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Probabilistic Modelling and Verification of Biological Systems Paolo Milazzo Outline Probabilistic Modelling and Verification of Introduction Biological Systems Biological Systems as Concurrent Systems Examples of Models Discussion on Biological Systems Quantitative Paolo Milazzo MultiSet Rewriting Stochastic MSR (SMSR) Probabilistic MSR milazzo@di.unipi.it (PMSR) Parallel Probabilistic MSR (PPMSR) Comparing SMSR, Ph.D. Thesis Proposal PMSR and PPMSR Pisa – February 14, 2005 Modelling Molecular Biology Simulation Results Future Works Conclusions 1/34

Probabilistic Modelling and Introduction Verification of Biological Systems Biological Systems as Concurrent Systems Paolo Milazzo Examples of Models Discussion on Biological Systems Outline Introduction Biological Systems as Quantitative MultiSet Rewriting Concurrent Systems Examples of Models Stochastic MSR (SMSR) Discussion on Biological Systems Probabilistic MSR (PMSR) Quantitative MultiSet Rewriting Parallel Probabilistic MSR (PPMSR) Stochastic MSR (SMSR) Comparing SMSR, PMSR and PPMSR Probabilistic MSR (PMSR) Parallel Probabilistic MSR (PPMSR) Modelling Molecular Biology Comparing SMSR, PMSR and PPMSR Simulation Results Modelling Molecular Biology Simulation Results Future Works Future Works Conclusions Conclusions 2/34

Biological systems Probabilistic Modelling and Verification of Biological Systems Biology is “the science that studies living organisms”. It Paolo Milazzo includes: Outline ◮ the analysis of molecular interactions at the level of Introduction proteins, enzymes, etc; Biological Systems as Concurrent Systems Examples of Models ◮ the study of cells and tissues; Discussion on Biological Systems ◮ the study of the origin, development and distribution of Quantitative MultiSet Rewriting animals and plants. Stochastic MSR (SMSR) Probabilistic MSR Common characteristics of almost all the fields of biology: (PMSR) Parallel Probabilistic MSR (PPMSR) ◮ systems composed by a huge number of (often simple) Comparing SMSR, PMSR and PPMSR interactive elements; Modelling Molecular Biology ◮ systems exhibit very complex overall behaviors. Simulation Results These characteristics suggest the application to biology of Future Works models originally developed to describe concurrent Conclusions interactive software systems. 3/34

Modelling biological systems Probabilistic Modelling and Verification of Biological Systems Advantages of modelling biology with formalisms for Paolo Milazzo concurrent interactive systems: Outline ◮ systems can be described precisely : it is possible to Introduction Biological Systems as compute all the reachable states; Concurrent Systems Examples of Models ◮ systems can be described compositionally : once the Discussion on Biological Systems invidual behaviors of some subsystems has been Quantitative MultiSet Rewriting understood, it is possible to predict the behavior of the Stochastic MSR (SMSR) whole system; Probabilistic MSR (PMSR) Parallel Probabilistic ◮ simulators can be developed; MSR (PPMSR) Comparing SMSR, PMSR and PPMSR ◮ automatic analysis techniques for systems of software Modelling components can be applied or adapted to verify Molecular Biology Simulation Results properties of biological systems. Future Works At the moment, the main application fields are biochemistry Conclusions and cellular biology. 4/34

Qualitative and quantitative aspects Probabilistic Modelling and Verification of Biological Systems Paolo Milazzo In biological systems there are both qualitative and Outline quantitative aspects to consider: Introduction qualitative aspects are related to state dependent properties Biological Systems as Concurrent Systems (such as reachability); Examples of Models Discussion on Biological Systems quantitative aspects are related to time and space Quantitative dependent properties. MultiSet Rewriting Stochastic MSR (SMSR) Aim of the proposed thesis: Probabilistic MSR (PMSR) Parallel Probabilistic to develop formal models and verification MSR (PPMSR) Comparing SMSR, techniques for biological systems by considering PMSR and PPMSR Modelling both qualitative and quantitative aspects. Molecular Biology Simulation Results Most of the existing models are based on the π –calculus Future Works process algebra. Conclusions 5/34

Examples of models: the κ –calculus Probabilistic Modelling and Verification of Biological Systems Developed by Danos and Laneve in 2003, the κ –calculus Paolo Milazzo ◮ describes formally protein–protein interactions ; Outline ◮ is enriched with a very intuitive graphical notation; Introduction Biological Systems as Concurrent Systems ◮ has been encoded into the π –calculus. Examples of Models Discussion on Biological Systems In the κ –calculus proteins (a) and complexes (b) are Quantitative represented by graphs with sites: MultiSet Rewriting Stochastic MSR (SMSR) Probabilistic MSR (PMSR) Parallel Probabilistic MSR (PPMSR) Comparing SMSR, PMSR and PPMSR Modelling Molecular Biology Simulation Results Future Works Conclusions 6/34

