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Computational Modelling in Systems and Synthetic Biology Fran Romero Dpt Computer Science and Artificial Intelligence University of Seville [email protected] www.cs.us.es/~fran Models are Formal Statements of Our Current Knowledge A non ambiguous description of our understanding of the elements of a system of interest, their states and interactions. Feature selection is key in model development. According to the semantics used in the simulations: Denotational Semantics Models: Set of equations showing relationships between aggregates of components and how they change over time (i.e. DE). Operational Semantics Models: Algorithm executable by an abstract machine whose computation resembles the behaviour of the system (I.e. Finite State Machine) Fisher et al (2008) Executable cell biology. Nature Biotechnology, 25, 11, 1239-1249 (2008) How you select features, disambiguate and quantify depends on the goals behind your modelling enterprise Systems Biology Synthetic Biology Basic goal: to clarify current understandings by formalising what the constitutive elements of a system are and how they interact Intermediate goal: to test current understandings against experimental data; calculate/simulate Advanced goal: to predict beyond current understanding and available data; calculate/simulate + analyse 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 Systems Biology and Synthetic Biology Systems Biology Synthetic Biology • Understanding • Integration • Prediction • Life as it is Computational modelling to elucidate and characterise modular patterns exhibiting robustness, signal filtering, amplification, adaption, error correction, etc. • Control Colonies Cells Networks • Design • Engineering • Life as it could be Computational modelling to engineer and evaluate possible cellular designs exhibiting a desired behaviour by combining well studied and characterised cellular modules Stochasticity is important in Cellular Systems Sources of noise are low number of molecules and slow molecular interactions. Over 80% of genes in E. coli express fewer than a hundred proteins . 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 synthetis of the myriad low copy number proteins in E. Coli. BioEssays, 17, 11, 987-997. Spatial Localisation is Important in Cellular Systems Cellular Biology Exhibits Modularity 2008 Nobel Prize in Chemistry for the discovery and development of the Green Fluorescence Protein We Look for Specific Requirements in our Modelling Formalism o Individual cells as the elementary unit in the system. o Explicit representation of their compartmental structures. o Spatial and geometric information in multicellular systems. o The molecular interactions as discrete and stochastic processes. Executable semantics. o Modularity in cellular systems, especially in gene regulatory networks. There exists different Computational Frameworks Most computational models are implemented in custom programs. Computational formalisms which cope with complex, concurrent, interactive systems has been successfully applied. Petri Nets π-calculus Monika Heiner, David Gilbert, Robin Donaldson. Petri Nets for Systems and Synthetic Biology SFM 2008, 215 – 264 (2008) Aviv Regev, Ehud Shapiro. Modelling in Molecular Biology (2004) P systems are Abstractions of Single Cells Abstraction of the structure and functioning a single cell. Objects o Compartmental models o Rule-based modelling approach o Discrete and stochastic semantics Membranes Rewriting Rules Stochastic P Systems Molecular Species are represented as objects or strings A molecular species can be represented using individual objects. LasR A molecular species with relevant internal structure can be represented using a string. cap ⋅ prom ⋅ op ⋅ lacZ1 lacZ 30 ⋅ lacY1 lacY12 ⋅ lacA1 lacA6 Molecular Interactions are Represented as Rules Comprehensive and relevant rule-based schema for the most common molecular interactions taking place in living cells. Protein-protein interactions { Transformation/Degradation Complex Formation and Dissociation Diffusion in / out Binding and Debinding Recruitment and Releasing { Transcription Factor Binding/Debinding Transcription/Translation Gene expression Molecular Interactions Inside Compartments Passive Diffusion of Molecules Signal Sensing and Active Transport Specification of Transcriptional Regulatory Networks Compartments / Cells are Specified using Membranes • Compartments and regions are explicitly specified using membrane structures. Colonies / Tissues are Represented using Collections of P systems Colonies and tissues are representing as collection of P systems distributed over a lattice. v Objects can travel around the lattice through translocation rules. Lattice Population P Systems LPP = (Σ, Lat, (Π1, ... , Πp), Pos, (T1,…,Tp) ) Σ is an alphabet of objects representing molecular species. Lat is a finite geometrical lattice in R2 or R3 Π1, ... , Πp are individual stochastic P systems Pos : Lat (Π1, ... , Πp) associates a specific P system with each position in the lattice. T1,…,Tp are translocation rules added to the skin membrane of each P system. Stochastic P Systems Are Executable Programs The virtual machine running these programs is a “Gillespie Algorithm (SSA)”. It generates trajectories of a stochastic syste: A stochastic constant is associated with each rule. 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. 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 Stochastic P Systems Maximal parallelism and non determinism fails to accurately replicate the rate of molecular interactions. Gillespie Stochastic Simulation Algorithm (SSA) generates exact trajectories of a stochastic system in a single volume: 1) A stochastic constant ci is associated with each rule. 2) A propensity ai is computed for each 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: j 1 1 j0 = min j / ai > r2 a0 τ = ln a0 r1 i =0 ∑ D. T. Gillespie. Stochastic simulation of chemical kinetics. Annual Review of Physical Chemistry, 58:35–55, 2007. Rules are applied according to operational semantics based on Gillespie Algorithm 1 3 r31, …,r3n3 Local Gillespie r11, …,r1n1 ( 1, τ1, r01) M1 ( 2, τ2, r02) M3 r21, …,r2n2 ‘ 2 ( 3, τ3, r03) Sort Compartments τ2 < τ1 < τ3 M2 ( 2, τ2’, r02) ( 1, τ1, r01) τ2’’=τ2’+ tsim ( 1, τ1, r01) ( 2, τ2’ ’ , r02) ( 3, τ3, r03) tsim =τ2 Insert new triplet τ1 <τ2 ’ ’ < τ3 ( 3, τ3, r03) Update Global Time ( 2, τ2, r02) ( 1, τ1, r01) ( 3, τ3, r03)