the name of specific genes to represent a construct where the gene is fused to the promoter or cluster of TF binding sites specified by the module. 60 /203 Thursday, 9 July 2009
  76. 76. Representing transcriptional fusions  Objects Variables can be instantiated with the name of specific genes to represent a construct where the gene is fused to the promoter or cluster of TF binding sites specified by the module. 60 /203 Thursday, 9 July 2009
  77. 77. Representing transcriptional fusions  Objects Variables can be instantiated with the name of specific genes to represent a construct where the gene is fused to the promoter or cluster of TF binding sites specified by the module. 60 /203 Thursday, 9 July 2009
  78. 78. Representing transcriptional fusions  Objects Variables can be instantiated with the name of specific genes to represent a construct where the gene is fused to the promoter or cluster of TF binding sites specified by the module. 60 /203 Thursday, 9 July 2009
  79. 79. Representing transcriptional fusions  Objects Variables can be instantiated with the name of specific genes to represent a construct where the gene is fused to the promoter or cluster of TF binding sites specified by the module. 60 /203 Thursday, 9 July 2009
  80. 80. Representing Directed Evolution  Variables for stochastic constants can be instantiated with specific values in order to represent directed evolution. 61 /203 Thursday, 9 July 2009
  81. 81. Representing Directed Evolution  Variables for stochastic constants can be instantiated with specific values in order to represent directed evolution. 61 /203 Thursday, 9 July 2009
  82. 82. Representing Directed Evolution  Variables for stochastic constants can be instantiated with specific values in order to represent directed evolution. A 61 /203 Thursday, 9 July 2009
  83. 83. Representing Directed Evolution  Variables for stochastic constants can be instantiated with specific values in order to represent directed evolution. A 61 /203 Thursday, 9 July 2009
  84. 84. Representing synthetic transcriptional networks  The genes used to instantiate variables in our modules can codify other TFs that interact with other modules or promoters producing a synthetic gene regulatory network. 62 /203 Thursday, 9 July 2009
  85. 85. Representing synthetic transcriptional networks  The genes used to instantiate variables in our modules can codify other TFs that interact with other modules or promoters producing a synthetic gene regulatory network. 62 /203 Thursday, 9 July 2009
  86. 86. Stochastic P Systems  Gillespie Algorithm (SSA) generates trajectories of a stochastic system consisting of modified for multiple compartments/volumes: 1) A stochastic constant is associated with each rule. 2) A propensity is computed for each rule by multiplying the stochastic constant by the number of distinct possible combinations of the elements on the left hand side of the rule. 3) The rule to apply j0 and the waiting time τ for its application are computed by generating two random numbers r1,r2 ~ U(0,1) and using the formulas: F. J. Romero-Campero, J. Twycross, M. Camara, M. Bennett, M. Gheorghe, and N. Krasnogor. Modular assembly of cell systems biology models using p systems. International Journal of Foundations of Computer Science, 2009 63 /203 Thursday, 9 July 2009
