Modeling and Simulating Nano Devices in the calculus κ nano
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Modeling and Simulating Nano Devices in the nanoκ calculus A.Credi, M.Garavelli, C.Laneve, S. Pradalier, S.Silvi and G.Zavattaro Dipartimento di Chimica di Bologna, Dipartimento di Scienze dell’Informazione di Bologna, Polytechnique Paris 20 septembre 2007 Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 1 / 16 Motivations and endeavors for the nanoκ calculus A formal language convenient for : Descriptions ⇒ a formal graphical notation, chemical-like operators Simulations ⇒ a stochastic semantics Analysis ⇒ What properties ? Not an easy question... Application to real-case of molecular machines : Testing and comparing of plausible scenarios Hints on behaviors in non-observable experimental conditions Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 2 / 16 Nano devices What do we mean by nano devices ? Supramolecular systems : Assembly of a discrete number of molecular components Designed to perform a specific, predetermined function The function is (or is obtained through) a mechanical motion of some components with respect to others Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 3 / 16 The running example : the rotaxane [2]RaH What is a rotaxane ? A chemical event ⇒ a mechanical event = the function Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 4 / 16 The [2]RaH rotaxane and its motion [Ashton&all 98] and [Garaudée&all 05] Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 5 / 16 What is the level of abstraction of our modelings ? We are interested in the combinations of functions : Basic component : molecules or important functional sub-molecules No explicit description of atoms Yet explicit description of electronic charges if functional =⇒ corresponds to the abstraction level of the chemistry articles Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 6 / 16 Plan 1 Description of the running example : the rotaxane [2]RaH 2 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane The stochastic semantics 3 Results of the simulations Consistency checks Testing scenarios Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 7 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane II. The nanoκ calculus [Danos&Laneve 03] : the κ-calculus basic term : molecule sites can be free or linked fields ∼ records Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 8 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane II.1 Syntax and graphical notation [Danos&Laneve 03] : the κ-calculus basic term : molecule Gene sites can be free or linked Activator S repl:0 X Y T fields ∼ records Sylvain Pradalier (Polytechnique Paris) U Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 8 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane Modeling the rotaxane Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 9 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane Modeling the rotaxane Nh Bipy Axle Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 9 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane Modeling the rotaxane Nh Bipy Axle Axle Sylvain Pradalier (Polytechnique Paris) Nh Bipy Axle Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 9 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane Modeling the rotaxane Nh Bipy Axle Axle Sylvain Pradalier (Polytechnique Paris) Nh Bipy Axle Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 9 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane Modeling the rotaxane Nh Bipy Axle h:1 Axle Sylvain Pradalier (Polytechnique Paris) Nh Bipy Axle h:1 Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 9 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane Modeling the rotaxane Nh Bipy Axle Axle h:1 Ring Sylvain Pradalier (Polytechnique Paris) Nh Bipy Axle h:1 Ring Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 9 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane Modeling the rotaxane Ring Nh Bipy Axle Axle h:1 Nh Ring Bipy Axle h:1 Ring Link Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 9 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane Modeling the rotaxane Ring Nh Bipy Axle Axle h:0 Nh Axle Bipy Ring h:0 Ring Link Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 9 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane The 3 types of reactions Creations Destructions Exchanges Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 10 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane The 3 types of reactions x1, x2, ... s1, s2, ... x1', x2', ... s1, s2, ... Creations a Destructions Exchanges Sylvain Pradalier (Polytechnique Paris) a r b y1, y2, ... b t1, t2, ... y1', y2', ... t1, t2, ... Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 10 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane The 3 types of reactions x1, x2, ... s1, s2, ... x1', x2', ... s1, s2, ... Creations a Destructions Exchanges Sylvain Pradalier (Polytechnique Paris) a r b y1, y2, ... b t1, t2, ... y1', y2', ... t1, t2, ... Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 10 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane The 3 types of reactions x1, x2, ... s1, s2, ... x1', x2', ... s1, s2, ... Creations r Destructions Exchanges Sylvain Pradalier (Polytechnique Paris) y1, y2, ... t1, t2, ... y1', y2', ... t1, t2, ... Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 10 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane The 3 types of reactions Creations Destructions Exchanges Rates could be infinite Reactions are just patterns ⇒prevents explosion of the number of reactions Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 10 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane Some reactions of the modeling Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 11 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane Some reactions of the modeling An exchange : Nh Nh h:1 h:0 τ Acid h:0 Sylvain Pradalier (Polytechnique Paris) Acid h:1 Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 11 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane Some reactions of the modeling A destruction : Ring Ring Nh Nh τ h:0 Ring Ring Link Sylvain Pradalier (Polytechnique Paris) h:0 Link Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 11 / 16 The nanoκ calculus Syntax and graphical notation : the example of the rotaxane Some reactions of the modeling A creation : Ring Ring Bipy Bipy h:0 h:0 R.link Ring Ring Link Sylvain Pradalier (Polytechnique Paris) Link Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 11 / 16 The nanoκ calculus The stochastic semantics The stochastic semantics Can we use CTMCs ? Not directly, because of infinite rates a a τ We use Interactive Markov Chains ( = CTMCs + _ + _+_) a τ Maximal progress : _, _ λ >> _ τ Non-determinism of _ ? "Strictly markovian" ensure convergence So one recovers CTMCs Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 12 / 16 The nanoκ calculus The stochastic semantics The stochastic semantics Can we use CTMCs ? Not directly, because of infinite rates a a τ We use Interactive Markov Chains ( = CTMCs + _ + _+_) a τ Maximal progress : _, _ λ >> _ τ Non-determinism of _ ? "Strictly markovian" ensure convergence So one recovers CTMCs Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 12 / 16 The nanoκ calculus The stochastic semantics The stochastic semantics Can we use CTMCs ? Not directly, because of infinite rates a a τ We use Interactive Markov Chains ( = CTMCs + _ + _+_) a τ Maximal progress : _, _ λ >> _ τ Non-determinism of _ ? "Strictly markovian" ensure convergence So one recovers CTMCs Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 12 / 16 Results of the simulations III. Results of the simulations The nanoκ calculus is encoded into the stochastic π-calculus Simulations achieved in Spim (L.Cardelli and A.Phillips) Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 13 / 16 Results of the simulations III. Results of the simulations The nanoκ calculus is encoded into the stochastic π-calculus Simulations achieved in Spim (L.Cardelli and A.Phillips) Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 13 / 16 Results of the simulations Consistency checks III.1 Consistency checks Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 14 / 16 Results of the simulations Consistency checks III.1 Consistency checks First experiment : Ring Nh Bipy h:0 Axle Axle h:1 Nh Ring Bipy Axle h:1 + Acid Ring Link Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 14 / 16 Results of the simulations Consistency checks III.1 Consistency checks Second experiment : Ring Nh Bipy h:1 Axle Axle h:0 Nh Axle Bipy Ring h:0 + Base Ring Link Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 14 / 16 Results of the simulations Consistency checks III.1 Consistency checks 1st experiment 2nd experiment In black : nanoκ – In red : chemistry Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 14 / 16 Results of the simulations Testing scenarios Deprotonation/Protonation are "instantaneous" ? Chemistry gives rates for these reactions, according to the concentrations For concentrations 10−8 M, unobservable in practice : Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 15 / 16 Results of the simulations Testing scenarios Deprotonation/Protonation are "instantaneous" ? For concentrations 10−8 M, unobservable in practice : In grey : number of Ring in the left position – In black : number of protonated Nh Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 15 / 16 Results of the simulations Testing scenarios Perspectives What are the formal properties we want to prove ? Theory : automatization of the "Strictly markovian" property, ... Simulator of another kappa calculus team : W.Fontana, V.Danos, E.Ferret and J.Krivine Effective study of more complex nano-devices Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 16 / 16 Results of the simulations Testing scenarios Perspectives Effective study of more complex nano-devices + + + + + + Sylvain Pradalier (Polytechnique Paris) Modeling and Simulating Nano Devices in the nanoκ calculus 20 septembre 2007 16 / 16
