Synthetic Biology - Modeling and Optimisation

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Information about Synthetic Biology - Modeling and Optimisation
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Published on July 9, 2009

Author: nxk

Source: slideshare.net

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

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

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

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

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

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

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

•“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

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

•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

•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

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

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

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

 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

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

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

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

 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

 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

 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

 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

 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

 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

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

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

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

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

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

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

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

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

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

24 /203 Thursday, 9 July 2009

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

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

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

 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 individual objects.  A molecular species with relevant internal structure can be represented using a string. 42 /203 Thursday, 9 July 2009

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

Compartments / Cells  Compartments and regions are explicitly specified using membrane structures. 44 /203 Thursday, 9 July 2009

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

Molecular Interactions Inside Compartments 46 /203 Thursday, 9 July 2009

Passive Diffusion of Molecules 47 /203 Thursday, 9 July 2009

48 /203 Thursday, 9 July 2009

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

Transport Modalities 5 2 1 4 3 Phagocitosys Endocitosys Pinocitosys Exocitosys 50 /203 Thursday, 9 July 2009

Transport Modalities Highly specific: cell specific & topology specific 51 /203 Thursday, 9 July 2009

Signal Sensing and Active Transport 52 /203 Thursday, 9 July 2009

Specification of Transcriptional Regulatory Networks 53 /203 Thursday, 9 July 2009

Transcription as Rewriting Rules on Multisets of Objects and Strings 54 /203 Thursday, 9 July 2009

Translation as Rewriting Rules on Multisets of Objects and Strings 55 /203 Thursday, 9 July 2009

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

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

Basic P System Modules Used 58 /203 Thursday, 9 July 2009

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Multicompartmental Gillespie Algorithm 64 /203 Thursday, 9 July 2009

Multicompartmental Gillespie Algorithm 1 3 2 64 /203 Thursday, 9 July 2009

Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 r31,…,r3n3 M3 M1 2 r21,…,r2n2 M2 64 /203 Thursday, 9 July 2009

Multicompartmental Gillespie Algorithm 1 3 r11,…,r1n1 r31,…,r3n3 Local Gillespie M3 M1 2 r21,…,r2n2 M2 64 /203 Thursday, 9 July 2009

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

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

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

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

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

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

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

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

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

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

 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

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 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

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

Single protein represses gene p=1 74 /203 Thursday, 9 July 2009

When repression is weak (dissociation rate = 10) No obvious oscillatory behaviour in single simulation 75 /203 Thursday, 9 July 2009

When repression is weak (dissociation rate = 10) Mean of 100 runs shows convergence to steady state 76 /203 Thursday, 9 July 2009

When repression is strong (dissociation rate = 0.1) Oscillations evident in single simulation 77 /203 Thursday, 9 July 2009

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

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

1. Protein represses as dimer 80 /203 Thursday, 9 July 2009

1. Protein represses as dimer target mRNA levels oscillate ready but protein accumulates in the cytosol 81 /203 Thursday, 9 July 2009

2. Proteins repress cooperatively 82 /203 Thursday, 9 July 2009

2. Proteins repress cooperatively ta

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