  87. 87. Multicompartmental Gillespie Algorithm 64 /203 Thursday, 9 July 2009
  88. 88. Multicompartmental Gillespie Algorithm 1 3 2 64 /203 Thursday, 9 July 2009
  89. 89. Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 r31,…,r3n3 M3 M1 2 r21,…,r2n2 M2 64 /203 Thursday, 9 July 2009
  90. 90. Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 r31,…,r3n3 Local Gillespie M3 M1 2 r21,…,r2n2 M2 64 /203 Thursday, 9 July 2009
  91. 91. Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 ( 1, τ1, r01) r31,…,r n3 3 Local Gillespie M3 M1 2 r21,…,r2n2 M2 64 /203 Thursday, 9 July 2009
  92. 92. Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 ( 1, τ1, r01) r31,…,r n3 3 Local Gillespie M3 M1 ( 2, τ2, r02) 2 r21,…,r2n2 M2 64 /203 Thursday, 9 July 2009
  93. 93. Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 ( 1, τ1, r01) r31,…,r n3 3 Local Gillespie M3 M1 ( 2, τ2, r02) 2 ( 3, τ3, r03) r21,…,r2n2 M2 64 /203 Thursday, 9 July 2009
  94. 94. Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 ( 1, τ1, r01) r31,…,r n3 3 Local Gillespie M3 M1 ( 2, τ2, r02) 2 ( 3, τ3, r03) r21,…,r2n2 Sort Compartments M2 τ2 < τ1 < τ3 64 /203 Thursday, 9 July 2009
  95. 95. Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 ( 1, τ1, r01) r31,…,r n3 3 Local Gillespie M3 M1 ( 2, τ2, r02) 2 ( 3, τ3, r03) r21,…,r2n2 Sort Compartments M2 τ2 < τ1 < τ3 ( 2, τ2, r02) ( 1, τ1, r01) ( 3, τ3, r03) 64 /203 Thursday, 9 July 2009
  96. 96. Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 ( 1, τ1, r01) r31,…,r n3 3 Local Gillespie M3 M1 ( 2, τ2, r02) 2 ( 3, τ3, r03) r21,…,r2n2 ‘ Sort Compartments M2 τ2 < τ1 < τ3 ( 2, τ2, r02) ( 1, τ1, r01) ( 3, τ3, r03) 64 /203 Thursday, 9 July 2009
  97. 97. Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 ( 1, τ1, r01) r31,…,r n3 3 Local Gillespie M3 M1 ( 2, τ2, r02) 2 ( 3, τ3, r03) r21,…,r2n2 ‘ Sort Compartments M2 τ2 < τ1 < τ3 ( 2, τ2, r02) ( 1, τ1-τ2, r01) ( 1, τ1, r01) ( 3, τ3-τ2, r03) ( 3, τ3, r03) Update Waiting Times 64 /203 Thursday, 9 July 2009
  98. 98. Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 ( 1, τ1, r01) r31,…,r n3 3 Local Gillespie M3 M1 ( 2, τ2, r02) 2 ( 3, τ3, r03) r21,…,r2n2 ‘ Sort Compartments M2 τ2 < τ1 < τ3 ( 2, τ2, r02) ( 2, τ2’, r02) ( 1, τ1-τ2, r01) ( 1, τ1, r01) ( 3, τ3-τ2, r03) ( 3, τ3, r03) Update Waiting Times 64 /203 Thursday, 9 July 2009
  99. 99. Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 ( 1, τ1, r01) r31,…,r n3 3 Local Gillespie M3 M1 ( 2, τ2, r02) 2 ( 3, τ3, r03) r21,…,r2n2 ‘ Sort Compartments M2 τ2 < τ1 < τ3 ( 2, τ2, r02) ( 2, τ2’, r02) ( 1, τ1-τ2, r01) ( 1, τ1, r01) ( 3, τ3-τ2, r03) Insert new triplet ( 3, τ3, r03) τ1-τ2 <τ2’ < τ3-τ2 Update Waiting Times 64 /203 Thursday, 9 July 2009
  100. 100. Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 ( 1, τ1, r01) r31,…,r n3 3 Local Gillespie M3 M1 ( 2, τ2, r02) 2 ( 3, τ3, r03) r21,…,r2n2 ‘ Sort Compartments M2 τ2 < τ1 < τ3 ( 2, τ2, r02) ( 1, τ1-τ2, r01) ( 2, τ2’, r02) ( 1, τ1-τ2, r01) ( 1, τ1, r01) ( 2, τ2’, r02) ( 3, τ3-τ2, r03) ( 3, τ3-τ2, r03) Insert new triplet ( 3, τ3, r03) τ1-τ2 <τ2’ < τ3-τ2 Update Waiting Times 64 /203 Thursday, 9 July 2009
  101. 101.  Using P systems modules one can model a large variety of commonly occurring BRN:  Gene Regulatory Networks  Signaling Networks  Metabolic Networks  This can be done in an incremental way. F. J. Romero-Campero, J. Twycross, M. Camara, M. Bennett, M. Gheorghe, and N. Krasnogor. Modular assembly of cell systems biology models using p systems. International Journal of Foundations of Computer Science, 2009 65 /203 Thursday, 9 July 2009