Examples of models: the κ –calculus Probabilistic Modelling and Verification of Biological Systems Reactions (protein–protein interactions) are represented by Paolo Milazzo graph–rewriting rules: Outline Introduction Biological Systems as Concurrent Systems Examples of Models Discussion on Biological Systems Quantitative MultiSet Rewriting Stochastic MSR (SMSR) Probabilistic MSR (PMSR) Parallel Probabilistic MSR (PPMSR) Comparing SMSR, PMSR and PPMSR Modelling Molecular Biology Simulation Results Future Works Conclusions 7/34

Examples of models: BioAmbients Probabilistic Modelling and Verification of Biological Systems Developed by Regev, Panina, Silverman, Cardelli and Paolo Milazzo Shapiro in 2003, the BioAmbients calculus Outline ◮ is inspired by both the π –calculus and the Mobile Introduction Ambients calculus; Biological Systems as Concurrent Systems ◮ describes biochemical systems with compartments (such Examples of Models Discussion on Biological Systems as membranes). Quantitative Example in BioAmbients of interaction of a cell with a MultiSet Rewriting Stochastic MSR vescicle containing a molecule: (SMSR) Probabilistic MSR (PMSR) Parallel Probabilistic MSR (PPMSR) cell[accept v | golgi[merge+ g .PROTEIN]] | Comparing SMSR, PMSR and PPMSR vesc[enter v .merge- g .MOLECULE] Modelling ↓ Molecular Biology cell[vesc[merge- g .MOLECULE] | Simulation Results golgi[merge+ g .PROTEIN]] Future Works ↓ Conclusions cell[golgi[MOLECULE | PROTEIN]]] 8/34

Examples of models: the stochastic π –calculus Probabilistic Modelling and Verification of Biological Systems Regev and Shapiro in 2001 proposed to describe Paolo Milazzo ( quantitatively ) molecular systems as processes in the Outline stochastic π –calculus. Introduction Biological Systems as Concurrent Systems Inspired by Gillespie’s stochastic algorithm for simulating Examples of Models Discussion on chemical reactions (1977). Biological Systems Quantitative ◮ Reactions are represented by communications on MultiSet Rewriting Stochastic MSR π –calculus channels; (SMSR) Probabilistic MSR (PMSR) ◮ a rate constant is associated with each communication Parallel Probabilistic MSR (PPMSR) channel; Comparing SMSR, PMSR and PPMSR ◮ the time of the next communication is exponentially Modelling Molecular Biology distributed with the rate of the channel as parameter. Simulation Results Future Works We proposed an alternative to Gillespie’s algorithm that Conclusions considers discrete time steps (to appear). 9/34

Discussion on biological systems and models Probabilistic Modelling and Verification of Biological Systems Paolo Milazzo Most of the formal models for biology deal with molecular Outline and cellular systems. Introduction Common characteristics of many biological systems (not Biological Systems as Concurrent Systems only molecular ones) are: Examples of Models Discussion on Biological Systems ◮ there is a huge number of instances of a few kinds of Quantitative elements; MultiSet Rewriting Stochastic MSR (SMSR) ◮ interactions occur among a small number (often Probabilistic MSR (PMSR) couples) of elements; Parallel Probabilistic MSR (PPMSR) Comparing SMSR, ◮ interactions involving different elements may occur PMSR and PPMSR Modelling concurrently . Molecular Biology Simulation Results Molecular systems are an example, another example are Future Works populations of living organisms. Conclusions 10/34

Populations and sympatric speciation Probabilistic Modelling and Verification of Biological Systems Paolo Milazzo “Speciation” is the separation of one species into two (such Outline as humans and chimpanzees) Introduction Biological Systems as Concurrent Systems ◮ easy to explain if the two populations live in separate Examples of Models Discussion on environments ( allopatric speciation ); Biological Systems Quantitative ◮ more difficult to explain if they live in the same MultiSet Rewriting Stochastic MSR environment ( sympatric speciation ). (SMSR) Probabilistic MSR (PMSR) Parallel Probabilistic Some hypothesis on the reason of sympatric speciation have MSR (PPMSR) Comparing SMSR, PMSR and PPMSR been formulated by physicists and biologists, for instance Modelling sexual selection . Molecular Biology Simulation Results Future Works This is another example of biological system. Conclusions 11/34