  102. 102. InfoBiotics Pipeline 66 /203 Thursday, 9 July 2009
  103. 103. SBML from CellDesigner 67 /203 Thursday, 9 July 2009
  104. 104. Runs simulations and extract data 68 /203 Thursday, 9 July 2009
  105. 105. Plot Timeseries 69 /203 Thursday, 9 July 2009
  106. 106. in time and space 70 /203 Thursday, 9 July 2009
  107. 107. Synthetic Biology Examples 71 /203 Thursday, 9 July 2009
  108. 108. Multi-component negative- feedback oscillator Oscillations caused by time-delayed negative-feedback: Negative-feedback: gene-product that represses it's gene Time-delay: mRNA export, translation and repressor import Novak & Tyson: Design Principles of Biochemical Oscillators. Nat. Rev. Mol. Cell. Biol. 9: 981-991 (2008) 72 /203 Thursday, 9 July 2009
  109. 109. Multi-component negative- feedback oscillator  Mathematical model − Xc = [mRNA in cytosol] − Yc = [protein in cytosol] − Xn = [mRNA in nucleus] − Yn = [protein in nucleus] − E = [total protease] − p = “integer indicating whether Y binds to DNA as a monomer, trimer, or so on” Executable Biology makes this more obvious: we can vary the value of p and the sequence of binding... 73 /203 Thursday, 9 July 2009
  110. 110. Single protein represses gene p=1 74 /203 Thursday, 9 July 2009
  111. 111. When repression is weak (dissociation rate = 10) No obvious oscillatory behaviour in single simulation 75 /203 Thursday, 9 July 2009
  112. 112. When repression is weak (dissociation rate = 10) Mean of 100 runs shows convergence to steady state 76 /203 Thursday, 9 July 2009
  113. 113. When repression is strong (dissociation rate = 0.1) Oscillations evident in single simulation 77 /203 Thursday, 9 July 2009
  114. 114. When repression is strong (dissociation rate = 0.1) Averging 100 runs dampens oscillations due to different phases but observable. Protein levels steady. 78 /203 Thursday, 9 July 2009
  115. 115. Repressor binding sequence  When p=2 there are two possible scenarios: – First protein binds to second protein weakly then protein-dimer binds to gene strongly – First protein binds to gene weakly then second protein binds to protein-gene dimer strongly  In the following only the model structure is changed, not the parameters  First dissociation rate = 10  Second dissociation rate = 0.1 79 /203 Thursday, 9 July 2009
  116. 116. 1. Protein represses as dimer 80 /203 Thursday, 9 July 2009
  117. 117. 1. Protein represses as dimer target mRNA levels oscillate ready but protein accumulates in the cytosol 81 /203 Thursday, 9 July 2009
  118. 118. 2. Proteins repress cooperatively 82 /203 Thursday, 9 July 2009
  119. 119. 2. Proteins repress cooperatively target Oscillations are steady and protein levels are controlled 83 /203 Thursday, 9 July 2009
  120. 120. An example: Ron Weiss' Pulse Generator  Two different bacterial strains carrying specific synthetic gene regulatory networks are used.  The first strain produces a diffusible signal AHL.  The second strain possesses a synthetic gene regulatory network which produces a pulse of GFP after AHL sensing.  These two bacterial strains and their respective synthetic networks are modelled as a combination of modules.  S. Basu, R. Mehreja, et al. (2004) Spatiotemporal control of gene expression with pulse generating networks, PNAS, 101, 6355-6360 84 /203 Thursday, 9 July 2009
  121. 121. Sending Cells 85 /203 Thursday, 9 July 2009
  122. 122. Sending Cells 85 /203 Thursday, 9 July 2009
  123. 123. Sending Cells Pconst 85 /203 Thursday, 9 July 2009
  124. 124. Sending Cells Pconst luxI 85 /203 Thursday, 9 July 2009
  125. 125. Sending Cells Pconst({X = luxI },…) Pconst luxI 85 /203 Thursday, 9 July 2009
  126. 126. Sending Cells AHL Pconst({X = luxI },…) LuxI AHL PostTransc({X=LuxI},{c1=3.2,…}) Diff({X=AHL},{c=0.1}) Pconst luxI 85 /203 Thursday, 9 July 2009
  127. 127. Pulse Generating Cells 86 /203 Thursday, 9 July 2009
  128. 128. Pulse Generating Cells 86 /203 Thursday, 9 July 2009
  129. 129. Pulse Generating Cells LuxR Pconst luxR 86 /203 Thursday, 9 July 2009
  130. 130. Pulse Generating Cells AHL AHL LuxR Pconst luxR 86 /203 Thursday, 9 July 2009
  131. 131. Pulse Generating Cells AHL AHL LuxR GFP PluxOR1 Pconst gfp luxR 86 /203 Thursday, 9 July 2009
  132. 132. Pulse Generating Cells AHL AHL LuxR GFP PluxOR1 Pconst gfp luxR Plux cI 86 /203 Thursday, 9 July 2009
  133. 133. Pulse Generating Cells AHL AHL LuxR GFP PluxOR1 Pconst gfp luxR CI Plux cI 86 /203 Thursday, 9 July 2009
  134. 134. Pulse Generating Cells AHL AHL Pconst({X=luxR},…) LuxR GFP PluxOR1({X=gfp},…) PluxOR1 Plux({X=cI},…) Pconst gfp luxR … … CI Diff({X=AHL},…) Plux cI 86 /203 Thursday, 9 July 2009
  135. 135. Spatial Distribution of Senders and Pulse Generators AHL GFP AHL LuxR Pconst PluxOR1 luxR gfp LuxI AHL CI Pconst luxI Plux cI 87 /203 Thursday, 9 July 2009
  136. 136. AHL Spatial Distribution of Senders and Pulse Generators AHL GFP AHL LuxR Pconst PluxOR1 luxR gfp LuxI AHL CI Pconst luxI Plux cI 87 /203 Thursday, 9 July 2009
  137. 137. Wave propagation simulation I SIMULATION I 88 /203 Thursday, 9 July 2009
  138. 138. Pulse Generating Cells AHLWith Relay AHL LuxR GFP PluxOR1 Pconst gfp luxR CI Plux cI 89 /203 Thursday, 9 July 2009
  139. 139. Pulse Generating Cells AHLWith Relay AHL LuxR GFP PluxOR1 Pconst gfp luxR Plux CI luxI LuxI Plux cI AHL 89 /203 Thursday, 9 July 2009
  140. 140. Pulse Generating Cells AHLWith Relay AHL Pconst({X=luxR},…) LuxR GFP PluxOR1 Pconst gfp luxR Plux CI luxI LuxI Plux cI AHL 89 /203 Thursday, 9 July 2009
  141. 141. Pulse Generating Cells AHLWith Relay AHL Pconst({X=luxR},…) LuxR GFP PluxOR1({X=gfp},…) PluxOR1 Pconst gfp luxR Plux CI luxI LuxI Plux cI AHL 89 /203 Thursday, 9 July 2009
  142. 142. Pulse Generating Cells AHLWith Relay AHL Pconst({X=luxR},…) LuxR GFP PluxOR1({X=gfp},…) PluxOR1 Plux({X=cI},…) Pconst gfp luxR Plux CI luxI LuxI Plux cI AHL 89 /203 Thursday, 9 July 2009
  143. 143. Pulse Generating Cells AHLWith Relay AHL Pconst({X=luxR},…) LuxR GFP PluxOR1({X=gfp},…) PluxOR1 Plux({X=cI},…) Pconst gfp luxR … Plux CI luxI LuxI Plux cI AHL 89 /203 Thursday, 9 July 2009
  144. 144. Pulse Generating Cells AHLWith Relay AHL Pconst({X=luxR},…) LuxR GFP PluxOR1({X=gfp},…) PluxOR1 Plux({X=cI},…) Pconst gfp luxR … … Plux CI luxI LuxI Plux cI AHL 89 /203 Thursday, 9 July 2009
  145. 145. Pulse Generating Cells AHLWith Relay AHL Pconst({X=luxR},…) LuxR GFP PluxOR1({X=gfp},…) PluxOR1 Plux({X=cI},…) Pconst gfp luxR … … Plux CI luxI Diff({X=AHL},…) LuxI Plux cI AHL 89 /203 Thursday, 9 July 2009
  146. 146. Pulse Generating Cells AHLWith Relay AHL Pconst({X=luxR},…) LuxR GFP PluxOR1({X=gfp},…) PluxOR1 Plux({X=cI},…) Pconst gfp luxR … … Plux CI luxI Diff({X=AHL},…) Plux Plux({X=luxI},…) LuxI cI AHL 89 /203 Thursday, 9 July 2009
  147. 147. Wave propagation simulation II SIMULATION II 90 /203 36 Thursday, 9 July 2009
  148. 148. AHL Spatial Distribution of Pulse Generators and Seed AHL LuxR GFP Pconst PluxOR1 luxR gfp Plux CI luxI Plux cI LuxI AHL 91 /203 Thursday, 9 July 2009
  149. 149. Wave propagation with Four Droplets of Signal SIMULATION III 92 /203 38 Thursday, 9 July 2009
  150. 150. Pulse Generating Cells AHLWith Relay LuxR AHL PulseGenerator(X ) = PluxOR1 { Pconst({X=luxR},…) , Pconst luxR PluxOR1({X},…) , Plux({X=cI},…) , Plux … CI luxI Diff({X=AHL},…) , LuxI Plux cI Plux({X=luxI},…) } AHL 93 /203 Thursday, 9 July 2009
  151. 151. Combining Complex Modules AHL AHL Inverter(X ) = LuxR { Pconst({X=luxR},…) , PluxOR1({X=lacI},…) , Pconst PluxOR1 Plac({X},…) , luxR lacI … LacI Diff({X=AHL},…)} Plac 94 /203 Thursday, 9 July 2009
  152. 152. Combining Complex Modules AHL AHL Inverter(X ) = LuxR { Pconst({X=luxR},…) , PluxOR1({X=lacI},…) , Pconst PluxOR1 Plac({X},…) , luxR lacI … LacI Diff({X=AHL},…)} Plac PulseGenerator({X=lacI}) Inverter({X=gfP}) 94 /203 Thursday, 9 July 2009
  153. 153. Inversion Through a Propagating Wave SIMULATION IV 95 /203 41 Thursday, 9 July 2009
  154. 154. Outline •Brief Introduction to Computational Modeling •Modeling for Top Down SB •Executable Biology •A pinch of Model Checking •Modeling for the Bottom Up SB •Dissipative Particle Dynamics •Automated Model Synthesis and Optimisation •Conclusions 96 /203 Thursday, 9 July 2009
  155. 155. Probabilistic Model Checking  A precise computational/mathematical model allows us to perform formal verification techniques: Probabilistic model checking.  Properties are expressed formally using temporal logic and analysed.  The fundamental components of the PRISM language are modules, variables and commands. • A model is composed of a number of modules which can interact with each other. • A module contains a number of local variables and commands. 97 /203 Thursday, 9 July 2009
  156. 156. P Systems and PRISM P System Component PRISM Component Membrane Module Multisets of Objects Local Variables Rewriting rules Commands  Rewards/Costs are associated with states and transitions representing the number of objects and the application of rules.  Some Properties:  Expected Number of objects over time: R = ? [ I = T ]  Expected Number of rule application over time: R = ? [ C <= T ]  Expected Time to reach a state: R = ? [ F molec_1 = K ]  Transient properties: P = ? [ true U[t_1 t_2] molec_1 >= K_1 ]  Steady State/Long run properties: S = ? [ molec_1 >= K_1] PRISM is used as an example. Other model checkers are more appropriate for larger systems 98 /203 Thursday, 9 July 2009
  157. 157. Post-transcriptional Regulation Post-transcriptional regulation [ gene ]b  [ gene + rna ]b ctrc ctrc*ctrl = 1.13 [ rna ]b  [ ]b c2=0.3465 10 proteins in [ rna ]b  [ rna + Protein ]b ctrl steady State [ Protein ]b  [ ]b c4=0.3465 99 /203 Thursday, 9 July 2009
  158. 158. Post-transcriptional Regulation R = ? [ I = 240 ] P = ? [ true U[240,240] Proteins = N ] 100 /203 Thursday, 9 July 2009
  159. 159. Positive Regulation [ TF + gene ] b  [ TF.gene ] b con [ TF.gene ] b  [ TF + gene ] b coff [ gene ]b  [ gene + rna ]b ctrc [ rna ]b  [ ]b c2 [ rna ]b  [ rna + Protein ]b ctrl [ Protein ]b  [ ]b c4 101 /203 Thursday, 9 July 2009
  160. 160. Positive Regulation R = ? [ C <= 100 ] R = ? [ C <= 100 ] P = ? [ true U[60,60] Proteins = N ] 102 /203 Thursday, 9 July 2009
  161. 161. Model Checking on the Pulse Generator  The simulation of the Pulse Generator show some interesting properties that were subsequently analysed using model checking.  Due to the complexity of the system (state space explosion) we perform approximate model checking with a precision of 0.01 and a confidence of 0.001 which needed to run 100000 simulations. 103 /203 Thursday, 9 July 2009
  162. 162. Model Checking on the Pulse Generator  The simulations show that although the number of signals reaches eventually the same level in all the cells in the lattice those cells that are far from the sending cells produce fewer number of GFP molecules.  The difference between cells close to and far from the sending cells is the rate of increase of the signal AHL.  We study the effect of the rate of increase of the signal AHL in the number of GFP produced. S. Basu, R. Mehreja, et al. Spatiotemporal control of gene expression with pulse generating networks, PNAS, 101, 6355-6360 104 /203 Thursday, 9 July 2009
  163. 163.  We studied the expected number of GFP molecules produced over time for different increase rates of AHL. R = ? [ I = 60 ] rewards molecule = 1 : proteinGFP; endrewards The system is expected to produce longer pulses with lower amplitudes for slow increase rates of AHL signals. 105 /203 Thursday, 9 July 2009
  164. 164.  In order to get a clearer idea, the probability distribution of the number of GFP molecules at 60 minutes was computed. P = ? [ true U[60,60] ((proteinGFP > N) & (proteinGFP <= (N + 10))) ] Note that for slow increase rates of AHL the probability of having NO GFP molecules at all is high. 106 /203 Thursday, 9 July 2009
  165. 165.  Finally, assuming that for a cell to be fluorescence it needs to have a given number of GFP for an appreciable period of time we studied the expected amount of time a cell have more than 50 GFP molecules during the first 60 minutes after the signals arrive to the cell. R = ? [ C <= 60 ] rewards true : proteinGFP; endrewards 107 /203 Thursday, 9 July 2009
  166. 166. Outline •Brief Introduction to Computational Modeling •Modeling for Top Down SB •Executable Biology •A pinch of Model Checking •Modeling for the Bottom Up SB •Dissipative Particle Dynamics •Automated Model Synthesis and Optimisation •Conclusions 108 /203 Thursday, 9 July 2009
  167. 167. A (Proto)Cell as an Information Processing Device LeDuc et al. Towards an in vivo biologically inspired nanofactory. Nature (2007) 109 /203 Thursday, 9 July 2009
  168. 168. Towards a synthetic cell from the bottom up  Biocompatible vesicles as long-circulating carriers  Polymer self-assembly into higher-order structures  Cell-mimics with hydrophobic ‘cell-wall’ and glycosylated surfaces  Potential for cross-talk with biological cells Pasparakis, G. Angew Chem Int Ed. 2008 47 (26), 4847-4850 110 /203 Thursday, 9 July 2009
  169. 169. Vesicle Biorecognition Pasparakis, G. et al, Angew Chem Int Ed. 2008 47 (26), 4847-4850 111 /203 Thursday, 9 July 2009
  170. 170. ‘Talking’ to cell-vesicle aggregates Pasparakis, G. Angew Chem Int Ed. 2008 47 (26), 4847-4850 112 /203 Thursday, 9 July 2009
  171. 171. Outline •Brief Introduction to Computational Modeling •Modeling for Top Down SB •Executable Biology •A pinch of Model Checking •Modeling for the Bottom Up SB •Dissipative Particle Dynamics •Automated Model Synthesis and Optimisation •Conclusions 113 /203 Thursday, 9 July 2009
  172. 172. Dissipative Particle Dynamics  Simulate movement of particles which represent several atoms / molecules  Calculate forces acting on particles, integrate equations of motion  Used extensively for investigating the self-assembly of lipid membrane structures at the mesoscale  Typical simulations contain ~105-106 particles, for ~105-106 time steps  Particles interact with each other within a finite radius much smaller than the simulation space, algorithmic optimisations of force calculations are possible 114 /203 Thursday, 9 July 2009
  173. 173. Dissipative Particle Dynamics  First introduced by Hoogerbrugge and Koelmann in 1992.  Statistical mechanics of the model derived by espanol and warren in 1995.  A coarse graining approach is used so that one simulation particle represents a number of real molecules of a given type.  Since the timescale at which interactions occur is longer than in MD, fewer time-steps are required to simulation the same period of real time.  The short force cut-off radius enables optimisation of the force calculation code to be performed. O H H W O O H H H H 115 /203 Thursday, 9 July 2009
  174. 174. Dissipative Particle Dynamics Conservative Force i W P Dissipative Force j W P Random Force 116 /203 Thursday, 9 July 2009
  175. 175. Dissipative Particle Dynamics  Polymers  A number of simulation beads are tied together to represent the original molecule.  Two new forces are introduced between polymer particles, a Hookean spring force and a bond angle force. 117 /203 Thursday, 9 July 2009
  176. 176. Liposome Formation in DPD 118 /203 Thursday, 9 July 2009
  177. 177. 119 /203 Thursday, 9 July 2009
  178. 178. Case Study One: Vesicle Diffusion Polar heads Non polar tails Pores J. Smaldon, J. Blake, D. Lancet, and N. Krasnogor. A multi-scaled approach to artificial life simulation with p systems and dissipative particle dynamics. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2008), ACM Publisher, 2008. 120 /203 Thursday, 9 July 2009
  179. 179. Case Study One: Vesicle Diffusion  The regions were formed by allowing vesicles to self- assemble from phospholipids in the presence of pore inclusions  Pores are simple channels with an exterior mimicking the hydrophobic/hydrophilic profile of the bilayer 121 /203 Thursday, 9 July 2009
  180. 180. 122 /203 Thursday, 9 July 2009
  181. 181. Case Study One: Vesicle Diffusion Tagged solvent particles were placed within the liposome inner volume, the change in concentration due to diffusion of solvent through the membrane pores was measures 123 /203 Thursday, 9 July 2009
  182. 182. Case Study Two: Liposome Logic  The behaviour of some prokaryotic RNA transcription motifs matches that of boolean logic gates[1]  DPD was extended with mesoscale collision based reactions.  transcriptional logic gates were simulated in bulk solvent and within a liposome core volume. 124 /203 Thursday, 9 July 2009
  183. 183. 125 /203 Thursday, 9 July 2009
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